Do -24 and -24 cancel each other out

Which of the following is a solution to this inequality? y greater than three fifths times x minus 2 (5, 0) (0, −2) (1, 1) (−5,

storchak [24]

Answer:

(1,1)

Step-by-step explanation:

we have

$y > \frac{3}{5}x-2$

we know that

If a ordered pair is a solution of the inequality, then the ordered pair must satisfy the inequality

<u><em>Verify each ordered pair</em></u>

case A) we have

(5,0)

Substitute the value of x and y in the inequality

$0 > \frac{3}{5}(5)-2$

$0 > 1$ ----> is not true

therefore

The ordered pair is not solution to the inequality

case B) we have

(0,-2)

Substitute the value of x and y in the inequality

$-2 > \frac{3}{5}(0)-2$

$-2 > -2$ ----> is not true

therefore

The ordered pair is not solution to the inequality

case C) we have

(1,1)

Substitute the value of x and y in the inequality

$1 > \frac{3}{5}(1)-2$

$1 > -\frac{7}{5}$ ----> is true

therefore

The ordered pair is a solution to the inequality

case D) we have

(-5,-6)

Substitute the value of x and y in the inequality

$-6 > \frac{3}{5}(-5)-2$

$-6 > -5$ ----> is not true

therefore

The ordered pair is not solution to the inequality

7 0

3 years ago

Read 2 more answers

Use angle relationships to complete the top equation. Then, solve for x and find the measure of both angles.

VashaNatasha [74]

7x + 5 = 180
x = 25
6x = 150
x + 5 = 30

7 0

3 years ago

Which equation does this image represent?

nirvana33 [79]

Given:

Image of the ellipse

To find:

The equation of the image

Solution:

The given image is a ellipse.

Center of the ellipse = (0, 0)

x-axis points are (-3, 0) and (3, 0).

y-axis points are (2, 0) and (-2, 0).

Standard form of equation of ellipse:

$$\frac{(x-h)^{2}}{a^{2}}+\frac{(y-k)^{2}}{b^{2}}=1$

where (h, k) is the center = (0,0)

a is the point on x-axis where y = 0. Hence a = 3.

b is the point on y-axis where x = 0. Hence b = 2.

Substitute this in the standard form of ellipse.

$$\frac{(x-0)^{2}}{3^{2}}+\frac{(y-0)^{2}}{2^{2}}=1$

$$\frac{x^{2}}{9}+\frac{y^{2}}{4}=1$

To make the denominator same multiply 1st term by $\frac{4}{4}$ and 2nd term by $\frac{9}{9}$ .

$$\frac{4x^{2}}{4\times9}+\frac{9y^{2}}{9\times4}=1$

$$\frac{4x^{2}}{36}+\frac{9y^{2}}{36}=1$

$$\frac{4x^{2}+9y^{2}}{36}=1$

Multiply by 36 on both sides

$$\frac{4x^{2}+9y^{2}}{36}\times 36=1\times 36$

$${4x^{2}+9y^{2}}={36}$

The equation of the image is $${4x^{2}+9y^{2}}={36}$ .

8 0

4 years ago

A parabola opening up or down has vertex (0,-7) and passes through (4,-3). Write its equation in vertex form

soldier1979 [14.2K]

Answer:

y = $\frac{1}{4}$ x² - 7

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Here (h, k) = (0, - 7), thus

y = a(x - 0)² - 7

To find a substitute (4, - 3) into the equation

- 3 = a(4 - 0)² - 7, that is

- 3 = 16a - 7 ( add 7 to both sides )

4 = 16a ( divide both sides by 16 )

a = $\frac{1}{4}$ , thus

y = $\frac{1}{4}$ x² - 7

3 0

4 years ago

Steven is moving to another city next weekend and wants to rent a moving truck. The rental rates for two companies in his area a

ASHA 777 [7]

Answer:

Company (1) charges $1.12 per mile and company (2) charges $0.85 per mile

Company (2) is $7.4 cheaper.

Step-by-step explanation:

From the tables given in the picture,

Let the equation representing the rental 'y' and distance traveled 'x' is represented by,

y = mx + b

For company (1),

Here m = per mile rental charges = Slope of the graph

b = Initial charges

Since slope of the line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by,

m = $\frac{y_2-y_1}{x_2-x_1}$

Therefore, slope of the line passing through (30, 53.55) and (60, 87.15) will be,

m = $\frac{87.15-53.55}{60-30}$ = $1.12 per mile

So the equation will be,

y = 1.12x + b

Since this line passes through (30, 53.55),

53.55 = 1.12(30) + b

b = 53.55 - 33.6

b = 19.95

So the expression representing charges for the company (1) will be,

y = 1.12x + 19.95

For company (2),

Per mile charges = slope of the line

m = $\frac{78-56.75}{50-25}$

m = $0.85 per mile

Equation for the charges will be,

y = 0.85x + b

Since this line passes through (25, 56.75),

56.75 = 0.85(25) + b

b = 56.75 - 21.25

b = 35.5

Therefore, equation representing total charges for company (2) will be,

y = 0.85x + 35.5

By comparing per mile charges,

Company (1) charges $1.12 per mile and company (2) charges $0.85 per mile

Steven plans to drive 85 km in rental truck.

Charges for company (1),

y = 1.12x + 19.95

y = 1.12(85) + 19.95

y = $115.15

Charges for company (2),

y = 0.85x + 35.5

y = 0.85(85) + 35.5

y = $107.75

Difference in charges of both the companies = 115.15 - 107.75 = $7.4

Therefore, company (2) is $7.4 cheaper.

6 0

3 years ago