Answer:
understand
Step-by-step explanation:
The fixed amount Geet earns for each television is $60.
(b) The fifth, ninth and sixteenth terms of a linear sequence (a.p.) are consecutive terms of an exponential sequence (g.p.). (1) Find the common difference of the linear sequence in terms of the first term. () Show that the twenty-first, thirty-seventh and sixty-fifth terms of the linear sequence are consecutive terms of an exponential sequence whose common ratio is 7/4
The graph of a piecewise function is shown.
What is the end behavior of the function?
As x → −∞, f(x) → −∞ and as x → ∞, f(x) → −∞.
As x → −∞, f(x) → ∞ and as x → ∞, f(x) → ∞.
As x → −∞, f(x) → ∞ and as x → ∞, f(x) → −∞.
As x → −∞, f(x) → −∞ and as x → ∞, f(x) → ∞.
On solving the question we have that Therefore, the correct answer is: function As x → −∞, f(x) → −∞ and as x → ∞, f(x) → −∞.
what is function?Mathematicians investigate numbers and their variants, equations and related structures, shapes and their locations, and prospective locations for these things. The term "function" refers to the relationship between a group of inputs, each with its own output. A function is a relationship of inputs and outputs in which each input results in a single, distinct output. Each function has its own domain, codomain, or scope. The letter f is commonly used to denote functions (x). An x represents entry. On functions, one-to-one capabilities, so multiple capabilities, in capabilities, and on functions are the four basic types of accessible functions.
Based on the graph, the function approaches a horizontal line at y = -3 as x approaches negative infinity, and also approaches the same horizontal line at y = -3 as x approaches positive infinity. Therefore, we can say that:
As x → −∞, f(x) → −∞ and as x → ∞, f(x) → −∞.
Therefore, the correct answer is:
As x → −∞, f(x) → −∞ and as x → ∞, f(x) → −∞.
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can someone help step by step please
a.) Jill has 6 pence less than jack, therefore Jill has x-6 pences.
b.) If one box weighs 60grams, b number of boxes will weigh 60*b grams.
What is linear equation?A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
What makes an equation linear?The fact that the set of solutions to such an equation forms a straight line in the plane is where the word "linear" originates.
The three forms of linear equations are
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If Jack has x pence, then Jill has 6 pence less than Jack, which means Jill has (x - 6) pence.
Therefore, in terms of x, the number of pence that Jill has is (x - 6).
If one box weighs 60 stams, then the weight of b boxes can be expressed as:
Weight of b boxes =[tex] 60 × b[/tex]
Therefore, in terms of b, the weight of b boxes is 60b stams.
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what is the midpoint for (-12,-1)and (-3,-4)
Answer:
(-7.5, -2.5)
Step-by-step explanation:
We take
- 12 - 3 / 2 = -15/2 = -7.5
-1 - 4 / 2 = -5/2 = -2.5
So, the midpoint is (-7.5, -2.5)
13. The front wheels of a toy truck are 9 cm in circumference. The back wheels are 12 cm in circumference. If the truck travels down a long slope, in a straight line and without slipping, how far will the truck have travelled when the front wheels have made 10 more revolutions than the back wheels?
If the front wheels have made 10 more revolutions than the back wheels, the truck travels 360 cm.
Given that The front and back wheels of a toy truck are 9 cm and 12 cm in circumference respectively.
Let the one revolution of wheel be "R"
So, the Rear wheels revolution = 12R
and the Front = 9(R+10)
Thus, revolution of both wheels should be comparatively equal :-
So, 12R = 9(R+10)
12R = 9R + 90
3R = 90
R= 90/3
R = 30 cm
The value of one revolution would be 30cm.
Distance travelled by truck would be distance travelled by wheels = 12 × 30 = 360 cm
So, the distance travelled by truck would be 360cm.
