Look at the tally chart or line plot from Exercise 2 above. What was the total distance ridden by all of the children?

The elimination method is ideal for solving this system of equations. By which number must you multiply the second equation to e

shutvik [7]

Given:

The system of equations is

$x+3y=42$ ...(i)

$2x-y=14$ ...(ii)

To find:

The number that must be multiplied with the second equation to eliminate the y-variable.

Solution:

Coefficient of y variable in equation (i) is 3 and in equation (ii) is -1.

To eliminate y-variable the absolute value of coefficients of y-variables should be same.

So, we need to multiply the second equation by 3 to eliminate the y-variable

Multiplying equation (ii) by 3, we get

$6x-3y=42$ ...(iii)

Adding (i) and (iii), we get

$x+3y+6x-3y=42+42$

$7x=84$

Divide both sides by 7.

$x=12$

Put x=12 in (i).

$12+3y=42$

$3y=42-12$

$3y=30$

Divide both sides by 10.

$y=10$

Therefore, x=12 and y=10.

7 0

3 years ago

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Please help soon!

Jlenok [28]

Answer:

a) Translate the graph of f(x) down 3 units.

b) (8,-1) is a point on the graph of g(x)

Step-by-step explanation:

The transformations that subtract a constant number of units from the functional expression f(x) are transformations that lower the graph of the function in those many units,

Therefore they correspond to a translation of the original graph down the number of units involved.

In this case, the number of units involved is "3" (due to the "-3" added to the expression for f(x). So he correct answer for the first part is: Translate the graph of f(x) down 3 units.

For the second part, one has to try each of the coordinate pairs given in the new function g(x) to see which one results in a true statement:

1) Testing (-8,-1) by checking if replacing x with the value "-8" renders "-1" for the y-value: $g(x)=\sqrt[3]{x} -3\\g(-8)=\sqrt[3]{-8} -3\\g(-8)=-2-3\\g(-8)=-5$

so this is NOT a point on the graph of g(x).

2) Testing (-1,-2) by checking if replacing x with the value "-1" renders "-2" for the y-value: $g(x)=\sqrt[3]{x} -3\\g(-1)=\sqrt[3]{-1} -3\\g(-1)=-1-3\\g(-1)=-4$

so this is NOT a point on the graph of g(x).

3) Testing (2,-1) by checking if replacing x with the value "2" renders "-1" for the y-value: $g(x)=\sqrt[3]{x} -3\\g(2)=\sqrt[3]{2} -3\\$

the cubic root of 2 is not a rational number, because 2 is not a perfect cube, so the expression cannot be reduced, so this is NOT a point on the graph of g(x).

4) Testing (8,-1) by checking if replacing x with the value "8" renders "-1" for the y-value: $g(x)=\sqrt[3]{x} -3\\g(8)=\sqrt[3]{8} -3\\g(8)=2-3\\g(8)=-1$