Find the length of the arc.
120°
6ft

The expression [tex](\frac{x^a}{x^b})^{a + b} \cdot (x^{b + c})^{b - c} \cdot (x^{c + a})^{c - a}[/tex] is an algebraic expression, and the result of simplifying the expression [tex](\frac{x^a}{x^b})^{a + b} \cdot (x^{b + c})^{b - c} \cdot (x^{c + a})^{c - a}[/tex] is 1

The expression is given as:

[tex](\frac{x^a}{x^b})^{a + b} \cdot (x^{b + c})^{b - c} \cdot (x^{c + a})^{c - a}[/tex]

Apply the power rule of indices

[tex](x^{a-b})^{a + b} \cdot (x^{b + c})^{b - c} \cdot (x^{c + a})^{c - a}[/tex]

Expand the exponents of the expression

[tex]x^{a^2-b^2} \cdot x^{b^2 - c^2} \cdot x^{c^2 - a^2[/tex]

Apply the product rule of indices

[tex]x^{a^2-b^2+b^2 - c^2+c^2 - a^2[/tex]

Collect like terms

[tex]x^{a^2- a^2-b^2+b^2 - c^2+c^2[/tex]

Evaluate the differences

[tex]x^{0-0 - 0[/tex]

This gives

[tex]x^{0[/tex]

Evaluate the exponent

1

Hence, the result of simplifying the expression [tex](\frac{x^a}{x^b})^{a + b} \cdot (x^{b + c})^{b - c} \cdot (x^{c + a})^{c - a}[/tex] is 1

Read more about simplifying expressions at:

https://brainly.com/question/723406

1) There are 90 + 74 people who are "at least 175 cm tall" (164 ppl)

2) probability is 164/250 = 0.656

D. 0.656

Step-by-step explanation:

[tex]2(5 + 5) + 3(2 + 3)[/tex]

[tex]2(10) + 3(5)[/tex]

[tex]20 + 15[/tex]

[tex]35[/tex]

Answer:

B. seconds

Step-by-step explanation:

We have d=rt

means that t= [tex]\frac{d}{r}[/tex]

Given the units of each:

d: feet

r: feet/second

Replace each with its unit:

 t=    [tex]\frac{feet}{\frac{feet}{second} }[/tex]   =  [tex]\frac{feet.second}{feet}[/tex]  = second

So the unit of t is seconds (option B.)

Answer:

Step-by-step explanation:

Given

To Find :

Solving :

Answer:

994

Step-by-step explanation:

8+t(3) - 6 = 1000-6= 994

Answer:

-2x + 10

Step-by-step explanation:

3 - x + 4 - (x - 3)

1. Combine like terms:

-x + 7 - (x - 3)

2. Apply the distributive law - (a - b) = -a + b :

-x + 7 -x + 3

3. Combine like terms:

-2x + 10

hope this helps!

Answer: 64

Step-by-step explanation:

Answer:

  C and D

Step-by-step explanation:

Population density is the ratio of population to area. Its units are persons per square mile. Here, you're being asked to compare the population densities of several countries to the average population density in several US states.

__

The idea of "average population density of the 10 states listed" is somewhat ambiguous. It could mean either of (a) the ratio of the total of the states' population to the total of their land area, or (b) the average of the population densities of the states. (In the attached, we computed both, but the answer remains the same using either number.)

When there are numerous identical calculations to be performed, it is convenient to let a spreadsheet do them. The attached spreadsheet shows the population densities for the 10 states and 5 countries listed.

Depending on how you define it, the average population density of the 10 states is about 10.5 or about 15.7 people per square mile. (15.7 is the average of the density numbers, found using the spreadsheet AVERAGE function.)

__

The 5 countries have population densities ranging from about 7.7 to 236 people per square mile. Two of the countries have density below 10.5, so are the answers to the question asked.

  Canada (C) and Iceland (D) have population density below the US state average.

Answer:

like 30% cause there are more red grapes then green

Step-by-step explanation:

I'm not sure cause I don't see any answer choices

Answer:

A I think

Step-by-step explanation:

Answer: y = -2x + 1

Step-by-step explanation:

The formula for slope-intercept form is y = mx + b. Keep y and x as the variables. Replace m with the slope, which can be found by doing rise/run, and replace b with the y-intercept. The y-intercept is the spot where the line intersects the y-axis.

Hope this helps! Have a great day! :)

Answer:

6.75 kg

Step-by-step explanation:

6/8 = 0.75

0.75 x 9 = 6.75

Answer:

6 3/4 kg

Step-by-step explanation:

9 x 6/8 = 6 3/4

Answer:

$57

Step-by-step explanation:

I'm not a good person explaining answers, so I will just give the equation.

