Answer:
See below.
Step-by-step explanation:
We are asked to find measures of the unknown sides for the given area.
Let's keep in mind that a rectangle's area is; [tex]Area = (width) \times (height)[/tex]
One simple way to find all of the possible side lengths is to find all of the factors of 16.
What are Factors?
Factors are 2 whole numbers that multiply together to have the product of that given number.
Think of how many ways we can get to 16 by multiplying 2 numbers.
[tex]f_{1} \times f_{2} = 16\\f \ represents \ a \ factor.[/tex]
Here's all of the possible ways we can get to 16 with whole numbers.
[tex]8 \times 2 = 16\\4 \times 4 = 16\\2 \times 8 = 16\\1 \times 16 = 16\\16 \times 1 = 16[/tex]
Remember that the Width and Length of a Rectangle can have different values even with the same numbers multiplied.
[tex](8 \times 2) \ and \ (2 \times 8)\\Length \ can \ equal \ 2, \ or \ 8.\\Width \ can \ equal \ 8, \ or \ 2.[/tex]
These are all of the possible answers.
PLSSSS HELPP WILL GIVE BRAINLIEST!!!!
Answer:
Proved
Step-by-step explanation:
In triangles ABD and CBD,
Angle CDB = Angle ADB (given in Question)
Angle CBD = Angle ABD ( Angle Bisector Therom)
BD = BD ( Common side)
Therefore Triangle ABD is congruent to Triangle CBD by ASA
Hope it helps :)
The area of the triangle below is 1/16 square centimeters. What is the length of the base. Express your answer as a fraction in simplest form
The length of the base is 1/64 and can be simplified to the fraction 1/64 = 1/64 in simplest form.
What does fraction mean?A fraction is a mathematical expression which represents a part of a whole. It is written as a ratio that compares two numbers, the numerator and denominator. The numerator indicates the number of parts, the denominator indicates the total number of parts that make up the whole. Fractions can be expressed as decimals, percentages, and other forms of representation.
To solve this problem, we must use the formula for area of a triangle. This formula states that the area of a triangle is equal to one-half the product of the base and the height. In this problem, the area of the triangle is given as 1/16 square centimeters. This means that the base times the height must equal 1/8.
To find the length of the base, we must isolate the base from the equation. To do this, we must divide both sides of the equation by the height. This will leave us with the equation base = 1/8/height. Since the height is unknown, we can solve for it by taking the reciprocal of the base. This will give us the equation height = 1/8/base.
Combining both equations, we can solve for the base by multiplying both sides of the equation by 1/8. This will give us the equation base = (1/8)(1/8) = 1/64. The length of the base is 1/64 and can be simplified to the fraction 1/64 = 1/64 in simplest form.
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w is proportional to d
when d=35 the value of w 133
work out the value of w when d=25
Accοrding tο given proportional data when d = 25, the value οf W is 95.
What is prοpοrtiοnality?Relatiοnships between the twο variables that are prοpοrtiοnal οccur when their ratiοs are equal. Anοther apprοach tο cοnsider is that in a prοpοrtiοnal relatiοnship, οne variable is cοnsistently equal tο the οther's cοnstant value. This parameter is referred tο as the "cοnstant οf prοpοrtiοnality".
Accοrding tο the given infοrmatiοn:
Using the prοpοrtiοnality relatiοn W ∝ d, we can set up the fοllοwing prοpοrtiοn:
W/d = k, where k is the cοnstant οf prοpοrtiοnality.
Tο sοlve fοr k, we can use the values given in the prοblem:
133/35 = k
Simplifying, we get:
k = 3.8
Nοw, we can use this value οf k tο find the value οf W when d = 25:
W/25 = 3.8
Simplifying, we get:
W = 95
Therefοre, accοrding tο given infοrmatiοn when d = 25, the value οf W is 95.
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help me bro help me bro help me bro help me bro help me bro
By writting all the numbers as decimals we can see that the lake that lost the least amount of water is the last one.
Which lake lost the least amount of water?The first lake lost a fraction of 5/6 of its total water.
