Y-1= -1/3(x-6) in standard form

The transformed function is y = -f(x + 3) - 2, obtained by reflecting the quadratic function over the x-axis, shifting it left by 3 units, and down by 2 units.

To reflect a quadratic function over the x-axis, we need to multiply the function by -1. Let's assume that our original quadratic function is f(x).

After reflecting the function over the x-axis, we get the new function g(x) = -f(x).

To perform a horizontal shift left 3 units, we need to replace x with (x + 3) in the function g(x). This gives us the new function h(x) = g(x + 3) = -f(x + 3).

Finally, to shift the function down 2 units, we need to subtract 2 from the entire function h(x).

Note that the order of the transformations is important. We first reflect the function over the x-axis, then shift it horizontally, and finally shift it vertically.

Hence,

The transformed function is y = -f(x + 3) - 2, obtained by reflecting the quadratic function

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Answer: 159 bpm

Step-by-step explanation:

if his rate is 53 beats in 1/3 of a minute, in 3/3 of a minute, (1 full minute), it will be 53 x 3 = 159 beats

so we can say his heart rate is 159 beats/minute, or 159 bpm

Answer:

y=5

divide 40 by 8

times 5 by 8 to check your solution

Answer:

see explanation

Step-by-step explanation:

40 = 8y ( isolate y by dividing both sides by 8 )

5 = y

As a check

substitute y into the right side of the equation and if both sides are equal then it is the solution.

right side = 8y = 8 × 5 = 40 = left side

since both sides are equal then y = 5 is the solution to the equation

The area of an equilateral triangle is 16√3 m² and the perimeter of an equilateral triangle is 24 m.

In an equilateral triangle, median, angle bisector and altitude for all sides are all the same and are the lines of symmetry of the equilateral triangle. The area of an equilateral triangle is √3/4 ×a².

From the given figure, side of the equilateral triangle is 8 m.

Now, area of an equilateral triangle is

√3/4 ×8²

= √3/4 ×64

= 16√3 m²

The perimeter of an equilateral triangle is 3a.

Now, the perimeter is 3×8

= 24 m

Therefore, the area of an equilateral triangle is 16√3 m².

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Step-by-step explanation:

sorry for the wait I hope this helps you with you're problem

Answer: hhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh

Step-by-step explanation:

a. Jada is the input and 4 is output, the output is 4 because there are 4 letters in Jada word.

b. G(Diego) =5

A relation is a function if it has only One y-value for each x-value.

Given that a  Function G takes a student's first name for its input and gives the number of letters in the first name for its output.

a.

Given that G(Jada) = 4

In the above function Jada is the input and 4 is output, the output is 4 because there are 4 letters in Jada word.

b. We need to find the value of G(Diego)

In the above function Diego is the input and 5 will be output, the output is 5 because there are 5 letters in Diego word.

G(Diego) =5

Hence, a. Jada is the input and 4 is output, the output is 4 because there are 4 letters in Jada word.

b. G(Diego) =5

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Answer:

B. 5/22

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

Total number of students is:

Probability of a first girl is 6 of 12:

Probability of a second girl is 5 of 11 since both numbers reduced by one:

Probability of the two events is:

Correct choice is B.

Answer:

SOLVE IT!

Step-by-step explanation:

A. 45.50+0.11= answer

B. 65.50+0.17= answer

Minus A plus B to get answer!

The algebraic expression G x C, where G represents the total number of gallons needed and C represents the cost per gallon.

In mathematics, an expression is a combination of one or more numbers, variables, and/or operators that represent a quantity or a mathematical relationship.

To calculate the total cost of gasoline, we first need to determine how many gallons of gasoline will be needed for the entire trip. This can be done by dividing the total distance traveled by the car's miles per gallon (MPG) rating. Let's use "G" to represent the total number of gallons needed.

G = Total Distance Traveled / MPG

To find the total cost of gasoline, we can multiply the number of gallons needed by the cost per gallon. Let's use "T" to represent the total cost of gasoline.

