If f(x) = 3^x + 10x and g(x) = 5x - 3 find (f - g)(x)

Answer: b

Step-by-step explanation:

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The transformation of a function may involve any change. The correct option is A.

The transformation of a function may involve any change.

Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs) etc.

If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:

Horizontal shift (also called phase shift):

Vertical shift

Stretching:

Given the function of f(x) as sin(x), Now it can be seen the graph of the two functions is parallel, but the function f(x) has a y-intercept of 0, while h(x) has a y-intercept of 1. Therefore, we can write,

h(x) = f(x) + 1

The function is shifted up by 1 unit.

Hence, the transformation of the function is correctly described in the first option.

Learn more about Transforming functions:

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Answer:

Step-by-step explanation:

[tex]4\sqrt{3-\frac{1}{x} } -\sqrt{\frac{x}{3x-1} } =3\\4\sqrt{\frac{3x-1}{x} } -\sqrt{\frac{x}{3x-1} } =3\\\\put ~\sqrt{\frac{3x-1}{x}} =a\\4a-\frac{1}{a} =3\\4a^2-1-3a=0\\4a^2-4a+1a-1=0\\4a(a-1)+1(a-1)=0\\(a-1)(4a+1)=0\\a=1,-\frac{1}{4}\\[/tex]

[tex]\sqrt{\frac{3x-1}{x} } =1\\3x-1=x\\3x-x=1\\2x=1\\x=\frac{1}{2}[/tex]

when a=-1/4

[tex]\sqrt{\frac{3x-1}{x} } =-\frac{1}{4} \\[/tex]

[tex]\frac{3x-1}{x} =\frac{1}{16} \\48x-16=x\\47x=16\\x=\frac{16}{47}[/tex]

[tex]\frac{(1-2x)^2 \times (x^2-9)}{-x^2-x+6} \geq 0,\\both ~numerator ~and~denominator ~are~of~same~sign.\\\frac{(1-2x)^2(x^2-9)}{-x^2-3x+2x+6} \geq 0\\\frac{(1-2x)^2(x+3)(x-3)}{-x(x+3)+2(x+3)} \geq 0\\\frac{(1-2x)^2(x+3)(x-3)}{(x+3)(-x+2)} \geq 0\\(1-2x)^2\geq 0~(always)\\x\neq -3\\case.~1.\\both~numerator~and~denominator >0\\\frac{x-3}{-x+2} \geq 0\\x-3\geq 0\\x\geq 3\\-x+2> 0\\-x>-2\\x<2\\so~ solution~ is~ (-\infty,-3)U(-3,2)U[3,\infty)[/tex]

case 2.

both numerator and denominator are negative.

[tex]x-3\leq 0\\x\leq 3\\-x+2\leq 0\\-x\leq -2\\x\geq 2\\solution~is~(-\infty,-3)U(-3,3]U[2,\infty)[/tex]

Answer:

Step-by-step explanation:

Yikes. This is quite a doozy, so pay attention. We will begin by factoring by grouping. Group the first 2 terms together into a set of parenthesis, and  likewise with the last 2 terms:

[tex](2d^4+6d^3)-(18d^2-54d)[/tex] and factor out what's common in each set of parenthesis:

[tex]2d^3(d+3)-18d(d+3)[/tex]. Now you can what's common is the (d + 3), so factor that out now:

[tex](d+3)(2d^3-18d)[/tex] BUT in that second set of parenthesis, we can still find things common in both terms, so we continue to factor that set of parenthesis, carrying with us the (d + 3):

[tex](d+3)2d(d^2-9)[/tex] BUT that second set of parenthesis is the difference of perfect squares, so we continue factoring, carrying with us all the other stuff we have already factored:

[tex](d+3)2d(d+3)(d-3)[/tex]. That's completely factored, but it's not completely simplified. Notice we have 2 terms that are identical: (d + 3):

[tex]2d(d+3)^2(d-3)[/tex] is the completely factored and simplified answer, choice 3)

Answer:

(-2, -2)

Step-by-step explanation:

To scale a factor by 1/4, you just need to divide the numbers by 4, or multiply them by 1/4.

-8/4=-2

Answer:

It would be (-2, -2)

Answer:

184

Step-by-step explanation:

First, note that the sides that are opposite to each other are congruent (this will come into play in a second). We can find the area of each triangle by doing 0.5(b)(h) (aka half * base* height). Since we've established tha opposite sides are congruent and the triangles are opposite to each other, they must be congruent. That means that the area is going to be the exact same for both triangles. So, we get the expression (0.5)(6)(4)(2), which comes out to 6*4 = 24. Then, to find the area of the 2 rectangles that are the sides, just do 5*10*2 = 100 square meters for both rectangles combines. Lastly, we need to find the area of the floor. The dimensions of the floor are 6 and 10, so we just do 6*10 = 60. Now, add all those numbers together. We get 100+60+24 = 184. Hope this helps! Let me know if anything is still confusing.

Answer:

I think it might be C but I'm not 100% sure!

Step-by-step explanation:

You have to find a line of best fit (a line through the dots) but it's kind of tricky to do that so I think it's probably C but it could also be A. Just use your best judgement on this one!

Answer:

C

Step-by-step explanation:

If you graph all 4 and plot  all 4 of the  point, line c  is the most accurate and lines up the best out of all 4.