The second lake lost the 85% of its water.
The last lake lost a fraction of 246/300 of its water.
We want to see which of these 3 numbers is the smaller one, we can write all of them as decimals ot get:
5/6 = 0.833
85% = 0.85
246/300 = 0.82
With this we conclude that the lake that lost the least amount of water is the last one.
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What equation is created by this ordered pair (1,1) (2,2) (3,4) (4,7) (5,12)?
The answer will be as follows after answering the supplied question It is equation worth noting that this equation is a cubic polynomial.
What is equation?A math equation is a process that relates two statements by using the equals sign (=) to indicate equivalence. In algebra, an equation is a mathematical statement that shows the equivalence of two mathematical expressions. In the equation 3x + 5 = 14, for example, 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 opposite sides of a letter. Frequently, the logo and the software are the same. For example, 2x - 4 = 2.
The degree n Lagrange polynomial that passes through n+1 unique points (x0,y0), (x1,y1),..., (xn,yn) is given by:
[j=0 to n] L(x) [i=0 to n, ij] * yj (x - xi)/(xj - xi) (xj - xi)
We have 5 points in our situation, thus n = 4. We get the following results by plugging the provided points into the Lagrange polynomial formula:
[tex]L(x) = 1*(x-2)(x-3)(x-4)(x-5)/(-1123) + 2(x-1)(x-3)(x-4)(x-5)/(1123) + 4(x-1)(x-2)(x-4)(x-5)/(1123) + 4(x-1)(x-2)(x-4)(x-5)/(1123) (2123)+ 12(x-1)(x-2)(x-3)(x-4)/(432*1)[/tex]
When we simplify this expression, we get:
[tex]L(x) = x^3/3 - 3x^2/2 + 11x/6 - 1[/tex]
As a result, the equation of the curve passing through the given locations is:
[tex]y = x^3/3 - 3x^2/2 + 11x/6 - 1[/tex]
It is worth noting that this equation is a cubic polynomial.
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Create an exponential equation passing through points (1960, 179323175) and (2010, 308745538) Round (a) and (b) to 3 decimal places
The exponential function passing through the points (1960, 179323175) and (2010, 308745538) is given as follows:
y = 0.1(1.01092581)^x.
How to define the exponential function?The standard definition of an exponential function is given as follows:
y = ab^x.
In which the coefficients a and b are explained as follows:
a is the initial value.b is the rate of change.The points for this problem are given as follows:
(1960, 179323175) and (2010, 308745538).
Considering that between 1960 and 2010 there is an increase of 50 in the input, the parameter b is obtained as follows:
b^50 = 308745538/179323175
b = (308745538/179323175)^(1/50)
b = 1.01092581.
Hence:
y = a(1.01092581)^x.
When x = 1960, y = 179323175, hence the parameter a is obtained as follows:
a = 179323175/[(1.01092581)^1960]
a = 0.1.
Hence the function is:
y = 0.1(1.01092581)^x.
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Three dozen blocks were in a bag. Four were red. What is the probability that a block removed at random will NOT be red?
Answer:
9
Step-by-step explanation:
1 dozen -12
there dozen - 36
thus
red blocks -4
36/4
= 9
Beth’s grandma makes homemade jam every year Beth helps her grandma by covering each jar with plastic wrap before storing the jam. each jar has a diameter of 7cm and a height of 11cm this years Beths grandma made 12 jars of jam how many square centimeters of plastic wrap will Beth need to completely cover all the jars
Beth will need approximately 3365.76 [tex]cm^{2}[/tex] of plastic wrap to cover all 12 jars of jam.
What is a Circle?
A circle is simply a round shape that has no corners or line segments. It is a closed curve shape in geometry. The points of circle are at a fixed distance from the center.
So now, to calculate the surface area of each jar, we need to find the area of the circular top and the area of the rectangular side.
The area of the circular top can be calculated using the formula for the area of a circle:
[tex]A=\pi r^{2}[/tex], where r is the radius of the circle.
