A Group of students is tracking a friend, John, who is riding a Ferris wheel. They know that John reaches the Maximum height of 11 m at 10 seconds and then reaches the minimum height of 1 m at 55 seconds.
What is the period of the function and what does it represent in this situation?

Answer:

B and E

Step-by-step explanation:

3^-8/3^-4 = 1/81 or .01234567...

I suggest that if you're having difficulty with a question like this again you go through all the answers individually so you can see what they equal! This method can really help in tests or where you can't get help.

3^-12 = 1/531441 <- not the answer

3^-4 = 1/81 <- answer!

3^2 = 9

1/3^2 = 1/9

1/3^4 = 1/81

1/3^12 = 1/531441

its also good to remember

3^-8/3^-4 would mean -8+4 = 3^-4 which would help you get your first answer.

Hope this helps!

[tex]B. \: {3}^{ - 4} \:✅\\ \\ E. \: \: \frac{1}{ {3}^{4} }\:✅ [/tex]

Step-by-step explanation:

[tex] \frac{ {3}^{ - 8} }{ {3}^{ - 4} } \\ \\ we \: know \: that \: \: \: \frac{ {a}^{m} }{ {a}^{n} } \: = \: {a}^{m - n} \\ \\= {3}^{ - 8 - ( - 4)} \\ \\ = {3}^{ - 8 + 4} \: ( \: ∵\: - \times - = + ) \\ \\ = {3}^{ - 4} \\ \\ ( \: or \: ) \\ \\= \frac{1}{ {3}^{4} } \\ \\( \: ∵\: {a}^{ - m} = \frac{1}{ {a}^{m} } \: ) \\\: [/tex]

[tex]\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{!}}}}}[/tex]

Answer:

x = -0.2 and x = -3.5

Step-by-step explanation:

Combine like terms in the given equation, by subtracting 2x^2 from both sides:

6x^2 + 15x + 3 = 2x^2

-2x^2                = -2x^2

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

4x^2 + 15x + 3 = 0

This is a quadratic equation.  We'll find the two solutions using the quadratic equation

      -b ± √(b^2 - 4ac)

x = ---------------------------

                  2a

Here the coefficients of the quadratic are a = 4, b = 15 and c = 3.

Thus, the discriminant b^2 - 4ac is 15^2 - 4(4)(3), or +177

and from that we know we'll find two real, unequal roots.

                                -15 ± √177

The roots are:  x = ------------------- , or x = -0.2 and x = -3.5

                                         8

Answer:

15.6

Step-by-step explanation:

We see a dilation. So the ratio between UT and XW is 2:7.8. That is 1:3.9. If we put 4 in the 1 place, then we get 15.6

Please give brainliest

Hope this helped

Given:

The expressions are:

[tex]2x(x^2-6x+3)[/tex]

[tex]2a^2(5b^2+3ab+6a+1)[/tex]

To find:

The product of each expression.

Solution:

According to the distributive property of multiplication over addition, we get

[tex]a(b+c)=ab+ac[/tex]

The first expression is:

[tex]2x(x^2-6x+3)[/tex]

Using distributive property of multiplication over addition, we get

[tex]2x(x^2-6x+3)=(2x)(x^2)+(2x)(-6x)+(2x)(3)[/tex]

[tex]2x(x^2-6x+3)=2x^3-12x^2+6x[/tex]

Therefore, the product of [tex]2x(x^2-6x+3)[/tex] is [tex]2x^3-12x^2+6x[/tex].

The second expression is:

[tex]2a^2(5b^2+3ab+6a+1)[/tex]

Using distributive property of multiplication over addition, we get

[tex]2a^2(5b^2+3ab+6a+1)=(2a^2)(5b^2)+(2a^2)(3ab)+(2a^2)(6a)+(2a^2)(1)[/tex]

[tex]2a^2(5b^2+3ab+6a+1)=10a^2b^2+6a^3b+12a^3+2a^2[/tex]

Therefore, the product of [tex]2a^2(5b^2+3ab+6a+1)[/tex] is [tex]10a^2b^2+6a^3b+12a^3+2a^2[/tex].

