The graph represents the height y, in feet above the ground of a rock x seconds after it is dropped from a building. Which statement is true? Select each correct answer.

-the rock hits the ground in 45 s.

-the rock rises above 45 ft before falling toward the ground.

-the maximum height of the rock occurs at x=0

-the rock is in the air for 3 s.

-the Maximum height of the rock is 45 ft.

Answer:

(- 1, 2)

Step-by-step explanation:

Given a quadratic in standard form y = ax² + bx + c : a ≠ 0

Then the x- coordinate of the vertex is

[tex]x_{vertex}[/tex] = - [tex]\frac{b}{2a}[/tex]

f(x) = x² + 2x + 3 ← is in standard form

with a = 1 and b = 2, hence

[tex]x_{vertex}[/tex] = - [tex]\frac{2}{2}[/tex] = - 1

Substitute x = - 1 into f(x) for corresponding value of y

f(- 1) = (- 1)² + 2(- 1) + 3 = 1 - 2 + 3 = 2

vertex = (- 1, 2 )

Answer:

90 units²

Step-by-step explanation:

The area (A) of a kite is calculated as

A = [tex]\frac{1}{2}[/tex] × d₁ × d₂ ← diagonals

d₁ = 3 + 3 = 6 and d₂ = 20 + 10 = 30, hence

A = 0.5 × 6 × 30 = 90 units²

Answer:

I'm not sure if this is the answer answer but this what the graph is a parabola

The function represented by the graph is y = 1/4(x - 2)^2 + 1

What function does this graph represent?

From the question, we have the following parameters that can be used in our computation:

The graph

The graph is the graph of a quadratic function

By definition:

A quadratic function is represented as

y = a(x - h)^2 + k

Where

Vertex = (h, k)

From the graph, we have

Vertex = (2, 1)

So, we have

y = a(x - 2)^2 + 1

Using the point (0, 2) on the graph, we have

a(0 - 2)^2 + 1 = 2

4a + 1 = 2

4a = 1

a = 1/4

So, we have

y = 1/4(x - 2)^2 + 1

Hence, the function this graph represent is y = 1/4(x - 2)^2 + 1

1st Answer: B.) (-1,170, -23,400) and (170, 3,400)

2nd Answer: 170

Answer:

that answer is verified 100% correct

Step-by-step explanation:

the equation that can be used to find width is B

Answer:

It's a

Step-by-step explanation:

I did it

Answer:

Maximum value of the function is 4.

Step-by-step explanation:

Given function of simple harmonic motion is [tex]d=4\sin\left(\frac{\pi}{8}t\right)[/tex].

Now we need to find about what is the maximum value of [tex]d=4\sin\left(\frac{\pi}{8}t\right)[/tex].

We know that value of sine function varies from -1 to 1.

that means for any value of t, maximum value of sine function is 1.

[tex]\sin\left(\frac{\pi}{8}t\right) \leq 1[/tex]

[tex]4 \sin\left(\frac{\pi}{8}t\right) \leq 4[/tex]

[tex]d \leq 4[/tex]

Hence maximum value of the function is 4.

Answer:

The formula for the area of a polygon is 1/2*a*p.

a = apothem, which is a line segment that is the shortest distance from the center to a side.

p = perimeter

Hope this helps. :)

Answer:

Step-by-step explanation:

There's no one formula for finding the area of any polygon.

There are specialized formulas for finding the area of a square, of a triangle, of a trapezoid, etc.  Beyond these, you have to invent approaches, such as breaking up an octagon into 8 triangles, finding the area of 1 such triangle, and then multiplying that area by 8.

Answer:

1 4/7

Step-by-step explanation:

11/7 As A Mixed Number Would Be 1 And 4/7

Answer:

A  = $2200(7.612) = $16,747.28

Step-by-step explanation:

You don't say whether this is simple interest or compound interest.  I will assume you meant compound interest, for which the appropriate formula is

A = P(1 + r)^t, where P is the principal amount, r is the interest rate as a decimal fraction, and t is the time in years.  Then:

A = $2200(1 + 0.0725)^29, or

A = $2200(1.0725)^29, or

A  = $2200(7.612) = $16,747.28

The amount in the account after 29 years will be approximately $8484.64.

To calculate the amount of money that will be in the account after 29 years, we can use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount ($2200 in this case), r is the annual interest rate (7.25% or 0.0725 as a decimal), n is the number of times interest is compounded per year (in this case, it's compounded annually, so n is 1), and t is the number of years (29 in this case). Plugging in the values, we get:

A = 2200(1 + 0.0725/1)^(1*29)

A = 2200(1.0725)^29

A ≈ $8484.64

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The answer is 8 times bigger.