Answer:

Step-by-step explanation:

It 1 2

Answer:

a₁₅ = 71

Step-by-step explanation:

The nth term of an arithmetic sequence is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 1 and d = 6 - 1 = 5 , then

a₁₅ = 1 + (14 × 5) = 1 + 70 = 71

Step-by-step explanation:

hear is your answer in attachment

Answer:

2(2x+7)=4x+14

2(3x+8)=6x+16

4x+14+6x+16

4x+6x+14+16

The answer is:

10x+30

Answer:

√100 = 10, √36 = 6, √225 = 15

Step-by-step explanation:

100 can be made by 10^2 (10 x 10), 36 has factors of 6 and can be made by 6^2, and 225 can be made by 15^2.

[tex] \sqrt{100} = \sqrt{10 \times 10} [/tex] = [tex]\boxed{10}[/tex]

[tex] \sqrt{36} = \sqrt{6 \times 6} [/tex] = [tex]\boxed{6}[/tex]

[tex] \sqrt{225} = \sqrt{15 \times 15} [/tex] = [tex]\boxed{15}[/tex]

[tex]\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35}}}}}[/tex]

Step-by-step explanation:

x=30° { ins angle inscribed angle Standing on arc are equal }

hope it helps

Step-by-step explanation:

A is the answer to the question

A) r^2 - 2rs+s^2

...............................

Answer:

15.2%

Step-by-step explanation:

There are 12 marbles in total and there are 5 red marbles, so the probability of getting a red marble is 5/12. There are now 11 marbles and there are 4 blue marbles. So the probability of getting a blue marble is 4/11.

You multiply these 2 values together.

5/12 * 4/11 = 20/132 = 0.1515

This is about 15.2%

Answer:

option b : 15.2 %

Step-by-step explanation:

5 Red , 4 Blue,  3 Yellow

Total balls = 12

[tex]Probability \ of \ choosing \ red = \frac{5C_1}{12C_1} = \frac{5}{12}\\\\Probability \ of \ choosing \ blue \ without \ replacement = \frac{4C_1}{11C_1} = \frac{4}{11}\\\\Probability \ of \ red \ and \ then \ blue = \frac{5}{12} \times \frac{4}{11} = 0.1515\\\\Probability \ in \ percentage = 0.1515 \times 100 = 15.15 = 15.2 \%[/tex]

Answer:

it is an infinite rule guiding it

Answer:

-16m^16 n^5

Step-by-step explanation:

(2m^4)^4*-n^5

= 2^4*m^16*(-n^5)

= 16 m^16 * (-n^5)

= -16m^16 n^5

hopefully this will help

Remember the rule

Answer:

84 :-)

Step-by-step explanation:

Answer:

<S= 88degrees

<Q = <R = 46degrees

Step-by-step explanation:

Since the base angles of the isosceles triangle are equal hence;

<Q = <R

5x - 14 = 4x -2

5x - 4x  = -2 +1 4

x = -2 + 14

x = 12

Since <Q = 5x - 14

<Q = 5(12) - 14

<Q = 60 - 14

<Q = 46degrees

Also <Q = <R = 46degrees

Similarly; <S + <Q + <R =180

<S +46 + 46 = 180

<+92 = 180

<S = 180 - 92

<S= 88degrees

Answer:

(i) no. of favourable out comes =7 i.e. {2,4,6,8,10,12,14}

∴ P=

15

7

(ii) no. of favourable outcomes =3 i.e {5,10,15}

∴ P=

15

3

=

5

1

Step-by-step explanation:

thats my answer thank you

Answer:

49

Step-by-step explanation:

7(4x + 7)

=7*4x + 7*7

=28x +49

Answer:

28x + 49

Step-by-step explanation:

7(4x + 7) = 28x +

28x + 49

Answer:

$280

Step-by-step explanation:

Please find attached the image of the tent

cost of the tent = cost per square inch x total surface area of a triangular prism

total surface area of a triangular prism = (perimeter x height) + 2(area of a triangle)

Area of a triangle = 1/2 x base x height = 1/2 x 40 x 50 = 1000in²

1000 x 2 = 2000

Perimeter = 50 + 50 + 50 = 150

150 x 80 = 12,000

total surface area = 12,000 + 2000 = 14,000

Total cost = 14,000 x 0.02 = $280

Answer:

D.

Theorems, Defintions, Postulates, Properties

Step-by-step explanation:

Answer:

C. 24%

Step-by-step explanation:

hope it works

Answer:

39%

Step-by-step explanation:

Answer:

Shoe rent is $4.5

Step-by-step explanation:

Let the shoe rent is "x" which will remain the same irrespective of the number of bowling and "y" is bowling.

thus, x + 2y = 16.50

Rewrite, x = 16.50 - 2y

When bowling is 4 time then:

x + 4y = 28.50

Rewrite, x = 28.50 - 4y

Now solve both equations for the value of "y".

Thus, 16.50 - 2y = 28.50-4y

-2y + 4y = 28.50 - 16.50

2y = 12

y = 6

Insert y = 6 in the x - 2y = 16.50

x = 16.50 - 2y

x = 16.50 - 2 (6)

x = $4.5

Shoe rent is $4.5

Answer:

35=10+5+5

35=20+p

35-20=p

p=15

Answer:

C) 93o

Step-by-step explanation:

Trust the process

edge 2021

Answer:

Got a 100% on the Unit Test on Edge and 93 is the correct answer like the person above added! :D

Answer: 7$

Step-by-step explanation: 40-4= 36 | 3x5=15 | 36-15=21 | 21/3=7