Answer:

Step-by-step explanation:

Answer:

An equation is needed to evaluate h(0).

When you evaluate h(0), you find the y-intercept of the graph because the independent variable inside the brackets, probably x or t, equates to 0.

The problem is needed for its context to be explained.

Although in most math problems, when h(x) form is used, h usually represents height.

I assume h(0) is the initial height, maybe the height that the rocket was launched or the height that the person who threw the ball is.

Answer:

[tex]y=-2x+2[/tex]

Step-by-step explanation:

[tex]y=mx+b[/tex] is the slope intercept

[tex]m[/tex] is the slope

[tex]b[/tex] is the y-intercept

The slope in the graph is 4/2 or 2 simplified. From point (-2,6), you have to go down 4 and right 2 to get to the point (0,2)

The y-intercept is 2 because the line crosses the y axis at exactly 2.

Hope this helps

Answer:

x = -1/2, x = -5    OR    x = -0.5 and x = -4

Step-by-step explanation:

I’ll just put a picture, I can’t fully explain digitally.    ;D

Answer:

A general sinusoidal equation is:

y = A*sin(w*x + p) + M

where:

A is the amplitude

w is the angular frequency

p is the phase shift

M is the midline.

Now, we know that:

Amplitude must be 6, so A = 6

period is 2*pi/3

Remember that the frequency is the inverse of the period, then:

f = 1/T

f = 1/(2*pi/3) = 3/(2*pi)

And the angular frequency is 2*pi times the normal frequency, then:

w = 2*pi*f = 2*pi*(3/2*pi) = 3

w = 3

Here we not have information about the midline, so M = 0.

And we know that the phase shift is one unit to the left.

Remember horizontal translations:

for a function f(x), an horizontal translation of N units is written as:

g(x) = f(x + N)

if N > 0, then the translation is to the left

if N < 0 , then the translation is to the right,

Here we know that the phase shift is to the left, so p must be positive, and we know that the shift is 1 unit to the left, then:

p = +1

Replacing these in the equation we get:

y = 6*sin(3*x + 1) + 0

y = 6*sin(3*x + 1)

y = -19

I started by adding 18 to both sides(inverse operation) then dividing by -2 to isolate the variable. What you do to one side must be done to the other

Answer:

5.83 ft

Step-by-step explanation:

Pythagorean Theorem:

a² + b² = c²

3² + 5² = c²

9 + 25 = c²

34 = c²

c ≈ 5.8309 ≈ 5.83

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

-2

Step-by-step explanation:

negative times positive equal negative so

-1×2= -2

Answer:

[tex] \large{ \tt{✺ \: EXPLANATION}} : [/tex]

[tex] \large{ \boxed{ \boxed{ \tt{↝OUR \: FINAL \: ANSWER: \boxed{1}}}}}[/tex]

▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁

Answer:

14.286% increase

Step-by-step explanation:

Since the admission to the amusement park increased by $10 we need to find what percentage of $70 equals $10.

We can find this percentage by multiplying 10 (the difference in money) by 100 (a hundred percent), and dividing that by 70 (the initial cost)

[tex]10*100/70=14.286[/tex]

Answer:

Rida is 10 years old and her father is 40 years old.

Step-by-step explanation:

Given:

Present age

Present age of Rida = x

Present age of Rida's father = 4x

Age after 5 years

Age of Radi after 5 years = x + 5

Age of Radi's father after 5 years = 3(x + 5)

What To Find:

The present age of Rida and Rida's father.