T = G x C

Using the expression we developed earlier, we can now find the total cost of gasoline for the full-size car:

=> T = G x C

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Complete Question:

Four friends plan to rent a car to go on a camping trip. They will drive a total of 450 miles. The cost of gasoline is $2.20 per gallon Type of Car SUV Full size Compact Rental Cost $283 $215 $183 Insurance Cost $120 $108 $95 Miles per Gallon 24 25 33 Total Gas Cost $ $ $ Cost per Person.

Write an algebraic expression for the total cost of the gasoline.

Answer:

Step-by-step explanation:

ghjhkvfgfgnfdgn

(1) The hypothesis is stated that completing a 2-week mindfulness training course

(2) The type of study design this is randomized controlled trial.

(3) The choice of the study type is randomized controlled trial is justified. (4) The list of the two variables with their operational definitions is 2-week mindfulness training course and GRE scores.

(5) Yes, this study demonstrate that the relationship between the two variables is causal

In a study conducted by Mrazek et al. (2013), it was found that students who completed a 2-week mindfulness training course scored higher on the GRE than those who did not participate in the training.

The hypothesis of this study is that completing a 2-week mindfulness training course will result in higher scores on the GRE compared to those who do not complete the training.

This study design is a randomized controlled trial. In this type of study, participants are randomly assigned to either a treatment or control group, and the effects of the treatment are compared to the effects of no treatment (or a placebo). In this case, the treatment group received the 2-week mindfulness training course, while the control group did not.

The choice of study type as a randomized controlled trial is justified because it allows for the comparison of two groups while minimizing the effects of confounding variables. Random assignment to groups helps to ensure that any differences in outcomes between the groups are due to the treatment and not some other factor.

The two variables in this study are the completion of the 2-week mindfulness training course and GRE scores. The operational definition of completion of the training course is that participants in the treatment group attended all sessions of the 2-week course. The operational definition of GRE scores is the score that participants received on the exam.

This study does suggest a causal relationship between completion of the mindfulness training course and higher GRE scores. The randomized controlled trial design helps to reduce the effects of confounding variables, making it more likely that any observed differences in outcomes between the treatment and control groups are due to the treatment.

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In 9 years, assuming a 4% annual inflation rate, a typical family of four should budget $1254.77 a month for food.

In order to determine how much a normal family of four should budget for food in 9 years, we must take inflation into consideration.

To account for inflation, we can use the formula below to determine the future worth of the current food expenditures:

Future value = Present value * (1 + inflation rate)^n

where:

Present value = $897.20/month

Inflation rate = 4% per year

n = number of years

When we substitute the specified values, we get:

Future value = $897.20 * [tex](1 + 0.04)^9[/tex]

= $897.20 * 1.3981

= $1254.77 (to two decimal places in rounding)

Therefore, In 9 years, assuming a 4% annual inflation rate, a typical family of four should budget $1254.77 a month for food.

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The missing value is given as follows:

x = 11.3 cm.

The Pythagorean Theorem states that for a right triangle, the length of the hypotenuse squared is equals to the sum of the squared lengths of the sides of the triangle.

The parameters for this problem are given as follows:

Hence the missing value is obtained as follows:

14² + x² = 18²

x = sqrt(18² - 14²)

x = 11.3 cm.

We have a triangle in which:

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The surface area is changing at a rate of approximately 2.94 square meters per second when the volume is 36 cubic meters and the balloon is being inflated at 3 cubic meters per second.

Volume of a sphere in terms of its radius = V = (4/3)π[tex]r^3\\[/tex]     .......(1)

Differentiating on both sides,                       [tex]\frac{dV}{dt}[/tex] = 4π[tex]r^{2}[/tex][tex]\frac{dr}{dt}[/tex]      .......(2)      

r = radius of the sphere.

Spherical balloon is being inflated at a rate of 3 cubic meters per second.