The diameter of the jar is given as 7 cm, so the radius is half of that:
r = [tex]\frac{7}{2}[/tex] cm = 3.5 cm
Therefore, the area of the circular top is:
A_top = [tex]\pi r^2[/tex] = π[tex](3.5)^{2}[/tex] = 38.48 [tex]cm^{2}[/tex]
The area of the rectangular side can be calculated using the formula for the area of a rectangle:
A_side = base x height
The base of the rectangle is the circumference of the circular top, which can be calculated using the formula:
C = 2πr
C = 2π(3.5) = 22 cm
So the base of the rectangle is 22 cm, and the height is 11 cm, since that is the height of the jar.
Therefore, the area of the rectangular side is:
A_side = base x height = 22 cm x 11 cm = 242 [tex]cm^{2}[/tex]
To find the total surface area of each jar, we can add the area of the circular top and the area of the rectangular side:
A_total = A_top + A_side = 38.48 [tex]cm^{2}[/tex]+ 242 [tex]cm^{2}[/tex] = 280.48 [tex]cm^{2}[/tex]
For 12 jars, the total surface area of plastic wrap needed would be:
Total area = 12 x A_total = 12 x 280.48 [tex]cm^{2}[/tex] = 3365.76 [tex]cm^{2}[/tex]
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Given the pre-image ABCD and the image after a dilation, A'B'C'D', what is true about the polygons? Check all that apply.
The length AB is 2.
The length A'B' is 3.
The image is smaller than the pre-image.
The scale factor is Three-halves.
The scale factor is Two-thirds.
For the given dilation of the polygons the correct answer are The length AB is 2. The length A'B' is 3. The scale factor is Three-halves.
What is dilation?Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is a picture with the same shape as the original. Yet, there is a variation in the shape's size. The initial form should be stretched or contracted during a dilatation. The phrase "scale factor" describes this transition.
The distance formula for the coordinates is given as:
d(A, B) = |x1 - x2|
From the figure we observe that,
d(A, B) = |2 - 4|
d(A, B) = |-2|
d(A, B) = 2 units.
Hence, option A is correct.
Also, the length of A'B' is:
d(A', B') = |3 - 6| = |-3| = 3 units.
Hence, option B is correct.
The original shape is called the pre-image in a transformation (in this example, a dilation), and the transformed shape is called the image.
The third response is untrue since the picture is larger than the pre-image.
The scale factor of the images is:
2k = 3
k = 3/2.
Hence, option 4 is correct.
The last option is also false, as the scale factor is already determined.
Hence, for the given dilation of the polygons the correct answer are The length AB is 2. The length A'B' is 3. The scale factor is Three-halves.
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The complete question is:
Please can someone help!
Answer: 20.1 m
Step-by-step explanation:
using the formula circumference = 2pi r:
[tex]126=2\pi r[/tex]
divide 2 pi on both sides
[tex]r=\frac{126}{2\pi }[/tex]
r = 20.05
r = 20.1 m
I need helppp do these all plsss show workk too
1. A team of 7 construction workers worked together to build 3
sheds in 10 days. How much of a shed did each of them build?
2. The construction of an 80-meter bridge was finished in 12
weeks. How much of the bridge was built on average each
week?
3. A 4-story building is 29 feet tall. Between which two whole
numbers do the height of each story lie?
1. Josh used 3 packages of spaghetti to make dinner for 19
guests. How much did each guest have?
2. According to a recipe, 190 grams of sugar is needed to make 9
cupcakes. Between which two whole numbers does the weight
of sugar used for each cupcake lie?
3. A 2-liter pitcher of juice was poured into 8 cups. How much
juice was in each cup?
There was 5
8
of a pie left in the fridge. Daniel ate 1/4 of the leftover pie. How much of a pie did he have?
2. Olivia took out 8 glasses and poured juice from the pitcher. The
capacity of each glass is 3/10
liter. If there was enough juice for 6 glasses, how much juice was there?
3. Pam baked some cupcakes for her friends. She baked 24
cupcakes. Each cupcake is 2/15
pound. If she packed 6
cupcakes in each box, what is the weight of each box?