Hope this helps!

Answer:

2times bigger.

Step-by-step explanation:

Original volume of a rectangular prism = length × width × height

V = lwh... (1)

If the original dimension is doubled

New volume V2 = 2l × 2w × 2h

V2 = 2(lwh)...(2)

Taking the ratio of both volumes

V2/V = 2(lwh)/lwh

V2/V = 2

V2 = 2V

This shows that the new volume was two times bigger than the original volume

Answer: is D

                 Visit Dentist Yearly Don’t Visit Dentist Yearly

Below 40                0.27                    0.73

Above 40              0.57                      0.43

Work: 8+22=30        17+13=30     turn into a fraction then simplify to get answer;

22/30   simp= 73.0 (0.73)

13/30     simp= 43.0 (0.43)

8/30      simp= 26.667 (0.27)

17/30      simp= 56.667 (0.57)

Answer with Step-by-step explanation:

              Visit Dentist Yearly Don’t Visit Dentist Yearly

Below 40      8                                        22

Above 40      17                                 13

Relative frequency of people above 40 years old who do not visit a dentist once a year

=Number of people above 40 years old who do not visit a dentist yearly/Number of people above 40

=13/(17+13)

=13/30

=0.43

Hence, Relative frequency of people above 40 years old who do not visit a dentist once a year is:

0.43

Answer:

Each friend will get more than 4 whole bagels.

Step-by-step explanation:

First off, although the question asks for 13 bagels divided between 3 friends, let's use a number that results in a whole number when divided by 3, but is close to 13.

This number can be 12.

12 divided by 3 is 4, so each friend gets 4 bagels if there are a total of 12 bagels.

However, there are more than 12 bagels so we know that each of the the 3 friends will get more than 4 bagels each.

Each friend will get 4 whole bagels, with 1 bagel left over.

In a baker's dozen, there are 13 bagels. Hillary, Mark, and Tam share the bagels equally. To determine if each friend will get more than or fewer than 4 whole bagels, we divide the total number of bagels by the number of friends.

13 bagels / 3 friends = 4 remainder 1

Each friend will get 4 whole bagels, with 1 bagel left over.

Division is one of the four basic operations of arithmetic. The other operations are addition, subtraction, and multiplication. What is being divided is called the dividend, which is divided by the divisor, and the result is called the quotient.

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Answer: (1) 120° (2) 6.5

Step-by-step explanation:

(1)

[tex]\dfrac{major\ arc-minor\ arc}{2}=intercepted\ angle\\\\\\\dfrac{(360-x)-x}{2}=60[/tex]

360 - 2x =  120

       - 2x = -240

            x = 120

(2)  

2.5²  +  6² = x²

6.25 + 36 = x²

     42.25 = x²

         6.5 = x

Answer:

Multiplying the decimal number by 1000

Step-by-step explanation:

consider the number 12.2345.

For you to move the decimal point three places to the right, you have to multiply the number with 10³=1000

12.2345×1000= 12234.5

The decimal has moved from three places as it has skipped three places values to the right.

The choice which is the same as moving the decimal point 3 places to the right in a decimal number is; Multiplying the number by 1000.

According to the task content;

Since, a decimal point movement one space to the right indicates a multiplication by 10, hence, it follows that the required multiplication is 1000.

Read more on decimal point;

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Answer:

10 or 100

Step-by-step explanation:

Answer:

100^1,000 if that's what you mean or 100 ^10 to make 1,000

Step-by-step explanation:

IF RIGHT PLZ MARK BRAINLIEST!! PLZZZ!!!!!!!!!!!!!

QUESTION 1

[tex] \boxed {f(x) = 2x + 6 \to \: g(x) = \frac{1}{2}x - 3 } [/tex]

The reason is that:

[tex]g(f(x)) = 2( \frac{1}{2} x - 3) + 6[/tex]

Expand:

[tex]g(f(x)) = x - 6+ 6 [/tex]

[tex]g(f(x)) = x[/tex]

QUESTION 2

[tex]\boxed {f(x) =3 - 2x \to \: g(x) = - \frac{1}{2}(x - 3)} [/tex]

The reason that

[tex]g(f(x)) = - \frac{1}{2} (3 - 2x - 3)[/tex]

[tex]g(f(x)) = - \frac{1}{2} (- 2x )[/tex]

[tex]g(f(x)) =x[/tex]

QUESTION 3

[tex]\boxed {f(x) = \sqrt[3]{3x}+ 2 \to \: g(x) = \frac{ {(x - 3)}^{3} }{3} } [/tex]

The reason is that:

[tex]f(g(x)) = \sqrt[3]{ \frac{3 {(x - 2)}^{3} }{3} } + 2[/tex]