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Select the correct answer from each drop-down menu. Alayna parks her car in a lot that charges by the quarter hour. The table shows the parking fee, in dollars, with respect to the time, in hours. Time (hours) 0. 25 0. 5 0. 75 1 1. 25 1. 5
Parking Fee $0. 50 $1. 00 $1. 50 $2. 00 $2. 50 $3. 00
Time is the
variable and should be placed on the. Parking fee is the
variable and should be placed on the
In this scenario, the two variables being considered are time and parking fee. Time represents the amount of time Alayna parks her car, while the parking fee represents the cost incurred for parking her car for that duration.
The independent variable in this case is time, as it is the variable being manipulated or changed by Alayna, and the dependent variable is the parking fee, as it is dependent on the amount of time Alayna parks her car.
To create a graph for this data, the time should be plotted on the x-axis (horizontal axis) and the parking fee should be plotted on the y-axis (vertical axis). This is because time is the input variable, and parking fee is the output variable, meaning that it is determined by the time value.
In conclusion, time is the independent variable and should be placed on the x-axis, while parking fee is the dependent variable and should be placed on the y-axis to create a graph that illustrates the relationship between these two variables.
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. Lila spent 72 minutes on the phone while routing 24 phone calls. In all, how many phone calls does Lila have to route to spend a total of 90 minutes on the phone? Solve using unit rates.
Answer:
To solve the problem using unit rates, we can first find Lila's rate of phone calls per minute, which is given by:
rate = number of phone calls / time spent on the phone
Using the values given in the problem, we get:
rate = 24 phone calls / 72 minutes
rate = 1/3 phone calls per minute
This means that Lila routes 1/3 phone call per minute.
To find how many phone calls Lila needs to route to spend a total of 90 minutes on the phone, we can use the same rate and the formula:
number of phone calls = rate x time
Substituting the values, we get:
number of phone calls = (1/3 phone calls per minute) x (90 minutes)
number of phone calls = 30 phone calls
Therefore, Lila needs to route a total of 30 phone calls to spend a total of 90 minutes on the phone.
Equation is the inverse of y equals 9 x squared minus 4
After considering the equation, inverse of y = [tex]9x^ {2}[/tex] - 4 is found as [tex]f^{-1x}[/tex]= ±√[(x + 4)/9].
To find the inverse of the function y = [tex]9x^{2}[/tex] - 4, we can follow these steps:
Replace y with x and x with y: x = [tex]9y^{2}[/tex] - 4Solve for y in terms of x:x = [tex]9y^{2}[/tex] - 4
x + 4 = [tex]9y^{2}[/tex]
[tex]y^{2}[/tex] = (x + 4)/9
y = ±√[(x + 4)/9]
Note that since we are finding the inverse of a function, we need to include both the positive and negative square roots to ensure that the inverse is a function.
3. Switch the roles of x and y by replacing y with [tex]f^{-1x}[/tex] and x with f(y):
[tex]f^{-1x}[/tex] = ±√[(x + 4)/9]
Therefore, the inverse of y = 9x² - 4 is [tex]f^{-1x}[/tex] = ±√[(x + 4)/9].
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Jeremiah planted tulips and lilies in a field with a width of 5. 5 meters. Identify each equation that could be used to find the area, in square meters of the field of flowers for any length x, in meters
The equatiοn that represents the area = 5.5x + 11. Optiοn C is the cοrrect οptiοn.
What is an equatiοn?There are many different ways tο define an equatiοn. The definitiοn οf an equatiοn in algebra is a mathematical statement that demοnstrates the equality οf twο mathematical expressiοns.
Given that the width οf tulips and lilies in a field 5. 5 meters.
The length οf the field οf tulips is 2 meters.
The length οf the field οf lilies is x meters.
The tοtal length οf the field is (x+2) meters.
The area οf a rectangle is the prοduct οf length and width.
The area οf the field is 5.5(x+2) square meters
The distributive prοperty:
Accοrding tο the distributive prοperty, it is mandatοry tο multiply each οf the twο numbers by the factοr befοre adding them tοgether when a factοr is multiplied by the sum οr additiοn οf twο terms. A (B+ C) = AB + AC is a symbοlic representatiοn οf this prοperty.