Answer:
number 2 is 4
Step-by-step explanation:
The reading on the thermometer is -20 degrees Fahrenheit and the temperature rises with 20 degrees Fahrenheit. What will be the new reading be?
As per the given temperature, the new reading is 0°F
The formula for converting Fahrenheit to Celsius is (°F - 32) x 5/9 = °C. We can use this formula to determine the new temperature in Celsius and then convert it back to Fahrenheit.
First we have to convert the initial temperature to Celsius
(-20°F - 32) x 5/9 = -28.89°C
Now we have to add 20 degrees Fahrenheit to the initial temperature
-20°F + 20°F = 0°F
And then we have to convert the new temperature to Celsius
(0°F - 32) x 5/9 = -17.78°C
When we convert the new temperature from Celsius back to Fahrenheit
-17.78°C x 9/5 + 32 = 0°F
Therefore, the new reading on the thermometer will be 0 degrees Fahrenheit, which indicates that the temperature has risen by 20 units on the Fahrenheit scale.
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Find m angle 1 and angle 2
According to the figure and using the corresponding angle theorem we have that
angle 1 = 82 degreesangle 2 = 122 degreesHow to find angle 1 and 2Corresponding angles are pairs of angles that are formed when a straight line intersects two parallel lines.
They are located on opposite sides of the transversal (the line that intersects the parallel lines) and in corresponding positions. Corresponding angles have the same degree measurement as each other.
angle 1 = 82 degrees corresponding angles are equal
angle a = 58 degrees corresponding angles are equal
angle a and angle 2 are linear pair hence angle a and angle 2 are supplementary angles
hence we have that
angle a + angle 2 = 180 degrees
58 + angle 2 = 180
angle 2 = 180 -58
angle 2 = 122 degrees
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Martin is x years old. Jennifer is 3 years younger than Martin. Connor is twice as old as Martin. Write an expression for Jennifer’s age.
Answer:
x-3
Step-by-step explanation:
martin = x
jennifer = x-3
connor = 2x
what is jennifer's age?
The average high temperatures in degrees for a city are listed. 58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57 if a value of 110.5° is added to the data, how does the mean change and by how much? a. the mean increases by 2.3°.b. the mean increases by 2.7°. c. the means stays at 80.4°. d. the mean stays at 82.7°.
Answer:
The measure which changes the most is the mean and the new value is 84°
The correct answer option is option B
Step-by-step explanation:
How to calculate mean and median?
Given data set:
58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57
Median = (100 + 105) / 2
= 205/2
= 102.5°
Mean = (58 + 61 + 71 + 77 + 91 + 100 + 105 + 102 + 95 + 82 + 66 + 57) / 12
= 965 /12
= 80.4°
Range = Highest value - lowest value
= 105 - 57
= 48°
Interquartile range = Third quartile - First quatile
= 88.5° - 74°
= 14.5°
If 58° is changed to 101°
101, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57
Median = (100 + 105) / 2
= 205/2
= 102.5°
Mean = (101 + 61 + 71 + 77 + 91 + 100 + 105 + 102 + 95 + 82 + 66 + 57) / 12
= 1008 /12
= 84°
Range = Highest value - lowest value
= 105 - 57
= 48°
First quartile = (71 + 77) / 2
= 148/2
= 74°
Third quartile = (95 + 82)/2
= 177/2
= 88.5°
Interquartile range = Third quartile - First quatile
= 88.5° - 74°
= 14.5°
Therefore, the new mean is 84°
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Which is the smallest?
(a) -1,
(b) -1/2,
(c) 0,
(d) 3.
Answer:
A
because it is a negative number and because it is less than -1/2
Answer:
Step-by-step explanation:
the answer is -1 as negative integers become smaller as they go to the left.
no problem
Trinagle abc is similar to triangle def. The following ratios of corresponding sides are equal. 8/10 = 16/20 = 4x+6/4x+11
The value of x is 0. This means that [tex]8/10 = 16/20 = 4x+6/4x+11[/tex], so the corresponding sides of triangles abc and def have the same ratio.
