Consider the graph of the function f(x) = 2^x Which statements describe key features of function g if g(x) = f(x + 2)?

hmmm first of all, let's keep in mind that any expression multiplied by 1 is always the same expression

[tex]12\cdot 1=12\qquad 13567\cdot 1=13567\qquad spaghetti\cdot 1=spaghetti[/tex]

and so on.

now, hmm 1 can be expressed as a rational, 1/1 = 1, but but but, we can really express it as

[tex]\cfrac{9999}{9999}\implies \cfrac{7857}{7357}\implies \cfrac{\sqrt[11]{1375}}{\sqrt[11]{1375}}\implies \cfrac{spaghetti}{spaghetti}\implies \cfrac{lettuce}{lettuce}\implies \text{\Huge 1}[/tex]

so let's do the so-called rationalizing of the denominator, we can also do it with the numerator btw, but we only need it for the denominator right now, by multiplying for 1 :), 1 is Da Bomb baby!!

[tex]\cfrac{5}{2\sqrt{5}}\cdot \text{\LARGE 1}\implies \cfrac{5}{2\sqrt{5}}\cdot \cfrac{\sqrt{5}}{\sqrt{5}}\implies \cfrac{5\sqrt{5}}{2\sqrt{5^2}}\implies \cfrac{5\sqrt{5}}{2(5)}\implies \cfrac{5\sqrt{5}}{10}\implies {\Large \begin{array}{llll} \cfrac{\sqrt{5}}{2} \end{array}}[/tex]

Answer:

I think this is correct.

Step-by-step explanation:

y=-3x+10

In  linear equations, 103.75 inches per month tall has it been since sarah planted the tree.

What are instances of linear equations?

Sarah planted a tree in her yard = 24 inches tall

 grew at a rate =2.5 inches per month

When tree is now 41.5 inches tall = 41 . 5 * 2.5

                                                        = 103.75

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The rational number that can be written as a decimal in which one or more nonzero digits repeat is given by:

D. 5/9.

The set of rational numbers is composed by numbers that can be represented by fractions, such as numbers that have no decimal parts, or numbers in which the decimal parts are terminating or repeating.

For this problem, we have a focus on numbers that have repeating decimal part. The most known case is the division by 9, as when an integer that is not a multiple of 9 is divided by 9, the result is a decimal with a repeating decimal part.

To find the equivalent decimal to 5/9, we divide the numerator of 5 by the denominator of 9, hence:

5/9 = 0.55555...

The decimal digit 5 repeats infinitely, hence option D is correct.

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John holds 26 percent of the debt from discover bank in its total debt obligation.

The Total debt represents the obligations being taken by a company in the form of debt and yet to be repaid by them to the lender.

Given that the Debt hold in discover bank is $10,000

Total debt: $26,000

Computation of ratio of debt in discover bank:

Debt proportion = Debt hold in discover bank / Total debt

Debt proportion = 10,000/ 26,000

Debt proportion = 26%

Therefore, John holds 26 percent of the debt from discover bank in its total debt obligation.

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Note the - sign in the evaluation of f(x), which changes the function directly, and the term -4 indicates a displacement vertically (down), but the graph goes up because of the sign -, therefore, the only option with these conditions is option b.

The correct answer is option b.

Answer:

1512 cm²

Volume is also multiplied by [tex]\dfrac{3}{2}[/tex]

Step-by-step explanation:

The volume of a pyramid is given by the expression

[tex]V = \dfrac{1}{3} l\cdot w\cdot h[/tex]

where l = base length, w = base width and h = height

The volume of this pyramid

[tex]= \dfrac{18\cdot 12\cdot 14}{3} = 1008\; cm^3[/tex]

If we multiply the height by [tex]\dfrac{3}{2}[/tex] then new height

= [tex]14 \cdot \dfrac{3}{2} = 21 cm[/tex]

New Volume [tex]= \dfrac{18\cdot 12\cdot 21}{3} = 1512\; cm^3[/tex]

[tex]\dfrac{\text{NewVolume}}{\text{Old Volume}} = \dfrac{1512}{1008} = \dfrac{3}{2}[/tex]

So volume is also multiplied  by 3/2

Answer:

Step-by-step explanation:

1. Set x equal to the amount of money Jim has

2. Create equations of the amount of money the other people have based on x

3. Now, we set all of these equations as equal to 68

4. Combine the like terms, which means that the previous equation will simplify to:

5. Add 8 to both sides

6. Divide 76 by 4

7. Plug the value of x into the previous equations:

Final Answer:

Answer:

side length = 5cm

Step-by-step explanation:

The volume of the prism is:

V = l × w × h

But we only know the width and height which are both 3cm. See image.

