Which of the following statements are true about the graph of f(x) = 6(x + 1)² -9?
Check all of the boxes that apply.

A. The vertex is (1, -9).

B. The graph opens upward.

C. The graph is obtained by shifting the graph of f(x) = 6(x + 1)² up 9 units.

D. The graph is steeper than the graph of f(x) = x².

E. The graph is the same as the graph of f(x) = 6x² + 12x - 3.

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Thank you!

-Charlie

Final answer:

Explanation on solving the equation p = 55 - 0.5w to find Rocco's weight after w weeks.

Explanation:

Solving the Equation:

Since Rocco lost half a pound per week, the equation would be: p = 55 - 0.5w, where p is Rocco's weight in pounds and w is the number of weeks.

Substitute the value for the first week: p = 55 - 0.5(1) = 55 - 0.5 = 54.5 pounds.

Therefore, Rocco's weight after w weeks would be p = 55 - 0.5w.

Answer:

The equation of the scenario is

✔ p = 55 – 0.5w

.

The values of p must be

✔ any real number 45 to 55

Step-by-step explanation:

Answer:

  x equals the quantity negative B times y minus C all over A

Step-by-step explanation:

Subtract By and divide by A:

  Ax + By = -C . . . . starting equation

  Ax = -By -C . . . . . subtract By from both sides

  x = (-By -C)/A . . . . divide both sides by A

Answer:

A

Step-by-step explanation:

Answer:

ST, RS, and RT

Step-by-step explanation:

A line is tangent to a circle if it intersects it at only one point.

ST, RS, and RT are all tangent to circle A.

AP intersects the circle at two points when extended.

XT intersects the circle at two points as well.

Answer:

A. [tex]\overline{ST}[/tex]

B. [tex]\overline{RS}[/tex]

D. [tex]\overline{RT}[/tex]

Step-by-step explanation:

We have been given that triangle RST is circumscribed about circle A. We are asked to choose that tangent of our given circle fro the provided choices.

We know that tangent of circle is a straight line that touches the circle exactly at one point. This point is known as point of tangency.

Upon looking at our given diagram, we can see that line segment RX touches circle A exactly at one point that is X. Line segment SX touches circle A exactly at one point that is X, therefore, line segment RS is tangent to our given circle.

Similarly, line segments SQ and TQ touch circle A exactly at one point that is Q, therefore, line segment ST is tangent to our given circle.

We can see that line segments RP and TP touch circle A exactly at one point that is P, therefore, line segment ST is tangent to our given circle.

AP is radius of circle, therefore, AP is not a tangent for our given circle.

If we draw a line joining points XT, it will intersect circle at two points, therefore, XT is not a tangent for our given circle.

Answer:

|x − 37,500| ≤ 4,500

Step-by-step explanation:

salary - 37,500 can be up  +4500 or as negative -4500

as much as means less than or equal to

We use absolute values to indicate this

|x − 37,500| ≤ 4,500

Answer:

|x − 37,500| ≤ 4,500

Step-by-step explanation:

Let x represents the new salary paid (In dollars ),

∵ The actual salary = $ 37,500

∵ Maximum difference in salaries = $ 4500

Case 1 : If x > 0

⇒ x - 37500 ≤ 4500 -----(1)

Case 2 : If x < 0

⇒ 37500 - x ≤ 4500

⇒ -(x-37500) ≤ 4500 -----(2)

By combining inequalities (1) and (2),

| x - 37500 | ≤ 4500  ( ∵ |a| < b ⇒ -a < b or a < b )

Which is the absolute value inequality to determine the range of salaries at this company.

FIRST option is correct.

Answer:

I don't know for sure but is 69 an option? is so that might be it

Answer:

x = 58

Step-by-step explanation:

Given an angle outside a circle formed by a tangent and a secant then

angle = [tex]\frac{1}{2}[/tex] difference of the measures of the intercepted arcs, that is

51 = [tex]\frac{1}{2}[/tex] (160 - x) ← multiply both sides by 2

160 - x = 102 ( subtract 160 from both sides )

- x = - 58 ( multiply both sides by - 1 )

x = 58

Answer:

$12,993.71

Step-by-step explanation:

The formula we want for this is exponential decay which is

[tex]A(t)=a(1-r)^t[/tex]

where A(t) is the value of the car after the depreciation, a is the initial value of the car, r is the interest rate at which it depreciates in decimal form, and t is the time in years.  We have everything we need to fill in to solve for A(t):

[tex]A(t)=66,000(1-.15)^{10}[/tex]

We will do some simplifying first:

[tex]A(t)=66,000(.85)^{10}[/tex]

First raise .85 to the 10th power to get

A(t) = 66,000(.1968744043)

and then multiply to get

A(t) = $12,993.71

Answer:

$12,993.71

Step-by-step explanation:

First raise .85 to the 10th power to get

A(t) = 66,000(.1968744043)

and then multiply to get

A(t) = $12,993.71

ANSWER[tex]q(x) = 7x + 4[/tex]

EXPLANATION

We want to find the quotient when [tex]7{x}^{2}-3x-9[/tex] is divided by x-1

We can quickly perform a synthetic division.