The similarity of two triangles can be determined by the ratio of their corresponding sides. In the case of triangles abc and def, the ratio of corresponding sides is [tex]8/10 = 16/20 = 4x+6/4x+11[/tex].
To calculate the value of x, we can use the first two ratios and cross-multiply. With 8/10 = 16/20, we get 8*20=16*10, which simplifies to 160=160. Therefore, the first two ratios are equal.
To calculate the value of x using the third ratio, we can use the same method. With 4x+6/4x+11, we get ([tex]4x+6)*(4x+11)=4x^2+44x+66[/tex]. This simplifies to [tex]4x^2+44x+66=4x^2+44x+66[/tex], so the third ratio is also equal.
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Complete question:
What is the value of x in the ratio 8/10 = 16/20 = 4x+6/4x+11?
The couple asked the architect to add a square garden shed to the plans that she
drew. She added a square garden shed with coordinates (-2,8), (1,8), (1, 11), and
(-2, 11) to the plans. Discuss the following with a partner:
• How could you find the perimeter and area of the shed without graphing
the coordinates?
• How is this problem different from finding the perimeter and area of the
base of the house?
. Can you use the same strategy to solve both problems? Why or why not?
Answer:
To find the perimeter and area of the square garden shed without graphing the coordinates, you can use the distance formula to calculate the length of one side of the square. The distance formula is d = √((x2 - x1)^2 + (y2 - y1)^2), where (x1, y1) and (x2, y2) are the coordinates of two points. Using this formula with the coordinates of two adjacent corners of the square, such as (-2,8) and (1,8), we find that the length of one side of the square is 3 units. Since all sides of a square are equal in length, the perimeter is 4 times the length of one side, or 12 units. The area of a square is equal to the length of one side squared, so the area of the square garden shed is 9 square units.
This problem is different from finding the perimeter and area of the base of a house because it involves a square shape rather than a more complex shape. However, you can use similar strategies to solve both problems by calculating distances between points and using geometric formulas to find perimeter and area. The specific formulas used may vary depending on the shape of the base of the house.
Whitney deposited money into an account in which interest is compounded quarterly at a rate of
2. 9%. She made no other deposits or withdrawals and the total amount in her account after 12 years
was $10,891. 31.
How much did she deposit?
O
$7700
O
$8650
O
$9700
o $10,580
Next
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 10891.31\\ P=\textit{original amount deposited}\\ r=rate\to 2.9\%\to \frac{2.9}{100}\dotfill &0.029\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &12 \end{cases}[/tex]
[tex]10891.31 = P\left(1+\frac{0.029}{4}\right)^{4\cdot 12} \implies 10891.31=P(1.00725)^{48} \\\\\\ \cfrac{10891.31}{1.00725^{48}}=P\implies 7700\approx P[/tex]
molly has a $2500 down payment saved for this purchase, and the dealers $1500 cash allowance will come straight off her total. How much loan does molly need?
Based on the given question, Molly needs a loan of $1,000
What is a Loan?A loan occurs when one or more people, businesses, or other entities lend money to other people, businesses, or other entities.
The recipient incurs a debt and is often responsible for both the principal amount borrowed as well as interest payments until the debt is repaid.
How to calculate the amount of loan that Molly needs?
Molly has a $2500 down payment saved for a purchase
The dealer's cash allowance is $1500, this will be deducted from her total
The amount of loan that Molly needs can be calculated by subtracting the dealer's cash allowance from Molly's down payment
Loan= Down payment-cash allowance= 2500 - 1500= 1000
Hence Moly needs a loan of $1,000
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Which inequality is equivalent to 5(2x-6)+6(3-x)<2x+4
By answering the given question, we may state that Therefore, the equivalent inequality is: x < 2
What is inequality?A relationship between two terms or values which is not equal is known as an inequality in mathematics. Inequality follows imbalances, therefore. In mathematics, an inequality makes a link among two quantities that are not equal. Egality and inequality are different. Use the not similar symbol most frequently when two components are not equal (). Various inequalities are employed to contrast values of all sizes. By changing the two parts until only the variables are left, one can solve many straightforward inequalities. However a variety of factors support inequality: Negative values are split or added on either side. Switch between the left & right.
