All categories

2 months ago

The graph shows the relationship between pounds of grapes, g, and their cost, c.

Mathematics

2 answers:

Inessa [12.5K]2 months ago

5 0

Spending one dollar allows you to buy half a pound of grapes.
To purchase one pound of grapes, you need to pay two dollars.

I hope this clarifies things! If so, please show some appreciation. Have a wonderful day!

AnnZ [12.3K]2 months ago

3 0

Step 1

Define variables:

x – cost in dollars

y – weight of grapes in pounds

$A(0,0)\ B(2,1)$

We know that the relationship between x and y represents direct variation if it follows the form $y/x=k$ or $y=kx$ .

The line illustrated in the graph represents such a direct variation.

Determine the proportionality constant k.

$y/x=k$ – substitute coordinates of point B –> $1/2=k$

The slope corresponds to the constant of proportionality.

Therefore,

$m=0.50\ \frac{pounds}{\$}$

The linear equation is $g=0.50c$ .

Hence,

Answer to part (a):

You can obtain $0.50$ pounds of grapes per dollar spent.

Step 2

Calculate the cost per pound of grapes.

Let

$g=1\ pound$

Insert the value of g into the equation and solve for c.

$g=0.50c$

$1=0.50c$

$c=1/0.50=2\$$

Therefore,

Answer to part (b):

The price is $2\$$ for each pound of grapes.

You might be interested in

2 box plots. The number line goes from 175 to 450. For resort A, the whiskers range from 175 to 375, and the box ranges from 250

lawyer [12517]

Answer: 275 for one, and 325 for two

Step-by-step explanation:

I completed the calculations

3 0

1 month ago

Read 2 more answers

What is Question I (if m<EBF = 117°, fine m<ABE)

tester [12383]

Answer:

m∠ABE = 27°

Step-by-step explanation:

* To analyze the figure to address the query

- AC represents a line

- Ray BF crosses line AC at point B

- Ray BF is perpendicular to line AC

Thus, both ∠ABF and ∠CBF are classified as right angles

Which gives us ∠ABF = ∠CBF = 90°

- Rays BE and BD meet line AC at point B

Since m∠ABE is equal to m∠DBE, as indicated by the same symbol in the figure

It implies that BE acts as the angle bisector of angle ABD

Given that m∠EBF = 117°

Then m∠EBF = m∠ABE + m∠ABF

Where m∠ABF = 90°

So, 117° = m∠ABE + 90°

- By subtracting 90 from both sides

It follows that m∠ABE = 27°

4 0

2 months ago

Read 2 more answers

In right triangle qrs, angle r is a right angle. The altitude rt is drawn to hypotenuse qs. If qr is 20 and qs is 25 then find t

lawyer [12517]

Answer:

qt's length = 16

Step-by-step explanation:

The problem states that qrs is a right triangle,

where qr = 20

sr =?

qs = 25

qt =?

1)

Calculate sr

hypotenuse² = base² + height²

sq² = sr² + rq²

25² - 20² = sr²

sr = √(25² - 20²)

sr = 15

When altitude rt is dropped to hypotenuse qs, it creates

two right triangles: rtq and rts.

Δrtq

height = rt

base= tq = 25 - x

hypotenuse = qt = 20

Δrts

height = rt

base= ts = x

hypotenuse = sr = 15

Both triangles share the same height, which is rt

Using the Pythagorean theorem:

Δ rtq Δ rts

hypotenuse² - base² = height²

20² - (25 - x)² = 15² - x²

400 - (625 + x² - 50x) = 225 - x²

400 - 625 - x² + 50x = 225 - x²

-225 - x² + 50x - 225 + x² = 0

-450 + 50 x = 0

50x = 450

x = 450/50

x = 9

Base of Δ rtq = tq = 25 - x

tq = 25 - 9

tq = 16

5 0

2 months ago

Read 2 more answers

In ΔHIJ, the measure of ∠J=90°, JI = 4, HJ = 3, and IH = 5. What ratio represents the tangent of ∠I?

Inessa [12570]

Answer:

The ratio $\frac{3}{4}$ corresponds to the tangent of ∠I.

Step-by-step explanation:

Let’s revisit the trigonometric ratios:

sin Ф = $\frac{opposite}{hypotenuse}$
cos Ф = $\frac{adjacent}{hypotenuse}$
tan Ф = $\frac{opposite}{adjacent}$

For triangle HIJ

∵ m∠J = 90°

- The hypotenuse is the side opposite the right angle.

So, HI is the hypotenuse.

∵ HJ = 3 units

∵ IH = 5 units

- We’ll apply the Pythagorean Theorem to solve for HJ.

∵ (HJ)² + (IJ)² = (IH)²

∴ 3² + (IJ)² = 5²

∴ 9 + (IJ)² = 25

- Subtract 9 from both sides.

∴ (IJ)² = 16

- Taking the square root on both sides gives:

∴ IJ = 4 units

To determine the tangent of ∠I, identify the sides that are opposite and adjacent to it.

∵ HJ is opposite to ∠I

∵ IJ is adjacent to ∠I

- Utilizing the rule of tan above:

∴ tan(∠I) = $\frac{HJ}{IJ}$

∴ tan(∠I) = $\frac{3}{4}$

The ratio $\frac{3}{4}$ indicates the tangent of ∠I.

7 0

2 months ago

The value of a car t years after it is purchased is given by the decreasing function V, where V(t) is measured in dollars. The r

PIT_PIT [12445]

Answer:

dV(t)/dt = kV(t)

Step-by-step explanation:

The annual change in the car's value, represented by dV(t)/dt, has a proportional relationship with V(t), the car's current value.

dV(t)/dt ∝ V(t)

dV(t)/dt = kV(t)

7 0

2 months ago