Given the system y=2x+2 and y=2x^2, which statement below is true?

Find the slope of a line that passes through points (-1,-5) and (6,9).

Nana76 [90]

Answer:

${ \rm{slope = \frac{y _{2} - y _{1} }{x _{2} - x _{1} } }} \\ \\ { \rm{slope = \frac{9 - ( - 5)}{6 - ( - 1)} }} \\ \\ { \rm{slope = \frac{14}{7} }} \\ \\ { \boxed{ \rm{ \: \: slope = 2 \: \: }}}$

5 0

2 years ago

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a private school admits no more than 100 students every year. additionally, at least 30 of these students must be girls, and the

Thepotemich [5.8K]

2/2 part of the equation is ≤ B
maybe 30/100 ≤ B

7 0

2 years ago

(c) If a pizza contains 8 slices and there are 4

slavikrds [6]

2 slices per person

7 0

2 years ago

Read 2 more answers

Using the function attached. Find (f+G)(x)

sp2606 [1]

We have been given two functions $f(x)=-8x^3+5x^2+7x+4$ and $g(x)=8x^3-2x+3$ . We are asked to find $(f+g)(x)$ .

We will use composite function property $(f+g)(x)=f(x)+g(x)$ to solve our given problem.

$(f+g)(x)=-8x^3+5x^2+7x+4+8x^3-2x+3$

Now we will combine like terms as:

$(f+g)(x)=-8x^3+8x^3+5x^2+7x-2x+4+3$

$(f+g)(x)=5x^2+5x+7$

Therefore, the value of $(f+g)(x)$ would be $5x^2+5x+7$ .

8 0

2 years ago

Geometry problem help! Please refer to the image below...

Vinil7 [7]

Answer:

A. 1/3

B. √10

C. -1, 1

D. √8, 6

E. congruent and opposite pairs parallel

F. perpendicular, not congruent

G. rhombus, explanation below

Step-by-step explanation:

Hey there! I'm happy to help!

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A.

Slope is the rise over the run. Let's look at F to G.

We are going from -1 to 2 on our x-axis (run), so our run is 3 units.

Our rise is 1 unit as we go from 2 to 3 on the y-axis.

$slope=\frac{rise}{run} =\frac{1}{3}$

This slope is the same for all of the sides.

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B.

We will use the distance formula (which is basically just the Pythagorean Theorem) to calculate the length of each side. Let's go between F and G again, but this distance is the same for all the sides.

$\sqrt{(x_{2}-x_1)^2+(y_{2}-y_1)^2 } \\\\(x_1,y_1)=(-1,2)\\\\(x_2,y_2)=(2,3)\\\\\\\sqrt{(2+1)^2+(3-2)^2 } \\\\\sqrt{(3)^2+(1)^2 }\\\\\sqrt{9+1 }\\\\\sqrt{10}$

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C.

The diagonals are the lines that connect the non-adjacent vertices.

Our two diagonals are FH and GE.

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FH

We go from x-value -1 to 1 from F to H, so our run is 2.

We go from y-value 2 to 0. so our rise is -2.

$slope=\frac{rise}{run} =-\frac{2}{2} =-1$

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GE

We go from x-value -2 to 2 from E to G, so our run is 4.

We go from y-value -1 to 3. so our rise is 4.

$slope=\frac{rise}{run} =\frac{4}{4} =1$

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D.

Let's use the distance formula on each of our diagonals.

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FH

$\sqrt{(x_{2}-x_1)^2+(y_{2}-y_1)^2 } \\\\(x_1,y_1)=(-1,2)\\\\(x_2,y_2)=(1,0)\\\\\\\sqrt{(1+1)^2+(0-2)^2 } \\\\\sqrt{(2)^2+(-2)^2 }\\\\\sqrt{4+4 }\\\\\sqrt{8}$

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GE

$\sqrt{(x_{2}-x_1)^2+(y_{2}-y_1)^2 } \\\\(x_1,y_1)=(-2,-1)\\\\(x_2,y_2)=(2,3)\\\\\\\sqrt{(2+2)^2+(3+1)^2 } \\\\\sqrt{(4)^2+(4)^2 }\\\\\sqrt{16+16 }\\\\\sqrt{36}\\\\6$

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E.

They are congruent as they all have the same length (√10) and the opposite sides are parallel as they have the same slope (1/3)

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F.

They are perpendicular diagonals as their slopes are negative reciprocals (1 and -1), and they are not congruent as they have different lengths (√8 and 6).

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G.

Parallelogram- quadrilateral with opposite pairs of parallel sides.

Rhombus- a parallelogram with four equal sides

Square- a rhombus with four right angles

We can see that this is a parallelogram as we saw that the opposite sides are parallel due to having the same slope, and the perpendicular diagonals show that as well. This is also a rhombus because if we use that distance formula on all the sides, it will be the same. It is not a square though because it does not have four right angles, so this is a rhombus.

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Have a wonderful day and keep on learning!

8 0

2 years ago