Instructions: Use the ratio of a 30-60-90 triangle to solve for the variables. Leave your
answers as radicals in simplest form.

Answer:

there is not a complete question here ...

[tex]\sqrt{2} +1[/tex] is not in a denominator to rationalize

if it were you would multiply the rational expression (the fraction)

by [tex]\frac{\sqrt{2} -1}{\sqrt{2} -1}[/tex] the result (in the denominator would end up being "2 -1"

which is 1

Step-by-step explanation:

Answer:

The height of the tomato soup can is 2.6 in.

Step-by-step explanation:

"The can of chicken noodle soup has a height of 4 inches and a radius of 2 inches."

We can find the volume of this can.

V = pi r² h

V = 3.14 * (2 in.)² * (4 in.)

V = 50.24 in.³

"The can of tomato soup has the same volume, but a radius of 2.5 inches."

Now we know the volume of the can, so we can find the height, h.

V = pi r² h

50.24 in.³ = 3.14 * (2.5 in.)² * h

50.24 in.³ = 19.625 in.² * h

h = (50.24 in.³)/(19.625 in.²)

h = 2.56 in.

Answer: The height of the tomato soup can is 2.6 in.

Answer:

:Volume of can of chicken noodle soup=50.24inch^3

:Height of can of tomato soup=2.56inches

Step-by-step explanation:

CHICKEN NOODLE SOUP :height=4inches

:radius=2inches

[ V=πr2h]

V=(3.14×2×2×4)=50.14

Now, Volume is same of both the can.

Volume of can of tomato soup=50.24;radius=2.5inches;

Height of can of tomato soup,

50.24=(3.14×2.5×2.5×h)

50.24=19.625h

h=50.24/19.625

=2.56inches

Step-by-step explanation:

8²+10²= x²

64+100 =x²

164=x²

√164=√x²

square and squre root do cancel each other

x=√164

hope this helps

Answer:

x = [tex]\sqrt{164[/tex]

Step-by-step explanation:

In order to find the hypotenuse of a right triangle, you have to add,

[tex]8^{2} + 10^{2}[/tex]

which simplifies to,

64 + 100 =

[tex]\sqrt164[/tex]

Hope this helps! :)

Answer:

Step-by-step explanation:

from the picture:

QP = QR

and

QR = RS

so

PQ + RS = QS

Answer:  True

Explanation:

Consider a 3D cardboard box that you can unfold. It would unfold into a 2D net that you can then re-fold back into its 3D form. The 2D net is useful to help visualize and calculate the surface area. The surface area is simply the total area of all the external faces.

Answer:

Square root of 100.  

Step-by-step explanation:

Step-by-step explanation:

We can write 10 as a fraction 10/1, therefore,[tex]\sqrt{}[/tex]100   is a rational number.

Part A : A rational no. between 5.2 and 5.5 is 5.3.  

It is rational because it can be expressed in the form  

p/q where p and q are integers and q is not equal to 0, which is 53/10

Part B: A rational no. between 5.2 and 5.5 is 5.29150262213

An irrational number between 5.2 and 5.5 is 5.29150262213. It is irrational because there is no pattern that repeats and it cant be written as a fraction of two whole numbers.

Answer:

Step-by-step explanation:

Square root of all prime numbers is irrational.

97 is an prime number. So √97 is an irrational number.

√98 = [tex]\sqrt{2*7*7}=7\sqrt{2}[/tex]  is an irrational number.

[tex]\sqrt{99}=\sqrt{3*3*11} =3\sqrt{11}[/tex] is an irrational number

√100 = 10 is a rational number.

Part A:

5.3 is a rational number.

Rational can be written in p/q form and when divided the result will either terminating decimal or non terminating repeating decimal

Part B:

5.3020050......

