An engineer is using a polynomial function to model the height of a roller coaster over time x, as shown.
On a coordinate plane, a curve increases from quadrant 3 and crosses the y-axis at (0, 4). It then decreases and crosses the x-axis at (5, 0). It continues to decrease and then starts to increase and crosses the x-axis at (8, 0).
The engineer wants to modify the roller coaster design by transforming the function. Which represents 2 f (0.3 x minus 1) + 10, the modified design of the roller coaster?

Answer:

17/4

or

17 ÷ 4

Step-by-step explanation:

This equals 4.25.

hope this helps

have a good day

The quotient of seventeen and four in the mixed fraction form will be 4 ¹/₄. Then the correct option is A.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Convert the statement 'quotient of seventeen and four' into a mathematical expression. Then we have

⇒ 17 / 4

Convert the fraction number into a mixed fraction number, then we have

⇒ 17 / 4

⇒ 4 ¹/₄

The quotient of seventeen and four in the mixed fraction form will be 4 ¹/₄. Then the correct option is A.

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The missing options are given below.

A. 4 1/4      B. 4 3/4      C. 3 1/4      D. 3 3/4

By definition of tangent,

tan(θ - x) = sin(θ - x) / cos(θ - x)

Expand the sine and cosine terms using the angle sum identities,

sin(x ± y) = sin(x) cos(y) ± cos(x) sin(y)

cos(x ± y) = cos(x) cos(y) ∓ sin(x) sin(y)

from which we get

tan(θ - x) = (sin(θ) cos(x) - cos(θ) sin(x)) / (cos(θ) cos(x) + sin(θ) sin(x))

Also recall the Pythagorean identity,

cos²(x) + sin²(x) = 1

from which we have two possible values for each of cos(θ) and sin(x):

cos(θ) = ± √(1 - sin²(θ)) = ± 3/5

sin(x) = ± √(1 - cos²(x)) = ± 12/13

Since there are 2 choices each for cos(θ) and sin(x), we'll have 4 possible values of tan(θ - x) :

• cos(θ) = 3/5, sin(x) = 12/13 :

tan(θ - x) = -56/33

• cos(θ) = -3/5, sin(x) = 12/13 :

tan(θ - x) = 16/63

• cos(θ) = 3/5, sin(x) = -12/13 :

tan(θ - x) = -16/63

• cos(θ) = -3/5, sin(x) = -12/13 :

tan(θ - x) = 56/33

Now

cos(ø-x)

sin(ø-x)

So

tan(ø-x)

Answer:

-2

Step-by-step explanation:

3(a+1.5)=-1.5

a+1.5 = - 1.5/3 = - 0.5

a = - 0.5 - 1.5 = - 2

Answer:

Step-by-step explanation:

3a + 4.5 = -1.5

3a = -6

a = -2

Recall the Maclaurin expansion for cos(x), valid for all real x :

[tex]\displaystyle \cos(x) = \sum_{n=0}^\infty (-1)^n \frac{x^{2n}}{(2n)!}[/tex]

Then replacing x with √5 x (I'm assuming you mean √5 times x, and not √(5x)) gives

[tex]\displaystyle \cos\left(\sqrt 5\,x\right) = \sum_{n=0}^\infty (-1)^n \frac{\left(\sqrt5\,x\right)^{2n}}{(2n)!} = \sum_{n=0}^\infty (-5)^n \frac{x^{2n}}{(2n)!}[/tex]

The first 3 terms of the series are

[tex]\cos\left(\sqrt5\,x\right) \approx 1 - \dfrac{5x^2}2 + \dfrac{25x^4}{24}[/tex]

and the general n-th term is as shown in the series.

In case you did mean cos(√(5x)), we would instead end up with

[tex]\displaystyle \cos\left(\sqrt{5x}\right) = \sum_{n=0}^\infty (-1)^n \frac{\left(\sqrt{5x}\right)^{2n}}{(2n)!} = \sum_{n=0}^\infty (-5)^n \frac{x^n}{(2n)!}[/tex]

which amounts to replacing the x with √x in the expansion of cos(√5 x) :

[tex]\cos\left(\sqrt{5x}\right) \approx 1 - \dfrac{5x}2 + \dfrac{25x^2}{24}[/tex]

The value of b is 7 and a statement which is true about the x-intercepts of this function is that it can have up to 2 x-intersept.

The x-intercept is the point on the coordinate at which a line, curve or plane intersect with the x-axis.

Number 5 is the one x-intercept of the equation,

[tex]y = x^2 + bx + 10[/tex]

Put the value of y as 0 and x as 5 at the to find the value of b.