[tex]\frac{dV}{dt}[/tex] = 3 [tex]m^3/sec[/tex]

Volume is 36 cubic meters.

V = 36 [tex]m^3[/tex]

From equation (1), [tex]r^3[/tex] = [tex]\frac{3V}{4\pi }[/tex]

                              [tex]r^3[/tex] = [tex]\frac{3*36}{4*\pi }[/tex]

                              [tex]r^3\\[/tex] = [tex]8.59^1^/^3[/tex]

                               r = 2.04 meters

Substituting this in equation (2),  [tex]\frac{dr}{dt}[/tex]  =   [tex]\frac{dV}{dt}[/tex] / 4π[tex]r^{2}[/tex]

                                                     [tex]\frac{dr}{dt}[/tex]  =   3/(4π[tex]2.04^{2}[/tex])

                                                     [tex]\frac{dr}{dt}[/tex]  =   0.05737 m/sec

Now, surface area of sphere = A = 4π[tex]r^{2}[/tex]

Differentiating on both sides,

Rate of change of surface area  [tex]\frac{dA}{dt}[/tex] = [tex]8\pi r\frac{dr}{dt}[/tex]

                                                       = 8* 3.14* 2.04* 0.05737

                                                       = 2.94 [tex]m^2/sec\\[/tex]

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Answer:

minimum is $14.40

maximum is $18

she can get 9 ice cream cups

Step-by-step explanation:

The equation of the line that passes through (18, 16) and has a slope of 11/8 is 8y = 11x - 70.

The equation of a straight line that passes through a particular point and is inclined at a specific angle to the x-axis can be found using the point slope form. Every point on a line must satisfy the equation for the line in order for it to exist. This implies that a line is represented by a linear equation in two variables. Depending on the facts at hand, there are different ways to find a line's equation. Several techniques include:

Form of point slope, Form of a slope-intercept, Two-point form for intercepting.

The point slope form is given as:

(y - y1) = m (x - x1)

The point is (18, 16) and the slope is 11/8.

Substituting the values we have:

y - 16 = 11/8 (x - 18)

8(y - 16) = 11(x - 18)

8y - 128 = 11x - 198

8y = 11x - 70

Hence, the equation of the line that passes through (18, 16) and has a slope of 11/8 is 8y = 11x - 70.

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To buy down the quoted interest rate from 4.75% to 4.5% will cost Trystan and Kendall $4,800 after the down payment.

The down payment refers to the initial cash payment for the purchase of an item on mortgage.

The down payment is required by the financier to evaluate the buyer's financial readiness.

The cost of the new home = $300,000

Down payment = 20% or $60,000 ($300,000 x 20%)

Mortgage loan required = $240,000 ($300,000 - $60,000)

Bank quoted interest rate = 4.75%

Desired interest rate = 4.5%

Difference in interest rate = 0.25% (4.75% - 4.5%)

Rate of buy down of the quoted interest per point = 0.125%

The number of points to buy down the interest rate = 2 (0.25/0.125)

The cost of each point = 1% of $240,000 = $2,400

The total cost of 2 points = $4,800 ($2,400 x 2)

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Answer: The simple interest will be 20%.

Step-by-step explanation:

we know the simple interest of borrowed amount is:

S.I.= (P x R x T)/100 ..... (i)

where P⇒ Principal amount

R⇒ rate of interest

T⇒ time

and

total Pays Back amount = Principal amount + S.I.

Hence S.I. = Pays Back amount - Principal amount

Now, as per the question: Clinton pays back Double of the amount hi borrowed. Means

if Principal amount = P

then Pays Back amount = 2P ⇒ S.I.= P

Rate of Interest = R

and Time = 5 years

P= (P x R x 5)/100

R= 100/5

R = 20%

Therefore, the simple interest is 20% annually.

