a is correct
Question 1 (1 point )If y varies directly as x and y = 15 when x = 12, find y when x = 32. The value of y when x = 32 is 40.How to solve direct variation problems?A direct variation is a function that can be expressed in the form y = kx, where k is a nonzero constant. Two quantities x and y are said to be in direct variation if they satisfy this relationship. To solve direct variation problems, you can use the following formula: y = kx, where k is the constant of variation.The solution to the problem is given below:Given:y varies directly as xx = 12, y = 15To find:y when x = 32Formula:Since y varies directly as x, we have:y = kxLet's substitute x and y values in the above equation:15 = k × 1215/12 = kk = 5/4Thus, the equation of the direct variation is: y = (5/4) xTo find the value of y when x = 32, substitute 32 for x:y = (5/4) × 32y = 40Therefore, y = 40 when x = 32. Hence, the option (a) is correct.
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PLEASE HELP THANK YOU
The steps below can be used to show that the angles in a triangle sum to 180°. Which angle facts should replace A, B and C to complete the steps? I have attached the picture of A,B and C.
These are the angle facts you need to choose from:
Corresponding angles are equal
Vertically opposite angles are equal
Alternate angles are equal
Angles around a point sum to 360°
Angles which make a straight line sum to 180°
Co-interior angles sum to 180°
Answer:
A=Alternate angles are equal
B=Alternate angles are equal
C=Angles which make a straight line sum to 180°
Step-by-step explanation:
A and B: if two lines are parallel and are intersected by a line then the angles on the opposite sides are equal to each other
C: a flat line is equal to 180 degrees
Answer:
X. Alternate angles are equal.
Y. Alternate angles are equal
Z. Angles on a straight line add up to 180°
Factor the expression completely.
−
100
�
5
+
90
−100x
5
+90
The expression [tex]-100^5 + 90[/tex] is completely factored as [tex]-(10^5 + 3)(10^5 - 3)[/tex].
What is an expressiοn?Mathematical expressiοns cοnsist οf at least twο numbers οr variables, at least οne arithmetic οperatiοn, and a statement. It's pοssible tο multiply, divide, add, οr subtract with this mathematical οperatiοn.
The expression [tex]-100^5 + 90[/tex] can be factοred as follows -
Grοup the negative sign with the first term -
[tex]= -(100^5) + 90[/tex]
Evaluate [tex]100^5[/tex] as [tex](10^2)^5 = 10^{10}[/tex] -
[tex]= -(10^{10}) + 90[/tex]
Factor οut a negative sign -
[tex]= -(10^{10} - 90)[/tex]
Factor the difference of twο squares, where [tex]a = 10^5[/tex] and b = 3 -
[tex]= -(10^5 + 3)(10^5 - 3)[/tex]
Therefore, the expressiοn is factored as [tex]-(10^5 + 3)(10^5 - 3)[/tex].
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How do I do this?I already know the answer I just don’t know how to do it
triangles are similar, angles are all the same or congruent.
Check the picture below.
whats the missing side lengths!
Answer:
x = 3[tex]\sqrt{2}[/tex] , y = [tex]\frac{3\sqrt{2} }{2}[/tex]
Step-by-step explanation:
this is a 90- 45- 45 isosceles triangle with legs congruent , that is
y = [tex]\frac{3\sqrt{2} }{2}[/tex]
using Pythagoras' identity in the right triangle
x² = ( [tex]\frac{3\sqrt{2} }{2}[/tex] )² + y²
= ( [tex]\frac{3\sqrt{2} }{2}[/tex] )² + ( [tex]\frac{3\sqrt{2} }{2}[/tex] )² = 9 + 9 = 18 ( take square root of both sides )
x = [tex]\sqrt{18}[/tex] = [tex]\sqrt{9(2)}[/tex] = [tex]\sqrt{9}[/tex] × [tex]\sqrt{2}[/tex] = 3[tex]\sqrt{2}[/tex]
Question 3
In the figure below, if AB = 1964, what is BC?
The length of BC is 19/8.
Describe Right Angle Triangle?A right triangle, also known as a right-angled triangle, is a triangle in which one of its angles measures exactly 90 degrees (a right angle). The other two angles are acute angles, which means they measure less than 90 degrees.
