A right angled triangle has two shorter sides and one is twice as long as the other. The hypotenuse is 25cm long. What are the lengths of the two shorter sides.

Answers

Answer 1

Answer:  x =  14.43

Step-by-step explanation:

The Pythagorean Theorem states the following:  

a^2 + b^2 = c^2  

Make one side of the triangle x  

Make the second side of the triangle 2x  

Now, you can plug the values into the equation,  right?  

x^2 + 2x^2 = 25^2 or 625  

3x^2 = 625

Divide each side by 3 and you are left with:  

x^2 =  208.33

Now, take the square root of 208.33

x =  14.43

That is the shorter side. The longer side is twice that value: Therefore, 14.43 x 2 = 28.86 14.43 is one side of the triangle. The other is that same value times two. Therefore, the sides of your triangle are: 14.43 Shorter side 28.86 Longer side

Answer 2
Answer: The ameliorated retort to the peculiar proposed interrogate is identified as 14.43 centimeters (cm).

Step-by-Step Explanation:

The following configurations are stated throughout the interrogate:

- Hypotenuse: 25 centimeters (cm).
- Opposite: b
- Adjacent: 2b

Utilizing the Pythagorean Theorem, established circa 1900 B.C.

A^2 + b^2 = c^2

Extend the equation and equate such values, as necessary,

2b^2 + b^2 = 25^2

Further evaluate,

3b^2 = 625

B^2 = 208.33

Evaluate, on the behalf of the root,

[sqrt root] b^2 = [sqrt root] 208.33

B = 14. 43 centimeters (cm).

Thus far, such agglomeration, referring to the 14. 43 centimeters, is equated to that of the value of the ‘Opposite’.

Since the ‘Adjacent’ is equivalent to twice of that of the opposite,
Adjacent = 28.86 centimeters (cm).

Henceforth, given such configured dissemination(s), the interrogate has contemporaneously been evaluated for.

*I hope this helps.

Related Questions

Simplfy: -1| 2/3 - 4| / 5/6

Answers

Step-by-step explanation:

-1| 2/3 - 4| / 5/6

=-1 paxi ko sign k hola

Please help me solve this problem guys

Answers

Answer:

17%

Step-by-step explanation:

Again, as the amount of years increase, the population of bees gets multiplied by 0.83. We can rewrite this to 83%, and then again rewrite this to 100%-17%. We can see now that the population of bees decreases by 17% each year.

Julie assembles shelves for a department store and gets paid $3.25 per shelf. She can assemble 5 per hour and works 8 hours per day. Determine Julie’s gross pay for 1 week

Answers

Pay per shelf = $3.25

No of shelfs per hour = 5

Total hours per day = 8

Total days to find pay of = 7

= 3.25×5×8×7

= 910

Therefore she is paid $910 after 1 week.

Must click thanks and mark brainliest

Find the volume of the cylinder please

ASAP

Answers

Answer:

33ft^3

Step-by-step explanation:

radius is half the diameter, half of 2=1 and 1^2=1

3(1)(11)=33

Answer: V = 33 ft³

Step-by-step explanation:

π = 3

r = (1/2)d = (1/2) (2) = 1 ft

h = 11 ft

Given Formula

V = π r² h

Substitute values into the formula

V = (3) (1)² (11)

Simplify exponents

V = (3) (1) (11)

Simplify by multiplication

V = 33 ft³

Hope this helps!! :)

Please let me know if you have any questions

The weekly wages of employees of Volta gold are normally distributed about a mean of$1250 with a standard deviation of $120. Find the probability of an employee having a weekly wage lying 1) between $1320 and $970 2) over $1290 3) under $1400

Answers

Answer:

1) 0.7104 = 71%

2) 0.6615 = 66%

3) 0.8944 = 89%

Step-by-step explanation:

1)

Z(low)=-2.333 0.009815329

Z(upper)=0.583 0.720165536

2)

Z(low)=0.333 0.63055866

Z(upper)=8322.908 1

3)

Z(low)=-10.417 0

Z(upper)=1.25 0.894350226

A survey was conducted by asking 120 students in a town how they traveled to school.
The following pie chart shows the result of the survey
Car 30%
Cycle 25%
Walk 10%
Bus ?

What are the number of students that travel to school by bus

Answers

Answer:

42

Step-by-step explanation:

30+25+10=65%

bus=35%

35/100×120=42

BUS=42

car- 30/100 x120
= 36 students

cycle- 25/100 x 120
= 30 students

Walk- 10/100 x 120
=12 students

Bus- 120-36-30-12= 42 students

a rectangular postage stamp has a length of 3/2 inches and a width of 3/4 inch. what is the area of the stamp in square inches?