inequality using basic algebraic operations:
5(2x-6)+6(3-x)<2x+4
10x-30+18-6x < 2x+4
4x - 8 < 0
4x < 8
x < 2
Therefore, the equivalent inequality is:
x < 2
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Mr Cobb says that increasing something by 10% then decreasing it by 10% will just give you the original amount. Mr Pathuis says the new amount will be bigger. Mr Drake says the new amount will be smaller. Who is right and why?
Answer:
Mr Drake is right.
Step-by-step explanation:
Because you first decreased it by 10% of the ORIGINAL value.
You then increased it by 10% of the DECREASED value.
The percentages are the same percentages, but on different base amounts.
Simple example:
$100 decreased by 10% of $100 ($10) is $90.
$90 increased by 10% of $90 ($9) is $99.
Answer:
Mr Drake Is correct
Step-by-step explanation:
When you increase something by 10%, you multiply the original value by 1.1. When you decrease it by 10%, you multiply the increased value by 0.9. So the final amount is:
original value x 1.1 x 0.9 = 0.99 x original value
Therefore, the new amount will be slightly smaller than the original amount, and Mr. Drake is correct.
What is 24/32 reduced as much as possible?
Answer:
3/4
Step-by-step explanation:
Hope this helps! Pls give brainliest!
Which expression has a value of 15 when p=12
Answer: p+3
Step-by-step explanation:
if p=12 and you need the answer to be 15, all you need to do is find 12+_= 15. Since 12+3=15 your answer would be p+3.
You are currently at point A on a circle, and you want to get to point B on the circle. You are trying to minimize the distance walked. You can either walk into the middle of the circle and then out of the circle, or you can walk around the edge of the circle. At what minimum distance between A and B do you walk in and then out of the circle in order to minimize the distance walked? State the answer as a % of total circumference.
To minimize the distance walked, and the minimum distance is 31.8% of the total circumference of the circle.
What is the minimum distance between A and B?
If we draw a line segment from A to B, it will intersect the circle at two points, C and D. We can find the distance AC and the distance BD by using the Pythagorean theorem.
Let r be the radius of the circle, and let x be the distance we walk in and then out of the circle.
Then, we have:
AC = √(r^2 - (x/2)^2)
BD = √(r^2 - (x/2)^2)
The total distance we walk is AC + BD + AB. Since AB is fixed, we want to minimize AC + BD.
AC + BD = 2√(r^2 - (x/2)^2)
To minimize this expression, we need to maximize the value inside the square root. That means, we need to set (x/2)^2 to be as small as possible.
In other words, we want x to be as large as possible.
The maximum value of x is the diameter of the circle, which is 2r.
If we walk in and out of the circle along the diameter, then AC and BD are both equal to r, and the total distance we walk is 2r + AB.
Therefore, the percentage of the total circumference that we walk in and out of the circle is:
2r / (2πr) * 100% = 100/π ≈ 31.8%
So, we need to walk in and out of the circle at two points that are opposite to each other, along a diameter, to minimize the distance walked, and the minimum distance is approximately 31.8% of the total circumference of the circle.
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need the measure of angle ABC please
Answer:
∠ ABC = 38°
Step-by-step explanation:
given AB = DB then Δ ABD is isosceles with base angles congruent, that is
∠ BDA = ∠ BAD = 71°
the sum of the 3 angles in Δ ABD = 180° , so
∠ ABC + 71° + 71° = 180°
∠ ABC + 142° = 180° ( subtract 142° from both sides )
∠ ABC = 38°
ivy received a bank statement reposrting the recent changes to her account. the statement showed an overall increase in the account balance of $1,692.45. during the time shown on the statement, ivy was paid twice and withdrew a total of $1,876.23 to cover all her bills and expenses. how much (x) is each of ivay's paychecks? help me please
if Ivy received two Paychecks during the time period shown on the statement, each paycheck would be $1,784.34.
