A tether ball is attached to the top of a 15-foot pole. Maddy holds the ball 3 feet off the ground and 4 feet from the pole. How long is the rope that the tether ball is attached to?

Answer:

7.2

Step-by-step explanation:

Apply Law of Cosines, given that b is 13.5, c is 8.9, and Angle a is 29.

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

[tex] {a}^{2} = {13.5}^{2} + {8.9}^{2} - 2(13.5)(8.9) \times \cos(29) [/tex]

[tex] {a}^{2} = 182.25 + 79.21 - 240.3 \times 0.8746[/tex]

[tex] {a}^{2} = 182.25 + 79.21 - 210.1711[/tex]

[tex]a = 7.2[/tex]

Answer:

[tex]a\approx7.2[/tex]

Step-by-step explanation:

The given problem presents one with the following information:

To solve this problem, one can use the law of cosines. The law of cosines is a property that can apply to any triangle. This property comes in the form of a formula, which is as follows:

[tex]a^2=\sqrt{b^2+c^2-2bc(cos(A))}[/tex]

Where (a), (b), and (c) are sides of the triangle, and (<A) is the angle opposite the side (a).

Substitute the given information into the formula and solve for the unknown side (a):

[tex]a=\sqrt{b^2+c^2-2bc(cos(A))}[/tex]

[tex]a=\sqrt{(13.5)^2+(8.9)^2-2(13.5)(8.9)(cos(29))}[/tex]

Simplify,

[tex]a=\sqrt{(13.5)^2+(8.9)^2-2(13.5)(8.9)(cos(29))}[/tex]

[tex]a=\sqrt{182.25+79.21-240.3(cos(29))}[/tex]

[tex]a=\sqrt{261.46-240.3(cos(29))}[/tex]

[tex]a=\sqrt{261.46-210.1711}[/tex]

[tex]a=\sqrt{51.2889}[/tex]

[tex]a\approx7.2[/tex]

Answer:

false it would be something like x root 2

Step-by-step explanation:

Answer:

2nd answer

Step-by-step explanation:

4x^3+2

4*(-1)^3+2

4*(-1)+2

-4+2

-2

Answer: -2

Step-by-step explanation:

Replacing x for -1 would make the equation [tex]4(-1^3)+2[/tex]. Knowing PEMDAS, we know that the parentheses goes first. [tex]-1^3[/tex] means that we need to multiply -1 by itself 3 times ([tex]-1*-1*-1[/tex],  * equals "times"). [tex]-1*-1=1[/tex] so [tex]1*-1=-1[/tex]. Now our equation is [tex]4(-1)+2[/tex].    [tex]4*-1=-1[/tex] and -4 + 2 = -2. Hope this explanation helps :)

Answer:

90

Step-by-step explanation:

Use angle-arc relation,

For a and 45, Inscribed angle's relation can be utilized

Inscribed angle=Half the arc

45=1/2a

Therefore, a=90

Answer:

-p^4 + 4p^3 - 5p^2 + 8p - 6

Step-by-step explanation:

Distribute the -p^2 to the p^2 and the 2. Then distribute the 4p to the p^2 and the 2. Then distribute the -3 to the p^2 and the 2.

When we expand:

-p^4 - 2p^2

+ 4p^3 + 8p

-3p^2 - 6

Group, ordering from highest to lowest "degree" (exponent).

-p^4 + 4p^3 - 2p^2 - 3p^2 + 8p - 6

Combine like terms.

-p^4 + 4p^3 - 5p^2 + 8p - 6

Hi there!

check the pic

#YoghurtCup!

Answer: F

Step-by-step explanation:

Put all numbers with 1 exponent.

[tex](\sqrt{8^4} *\sqrt{6^4} )^{\frac{3}{2} }\\\\=(2^{\frac{3*4}{2} }*(2^{\frac{4}{2} }*3^{\frac{4}{2}} )\ )^{\dfrac{3}{2} }\\\\\\=(2^6*2^2*3^2)^{\dfrac{3}{2} }\\\\=2^{8*\frac{3}{2} }*3^{2*\frac{3}{2}} \\\\\\\boxed{=2^{12}*3^3}\\\\\\Answer\ F[/tex]

if you convert it all into one hour, Team B clearly worked at a faster pace.

Answer:

[tex]team \: a \: \\ 8in \: number \: with \: in \: 2 \: hours \\ so \: in \: 1 \: hour \: \frac{8}{2} = 4 \: in \: number \\ \\ team \: b \\ 5 \: in \: 1hour \\ so \: \: team \: b \: work \: in \: fast \\ thank \: you[/tex]

Lets solve

[tex]\\ \sf\longmapsto 7w<-56[/tex]

[tex]\\ \sf\longmapsto w<dfrac{-56}{7}[/tex]

[tex]\\ \sf\longmapsto w<-8[/tex]

Answer:

[tex]\boxed {\boxed {\sf w < -8}}[/tex]

Step-by-step explanation:

We are given an inequality and asked to solve for the variable w.

[tex]7w < -56[/tex]

In order to solve for w, we must isolate the variable. It is being multiplied by 7. The inverse of multiplication is division, so we divide both sides of the inequality by 7.

[tex]\frac {7w}{7} < \frac {-56}{7}[/tex]

[tex]w < \frac{-56}{7}[/tex]

[tex]w < -8[/tex]

w is less than -8 or w < -8.

