what transformations take f(x) = 3x+1 to g(x) = −3x−5 ?

In the first case the equation has only one unique solution and in the second case the equation has many solutions.

We are given the equation a|x + b| + c = d and we need to determine the solution of this equation when a > 0 and c = d. The equation contains absolute value symbol which always gives a positive value. The equation can be written as

a|x + b| + c = d

a|x + b| = d - c, since c = d then we can write equation as

a|x + b| = 0, Now, a > 0

=> |x + b| = 0

=> x = -b that is only one unique solution.

Now, in second case a < 0 and c > d then

a|x + b| = d - c

If c > d, then the left-hand side of the equation becomes negative and also a < 0 so the right-hand side also becomes negative. So, the equation will have many solutions in this case.

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To find the inverse of a function:

[tex]f(x)= 2x-\dfrac{9}{4}[/tex]

⇒ Replace f(x) with y:

[tex]y= 2x-\dfrac{9}{4}[/tex]

⇒ Switch around y and x:

[tex]x= 2y-\dfrac{9}{4}[/tex]

⇒ Isolate y:

[tex]x+\dfrac{9}{4}= 2y\\\\\dfrac{1}{2}(x+\dfrac{9}{4})= 2y(\dfrac{1}{2})\\\\\dfrac{1}{2}x+(\dfrac{1}{2}*\dfrac{9}{4})= y\\\\\dfrac{1}{2}x+\dfrac{9}{8}= y\\\\y=\dfrac{1}{2}x+\dfrac{9}{8}[/tex]

⇒ Replace y with f⁻¹(x):

[tex]f^{-1}(x)=\dfrac{1}{2}x+\dfrac{9}{8}[/tex]

[tex]f^{-1}(x)=\dfrac{1}{2}x+\dfrac{9}{8}[/tex]

Answer:

h(1) = 6

Step-by-step explanation:

h(1) will be

h(x) = 2x² + 4

h(1) = 2(1)² + 4 = 2 + 4

h(1) = 6

Answer:

-5x1/2= -2.5 14x1/8= 1.75

Step-by-step explanation:

-2.5+1.75=-0.75

Answer:

-3/4

Step-by-step explanation:

Plug in values of x and y into expression:

[tex]-5(\frac{1}{2})+14(\frac{1}{8})=[/tex]

[tex]-\frac{5}{2} +\frac{14}{8}=[/tex]

Find common denominator:

[tex]-\frac{5*4}{2*4} +\frac{14}{8}=[/tex]

[tex]-\frac{20}{8} +\frac{14}{8}=\frac{14}{8}-\frac{20}{8}=[/tex]

Solve numerator:

[tex]14-20=-6[/tex]

So,

[tex]=-\frac{6}{8}=-\frac{3}{4}[/tex]

The three sides of the triangle will be 82, 63, and 41 feet.

Triangle is a shape made of three sides in a two-dimensional plane. the sum of the three angles is 180 degrees. The perimeter of the triangle is the sum of all three sides of the triangle.

That a flower bed is in the shape of a triangle with one side twice the length of the shortest​ side, and the third side 22 feet more than the length of the shortest side.

Let the three sides of the triangle be A, B, and C. Here A is the longest side B is the shortest side and C is the third side.

Perimeter = A + B + C

A = 2B and C = 22 + B

Put the values in the equation as solve:-

Perimeter = A + B + C

186 = 2B + B + 22 + B

186 = 4B + 22

4B = 186 - 22

4B = 164

B = 164 / 4

B = 41 feet

Longest side = 2B = 2 x 41 = 82 feet

Shirtest side = B = 41 feet

Third side = 22 + B = 22 + 41 = 63 feet

Therefore, the three sides of the triangle will be 82, 63, and 41 feet.

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Answer:

He still owes Nikki $5.

Step-by-step explanation:

7 - 2 = 5

Answer:

5

Step-by-step explanation:

7-2=5

According to the graph we have:

Domain are the values of x. We can see that the graph extends horizontally from -5 to 3, but -5 and 3 are not included. Then, the domain is

Range are the values of y. Therefore, we see that the graph extends vertically from 4 to -3, so the range is:

Answer:

a. domain = (-5, 3)

b. range = (-3, 4)

The maturity value is the sum of the interest and the principal. The formula for calculating interest is expressed as

I = PRT

where

I is the interest after time t

P is the principal or initial amount

R is the interest rate

T is the time in years

From the information given,

P = 10800

R = 8/100 = 0.08

T = 8 months

We would convert 8 months to years. Recall,

12 months = 1 yr

8 months = 8/12 = 0.67

Thus,

t = 0.67 yr

By substituting these values into the formula, we have

I = 10800 x 0.08 x 0.67

I = 578.88

Thus,

Maturity value = 10800 + 578.88

Maturity value = $11378.88

Option A, Y- axis is the line of reflection used to map the preimage to its image.