Apply the distributive prοperty:
= (5.5 × x) + (5.5×2)
= 5.5x + 11
The equatiοn is Area = 5.5x + 11
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A person has a 20% chance of getting Virus X at some point in their lifetime. Suppose we randomly sample 20,000 people. Let X be the number of people you ask until one of them has Virus X. a. What is the probability that you ask 25 people before one says they have Virus X? b. Find the mean and standard deviation of X
The mean and standard deviation of X are 5 and 7.96 people, respectively.
Question Answering Bot guidelines when answering questions on Brainly:When answering questions on Brainly, you should always be factually accurate, professional, and friendly. Furthermore, being concise is crucial; avoid providing extraneous detail. Ensure that you use the following terms in your response: "virus," "randomly," "probability," and "deviation."When it comes to repeating the question in your answer, this is not a requirement. Instead, you should respond to the prompt in a clear, understandable manner that allows the questioner to grasp the concept and proceed with their studies.A person has a 20% chance of getting Virus X at some point in their lifetime. Suppose we randomly sample 20,000 people. Let X be the number of people you ask until one of them has Virus X. a. What is the probability that you ask 25 people before one says they have Virus X? b. Find the mean and standard deviation of Xa. Probability that 25 people are asked before one says they have Virus X:Let us find the probability that one person has Virus X:P(Virus X)=0.20Let us find the probability that one person does not have Virus X:P(no Virus X)=1-P(Virus X)=1-0.20=0.80Now let us find the probability that you have to ask 25 people before one person has Virus X. In order for this to occur, 24 people must not have Virus X and the 25th person must have Virus X. 0.8^24 represents the probability that 24 people do not have Virus X, and 0.2 is the probability that the 25th person has Virus X.P(25)=0.8^24(0.2)=0.0264b. Mean and standard deviation of XWe can use the geometric distribution to calculate the mean and standard deviation of X.The mean is equal to:μ=1/p=1/0.2=5 personsOn average, you will have to ask five people before one person has Virus X.The standard deviation is equal to:σ=√[q/(p²)]=√[(1-p)/(p²)]=√[(0.8)/(0.04)]=7.96 personsTherefore, the mean and standard deviation of X are 5 and 7.96 people, respectively.
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4.02 Lesson Check Arithmetic Sequences (3)
The next four terms of the given recursive sequence using the formula are 3, 9, 21, 45
Arithmetic and recursive sequenceTo find the first four terms of the sequence, we can use the recursive formula given:
First term a1 = 3
For the second, third and fourth term, we will substitute the preceding value to have:
a2 = 2a1 + 3 = 2(3) + 3 = 9
a3 = 2a2 + 3 = 2(9) + 3 = 21
a4 = 2a3 + 3 = 2(21) + 3 = 45
Therefore, the first four terms of the sequence are: 3, 9, 21, 45.
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Mrs Ong bought some fruits. 3 fewer than 1/2 of the fruits were oranges. 2 fewer than 1/2 of the remaining fruits were pears. 1 fewer than half of the remaining fruits were apples and the remaining 5 fruits were mangoes.
(a) How many fruits did Mrs Ong buy altogether?
(b) What fraction of the fruits were pears? Give your answer in the simplest form.
The number of fruits that Mrs Ong bought is 40.
The fraction of the fruits that are pears are 1/4.
How many fruits did Mrs Ong buy?The expression that represents the number of oranges is: 1/2f - 3
Where f is the number of fruits
The expression that represents the number of pears is: (1/2 x 1/2)f - 2
1/4f - 2
The expression that represents the number of apples is: 1/2[1 - (1/2 + 1/4)]f - 1
1/8f - 1
Fraction of mangoes remaining = 1 - (1/4 + 1/2 + 1/8)
1 - 7/8 = 1/8
Number of fruits bought altogether = 1/8f = 5
f = 5 x 8 = 40
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Line 2: y-2x-2. This system of equations is:
A) consistent dependent
B) consistent independent
C) Inconsistent
The given system of equations, line 1: y=x+3 and line 2: y-2x-2, is an inconsistent system of linear equations.