We write out the coefficients of the polynomial

[tex]7{x}^{2}-3x-9[/tex]

   7     -3     -9

1|         7      4

  7      4       -5

To obtain the top row.When we equate the divisor to zero, we get;[tex]x - 1 = 0[/tex][tex]\implies\:x=1[/tex]

This gives the 1 in the far left.The first two numbers in the last row are the coefficients of the quotient. The last number in the last row is the remainder.Therefore the quotient is [tex]7x + 4[/tex] and the remainder is -5

Remember this polynomial can be written as:

Dividend= Divisor * Quotient     + Remainder

[tex]7x^2-3x-9=(x-1)(7x+4)-5[/tex]

Therefore Quotient=7x+4

Answer:

It's 90 degrees.

Step-by-step explanation:

You have to use your instincts here, the angle is not acute, so it can't be 60. The angle is not obtuse either, so it can't be 120 or 180, leaving 90. Also the degree of the arc of a circle is usually 2x the measure of the corresponding angle.

Answer:

90 degrees

Step-by-step explanation:

I never came across a question like this one. Time to reason my way to the answer.

We know that f(x) = y.

In the point given, y = 8.

So, f(x) - 2 = y - 2 = 8 - 2 = 6.

The corresponding point should be (-5, 6).

Answer:

x² + 4y²+ 2x - 24y + 33 = 0

= (x+1)² + 4(y-3)² - 1 - 36 + 33 = 0

= (x+1)² + 4(y-3)² = 4

= (x + 1)²/2² + (y - 3)²/1² = 1

This is an Ellipse:  C(-1,3)

The Standard Form of an Equation of an Ellipse is : (x - h)²/a²/ (y - k)²/b² = 1

where Pt(h,k) is the center. (a variable positioned to correspond with major axis)

a and b  are the respective vertices distances from center

and√a² - b²are the foci distances from center: a > b

Answer:

30° and 90°

Step-by-step explanation:

The perpendicular bisector of an equilateral triangle forms a 90° angle with one side and a 30° angle with the other side.

Answer:

  Cassie is traveling 63.6 mph

Step-by-step explanation:

If the three numbers, left to right, are A, B, C, then the tire radius in millimeters is ...

  A×B/100 + 12.7×C

For the factory tires, the tire radius is ...

  240·75/100 + 12.7·16 = 180 +203.2 = 383.2 . . . . millimeters

For the replacement tires, the tire radius is ...

  290·70/100 +203.2 = 406.2 . . . . millimeters

The speedometer is calibrated based on the number of revolutions the tire makes in a given time period. If the truck goes farther for each revolution, its speed is higher by the same proportion.

If the speedometer on the truck with these replacement tires reads 60 mph, the actual speed is ...

  (406.2/383.2)×60 mph = 63.6 mph

_____

Comment on the problem statement

Caroline's truck has the replacement tires. If Cassie's speedometer reads 60 mph, we have no reason to assume Cassie is traveling at any speed other than 60 mph.

Final answer:

By setting up an equation where the total costs for both electricians are equal and solving for h, we find that the number of hours for which the costs are the same is 4 hours.

Explanation:

To determine the number of hours, h, for which the cost would be the same for hiring both electricians, we set up an equation where both cost expressions are equal. The equation, which expresses the total cost for each electrician's services, is:

First electrician: Cost = $60 + $55h

Second electrician: Cost = $20 + $65h

We now equate the two expressions and solve for h:

$60 + $55h = $20 + $65h

$55h - $65h = $20 - $60

-$10h = -$40

Divide each side by -10: h = 4

Thus, the number of hours for which the costs are the same is 4 hours.

Final answer:

The number of hours for which both electricians would charge the same is 4 hours. We find this by setting up an equation based on their fees and hourly rates, solving this equation yields the result of 4 hours.

Explanation:

To determine the number of hours, h, for which the cost would be the same for hiring both electricians, we can set up an equation based on their charges. The first electrician charges a service call fee of $60 and $55 per hour. Therefore, the cost for the first electrician, C1, can be expressed as:

C1 = 60 + 55h

The second electrician charges a service call fee of $20 plus $65 per hour, which means the cost for the second electrician, C2, is:

C2 = 20 + 65h

To find when the costs are the same (C1 = C2), we set the two expressions equal to each other:

60 + 55h = 20 + 65h

Now we solve for h:

60 + 55h = 20 + 65h

55h - 65h = 20 - 60

-10h = -40

h = 4

The costs are the same when the electricians work for 4 hours.

