Circle the two equations that represent the linear function graphed below.

Each week, Stephanie is paid a $180 base salary and a 3% commission on her total sales generated for the week. Which expression

prisoha [69]

The expression that represents her weekly income is:
180 + 0.03w

8 0

2 years ago

Chris plans to mulch the Border surrounding a rectangular Garden in his backyard if the length of L of the garden (exculding its

Naya [18.7K]

The answer by the sequence:

Width of the garden = w
Length of the garden = 2w+3

Width of the entire plot = w + 0.5w = 1.5w
Length of the entire plot = (2w + 3) 0.5w = 2.5w + 3

Area of the garden = w (2w + 3)
Area of the entire plot = 1.5w (2.5w + 3)

Area of the garden = 2w² + 3w
Area of the entire plot = 3.75w² + 4.5w

Area of border = area of the entire plot - area of the garden
= 3.75w² + 4.5w - (2w² + 3w)

Area of the border = 3.75w² + 4.5w - 2w² - 3w

Area of the border = 1.75w² + 1.5w

3 0

3 years ago

Explain proportionality to me 7th grade math

kari74 [83]

If two quantities a and b are directly proportional to one another, then both a and b change in the same direction.

For example, if the amount/volume of coffee I have in a cup is directly proportional to the total volume of the cup, then the larger the cup gets, the more coffee I can fill it with. On the other hand, if the cup gets smaller, the amount of coffee it can hold also gets smaller.

Both a and b don't necessarily change at the same rate, though, which means one of these needs to get appropriately scaled by some factor k, so that

a = kb

Continuing the coffee example: Suppose I only fill my cup halfway. If the total volume of the cup is a, then the amount of coffee I pour in is b = 1/2 a. So the relationship of these two quantities is governed by the equation,

a = 2b

and in this case, k = 2.

If instead a and b are inversely proportional, this means as one quantity changes, the other changes in the opposite direction.

Suppose I have two cups that I use for coffee that can both hold the same amount k if they are filled completely, but one cup is taller than the other. In order for both cups to be able to hold the same volume of coffee, the taller cup must have a thinner profile.

The cups are cylindrical, so that their volumes are equal to the products of the area of their base a and their height b. If one cup is twice as tall as the other, then for the smaller cup we could have

ab = k

and for the taller one,

a (2b) = k

But in order to get the same volume, the quantity a for the shorter cup must be cut in half to preserve equality:

(1/2 a) (2b) = ab = k

So one quantity is doubled (increases), while the other gets halved (decreases).

5 0

3 years ago

Evaluate f(x)3x + 8 for x = 1. A. -11 B. 5 C. 11 D. 3

mariarad [96]

Answer:11

Step-by-step explanation:

f(x)=3x+8

f(1)=3(1)+8

f(1)=3+8

f(1)=11

5 0

3 years ago

f(x) = 0.2^x is transformed 9 units right, compressed vertically by a factor of 1/6 and reflected across the x-axis. Write the t

postnew [5]

Answer:

The function g(x) is defined as $g(x)=-\frac{1}{6}(0.2)^{x-9}$ .

Step-by-step explanation:

The given function is

$f(x)=-(0.2)^x$

The function f(x) transformed 9 units right, compressed vertically by factor of 1/6 and reflected across the x-axis.

The transformation of function is defined as

$g(x)=kf(x+b)+c$

Where, k is vertical stretch, b is horizontal shift and c is vertical shift.

If b>0, then the graph of f(x) shifts b units left and if b>0, then the graph of f(x) shifts b units right.

If c>0, then the graph of f(x) shifts c units upward and if c>0, then the graph of f(x) shifts c units downward.

The value of b is -9 because the graph shifts 9 units right. The value of k is 1/6. If the graph of function f(x)reflect across x-axis, therefore the function is defined as -f(x).

$g(x)=\frac{1}{6}(-f(x-9))$

$g(x)=-\frac{1}{6}(0.2)^{x-9}$ $[\because f(x)=-(0.2)^x]$

Therefore the function g(x) is defined as $g(x)=-\frac{1}{6}(0.2)^{x-9}$ .

7 0

3 years ago

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