[2(5+8.25+10.50)+ 23.75) x 4]  ÷ 5

Hope this helps :)

The shape with a rotational symmetry would remain the same when rotated

The shape with the smallest angle of rotational symmetry of 180 degrees is shape D

To do this, we simply examine each of the options

Shape A: Cross

The shape has 4 equal sides.

So, the smallest angle of rotational symmetry is:

Angle = 360/4

Angle = 90

The smallest angle of rotational symmetry is 90 degrees

Shape B: Star

The shape has 5 vertices.

So, the smallest angle of rotational symmetry is:

Angle = 360/5

Angle = 72

The smallest angle of rotational symmetry is 72 degrees

Shape C: Composite figure

This shape has a square and a triangle merged together at two ends

This means that the smallest angle of rotational symmetry is a complete rotation of 360 degrees

Shape D: Circle

The circle is divided into two equal segments.

The angle on the straight line of each segment is:

Angle = 360/2

Angle = 180

The smallest angle of rotational symmetry is 180 degrees

Hence, the shape with the smallest angle of rotational symmetry of 180 degrees is shape D

Read more about rotational symmetry at:

https://brainly.com/question/12214455

Answer:

B Infinite Solutions

Step-by-step explanation:

3 (x - 8) = 3x - 24

3x - 24 = 3x - 24

    + 24        + 24

3x = 3x

x = x

Infinite solutions

Answer:

28.2°

Step-by-step explanation:

formula for an included angle (law of cosines)

[tex] - \cos( \frac{ {a }^{2} + {b}^{2} - {c}^{2} }{2ab} )[/tex]

(the variables change depending on the question, this one is switched, for example...it is actually b squared+ c squared - a squared over 2(bc) in this case)

after you plug it all in, you get cos⁻¹(0.88125), and an answer to the nearest tenth of 28.2

If you found this answer helpful, I would greatly appreciate brainliest :D.

Answer:

Answer is 7.

Step-by-step explanation:

(a + 2)^4- 20(a + 2)^2+ 64 = 0

2a^4- 20(2a)^2+ 64 = 0

16a-20(4a)+64=0  

-4a    -64  -4a          -64

12a-84=0

    +84 +84

12a=84

84/12=7

Answer:

A) 30

B) 2h 23m

C) 13-17

D) 70 MPH

Step-by-step explanation:
D) It is a safe speed for people to go

The triangle ABC are not similar because angle E is not equal to angle B

Similar triangles have the same corresponding angle measures and proportional side lengths.

This means that similar triangles have corresponding equal angles.

And also the ratio of the corresponding sides of Similar triangles are equal.

Since angle ACB = angle DCE

angle B = 180-( 38+94)

= 180- 132

= 48°

angle D = 180-( 94+15)

= 180-109

= 71°

Therefore;

angle A is not equal to angle D and angle B is not equal to angle E, We can therefore say that triangles ABC is not similar to triangle DEC

learn more about similar triangles from

https://brainly.com/question/14285697

#SPJ1

Answer:

1000a

Step-by-step explanation:

[tex] 10^3 \times a = 10 \times 10 \times 10 \times a = 1000 \times a = 1000a [/tex]

ans = 20.85

hope it helps...!!!

Answer:

The volume is 30 cubic inches

Step-by-step explanation:

If it helped mark brainliest :)

Answer:

I would I don't know cause I am only in six grade

Step-by-step explanation:

Where do you want to go from here?

What do you want to accomplish?

What obstacles will you have to overcome?

What problems will you have to solve?

What additional knowledge, skills, or resources will you require to achieve your strategic objectives?

The required Strategic planning answers the question "Where do we want to go and how do we get there?"

Strategic planning is the process of defining an organization's vision, mission, values, goals, and objectives, and developing a roadmap to achieve them.

Here,

"Where do we want to go and how do we get there?"

Strategic planning is the process of defining an organization's vision, mission, values, goals, and objectives, and developing a roadmap to achieve them. It involves assessing an organization's current situation, identifying strengths, weaknesses, opportunities, and threats, and developing strategies to leverage strengths, address weaknesses, seize opportunities, and mitigate threats.

The end result is a plan that sets the direction for the organization and guides decision-making and resources allocation to achieve its goals and objectives.