The side opposite the right angle is called the hypotenuse, and it is the longest side of the triangle. The other two sides are called legs, and they form the right angle.
We can start by using the Pythagorean theorem in each of the triangles to find the lengths of the sides.
In triangle ABE, we have:
AB² = AE² + BE²
AB² = (2BE)² + BE² (since AE = 2BE, as angle AEB = 60 degrees)
AB² = 5BE²
BE = AB/√5
In triangle BED, we have:
BE² = BD² + DE²
AB²/⁵ = BD² + (BD/√2)² (since BE = AB/√5 and angle EBD = 45 degrees)
AB²/5 = 3BD²/2
BD = AB/√(10/3)
In triangle BCD, we have:
BC² = BD² + CD²
BC² = (AB/√(10/3))² + (AB/2)² (since angle BCD = 30 degrees and BD = AB/√(10/3))
BC² = (19/4)² * (1/10 + 1/4)
BC² = (19/4) * (3/20)
BC² = (361/80)
BC = √(361/80)
Therefore, BC = (19/4) * √(1/80) * √361 = (19/4) * (19/40) * √361 = 19/8. So the length of BC is 19/8.
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A sample of 18 widgets has a mean of 34.800 and standard
deviation of 9.050. At 99% confidence, the upper limit with 3
decimal places is
upper limit with 3
To obtain the upper limit with 3 decimal places, use the following formula for the confidence interval with a population mean.In this case, n = 18, sample mean = 34.8, sample standard deviation = 9.05, and confidence level = 99%. {z }_{\frac{\alpha}{2}}=\frac{\text{critical value}}{\sqrt{n}}Therefore, 99% confidence interval is {34.8 ± 3.053}. The upper limit of the confidence interval is obtained as 34.8 + 3.053 = 37.853 (rounded to three decimal places). Therefore, the upper limit with three decimal places is 37.853.A confidence interval is an estimated range of scores or values used to estimate the true population value. A confidence interval provides a range of values within which the true value is expected to fall with a certain degree of confidence. In the given question, we have to find the upper limit with 3 decimal places.
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HELPPP.
Create a table to represent the following situation: Gina is 5 years older than Sam. Gina’s age in years is x + 5, where x is Sam’s age, in years
Sam is 10 years old, and Gina is 15 years old.
Here's a table to represent the situation:
Person ║ Age
Sam ║ x
Gina ║ x+5
In this table, the first column lists the two people in the situation, Sam and Gina. The second column shows their ages in years. According to the problem statement, Gina is 5 years older than Sam, so we can represent Gina's age as x + 5, where x is Sam's age.
To find the solution, we need to use the information given in the problem statement to solve for x, which represents Sam's age. We know that Gina's age is x + 5, so we can set up an equation:
Gina's age = Sam's age + 5
x + 5 = x + 5
Simplifying the equation, we can see that x cancels out:
x + 5 - x = 5
5 = 5
This equation is always true, which means that there are infinitely many possible solutions. However, we can find a specific solution if we are given additional information. For example, if we are told that Gina is 15 years old, we can substitute x + 5 = 15 into the equation and solve for x:
x + 5 = 15
x = 10
Therefore, Sam is 10 years old, and Gina is 15 years old.
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C=9 when p=7 write an equation for c in terms of p
The equation for c in terms of p is c = (9/7)p. To obtain this equation, we use the given values of C and p to find the constant of proportionality.
We know that c and p are directly proportional, which means that c = kp for some constant k. We can find k by plugging in the given values:
9 = k(7).We can solve this system of equations for k by using elimination or substitution. Solving for k, we get
k = 9/7.Thus, the equation for c in terms of p is
c = (9/7)p.
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If you have the following data about a bag of chips, about
how many chips are estimated to be in the bag?
Mass of Chips + Bag = 369 grams
Mass of 25 Chips = 45 grams
Mass of Bag ONLY = 28 grams
Approximately, how many chips are in the bag?
Answer:
189 chips are estimated to be in the bag.