We put it in the calibrated container (container with markings on it) We find out the volume is 45. Because 115 - 70 is 45.

Divide to find the missing length. See image.

Vol

= 3 × 3 × sidelength

V = 9s

45 = 9s

5 = s

see image.

54 + 63 = 13 * 9 is the expression obtained as the product of a number and relatively prime addends.

A prime number is a number that can be divided only by 1 and itself.

54+63                                   (given)

We now have to find the sum of the given numbers as the product of relatively prime numbers.

In order to find the numbers we will find first sum and then factor

Sum=54+63=117

Factors of 117 are 13 and 9

117 = 13 * 9

13 and 9 are relatively prime because the factor of 13 and 9 is 1.

Therefore, 54 + 63 = 13 * 9 is the expression obtained as the product of a number and relatively prime addends.

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x represents the amount of gas in the tank, has a domain described by which inequality

[tex]0 \leq x \leq 3[/tex]

This is further explained below.

Generally, A typical 3-gallon lawnmower requires 0.6 gallons of petrol per hour.

This circumstance is modeled by a function, where x is the volume of gas in the tank.

The lawnmower's gas tank has a maximum capacity of gallons and may be completely empty (having 0 gallons of gas).

In conclusion, a function's domain is

[tex]0 \leq x \leq 3[/tex]

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Answer:

Step-by-step explanation:

5 over 12 is 5/17

Reason:

The smallest |x-5| can get is 0 since the result of an absolute value is never negative (because it represents distance).

So the smallest f(x) = |x-5|-3 can get is 0-3 = -3

f(x) = -3 or f(x) > -3 are the only two options for the output f(x).

Condense that into [tex]f(\text{x}) \ge -3[/tex] to arrive at choice C as the final answer.

The fancy notation of f(x) ∈ ℝ translates to "f(x) is a real number".

If you were to graph this using a tool like Desmos, then notice how the lowest point occurs when y =  -3

See the diagram below.

Answer:

R: {f(x) ∈ ℝ | f(x) ≥ –3}

Step-by-step explanation:

I got it right on the test.

Hi :)

[tex]\star\sim\star\sim\star\sim\star\sim\star\sim[/tex]

    - we just insert the number for slope before x in the y=mx+b formula and then write the y-intercept

[tex]\star\sim\star\sim\star\sim\star\sim\star\sim[/tex]

Answer : 11 15

Reasoning : The fraction is in simplest form

9 21 is able to be simplified to 3 7,

12 18 is able to be simplified to 2 3

14 24 is able to be simplified to 7 12

Answer:

there are 720 three digit numbers that can be created from the digits provided given that no digit may be repeated.

Step-by-step explanation:

The revenue of the the agency is given by the function

R(x) = 5000 - 50 x - 3x² .

A function is a relationship between an independent variable and a dependent variable which defines all points on a cartesian plane which satisfies the given condition.

Now in the given Agency it is given that the charge of each tourist is $100 . Now for every tourist above 50 the charge is reduced by 3 dollars.

So for x people above 50 charge will be ( 100-3 x ) for all members.

The total revenue can be measured by the function

R(x) = ( 50 + x ) ( 100 - 3x )

or , R(x) = 5000 - 150 x + 100 x - 3x²

or, R(x) = 5000 - 50 x - 3x²

Hence the revenue function is given as : R(x) = 5000 - 50 x - 3x²

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m = -19 is the solution to the equation -2(m - 2) = -3(m + 5).

Given the data in the question;

To determine the numerical value of m, remove the parenthesis and simplify.

-2(m - 2) = -3(m + 5)

Apply distributive property

-2(m - 2) = -3(m + 5)

m(-2) - 2(-2) = m(-3) + 5(-3)

-2m + 4 = -3m - 15

Now, collect like terms by bring all values containing variable m to the left and all constant to the right side of the equation.

