Find the value of x and y. Triangle MNP = triangle TUS

Given:

One diagonal of the kite is three times as long as the other diagonal.

The area of the kite is 48 square meters.

To find:

The length of each diagonal.

Solution:

We know that, the area of the kite is:

[tex]A=\dfrac{d_1d_2}{2}[/tex]

Where, [tex]d_1,d_2[/tex] are two diagonals of a kite.

It is given that, one diagonal of the kite is three times as long as the other diagonal.

Let [tex]d_1=3d_2[/tex]. Then the area of the kite is:

[tex]A=\dfrac{3d_2d_2}{2}[/tex]

[tex]A=\dfrac{3d_2^2}{2}[/tex]

The area of the kite is 48 square meters.

[tex]\dfrac{3d_2^2}{2}=48[/tex]

[tex]3d_2^2=2(48)[/tex]

[tex]d_2^2=\dfrac{96}{3}[/tex]

[tex]d_2^2=32[/tex]

Taking square root on both sides, we get

[tex]d_2=\sqrt{32}[/tex]       [It is only positive because side length cannot be negative]

[tex]d_2=4\sqrt{2}[/tex]

Now,

[tex]d_1=3d_2[/tex]

[tex]d_1=3(4\sqrt{2})[/tex]

[tex]d_1=12\sqrt{2}[/tex]

Therefore, the diagonals of the kite are [tex]4\sqrt{2}[/tex] units and [tex]12\sqrt{2}[/tex] units.

Answer:

$3,442.40

$3,057.60

Step-by-step explanation:

The computation of the each investment is as follows:

let us assume the one investment be x

And, the other investment be y

So

According to the question

x + y = $6,500

And,

-7x + 8y = $364

Now multiply by 7 in equation 1

7x +  7y = $45,500

-7x + 8y = $364

15y = $45,864

y = $3,057.60

x = $6,500 - $3,0657.60

= $3,442.40

The interquartile range of the data will be 9.1.

Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.

Given that;

The table shows the blood pressures of 16 clinic patients.

Now,

Since, The data set is,

⇒ 81.6, 84.1, 87.6, 82.8, 82.0, 88.9, 86.7, 96.4, 84.6, 104.9, 90.8, 94.0, 69.4, 78.9, 75.2, 91.0

Arrange in ascending order as;

⇒ 69.4, 75.2, 78.9, 81.6, 82.0, 82.8, 84.1, 84.6, 86.7, 87.6, 88.9, 90.8, 91.0, 94.0, 96.4, 104.9

Clearly, There are 16 clinic patients.

Hence, The lower quartile (Q₁) = 81.6 + 82 / 2

                                               = 81.8

And, The Upper quartile (Q₃) = 90.8 + 91 / 2

                                             = 90.9

Thus, The interquartile range of the data = Q₃ - Q₁

                                                               = 90.9 - 81.8

                                                               = 9.1

Therefore, The interquartile range of the data = 9.1

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Answer:

83/5

Step-by-step explanation:

83/5 would be equivalent to 16 3/4.

Answer:

8, or B on Edge.

Just took the quiz. Have a great day

Answer:

x=-0.5

Step-by-step explanation:

6.8x + 9.3= -9.4 + 3.4 (2-5x)

6.8x + 9.3 = -9.4 + 6.8 - 17x

6.8x + 9.3 = -2.6 - 17x

22.8x = -11.9

x = -0.5

Answer:

If y is inversely proportional to x then y is 3

Answer: 4,000,000,000 mm

Step-by-step explanation:

One kilometer is 10^6 or 1000000 millimeters

So 4000x1000000

4x1 is 4

Annex the zeros. There are 9 zeros.

= 4,000,000,000 millimeters

The distance between the two cities in millimetres of 4,000,000,000 mm

Distance is defined as the length between the two points just like in the question it is the length between the two cities.

We know that:-

One kilometer is 10^6 or 1000000 millimeters

So 4000x1000000

4x1 is 4

Annex the zeros. There are 9 zeros.

= 4,000,000,000 millimeters

Therefore the distance between the two cities in millimetres of 4,000,000,000 mm

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Answer:

5% times 3=15%

4% times 3=12%

15-12=3

1300 times 0.03= $39

39 dollars.

Answer:

x=1+√3

Step-by-step explanation:

Let's solve your equation step-by-step.

6x^2+6=12x+18

Step 1: Subtract 12x+18 from both sides.