Step-by-step explanation:
Subtracting the massMass of Chips = Mass of Chips + Bag - Mass of Bag
Mass of Chips = 369 g - 28 g
Mass of Chips = 341 g
Dividing the massMass of 1 Chip = Mass of 25 Chips / 25
Mass of 1 Chip = 45 g / 25
Mass of 1 Chip = 1.8 g
Dividing the mass of chips in the bag by the mass of one chipNumber of Chips = Mass of Chips / Mass of 1 Chip
Number of Chips = 341 g / 1.8 g
Number of Chips ≈ 189
Please refer to the photo
Any help or clarification is appreciated
The equivalent expression is 9b^6/a^4c^6
What is an equivalent expression?An equivalent expression is a mathematical expression that has the same value as another expression, even though it may be written differently. Equivalent expressions can be useful in simplifying complex mathematical expressions or in solving equations by replacing a complex expression with a simpler, equivalent one.
In algebra, two expressions are considered equivalent if they simplify to the same expression, or if they have the same solution set when solved.
We have that;
(-3ab^2c^-3/a^3b^-1)^2
9a^2b^4c^-6/a^6b^-2
9a^-4b^6c^-6
9b^6/a^4c^6
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Compare representing points in the table and in the coordinate plane?
(7,9) ,(9,7), (0,6), (3,8), (7,5), (8,3), (6,0), (9,10), (5,2), (2,5)
The points (7,9), (9,7), (0,6), (3,8), (7,5), (8,3), (6,0), (9,10), (5,2), and (2,5) can be represented in a table with two columns - one for the x-coordinate and one for the y-coordinate. This format is useful for organizing and manipulating data, but it does not provide a visual representation of the location of the points.
On the other hand, a coordinate plane is a visual tool that allows us to plot and view the location of points in two-dimensional space. The x-axis and y-axis intersect at the origin (0,0), and each point is represented by a unique combination of x and y coordinates. This format is particularly useful for understanding the relationships and patterns among the points.
A table lists the coordinates of points in a tabular format, a coordinate plane allows us to plot and visualize the location of points in two-dimensional space.
Representing points in a table and in a coordinate plane are two common ways to visually display data. While a table lists the coordinates of points in a tabular format, a coordinate plane is a graphical representation that allows us to plot and visualize the location of points in two-dimensional space.
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Solve for x and z:
a+bz/a+b=c+dz/d+c
if bc=ad
When we solve for x and z if bc =ad, We can start by cross-multiplying to get rid of the denominators: d(a+bz) = b(c+d)z + ac, then the linear equation has infinitely many solutions for any values of x and z.
Multiplying both sides by (a + b)(d + c) to remove the denominators, we get:
(a + bz)(d + c) = (c + dz)(a + b)
If z = 0, then we can substitute back into the original equation and solve for x:
a/b = (c - 1)/(1 - c).
thus, the solutions are:
If bc =ad, then the equation has infinitely many solutions for any values of x and z.
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Two forces are each applied to an area of 0. 09 m2. The first is applied with a pressure of 90 N/m2, and the second with a pressure of 70 N/m2. Find the difference between the size of the forces
There is a 1.8 N difference between the two forces
To find the difference between the size of the forces applied to two areas with different pressures, we need to use the formula:
Force = Pressure x Area
For the first force, with a pressure of 90 N/m² and an area of 0.09 m², the force can be calculated as:
Force1 = 90 N/m² x 0.09 m² = 8.1 N
For the second force, with a pressure of 70 N/m² and the same area of 0.09 m², the force can be calculated as:
Force2 = 70 N/m² x 0.09 m² = 6.3 N
Therefore, the difference between the size of the two forces is:
Force1 - Force2 = 8.1 N - 6.3 N = 1.8 N
So, the difference between the two forces is 1.8 N. The force with the higher pressure applies a larger force to the area, resulting in a larger force being applied overall.
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An arithmetic sequence starts at 0 and each successive number equals the previous number plus 6. Thus a1=0 and the distance d=6 What is the sum of the first 36 terms?