The graph shows that if the graph is folded by a y-axis, Point G will cross Point G', which is two coordinates away from the y-axis.

Point F will cross point F', which is four coordinates away from the y-axis.

Points H will cross point H', which is in negative coordinates and 7 coordinates away from the y-axis.

Mirror images are symmetrical from any axis, which might be the x-axis or the y-axis. Flipping geometry refers to reflection. Mirror reflection is a type of reflection. When lines reflect an image, reflection lines form. A form is said to mirror another shape if each of its points is equidistant from each of the other shape's points.

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Answer:

[tex]t = 18.9[/tex]

Information given :

We know that:

- Element X is a radioactive isotope such that every 20 years, its mass decreases by half

- the initial mass of a sample of Element X is 770 grams

And we must find how long it would be until the mass of the sample reached 400 grams

Step-by-step explanation:

To find it, we need to use the following formula:-

[tex]A(t) = A(0)(0.5)^{\frac{t}{20} }[/tex]

- A(0) is the initial amount

From given information, A(0) = 770 grams

Now, replacing the value in t :

[tex]A(t) = (770)(0.5)^{\frac{t}{20} }[/tex]

Then, we must solve for t :-

[tex]400 = 770(0.5)^{\frac{t}{20} } \\\frac{400}{700}= (0.5)^{\frac{t}{20} } \\\\ 0.51948 = (0.5)^{\frac{t}{20} } \\\\log(0.51948) = log((0.5)^{\frac{t}{20} }) \\\\\\log(0.519,48) = \frac{t}{20} log (0.5)\\t=\frac{20*log(0.519,48)}{log(0.5)} \\t=\frac{20(-0.284431}{-0.301029} \\giving\\t=18.9[/tex]

Hope this helps you out and if does so just mark me as brainliest as this answer took a lot of time to plot down so that it acts as a fuel to your learning,

Stay positive,

a fellow comrade,

Cheers !

Answer: P=212*(1.240)n

Step-by-step explanation:

1) Find the % growth

263-212= 51

51/212 = 0.240566037735849

2) Add 1 to the decimal as the population isn't decreasing but increasing.

0.240566037735849 + 1 = 1.240

3) Fill in the equation

P=212*(1.240)n

A tangent and a radius of a circle meet to form a 90 angle is a true statement about a tangent and a radius.

The straight line that "just touches" the curve at a particular location is known as the tangent line (or simply tangent) to a plane curve in geometry. A circle or sphere's radius is any line segment that connects the object's center to its perimeter in classical geometry; in more contemporary use, it also refers to the length of such line segments.

A tangent is a line that very slightly touches the circumference of a circle. The angle between a radius and a tangent is always exactly 90 degrees if the radius and circumference are drawn at the same location.

Hence the correct option is B

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If  the interest rates suddenly rise by 2 percent,  the percentage change in the price of these bonds are : 19.73%, 16.56%.

Using this formula to find the current price of a bond

P=C×1-1(1+YTM)^n/YTM +F /(1+YTM)^n

Where:

P =Current price of a bond

C = Coupon payment,

YTM = Yield to maturity

n = Time to maturity

F =Face value of a bond

The Faulk Corp. bond

C = Coupon rate / number  of payments per year × face value = 4% / 2×$1,000 = $20

n = 13 years = 36 half-year periods

YTM = 7% annually = 7% / 2 = 3.5% semiannually

F = $1,000

hence,

P=20× 1- 1/(1+0.035)^26/0.035 +1,000/ (1+0.035)^36

P=20× 1- 1/(1.035)^36/0.035 +1,000/ (1.035)^36

P= $405.81 + $289.83

P=$695.61

Assuming the annual YTM rises by 2%, the semiannual YTM = 9% / 2 = 4.5%.

