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[tex](i)\\\\2A = \begin{pmatrix}3x \times 2 & 1 \times 2 & 5 \times 2\\0\times 2 & 2x \times 2 & -3 \times 2\end{pmatrix} = \begin{pmatrix}6x & 2 & 10\\0 & 4x & -6\end{pmatrix}\\\\\\(ii)\\\\2A + B = C\\\\\implies \begin{pmatrix}6x & 2 & 10\\0 & 4x & -6\end{pmatrix} + \begin{pmatrix}y & 0 & -4\\1 & -3y & 2\end{pmatrix} = \begin{pmatrix}31& 2 & 6\\1 & 17& -4\end{pmatrix}[/tex]

[tex]\implies \begin{pmatrix}6x+y & 2+0 & 10-4\\0+1 & 4x-3y & -6+2\end{pmatrix} = \begin{pmatrix}31 & 2 & 6\\1 & 17& -4 \end{pmatrix}\\\\\\\implies \begin{pmatrix}6x+y & 2 & 6\\1 & 4x-3y & -4\end{pmatrix} = \begin{pmatrix}31 & 2 & 6\\1 & 17& -4 \end{pmatrix}\\\\\text{System of equations},\\\\6x +y =31,~~ 4x -3y = 17\\\\\\(iii)\\\\6x +y-31 =0 \\\\4x-3y -17=0\\\\\text{Solving by cross multiplication method}\\\\\\\dfrac x{1(-17) - (-31)(-3)} = \dfrac y{4(-31) - 6(-17)} = \dfrac 1{6(-3) - 4(1)}[/tex]

[tex]\implies \dfrac{x}{-17 -93} = \dfrac{y}{-124 +102} = \dfrac 1{-18-4}\\\\\\\implies -\dfrac{x}{110} = -\dfrac{y}{22} = -\dfrac 1{22}\\\\ \implies \dfrac{x}{110} = \dfrac{y}{22} = \dfrac 1{22}\\\ \\\text{Hence,}\\\\\\x=\dfrac{110}{22}=5,~~~~ y= \dfrac{22}{22} =1[/tex]

Answer:

  (i)

  [tex]2A=\left[\begin{array}{ccc}6x&2&10\\0&4x&-6\end{array}\right][/tex]

  (ii) 6x+y=31; 4x-3y=17

  (iii) (x, y) = (5, 1)

Step-by-step explanation:

The matrix 2A is written by multiplying each element of A by 2.

  [tex]2A=\left[\begin{array}{ccc}6x&2&10\\0&4x&-6\end{array}\right][/tex]

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Variables are seen in elements (1, 1) and (2, 2) of the matrices A and B, so the simultaneous equations can be chosen from those elements of the equation 2A+B=C.

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A graphing calculator shows the solution to be (x, y) = (5, 1).

Answer: a. [tex]f(x)=3^{x}[/tex]

Step-by-step explanation:

You can plug in the x and y values to get [tex]f(x)=3^{x}[/tex]

The dimensions of the dilated image is 125 millimeters by 300 millimeters.

An image is dilated if the dimensions of the image is resized in a way that does not change the shape of the image. When an image is dilated, it is made larger.

The scale factor is 2.5. This means that the dimensions are 2.5 larger. Dimensions of the dilated image : 50 x 2.5 and 120 x 2.5 = 125 mm by 300 mm

To learn more about dilation, please check: https://brainly.com/question/3457976

Answer:

135°

Step-by-step explanation:

seg AB=seg OB

tan ∠AOB = 1

∠AOB = 45°

∠AOC = 135°

Answer:

Lateral : 103.67 in²

Total : 864 in²

Step-by-step explanation: there you go

Answer:16

Step-by-step explanation:

144^0.5 = 12

400^0.5 = 20

a^2=b^2+c^2

20^2 = 12^2 +x^2

x^2 = 400-144= 256

x =16

Answer:

16

Step-by-step explanation:

Answer:

The slope is -2

Step-by-step explanation:

y+6=24-2x

Subtract 6 from each side

y+6-6=24-6-2x

y = 18 -2x

Rewriting

y = -2x+18

This is in slope intercept form

y = mx+b  where m is the slope and b is the y intercept

The slope is -2 and the y intercept is 18

Answer:

1/3 ^ 1/3 * 1/3 = (1/3)^3 = 1/27

Answer:

67-63x

Step-by-step explanation:

Answer:

2.45 days.

Step-by-step explanation:

35% of 7 days is 2.45 days :) please thank.

This should be 20.

50% of 20 is 10. If you subtracted 15% from 10, you would get 3 which then makes it 7. Therefore, 35% of 20 days is 7 days.