Learn more about Strategic planning here:
https://brainly.com/question/30562644
#SPJ2

Answer:

[B] [tex]\begin{bmatrix}x+2y=-6\\ y+2z=-6\\ x-y-z=2\end{bmatrix}[/tex]

Step-by-step explanation:

Going through all answer choice to find the solution:

[A]  [tex]\begin{bmatrix}x+y=0\\ y-z=-2\\ x+y-z=-4\end{bmatrix}[/tex]

[tex]\mathrm{Isolate\;x\;for\;x+y=0;x=-y}[/tex]

[tex]\mathrm{Substitute\:}x=-y[/tex]

[tex]\begin{bmatrix}y-z=-2\\ -y+y-z=-4\end{bmatrix}[/tex]

[tex]\mathrm{Simplify}[/tex]

[tex]\begin{bmatrix}y-z=-2\\ -z=-4\end{bmatrix}[/tex]

[tex]\mathrm{Isolate\;z\;for\;-z=-4;z=4}[/tex]

[tex]\mathrm{Substitute\:}z=4[/tex]

[tex]\begin{bmatrix}y-4=-2\end{bmatrix}[/tex]

[tex]\mathrm{Isolate\;y\;for\;y-4=-2;y=2}[/tex]

[tex]\mathrm{For\:}x=-y[/tex]

[tex]\mathrm{Substitute\:}z=4,\:y=2[/tex]

[tex]x=-2[/tex]

[tex]\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}[/tex]

[tex]x=-2,\:z=4,\:y=2[/tex]

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

[B] [tex]\begin{bmatrix}x+2y=-6\\ y+2z=-6\\ x-y-z=2\end{bmatrix}[/tex]

[tex]\begin{bmatrix}y+2z=-6\\ z-y-z=2\end{bmatrix}[/tex]

[tex]\mathrm{Substitute\:}y=-2[/tex]

[tex]\begin{bmatrix}-2+2z=-6\end{bmatrix}[/tex]

[tex]\mathrm{For\:}x=-6-2y[/tex]

[tex]\mathrm{Substitute\:}z=-2,\:y=-2[/tex]

[tex]x=-6-2\left(-2\right)[/tex]

[tex]x=-2[/tex]

[tex]\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}[/tex]

[tex]x=-2,\:z=-2,\:y=-2[/tex]

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

[C] [tex]\begin{bmatrix}3x-y=-8\\ y-3z=-8\\ x+y+z=-8\end{bmatrix}[/tex]

[tex]\mathrm{Substitute\:}x=\frac{-8+y}{3}[/tex]

[tex]\begin{bmatrix}y-3z=-8\\ \frac{-8+y}{3}+y+z=-8\end{bmatrix}[/tex]

[tex]\mathrm{Simplify}[/tex]

[tex]\begin{bmatrix}y-3z=-8\\ z+\frac{-8+4y}{3}=-8\end{bmatrix}[/tex]

[tex]\mathrm{Substitute\:}y=-8+3z[/tex]

[tex]\begin{bmatrix}z+\frac{-8+4\left(-8+3z\right)}{3}=-8\end{bmatrix}[/tex]

[tex]\mathrm{Simplify}[/tex]

[tex]\begin{bmatrix}\frac{15z-40}{3}=-8\end{bmatrix}[/tex]

[tex]\mathrm{For\:}y=-8+3z[/tex]

[tex]\mathrm{Substitute\:}z=\frac{16}{15}[/tex]

[tex]y=-8+3\cdot \frac{16}{15}[/tex]

[tex]y=-\frac{24}{5}[/tex]

[tex]\mathrm{For\:}x=\frac{-8+y}{3}[/tex]

[tex]\mathrm{Substitute\:}z=\frac{16}{15},\:y=-\frac{24}{5}[/tex]

[tex]x=\frac{-8-\frac{24}{5}}{3}=x=-\frac{64}{15}[/tex]

[tex]\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}[/tex]

[tex]x=-\frac{64}{15},\:z=\frac{16}{15},\:y=-\frac{24}{5}[/tex]

[tex]x=-\frac{64}{15}=-4.26666666667, z=\frac{16}{15}=1.06666666667,y=-\frac{24}{5}=-4.8[/tex]

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

[D] [tex]\begin{bmatrix}x-2y+z=0\\ 2y+9z=-20\\ x-y+z=0\end{bmatrix}[/tex]

[tex]\mathrm{Substitute\:}y=\frac{-20-9z}{2}[/tex]

[tex]\begin{bmatrix}x-2\cdot \frac{-20-9z}{2}+z=0\\ x-\frac{-20-9z}{2}+z=0\end{bmatrix}[/tex]

[tex]\mathrm{Simplify}[/tex]

