Find the area. Simplify your answer.

Answer:

[tex](a)\ 5, \sqrt 6, \sqrt{31[/tex]

[tex](c)\ 9, 12, 15[/tex]

Step-by-step explanation:

Required

Side lengths that form a right triangle

Applying Pythagoras theorem

[tex]a^2 = b^2 + c^2[/tex]

Where a is the longest side.

So, we have:

[tex](a)\ 5, \sqrt 6, \sqrt{31[/tex]

[tex](\sqrt{31})^2 = 5^2 + (\sqrt 6)^2[/tex]

[tex]31 = 25 + 6[/tex]

[tex]31 = 31[/tex]

This forms a right triangle

[tex](b)\ \sqrt 5, \sqrt 5, 50[/tex]

[tex]50^2 = (\sqrt 5)^2 + (\sqrt 5)^2[/tex]

[tex]2500 = 5 + 5[/tex]

[tex]2500 \ne 10[/tex]

This does not form a right triangle

[tex](c)\ 9, 12, 15[/tex]

[tex]15^2 = 12^2 + 9^2[/tex]

[tex]225 = 144 + 81[/tex]

[tex]225 = 225[/tex]

This forms a right triangle

Answer:

1/8 = 0.125

1/9 = 0.1

2/3 = 0.6

4/7 = 0. 571428

3/10 = 0.3

5/3 = 1.6

9/5 = 1.8

5/6 = 0.83

Answer:

It is important because it allows you to calculate the surface area of a trapezoidal prism

Step-by-step explanation:

9514 1404 393

Answer:

  37°

Step-by-step explanation:

The diagonals of a rhombus are angle bisectors. Angle 1 matches the other half of angle L.

  ∠1 = 37°

__

Angle 2 is the complement, 53°, and angle 3 is the same as angle 2, 53°.

The diagonals of a rhombus are perpendicular bisectors of each other, so angle 4 is 90°.

Answer: 5982

Step-by-step explanation:

The area of the rectangle is L*w so 100*50= 5000

the area of the semi-circle on top is

[tex]\frac{1}{2} \pi r^{2} \\\frac{1}{2} \pi 2^{2} \\\frac{1}{2} \pi 625\\\frac{1}{2} (1963.50)\\= 981.75[/tex]

Total area is 5000+981.75= 5981.75

round up to 5982

Answer:

729

Step-by-step explanation:

[tex]\frac{1}{2}log_{2}x=3log_{2}3 \\[/tex]

[tex]log_{2}\sqrt{x} =log_{2}3^{3}[/tex]

[tex]\sqrt{x} =27 \\[/tex]

x=27²=729

9514 1404 393

Answer:

  WX = 33

  (x, y) = (2, 10)

Step-by-step explanation:

The hash marks tell you WX is a midline, so has the measure of the average of the two bases.

  WX = (PQ +SR)/2 = (27 +39)/2 = 66/2

  WX = 33

__

The hash marks also tell you ...

  PW = WS

  y +4x = 18 . . . . . . substitute the given expressions

and also

  QX = XR

  2y +x = 22 . . . . . substitute the given expressions

__

If you solve the first equation for y, you get ...

  y = 18 -4x

Substituting that into the second equation gives ...

  2(18-4x) +x = 22

  36 -7x = 22 . . . . . . . simplify

  14 = 7x . . . . . . . . . . . add 7x-22 to both sides

  2 = x . . . . . . . . . . . . divide by 7

  y = 18 -4(2) = 10 . . . find y using the above relation

The values of x and y are 2 and 10, respectively.

__

My favorite "quick and dirty" way to solve a set of linear equations is using a graphing calculator. It works well for integer solutions.

Answer:

1 1/2 pinyt

Step-by-step explanation:

Answer:

I think A

Step-by-step explanation:

   But im not sure

Answer:

r = 29.82

Step-by-step explanation:

r/7.1 = 4.2

r = 7.1 x 4.2

r = 29.82

Answer:

29.82

Step-by-step explanation:

First, we multiply all terms by the same number to get rid of the denominators.

71 x /71/10 = 71 x 42

Next, we cancel the multiplied terms in denominator.

10 = 71 x 4.2

Solve!

10 = 29.82

Answer:

-1.5, -(-2), 2.5, 8/3

Step-by-step explanation:

pretty sure this is right

Answer:

It's geometric and common difference is 3

Step-by-step explanation:

15/5=3

45/15=3

Answer:

its geometric and the common ratio is 3

Step-by-step explanation:

Answer: [tex]9 \frac{1}{2} x+5[/tex]

Step-by-step explanation:

In order to find the Perimeter, we add all the segments up.

