If the clock tower in "Back to the Future" had a big hand length of 3 feet, what would be the length of the arc, in feet, the tip travels from 6:00pm to 6:20pm. Round to the nearest foot.

Answer:

b.  -x + y = 0

Step-by-step explanation:

Direct variation:

Direct variation means "y varies directly as x”:

[tex]y \propto x \implies y=kx[/tex]

where k is the (non-zero) constant of variation.

To determine which of the given equations represents a direct variation, isolate y for each and compare with the direct variation equation.

Equation a

[tex]y=\dfrac{4}{3}x-2[/tex]

This is not a direct variation equation as there is an addition of -2.

Equation b

[tex]-x+y=0[/tex]

[tex]\implies y=x[/tex]

This is a direct variation equation where the constant of variation is 1.

Equation c

[tex]xy=8[/tex]

[tex]\implies y=\dfrac{8}{x}[/tex]

This is not a direct variation equation as y is inversely proportional to x.

Equation d

[tex]y=14[/tex]

This equation does not include the variable x, and so is therefore not a direct variation equation.

If y varies inversely with x then the line must be linear and increasing

And the y intercept must be 0 in y=mx+c

#1

c=-2

#2

Yes

#3

No

#4

Parallel to x axis no direct variation

The density in pounds per cubic meter is 83 pounds per cubic metre.

The density is mass of a unit volume of a material substance.

In other words, density is the ratio between mass and volume or mass per unit .

Therefore, density can be represented mathematically as follows:

density = mass / volume

Hence,

mass = 5 ounces

5 ounces = 0.3125 pounds

1 gallon = 0.00378541 pounds

Therefore,

density = 0.3125 / 0.00378541

density = 82.5538052681

density = 83 pounds per cubic metre.

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Step-by-step explanation:

Well first let's find the derivative in using the power rule

h'(t) = (-4.9)t + 157

h'(t) = -9.8t + 157

we can see from the image above that the maximum height is 1452.602 so that is the answer to the second question.

h'(1452.602) = -9.8(1452.602) + 157

h' = 14,078.500

Answer:

53

Step-by-step explanation:

Let yazid's score be x

x + x + 17 + 2x = 161

4x + 17 = 161

4x = 144

x = 36

jack = x + 17

jack = 53

Answer:

Jack:  36

Bonus:  Yazid:  53 and Susan:  72

Step-by-step explanation:

Let J, Y, and K stand for Jack, Yazin, Susan's scores.

We are told that:

J = Y + 17  [Jack scored 17 marks more than Yazid]

S = 2Y  [Susan scored twice Yazid's score]

J + Y + S = 161  [total score is 161]

Substitute the first two expressions into the last equation:

J + Y + S = 161

(Y+17) + Y + (2Y) = 161

4Y = 144

Y = 36

Use Y = 36 to find the other scores:

J = Y + 17

J = 36 + 17

J = 53

S = 2Y

S = 2*(36)

S = 72

CHECK:

Does 36+53+72 = 161?

YES

The distance between the helicopter and the first home is 369. 87 m

The distance between the helicopter and the first home can be found using sine law,

Therefore,

180 - 72 - 49 = 59 degrees.

Hence,

420 / sin 59 = A / sin 49°

where

A  = distance form the first home to the helicopter.

cross multiply

420 sin 49 = A sin 59°

A = 420 sin 49 / sin 59

A = 316.978023694 / 0.8571673007

A = 369.869339199

A = 369. 87 m

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Answer:

24

Step-by-step explanation:

3x4x2=24

When finding the answer to this problem, you times all of the options by each other.

Answer:

[tex]\huge\boxed{\sf 81x^4 - 16y^4}[/tex]

Step-by-step explanation:

= (3x - 2y)(3x + 2y)(9x² + 4y²)

= [(3x)² - (2y)²] (9x² + 4y²)

= (9x² - 4y²)(9x² + 4y²)

Using the above formula again

= (9x²)² - (4y²)²

[tex]\rule[225]{225}{2}[/tex]

Pairs of triangles appear to be congruent are :

Triangles 2 and 3. Option B

Triangles 2 and 4. Option D

Triangles 3 and 4. Option E

Congruent triangles can be defined as the pairs of triangles with same measurement

Triangles 2 and 3 :

After observing triangles 2  and  3  it appears that triangle  is congruent to triangle  .

Option C

Triangles 2 and 4

After observing triangles 2  and 4   it appears that triangle 2 is congruent to triangle 4 .

Option D

E. Triangles 3 and 4

After observing triangles 3  and 4. They are congruent

Option E

Hence, Option B, D and E are correct of the triangles

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Answer:

Triangles 3 and 4
Triangles 1 and 4
Triangles 1 and 3

Step-by-step explanation:

if this is wrong tell me so i can edit the answer, but this is what i got

Answer:

{x:x is a real number}

Since any value can replace x to give an integer.

