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3 years ago

6

Find the base and height of a rectangle with vertices (–4, 7), (–2, 7), (–2, 1), and (–4, 1). The height is units. The base is u

nits.

2 answers:

julia-pushkina [17]3 years ago

8 0

Answer: The base is 2 units and the height is 6 units.

Step-by-step explanation:

You can plot the points (-4, 7), (-2, 7), (-2, 1), and (-4, 1) and obtain the rectangle shown in the figure attached.

As you can see in the figure, the distance between the points of the base is:

$d=\sqrt{(-2-(-4))^2+(1-1)^2}\\d=2$

Then the lenght of the base is 2 units

The distance between the points of the height is:

$d=\sqrt{(-2-(-2))^2+(1-7)^2}\\d=6$

Then the height is 6 units

vovikov84 [41]3 years ago

6 0

ANSWER

The height is 6 units.

The base is 2 units.

EXPLANATION

The given rectangle has vertices (–4, 7), (–2, 7), (–2, 1), and (–4, 1).

To find the height of the rectangle, we use the points (-2,7) and (-2,1) or

(-4,7) and (-4,1) because they form the vertical side of the rectangle.

The height is

$|7-1|=6 units$

To find the base, use the points (-2,7) and (-4,7) or (-2,1) and (-4,1).

The base is

$|-2--4|=2 units$

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What expression is equivalent to 1/36

IrinaVladis [17]

The expression equivalent to 1/36 are :-

$\frac{1}{36} \: = \: \frac{2}{72} ; \frac{3}{108} ; \frac{4}{144} ; \frac{5}{180}$

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3 0

2 years ago

Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. 2x-y=

Bond [772]

Answer:

The system of linear equations has infinitely many solutions

Step-by-step explanation:

Let's modified the equations and find the answer.

Using the first equation:

$2x-y=5$ we can multiply by 2 in both sides, obtaining:

$2*(2x-y)=2*5$ which can by simplified as:

$4x-2y=10$ which is equal to:

$4x=2y+10$

Considering the second equation:

$=4x+ky=2$

Taking into account that from the first equation we know that: $4x=2y+10$ , we can express the second equation as:

$2y+10+ky=2$ , which can be simplified as:

$(2+k)y=2-10$

$(2+k)y=-8$

$y=-8/(2+k)$

Because (-8) is being divided by (2+k), then (2+k) can't be equal to 0, so:

$2+k=0$ if $k=-2$

This means that k can be any number different than -2, and for each of these solutions, there is a different solution for y, allowing also, different solutions for x.

For example, if k=0 then

$y=-8/(2+0)$ which give us y=-4, and, because:

$4x=2y+10$ if y=-4 then $x=(-8+10)/4=0.5$

Now let's try with k=-1, then:

$y=-8/(2-1)$ which give us y=-8, and, because:

$4x=2y+10$ if y=-8 then $x=(-16+10)/4=-1.5$ .

Then, the system of linear equations has infinitely many solutions

8 0

3 years ago

Geometry problem help!<br><br> 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!

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

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.

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

Have a wonderful day and keep on learning!

8 0

3 years ago

Identify an equation in point-slope form for the ine parallel to y = -2/3 x+8 that

zlopas [31]

Answer:

$y +5 = -\frac{2}{3}(x - 4)$

Step-by-step explanation:

Given

$y = -\frac{2}{3}x + 8$

Point (4,-5)

Required

Determine the line equation

From the question, we understand that the line is parallel to $y = -\frac{2}{3}x + 8$

This implies that they have the same slope, m

A linear equation is:

$y = mx + b$

Where

$m = slope$

By comparison: $y = mx + b$ and $y = -\frac{2}{3}x + 8$

$m = -\frac{2}{3}$

Next, we determine the line equation using:

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

Where

$(x_1,y_1) = (4,-5)$ and $m = -\frac{2}{3}$

$y - (-5) = -\frac{2}{3}(x - 4)$

$y +5 = -\frac{2}{3}(x - 4)$

Hence,

<em>Option C is correct</em>

<em />

4 0

3 years ago

Is the function y=x+2 linear or nonlinear?

AlladinOne [14]

Answer:

Linear

Step-by-step explanation:

It is linear as it has degree 1.

7 0

2 years ago

Read 2 more answers