Answer:
228
Step-by-step explanation:
sum of the first n term = (n/2) [ 2a +(n-1)d]
sum of the first 36 terms =(36/2)[ 2×0+ (36-1)6]
= 228
A company that explores for oil in the ocean is considering two new sites, A and B. The exploration will take the entire year. The company estimates the probability of finding oil is 0. 25 at site A and 0. 36 at site B. The sites are far enough apart so that whether or not oil is found at one site, is independent of its being found at the other. Rounding your answer to two decimal places, find the probability that the company will find oil at both sites Correct only one of the sites neither of the sites Correct least one of the sites
Thus, a. 0.09 and b. 0.43 are the correct answers to this question. We must study a bit about set theory in order to understand this.
How to find out Union and intersection?A and B are the two sites that are accessible. As A and B are both distinct entities, they are both exploring oil at different locations.
Oil is discovered at the site
A with a probability of P(A) = 0.25, and oil is discovered at the site
B with a probability of P(B) = 0.36.
In two iterations of the experiment, when they are separate entities, they do not change the likelihood that others will happen.
a. Probability of oil found at both the sites = P(A ∩ B)
P(A ∩ B)=[tex]P(A)*P(B)=0.25*0.36=0.09[/tex]
b. Now if A finds oil in site A and not in site B and B finds oil in site B and does not find oil in site A,
[tex]P(A')=1-P(A)=1-0.25=0.75[/tex]
[tex]P(B')=1-P(b)=1-0.36=0.64[/tex]
P(A ∩ B') ∪ (A' ∩ B)=P(A ∩ B')+P(A' ∩ B)
=[tex][P(A)*P(B')][/tex] + [tex][P(A')*P(B)][/tex]
=[tex](0.25*0.65)+(0.75*0.37)[/tex]
=0.16+0.27=0.43
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2. Consider the parent function f(x) = x. Which transformations occurred to create g(x) = -2]x-81+7?
2
a. vertical translation 7 units up
b. horizontal translation 8 units right
C. vertical translation 7 units down
d. reflection in the x-axis
c.horizontal translation 8 units left
f.reflection in y axis
g.vertical stretch by a factor of 2
h.horizontal stretch by a factor of 2
Answer: The transformations that occurred to create g(x) = -2(x-8)²-81+7 from f(x) = x are:
- Horizontal translation 8 units to the right: The term (x - 8) in the equation of g(x) means that the graph of g(x) has been shifted horizontally 8 units to the right compared to f(x) = x.
- Vertical stretch by a factor of 2: The coefficient -2 in front of the term (x - 8)² means that the graph of g(x) has been vertically stretched by a factor of 2 compared to f(x) = x.
- Vertical translation 81 units down and 7 units up: The terms -81 and +7 in the equation of g(x) mean that the graph of g(x) has been shifted vertically 81 units down and then 7 units up compared to f(x) = x.
Therefore, the correct answer is (a) vertical translation 7 units up.
Step-by-step explanation:
4x^4+31x^2-90=0
Help
Answer:
The answer would not be 0, it would be -12, and here is why.
4x^4+ 16x+31x^2=62x-90.
In thia case i ignpored the variable, i think its a variable..
You woulkd add 62+16, you get 78.
78-90= -12
The area of a semicircle is 0.1413 square meters. What is the semicircle's radius?
[tex]\textit{area of a semicircle}\\\\ A=\cfrac{\pi r^2}{2} ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ A=0.1413 \end{cases}\implies 0.1413=\cfrac{\pi r^2}{2}\implies 0.2826=\pi r^2 \\\\\\ \cfrac{0.2826}{\pi }=r^2\implies \sqrt{\cfrac{0.2826}{\pi }}=r\implies 0.30\approx r[/tex]
(6x + 5 - 3x + 16)/3 x 15/5
The solution to the given expression [tex]\frac{6x + 5 - 3x + 16}{3} \cdot \frac{15}{5}[/tex] when simplified is 3x + 21.
How to simplify the expressionTo simplify the expression [tex]\frac{6x + 5 - 3x + 16}{3} \cdot \frac{15}{5}[/tex],
We can first combine like terms in the numerator to get [tex]\frac{3x + 21}{3}[/tex]
We can then simplify this further by dividing both the numerator and denominator by 3, which gives us x + 7 in the numerator.
