Which is the graph of y = 5x + 5?

Annabelle read 10 books in 2 months. What was her rate of reading, in books per month?

goblinko [34]

Answer:

5 books per month

Step-by-step explanation:

We are trying to find a rate.

To find books per month, we would take the number of books and divide it by the number of months.

This would give us 10 books/2 months.

10/2 simplifies to 5.

Therefore the answer would be 5 books per month.

8 0

2 years ago

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What expression can be used for estimating 868 divided by 28

vovangra [49]

Round 28 to nearest ten and 868 to nearest hundred
900 ÷ 30 = 30

7 0

3 years ago

Need your help now please; the assignment is due tonight and this is the last problem I am having trouble with. The red box is t

Kobotan [32]

The volume of the region R bounded by the x-axis is: $\mathbf{\iint_R(x^2+y^2)dA = \int ^{tan^{-1}(4)}_{0} \int^{\frac{2}{cos \theta}}_{0} \ r^3 dr d\theta}$

<h3>What is the volume of the solid (R) on the X-axis?</h3>

If the axis of revolution is the boundary of the plane region and the cross-sections are parallel to the line of revolution, we may use the polar coordinate approach to calculate the volume of the solid.

From the given graph:

The given straight line passes through two points (0,0) and (2,8). Thus, the equation of the straight line becomes:

$\mathbf{y-y_1 = \dfrac{y_2-y_1}{x_2-x_1}(x-x_1)}$

here:

(x₁, y₁) and (x₂, y₂) are two points on the straight line

Suppose we assign (x₁, y₁) = (0, 0) and (x₂, y₂) = (2, 8) from the graph, we have:

$\mathbf{y-0 = \dfrac{8-0}{2-0}(x-0)}$

y = 4x

Now, our region bounded by the three lines are:

y = 0
x = 2
y = 4x

Similarly, the change in polar coordinates is:

x = rcosθ,
y = rsinθ

where;

x² + y² = r² and dA = rdrdθ

Therefore;

rsinθ = 0 i.e. r = 0 or θ = 0
rcosθ = 2 i.e. r = 2/cosθ
rsinθ = 4(rcosθ) ⇒ tan θ = 4; θ = tan⁻¹ (4)

⇒ r = 0 to r = 2/cosθ
θ = 0 to θ = tan⁻¹ (4)

Then:

$\mathbf{\iint_R(x^2+y^2)dA = \int ^{tan^{-1}(4)}_{0} \int^{\frac{2}{cos \theta}}_{0} \ r^2 (rdr d\theta )}$

$\mathbf{\iint_R(x^2+y^2)dA = \int ^{tan^{-1}(4)}_{0} \int^{\frac{2}{cos \theta}}_{0} \ r^3 dr d\theta}$

Learn more about the determining the volume of solids bounded by region R here:

brainly.com/question/14393123

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3 0

1 year ago

The cost of 4 pounds of bananas is $1.88. What is the constant of proportionality that relates the cost in dollars, y, to the nu

aniked [119]

Answer:

47 cent per banana

5 0

3 years ago

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Two piecewise functions are shown below. What is the value of

gizmo_the_mogwai [7]

Step-by-step explanation:

I am not sure what your problem here is.

you understand the inequality signs ?

anyway, to get

6×f(-2) + 3×g(1)

we can calculate every part of the expression separately, and then combine all the results into one final result.

f(-2)

we look at the definition.

into what category is -2 falling ? the one with x<-2, or the one with x>=-2 ?

is -2 < -2 ? no.

is -2 >= -2 ? yes, because -2 = -2. therefore, it is also >= -2.

so, we have to use

1/3 x³

for x = -2 that is

1/3 × (-2)³ = 1/3 × -8 = -8/3

g(1)

again, we look at the definition.

into what category is 1 falling ? the one with x > 2 ? or the one with x <= 1 ?

is 1 > 2 ? no.

is 1 <= 1 ? yes, because 1=1. therefore it is also <= 1.

so we have to use

2×|x - 1| + 3

for x = 1 we get

2×0 + 3 = 3

6×f(-2) = 6 × -8/3 = 2× -8 = -16

3×g(1) = 3× 3 = 9

and so in total we get

6×f(-2) + 3×g(1) = -16 + 9 = -7

3 0

2 years ago