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Answer:

Midpoint M (2,5)

S (3,2)

R (x,y) {we will find values for x and y}

(x + 3) / 2 = 2 and (y + 2) /2 = 5

x + 3 = 4 and y + 2 = 10

x = 4-3 and y = 10-2

x = 1 and y = 8

Therefore, coordinates of R (1,8)

Answer:

10) m∠2 = 139°

11) m∠3 = 139°

12) m∠4 = 41°

Step-by-step explanation:

Question 10

∠2 and the adjacent angle of 41° are supplementary angles since they lie on opposite sides of the same line; they must add up to 180°

m∠2 + 41° = 180°

m∠2 = 180-41 =139°

Question 11

∠2 and ∠3 are formed by the intersection of two rays. They are vertically opposite angles and therefore they must be equal

m∠3 = m∠2 = 139°

Question 12

Angles  ∠3 and ∠4 are supplementary angles (same reasoning as q 10)

Therefore m∠4 = 180°  - m∠3

= 180° - 139° = 41°

Note that there are many ways to arrive at the answers for m∠4

Answer:

A composite figure is made up of simple geometric shapes. To find the area of a composite figure or other irregular-shaped figure,divide it into simple, nonoverlapping figures. Find the area of each simplerfigure, and then add the areas together to find the total area of the compositefigure

Step-by-step explanation:bc of the way u gave it im showing it to u

Step-by-step explanation:

A.Rational because by using the discrmant formula, Since our coefficients are integers, and if we get a perfect square, inside a radicand , we will have a rational numbers.

For example:

[tex] \sqrt{ {7}^{2} - 4(4)(3) } = \sqrt{49 - 48} = \sqrt{1} = 1[/tex]

Since root 1, is a perfect square, we will have rational roots.

B.

[tex] {b}^{2} - 4ac < 0[/tex]

[tex]49 - 16c < 0[/tex]

[tex] - 16c < - 49[/tex]

[tex]c > \frac{49}{16} [/tex]

If c is greater than 49/16, we will have no x intercepts.

Answer:

Step-by-step explanation:

a) As the function is a quadratic you could restrict the domain by taking only values either side of the line x = 3. This means the domain will be

a) 3<x<∞

Or

b) -∞<x<3

b) the graph is attached below.

c) The equation of the inverse of f(x) can be found by switching x and y:

X = (y-3)²

√x = y - 3

y = √x + 3

However this takes in positive and negative values of the square root function. So in order to restrict this, we can take the positive square root only.

Thus y = +√x + 3

The missing side length is x = 30

What are basic Trigonometric functions?

The angles of sine,  cosine, and tangent are the primary classification of functions of trigonometry. And the three functions which are cotangent, secant, and cosecant can be derived from the primary functions. Basically, the other three functions are often used as compared to the primary trigonometric functions.

In a Right-angled triangle, the tan of an angle is equal to the opposite side/adjacent side

from the given figure,

tan 37° = x/40

0.75 = x/40

x = 30

Therefore, The missing side is 30.

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Answer: pay attention

Step-by-step explanation:

The volume of a cylinder can be calculated as π * radius^2 * height. In this case, the radius is 0.5 ft and the height is 25 ft, so the volume is:

π * 0.5^2 * 25 = 19.63 cubic feet

So the cost of the utility pole would be 19.63 * $25.81 = $509.24

Rounding to the nearest cent, the cost of the utility pole would be $509.24, which can be rounded to $509.00.

Answer:

First, we need to find the area of Site A and Site B. The area of a rectangle is found by multiplying its length and width, so:

Site A: 60 m x 40 m = 2400 m^2

Site B: 45 m x 40 m = 1800 m^2

Next, we need to find the perimeter of each site, which is the distance around the edges of the rectangle. The perimeter is found by adding up the lengths of all four sides, so:

Site A: 2 x (60 m + 40 m) = 2 x 100 m = 200 m

Site B: 2 x (45 m + 40 m) = 2 x 85 m = 170 m

Finally, to find the total amount of rope needed, we add up the perimeters of both sites:

200 m + 170 m = 370 m

So, we need a total of 370 meters of rope to rope off both sites.

Answer:350

ITS NOT 370