Irrational numbers are non terminating non repeating numbers

Perhaps you know that

[tex]S_2 = \displaystyle\sum_{k=1}^n k^2 = \frac{n(n+1)(2n+1)}6[/tex]

and

[tex]S_3 = \displaystyle\sum_{k=1}^n k^3 = \frac{n^2(n+1)^2}4[/tex]

Then the problem is trivial, since

[tex]\displaystyle\sum_{k=1}^n k^2(k+1) = S_2 + S_3 \\\\ = \frac{2n(n+1)(2n+1)+3n^2(n+1)^2}{12} \\\\ = \frac{n(n+1)\big((2(2n+1)+3n(n+1)\big)}{12} \\\\ = \frac{n(n+1)\big(4n+2+3n^2+3n\big)}{12} \\\\ = \frac{n(n+1)(3n^2+7n+2)}{12} \\\\ = \frac{n(n+1)(3n+1)(n+2)}{12}[/tex]

Then

[tex]12\bigg(1^2\cdot2+2^2\cdot3+3^2\cdot4+\cdots+n^2(n+1)\bigg) = n(n+1)(n+2)(3n+1)[/tex]

so that a = 3 and b = 1.

The only 2-digit number that is lesser than 50 and the sum of its digits remain unaffected despite being multiplied by a number < 1 would be '18.'

To prove, we will look at some situations:

If we add up the two digits of 18. We get,

[tex]1 + 8 = 9[/tex]

And we multiply 18 by 2 which is greater than 1. We get,

[tex]18[/tex] × [tex]2 = 36[/tex]

The sum remains the same i.e. [tex]3 + 6 = 9[/tex]

Similarly,

If 18 is multiplied to 3(greater than 1), the sum of the two digits comprising the number still remains the same;

[tex]18[/tex] × [tex]3 = 54[/tex]

where (5 + 4 = 9)

Once more,

Even if 18 is multiplied to 4 or 5(greater than 1), the sum of its digits will still be 9.

 [tex]18[/tex] × [tex]4 = 72[/tex]

[tex](7 + 2 = 9)[/tex]

[tex]18[/tex] × [tex]5 = 90[/tex]

[tex](9 + 0 = 9)[/tex]

Thus, 18 is the answer.

Learn more about 'numbers' here: brainly.com/question/1624562

Answer:

40%

Step-by-step explanation:

Percent is out of 100

2/5 * 20/20

40/100

40%

Answer:

Step-by-step explanation:

Divide 2 by 5 to get the decimal .4. Multiply that by 100 to get the percent:

40%, choice d.

Answer:

t=-2

Step-by-step explanation:

Solve Exponent.

5t=0.04

log(5t)=log(0.04)(Take log of both sides)

t*(log(5))=log(0.04)

t=log(0.04)÷log (5)

t=−2

Answer:

52

Step-by-step explanation:

The minimum of the data set is the smallest number. Therefore, the minimum is 52.

Answer: The father is 36 right now and the son is 4

Step-by-step explanation: 9x4 is 36 and 36/9=4.

Answer:

15u = 135

Divide both sides by 15

u = 135/15 = 9

U is equal to 9

Hope this helps!

[tex]15 \times 4 = 135 \\ divide \: both \: sides \: of \: equcation \\ by \: 15 \\ \frac{15u}{15} = \frac{135}{15} \\ u = \frac{135}{15} \\ u = 9[/tex]

The line was reflected about the line y = -x.

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

This question is solved using reflection concepts.

There are various kinds of reflections, 90º clockwise about the origin, 90º counterclockwise, among other, and each of them has a rule.

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

In this question:

From this, we have the following rule: (x,y) -> (-y,-x)

Checking the rules, it can be said that the line was reflected about the line y = -x.

A similar question can be found at https://brainly.com/question/16130908

Answer:

Step-by-step explanation

- 7(6x-1)+x=36

- 11-2(8+3p)=7²

-  1/4(5b+11)=19

- 2/7(4m-18)=12

Answer:

156m^2

Step-by-step explanation:

I dont know what you mean by "each figure," but if you need the surface area for the rectangular prism, then the answer is 156, because the top square has a surface area of 3*6, then it equals 18, and the bottom square is the same, so it is also 18, 18*2=36

The 4 rectangle on the side are all the same, and they are all 10x3 which is 30, so 30*4 because there are 4 rectangles, equals 120.