-2m + 3m = -15 - 4

m = -15 - 4

m = -19

Therefore, the numerical value of m is -19.

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Answer:

============================

This is an absolute value function and is the translation of f(x) = |x| down by 5 units.

We know that f(x) = |x| is never negative as per definition of absolute value. So its range is zero or positive numbers:

The given function (|x| - 5) can get values 5 less than the parent function (|x|), so its range is:

This is option B.

Answer:

you have the values of a, b and c

all you gotta do is just plug them in so

ab+bc is (3)(6)+(6)(5)

which equals 48.

Answer:

48

Step-by-step explanation:

since a=3, b=6 and c=5, you would replace the letters in ab+bc with their numbers, making it (3)(6)+(6)(5). then you would multiply 3 x 6 which would be 18, and 6 x 5, which would be 30, making your expression 18+30. finally you would add them together, making it 48.

Answer:

x = 21

Step-by-step explanation:

To get your answer, you can turn these to fractions: 5/7 = 15/x

5 * 3 = 15

7 * 3 = x

x = 21

Answer: is 7

Step-by-step explanation: Its 7 cuz 14 weeks

Answer:

(-6, -5).

Step-by-step explanation:

f(x)+3 represents the graph of f(x) shifted up 3 units, meaning we add 3 to the y-coordinate

The sum and the difference in the amount saved in the accounts will be 180 + 50w and 20 + 30w respectively.

From the information, I have have $100 in a savings accoun and save an additional $40 each week.

Let the number of weeks be represented by w. The expression to represent this will be:

= 100 + 40w

My friend has $80 in a savings account and saves and addtional $10 each week. This will be:

= 80 + 10w

The sum will be:

= 100 + 40w + 80 + 10w

= 180 + 50w

The difference in the amount will be:

= 100 + 40w - (80 + 10w)

= 20 + 30w

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Unit analysis is a helpful tool we can use to convert units.

All we have to do is multiply the original value by a fraction, to cancel out the units that we don't want.

We're given:

There are a couple things we need to know before we tackle this question:

Step 1 ⇒ Multiply [tex]\dfrac{20\hspace{4}miles}{hour}[/tex] by [tex]\dfrac{5280\hspace{4}feet}{mile}[/tex] to change miles to feet:

[tex]\dfrac{20\hspace{4}miles}{hour}\times\dfrac{5280\hspace{4}feet}{mile}\\\\= \dfrac{20\times5280\hspace{4}feet}{hour}\\\\= \dfrac{105600\hspace{4}feet}{hour}[/tex]

Step 2 ⇒ Multiply [tex]\dfrac{105600\hspace{4}feet}{hour}[/tex] by [tex]\dfrac{hour}{60\hspace{4}minutes}[/tex] to change hours to minutes:

[tex]\dfrac{105600\hspace{4}feet}{hour}\times\dfrac{hour}{60\hspace{4}minutes}\\\\=\dfrac{105600\hspace{4}feet}{60 minutes}\\\\=\dfrac{1760\hspace{4}feet}{minute}[/tex]

Step 2 ⇒ Multiply [tex]\dfrac{1760\hspace{4}feet}{minute}[/tex] by [tex]\dfrac{minute}{60\hspace{4}seconds}[/tex] to change minutes to seconds:

[tex]\dfrac{1760\hspace{4}feet}{minute}\times\dfrac{minute}{60\hspace{4}seconds}\\\\= \dfrac{1760\hspace{4}feet}{60\hspace{4}seconds}\\\\= \dfrac{29.3\hspace{4}feet}{second}[/tex]

[tex]\dfrac{29.3\hspace{4}feet}{second}[/tex]

The number of elements in the complement of a set A is the total number of elements in the universal set minus the number of elements in the set A.

It is given that A={volleyball players who are younger than 8 years old}.

From the table, volleyball players who are younger than the age of 8, are players who are 7 years old.

Hence, the number of players in A is 5.

Add the number of players for each age to get the total number of players:

It follows that the number of players in the complement of A is:

Hence, the number of players in the comp

Capacity of 1 thumb drives = 4 gigabytes.

Capacity of 1 compact disk = 2 gigabytes.

What is linear expression?

A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power.

Let capacity of a thumb dives = x

And, Capacity of a compact disk = y

Then, For first condition;

''4 thumb drives and 1 compact disk have a total capacity of 18 gigabytes.''