6x^2+6−(12x+18)=12x+18−(12x+18)

6x^2−12x−12=0

For this equation: a=6, b=-12, c=-12

6x^2+−12x+−12=0

Step 2: Use quadratic formula with a=6, b=-12, c=-12.

x=−b±√b2−4ac/2a

x=−(−12)±√(−12)2−4(6)(−12)/2(6)

x=12±√432/12

x=1+√3

Answer:

The sum is Rs 1,250 and Rs 650

Step-by-step explanation:

Let the amounts be represented as $x and $y

The sum of both is 1900

Thus;

x + y = 1,900 •••••(i)

Mathematically, the interest on the amount borrowed is;

I = PRT/100

where p is the principal, representing the amount borrowed

R is the rate

T is the time

for the first amount of $x ; we have interest as;

I = (x * 5 * 4)/100 = 20x/100

for the second, we have

I = (y * 9 * 4)/100 = 36y/100

The sum of both is 580

Thus;

20x/100 + 36y/100 = 580

20x + 36y = 58000 •••••(ii)

From equation i;

x = 1,900 - y

Substitute this into equation ii

We have this as;

20(1900-y) + 36y = 58,000

38000 - 20y + 36y = 58,000

16y = 58000 - 38000

16y = 20,000

y = 20,000/16

y = 1250

From equation 1;

x + y = 1900

x = 1900-y

x = 1900-1250

y = 650

Answer:

2x+8

Step-by-step explanation:

Answer:

[tex]4x^{2} +2x[/tex]

Step-by-step explanation:

I'm not sure what you want, because it says "which expression", but you didn't provide any answer choices.

So all you have to do for this is combine like terms, and the only ones were 7x and -5x, which equals 2x.

The decimal is a repeating decimal, and the actual fraction represented by 0.64⁻ is 64/99

The decimal number is given as:

0.64⁻

There are two numbers after the decimal point

So, the number of repeating digits is 2

In (a), we have the number of repeating digits to be 2.

So, the value multiplied on both sides is:

Value = 10²

Value = 100

Hence, the value multiplied on both sides of the equals sign is 100

The number is the decimal points is 64.

And the value multiplied on both sides of the equals sign is 100.

So, the fraction is:

64/(100 - 1)

This gives

64/99

Hence, the actual fraction represented by 0.64⁻ is 64/99

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Answer:

2, 100, 64/99

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

exchange y and x

then find y

Answer:

C. Subtraction property of equality

Step-by-step explanation:

Answer:

C  ( 9 , 15)

Step-by-step explanation:

Answer:

PE = 102.9 Joules

Step-by-step explanation:

PE = mgh

= (7.0 kg)(9.8 m/s^2)(1.5 m)

= 102.9 Joules

Answer:

c

Step-by-step explanation:

Answer:

I believe it would be A

Step-by-step explanation:

A deck of cards has 52 cards in it, so it cant be C or D, and with all the possibilities it could not be B

Answer:

the corect answer for this question is (-x,y)

Answer:

the answer is D

you would end up with 14% and 14 is in between 12 ns 18

Step-by-step explanation:

Answer:

This is the answer

Step-by-step explanation:

40/50 - 80%

13% - 0.13

1.75 - 1 3/4

155% - 1 11/20

Hope this helps

Answer:

I think neither

Step-by-step explanation:

Answer:

30%

Step-by-step explanation:

Find the percent discount by dividing the change in the price by the original price:

(684 - 478.6) / 684

205.4 / 684

= 0.3

So, the percent discount was approximately 30%

The required measure of angle value of the m2 is 48°.

Given that,
The sum of two angles m1 and m2 is 90, where m1 = 42°,
What is the value of m2 is to be determined.

The angle can be defined as the one line inclined over another line.

The process in mathematics to operate and interpret the function to make the function simple or more understandable is called simplifying and the process is called simplification.

m1 + m2 = 90
42 + m2 = 90
m2 = 48°

Thus, the required value of the m2 is 48°.

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Answer:

36

Step-by-step explanation:

According to the scenario, computation of the given data are as follows,

Let the number be x, then

First subtract 14 from number x, then

x - 14

Now multiply difference by -2, results -44

(x - 14) × -2 = -44

By solving equation,

-2X + 28 = - 44

- 2X = -44 - 28

X = -72 ÷ -2

x = 36

So, Peter's number is 36.

Answer:

Random numbers for experimental probability. This means that if we roll a die 60 times we can expect each of the six faces to come up.

hope this helps

have a good day :)

Step-by-step explanation:

Answer: 6 hours

Step-by-step explanation:

48/6 = 8

36/6 = 6

Answer:

The substitution method consists of solving for in one of the equations, basically the one that is easiest, and substituting the resulting expression in the other. With this, the second equation is converted into a linear equation with one unknown, which is solved by simply solving for.

Step-by-step explanation:

l hope and this can help you

Answer and Step-by-step explanation:

First off, we need to get the variable by itself. We do this by adding 4 to each side of the inequality.

x < -6

Our answer is x < -6, so all values that are inputted to x and are less than -6 are solutions to the inequality.

#teamtrees #PAW (Plant And Water)

Answer:

3sqrt2 is the distance between these two points