Next, we can simplify the fraction 15/5 by dividing both the numerator and denominator by 5, which gives us 3
So, we have
[tex]\frac{6x + 5 - 3x + 16}{3} \cdot \frac{15}{5} = \frac{3x + 21}{3} \cdot 3[/tex]
[tex]\frac{6x + 5 - 3x + 16}{3} \cdot \frac{15}{5} = 3x + 21[/tex]
Hence, [tex]\frac{6x + 5 - 3x + 16}{3} \cdot \frac{15}{5}[/tex] simplifies to 3x + 21.
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Complete question
Simplify (6x + 5 - 3x + 16)/3 * 15/5
(2t + 7) (2t -5) solve using identities
Answer:
[tex]4t^{2}+4t-35[/tex]
Step-by-step explanation:
[tex](2t+7)(2t-5)\\4t^{2}-10t+14t-35\\4t^{2}+4t-35[/tex]
3. Find the constant proportionality for the table and writ in the form
of y=mx.
Boxes of Candy (x)
9
10
Pieces of Candy (y) 150 135
2
6
3
30 90 45
a. Figure the slope/rate and put it in the formula where slope/rate
goes.
b. Why would you need to know the rate of pieces of candy per
box? Make up a job or reason you would need to know this rate
and write in complete sentences.
The constant proportionality is 15, which means that for every box of candy, there are 15 pieces of candy. The equation is 15x.
What is constant and variable?A variable in mathematics is a sign that denotes a value that may vary, as opposed to a constant, which is a set number that never changes. Variables are used to represent unknown or changing quantities, such as time (t) or the distance (d) travelled by an item, whereas constants are used to represent fixed numerical values, such as pi or the speed of light (c). In contrast to variables, which are often represented by lowercase letters, constants are typically represented by capital letters. In mathematical equations and formulae, the distinction between constants and variables establishes which values are fixed and which values are subject to change.
The slope of line is given as:
m = (change in y) / (change in x)
Substitute the values from the table:
m = (135 - 150) / (9 - 10) = -15/-1 = 15
For the equation to be of the form y = mx we have:
y = mx + b
150 = 15(10) + b
b = 0
Substituting the values the equation is:
y = 15x
Hence, the constant proportionality is 15, which means that for every box of candy, there are 15 pieces of candy. The equation is 15x.
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HELP ME!!!!! THIS IS DUE TODAY( answer only question 18)
The correct proportion for corresponding sides is option C.
Describe Corresponding Sides?In geometry, corresponding sides are sides of two or more geometric figures that are in the same relative position, shape, and orientation. More specifically, corresponding sides are sides that are opposite or facing each other in congruent or similar figures. Corresponding sides have the same length and are parallel to each other. For example, if we have two congruent triangles, the corresponding sides of each triangle are the sides that are opposite to the same angle in both triangles. Similarly, if we have two similar polygons, the corresponding sides of each polygon are the sides that have the same relative position, shape, and orientation in both polygons. Corresponding sides can be used to determine whether two figures are congruent or similar, as well as to find the length of unknown sides in geometric figures using proportions.
For example, consider two similar triangles ABC and DEF. The sides of triangle ABC are AB, BC, and AC, while the corresponding sides of triangle DEF are DE, EF, and DF. The side AB corresponds to the side DE, the side BC corresponds to the side EF, and the side AC corresponds to the side DF. The ratios of the lengths of corresponding sides are equal:
AB/DE = BC/EF = AC/DF
This property of corresponding sides is important in solving problems involving similar figures, such as finding missing side lengths or areas. By setting up and solving ratios of corresponding sides, we can determine the relationship between the sizes of the figures and their corresponding parts.
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3. a. Explain why we can find the area of a 4-cm-by 8 -cm rectangle by multiplying \( 4 \cdot 8 \) by showing how to create equal groups in the situation. b. Discuss how to relate your explanation in p
Therefore , the solution of the given problem of area comes out to be 4-cm by 8-cm rectangle, we can keep adding rows of four-square units.
What exactly is an area?Its total size can be determined by figuring out how much room would be required to completely cover the outside. The surroundings are also taken into consideration when determining this same surface that has a trapezoidal shape. Something's total dimensions are determined by its surface area. The volume of water that a cuboid can contain inside depends on the number of edges that are present between its four trapezoidal extremities.
