What degree of rotation about the origin will cause the triangle below to map onto itself?

Answer:

36x^2 -1

Step-by-step explanation:

6x times 6x= 36x^2

6x times 1= 6x

-1 times 6x= -6x

-1 times 1= -1

so, ...

36x^2+6x+(-6x)+(-1) = 36x^2 -1

Answer: [tex]2.25\sqrt{3}[/tex]

Not sure what you mean by terms of pi, unless you want us to find the area of the sector, not the triangle.

Step-by-step explanation:

Assuming you mean the area of the triangle...

First draw an altitude from the 120 degree angle to the opposite base.  You will find that the altitude will also be a median.  This forms 2 30-60-90 right triangles.  Thus, the height of the altitude is 1.5 and the base of the triangle is 1.5*root3.  Thus, the base of the triangle is [tex]3\sqrt{3}[/tex] and the height is 1.5.  Thus, the area of the triangle is [tex]2.25\sqrt{3}[/tex]

Answer: m∠E = 20.5°

              m∠GPF = 47°

Step-by-step explanation: An inscribed angle is an alge formed with its vertex on the circle. Its relation with arc is that the measure of an inscribed angle is half the measure of the intersected arc. For that reason:

m∠E = [tex]\frac{arcFG}{2}[/tex]

m∠E = [tex]\frac{41}{2}[/tex]

m∠E = 20.5°

Angle in F is:

m∠F = [tex]\frac{arcEH}{2}[/tex]

m∠F = [tex]\frac{53}{2}[/tex]

m∠F = 26.5°

The angle GPF is external to the triangle EPF, so the angle can be found by the following definition: The measure of an external angle of a triangle equals the sum of the non-adjacent angles, i.e.:

m∠GPF = m∠E + m∠F

m∠GPF = 20.5 + 26.5

m∠GPF = 47°

Answer:

b

Step-by-step explanation:

Answer:

The answer to your question is 18

Step-by-step explanation:

Process

1.- Write the fraction given

              [tex]\frac{-108}{-6}[/tex]

2.- Divide the numbers as usual

               18

         6  108

               48

                 0

3.- Divide the signs

      negative / negative = positive

4.- Write the answer

        [tex]\frac{-108}{-6}= 18[/tex]

5.- Check the result

Multiply 18 by -6 and the result must be -108

       -6 x 18 = 108

We know a negative times a negative is equal to a positive.

- 108 / - 6      is the same as 108 / 6     because the larger number is on top.

Therefore she can drop the negative signs and solve 108/6 to verify her answer.

Answer:

The flight speed should be 84.79 miles per hour at angle of 22.92° Northeast

Step-by-step explanation:

The given information are;

The distance from Parrot Point Airport to Ivy Cliffs = 291 miles

The direction from Parrot Point Airport to Ivy Cliffs = 9.1° Northeast

The speed of the wind = 25 miles per hour

The direction of the wind = Southeast

The time for the journey = 3 hours

The component of the wind velocity are;

For Southeast direction which is an inclination of 45°

Speed of the wind = -25 × sin(45) + 25 × cos(45)

Without the wind, the velocity of flight will be V = Displacement/time, which gives;

V = 291/3 = 97 miles/hour = 97 mph

Let the required velocity of flying = X, we have;

X×sin(θ) + X×cos (θ)  -25× sin(45) + 25 × cos(45) = 97×sin(9.1) + 97×cos(9.1)

X×sin(θ) -25× sin(45) = 97×sin(9.1)

X×sin(θ) =  97×sin(9.1 )+25× sin(45 ) = 33.02

X×sin(θ) =  33.02

X×cos (θ) +  25 × cos(45) =  97×cos(9.1)

X×cos (θ) =  97×cos(9.1)-  25 × cos(45) = 78.1

X×cos (θ) =   78.1

∴X×sin(θ)/(X×cos (θ)) = tan(θ) = 33.02/78.1 = 0.423

tan⁻¹(0.423) = 22.918≈ 22.92°

X×sin(θ) =  33.02

X = 33.02/(sin(θ)) = 33.02/(sin(22.92°)) = 84.79 miles per hour

Therefore, the flight speed should be 84.79 miles per hour at angle of 22.92° Northeast.

Answer:

740 m^2

Step-by-step explanation:

Answer:

The correct option is;

A'(4, 4), B'(0, 4), C'(8, 8).

Step-by-step explanation:

The beginning coordinates are;

A -2, 2

B - 0, 2

C - 4, 4

Given that triangle ABC is dilated by 2, the center of dilation being the origin, (0, 0), we have;

Given that the center of dilation is the origin, we multiply the x, and y values by the scale factor as follows;

(x, y) → (2·x, 2·y)

Which gives;

A - (2, 2) → A'(2×2, 2×2) = A'(4, 4)

B - (0, 2) → B'(2×0, 2×2) = B'(0, 4)

C - (4, 4) → C'(2×4, 2×4) = C'(8, 8)

The correct option is A'(4, 4), B'(0, 4), C'(8, 8).

