Find the intercept of the line -2x+5y=7

2. Carl needs 15 hours longer than Jennifer to paint a room. If they work together, they can complete the job in 4 hours. Explai

nasty-shy [4]

Answer:

Jennifer would complete the job on her own in 5 hours.

Step-by-step explanation:

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

$ax^{2} + bx + c, a\neq0$ .

This polynomial has roots $x_{1}, x_{2}$ such that $ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})$ , given by the following formulas:

$x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}$

$x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}$

$\Delta = b^{2} - 4ac$

Rates

The together rate is the sum of their separates rate.

We have that:

Jennifer takes x hours to complete the job on her own, so her rate is 1/x.

Carl needs 15 hours longer than Jennifer, that is, 15 + x hours, so his rate is 1/(15+x).

The together rate is 1/4. So

$\frac{1}{4} = \frac{1}{x} + \frac{1}{15+x}$

$\frac{1}{4} = \frac{15 + x + x}{x(15+x)}$

$\frac{1}{4} = \frac{15 + 2x}{x(15+x)}$

Applying cross multiplication.

$x^2 + 15x = 4(15 + 2x)$

$x^2 + 15x = 60 + 8x$

$x^2 + 7x - 60 = 0$

Quadratic equation with $a = 1, b = 7, c = -60$ . So

$\Delta = 7^{2} - 4*1*60 = 289$

$x_{1} = \frac{-7 + \sqrt{289}}{2} = 5$

$x_{2} = \frac{-7 - \sqrt{289}}{2} = -12$

Since the time to complete the job has to be a positive value.

Jennifer would complete the job on her own in 5 hours.

4 0

3 years ago

A line passes through the point (-6, -8) and has a slope of 3/2

garri49 [273]

Answer:

y=3/2(x) -1, or y = 1.5x - 1

Step-by-step explanation:

To write the equation in slope-intercept form, you have to determine the y-intercept for the line. Since you have the slope and at least one ordered pair, you can find this by substituting the points and slope into this formula:

y=mx+b.

For this particular line, you would write:

-8 = 3/2(-6)+b

-8 = -18/2 + b

-8 = -9 + b

add 9 to both sides to isolate the b

-1 = b.

Now that you have the answer for b (-1), you can write the equation as:

y=3/2(x) -1

7 0

3 years ago

Two boats leave a port at the same time, one going north and the other traveling south. The northbound boat travels 18 mph fast

shutvik [7]

Answer:

10 hours

Step-by-step explanation:

Two boats leave a port at the same time, one going north and the other traveling south.

Southbound boat rate = 40 mph

The northbound boat travels 18 mph faster than the southbound boat.

Northbound boat rate = 40 + 18 = 58 mph

Two boats rate = 40 + 58 = 98 mph (this means they are apart 98 km after one hour)

Total distance = 980 miles

Total rate = 98 mph

Time $=980:98=10$ hours

3 0

3 years ago

Evaluate x6 + y(-9) When x= -2, y = 4

11111nata11111 [884]

Answer:

the answer is -48. _______

4 0

3 years ago

Which would not be a step in finding the area of a circle by cutting it

Mkey [24]

Answer:

D. Continue cutting smaller and smaller slices.

Step-by-step explanation:

While, in theory, this could be a step, it would be a pointless one. You would have to eventually rearrange the pieces, but now there would be more of them.

Hope this helps!

4 0

3 years ago