Price of the Faulk Corp. bond:

P=20× 1- 1/(1+0.045)^36/0.045 +1,000/ (1+0.045)^36

P=20× 1- 1/(1.045)^36/0.045 +1,000/ (1.045)^36

P= $353.32 +$205.03

P=$558.38

Percentage change:

Percentage change = $558.38 - $695.61/$695.61×100%

Percentage change =19.73%

Gonas Company bond:

C =Coupon rate / number of payments per year× face value = 10% / 2 × $1,000 = $50

n = 18 years = 36 half-year periods,

YTM = 7% annually = 7% / 2 = 3.5% semiannually

F = $1,000

P=50× 1- 1/(1+0.035)^26/0.035 +1,000/ (1+0.035)^36

P=50× 1- 1/(1.035)^36/0.035 +1,000/ (1.035)^36

P= $1,014.52 + $289.83

P=$1,304.35

Assuming the annual YTM rises by 2%, the semiannual YTM = 9% / 2 = 4.5%, bond :

P=50× 1- 1/(1+0.045)^36/0.045 +1,000/ (1+0.045)^36

P=50× 1- 1/(1.045)^36/0.045 +1,000/ (1.045)^36

P= $883.30 +$205.03

P=$1,088.33

Percentage change:

Percentage change = $1,088.33 - $1,304.35/$1,304.35×100%

Percentage change =16.56%

Therefore the percentage change in the price of these bonds are : 19.73%, 16.56%.

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the probability that the card you select is a diamond or 7 is 4/13

Mathematical representations of the likelihood of an event occurring or of a proposition being true are dealt with in the area of probability. A number between 0 and 1 represents the likelihood of an event, with 0 roughly denoting impossibility and 1 representing certainty.

Lets take diamond first total diamonds are 13 and total cards are 52 So prob is 13/52 which is 1/4

Lets take 7s

total 10s in the deck is 4 (one in each suite) (one in each suite)

Prob of 7s is 4/52 which is 1/13

Final answer =1/13+1/4=17/52 Total prob is addition of above two as it is "or."

Because the prob of the 7th diamond has been inserted twice, edit it as follows: 17/52-1/52=16/52=4/13

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To carry out the vertical analysis of an income statement, set the Revenue as the base figure to 100% for each line item.

Vertical analysis of a financial statement compares each line item on the financial statement as a percentage of a base figure.

The base figure is the revenue in the income statement or the total assets in the balance sheet.

The formula for vertical analysis is given as a financial statement line item divided by the total base figure X 100.

Examples of vertical analysis can be shown with AT$T and Verizon below:

                                                       AT&T        Percent

Revenue                                     $132,447        100%

Cost of Services (Expenses)         60,611        45.8% ($60,611/$132,447 x 100)

Selling & Marketing Expense      39,697       30.0%  

Depreciation & other expenses 20,393        15.4%

Operating Income                       $11,746         8.9%

                                                     Verizon      Percent

Revenue                                     $127,079       100%

Cost of Services (Expenses)         49,931        39.3% ($49,931/$127,079 x 100)

Selling & Marketing Expense        41,016       32.3%

Depreciation & other expenses   16,523       13.0%

Operating Income                      $19,599       15.4%

Thus, we have performed the vertical analysis of AT$T and Verizon above.

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Income Statements of AT&T and Verizon (in millions) are:

                                                       AT&T         Verizon

Revenue                                     $132,447     $127,079

Cost of Services (Expenses)         60,611          49,931

Selling & Marketing Expense      39,697          41,016

Depreciation & other expenses 20,393          16,523

Operating Income                       $11,746       $19,599

If there are 189 children, then there are 189 divided 7 = 27 groups of 7 children.

As mentioned in the problem, for every 7 children, there are 2 caretakers therefore, there are a total of 2 x 27 = 54 caretakers in the local daycare.

So, in total, there are 189 children + 54 caretakers = 243 people in the daycare facility.

Answer:

  17%

Step-by-step explanation:

You want the percentage represented by a tip of $10.34 on a dinner bill of $61.66.

A percentage is a fraction that has been multiplied by 100%:

  10.34/61.66 × 100%

  ≈ 0.168 × 100%

  ≈ 17%

The tip was about 17% of the original bill.

The common difference in the given arithmetic sequence is 8.

So, formula for common differences:

Now, insert terms in the formula as follows:

Therefore, the common difference in the given arithmetic sequence is 8.