Answer:

C.I = (371.88  , 458.12)

Step-by-step explanation:

Given that:

sample size n = 100

sample mean [tex]\overline x =[/tex] 415

standard deviation = 220

The objective is to calculate the  95% confidence interval for the average increase in number of words students who can read in a minute without losing comprehension.

At 95% confidence interval; level of significance ∝ = 1 - 0.95

level of significance ∝ = 0.05

[tex]z_{\alpha/2} = 0.05/2[/tex]

[tex]z_{\alpha/2} = 0.025[/tex]

The critical value at [tex]z_{\alpha/2} = 0.025[/tex] is 1.96

C.I = [tex]\overline x \pm M.O,E[/tex]

C.I = [tex]\overline x \pm z_{\alpha/2} \dfrac{\sigma }{\sqrt{n}}[/tex]

C.I = [tex]415\pm 1.96 \dfrac{220 }{\sqrt{100}}[/tex]

C.I = [tex]415\pm 1.96 *\dfrac{220 }{10}[/tex]

C.I = [tex]415\pm 1.96 *22[/tex]

C.I = [tex]415\pm 43.12[/tex]

C.I = (371.88  , 458.12)

Answer:

0.92 and 1.25 respectively

Step-by-step explanation:

0.92 and 1.25 respectively

first the mean of each value which is 9.7 and 9.8 respectively

standard deviation = square root of the mean deviation of each value

then deduct the mean from each element

and square each value and add them together. not you should square each deviation value before you add them

at last divide the result by the number of frequency and find it's square root

Answer:

0.92 and 1.25

Step-by-step explanation:

My other answer was deleted, I'm not sure why.

9.77 in

Step-by-step explanation:

arc length is 80/360 × 2 × pi × radius

2/9 × 2 × 22/7 × 7

88/9

9.77in

Answer:

arc length = 9,76(8) inches

Step-by-step explanation:

Formula

2π·r(x°/360°)

= 2·3,14·7in·80°/360°

= 3516,8in/360

= 9,76(8) inches

Answer:

No.

Step-by-step explanation:

They are giving us the information that Imani has 5 fewer wins than Jamie and they combine for 30 wins total. The question is asking us is it possible for Jamie to have one 11 games. To find how many games Imani won, we have to subtract 5 from Jamie's wins. 11-5 = 6. To then see if the wins add up to 30, we have to add Jamie's and Imani's wisn together, 11 + 5 ≠ 30, so therefore it is not possible for Jamie to have won 11 games.

Answer:

[tex] y = 9.1 [/tex]

Step-by-step explanation:

y can be found using the Law of sines as explained below:

m < Y = 106°

m < X = 58°

WY = x = 8

WX = y = ?

Thus,

[tex] \frac{x}{sin(X)} = \frac{y}{sin(Y)} [/tex]

[tex] \frac{8}{sin(58)} = \frac{y}{sin(106)} [/tex]

[tex] \frac{8}{0.848} = \frac{y}{0.961} [/tex]

Multiply both sides by 0.961 to solve for y

[tex] \frac{8}{0.848}*0.961 = \frac{y}{0.961}*0.961 [/tex]

[tex] \frac{8*0.961}{0.848} = y [/tex]

[tex] \frac{8*0.961}{0.848}*0.961 = y [/tex]

[tex] 9.07 = y [/tex]

[tex] y = 9.1 [/tex] (to the nearest tenth)

Answer:

cost of one drink: $1.70

Step-by-step explanation:

P = price of pizza

L = Price of each large drink

Gift certificate discount =$ 7

Net paid= $12.10

P +3L -7 = 12.10

14 +3L -7 =12.10

7+3L =12.10

3L = 12.10 -7 = 5.10

 L = $1.70 for each large drink

hopefully this helped :3

Answer: The equation to model this situation is  3d + $14.00 – $7.00 =     $12.10 and the cost of one large drink is $1.7 .

Step-by-step explanation:

As given

John and 2 friends are going out for pizza for lunch.

They split one pizza and 3 large drinks. The pizza cost $14.00. After using a $7.00 gift certificate, they spend a total of $12.10.

let us assume that the numbers of large drinks are represented by d .

Than the equation becomes

Total money spend = Number of drinks × d + Pizza cost  - Gift certificate amount .

Putting all the values in the above

12.10 = 3d + 14.00 - 7.00

Simplify the aboves

12.10 = 3d + 14 - 7

12.10 = 3d + 7

12.10 - 7 = 3d

5.1 = 3d

d = $ 1.7

Therefore the equation to model this situation is  3d + $14.00 – $7.00 = $12.10 and the cost of one large drink is $1.7 .