We can formulate;

4x + y = 18  .... (i)

And, For second condition;

'3 compact disks and 4 thumb drives have a total capacity of 22 gigabytes.'

We can formulate;

4x + 3y = 22 .... (ii)

Solve the equation (i) and (ii) we get;

Subtract (ii) by equation (i) we get;

2y = 4

y = 2

And, 4x + 2 = 18

4x = 16

x = 4

So, Capacity of 1 thumb drives = 4 gigabytes.

Capacity of 1 compact disk = 2 gigabytes.

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An ordered pair of point in Quadrant II is 8 units away from this point, the resulting point will be (-7.25, 4.25)

In this question, we need to find an ordered pair for the point in Quadrant II, that is 8 units away from the point Q(0.75 -3.25) on a coordinate plane.

If we have a coordinate point (x, y) in Quadrant ||, if the coordinate is 8 units away, the resulting coordinate will be expressed as (x - 8, y + 8)

Given the point Q(0.75, -3.25) on the coordinate  the plane, if a point in  Quadrant II is 8 units away from this point, the resulting point will be (0.75 - 8, -3.25 + 8) which is (-7.25, 4.25)

Therefore, an ordered pair a point in Quadrant II is 8 units away from this point, the resulting point will be (-7.25, 4.25)

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1.The slope -intercept form of the function is  y = 7x

2.The slope -intercept form of the function is y = x - 8

3.The slope -intercept form of the function is y = -2x +9

4.The slope -intercept form of the function is [tex]y = \frac{1}{3}x+9[/tex]

5.The slope -intercept form of the function is  y = 0.5x - 1.5

6.The slope -intercept form of the function is   y = 3x - 12

How is the slope -intercept form calculated?

1. The slope -intercept form of the equation of the function is  y = 7x

Slope = m

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\m =\frac{0+7}{0+1} \\\\m= 7[/tex]

Substituting point (-1,-7)  and m in the slope-intercept form of the equation,

y = mx+ c   ----(1)

-7 = 7(-1) + c

c = 7 -7

c = 0

Substituting m and c in  (1)

y = 7x

2. The slope -intercept form of the equation of the function is y = x - 8

Slope = m

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\m =\frac{-8+17}{0+9} \\\\m= \frac{9}{9} =1[/tex]

Substituting point (-9,-17)  and m in the slope-intercept form of the equation,

y = mx+ c   ----(1)

-17 = (-9) + c

c = -17 +9

c = -8

Substituting m and c in  (1)

y = x - 8

3. The slope -intercept form of the equation of the function is y = -2x +9

Slope = m

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\m =\frac{5-9}{2-0} \\\\m= \frac{-4}{2} =-2[/tex]

Substituting point (0,9)  and m in the slope-intercept form of the equation,

y = mx+ c   ----(1)

9 =  -2 (0) + c

c = 9

Substituting m and c in  (1)

y = -2x +9

4.The slope -intercept form of the equation of the function is  [tex]y = \frac{1}{3}x+9[/tex]

Slope = m

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\m =\frac{8-7}{-3+6} \\\\m= \frac{1}{3}[/tex]

Substituting point (0,9)  and m in the slope-intercept form of the equation,

y = mx+ c   ----(1)

9 =  1/3 (0) + c

c = 9

Substituting m and c in  (1)

[tex]y = \frac{1}{3}x+9[/tex]

5. The slope -intercept form of the equation of the function is

y = 0.5x - 1.5

Slope = m

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\m =\frac{1-0.5}{5-4} \\\\m= \frac{0.5}{1}= 0.5[/tex]

Substituting point (5,1)  and m in the slope-intercept form of the equation,

y = mx+ c   ----(1)

1 =0.5 (5) + c

1 -2.5 = c

c = - 1.5

Substituting m and c in  (1)

y = 0.5x - 1.5

6. The slope -intercept form of the equation of the function is y = 3x - 12

Slope = m

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\m =\frac{9-3}{7-5} \\\\m= \frac{6}{2}\\\\m= 3[/tex]

Substituting point (5,3)  and m in the slope-intercept form of the equation,

y = mx+ c   ----(1)

3 =3(5) + c

3 -15 = c

c = - 12

Substituting m and c in  (1)

y = 3x - 12

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