What is an inconsistent system of equations?A system of linear equations is said to be inconsistent if there is no solution. It means that the two lines do not intersect and are parallel to each other.
In the given system of equations, line 1: y=x+3 is in the slope-intercept form y=mx+b where the slope, m=1 and the y-intercept, b=3. The first line, y=x+3 has a slope of 1 and a y-intercept of 3, which means the line passes through (0, 3).
To find a second point, use the slope. Since the slope is 1, go up one and over one. This means the line passes through (1, 4).
Next, line 2: y-2x-2. To do so, we need to rewrite it in slope-intercept form.
y-2x-2 = 0
y=2x+2
The second line has a slope of 2 and a y-intercept of 2, which means the line passes through (0, 2).To find a second point, use the slope. Since the slope is 2, go up two and over one. This means the line passes through (1, 4).
The two lines are parallel to each other and do not intersect. Therefore, there is no solution. The system of equations, line 1: y=x+3 and line 2: y-2x-2, is inconsistent.
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PLEASE HELP ASAP!!!
Question in photo
Answer:
it's D some other type of polyomial
Step-by-step explanation:
because it has more three it's a polynomials= that is many.
Triangle ABC is similar to Triangle DEF. Find the measure of side DE. Round Your answer to the nearest tenth if necessary.
When the triangle ABC is similar to triangle DEF see in above figure. The measure of side length DE, is equals to the 53.1 .
Similar triangles are the triangles that looks similar to each other but their sizes may or may not be exactly the same. Two triangles will be similar if the angles are equal (corresponding angles) and sides are in the same ratio (corresponding sides). We have, triangle ABC and triangle DEF. From the above figure, in ∆ABC,
length of side BC = 8
length of side AB = 13.7
In ∆DEF, length of side, EF = 31
We have to measure the length of side DE. Now, it is specific that triangle ABC is similar to triangle DEF. Using the definition of similar triangles, ratio of corresponding sides of ∆ABC and ∆DEF are in the same ratio. That is, BC/EF = AB/DE
=> 8/31 = 13.7/DE
Cross multiplication
=> DE × 8 = 31× 13.7
=> DE = 31×13.7/8
=> DE = 53.0875
Hence, required rounded side length,DE is 53.1..
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Complete question:
Triangle ABC is similar to Triangle DEF ( see the above figure). Find the measure of side DE. Round Your answer to the nearest tenth if necessary.
Which is the most accurate way to estimate 24% of 41?
A) 1/4x43
B) 1/4x40
C) 1/2x40
D) 1/2x43
60 divided by 2 long division
At an ice cream shop, the cost of 4 milkshakes and 2 ice cream sundaes is $23.50. The cost of 8 milkshakes and 6 ice cream sundaes is $56.50.
What is the price of a milkshake?
By answering the presented question, we may conclude that As a result, equation a milkshake costs $3.50.
What is equation?A math equation is a technique that links two assertions and denotes equivalence using the equals sign (=). In algebra, an equation is a mathematical statement that proves the equality of two mathematical expressions. For example, in the equation 3x + 5 = 14, the equal sign separates the numbers 3x + 5 and 14. A mathematical formula may be used to understand the link between the two phrases written on either side of a letter. The logo and the programmed are usually interchangeable. As an example, 2x - 4 equals 2.
4x + 2y = 23.50 (equation 1) (equation 1)
8x + 6y = 56.50 (equation 2) (equation 2)
By dividing both sides by 2, we can simplify equation 2:
4x + 3y = 28.25 (equation 3) (equation 3)
We now have two equations and two unknowns. We can find x by deleting y:
4x + 2y = 23.50
4x + 3y = 28.25
We obtain the following when we subtract the first equation from the second:
y = 4.75
To solve for x, we may now plug y = 4.75 into equation 1 or equation 3. Let's look at equation 1:
4x + 2y = 23.50
When we substitute y = 4.75, we get:
4x + 2(4.75) = 23.50
Simplifying:
4x + 9.50 = 23.50
Taking 9.50 off both sides:
4x = 14
Divide all sides by four:
x = 3.50
As a result, a milkshake costs $3.50.