Here,
A 4-cm by 8-cm rectangle has an area
=> 4⋅8=32
square centimetres when its length and breadth are multiplied. Starting with a row of four tiny squares,
we can then layer another row of four tiny squares on top of it. We now have a total of 8 tiny squares, which together measure 4 by 2 centimetres.
Then, after the first two rows, add a third row of four little squares to complete the procedure.
We now have a total of 12 little squares, which together make a rectangle measuring 4 centimetre by 3 cm.
Up until we have 32 small squares in total, which make up the complete 4-cm by 8-cm rectangle, we can keep adding rows of four-square units.
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Which correctly reWhich correctly represents the statement, “the product of 4 and a number, n, subtracted from 10”? Responsespresents the statement, “the product of 4 and a number, n, subtracted from 10”? Responses
The expression that correctly represents the statement "the product of 4 and a number, n, subtracted from 10" is 10 - 4n.
What is statement ?In general, a statement is a declarative sentence that is either true or false. It is a sentence that makes a claim or assertion about something, and it can be either a simple statement or a complex one.
According to given information:The statement "the product of 4 and a number, n, subtracted from 10" is an example of a mathematical expression that involves a variable, which is represented by the letter "n". In this expression, we are asked to find the difference between the number 10 and the product of 4 and the variable "n".
To simplify this expression, we can use the order of operations, which tells us to perform the multiplication before subtraction. Therefore, we first multiply 4 and n to get the product of 4n. Then, we subtract that product from 10 to get the final expression:
[tex]$10 - 4n$[/tex]
This expression represents the result of subtracting the product of 4 and the variable "n" from the number 10. We can evaluate this expression for different values of "n" to find the corresponding result. For example, if we substitute "n" with 2, we get:
[tex]$10 - 4(2) = 10 - 8 = 2$[/tex]
This means that when "n" is equal to 2, the result of subtracting the product of 4 and "n" from 10 is equal to 2. Similarly, we can substitute different values of "n" into the expression to find their corresponding results.
Therefore, The expression that correctly represents the statement "the product of 4 and a number, n, subtracted from 10" is 10 - 4n.
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URGENT !!!
Write the multiplication sentence modelled by each diagram.
NEED STEP BY STEP ON HOW TO GET (30pnts) (only need a)
Answer:
Step-by-step explanation:
Post a link to the paper then i will edit it and send it back and then give you the answers on the paper you share with me
5 melons cost £3.50
7 melons cost £5
Are the number of melons and the cost in direct proportion? Explain how you know.
.m
(2 marks)
****
yes, it is direct proportion becuz in direct proportion if the prize of one quantity increases the other too will have to increase. here in this question as you can see 5melons were costing 3.50 and on increasing it to 7 melons cost is too increasing soo it is a direct proportion.
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Find the Rank of matrix by reducing to nomal form. A=[[2,3,-1,-1],[1,-1,-2,-4],[3,1,3,-2],[6,3,0,-7]]
4
The rank of a matrix can be determined by converting it to its reduced row echelon form. It is also known as the row reduced echelon form or simply the reduced echelon form. The rank of a matrix is the number of non-zero rows in its reduced row echelon form. The given matrix is,
`A=[[2,3,-1,-1],[1,-1,-2,-4],[3,1,3,-2],[6,3,0,-7]]`
We need to convert the given matrix to its reduced row echelon form. It is done by applying elementary row operations on the matrix. The elementary row operations are as follows:
- Interchange the order of two rows.
- Multiply a row by a non-zero scalar.
- Add a multiple of one row to another row.
