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2 years ago

7

The perimeter of a rectangle equals one and a half times its area. Express the length of the rectangle in terms of the width (us

e the variable ???? for the width).

1 answer:

WITCHER [35]2 years ago

4 0

Answer:

Step-by-step explanation:

let x and y be length and width of rectangle.

Perimeter=2(x+y)

area=xy

2(x+y)=1/2 xy

4(x+y)=xy

4x+4y=xy

x y-4y=4 x

y(x-4)=4 x

$y=\frac{4x}{x-4}$

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A kite is made up of two isosceles triangles, KIT and KET, with the lengths shown. The top triangle of the kite, ΔKIT, is made f

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The correct answer would be 48 square inches

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2 years ago

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Match each pair of points to the equation of the line that is parallel to the line passing through the points.

Paraphin [41]

we know that

If two lines are parallel, then, their slopes are equal.

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

we will proceed to calculate the slope in each case, to determine the solution of the problem

<u>Case A)</u> Point $B(5,2)\ C(7,-5)$

Find the slope BC

Substitute the values in the formula

$m=\frac{-5-2}{7-5}$

$m=\frac{-7}{2}$

$m=-3.5$

so

The equation $y=-3.5x-15$ is parallel to the line passing through the points $B(5,2)\ C(7,-5)$

therefore

<u>the answer Part A) is</u>

$B(5,2)\ C(7,-5)$ ------> $y=-3.5x-15$

<u>Case B)</u> Point $D(11,6)\ E(5,9)$

Find the slope DE

Substitute the values in the formula

$m=\frac{9-6}{5-11}$

$m=\frac{3}{-6}$

$m=-0.5$

so

The equation $y=-0.5x-3$ is parallel to the line passing through the points $D(11,6)\ E(5,9)$

therefore

<u>the answer Part B) is</u>

$D(11,6)\ E(5,9)$ ------> $y=-0.5x-3$

<u>Case C)</u> Point $F(-7,12)\ G(3,-8)$

Find the slope FG

Substitute the values in the formula

$m=\frac{-8-12}{3+7}$

$m=\frac{-20}{10}$

$m=-2$

so

Any linear equation with slope $m=-2$ will be parallel to the line passing through the points $F(-7,12)\ G(3,-8)$

<u>Case D)</u> Point $H(4,4)\ I(8,9)$

Find the slope HI

Substitute the values in the formula

$m=\frac{9-4}{8-4}$

$m=\frac{5}{4}$

$m=1.25$

so

The equation $y=1.25x+4$ is parallel to the line passing through the points $H(4,4)\ I(8,9)$

therefore

<u>the answer Part D) is</u>

$H(4,4)\ I(8,9)$ ------> $y=1.25x+4$

<u>Case E)</u> Point $J(7,2)\ K(-9,8)$

Find the slope JK

Substitute the values in the formula

$m=\frac{8-2}{-9-7}$

$m=\frac{6}{-16}$

$m=-0.375$

so

Any linear equation with slope $m=-0.375$ will be parallel to the line passing through the points $J(7,2)\ K(-9,8)$

<u>Case F)</u> Point $L(5,-7)\ M(4,-12)$

Find the slope LM

Substitute the values in the formula

$m=\frac{-12+7}{4-5}$

$m=\frac{-5}{-1}$

$m=5$

so

The equation $y=5x+19$ is parallel to the line passing through the points $L(5,-7)\ M(4,-12)$

therefore

<u>the answer Part F) is</u>

$L(5,-7)\ M(4,-12)$ ------> $y=5x+19$

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2 years ago

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In exercises 1 and 2, find m<1 and m<2. Tell which theorem you used in each case.

solniwko [45]

Answer:

m∠2 = 78°

Step-by-step explanation:

From the given picture,

lines 'm' and 'n' are the parallel lines and line 't' is the transverse line.

∠1 and angle with the measure of 78° are corresponding angles.

Therefore, m∠1 = 78°

m∠1 = m∠2 [Vertical angles are equal]

m∠2 = 78°

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2 years ago

Sarah can bicycle a loop around the north part of Lake Washington in 2 hours and 30 minutes. If she could increase her average s

netineya [11]

Answer:

The length of the loop is approximately 49.58 km.

Step-by-step explanation:

Given:

Time required to ride bicycle in loop = 2 hours and 30 mins

Now we know that;

60 mins = 1 hour

30 mins =0.5 hour

so 2 hour and 30 mins = $2+0.5 = 2.5\ hrs$

∴ Time required to ride bicycle in loop = 2.5 hrs

Let the speed at which she is riding the bicycle be 's'.

and let Total distance of the loop be 'd'

Now we know that;

Distance is given by speed multiplied by time.

framing in equation form we get;

$d =2.5s \ \ \ \ equation \ 1$

Now Given:

If she increase the speed by 1 km/hr, it would reduce her time around the loop by 7 minutes.

Hence we can say;

Speed = $s+1$

Also time will be reduce to 7 mins.

7 mins =0.12 hrs

Now time = 2.5-0.12 =2.38

Again Distance is given by speed multiplied by time.

framing in equation form we get;

$d =2.38(s+1) \ \ \ \ equation \ 2$

Now distance is same for both so we will calculate the speed by equating the equations.

$2.5s = 2.38(s+1)\\\\2.5s=2.38s+2.38\\\\2.5s-2.38s =2.38\\\\0.12s= 2.38\\\\s =\frac{2.38}{0.12} \approx 19.83\ km/hr$

Now Speed = 19.83 km/hr

Length of the loop (d) = $19.83\times 2.5 = 49.58 \ km$

Hence the length of the loop is approximately 49.58 km.

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2 years ago

There were 8 judges at a gymnastics competition. Kathleen received these scores for her performance on the uneven parallel bars.

Korolek [52]

Answer:

below

Step-by-step explanation:

mean : 8.8

The mean is the average, so you find it by adding all the numbers together and dividing by n, or how many numbers there are. For this, I added to get 70.4 and divided that by 8 (8 total scores).

70.4/8 = 8.8.

median : 8.85

The median is the middle of the data set, so you put the numbers in increasing order (lowest number to highest number) and then finding the middle of that set. For this set, since there is an even number of numbers (8), you have to find the middle by adding the two middle numbers and dividing by 2.

8.2, 8.7, 8.8, 8.8, 8.9, 8.9, 8.9, 9.2

The middle numbers are 8.8 and 8.9, so you add those together and divide by 2 to get 8.85.

mode : 8.9

The mode is just what number appears most often. Because 8.9 appears three times in this data set, more than any other number, the mode is 8.9.

b. The mean reflects a typical score because it is the average, and is used most often when someone is expressing a typical or "average" score. It is the score most people are likely to get, and as there are no outliers in this data set, it reflects a typical score for this data set. It is also the same as the mode, or most often score, in this data set.

6 0

2 years ago

Read 2 more answers