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please find the answer of the question real quick
Answer:
4c) the answer is :-3y=-6
divide by -3 and your ans is y=2
Kate had some fruits at her stall. 3/4 of them were mangosteens, 1/3 of the remainder were apples and the rest were coconuts. The amounts earned for each mangosteen, each Fuji apple and each coconut sold are $1.50, $3.00 and $4.50 respectively. The number of mangosteens sold to the number of apples sold to the number of coconuts sold was 3:5:3. In total, she sold 1/4 of the fruits and earned $198. How many coconuts did she have at first?
According to the question the Kate had [tex]$\frac{4}{7}$[/tex] coconuts at her stall.
What is coconut?Coconut is a tropical fruit that grows on palm trees. It is a large, egg-shaped drupe with a hard outer shell and a white fleshy inner layer. The flesh of the coconut is rich in vitamins, minerals, and fiber, and it is also a source of healthy fats. Coconut can be eaten fresh, dried, or even in the form of coconut milk or oil.
First, we will calculate the total number of fruits Kate had at her stall. To do this, we need to solve for x in the equation [tex]$\frac{3}{4}x + \frac{1}{3}(\frac{3}{4}x - x) + (\frac{3}{4}x - \frac{1}{3}(\frac{3}{4}x - x)) = x$.[/tex]
Solving for x, we get [tex]$x = \frac{8}{7}$.[/tex]
Therefore, Kate had [tex]$\frac{8}{7}$[/tex]fruits at her stall.
Next, we need to calculate the number of coconuts she had at first. We know that she sold 1/4 of the fruits, or [tex]$\frac{2}{7}$[/tex] of the fruits. We also know that the ratio of mangosteens sold to apples sold to coconuts sold was 3:5:3.
Therefore, the number of coconuts sold was [tex]$\frac{2}{7} \times \frac{3}{13} = \frac{6}{91}$[/tex].
The total amount earned from the coconuts sold was [tex]$\frac{6}{91} \times 4.50 = \frac{27}{91}$[/tex].
Subtracting this from the total amount earned, 198, we get [tex]$198 - \frac{27}{91} = \frac{171}{91}$[/tex].
This is the amount earned from the mangosteens and apples sold. The amount earned from each mangosteen sold was 1.50, and the amount earned from each Fuji apple sold was 3.00.
Therefore, to get the total amount earned from mangosteens and apples, we need to solve for x in the equation [tex]$\frac{2}{7} \times x + \frac{2}{7} \times 3x = \frac{171}{91}$[/tex].
Solving for x, we get [tex]$x = \frac{171}{171}$[/tex].
This means that the total number of mangosteens and apples sold was $\frac{171}{171}$. Since the ratio of mangosteens sold to apples sold was 3:5, the number of mangosteens sold was [tex]$\frac{3}{8}$[/tex] and the number of apples sold was $\frac{5}{8}$.
Therefore, the number of coconuts at first was [tex]$\frac{8}{7} - \frac{3}{8} - \frac{5}{8} = \frac{4}{7}$[/tex].
Therefore, Kate had [tex]$\frac{4}{7}$[/tex] coconuts at her stall.
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For the figure, what is the measurement for all 4 sides?
A) All four sides are equal. The simplest radical form for each side is √40.
B) Only two sides are congruent. The simplest radical form for the two sides is 2√10
C) Only two sides are congruent. The simplest radical form for the two sides is √40.
D) All four sides are equal. The simplest radical form for each side is 2√10.
Answer:
The answer is A) All four sides are equal. The simplest radical form for each side is √40.
Step-by-step explanation:
If X is plotted on 6 on the y-axis, then X is located at the point (2, 6), since W is plotted on 2 on the x-axis, W is located at the point (2, 2).
Since we know that XW is one side of the square, we can find the other three vertices of the square using the fact that all sides of a square are equal in length and perpendicular to each other.