{x:x is a real number}

Answer:

[tex]BC=5\sqrt{2}[/tex], [tex]AC=5\sqrt{4}[/tex]

Step-by-step explanation:

In a 45-45-90 relation triangle the two shortest sides will have equal length, meaning:

[tex]BC=5\sqrt{2}[/tex]

To find the hypotenuse we must multiply the shortest side by [tex]\sqrt{2}[/tex], both sides are equal so it doesn't matter which we multiply.

[tex]AC=5\sqrt{2} \sqrt{2} \\AC=5\sqrt{4}[/tex]

Total possible outcomes are 312

We need to find that if you roll a 6-sided die and draw a card from a deck of 52 cards,what are total possible outcomes

Probability is a measure of the possibility that an event will occur. Many events cannot be predicted with absolute certainty. We can only predict the probability that an event will occur, i.e. how likely it is to occur, using it. Probability can range from 0 to 1, where 0 means an event is impossible and 1 means a certain event

An outcome is the result of an event that depends on probability. Probability refers to the likelihood that something will happen, and an event can have more than one possible outcome.

Enumeration of possible outcomes is the process of determining the number of possible outcomes for an event. There are various methods to carry out this process. The best way to calculate the number of possible outcomes of an event depends on the type of event and the structure of the event

If a 6-sided die and draw a card from a deck,

then each side has total possible outcome 52

so, total number of possible outcomes for 6 - sided dice are 52 * 6

= 312

Hence total number of possible outcomes are 312

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Answer:

We have,

According to given figure.

PQ=PR(giventhat)

QS=SR(Bydefinationofmidpoint)

PS=PS(Commonline)

Then,

ΔSPQ≅ΔSPR   (BY congruency S.S.S.)

Hence, PS bisects ∠PQR by definition of angle bisector.

10u + t is the expressions shows the value of the reversal of digits in a two digit number, t = the tens digit and u = the ones digit. This can be obtained by multiplying 10 with the tens digit and adding unit digit.

Given that, in a two digit number,

t = the tens digit

u = the ones digit

The expression for the digit will be ,

10×t + u = 10t + u

The value of its reversal,

u = the tens digit

t = the ones digit

10×u + t = 10u + t is the required expression

For example,

37 = 10×3 + 7 = 30 + 7 and its reverse 73 = 10×7 + 3 = 70 + 3

Hence 10u + t is the expressions shows the value of the reversal of digits in a two digit number, t = the tens digit and u = the ones digit.

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The correlation coefficient r between the two data sets is 0.33

From the table of values, we make use of the following representations:

Using the above representations, we can now plot our data values in the Excel software

From the Excel application, we have the following summary:

X Values

∑ = 424

Mean = 21.2

∑(X - Mx)2 = SSx = 101.2

Y Values

∑ = 151.8

Mean = 7.59

∑(Y - My)2 = SSy = 8.238

X and Y Combined

N = 20

∑(X - Mx)(Y - My) = 9.54

R Calculation

r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))

This gives

r = 9.54 / √((101.2)(8.238))

Evaluate

r = 0.3304

Approximate

r = 0.33

Hence, the correlation coefficient r between the two data sets is 0.33

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The amount I'll have in two years at the growth rate described is; $1.21x.

Since it follows that the savings grow by 10% each year, it can be concluded that the growth factor is; 110% = 1.1

Hence, in two years, we have;

= $x × (1.1)²

= $1.21x.

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Answer:

1.21x

Step-by-step explanation:

on rsm it says its correct

Answer:

Distributive property

Step-by-step explanation:

In order to solve this equation we first need to distribute 3 into 2y+5, we use the distributive property to do this.

Answer:

a = (9,8)

b=(10,6)

c=(4,3)

Step-by-step explanation:

basically, you just take the original coordinates and add the translation to it.

so a was -1,6 so just at 10 to -1 as they are x coordinates nad add 2 to 6 because they are Y coordinates and you just do it for all of the points.

Answer:

1.11

Step-by-step explanation:

A rule which describes the growth of the y-values of the function y=12^x over each interval is "multiply by 12."

By critically observing the given function, we can logically deduce that it is an exponential function. Also, the initial value of this exponential function is 1 with a growth factor is 12.

For instance, we have:

At x = -1

y = 12^(-1)

y = 1/12

At x=0

y = 12^(0)

y = 1

At x = 1

y = 12^(1)

y = 12

In conclusion, a rule which describes the growth of the y-values of the function y=12^x over each interval is "multiply by 12."

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Answer:

(2x + 20) ft^2.

Step-by-step explanation:

Area  = length * width

         =   2 * (x + 10)

         = (2x + 20) ft^2.

Answer:

D. The slope is -2. The y-intercept is (0,3)

Step-by-step explanation:

You can use any two points.

Let's use the first two points: (0, 3), (2, -1)

slope = (y_2 - y_1)/(x_2 - x_1)

slope = (-1 - 3)/(2 - 0)

slope = -4/2

slope = -2

The y-intercept occurs when x = 0. For x = 0, y = 3, so the y-intercept is 3 which means the point (0, 3).