Answer:

  x² +81 = x² +20x +100

Step-by-step explanation:

Square both sides of the original equation:

  (√(x² +81))² = (x +10)²

  x² +81 = x² +20x +100

Answer: point

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

arcsine is just sin -1 (theta) and can be entered in the calculator as such.

The function arcsine is represented as sin-1(θ). It is the inverse of the sine function, and it helps find the angle whose sine is a given value like 0.44. The arcsine function can be accessed using the sin-1 button on calculators, allowing for easy calculations.

Answer:

B

Step-by-step explanation:

Under a reflection in y = x

a point (x, y) → (y, x)

Given

H(17, 34 ) → H'(34, 17)

I(- 5, 10) → I'(10, - 5)

J(28, - 14) → J'(- 14, 28)

B represents the image coordinates of H, I, J

For the given figure with vertices H(17,34), I(-5,10), and J(28,-14) across the line y=x, the reflection will appear at H(34,17), I(10,-5), J(28,-14). This is because at y=x the reflection will have the coordinates with interchanged values.

Across y=x, the reflection will have interchanged coordinates.

that is (x, y) → (y, x)

For the given vertices across the line y=x,

H(17,34) → H'(34,17)

I(-5,10) → I'(10,-5)

J(28,-14) → J'(-14,28)

So, option (2) is correct that is H(34,17), I(10,-5), J(-14,28) which undergoes reflection across y=x.

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Answer:

(x - 2)² + (y +8)² = 49

Step-by-step explanation:

Points to remember

Equation of a circle passing through the point (x₁, y₁) and radius r is given by

(x - x₁)² + (y - y₁)² = r ²

To find the radius

It is given that, center of circle = (-5, -8) and passes through the point (2 -8)

By using distance formula,

r = √[(2 --5)² + (-8 --8)²]

 = √7²

r = 7

To find the equation of the circle

Here (x₁, y₁) = (2, -8)

Equation of circle is,

(x - x₁)² + (y - y₁)² = r ²

(x - 2)² + (y - (-8))² = 7²

(x - 2)² + (y +8)² = 49

Answer:

The equation of circle is [tex](x+5)^2+(y+8)^2=49[/tex].

Step-by-step explanation:

The standard form of a circle is

[tex](x-h)^2+(y-k)^2=r^2[/tex]              .... (1)

where, (h,k) is the center of the circle and r is the radius.

It is given that the center of the circle is (-5,-8). it means h=-5 and k=-8.

The circle passes through the point (2,-8). So, the radius of the circle is the distance between point (-5,-8) and (2,-8).

[tex]r=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

[tex]r=\sqrt{(2-(-5))^2+(-8-(-8))^2}[/tex]

[tex]r=\sqrt{7^2+0}[/tex]

[tex]r=7[/tex]

Substitute h=-5, k=8 and r=7 in equation (1), to find the equation of circle.

[tex](x-(-5))^2+(y-(08))^2=(7)^2[/tex]

[tex](x+5)^2+(y+8)^2=49[/tex]

Therefore the equation of circle is [tex](x+5)^2+(y+8)^2=49[/tex].

Answer:

  3022.08 . . . dollars per square meter

Step-by-step explanation:

The slope is multiplied by the factor that changes units:

  (280.76 dollars/ft²)×(1 ft²)/(.092303 m²) ≈ 3022.08 dollars/m²

To make predictions for house prices in square meters, you would have to multiply the given slope of 280.76 by the conversion factor of 1/0.092903, which will give an estimated slope of approximately 3017.9

The problem here is related to the conversion of units from square feet to square meters. Your friend gives you a simple regression fit for predicting house prices from square feet with an estimated intercept of -44850 and the estimated slope is 280.76.

Given that there are 0.092903 square meters in 1 square foot, a square foot equals to 1/0.092903 square meters. When you are making a prediction based on square meters rather than square feet, you need to consider this factor. This means the new slope would be calculated by multiplying the old slope with this conversion factor as:

Slope for prediction in square meters = Old slope * (1/0.092903) = 280.76 / 0.092903 = 3017.9 approximately.

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Answer:

  {52}

Step-by-step explanation:

The calculator function appears to be ...

  f(x) = {3x -1, x odd; x/2 +1, x not divisible by 4; x/4, x divisible by 4}

The inverse of the first function is ...

  x = 3y -1

  (x+1)/3 = y . . . . (y must be odd)

For x = 13, this is 14/3, which is not an integer.

__

The inverse of the second function is ...

  x = y/2+1

  2(x-1) = y . . . . (y must not be divisible by 4)

For x = 13, this is 2·12 = 24, which is divisible by 4, so 24 is not the input value.