To find out how much each of Ivy's paychecks is, we need to subtract the amount she withdrew from her account from the overall increase in her account balance.
So, the calculation would be:
Overall increase in account balance - Total amount withdrawn = Total amount deposited
$1,692.45 - $1,876.23 = -$183.78
This means that Ivy actually spent more than she earned during the time period shown on the statement. Therefore, we cannot determine the amount of each of her paychecks with the given information.
However, if we assume that Ivy did not have any other income or expenses during the time period, we can use the following equation:
2x - $1,876.23 = $1,692.45
where x is the amount of each paycheck.
Simplifying the equation, we get:
2x = $3,568.68
x = $1,784.34
Therefore, if Ivy received two paychecks during the time period shown on the statement, each paycheck would be $1,784.34.
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x= 2 cos³t y = 2 sin ³ t
find the cartesian equation
Answer:
[tex]y^2 = x^3 / 2^{3/2}[/tex] or [tex]y = x^{3/2} / 2^{3/4}[/tex]
Step-by-step explanation:
We can use the identity [tex]cos^3(t) = cos(t)*cos^2(t) and sin^3(t) = sin(t)*sin^2(t)[/tex] to rewrite the given parametric equations in terms of x and y:
[tex]x = 2cos(t)*cos^2(t) = 2x^2 - 2y^2[/tex]
[tex]y = 2sin(t)*sin^2(t) = 2xy^2[/tex]
Solving for y in terms of x, we get:
[tex]y = x^{3/2} / 2x^{3/4}[/tex]
Therefore, the cartesian equation of the curve is:
[tex]y = x^{3/2} / 2^{3/4}[/tex]
or, equivalently:
[tex]y^2 = x^3 / 2^{3/2}[/tex]
A test has 12 problems, and each problem is worth 5 marks. Full marks are given for a correct answer, 2 marks are given if there is no answer, and no marks are given for an incorrect answer. Some scores between 1 and 60, are impossible to get on this test. What is the sum of these impossible scores?
To make things easier, consider the residue when each integer between equation 1 and 60 is divided by 5. The remainders might be one, two, three, or four.
What is equation?A math equation is a process that relates two statements by using the equals sign (=) to indicate equivalence. In algebra, an equation is a mathematical statement that proves the equality of two mathematical expressions. In the equation 3x + 5 = 14, for example, 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 opposite sides of a letter. Frequently, the logo and the software are the same. For example, 2x - 4 = 2.
0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 = 0 (if all answers are wrong or not attempted) (if all answers are incorrect or not attempted)
5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 = 60 (assuming all answers are accurate) (if all answers are correct)
10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 = 120 (assuming all answers are accurate and attempted twice) (if all answers are correct and attempted twice)
. The impossible scores may be obtained by locating all the numbers between 1 and 60 that cannot be stated as a sum of 0, 5, or 10.
To make things easier, consider the residue when each integer between 1 and 60 is divided by 5. The remainders might be one, two, three, or four.
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Compare two functions: f(x) shown in the table below and g(x) which is described in the following way: Darya is 2 miles east of home and begins jogging east at a constant rate of 5 miles per hour. Let g(x) be her distance away from home and x be the time she has been jogging in hours.
Which of the following statements is NOT true?
f(x) is an exponential function whose base is 3.
f(x) is an exponential growth function that will keep growing larger.
g(x) is an exponential function because Darya keeps getting farther away from home.
g(x) is a linear function because Darya is jogging at a steady rate.
It is untrue to say that the exponential function f(x) has a base of 3.
What does the function's exponential mean?A mathematical function termed an exponential function has the formula f (x) = axe, where x is a variable and a constant called the base of the function, which must be greater than 0. The most often used exponential function basis is the transcendental number e, or approximately 2.71828.
What is an example of an exponential function?An exponential function has the form f(x) = bx for b > 0 and b 1. Like in any exponential expression, the base is b and the exponent is x. Bacterial growth serves as an example of an exponential function. Some bacteria grow by two per hour.
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