[tex]f(g(x)) = x-2 + 2[/tex]

[tex]f(g(x))=x[/tex]

QUESTION 4

[tex]\boxed {f(x)=3\sqrt[3]{x + 2} \to \: g(x) = \frac{1}{27} {x}^{3} - 2} [/tex]

The reason is that

[tex]f(g(x)) = 3 \sqrt[3]{ \frac{1}{27} {x}^{3} - 2 + 2} [/tex]

[tex]f(g(x)) = 3 \sqrt[3]{ \frac{1}{27} {x}^{3} } [/tex]

[tex]f(g(x)) = 3 \times \frac{1}{3} x[/tex]

[tex]f(g(x)) =x[/tex]

Answer:

[tex]y\geq 3x-2[/tex] and [tex]y\leq \frac{1}{2} x+3[/tex]

Step-by-step explanation:

Blue:

The inequality for the blue line is

[tex]y\geq 3x-2[/tex]

Yellow

The inequality for the yellow line is

[tex]y\leq \frac{1}{2} x+3[/tex]

This means that the correct answer is the third option,

[tex]y\geq 3x-2[/tex] and [tex]y\leq \frac{1}{2} x+3[/tex]

The graph shows the solution for the inequalities y ≥ 3x - 2 and y ≤ x + 3.

The inequalities can be found by substituting the coordinates of a point within the shaded area in both inequalities and seeing if they are satisfied.

The options are given.

Let us take the options one by one:

Now, substitute (0,0) in the inequalities:

0 ≥  2 and 0 ≤  3

This is not true.

Now, substitute (0,0) in the inequalities:

0 ≥ - 2 and 0 ≤ - 3

This is not true.

Now, substitute (0,0) in the inequalities:

0 ≥ - 2 and 0 ≤ 3

This is true.

Now, substitute (0,0) in the inequalities:

0 ≥ - 2 and 0 ≤ - 3

This is not true.

Therefore, we have found that the inequalities are y ≥ 3x - 2 and y ≤ x + 3. The correct answer is option C.

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What we are given:

r( x ) = x - 3

s( x ) = 4x²

We have to find:

( s + r )( x ) = ( x - 3 + 4x² )

→ 4x² + x - 3

( s - r )( x ) = ( x - 3 - 4x² )

→ -4x² + x - 3

For the last function, I am confused whether it is a multiplication or composite function, so I am going to do both.

Multiplication:

( x - 3 ( 4x² ))( 2 )

( 4x³ - 12x² )( 2 )

4(2)³ - 12(2)²

4(8) - 12(4)

32 - 48

→ -4

Composite function:

r(s(x))(2) = r(4x²) = 4x² - 3  = 4(2)² - 3 = 4(4) - 3 = 16 - 3

→13

Final answer:

The expressions for (s+r)(x) is 4x^2 + x - 3 and (s-r)(x) is 4x^2 - x + 3. The value of (s.r)(2) is 16.

Explanation:

To find the expression for (s+r)(x), we need to add the functions s(x) and r(x). Adding the two functions, we get (s+r)(x) = 4x^2 + (x-3). Simplifying this expression, (s+r)(x) = 4x^2 + x - 3.

To find the expression for (s-r)(x), we need to subtract the function r(x) from s(x). Subtracting the two functions, we get (s-r)(x) = 4x^2 - (x-3). Simplifying this expression, (s-r)(x) = 4x^2 - x + 3.

To evaluate (s.r)(2), we need to substitute 2 for x in the expression s(x) * r(x). Substituting 2 for x in the expression 4x^2, we get (s.r)(2) = 4(2)^2 = 16.

Answer:

Opt B. y=5-3x

Step-by-step explanation:

We need to write the given equation in slope-intercept form, so we can obtain the slope and the 'y' axis intercept point.

To do this, we need to isolate 'y' variable with a possitive sign, hence we perform the following operation:

Subtraction of -5 in both sides of equality sign.

-y=3x-5

Lets multiply by -1 the equation from above:

y= 5-3x.

From the above we can find the slope, is the coefficient of x. in this case -3

And the y-intercept point is 5.

Answer:

There is not enough information

Step-by-step explanation:

If you wanted to find all the factors, here’s a list.

1,2,4,8,16

Answer:

zero im pretty sure

Step-by-step explanation:

Answer:

An inconsistent linear system has  no solution(s).

Step-by-step explanation:

Just took the test.

To change the graph of f(x) = [tex]x^2[/tex] into g(x) = 4[tex]x^2[/tex] + 24x + 30, the transformations include a vertical stretch by a factor of 4 and a shift to the left by 3 units and up by 6 units. Completing the square helps identify these shifts.