__

The inverse of the third function is ...

  x = y/4

  4x = y . . . . (y must be, and is, divisible by 4)

For x = 13, this is 4·13 = 52.

The only possible input value for an output of 13 is 52.

Answer:

ok so check it the answer is 9.5 my good sir

Answer:

9.5

Step-by-step explanation:

Since the question is to round 9.45 to the nearest tenth / one decimal place, we have to see if the hundredths is greater than or equal to 5 so we can add 1 to the tenths and since 5 in the hundredths column and is greater than or equal to 5 it becomes 9.5

[tex]\bf \begin{array}{llll} \textit{logarithm of factors} \\\\ \log_a(xy)\implies \log_a(x)+\log_a(y) \end{array} ~\hspace{4em} \begin{array}{llll} \textit{Logarithm of exponentials} \\\\ \log_a\left( x^b \right)\implies b\cdot \log_a(x) \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ 3\log_b(q)+6\log_b(v)\implies \log_b(q^3)+\log_b(v^6)\implies \log_b(q^3v^6)[/tex]

Answer:

h = 9 and k = -8

Step-by-step explanation:

bearing in mind a leap year has 366 days, with February 29th.

[tex]\bf \begin{array}{ccll} ounces&days\\ \cline{1-2} 16&1\\ x&366 \end{array}\implies \cfrac{16}{x}=\cfrac{1}{366}\implies 5856=x[/tex]

that many ounces, how many gallons(US) is that?

well, there are 128 oz in 1 gallon(US), so in 5856 oz there are 5856 ÷ 128 = 45.75 gallons(US).

58.56 gallons of milk,a person will drink in a leap year.

What is leap year?

A Leap Year has 366 days (the extra day is the 29th of February).

How to know if it is a Leap Year:

Leap Years are any year that can be exactly divided by 4 (such as 2016, 2020, 2024, etc)

except if it can be exactly divided by 400, then it is (such as 2000, 2400)

How many galllons will a person drink in a leap year?

We have given,

Average person drinks 16 ounces of milk in 1 day.

We have to find milk consume by average person in 366 days in gallons.

We know, 1 ounce (oz)=0.01 gallons

So, 16 ounce = 16×0.01 gallons

=0.16 gallons

We can say milk consume in one day = 0.16 gallons

Therefore,milk consume in 366 days(in gallons)=366×milk consume in 1 day.

=366×0.16

=58.56 gallons.

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Answer:

Step-by-step explanation:

[tex]3.75\times 10^8=3.75\times 100,000,000=375,000,000.[/tex]

The decimal point is moved 8 places to the right. The number is "very large" in relation to most folks' personal experience with counting things, but is "very small" in relation to quantities and sizes in the known universe.

Answer:

This will convert to a very large number.

This is the same as the product of 3.75 and 100,000,000.

Step-by-step explanation:

scientific notation.

[tex]3.75 \cdot 10^8[/tex]

To get the standard form we multiply the decimal number by 10^8

When we multiply by 10^8, move the decimal 8 places the right

This will convert to a very large number

[tex]10^8 = 100,000,000[/tex]

[tex]3.75 \cdot 100000000[/tex]

This is the same as the product of 3.75 and 100,000,000.

Answer:

if the distance in the map is 3.5 inches the actual distance is 87.5 miles

Answer:

  24.5 cubic inches

Step-by-step explanation:

The formula for the volume of a cylinder is ...

  V = πr²h

A can with a diameter of 2.5 inches has a radius of 1.25 inches. Filling in the given values, the volume is ...

  V = π(1.25²)(5) = 7.8125π ≈ 24.54 . . . . cubic inches

The approximate volume is 24.5 cubic inches.

The volume of a cylinder is 24.54 inches³

The volume of a cylinder is equal to the product of the area of the circular base and the height of the cylinder. The volume of a cylinder is measured in cubic units.

We know that the volume of cylinder is

V = πr²h

Given that:

diameter = 2.5 inches

radius = 1.25 inches.

Height= 5 inches

V = π(1.25²)(5)

= 7.8125π

≈ 24.54 inches³

Hence, the volume of cylinder is 24.54 inches³

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Answer:

Parallel

Step-by-step explanation:

Note for any function h(x) = mx + b

m = slope of the function

in this case, both functions have the same slope of [tex]\frac{3}{5}[/tex]

Hence the functions must parallel

Answer:

Step-by-step explanation:

The answer is b. left skewed

Left-skewed describes the shape of the temperature data.

A distribution exists skewed if one of its tails is longer than the other. The first distribution shown includes a positive skew. This suggests that it has a long tail in the positive direction. The distribution below it has a negative skew since it includes a long tail in the negative direction.

In this distribution, the majority of the data is to the right of the graph.  The "tail" of the distribution is to the left.  This defines a left-skewed distribution.

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