Solution:

According to the statement the equation will be,

⇒ 4x + 5 = 3(x + 5)

Remove and solve the brackets,

⇒ 4x + 5 = 3x + 15

Take numbers to RHS and variable to LHS,

⇒ 4x - 3x = 15 - 5

Subtract 3x from 4x and 5 from 15,

⇒ x = 10

Now substitute the values of Rida's age and Rida's father's age,

Rida's age = x = 10 years

Rida's father's age = 4x = 4(10) = 40 years

Answer:

C

Step-by-step explanation:

I might be wrong. I hope it helps:)

Answer:

a^2 + b^2 = c^2

6^2 + 6^2 = c^2

36 + 36 = c^2

c^2 = 72

c = [tex]\sqrt{72}[/tex]

c=3[tex]\sqrt{8}[/tex]

c=8.485281374

Step-by-step explanation:

Answer:

452.4 mi^2

Step-by-step explanation:

area of circle=πr^2

=22/7*(12)^2

=3.142*144

=452.448

=452.4 mi^2

Answer:

C)    452.4 mi²

Step-by-step explanation:

a = πr²

a = π * 12²

a = π * 144

a = 452.3893421169

a = 452.4

Answer:

[tex]p(x) = k(x -1)^{3} * (x -4)^{2} * (x +3)[/tex] --- General polynomial

The degree is 6

[tex]p(x) = -\frac{1}{3}(x -1)^{3} * (x -4)^{2} * (x +3)[/tex] --- The polynomial precisely

Step-by-step explanation:

Given

[tex](a,b,c)= (1,4,-3)[/tex] --- zeros

[tex](m_1,m_2,m_3) =(3,2,1)[/tex] --- multiplicities

Solving (a): The polynomial

The polynomial is represented as:

[tex]p(x) = (x -a)^{m_1} * (x -b)^{m_2} * (x -c)^{m_3}[/tex]

So, we have:

[tex]p(x) = (x -1)^{3} * (x -4)^{2} * (x +3)^{1}[/tex]

[tex]p(x) = (x -1)^{3} * (x -4)^{2} * (x +3)[/tex]

Include constant k; So, the polynomial becomes

[tex]p(x) = k(x -1)^{3} * (x -4)^{2} * (x +3)[/tex]

Solving (b): The degree (d)

To do this, add up the multiplicities

[tex]d = m_1 +m_2 +m_3[/tex]

[tex]d = 3+2+1[/tex]

[tex]d = 6[/tex]

The degree is 6

Solving (c): The actual polynomial

In (a), we have:

[tex]p(x) = k(x -1)^{3} * (x -4)^{2} * (x +3)[/tex]

[tex]p(0)=16[/tex] means:

[tex](x,p(x)) = (0,16)[/tex]

This gives:

[tex]16 = k(0 -1)^{3} * (0 -4)^{2} * (0 +3)[/tex]

[tex]16 = k(-1)^{3} * (-4)^{2} * (3)[/tex]

[tex]16 = k*-48[/tex]

Solve for k

[tex]k = \frac{16}{-48}[/tex]

[tex]k = -\frac{1}{3}[/tex]

So:

[tex]p(x) = k(x -1)^{3} * (x -4)^{2} * (x +3)[/tex]

[tex]p(x) = -\frac{1}{3}(x -1)^{3} * (x -4)^{2} * (x +3)[/tex]

Answer:

Pythagoreas Theorem

Step-by-step explanation:

a^2+b^2=c^2

4^2+b^2=15^2

16+b^2=225

b^2= 209

14.45=b

Answer:

y = -0.2(x) + 3

Step-by-step explanation:

One way to find an equation for a line is to find two points and go from there. To find the second point, we can note that the y intercept means when x=0. In the line y=3, y is always 3, so when x=0, y = 3.

Our two points are then (5, 2) and (0,3)

To find the slope, we can use

[tex]\frac{y_2 - y_1}{x_2-x_1} = \frac{3-2}{0-5} \\= \frac{1}{-5} \\= -0.2[/tex]

Using the formula y = mx + b and the slope m = -0.2, plugging into (5, 2) and solving for b, we get

2 = -0.2 (5)  +b

2 = -1 + b

add 1 to both sides to isolate the b

b = 3

Our formula is thus

y = -0.2(x) + 3

Answer: 15 m

Step-by-step explanation:

Given

The area of the swimming pool is [tex]A=45\ m^2[/tex]

Width of the pool is [tex]w=3\ m[/tex]

Suppose l is the length of the pool

So, the area is given by the multiplication of length and width

[tex]\Rightarrow A=lw\\\Rightarrow 45=3l\\\Rightarrow l=15\ m[/tex]

So, the length of the pool is 15 m.