 (2x-1)+(4x+3)+(x+2)+(2x+2)+(1/10x-1)+(2/5x)

=2x-1+4x+3+x+2+2x+2+1/10x-1+2/5x ⇔ Expand Parenthesis

=2x-1+4x+3+x+2+2x+2+1/10x-1+4/10x ⇔ Convert fractions into same                              

                                                                  denominator

=(2x+4x+x+2x+1/0x+4/10x)+(3-1+2+2-1) ⇔ Put like terms together

=(9x+1/2x)+5 ⇔ Combine like terms

=9 1/2 x +5

Hope this helps!! :)

Please let me know if you have any questions

Answer:

Step-by-step explanation:

Using the expression for calculating the sum of an AP as:

Tn = Sn - Sn-1

When n = 10

T10 = S10 - S9

Given that;

Sn = n²-3n

S10 = 10²-3(10)

S10 = 100 - 30

S10 = 70

S9 = 9² - 3(9)

S9 = 81 - 27

S9 = 54

Substitute the given values

T10 = S10 - S9

T10 = 70 - 54

T10 = 16

Hence the 10th term of the sequence is 16

Answer:

The answer to this question is 13

9514 1404 393

Answer:

  73.5 km

Step-by-step explanation:

The magnitude can be found from the law of cosines. The angle between the two vectors is 140°, so the magnitude is ...

  c^2 = a^2 + b^2 -2ab·cos(C)

  c^2 = 32^2 +46^2 -2·32·46·cos(140°) ≈ 5395.2348

  c = √5395.2348 ≈ 73.452

The magnitude of the resultant vector is about 73.5 km.

Answer:

k

Step-by-step explanation:

Answer:

Step-by-step explanation:

The equation of the line that passes through the points (1, 50) and

(3, 120) is y = 35x + 15.

We have,

The point-slope form of a linear equation is given by:

y - y₁ = m(x - x₁)

Where (x₁, y₁) represents the coordinates of a point on the line, and m represents the slope of the line.

The slope (m) using the given points:

m = (y₂ - y₁) / (x₂ - x₁)

Substituting the values from the given points (1, 50) and (3, 120).

m = (120 - 50) / (3 - 1)

= 70 / 2

= 35

Use (1, 50)) and substitute its coordinates into the point-slope form:

y - y₁ = m(x - x₁)

y - 50 = 35(x - 1)

Simplifying further:

y - 50 = 35x - 35

y = 35x - 35 + 50

y = 35x + 15

Therefore,

The equation of the line that passes through the points (1, 50) and

(3, 120) is y = 35x + 15.

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Answer:

u = 10.88

Step-by-step explanation:

u - 6.46 = 4.42

u - 6.46 + 6.46 = 4.42 + 6.46

u = 10.88

Answer:

Step-by-step explanation:

1895 x 7895 + 6575 - 1.753

14961025 + 6575 - 1.753

14967600 - 1.753

14,967,598.247

Answer:

C

Step-by-step explanation:

Option c (20, 24, 26) doesn't follow the Pythagoras triplet, it is a not right-angle.

The right-angle triangle is a triangle in which the measure of two sides of a triangle is smaller than the longest side of the triangle.

To find the right angle triangle it should satisfy the Pythagoras theorem

a. 12, 16, 20

[tex]12^{2} +16^{2} = 144 + 256[/tex]

               = 400

[tex]20^{2}[/tex] = 400

Since it follows the Pythagoras triplet, it is a right-angle triangle.

b. 15, 36, 39

[tex]15^{2} +36^{2} \\= 1521[/tex]

[tex]39^{2} =1521[/tex]

Since it follows the Pythagoras triplet, it is a right-angle triangle.

c. 20, 24, 26

[tex]20^{2} + 24^{2} \\= 976[/tex]

[tex]26^{2} = 676[/tex]

Since it does not follow the Pythagoras triplet, it is a not right-angle triangle.

d. 30, 40, 50

[tex]30^{2} +40^{2} \\= 2500\\50^{2} = 2500[/tex]

Since it follows the Pythagoras triplet, it is a right-angle triangle.

Hence, option c doesn't follow the Pythagoras triplet, it is a not right-angle.

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Answer:

reflect over the y axis, move two units to the left and 8 units down

C. X > -1

Step-by-step explanation:

Step 1: Simplify both sides of the inequality.

−2x + 5 < 7

Step 2: Subtract 5 from both sides.

−2x + 5 − 5 < 7 − 5

−2x<2

Step 3: Divide both sides by -2.

−2x/−2 < 2/−2

x > −1

Answer:

i believe the answer is y =5

(13)^2 = (12)^2 +( y)^2

169= 144 + y^2

169-144= y^2

25= y^2

5 = y

Answer:

2oz are 1/4 cup

done easy.

Step-by-step explanation:

Answer:

I think 1

Step-by-step explanation:

Maybe not 100% $ure

Answer:3

because yeah that the answear and stuff

Answer:

15000000.00 mcg

Step-by-step explanation:

The probability that the Liam and Michael are 0.001422 as a fraction in lowest terms or a decimal rounded to the nearest millionth is 5 decimal.

Liam and Michael are going to play video games this afternoon.

Then, Liam going to play video games = 38

Michael going to play video games = 2

In 38 video games and 2 video games are exactly what Liam and Michael need.

So,

We can write,

Probability = [tex]\frac{2C_{2} }{38C_{2} }[/tex]

As only one case is possible,

That is, [tex]2C_{2}[/tex] = 1

Probability = 1/(38!/(38-2)!2!)

= 1/(38!/36!2!)

=( 2! * 36! )/38!

= (2! * 36! )/38!*37!*36!

= 2!/38!37!

= 1/19!37!

= 1/703

= 0.001422

Rounding to nearest million ( 5 decimal )

Required probability = 0.001422

Therefore,

The probability 0.001422 as a fraction in lowest terms or a decimal rounded to the nearest millionth is 5 decimal.

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