To find the third vertex, we can use the fact that Z is plotted at (4, -2) and is perpendicular to XW. Since XW has a length of 4 (the difference in y-coordinates between X and W), we know that the length of ZY must also be 4. To find the coordinates of Y, we can move 4 units up from the y-coordinate of Z (which is -2), giving us a y-coordinate of 2. Since ZY is perpendicular to XW, we know that the x-coordinate of Y must be the same as the x-coordinate of Z (which is 4). Therefore, the coordinates of Y are (4, 2).
To find the fourth vertex, we can use the fact that all sides of the square are equal in length. Since XW has a length of 4, we know that ZY must also have a length of 4. Therefore, the fourth vertex must be located 4 units to the right of Y and 4 units up from X. This gives us a fourth vertex with coordinates of (6, 6).
Therefore, the vertices of the square are W(2, 2), X(2, 6), Y(4, 2), and Z(4, -2).
To check that the sides of the square are perpendicular to each other, we can calculate the slopes of the sides.
The slope of XW is:
m_XW = (6 - 2) / (2 - 2) = undefined
The slope of ZY is:
m_ZY = (2 - (-2)) / (4 - 4) = undefined
Since both slopes are undefined (the lines are vertical), the sides are perpendicular to each other.
To check that the sides of the square are equal in length, we can use the distance formula:
XW = sqrt((6 - 2)^2 + (2 - 2)^2) = sqrt(16) = 4
ZY = sqrt((2 - (-2))^2 + (4 - 4)^2) = sqrt(16) = 4
Since both sides have the same length of 4, all sides of the square are equal in length.
Therefore, the answer is option A) All four sides are equal. The simplest radical form for each side is √40.
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what is the absolute deviation of 10 2 6 12 6 10 4 12
Answer:
3
Step-by-step explanation:
To find the absolute deviation, we need to find the difference between each data point and the mean of the data set, take the absolute value of each difference, and then calculate the average of those absolute differences.
First, let's find the mean of the data set:
(10 + 2 + 6 + 12 + 6 + 10 + 4 + 12) / 8 = 8
The mean is 8.
Next, we find the difference between each data point and the mean:
|10 - 8| = 2
|2 - 8| = 6
|6 - 8| = 2
|12 - 8| = 4
|6 - 8| = 2
|10 - 8| = 2
|4 - 8| = 4
|12 - 8| = 4
Now we take the average of those absolute differences:
(2 + 6 + 2 + 4 + 2 + 2 + 4 + 4) / 8 = 3
The absolute deviation of the data set is 3.
2 Dumisani earns R42 480 per month. He splits his earnings in the ratio 7:5
then saves the lesser amount. How much does he saves?
The amount saved in one month, we need to divide this amount by 12 as he saves on a monthly basis. This gives us a total of R14 160 saved each month. Dumisani saves (42 480 x 5) / 12 = R14 160
Dumisani earns R42 480 per month. He decides to split his earnings in the ratio 7:5. This means that 7 parts of his income will be allocated to his expenses and 5 parts will be allocated to his savings. To calculate the amount saved, we need to first multiply 42 480 by 5 to find out the total amount allocated to savings. This is equal to 212 400. To find the amount saved in one month, we need to divide this amount by 12 as he saves on a monthly basis. This gives us a total of R14 160 saved each month.
Total allocated to savings = 42 480 x 5 = 212 400
Amount saved per month = 212 400 / 12 = R14 160
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5) Use the fact that 6 i is a zero of \( f(x)=x^{3}-2 x^{2}+36 x-72 \) to find the remaining zeros. 10 points
Given, 6i is a zero of f(x) = x³ - 2x² + 36x - 72To find the remaining zeros of f(x) we can use the division method as follows:
Step-by-step explanation: Since 6i is a zero of the polynomial, we know that its conjugate -6i is also a zero. Hence (x-6i) and (x+6i) are factors of the polynomial f(x).