Let us apply these operations on the given matrix,
`[[2,3,-1,-1],[1,-1,-2,-4],[3,1,3,-2],[6,3,0,-7]]`
`= [R1, R2, R3, R4]`
`R1 → R1 - R2/2` (subtract half of R2 from R1)
`R2 → R2 - R1/2` (subtract half of R1 from R2)
`R3 → R3 - 3R1/2` (subtract three times half of R1 from R3)
`[[1,5/2,1/2,1/2],[0,-3/2,-5/2,-9/2],[0,-7/2,3/2,-7/2],[0,0,-3,-6]]`
`= [R1, R2, R3, R4]`
`R2 → -R2/3` (multiply R2 by -1/3 to make its first entry as 1)
`R3 → R3 - 7R2/3` (subtract 7 times -1/3 of R2 from R3)
`R4 → -R4/3` (multiply R4 by -1/3 to make its first entry as 1)
`[[1,5/2,1/2,1/2],[0,1,5/3,3/2],[0,0,-4/3,-4],[0,0,1,2]]`
`= [R1, R2, R3, R4]`
`R3 → -3R3/4` (multiply R3 by -3/4 to make its third entry as 1)
`[[1,5/2,1/2,1/2],[0,1,5/3,3/2],[0,0,1,1],[0,0,1,2]]`
`= [R1, R2, R3, R4]`
`R4 → R4 - R3` (subtract R3 from R4 to make its third entry as 0)
`[[1,5/2,1/2,1/2],[0,1,5/3,3/2],[0,0,1,1],[0,0,0,1]]`
`= [R1, R2, R3, R4]`
The given matrix is converted to its reduced row echelon form. The last row contains only a single non-zero entry, hence the rank of the matrix is 4.
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why does the decimal point always have to move when you rewrite a percent as a decimal and when you rewrite a decimal as a percent?
Answer:
When you rewrite a percent as a decimal, you need to move the decimal point two places to the left because a percent is a ratio that compares a number to 100. For example, 50% is the same as 50/100 or 0.5. To convert 50% to a decimal, you need to divide 50 by 100, which gives you 0.5. Moving the decimal point two places to the left achieves the same result.
Similarly, when you rewrite a decimal as a percent, you need to move the decimal point two places to the right because a percent expresses a number as a fraction of 100. For example, 0.75 is the same as 75/100 or 75%. To convert 0.75 to a percent, you need to multiply it by 100, which gives you 75. Moving the decimal point two places to the right achieves the same result.
Step-by-step explanation:
derek is experimenting with sizes of his square logo. he wants to increase his logo by 2 inches on one side and decrease it by 4 inches on the other side, to create a new, rectangular logo. derek writes the equation: A(x) =(x+2)(x-4). which expression represents the total area of derek’s logo, A(x), in vertex form
The quadratic equation written in vertex form is:
A(x) = x^2 - 4
How to write the equation in vertex form?Here we want to find the vertex form of the quadratic equation:
A(x) = (x + 2)*(x - 2)
Remember that for a quadratic equation with the vertex (h, k) and leading coefficient a is written as:
f(x) = a*(x - h)^2 + k
Now, notice that the zeros of the quadratic function are x = -2 and x = 2.
Then the vertex is just between these two, at x = 0.
Then h = 0, and the y-value of the vertex is what we get when we evaluate in x = 0.
k = (0 + 2)*(0 - 2) = 2*-2 = -4
Then the vertex is (0, -4) and the leading coefficient is 1, we can write the quadratic equation as:
A(x) = (x - 0)^2 -4
A(x) = x^2 - 4
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One angle of a triangle measures 10°. The other two angles are in a ratio of 3:14. What are the measures of those two angle
Answer: Let's denote the two unknown angles as x and y.
We know that the sum of the three angles in a triangle is 180 degrees. So we can set up the following equation:
10 + 3x + 14x = 180
Simplifying the equation:
17x = 170
x = 10
Now we can use the ratio of the other two angles to find the value of y:
3:14 can be simplified as 3x:14x or x:4.67x
So y is 4.67 times larger than x:
y = 4.67x = 4.67(10) = 46.7
Therefore, the measures of the two unknown angles are x = 10 degrees and y = 46.7 degrees.
Step-by-step explanation:
The measure of the remaining two angles are 46.7
What is the angle sum property of a triangle?The angle sum property of a triangle states that the sum of interior angles of a triangle is 180°
Given here, One angle of a triangle measures 100°. the other two angles are in a ratio of 3:14. Then let the measure of the angles be 3x and 14x
thus using the angle sum property we have
[tex]3x+14x=80[/tex]
[tex]17x= 80[/tex]
[tex]x = 46.7[/tex]
Hence, The measure of the remaining two angles are 46.7
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