[tex]\begin{bmatrix}x+20+10z=0\\ x+\frac{20+11z}{2}=0\end{bmatrix}[/tex]

[tex]\mathrm{Substitute\:}x=-10z-20[/tex]

[tex]\begin{bmatrix}-10z-20+\frac{20+11z}{2}=0\end{bmatrix}[/tex]

[tex]\mathrm{Simplify}[/tex]

[tex]\begin{bmatrix}\frac{20-9z}{2}-20=0\end{bmatrix}[/tex]

[tex]\mathrm{For\:}x=-10z-20[/tex]

[tex]\mathrm{Substitute\:}z=-\frac{20}{9}[/tex]

[tex]x=-10\left(-\frac{20}{9}\right)-20[/tex]

[tex]x=\frac{20}{9}[/tex]

[tex]\mathrm{For\:}y=\frac{-20-9z}{2}[/tex]

[tex]\mathrm{Substitute\:}x=\frac{20}{9},\:z=-\frac{20}{9}[/tex]

[tex]y=\frac{-20-9\left(-\frac{20}{9}\right)}{2}=0[/tex]

[tex]y=0[/tex]

[tex]\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}[/tex]

[tex]x=\frac{20}{9},\:z=-\frac{20}{9},\:y=0[/tex]

[tex]x=\frac{20}{9}=2.22222222222,\:z=-\frac{20}{9}-2.22222222222,\:y=0[/tex]

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Kavinsky

#RS

[tex]\\ \rm\Rrightarrow \dfrac{RS}{TS}=\dfrac{FG}{EF}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{RS}{12}=\dfrac{45}{18}=\dfrac{5}{2}[/tex]

[tex]\\ \rm\Rrightarrow RS=\dfrac{12(5)}{2}=6(5)=30[/tex]

#QR

[tex]\\ \rm\Rrightarrow \dfrac{HG}{EF}=\dfrac{QR}{TS}[/tex]

[tex]\\ \rm\Rrightarrow QR=TS=12[/tex]

#QU

[tex]\\ \rm\Rrightarrow \dfrac{UQ}{QR}=\dfrac{DH}{HG}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{UQ}{12}=\dfrac{45}{18}=\dfrac{5}{2}[/tex]

[tex]\\ \rm\Rrightarrow UQ=30[/tex]

Answer:

RS = 30, QR = 12, QU = 30

Step-by-step explanation:

Step 1:  Determine RS

We can see that RS on the left shape corresponds to FG on the right shape that is also larger.  We can use other sides to help us determine the ratio which will then give us the length of RS.  We can also see that the shape has been flipped so EF would match to ST.

[tex]RS/ST = FG/EF[/tex]

[tex]RS/12 = 45/18[/tex]

[tex]RS * 18 = 12 * 45[/tex]

[tex]\frac{18*RS}{18} = 540 / 18[/tex]

[tex]RS = 30[/tex]

Step 2:  Determine QR

We can see that QR on the left shape corresponds to HG on the right shape that is also larger.  We can use other sides to help us determine the ratio which will then give us the length of QR.  We can also see that the shape has been flipped so EF would match to ST.

[tex]QR/ST = HG/EF[/tex]

[tex]QR/12 = 18/18[/tex]

[tex]QR * 18 = 12 * 18[/tex]

[tex]\frac{18 * QR}{18} = 216 / 18[/tex]

[tex]QR = 12[/tex]

Step 3:  Determine QU

We can see that QR on the left shape corresponds to DH on the right shape that is also larger.  We can use other sides to help us determine the ratio which will then give us the length of QU.  We can also see that the shape has been flipped so EF would match to ST.

[tex]QU/ST = DH/EF[/tex]

[tex]QU/12 = 45/18[/tex]

[tex]QU * 18 = 12 * 45[/tex]

[tex]\frac{18*QU}{18} = 540/18[/tex]

[tex]QU = 30[/tex]

Answer:  RS = 30, QR = 12, QU = 30

Answer:

A factory makes aquariums. Each aquarium is in the shape of a triangular prism, as shown below. If the factory makes 126 aquariums, how much water will be needed to fill all of them (in cubic feet)?

Step-by-step explanation:

Answer:

C. 8

Step-by-step explanation:

d = 8

4 + [tex]\frac{d}{2}[/tex]

Substitute d for 8

4 + 8/2

Simplify

4+4

Simplify

8

Answer:

c = 8

Step-by-step explanation:

if d = 8, that would mean that

4 + 8/2 (because 8 has substituted for d)

then you do 8 ÷ 2 = 4

4 + 4 = 8