[tex]0= 5^2 + b\times 5 + 10\\0= 5^2 + b\times 5 + 10\\0=25+5b+10\\5b=35\\b=7[/tex]

Thus, the value of b is 7.

The given equation is a quadratic equation, and a quadratic equation may have 2 x-intercept. Thus, the true statement is that x-intercepts of this function can be up to 2.

Hence, the value of b is 7 and a statement which is true about the x-intercepts of this function is that it can have up to 2 x intercept.

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Answer:

18 centimeters

Step-by-step explanation:

Divide the circumference by π, or 3.14 for an estimation. The result is the circle's diameter.

Divide the diameter by 2.

There you go, you found the circle's radius

The consumption of electricity in May based on the model will be 1225kw.

The model that's given to calculate the consumption is:

C = 1200 + 5t

May = 5th month

The consumption in May will be:

C = 1200 + 5t

C = 1200 + 5(5)

C = 1200 + 25

C = 1225Kw

In conclusion, the consumption of electricity in May based on the model will be 1225kw.

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[tex]\blue\textsf{\textbf{\underline{\underline{Question:-}}}}[/tex]

3x²=75. What is x?

[tex]\blue\textsf{\textbf{\underline{\underline{Answer and How to Solve:-}}}}[/tex]

First, divide by 3 on both sides:-

x²=25       Next, take the square root of both sides:-

x=5, x=-5 (remember, x² =x times x (x times itself); 5 times itself gives 25, and -5 times itself also results in 25)

[tex]\dashrightarrow\bigstar\boxed{\boxed{\underline{\bold{So\:the\:value\:of\:x\:is\:5\:and\:-5}}}}\dashleftarrow[/tex]

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Answer:

sqrt(217)/19

Step-by-step explanation:

Ok so insead of using 01 as the angle ill use x. cos(θ) is the the x-value of the point on the unit circle, while sin(θ) is the y value. cos(x) here is -12/19. By constructing a triangle such that one of the verticies is at (-12/19, sin(x)), we know the x distance is -12/19, and the hypotenues is 1, because it's a unit circle. sqrt(1-144/361)=sqrt(217/361)=sqrt(217)/19. the y value must e positive because this point lays in the 2nd quadrant.

my explanation might be a but tricky so let me know if you have any questions.

Answer:

see explanation

Step-by-step explanation:

Step-by-step explanation:

The domain of the function is all real numbers less than or equal to −2 - FALSE;

The domain of the function is all real numbers less than or equal to 9 - FALSE;

The range of the function is all real numbers less than or equal to −2 - FALSE;

The range of the function is all real numbers less than or equal to 9 - TRUE.

PS. the domain is (-∝;+∝); the range is (-∝;9].

Answer:

x=1.13

Step-by-step explanation:

isolate the variable and the numbers and solve.

Answer:

y=ab^x

y=6.0.8^x

Step-by-step explanation:

find exponential function by substituting given values into y=ab^x and the solve

The effective rate of interest is given by the same formula but with the disbursed amount which is $838.50.

Simple interest is the concept that is used in many companies such as banking, finance, automobile, and so on.

Philippa took out an $860 discounted loan for a period of m months and the simple interest rate was 6%. The amount that was actually disbursed into her bank account was $838.50.

Then the effective interest rate of this loan, to the nearest 0.01% will be

So, from the question the interest that is deducted = $860-$838.50 = $21.50

Now, I = Prt/100

So, t = 100 (I/Pr) = 0.42 years = 5months

therefore m = 5months

So, the effective rate of interest is given by the same formula but with the disbursed amount which is $838.50.

I = Prt/100

Therefore, r = 100 (I/Pt) = 6.15%

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Answer:

D. 7

Step-by-step explanation:

42 + 70 = 112 stamps altogether.

112 can be divided by 2, 4, 7, 8, 14, 16, 28, 56

to be more simpler, since there are options, we can cross out the other numbers not shown in the options. then see that 6 and 10 are not divisible by 112, so cross them out. it will left with option A and option D.

option A is 2. if he uses two pages, then each page should have a total of 56 stamps. however, foreign stamps have an amount of 42 only, so it is quite impossible to fit in more than 42.

option D is 7. if he uses 7 pages, then each page could fit in 16 stamps.

so the answer will be option D.

Answer:

no because nkow one can explain

Answer:

1 = 10

Step-by-step explanation:

0.5 x X = 15

15/0.5 = 30

30/3 = 10

Using the given table, it is found that the mean number of children per household for these families is of 2.33.