Answer:

4.50

Step-by-step explanation:

[tex] \sin(40) \times 7 = 4.499513268[/tex]

round it up

[tex] = 4.50[/tex]

Answer:

I want to help but I don't understand the question. Can you plz send a picture of the question

Answer:

85%

Step-by-step explanation:

(40 - 6)/40 * 100%

34/40 * 100%

85%

[tex]\huge\color{purple}\boxed{\colorbox{black}{♡Solution}}[/tex]

8.

[tex]7 {x}^{3} + 3 {x}^{2} + 4x + 10 - 10 - 8x - 3 {x}^{3} \\ = 7 {x}^{3} - 3 {x}^{3} + 3 {x}^{2} + 4x - 8x + 10 - 10 \\ = 4 {x}^{3} + 3 {x}^{2}- 4x[/tex]

9.

[tex]5 {x}^{4} - 4 {x}^{3} - 3x - 4 - 2x + 6 {x}^{3} + 2 {x}^{4} \\ = 5 {x}^{4} + 2 {x}^{4} - 4 {x}^{3} + 6 {x}^{3} - 3x - 2x - 4 \\ = 7 {x}^{4} + 2 {x}^{3} - 5x - 4[/tex]

10.

[tex]7 {x}^{3} - 9 {x}^{2} - 7x - 8 - 8 + 4 {x}^{2} + 6 {x}^{3} \\ = 7 {x}^{3} + 6 {x}^{3} - 9 {x}^{2} + 4 {x}^{2} - 7x - 8 - 8 \\ = 13 {x}^{3} - 5 {x}^{2} - 7x - 16[/tex]

11.

[tex]4a + 20 - 5 {a}^{2} + 20a - 35 \\ = - 5 {a}^{2} + 24a - 15[/tex]

12.

[tex]8y + 48 - 6 {y}^{2} + 36y - 24 \\ = - 6 {y}^{2} + 44y + 24 \\ = 2( - 3 {y}^{2} + 22y + 12)[/tex]

13.

[tex]3c - 12 - 5 {c}^{2} - 20c + 40 \\ = - 5 {c}^{2} - 17c + 28[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique }}{\orange{♡}}}}}[/tex]

Answer:

y=3/4x + 10

Step-by-step explanation:

First, lets put this into Point-Slope form: y-4 = 3/4(x+8)

Now, lets modify the equation in our favor, getting the "y" alone on the left hand side:  y-4 = 3/4(x+8)

                     +4                   +4

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

                  y=3/4(x+8)+4

Now, lets simplify....

                  y=3/4x + 6 + 4 = y = 3/4x+10

And we are done!

Answer:

The answer is negative, the one you chose in the picture.

Step-by-step explanation:

Positive slope would be going upwards.

Negative slope would be going downwards.

Slopes that are zero would be horizontal.

Slopes that are undefined would be vertical.

So, the reason why the slope is negative is that the line is going downhill.

Hope this is helpful

Answer:

THREE AND SIX OR FOUR AND FIVE

Step-by-step explanation:

They're just opposite ends !

Step-by-step explanation:

Alternate Interior Angles: 3 and 6

Alternate Exterior Angles: 2 and 7

Answer:

80°

because its diagnol so the one in the top corner is the same as x

Answer:

x = 140°

Step-by-step explanation:

Sum of exterior angles of polygon is 360°

That is, x + 70 + 80 + 70 = 360

           x + 220 = 360

           x = 360 - 220 = 140°

Answer:

S(t) = 1000(0.729)^t

Step-by-step explanation:

S(t) = 1000(0.9)^(3t)

S(t) = 1000((.09)^(3))^t

S(t) = 1000(0.729)^t