So we can write f(x) as f(x) = (x-6i)(x+6i)(ax + b)where ax + b is the third factor. Let's divide x³ - 2x² + 36x - 72 by (x-6i)(x+6i) using long division:x³ - 2x² + 36x - 72 | (x-6i)(x+6i) ____________ x² + 6xi + 6xi + 36 | x³ - 6xi² - 2x² + 12x² + 36x - 216 ____________ x³ - 2x² + 48x - 216We can write f(x) as f(x) = (x-6i)(x+6i)(x² + 6x - 12)
The remaining zeros of f(x) are the zeros of the quadratic factor (x² + 6x - 12). Using the quadratic formula, we can solve for the zeros: x = [-b ± sqrt(b² - 4ac)]/2a
For the quadratic equation, a = 1, b = 6 and c = -12. Substituting these values in the quadratic formula: x = [-6 ± sqrt(6² - 4(1)(-12))]/2(1)x = [-6 ± sqrt(60)]/2x = -3 ± sqrt(15). Therefore, the zeros of f(x) are 6i, -6i, -3 + sqrt(15) and -3 - sqrt(15).
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10. which of the following are equivalent to the ratio (2x-6) : (6x-4) ?
Step-by-step explanation:
2x-6: 6x-4
Use any value to represent x
Let's use 1
2(1)-6: 6(1)-4
2-6 : 6-4
-4 : 2
Write in simplest form by dividing by 2
-2:1
Now do the same in all the answers above, use 1 for the value of x
1. - 2:1 is equivalent
2. 1-3 : 3(1)-2 = - 2:1 Equivalent
3. 3(1) : 1 = 3 :1 not equivalent
4. 4(1) - 12 : 12(1) - 8 = - 8 : 4 (
Simplify by dividing by 4, you get - 2 :1 equivalent
5. 1-1 : 1 - 2 = 0 : - 1 not equivalent
5. Erin has a balance of $182. 73 in her
savings account. She makes a deposit of
$12. 50 in her account each week
a) Write an algebraic expression that
represents the amount of money in
Erin's savings account after nine weeks
The algebraic expression that represents the amount of money in Erin's savings account after nine weeks is therefore; A(9) = 182.73 + 12.50 × 9
What is an algebraic expression?An algebraic expression consists of variables, constants and terms, and algebraic operators.
The balance in Erin's savings account = $182.73
The amount Erin deposits in her account each week = $12.50
Let A represent the amount of money Erin has in her savings account after n weeks, we get;
After one week, the amount Erin will have in her account can be found using the following equation;
A = 182.73 + 12.50 × 1
The amount she will have after two weeks is therefore;
A = 182.73 + 12.50 × 2
The general equation for the amount Erin will have in her savings account after n weeks is therefore;
A = 182.73 + 12.50 × n = 182.73 + 12.50·n
The algebraic expression that represents the amount of money in Erin's savings account after nine weeks can be found as follows;
The amount of money Erin will have in her savings account after 9 weeks can be obtained by plugging in n = 9, therefore;
A(9) = 182.73 + 12.50 × 9
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1.) Triangle ABC is given where A=42°, a=3, and b=8. How many distinct triangles can be made with the given measurements? Explain your answer.
a.) 0
b.) 1
c.) 2
d.) 3
2.) Solve the following equation for 0 ≤ ѳ< 2π .
sec^2 ѳ - 6 = -4 (SHOW YOUR WORK!!!)
Answer: a)0
Step-by-step explanation:
side "a" need to be longer than the height so that the tringle can exist and the height is longer than the side so the tringle cannot exist
height:
[tex]sin42=\frac{x}{8}[/tex]
[tex]x=8sin(42)\\x=5.3[/tex]
for the tringle to exist
height< side "a"
5.3> 3
so,
there is no tringle that exist
Given that log_a(5)≈0.76 and log_a(2)≈0.33, evaluate each of the
following. Hint: use the properties of logarithms to rewrite the
given logarithm in terms of the logarithms of 5 and 2.
