Find the solutions to 9x2

The table shows the ratio between the number of books ordered and their cost: Find equivalent ratios when the number of books or

Nana76 [90]

Answer:

The answer is below

Step-by-step explanation:

The table shows the ratio between the number of books ordered and their cost: Number of Books Cost (dollars) 7 21 8 24 9 27 Find equivalent ratios when the number of books ordered is 1, 2, and 3. Write them as ordered pairs in the form (x-coordinate, y-coordinate). Starting from the origin, explain how to plot the three equivalent ratios on a coordinate grid.

Answer: Let the number of books be represented as x and the cost (dollars) be represented as y. From the table the ordered pairs in the form (x, y) can be gotten. (7, 21), (8, 24), (9, 27). To get the relationship between the number of books and the cost, we can use the formula of a straight line.

Using point (7, 21) and (8, 24):

$y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-21=\frac{24-21}{8-7}(x-7)\\ \\y-21=3(x-7)\\\\y=3x-21+21\\\\y=3x$

When the number of books ordered is 1, 2, 3 the following pairs are:

For x = 1. y = 3x = 3(1) = 3

For x = 2 y=3x = 3(2) = 6

For x = 3 y = 3x = 3(3) = 9

The ordered pairs are (1, 3), (2, 6), (3, 9)

The graph is attached

To plot the ordered pairs, the number of books are plotted on the x coordinate and the cost on the y coordinate

8 0

4 years ago

Determine the transformation given the preimage ΔABC where A(1, 0), B(6,−7), and C(0,−4) and the image of ΔA′B′C′ where A′(0,−1)

Kazeer [188]

Answer:

rotation of 270°

Step-by-step explanation:

Consider the coordinates of of preimage and image of ABC

A(1, 0 ) → A'*0, - 1 )

B(6, - 7 ) → B'(- 7, - 6 )

C(0, - 4 ) C'(- 4, 0 )

What we note is the x- coordinate of the image is the y- coordinate of the preimage and the y- coordinate of the image is the negative of the x- coordinate of the preimage, that is

(x, y ) → (y, - x )

This is equivalent to a counterclockwise rotation about the origin of 270°

7 0

3 years ago

Hugh uses 0.63 of a piece of canvas to paint a picture.Draw a model to represent this decimal.How much of the canvas is left?

prohojiy [21]

.63 is a decimal. It represents part of something whole. I am not sure what you mean by model, but if .63 of the canvas is used, then 1-.63 is not used. 1 represents the full canvas.

1 - .63, or 1 minus .63 is equal to .37.
.37 of the canvas is left.

3 0

3 years ago

Read 2 more answers

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

#SPJ1

3 0

2 years ago

Help me out with this question please!

Mandarinka [93]

Answer:

1) Length of BC + Length of DE = 17 cm

2) The perimeter of the shape ABCDEF is 58 cm

Step-by-step explanation:

1) The given parameters are;

The length of the rectangular sheet of paper = 17 cm

The width of the rectangular sheet of paper = 12 cm

Therefore, we have;

The length of the side of the cut out square piece = DE = CD

By the definition of a square, the length of all sides of the square are equal

The length of BC + The length of one side of the square = The length of the rectangular paper = 17 cm

The length of BC + The length of one side of the square DE (or CD) = 17 cm

2) The perimeter, 'P', of the shape ABCDEF is given as follows;

P = Length of AB + Length of BC + Length of CD + Length of DE + Length of EF + Length of FA

Therefore, we have;

P = Length of AB + Length of BC + Length of DE + Length of CD + Length of EF + Length of FA

Length of BC + Length of DE = 17 cm

Similarly, we have;

Length of CD + Length of EF = 12 cm

∴ P = Length of AB + 17 cm + 12 cm + Length of FA

P = 12 cm + 17 cm + 12 cm + 17 cm = 58 cm

The perimeter of the shape ABCDEF = P = 58 cm.

6 0

3 years ago

Find the solutions to 9x2 - 63x = 0.