[tex]\boxed{\sf sin\Theta=\dfrac{P}{H}}[/tex]

[tex]\\ \sf\longmapsto sin\theta=\dfrac{4}{16}[/tex]

[tex]\\ \sf\longmapsto sin\theta=\dfrac{1}{4}[/tex]

[tex]\\ \sf\longmapsto sin\theta=\dfrac{sin30}{2}[/tex]

[tex]\\ \sf\longmapsto sin\theta=sin15[/tex]

[tex]\\ \sf\longmapsto \theta=15°[/tex]

Answer:

If the son’s age is x, the father’s age is 2x.

If the son’s age is x, the father’s age is 2x.Ten years ago:

If the son’s age is x, the father’s age is 2x.Ten years ago:(x - 10) + (2x - 10) = 52

If the son’s age is x, the father’s age is 2x.Ten years ago:(x - 10) + (2x - 10) = 523x + 20 = 52

If the son’s age is x, the father’s age is 2x.Ten years ago:(x - 10) + (2x - 10) = 523x + 20 = 523x = 72

If the son’s age is x, the father’s age is 2x.Ten years ago:(x - 10) + (2x - 10) = 523x + 20 = 523x = 72x = 24

If the son’s age is x, the father’s age is 2x.Ten years ago:(x - 10) + (2x - 10) = 523x + 20 = 523x = 72x = 242x = 48

If the son’s age is x, the father’s age is 2x.Ten years ago:(x - 10) + (2x - 10) = 523x + 20 = 523x = 72x = 242x = 48So the son’s age is 24 and the father’s is 48. Ten years ago, they were 14 and 38, which adds up to 52.

.

.

Step-by-step explanation:

Answer: 1/3

Step-by-step explanation:

On side of the smaller quadrilateral is 8, the same side on the larger one is 24. 8 times 3 is 24. So the scale factor from the smaller to the larger is 1/3.

Answer:

1/3

Step-by-step explanation:

similar means all sides are proportinal, in this case one side is 3x bigger in the 2nd figure, so the same must be true of the other fig.

Answer:

The answer is  x = 2y

Step-by-step explanation:

(3x + 2y) (3y + 2 y)

3x = 3y + 2y + 2y

3x = 7y

x = 7 ÷ 3

x = 2y

hi

(x+3)^2 -4 = ( (x+3) +2) ( (x+3)-2 )

= ( x+5) (x +1)

so

solutions are : x+5=0 so x=-5

x+1= 0. so x= -1

solution are -5 +and -1

X = 4×3 X + 7

Resultado

X = 12 X + 7

Forma alternativa

-11 X - 7 = 0

X = -7/11

Answer:

In the real world, a consumer may purchase more then one commodity. Let us assume that a consumer purchases two goods X and Y. How does a consumer spend his fixed money income in purchasing two goods so as to maximize his total utility? The law of equi­-marginal utility tells us the way how a consumer maximizes his total utilit

Answer:

$17,000 at 14% and $9,000 at 2%

Step-by-step explanation:

Let x = amount invested at 14%.

Let y = amount invested at 2%.

x + y = 26000

0.14x + 0.02y = 2560

     -0.02x - 0.02y = -520

(+)    0.14x + 0.02y = 2560

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

       0.12x              = 2040

x = 17,000

x + y = 26000

17000 + y = 26000

y = 9000

Answer: $17,000 at 14% and $9,000 at 2%

Answer:

i. 12cm

ii. 16.5cm

Step-by-step explanation:

The side lengths on an equilateral triangle are all equal to each other. So if one side is given we can find the perimeter of the triangle by multiplying one of the sides by 3.

4*3=12

5.5*3=16.5

Answer:

Step-by-step explanation:

The lateral surface area is:

[tex]\\ \tt\longmapsto SA=2\pi rh[[/te]

[tex]\\ \tt\longmapsto SA=2\times 22}{7}\times (2.5)(9.25)[/tex]

[tex]\\ \tt\longmapsto SA=145.23in^2[/tex]

Answer:

hope this helps

Step-by-step explanation:

hope this helps

Answer:

The answer is x=3. YOU add the 6 to the zero and then divide the 2x by 6 and you get 3

[tex]\\ \sf\longmapsto x+2x+90=180[/tex]

[tex]\\ \sf\longmapsto 3x+90=180[/tex]

[tex]\\ \sf\longmapsto 3x=180-90[/tex]

[tex]\\ \sf\longmapsto 3x=90[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{90}{3}[/tex]

[tex]\\ \sf\longmapsto x=30[/tex]

Now

[tex]\\ \sf\longmapsto x=2y[/tex](Opposite interior angles)

[tex]\\ \sf\longmapsto 2y=30[/tex]

[tex]\\ \sf\longmapsto y=\dfrac{30}{2}[/tex]

[tex]\\ \sf\longmapsto y=15[/tex]

And

[tex]\\ \sf\longmapsto x+z=180[/tex]

[tex]\\ \sf\longmapsto z+30=180[/tex]

[tex]\\ \sf\longmapsto z=180-30[/tex]

[tex]\\ \sf\longmapsto z=150[/tex]

Answer:

Straight angle is 180°:

Alternate interior angles are congruent:

Consecutive interior angles are supplementary:

Alternate interior angles:

Sum of interior angles of a triangle:

Step-by-step explanation:

Answer:

13.5

Step-by-step explanation:

Given

tan34° = [tex]\frac{x}{20}[/tex] ( multiply both sides by 20 )

20 × tan34° = x , then

x ≈ 13.5 ( to the nearest tenth )