Answer:

The answer is

Step-by-step explanation:

To find the volume of the sphere we must first find the radius

Surface area of a sphere = 4πr²

where r is the radius

From the question surface area = 3000m²

3000 = 4πr²

Divide both sides by 4π

750/π = r²

Find the square root of both sides

r = 15.45 cm

Volume of a sphere is 4/3πr³

So we have

4/3π(15.45)³

= 15448.06

= 15448m³ to the nearest hundredth

Hope this helps you

Answer:

Option D. 6√5.

Step-by-step explanation:

Please see attached photo for details.

The value of x can be obtained by using pythagoras theory as illustrated below:

In triangle ΔABC:

x² = z² + 12².... (1)

In triangle ΔABD:

15² = x² + y²...... (2)

In triangle ΔACD:

y² = z² + 3²....(3)

Substitute the value of y² in equation 3 into equation 2. We have:

15² = x² + y²

15² = x² + z² + 3²... (4)

From equation:

x² = z² + 12²

Make z² the subject

z² = x² – 12²

Substitute the value of z² into equation 4. We have:

15² = x² + z² + 3²

15² = x² + x² – 12² + 3²

15² = 2x² – 12² + 3²

225 = 2x² – 144 + 9

Collect like terms

225 + 144 – 9 = 2x²

360 = 2x²

Divide both side by 2

360/2 = x²

180 = x²

Take the square root of both side

x = √180

Expressing in surd form, we have:

x = √(36 x 5)

x = √36 x √5

x = 6√5

Answer:

3.47 and 3.21

Step-by-step explanation:

Let us assume the nails length be X

[tex]X \sim N(3.34,0.07^2)[/tex]

Value let separated the top 3% is T and for bottom it would be B

[tex]P(X < T)= 0.97[/tex]

Now converting, we get

[tex]P(Z < \frac{T-3.34}{0.07})= 0.97[/tex]

Based on the normal standard tables, we get

[tex]P(Z < 1.881)= 0.97[/tex]

Now compare these two above equations

[tex]\frac{T-3.34}{0.07} = 1.881 \\\\ T = 1.881 \times 0.07 + 3.34 \\\\ = 3.47[/tex]

So for top 3% it is 3.47

Now for bottom we applied the same method as shown above

[tex]P(Z < \frac{B-3.34}{0.07})= 0.03[/tex]

Based on the normal standard tables, we get

[tex]P(Z < -1.881)= 0.03[/tex]

Now compare these two above equations

[tex]\frac{B-3.34}{0.07} = -1.881[/tex]

[tex]= -1.881 \times 0.07 + 3.34 \\\\ = 3.21[/tex]

hence, for bottom it would be 3.21

Answer:

x > or equal to 0

Step-by-step explanation:

you're welcome

Answer:

x > or equal to 0

Answer:

3.6hours

Step-by-step explanation:

kevin-6hrs

so he gets 1/6 called in 1 minute

Anne-9 hrs

so she gets 1/9 called in 1 minute

together

1/6+1/9=5/18 called in one minute

so what about all which are 18/18

you get 3.6 hrs I guess

Answer:

Step-by-step explanation:

Independent Variable

The independent variable is the condition that you change in an experiment. It is the variable you control. It is called independent because its value does not depend on and is not affected by the state of any other variable in the experiment. Sometimes you may hear this variable called the "controlled variable" because it is the one that is changed. Do not confuse it with a "control variable," which is a variable that is purposely held constant so that it can't affect the outcome of the experiment.

Dependent Variable

The dependent variable is the condition that you measure in an experiment. You are assessing how it responds to a change in the independent variable, so you can think of it as depending on the independent variable. Sometimes the dependent variable is called the "responding variable."

Answer:

[tex]\boxed{\sf all \ real \ numbers \ greater \ than \ or \ equal \ to \ 0}[/tex]

Step-by-step explanation:

The domain of a function is all possible values for x.

[tex]\sf f(x)=\frac{2}{5} \sqrt{x}[/tex]

There are restrictions on x.

The square root of a number can be undefined if that number is less than 0.

The value of x is all real numbers greater than or equal to 0.

The domain of the function f(x) = (2/5)√x will be all real numbers greater than or equal to zero. Then the correct option is C.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The domain means all the possible values of x and the range means all the possible values of y.

The function is given below.

f(x) = (2/5)√x

The value under the square root should not be negative. Then the equation is given below.

x ≥ 0

Then the domain of the function f(x) = (2/5)√x will be all real numbers greater than or equal to zero.

Then the correct option is C.

