What is the unit rate of 360 miles travled on 12 gallons of gasoline

H(x)=2x^2+3x-7 <br> find h(-1)

nata0808 [166]

Answer:

que

Step-by-step explanation:

4 0

3 years ago

Jeff is baking a cake the recipe says that he has to mix 32 g of vanilla powder to the flower Jeff knows that one cup of that pa

Lady_Fox [76]

Two thirds of the one cup that he added is 80g, so he went over by 48g

6 0

3 years ago

Whats the answer ??????

docker41 [41]

Answer:

1.Javier did not write the coefficient raised to power of 3

2.Javier wrote x^4 instead of x^3

3.Javier did divide exponents instead of subtraction of exponents

4 0

3 years ago

Need help. not in college

dimaraw [331]

The length of ab is 24

4 0

3 years ago

A line passes through the points (-7, 2) and (1, 6).A second line passes through the points (-3, -5) and (2, 5).Will these two l

BlackZzzverrR [31]

Answer:

Yes, the lines intersect at (3,7). The solution is (3,7).

Explanation:

Step 1. The first line passes through the points:

(-7,2) and (1,6)

and the second line passes through the points:

(-3,-5) and (2,5)

Required: State if the lines intersect, and if so, find the solution.

Step 2. We need to find the slope of the lines.

Let m1 be the slope of the first line and m2 be the slope of the second line.

The formula to find a slope when given two points (x1,y1) and (x2,y2) is:

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

Using our two points for each line, their slopes are:

$\begin{gathered} m_1=\frac{6-2}{1-(-7)} \\ \\ m_2=\frac{5-(-5)}{2-(-3)} \end{gathered}$

The results are:

$\begin{gathered} m_1=\frac{6-2}{1-(-7)}=\frac{4}{1+7}=\frac{4}{8}=\frac{1}{2} \\ \\ \end{gathered}$ $m_2=\frac{5+5}{2+3}=\frac{10}{5}=2$

The slopes are not equal, this means that the lines are NOT parallel, and they will intersect at some point.

Step 3. To find the intersection point (the solution), we need to find the equation for the two lines.

Using the slope-point equation:

$y=m(x-x_1)+y_1$

Where m is the slope, and (x1,y1) is a point on the line.

For the first line m=1/2, and (x1,y1) is (-7,2). The equation is:

$y=\frac{1}{2}(x-(-7))+2$

Solving the operations:

$\begin{gathered} y=\frac{1}{2}(x+7)+2 \\ \downarrow\downarrow \\ y=\frac{1}{2}x+7/2+2 \\ \downarrow\downarrow \\ y=\frac{1}{2}x+5.5 \end{gathered}$

Step 4. We do the same for the second line. The slope is 2. and the point (x1,y1) is (-3, -5). The equation is:

$\begin{gathered} y=2(x-(-3))-5 \\ \downarrow\downarrow \\ y=2x+6-5 \\ \downarrow\downarrow \\ y=2x+1 \end{gathered}$

Step 5. The two equations are:

$\begin{gathered} y=\frac{1}{2}x+5.5 \\ y=2x+1 \end{gathered}$

Now we need to solve for x and y.

Step 6. Equal the two equations to each other:

$\frac{1}{2}x+5.5=2x+1$

And solve for x:

$\begin{gathered} \frac{1}{2}x+5.5=2x+1 \\ \downarrow\downarrow \\ 5.5-1=2x-\frac{1}{2}x \\ \downarrow\downarrow \\ 4.5=1.5x \\ \downarrow\downarrow \\ \frac{4.5}{1.5}=x \\ \downarrow\downarrow \\ \boxed{3=x} \end{gathered}$

Step 7. Use the second equation:

$y=2x+1$

and substitute the value of x to find the value of y:

$\begin{gathered} y=2(3)+1 \\ \downarrow\downarrow \\ y=6+1 \\ \downarrow\downarrow \\ \boxed{y=7} \end{gathered}$

The solution is x=3 and y=7, in the form (x,y) the solution is (3,7).

Answer:

Yes, the lines intersect at (3,7). The solution is (3,7).

6 0

1 year ago