The answer is 2 workers coz there can't be 2.08333... workers

The equation of a line so that it is perpendicular to a given point will be

y-y0=[tex]\frac{-1}{m}[/tex] (x - xo)

The equation of a line so that it is perpendicular to a given point will be

y-y0=m (x - xo)

The standard equation of the line is better written in point-slope form expressed as:

y-y0=m(x - xo)

where: m is the slope of the given line (x0, y0) is any point of the giuven line.

m is the slope of the given line

(x0, y0) is any point on the given line

If the given slope of the  line is m, the slope of the line perpendicular will be expressed as -1/m

The equation of a line so that it is perpendicular to a given point will be

y-y0=[tex]\frac{-1}{m}[/tex] (x - xo)

Answer:

29+8x

Step-by-step explanation:

5+8(3+x)

Expand 8(3+x)

= 5+24+8x (add the numbers)

= 29+8x

Answer:

49

Step-by-step explanation:

make an equation:

5/7x=35

x=35*7/5

x=7*7

x=49

x is the total amount

Answer:

(1,1)

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

1.5 c flour = 12 cupcake

0.75 c flour = 6 cupcake

1.5 + 1.5 + 0.75 = 3.75 c flour

Answer:

12.55

Step-by-step explanation:

Answer:

1.6 hrs remaining, or 3.12 km/h

Step-by-step explanation:

Answer:

33% of the marbles were red

Answer:

 70 * 0.895 = 62.65

OR

1   0.895

 70 x

-Cross-multiply

[tex]\frac{70 * 0.895}{1}[/tex] = 62.65

The interval which is horizontal and has a slope of zero shows no distance was covered while time kept increasing, therefore, the interval that shows Kendra stopping to tie her shoes and stretch is: C.

Recall:

Given the graph showing Kendra's morning run, where time running is plotted on the horizontal axis (x-axis) while distance run is plotted on the vertical axis (y-axis).

Learn more about horizontal graphs on:

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Answer:

3. x=14° y=7

4. x=29° y=3

Step-by-step explanation:

3. this is a 45 - 45- 90 triangle

so the side is a-a-a√2 ( two sides are the same)

4y-3=10+2y+1 -- collect like terms

4y-2y=10+1+3

2y=14

y=7

find the angle of the inside triangle

180-59-90 =

31°

we know the big triangle was a 45-45-90 angle

so x+31=45

x=45-31

x=14°

4. this is a square, all sides are same

5y+3y=24

8y=24

y=3

angle is 90°

x+x+9y+5=90

we know y=3 --substitute

x+x+9(3)+5=90

2x+27+5=90

2x=90-27-5

2x=58

x=58/2

x=29

Answer:

D. 4+2 = 2+4

Step-by-step explanation:

Commutative property of addition states that the answer does not change when you change the order of the equation.

Example:

a+b = b+a

Hope this helps! Have a great day!

Answer: 4+2=2+4

Step-by-step explanation:

Commutative property of addition states that the answer does not change when you change the order of the equation.

Example:

a+b = b+a

100% correct

The grocery store's sales from selling cereal if the grocery store buys 100 boxes and sells all of them are $247

From the given function, we can see that the equivalent function for a number of 100 boxes is given as;

c(n) = 1.9n

If n = 100

c(100) = 1.9(100)

c(100) = 190

Hence the cost of 100 boxes will be $190

Given the sales function s(c) = 1. 3c, the grocery store's sales from selling cereal if the grocery store buys 100 boxes will be expressed as:

[tex]s(c) = 1. 3c\\s(190)=1.3(190)\\s(190)=$247[/tex]

Hence the grocery store's sales from selling cereal if the grocery store buys 100 boxes and sells all of them are $247

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Answer:

a driver costs $19, while a putter costs $12

Step-by-step explanation:

driver = d

putter = p

1d + 2p = 43

3d + 1p = 69

d + 2p = 43. eq 1

3d + p = 69. eq 2

make d the subject of the equation

d = 43 - 2p. eq 3

substitute the value of d in eq 3 in eq 2

3(43 - 2p) + p = 69

129 - 6p + p = 69

collect like terms

129 - 69 = 6p - p

60 = 5p

p = 12

substitute the value of p in eq 3

d = 43 - 2(12)

d = 43 - 24

d = 19

The correlation coefficients off both the scatter plots are mentioned above.

        [tex]${\displaystyle {\begin{aligned}r_{xy}&={\frac {\sum x_{i}y_{i}-n{\bar {x}}{\bar {y}}}{ns'_{x}s'_{y}}}\\[5pt]&={\frac {n\sum x_{i}y_{i}-\sum x_{i}\sum y_{i}}{{\sqrt {n\sum x_{i}^{2}-(\sum x_{i})^{2}}}~{\sqrt {n\sum y_{i}^{2}-(\sum y_{i})^{2}}}}}.\end{aligned}}}[/tex]

       where [tex]{\displaystyle s'_{x}}[/tex] and [tex]{\displaystyle s'_{y}}[/tex] are the uncorrected sample standard deviations of        

       X and Y.

Given are the scatter plot graphs as shown.

For the graph {1}, the correlation coefficient is positive and is in range of between 0.7 to 0.8

For the graph {2}, the correlation coefficient is negative and is in range of between -0.4 to 0.45

Therefore, the correlation coefficients off both the scatter plots are mentioned above.

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