Which two values are solutions to the inequality r ≤ 5?

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:

Step-by-step explanation:

Let's say R is roses, L is lilies, and O is orchids.

R = 2L

O = R + 5

R + L + O = 45

Let's substitute the second equation into the third:

R + L + (R + 5) = 45

2R + L = 40

Now substitute the first equation:

2(2L) + L = 40

4L + L = 40

5L = 40

L = 8

Therefore:

R = 2L = 16

O = R + 5 = 21

There are 16 roses, 8 lilies, and 21 orchids.

Answer:

120

Step-by-step explanation:

x/6=20

×=20×6

=120

Hello There!

To find the mean we have to add up all the numbers and divide by how many numbers there are.

6+15+16+20+13+5+10+16

Now, I will add 2 numbers at a time to make it easier for myself.

21+36+18+26

Once I add up these numbers, I will get a sum of 101

Finally, I divide 101 by 8 and get a quotient of 12.625

6 + 15 + 16 + 20 + 13 + 5 + 10 + 16 = 101/8 = 12.6

mean: 12.6

Answer:

1 4/7

Step-by-step explanation:

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

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.

Let's do the same thing to evaluate g(-5):

-5Answer:

Step-by-step explanation:

Never heard of "synthetic substitution."  I think you meant "synthetic division," which is a great method of evaluating polynomials for given input values.

g(x) = x^5 – 8x^3 – 2x + 7 is missing two terms.

With all terms showing, it would read:

g(x) = x^5 – 0x^4 + 8x^3 – 0x^2 - 2x + 7.  The coefficients are {1, 0, 8, 0, -2, 7}.

Let's evaluate g(3).  Use 3 as divisor in synth. div.:

3   )  1   0   8   0   -2   7

            3   9  51  153 453

    ------------------------------

       1    3   17  51  151  460      Since the remainder is 460, the value of g(3) is also 460.

-5  )   1    9    8    0    -2       7

              -5  -20  60 -300 1510

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

       1      4    -12   60 -302   1517

The remainder is 1517, and so g(-5) = 1517.

Answer:

28, -2,108

Step-by-step explanation:

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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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!

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:

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.

You can find length by knowing the formula for perimeter: 2l+2w= p; where l= length, w= width, and p= perimeter. Substitute the things you know and solve.

In this case, the length would be 11 feet.

the equation that can be used to find width is B

Answer:

It's a

Step-by-step explanation:

I did it

Answer:

Around 79.17 weeks

Step-by-step explanation:

Answer:

if you want to know how many weeks are in one year and 27 weeks, i can help out

Step-by-step explanation: 1 year has 365 days in it and one week has 7 days in it. Divide 365 by 7.

365/7= about 52 weeks.

52+27=79 weeks.

The exact amount of weeks is 79.177457

hope this helped!!

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: 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

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

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:

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:

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.

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 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:

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:

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:

Step-by-step explanation:

Convert the fractions to the decimals (you can use the calculator):

2/3 = 2 : 3 = 0.6666...

3/5 = 3 : 5 = 0/6

We have

0.65

0.666...

0.6

0.5

The order from least to greatest:

0.5

0.6

0.65

0.666..

[tex]\begin{array}{c|c|c|c|c}0&.&5\\0&.&6\\0&.&6&5\\0&.&6&6&6...\end{array}[/tex]

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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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!!!!!!!!!!!!!

Answer:

240

Step-by-step explanation:

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

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

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