120+36=156. The surface area of the rectangle is 156m^2

Answer:

1/2

Step-by-step explanation:

Given:

(2 cubed) (2 superscript negative 4)

= (2³)(2^-4)

= (2³) (1 / 2⁴)

= (2³ * 1) / 2⁴

= 2³ / 2⁴

Both numerator and denominator has the same base. Thus, pick one of the bases

Also, in indices, division sign can be translated to subtraction

Therefore,

2³ / 2⁴

= 2^3-4

= 2^-1

= 1/2¹

= 1/2

(2³)(2^-4) = 1/2

Answer:

D

Step-by-step explanation:

bc i said so

Answer:

y^ -2

Step-by-step explanation:

We know that a^b^c = a^(b*c)

(y^-1/2)^4

y^(-1/2*4)

y^ -2

Answer:

Step-by-step explanation:

Answer:

20 days

Step-by-step explanation:

10kg= 10,000g

10,000g/500g= 20 days

Answer:

20 days

Step-by-step explanation:

1 kg=1000 grams

10 kg=10000 grams

10000÷500

=20 days

Answer:

Step-by-step explanation:

Answer:

B is the answer

Step-by-step explanation:

Answer:

The length of PQ is 24

Step-by-step explanation:

If you flip triangle PQR upside down the you can see which side corresponds to which. BC corresponds to QR and AB with PQ, the scalar is 6 because of BC (2) times 6 = QR (12). So you just have to do 4 times 6 which is 24.

Answer: 7.5 x 10^3 is the answer.

Step-by-step explanation: First, 7.5 x 10^9 is 7500000000. Next, if you convert it to kilometers you would get 7500. And, 7.5 x 10^3 = 7500. Thus, that is the answer.

Answer:

5 meters tall.

Step-by-step explanation:

We know that angle A (the bird) is 55. The opposite side from this angle is 4.5 meters, since that is the distance she is from the tree. From this, we can set up an equation tan(55)=4.5/x and simplify it to x= 4.5/tan(55). This would be height x, but it is not accounting for the 1.5 meters the apple is off the ground, so you need to add 1.5 to the result. The final answer would be 4.65 but you need to round to the nearest meter so it would be 5.

Answer:

A

Step-by-step explanation:

Cuz that’s the only graph that goes with the statement.

on this graph it’s saying the cost of 3 hair accessories is $10.

X = 3

Y = 10

Answer:

93°, 89°, 93°

Step-by-step explanation:

∠1 and ∠4 are supplementary angles:

m∠1 + m∠4 = 180°; m∠1 = 93°

∠2 and ∠4 are vertical angles:

m∠2 = m∠4 = 87°

∠3 and ∠4 are supplementary angles:

m∠3 + m∠4 = 180°; m∠3 = 93°

Answer:

33x+22

Step-by-step explanation:

The area of a rectangle is

A = l*w where l is the length and w is the width

A = 11(3x+2)

Distribute

   = 33x+22

Area of rectangle = Length * Width

⇛Area = 11(3x+2)

⇛Area = 33x + 22

Answer:

Approximately 17

Step-by-step explanation:

Number of starts getting hidden in 9 hours = 190 - 33

= 157

Therefore the nun of starts getting hidden in 9 hours is 157

9 hours = 157 stars

1 hours = x

Cross multiply

9 × x = 157 × 1

9x = 157

Divide both sides by 9

x = 157 ÷ 9

x = 17.4

Therefore 17.4 stars are getting hidden every hour.

Answer:

17 4/9 stars per hour

Step-by-step explanation:

First find the decrease in the number of stars

190-33 = 157

Divide by the hours that passed

157/9

17 4/9 stars per hour