More about the function link is given below.

https://brainly.com/question/5245372

#SPJ2

Answer:

363.741 feet

Step-by-step explanation:

Let the height of the cliff be represented by x. Applying the appropriate trigonometric function, we have;

Tan θ = [tex]\frac{opposite side}{adjacent side}[/tex]

Tan [tex]60^{0}[/tex] = [tex]\frac{x}{210}[/tex]

cross multiply to have;

   x = 210 × Tan [tex]60^{0}[/tex]

      = 210 × 1.7321

      = 363.741

The cliff is 363.741 feet high.

Answer:

Option (4)

Step-by-step explanation:

In the given picture,

Trapezoid PQRS has two points T and U as the midpoints of sides PS and RQ.

Segment TU joins the midpoints of the sides PS and RQ.

Mid-segment theorem states that "If a line joining midpoints of a trapezoid is parallel to the bases, length of this segment is half the sum of lengths of the bases."

Therefore, m(TU) = [tex]\frac{1}{2}(m\text{PQ}+m\text{SR})[/tex]

7x - 26 = [tex]\frac{1}{2}[(3x+23)+(9x-3)][/tex]

7x - 26 = 6x + 10

7x - 6x = 26 + 10

x = 36

m(TU) = 7x - 26

          = 7(36) - 26

          = 252 - 26

          = 226

Therefore, Option (4) will be the answer.

Hey there! I'm happy to help!

The domain is any possible number you can input into the function to get a real output. The domain of h just means the domain of this entire function, which is called h.

Let's look at the answer options.

OPTION A

All real values of x such that x≠0.

The only way to make it so that we do not have a real output is if we get a negative square root. You cannot multiply any number by itself to get a negative number unless you use imaginary numbers, but using imaginary numbers makes our output not real.

Anyways, plugging in 0 would give us √-10, which is not a real number. That part is correct, but this option says ALL REAL NUMBERS except for 0. The problem is is that we can take any number less than ten and plug it in and we would get a negative square root, a fake number. So, this option is incorrect.

OPTION B

All real values of x such that x≥10.

Let's say we use 10 for our x and plug it in. This gives us √0, which is 0, a real output. Anything bigger than this 10 will give us a real output as well, so this option is correct.

We don't even need to check the other options because we have already found the correct answer. C,D, and E are all incorrect though because they include values less ten, which would give us a negative square root, a fake number.

I hope that this helps! Have a wonderful day!

Answer:

w = 18

Step-by-step explanation:

w-3=15

Add 3 to each side

w-3+3=15+3

w = 18

Answer:

w = 18.

Step-by-step explanation:

w - 3 = 15

w = 15 + 3

w = 18

Check your work!

18 - 3 = 15.

Hope this helps!

Step-by-step explanation:

Hi there!!

Here, your equation is y= -2/3 x +1

so, let's find coordinate.

To find coordinate you must put the value of x.

so, when you keep value of x you will get,

x 0 3 6

y 1 -1 -3

Therefore, the coordinates are (0,1), (3,-1), (6,-3).

let me make you clear on using the value of x.

we generally put the value of variable (which is in right side) from a smaller digit like 0,1,2... or you may use 0,-1,-2... but they must be in eqaul interval such like i used the values in equal interval of 3 in above question.

I hope you got it...

if not you can ask me help..

now plot those points on graph, alright.

best of luck...

Answer:

294.5 m²

Step-by-step explanation:

portion of circle is 360 - 130 = 230

πr²*x/360 = π(11.1)²*230/360 = 247.3

then add the non-right triangle area, 1/2ab sinC

1/2(11.1)(11.1) sin 130 = 47.2

247.3 + 47.2 = 294.5 m²

The first digit can be 1 or 2.

For each one ...

The second digit can be 1 or 2.

For each one ...

The third digit can be 1 or 2.

That's (2•2•2)= 8 different possibilities.

Answer:

B is a trinomial.

Step-by-step explanation: A trinomial is a math equation with 3 terms connected by plus or minus notations. In these 4 answer choices, choice B is the only one with 3 terms.

Answer

13x^3 i think its the right answer but am not sure :(

Answer:

  $198,859.03

Step-by-step explanation:

The amortization formula is good for this. Fill in the given numbers and solve for the unknown.

 A = P(r/n)/(1 -(1 +r/n)^(-nt))

where A is the monthly payment, P is the principal amount of the loan, r is the annual interest rate, n is the number of times per year interest is compounded, and t is the number of years.

  1340.00 = P(0.0525/12)/(1 -(1 +0.0525/12)^(-12·20)) ≈ 0.00673844·P

  P ≈ 1340/0.00673844 ≈ $198,859.03

The family can afford a loan for $198,859.

Answer:

x+y

Step-by-step explanation:

#boys+#girls=#children