The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations.

Researching the problem on the internet, the table states that:

The total number of children is given by:

T = 2 x 4 + 16 x 2 + 13 x 3 + 5 x 1 = 84

Hence the mean number of children for the 36 households is given by:

M = 84/36 = 2.33.

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Answer: C

Step-by-step explanation:

By the alternate interior angles theorem, we know that [tex]5y+14=8y-13 \longrightarrow y=9[/tex].

So, this means that [tex]m\angle RPS=59^{\circ}[/tex].

Now, if we consider [tex]\triangle RPS[/tex], since angles in a triangle add to [tex]180^{\circ}[/tex], this means that [tex]59+2x+1+3x=180 \longrightarrow x=24[/tex].

So, [tex]m\angle RSP=\boxed{59^{\circ}}[/tex]

Answer:

a. 3

b. 12

c. In. and "

d. ft. and '

Step-by-step explanation:

c. 13in. or 13"

d. 13ft. or 13'

Answer:

Slope = 1

Step-by-step explanation:

Considering the piece-wise function, the value of the function at x = 2, that is, g(2), is given by:

C. 1.

It is a function that has different definitions based on the input.

In this problem, the function is defined by:

Due to the equal sign, x = 2 is part of the second definition, hence:

g(2) = 2³ - 9(2)² + 27(2) - 25 = 1.

Which means that option C is correct.

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The distance from point P to the foot of the flagpole is 13.42m. So, The height of the flagpole will be 17.7 m.

Trigonometric ratios for a right-angled triangle are from the perspective of a particular non-right angle.

In a right-angled triangle, two such angles are there which are not right-angled(not of 90 degrees).

The slanted side is called the hypotenuse.

From the considered angle, the side opposite to it is called perpendicular, and the remaining side will be called the base.

We know that

[tex]tan(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of base}}[/tex]

Let x be the distance from point P to the foot of the flagpole.

So, From point P the height h of the flagpole will be

[tex]tan(53) = \dfrac{height}{x}\\\\tan(53) x = h\\\\h = 1.32x[/tex]

From point Q, the height h will be

[tex]tan(28) = \dfrac{height}{20+x}\\\\tan(28) (20+x )= h\\\\h = 0.53 (20+x )[/tex]

From both values of h, we get

x = 13.42

Put the value of x in the first value of h,

h = 1.32 ( 13.42)

h = 17.7

Hence, the height of the flagpole will be 17.7 m.

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[tex]\blue{\textsf{\textbf{\underline{\underline{Question:-}}}}[/tex]

             Solve x²-5x+6

[tex]\blue{\textsf{\textbf{\underline{\underline{Answer:-}}}}[/tex]

(x-2)(x-3)

[tex]\blue{\textsf{\textbf{\underline{\underline{How\:to\:Solve:-}}}}[/tex]

                      First, we think of two numbers such that

     If we multiply them, we'll get 6

      If we add them, we'll get -5

These numbers are -2 and -3.

Write them here:

(x-2)(x-3)

Now, how do we get (x-2)(x-3) from x(x-2)-3(x-2)?

Notice that (x-2) is the common term, so we factor it out:

(x-2)

And now, we write the other two terms that are left in the parentheses:

(And the terms left are x and -3)

(x-2)(x-3)

Notice that we ended up with the same answer.

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Answer: 6h + 4.5d + 10 = 61

Explanation: We know that peanuts cost 5 each, and they bought two. So, 10 dollars.
We don't know how many hotdogs or drinks they've bought so that will be our variable.
Hot dogs = 6$
Drinks = 4.5$
Total Price = 61

6h + 4.5d + 10 = 61

Answer:

Step-by-step explanation:

I don't know what is meant by "analyze the function," but I can draw the functions.

Answer:

1217 I think

Step-by-step explanation:

Answer:

1217

Step-by-step explanation:

309 and 908 combined together is 1217

Answer:

78.55cm^2

Step-by-step explanation:

area of a circle = πr^2

where π= 3.142

r= radius= diameter/2

radius= 10/2= 5

area= 3.142×(5)^2

area= 3.142×25=78.55cm^2

Answer:

112.5 pi

Step-by-step explanation:

hi, to find this we need to know the formula for the area of a circle. it is:

a=pi*radius^2

so the radius is 30/2=15

now we can just plug 15 in to find the area.

a=pi*15^2

a=225pi

now, that is the area for the full circle, but here it is a semi circle, so we just divide 225 pi by 2 to get

112.5 pi, or 112.5π