Answer: D. The slope is -2. The y-intercept is (0,3)

[tex]\sqrt[3]{125x^{10}y^{13} } +\sqrt[3]{27x^{10}y^{13} }[/tex]=[tex]5\sqrt[3]{x^{10} y^{13} } +3\sqrt[3]{x^{10}y^{13} } = 8\sqrt[3]{x^{10}y^{13} }[/tex]

[tex]\sqrt[3]{125x^{10}y^{13} } +\sqrt[3]{27x^{10}y^{13} }[/tex]

Therefore,

125 = 5³

27 = 3³

Hence,

[tex]5\sqrt[3]{x^{10} y^{13} } +3\sqrt[3]{x^{10}y^{13} }[/tex]

Hence,

Both cube root are the same now,

Therefore, we have to add them together.

[tex]5\sqrt[3]{x^{10} y^{13} } +3\sqrt[3]{x^{10}y^{13} } = 8\sqrt[3]{x^{10}y^{13} }[/tex]

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Answer: SA = 445.05

Step-by-step explanation:

Answer:

20

Steps-by-step explanation:

sorry mistake

Answer:

12

Explanation: I just counted them! :) and there was 6 in the middle and on the outside so 6 + 6 = 12! :)

The median of the list of numbers is 7

The number is given as:

9.5, 4.4, 8.1, 2.9, 9.2, 3.2, 9.4, 7, 2.5

Rearrange the numbers in ascending order

2.5, 2.9, 3.2, 4.4, 7, 8.1, 9.2, 9.4, 9.5

The median is the middle number.

The middle number here is 7

Hence, the median of the list of numbers is 7

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Answer:

-2y= -23-15

-2y=-38

-y= -38/2

-y=19 proved

Using the concept of vertical and horizontal asymptotes, it is found that the function will have a horizontal asymptote at y = 2 and a vertical asymptote at x = 1 for a = -1 and m = 1.

In this problem, the function is:

[tex]f(x) = \frac{2x^m}{x + a}[/tex]

It has a vertical asymptote at x = 1, hence:

x + a = 0

1 + a = 0

a = -1

It has a horizontal asymptote at y = 2, hence:

[tex]\lim_{x \rightarrow \infty} f(x) = 2[/tex]

[tex]\lim_{x \rightarrow \infty} \frac{2x^m}{x + a} = 2[/tex]

[tex]\lim_{x \rightarrow \infty} \frac{2x^m}{x} = 2[/tex]

[tex]2^{m-1} = 2[/tex]

Then, since we want to simplify, the exponents at the numerator and the denominator have to be equal, hence m = 1.

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Putting the other player's king in check is always a good move. true

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The number of minutes it take to complete the same job if sandy and randy work together than if sandy works alone is 18mins.

According to this question, Sandy rakes and bags the leaves on her front lawn in 30 mins while Randy does the same job in 20 mins.

To calculate the time it will take both of them to work together, we use the following expression;

1/30 + 1/20 = 1/x

x = 12mins

Therefore, it will take 30 - 12 = 18 mins, to complete the same job if sandy and randy work together than if sandy works alone.

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The correct option is (2)  [tex]\frac{8}{5}[/tex] and (3)  [tex]\frac{1}{6}[/tex].

The factor of equation  f(x) = 60[tex]x^{4}[/tex] +  86[tex]x^{3}[/tex] – 46[tex]x^{2}[/tex] – 43[tex]x[/tex] + 8 are [tex]\frac{8}{5}[/tex] and [tex]\frac{1}{6}[/tex].

The rational root theorem, also referred to as the rational zero theorem, is a potent mathematical technique used to identify all potential rational roots of polynomial equations of order 3 and above.

For the given polynomial, the roots are given as;

[tex]$$P(x)=a_{n} x^{n}+a_{n-1} x^{n-1}+\cdots+a_{2} x^{2}+a_{1} x+a_{0}$$\\ \\$\pm \frac{\text { factors of } a_{0}}{\text { factors of } a_{n}}$.[/tex]

Factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 and factors of 8 are 1, 2, 4 and 8.

Out of the given options, only   [tex]\frac{8}{5}[/tex] and [tex]\frac{1}{6}[/tex] can be written in the form:  

[tex]\begin{aligned}&\frac{8}{5}=\frac{\text { a factor of } 8}{\text { a factor of } 60} \\&\frac{1}{6}=\frac{\text { a factor of } 8}{\text { a factor of } 60}\end{aligned}[/tex]

Therefore, the rational roots of polynomial f(x) = 60[tex]x^{4}[/tex] +  86[tex]x^{3}[/tex] – 46[tex]x^{2}[/tex] – 43[tex]x[/tex] + 8 are [tex]\frac{8}{5}[/tex] and [tex]\frac{1}{6}[/tex].

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The complete question is-

Which is a factor of f(x) = 60[tex]x^{4}[/tex] +  86[tex]x^{3}[/tex] – 46[tex]x^{2}[/tex] – 43[tex]x[/tex] + 8? use the rational root theorem to help you find your answer.