Answers

Answer:

9/8 or 1.125

Step-by-step explanation:

We want to find the area of a rectangular postage stamp

The area of a rectangle can be found by multiplying the length by the width

Given length: 3/2

Given width: 3/4

Area = 3/2 * 3/4 = 9/8 or 1.125

The area of a 2D form is the amount of space within its perimeter. The area of the stamp in square inches is 1 1/8 inches².

What is an area?

The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm², m², and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.

Given that a rectangular postage stamp has a length of 3/2 inches and a width of 3/4 inch. Therefore, the area of the stamp in square inches is,

Area of the stamp = Length × Width

                              = 3/2 inches × 3/4 inches

                              = 9/8 inches²

                              = 1 1/8 inches²

Hence, the area of the stamp in square inches is 1 1/8 inches².

Learn more about the Area here:

https://brainly.com/question/1631786

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100 POINTS AND BRAINLIEST FOR THIS WHOLE SEGMENT

a) Find zw, Write your answer in both polar form with ∈ [0, 2pi] and in complex form.

b) Find z^10. Write your answer in both polar form with ∈ [0, 2pi] and in complex form.

c) Find z/w. Write your answer in both polar form with ∈ [0, 2pi] and in complex form.

d) Find the three cube roots of z in complex form. Give answers correct to 4 decimal

places.

Answers

Answer:

See Below (Boxed Solutions).

Step-by-step explanation:

We are given the two complex numbers:

[tex]\displaystyle z = \sqrt{3} - i\text{ and } w = 6\left(\cos \frac{5\pi}{12} + i\sin \frac{5\pi}{12}\right)[/tex]

First, convert z to polar form. Recall that polar form of a complex number is:

[tex]z=r\left(\cos \theta + i\sin\theta\right)[/tex]

We will first find its modulus r, which is given by:

[tex]\displaystyle r = |z| = \sqrt{a^2+b^2}[/tex]

In this case, a = √3 and b = -1. Thus, the modulus is:

[tex]r = \sqrt{(\sqrt{3})^2 + (-1)^2} = 2[/tex]

Next, find the argument θ in [0, 2π). Recall that:

[tex]\displaystyle \tan \theta = \frac{b}{a}[/tex]

Therefore:

[tex]\displaystyle \theta = \arctan\frac{(-1)}{\sqrt{3}}[/tex]

Evaluate:

[tex]\displaystyle \theta = -\frac{\pi}{6}[/tex]

Since z must be in QIV, using reference angles, the argument will be:

[tex]\displaystyle \theta = \frac{11\pi}{6}[/tex]

Therefore, z in polar form is:

[tex]\displaystyle z=2\left(\cos \frac{11\pi}{6} + i \sin \frac{11\pi}{6}\right)[/tex]

Part A)

Recall that when multiplying two complex numbers z and w:

[tex]zw=r_1\cdot r_2 \left(\cos (\theta _1 + \theta _2) + i\sin(\theta_1 + \theta_2)\right)[/tex]

Therefore:

[tex]\displaystyle zw = (2)(6)\left(\cos\left(\frac{11\pi}{6} + \frac{5\pi}{12}\right) + i\sin\left(\frac{11\pi}{6} + \frac{5\pi}{12}\right)\right)[/tex]

Simplify. Hence, our polar form is:

[tex]\displaystyle\boxed{zw = 12\left(\cos\frac{9\pi}{4} + i\sin \frac{9\pi}{4}\right)}[/tex]

To find the complex form, evaluate:

[tex]\displaystyle zw = 12\cos \frac{9\pi}{4} + i\left(12\sin \frac{9\pi}{4}\right) =\boxed{ 6\sqrt{2} + 6i\sqrt{2}}[/tex]

Part B)

Recall that when raising a complex number to an exponent n:

[tex]\displaystyle z^n = r^n\left(\cos (n\cdot \theta) + i\sin (n\cdot \theta)\right)[/tex]

Therefore:

[tex]\displaystyle z^{10} = r^{10} \left(\cos (10\theta) + i\sin (10\theta)\right)[/tex]

Substitute:

[tex]\displaystyle z^{10} = (2)^{10} \left(\cos \left(10\left(\frac{11\pi}{6}\right)\right) + i\sin \left(10\left(\frac{11\pi}{6}\right)\right)\right)[/tex]

Simplify:

[tex]\displaystyle z^{10} = 1024\left(\cos\frac{55\pi}{3}+i\sin \frac{55\pi}{3}\right)[/tex]

Simplify using coterminal angles. Thus, the polar form is:

[tex]\displaystyle \boxed{z^{10} = 1024\left(\cos \frac{\pi}{3} + i\sin \frac{\pi}{3}\right)}[/tex]

And the complex form is:

[tex]\displaystyle z^{10} = 1024\cos \frac{\pi}{3} + i\left(1024\sin \frac{\pi}{3}\right) = \boxed{512+512i\sqrt{3}}[/tex]

Part C)

Recall that:

[tex]\displaystyle \frac{z}{w} = \frac{r_1}{r_2} \left(\cos (\theta_1-\theta_2)+i\sin(\theta_1-\theta_2)\right)[/tex]

Therefore:

[tex]\displaystyle \frac{z}{w} = \frac{(2)}{(6)}\left(\cos \left(\frac{11\pi}{6} - \frac{5\pi}{12}\right) + i \sin \left(\frac{11\pi}{6} - \frac{5\pi}{12}\right)\right)[/tex]

Simplify. Hence, our polar form is:

[tex]\displaystyle\boxed{ \frac{z}{w} = \frac{1}{3} \left(\cos \frac{17\pi}{12} + i \sin \frac{17\pi}{12}\right)}[/tex]

And the complex form is:

[tex]\displaystyle \begin{aligned} \frac{z}{w} &= \frac{1}{3} \cos\frac{5\pi}{12} + i \left(\frac{1}{3} \sin \frac{5\pi}{12}\right)\right)\\ \\ &=\frac{1}{3}\left(\frac{\sqrt{2}-\sqrt{6}}{4}\right) + i\left(\frac{1}{3}\left(- \frac{\sqrt{6} + \sqrt{2}}{4}\right)\right) \\ \\ &= \boxed{\frac{\sqrt{2} - \sqrt{6}}{12} -\frac{\sqrt{6}+\sqrt{2}}{12}i}\end{aligned}[/tex]

Part D)

Let a be a cube root of z. Then by definition:

[tex]\displaystyle a^3 = z = 2\left(\cos \frac{11\pi}{6} + i\sin \frac{11\pi}{6}\right)[/tex]

From the property in Part B, we know that:

[tex]\displaystyle a^3 = r^3\left(\cos (3\theta) + i\sin(3\theta)\right)[/tex]

Therefore:

[tex]\displaystyle r^3\left(\cos (3\theta) + i\sin (3\theta)\right) = 2\left(\cos \frac{11\pi}{6} + i\sin \frac{11\pi}{6}\right)[/tex]

If two complex numbers are equal, their modulus and arguments must be equivalent. Thus:

[tex]\displaystyle r^3 = 2\text{ and } 3\theta = \frac{11\pi}{6}[/tex]

The first equation can be easily solved:

[tex]r=\sqrt[3]{2}[/tex]

For the second equation, 3θ must equal 11π/6 and any other rotation. In other words:

[tex]\displaystyle 3\theta = \frac{11\pi}{6} + 2\pi n\text{ where } n\in \mathbb{Z}[/tex]

Solve for the argument:

[tex]\displaystyle \theta = \frac{11\pi}{18} + \frac{2n\pi}{3} \text{ where } n \in \mathbb{Z}[/tex]

There are three distinct solutions within [0, 2π):

[tex]\displaystyle \theta = \frac{11\pi}{18} , \frac{23\pi}{18}\text{ and } \frac{35\pi}{18}[/tex]

Hence, the three roots are:

[tex]\displaystyle a_1 = \sqrt[3]{2} \left(\cos\frac{11\pi}{18}+ \sin \frac{11\pi}{18}\right) \\ \\ \\ a_2 = \sqrt[3]{2} \left(\cos \frac{23\pi}{18} + i\sin\frac{23\pi}{18}\right) \\ \\ \\ a_3 = \sqrt[3]{2} \left(\cos \frac{35\pi}{18} + i\sin \frac{35\pi}{18}\right)[/tex]

Or, approximately:

[tex]\displaystyle\boxed{ a _ 1\approx -0.4309 + 1.1839i,} \\ \\ \boxed{a_2 \approx -0.8099-0.9652i,} \\ \\ \boxed{a_3\approx 1.2408-0.2188i}[/tex]

A child is picking 3 days of the 7 days of the week to have Jello for lunch. What is the size of the sample space in this experiment?

Answers

4 feet of space to figure this out

On two investments totaling $9,500, Peter lost 3% on one and earned 7% on the other. If his net annual receipts were $169, how much was each investment?

