Evaluate the expression. 4^2+5⋅3^2−4^2÷2^3

3. The path of an underground stream is given by the function y = 4x² +17x -32. Two

sineoko [7]

Answer:

The coordinate of the wells are

$(-4 -\sqrt[]{\frac{53}{2}}, 70+15\sqrt[]{\frac{53}{2}})$

$(-4 +\sqrt[]{\frac{53}{2}}, 70-15\sqrt[]{\frac{53}{2}})$

Step-by-step explanation:

The y coordinate of the stream is given by $y = 4x^2+17x-32$ . Also, the y coordinate of the houses are determined by y=-15x+10. We will assume that the houses are goint to be built on the exact position where we build the wells. We want to build the wells at the exat position in which both functions cross each other, so we have the following equation

$4x^2+17x-32 = -15x+10$

or equivalently

$4x^2+32x-42=0$ (by summing 15x and substracting 10 on both sides)

Dividing by 2 on both sides, we get

$2x^2+16x-21=0$

Recall that given the equation of the form $ax^2+bx+c=0$ the solutions are

$x = \frac{-b \pm \sqrt[]{b^2-4ac}}{2a}$

Taking a =2, b = 16 and c = -21, we get the solutions

$x_1 = -4 -\sqrt[]{\frac{53}{2}}$

$x_2 = -4 +\sqrt[]{\frac{53}{2}}$

If we replace this values in any of the equations, we get

$y_1 = 70+15\sqrt[]{\frac{53}{2}}$

$y_2 = 70-15\sqrt[]{\frac{53}{2}}$

4 0

3 years ago

What are the factors of x^2-144?

Ksju [112]

Answer:

(x-12) (x+12)

Step-by-step explanation:

If you factor it out since both are perfect squares you would place an x on each side and then find the square root of 144, which is 12 and put a positive and a negative in each parenthesis.

9 0

3 years ago

Find the equation of a line parallel to −4x−5y=−4 that contains the point (3,−2). Write the equation in slope-intercept form.

Temka [501]

Answer:

see explanation

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Rearrange - 4x - 5y = - 4 into this form

Add 4x to both sides

- 5y = 4x - 4 ( divide all terms by - 5 )

y = - $\frac{4}{5}$ + $\frac{4}{5}$ ← in slope- intercept form

with slope m = - $\frac{4}{5}$

Parallel lines have equal slopes, thus

y = - $\frac{4}{5}$ x + c ← is the partial equation

To find c substitute (3, - 2) into the partial equation

- 2 = - $\frac{12}{5}$ + c ⇒ c = - 2 + $\frac{12}{5}$ = $\frac{2}{5}$

y = - $\frac{4}{5}$ x + $\frac{2}{5}$ ← in slope- intercept form

4 0

4 years ago

Can someone help me with this math problem

Elis [28]

Answer:

C. Divide both sides of the equation by -2.

Step-by-step explanation:

The goal of the equation is to isolate x. In order to do that we have to remove the '-2' by doing the inverse operation. That is the opposite operation, for example addition and subtraction, multiplication and division.

Since x is being multiplied by -2, we do the inverse which is division.

5 0

3 years ago

Need help on #5, please help :)

Gre4nikov [31]

Okay i answered by comment but now i can make an official answer here:

a) i got 5,828.6 grams / about 13lb

b) i got 273,391.48$

hope this helps!

6 0

4 years ago