To transform the graph of f(x) = [tex]x^2[/tex] into the graph of g(x) = 4[tex]x^2[/tex] + 24x + 30, we can analyze the changes applied. First, the coefficient of x2 in g(x) is 4, which means the original parabola is vertically stretched by a factor of 4. Second, the term 24x indicates a horizontal transformation, specifically a shift, which is revealed when we complete the square.

To complete the square for the quadratic part of g(x), we rewrite the equation as 4([tex]x^2[/tex] + 6x) + 30 and add and subtract the square of half the coefficient of x inside the parentheses, giving us 4((x + 3)2 - 9) + 30. This simplifies to 4(x + 3)2 + 6, indicating that the graph of f(x) was also shifted to the left by 3 units and up by 6 units.

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Answer and Explanation :

Given : The data represents the number of traffic tickets written by two police officers in one day over the course of a week.

Officer 1: 21, 11, 14, 16, 10, 18, 5

Officer 2: 16, 19, 20, 17, 6, 13, 23          

To find : (a) Draw a box and whiskers plot for each officer

(b) Compare the median values of the data sets. What does this comparison tell you in terms of the situation the data represent?        

Solution :

a) We plot the box plot with the help of graphing calculator of both data.

Refer the attached figure below.

Figure 1 shows the data 1 with Median 14.

Figure 2 shows the data 2 with Median 17.

b) On comparing the median of both Officer's are different first officer has 14 median and second officer has 17 median.

Answer:

x=0 and x=1

Step-by-step explanation:

4(1)-4=0

2(3)^(1)-6=0

4(0)-4=-4

2(3)^(0)-6=-4

ANSWER

See attachment.

EXPLANATION

The given parent function is:.

[tex]y = \sqrt[3]{x} [/tex]

If this graph is reflected over the x-axis and then translated down 2 units to form f(x), then the f(x) has equation

[tex]f(x) = - \sqrt[3]{x} - 2[/tex]

The graph of this function is shown in the attachment.

Answer:

the second graph

Step-by-step explanation:

Answer:

240

Step-by-step explanation:

since that arc is 120 you subtract that form 360 and voila!

Answer:

8cm

Step-by-step explanation:

Since the area of a square is Side X Side (s x s) it is also s². The s² is also equivalent = 64cm². To find the length of a side you do the √64cm² and you get 8cm for a side. Great Job!

It's a much more interesting problem when we have to estimate the shadow length from a photo.

The crater is a curvy bumpy surface, but let's approximate it as part of a sphere and just conflate the arc and chord length, so the 400 m shadow corresponds to a 400 m chord from the edge at the surface to the bottom.

The shadow as a chord forms a hypotenuse right triangle with the depth d being the leg opposite the 48 degree angle of the sun.

[tex] d = 400 \sin 48 \approx 297 \textrm{  m}[/tex]

Answer: 297 m

The depth is 297.26 m.

It is the application of trigonometry.

It is a type of triangle in which one angle is 90 degrees and it follows the Pythagoras theorem and we can use the trigonometry function.

Given

The shadow is estimated to be 400 m long.

And the angle of elevation of the sun is 48°.

The depth of a crater.

Hypotenuse = 400m

Angle = 48°

The by the sine rule

[tex]\begin{aligned} \rm sin \theta &= \rm \dfrac{Depth}{Hypotenuse}\\\\\rm sin 48^o &= \rm \dfrac{depth}{400}\\\\\rm depth &= \rm sin 48^o * 400\\\\\rm depth &= 297.2579 \approx 297.26 \end{aligned}[/tex]

Thus, the depth is 297.26 m.

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Answer:

-9 < x

Step-by-step explanation:

6x-11-13x<7-5x

Combine like terms

-11-7x<7-5x

Add 7x to each side

-11-7x+7x<7-5x+7x

-11 < 7+2x

Subtract 7 from each side

-11-7 < 7-7+2x

-18 < 2x

Divide by 2

-18/2 < 2x/2

-9 < x

So we are given the following function: [tex]y=-(x + 2)^{2}[/tex].

Before we can solve this problem, we need to know the following:

Know we can solve the problem!

1. [tex]y=-(x + 4)^{2}[/tex]. Translated left by 2 units.

2. [tex]y=-(x + 2)^{2} - 2 [/tex] Translated down by 2 units

3. [tex]y=(x - 2)^{2}[/tex] Reflected across the x-axis and the y-axis

4. [tex]y= 2-(x + 2)^{2}[/tex] Translated up by 2 units

5. [tex]y=-(x)^{2}[/tex] Translated right by 2 units

6. [tex]y=(x + 2)^{2}[/tex] y = (x + 2)2 Reflected across the x-axis