Answers

Answer:

23$ was each investment

Step-by-step explanation:

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

by selling an article sonu makes a profit of 20%. if the cp decreased by 10% and sp also increased by 10%,calculate her profit percentage​

Answers

Answer:

37.8 %

Step-by-step explanation:

Let CP = 100

[tex]SP =\frac{100+profit}{100}*CP\\\\=\frac{120}{100}*100[/tex]

SP = 120

New CP:

CP decreased by 10%

 [tex]Decreased \ amount=\frac{10}{100}*CP\\\\=\frac{10}{100}*100[/tex]

 = 10

New CP = 100- 10 = 90

New SP:

SP increased by 10%

Increase amount = [tex]\frac{10}{100}*old \ SP[/tex]

                            [tex]= \frac{10}{100}*120\\\\= 12[/tex]

New SP = 120 + 12 = 132

Profit = new SP - new CP

         = 132 - 90 = 42

Profit percentage = [tex]\frac{Profit}{CP}*100[/tex]

                             [tex]= \frac{42}{90}*100\\[/tex]

                             = 46.67%

Step-by-step explanation:

Here your ans..

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Answers

ANS=40

hope this help you

bye have a great day :)

180-55=25
the interior angle of triangle is 180
so 180-115-25= 40
the answer is 40
give me brainliest if you can thank u!:)

Ray is making his reward winning lemonade recipe for a party he is comparison shopping for lemons at super pioneer supermarket he can buy 4 lemons for 1.60 ray visits keyfood and found 3 lemons cost 1.80 use the table below to compare the values

Answers

Answer:

classified info jk juss use a mf calculater

Step-by-step explanation:

Solve for x.

6(4x+2)= 3(8x+4)

Answers

Answer:

x = 1

Step-by-step explanation:

6(4x + 2) = 3(8x + 4)

24x + 12 = 24x + 12

x = 1
x = 1

6(4x+2) = 3(8x+4)
24x + 12 = 24x + 12
-12 -12
24x = 24x
-24 -24
x = x

Pls help it’s due in the morning ;(

Answers

9:-

(3,3)(-4,1)

[tex]\\ \sf\longmapsto m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

[tex]\\ \sf\longmapsto m=\dfrac{1-3}{-4-3}[/tex]

[tex]\\ \sf\longmapsto m=\dfrac{-2}{-7}[/tex]

[tex]\\ \sf\longmapsto m=\dfrac{2}{7}[/tex]

10:-

Points are (-7,6),(11,-4)

[tex]\boxed{\sf slope(m)=\dfrac{y_2-y_1}{x_2-x_1}}[/tex]

[tex]\\ \sf\longmapsto m=\dfrac{-4-6}{11+7}[/tex]

[tex]\\ \sf\longmapsto m=\dfrac{-10}{18}[/tex]

[tex]\\ \sf\longmapsto m=-\dfrac{5}{9}[/tex]

Answer:

Step-by-step explanation:

Slope = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

9) Mark any two point on the line

(x₁ , y₁) = (3 , 3)   ;   (x₂, y₂) = (-4 ,1)

[tex]Slope =\frac{1-3}{-4-3}\\\\=\frac{-2}{-7}\\\\=\frac{2}{7}[/tex]

10) (x₁ , y₁) = ( -7 , 6)   ;   (x₂, y₂) = (11 ,-4)

[tex]Slope =\frac{-4-6}{11-[-7]}\\\\ =\frac{-4-6}{11+7}\\\\=\frac{-10}{18}\\\\=\frac{-5}{9}[/tex]

what expression represents 19 more than 6 times a number, n
1. 19n+6
2. 6n-19
3.6n+19
4.19n-6

Answers

Answer:

6n+19

Step-by-step explanation:

6 times a number, n

6n

19 more

6n+19

Answer:

6n + 19

Step-by-step explanation:

Since the expression is 6 times n

We need to have 6 x n or simply just 6n

Since the expression is 19 more than 6n

We need to have 6n + 19

Find the equation of the linear function represented by the table below in slope-intercept form.

Answers

Answer:

y = 3x+1

Step-by-step explanation:

First find the slope

m = ( y2-y1)/(x2-x1)

    = (13-4)/(4-1)

    = 9/3

   = 3

Slope intercept form is

y = mx+b where m is the slope and b is the y intercept

y = 3x+b

Using a point from the table

10 = 3(3)+b

10 =9+b

10-9 =b

1=b

y = 3x+1

find the measure of the indicated angle to the nearest degree​

Answers

Answer:

43

Step-by-step explanation:

First you divide the opposite side from the angle by the hypotenuse.

33/44

then you take the inverse sine of 33/44, resulting in

43.43°, which rounds to 43°

Pls i need help
The continuous growth rate of wind energy per year is ?%

Answers

Answer:

Do you need it in percentage, a graph or just normal annual calculation?

