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omeli [17]
3 years ago
11

Need help with this??? Please!!!

Mathematics
1 answer:
Radda [10]3 years ago
3 0

Answer:

the first option

Step-by-step explanation:

(f-g)(x) simply means to subtract both expressions. really literally.

and we go through it power by power of x.

the highest power/exponent of x is 3 (x³). only f(x) has one.

so, -7x³ is the first part of f-g.

next is x².

11x² - 6x² = 5x², which is the second part of f-g.

next is x.

-8x - (-14x) = -8x + 14x = 6x, which is the third part of f-g.

next is x⁰ (in other words, no x, just a constant).

4 - (-3) = 4 + 3 = 7, which is the 4th part of f-g.

we have no x to the power of -1 or -2, so we have -3

0 - (-4x‐³) = 4x‐³, which is the last part of f-g.

so, it is clearly the first answer option.

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Answer:

See explanation.

Step-by-step explanation:

Graph the quadrilateral. By inspection, you can tell where the midpoint is. (see attachment 1)

Now, I'll draw a line through it. (see attachment 2)

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Do the same for the other points, and you'll have your image.

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Geometry problem help!<br><br> Please refer to the image below...
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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!

-----------------------------------------------------------------

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.

-----------------------------------------------------------------

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}

-----------------------------------------------------------------

C.

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

Our two diagonals are FH and GE.

-----------------------------

<u>FH</u>

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

-----------------------------

<u>GE</u>

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

-----------------------------------------------------------------

D.

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

-----------------------------

<u>FH</u>

<u />\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}<u />

-----------------------------

<u>GE</u>

\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

-----------------------------------------------------------------

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)

-----------------------------------------------------------------

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).

-----------------------------------------------------------------

G.

<u>Parallelogram-</u> quadrilateral with opposite pairs of parallel sides.

<u>Rhombus-</u> a parallelogram with four equal sides

<u>Square-</u> 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!

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