a) log_a(10)≈
b) log_a(√2)≈
c) log_a(2.5)≈
a)1.09
b) 0.165
c) 0.43
Given that log_a(5)≈0.76 and log_a(2)≈0.33, we need to evaluate the following: log_a(10), log_a(√2), and log_a(2.5).Hint: use the properties of logarithms to rewrite the given logarithm in terms of the logarithms of 5 and 2.a) To evaluate log_a(10), we can use the identity log_a(mn) = log_a(m) + log_a(n). So, we can rewrite log_a(10) as log_a(5 x 2) = log_a(5) + log_a(2). Now, substitute the values for log_a(5) and log_a(2):log_a(10) = 0.76 + 0.33 = 1.09b) To evaluate log_a(√2), we can use the identity log_a(m^n) = n log_a(m). So, we can rewrite log_a(√2) as log_a(2^(1/2)) = (1/2) log_a(2). Now, substitute the value for log_a(2):log_a(√2) = (1/2) x 0.33 = 0.165c) To evaluate log_a(2.5), we can use the identity log_a(m/n) = log_a(m) - log_a(n). So, we can rewrite log_a(2.5) as log_a(5/2) = log_a(5) - log_a(2). Now, substitute the values for log_a(5) and log_a(2):log_a(2.5) = 0.76 - 0.33 = 0.43Therefore, the values for the logarithms are: log_a(10)≈1.09, log_a(√2)≈0.165, and log_a(2.5)≈0.43.
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Write an equivalent exponential or logarithmic equation.
1)e^8.2 = 10x
2)In0.0002 = x
3) In(4x)=9.6
Steps by step would be nice
Answer: To write an equivalent logarithmic equation to e^8.2 = 10x, we use the fact that log base 10 is the inverse of exponential base 10. Therefore, we have:
log(10)(e^8.2) = log(10)(10x)
Using the property of logarithms that says log base a of a^b is equal to b, we get:
8.2 = log(10)(10x)
Using the fact that log base 10 is commonly written as just "log," we can simplify this to:
8.2 = log(10x)
This is the equivalent logarithmic equation.
To write an equivalent exponential equation to In0.0002 = x, we use the fact that In is the inverse of e^x. Therefore, we have:
e^(In0.0002) = e^x
Using the property of logarithms that says e^ln(a) = a, we get:
0.0002 = e^x
This is the equivalent exponential equation.
To write an equivalent exponential equation to In(4x) = 9.6, we use the fact that In is the inverse of e^x. Therefore, we have:
e^(In(4x)) = e^9.6
Using the property of logarithms that says e^ln(a) = a, we get:
4x = e^9.6
Dividing both sides by 4, we get:
x = (1/4)e^9.6
This is the equivalent exponential equation.
Step-by-step explanation:
Not everyone pays the same price for the same model of a car. The figure illustrates a normal distribution for the prices paid for a particular model of a new car. The mean is $23,000 and the standard deviation is $2000. Use the 68-95-99. 7 Rule to find what percentage of buyers paid between $21,000 and $23,000
68% of buyers paid between $21,000 and $23,000 for the car.The 68-95-99.7 Rule is a rule used to calculate the percentage of observations that fall within a given range of a normal distribution
The 68-95-99.7 Rule is a rule used to calculate the percentage of observations that fall within a given range of a normal distribution. The rule states that 68% of observations fall within one standard deviation of the mean, 95% of observations fall within two standard deviations of the mean, and 99.7% of observations fall within three standard deviations of the mean. In this case, the mean price paid is $23,000 and the standard deviation is $2000. Therefore, the range of prices between $21,000 and $23,000 is one standard deviation from the mean, and 68% of buyers paid between $21,000 and $23,000.Mathematically, this can be expressed as P(21,000<X<23,000) = P(μ- σ < X < μ + σ) = 0.68, where μ is the mean and σ is the standard deviation. By substituting the given values of μ and σ, this equation simplifies to P(21,000<X<23,000) = P(23,000 - 2000 < X < 23,000 + 2000) = 0.68. Therefore,68% of buyers paid between $21,000 and $23,000 for the car.
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