Select the correct answer from each drop-down menu.
A company makes cylindrical vases. The capacity, in cubic centimeters, of a cylindrical vase the company produces is given by the
function C() = 6.2873 + 28.26x2, where x is the radius, in centimeters. The area of the circular base of a vase, in square
centimeters, is given by the function A () = 3.14.2
To find the height of the vase, divide
represents the height of the vase.
the expressions modeling functions C(x) and A(z). The expression

Answers

Answer:

divide, 2x+9

Step-by-step explanation:

got it right

help help help

help
help help

Answers

Answer:

R= (-9, -10) S=(-1,-10) T=(-1, -8) U=(-9, -8)

Step-by-step explanation:

There isn't really an explanation it's just reading the points on the graph. Hope this helps!! :)

s the function represented by the table non-linear?

x
y
6
4
7
2
8
0
9
–2

Answers

All personnel decisions require the approval of the union, _______ the company slow to respond to market changes.

Select one:
A. making
B. will make
C. makes
D. made

help pleasseeeeeeeee

Answers

Answer:

-1

Step-by-step explanation:

I know that i^4 = 1

i^10 = i^4 * i^4 * i^2

     = 1 * 1 * i^2

We know that i^2 = -1

    =1 *1 *-1

    = -1

PLEASE HELP Find the value of the following expression (2 ^8 • 3 ^-5 • 6 ^0) ^-2 • (3 ^-2 over 2 ^3 ) ^4 •2 ^28

Answers

the answer is very simple if you don't understand ask to your teacher

can someone explain step by step how to get the answer?

Answers

Answer: x³+8x²+11x-20

Step-by-step explanation:

To find which polynomial has the roots of -5, -4, and 1, we want to first put them into an equation.

-5 is the same as x+5=0

-4 is the same as x+4=0

1 is the same as x-1=0

Now that we have the factors, we can multiply them together.

(x+5)(x+4)(x-1)                  [FOIL]

(x²+4x+5x+20)(x-1)          [combine like terms]

(x²+9x+20)(x-1)                 [FOIL]

x³-x²+9x²-9x+20x-20       [combine like terms]

x³+8x²+11x-20

Therefore, x³+8x²+11x-20 is the correct polynomial with those roots.

help me pls??????? :)

Answers

Answer:4 in each bad 2 left over

Step-by-step explanation:

Answer:

4 in each bag and 2 left over

Step-by-step explanation:

divide 14 by 3

3 goes into 14, 4 times

14 - 12 = 2

4 in each bag and then 2 left over

What is (9.3x10^34)
(3.1x10^17) in scientific notation?​

Answers

Answer:

3x10^17

Step-by-step explanation:

(9.3/3.1) * 10^(34-17) = 3^17

law of indices, x^m/x^n =x^m-n

a. linear pair
b. vertical angles
c. complementary angles d. supplementary

Answers

Answer:

b. vertical angles

Step-by-step explanation:

<2 and <5 are vertical angles

They are formed by the same lines, are opposite each other and share a vertex.  Vertical angles are equal

YA'LL PLEASE PLEASE PLEASE PLEASE PLEASE HELP MEEEEE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Find the equation of the line passing through (1, 5) and parallel to y = 3x – 1.

please show how you got it so I can see if the answer makes sense!!!!

Answers

Answer: y= 3x+2

Step-by-step explanation:

because....

The slope-intercept form is y= mx +b, where m is the slope and b is the y-intercept.Use the slope 3 and a given point (1,5) to substitute for  and  in the point-slope form .

y-(5)= 3*(x-(1))

After simplifying it,

the equation is going to be y= 3x+2.

* Hopefully this helps:) Mark me the branliest!

The ratio of Mitchell's age to Connor's age is 8:5. In thirty years, the ratio of their ages will be 6:5. How much older is Mitchell than Connor now?

Answers

Answer:

9 years older

Step-by-step explanation:

The ratio of their ages is 8 : 5 = 8x : 5x ( x is a multiplier )

In 30 years their ages will be 8x + 30 and 5x + 30 and the ratio 6 : 5 , so

[tex]\frac{8x+30}{5x+30}[/tex] = [tex]\frac{6}{5}[/tex] ( cross- multiply )

5(8x + 30) = 6(5x + 30) ← distribute parenthesis on both sides

40x + 150 = 30x + 180 ( subtract 30x from both sides )

10x + 150 = 180 ( subtract 150 from both sides )

10x = 30 ( divide both sides by 10 )

x = 3

Then

Michell is 8x = 8 × 3 = 24 years old

Connor is 5x = 5 × 3 = 15 years old

Mitchell is 24 - 15 = 9 years older than Connor

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