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Data:

Students: 180

Half male.

Male students: 180/2=90

Male teachers: 2

Ratio of male teachers to male students:

You can write the ratio in three different forms:

ANSWER:

m = -3/4

b = -3

STEP-BY-STEP EXPLANATION:

We have that the equation in its slope-intercept form is the following:

We calculate the slope as follows:

To calculate the slope we use the intercepts that are (-4, 0) and (0, -3), we replace:

Now, the value of b would be -3, since the y-intercept is (0,-3), therefore, the equation would be:

Let's begin by listing out the given information:

1 and 3

1 * 12 = 12

2 * 12 = 24

so 1 is true

7 * 5.14 = 36

9 * 5.14 = 46.26

so 2 is not true

7 * 4 = 28

2 * 4 = 8

so 3 is true

Answer:

[tex]\frac{-5}{2}[/tex]

Step-by-step explanation:

There are two blue dots on the graph.  It does not matter which dot you startr at.  Let's start at the bottom, right dot.  How many space up and to the left you do you have to move to get to the second dot?

You need to move 5 dots straight up.  Up is a positive direction.  Then you have to move 2 spaces left.  Left is a negative direction, so your slope will be negative.

- [tex]\frac{5}{2}[/tex]            [tex]\frac{-5}{2}[/tex]           [tex]\frac{5}{-2}[/tex]   All of these mean the same thing.

The correct option regarding the continuity of f(x) at x = 2 is given by:

B. lim x -> 2 f(x) exists, but f(2) exist.

A function f(x) is continuous at x = a if it is defined at x = a, and the lateral limits are equal, that is, if these three conditions are respected:

[tex]\lim_{x \rightarrow a^-} f(x) = \lim_{x \rightarrow a^+} f(x) = f(a)[/tex]

For this problem, the denominator of the function is:

8cos(0.5πx) + 2x²

At x = 2, the denominator of the function is:

8cos(0.5π(2)) + 2(2)² = 8cos(π) + 8 = -8 + 8 = 0 (as cos(π) = -1).

Then the function does not exist at x = 2, as the denominator is of 2.

From the graph of the function given at the end of the answer, we have that the lateral limits are as follows:

Since the lateral limits are equal, the limit exists, hence option B is correct.

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1) As we were told of the half-life formula along with the data, we can write out the following to get the remains after 170 years:

2) So, according to this model we can tell there will be left approximately

Step 1

Given; Austin has a granola recipe that requires 5/6 pounds of oats to make one batch of granola. if Austin uses 2 1/2 pounds of oats while making granola, how many batches has he made?

Step 2

Using ratio

Answer;

Answer:3

Step-by-step explanation:if austin has to make 1 granola with 5/6pounds but he is using only 5/2 pounds to make 1 granola so that he can make 3 granulas with 5/6

Answer:

72

Step-by-step explanation:

8 = 2×2^2

18 = 2×3^2

32 = 2×4^2

50 = 2×5^2

72 = 2×6^2

I adore BTS (the Korean boy band) because they encourage self-love. Their songs are artistically and romantically rich. They're well-known throughout the world and at the moment's top boy band in the US.

In this sense, understanding the worth and excellence of various musical genres is referred to as appreciation. The word "appreciation" has philosophical roots; in that discipline, it is defined in relation to music as "a type of formal counterpart of emotional experience."

Someone's mood can be improved by listening to their music, which can also thrill or calm the listener. Importantly, music also enables us to experience almost all of the emotions we go through in life. There are countless options. Dopamine release in the mesolimbic reward system can be triggered by listening to extremely pleasurable music.

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You can never achieve break even by selling any number of boxes of candy if it costs them an additional $3 to manufacture each box of candy.

In economics, business, and particularly cost accounting, the break-even point is the point at which total cost and total income are equal, or "even."

Although these opportunity costs have been paid and then capital has received the risk-adjusted, projected return, there is no net loss or gain, and one has "broken even."

Fixed cost (in manufacturing) = $500

Manufacturing cost of each candy = $3

and selling price of candy = $3

let x be a box of candy sold,

hence for no of box to be sold for a break even,

3x + 500 = 3x

but if you see above equation, that has no solution

Hence by providing each candy at $3 with $500 fixed cost and selling cost again at $3 you cannot achieve a break-even point.

hence there is no solution, and you will never be able to achieve break even.

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