Question 18 25
f(x) = 2x
g(x) = 4x + 1
Find
() (2). Include any restrictions on the domain.
A.
(4) (x) = 477³¹, x ≥ 0
○ B. ( 4 ) (x) = ¹⁄⁄², ¤ / 0
4c-1
x
O c. (1) (₂) -
O D. (5)(x) =
✓/2T
55-1
2,² / 1
2 / -4

Answer:

C

Step-by-step explanation:

A reflection of a graph on the x axis simply adds the opposite sign to the x^2, in this case, since f(x) = x^2 is positive, a reflection would mean that g(x) would be -x^2. As g(x) is also vertically translated down 2 units, the equation would then become g(x) = -x^2 - 2 and the correct answer would be C.

Answer:

61

Step-by-step explanation:

the question is asking to find the number of element of set b that are not in set a

to find this one must know the common elements

the question has given the common elements to be 5

now subtract the number of elements in set b with the common elements

i.e. 66-5

=61

The total amount due on the electricity bill is $55.64.

Here given that the last month's electricity consumption is 354 kWh

According to my contract with the electricity company, I agree to pay 11.3 cents per kWh.

So for 354 kWh of last month, I have to pay [tex]=11.3\times354=4000.2[/tex] cents

Now we know that 1 dollar = 100 cents

100 cents = $1

1 cent = [tex]\$\frac{1}{100}[/tex]

4000.2 cents [tex]=\$\frac{4000.2}{100}=\$40.002[/tex]

also, I have to pay a fixed charge of $15.63

So the total bill for last month will be [tex]=\$40.002+\$15.63=\$55.632\approx\$55.64[/tex]

Hence the total due amount on the electricity bill is $55.64 approximating the amount to the next two decimal place number.

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The ratio is given by 98:0.34.

The ratio of (1/5 of 245ml) to (0.2 of 0.84ml).

The ratio can be defined as the comparison of the fraction of one quantity towards others. e.g.- water in milk.

we have  (1/5 of 245ml) to (0.2 of 0.84ml).

⇒ [tex]\frac{1}{5} 245 :0.2*0.84[/tex]

⇒[tex]98:0.34[/tex]

Thus, the required ratio is 98:0.34.

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Answer:

Linear Equations In One Variable =

Next step :

in the equation y/6 = 156, it would be equivalent to y = 156 × 6.

so that :

y = 156 × 6

y = 936

this equation solved. (Answer : 936)

The probability that 5 would not be working is 0.18665, the probability that at least one machine would be working is 0.00602 and the probability that all would be working is 1.

Given a company has 200 machines. Each machine has a 12% probability of not working.

If we working pick 40 machines randomly then we have to find the probability that 5 would not be working, the probability that at least one machine would be working, and the probability that all would be working.

So

1) probability that 5 would not be working

C(40,5)·0.12⁵·0.88³⁵= 40!/(5!(40-5)!)·0.12⁵·0.88³⁵

                                ≈ 0.18665

2)  probability that at least one machine would be working

0.88⁴⁰ ≈ 0.00602

3) probability that all would be working

1 - 0.12⁴⁰ ≈ 1.0000

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Answer:

g(f(x)) = 1x² + 1

Step-by-step explanation:

We are given:
f(x) = x² - 1

g(x) = x + 2

And we want to find g(f(x)).

To do this, we substitute f(x) as x in x+2 (the expression that is equal to g(x)), as g(f(x)) is saying that f(x) is the value of x in g(x).

So, this will be:

g(f(x)) = x² - 1 + 2

Simplify

g(f(x)) = x² + 1

In your system, place 1 in front of x² - this is the coefficient of x², and also 1 after that - this is a constant.

Pauline has 371 stickers. Karl, Serene, and Pauline have 1281 stickers altogether.

A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.

Let Karl, Serene and Pauline have x, y, and z stickers.

Given condition;

Karl, Serene, and Pauline have 1281 stickers altogether;

x+y+z = 1281

Pauline had 3 times as many stickers as Serene.

z = 3 y

y=z/3

Karl had 175 stickers fewer than Pauline.

x=z -175

Substitute all the values in the terms of z;

x+y+z = 1281

z -175 + z/3 + z = 1281

8z/3 = 1281 +175

z=546

Pauline have;

x = z -175

x =546 -175

x = 371

Hence Pauline has 371 stickers.

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Answer:

9

Step-by-step explanation:

This problem is represented below.

=3(4+2)-9

=3(6)-9

=18-9

=9

Answer:

B

Step-by-step explanation:

Range is all the possible values of 'y'. As seen in the graph, the smallest value of 'y' is 20, where the point is (6, 20), and the largest value of 'y' is 60, where the point is (1, 60). Therefore, the range is B. 20≤y≤60

The justification for whether Skyler, Robert, or Kaitlyn was right or wrong stems from how they went about their processes:

1) SKYLER'S PROCESS:

Skyler wants to resolve the following issue;

Reduce 729 to the lowest base possible as a first step; [3^(6)]^x = 9

729^(x) = 9

The next thing she did was convert 6x to 9.

Since both sides must have the same base when dealing with exponent equality, she may have transformed 9 to have the same base of 3 as the left hand side before equating the exponents.

So Skyler is wrong.

2) ROBERT'S PROCESS:

Skyler failed to capture both bases equally, as we witnessed, but Robert has now made the right decision by;

9^(3x) = 9¹

After which he equated the exponents to get;

3x = 1

x = 1/3

Thus; Robert is correct

3) KAITLYN'S PROCESS:

Kaitlyn is also accurate since she adhered to the same method, which calls for comparing bases before comparing exponents.

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Answer:

[tex]\frac{3}{32}[/tex]

Step-by-step explanation:

-> Simplify

[tex]\frac{6}{64} =\frac{6/2}{64/2} =\frac{3}{32}[/tex]

6/64 simplified.

The Medication A mixed this week should be 10 milligrams.

We have,

Medications to be mixed in the proper proportions.

Last week's proportions as the doctor indicated ;

Medication A = 90 milligrams

Medication B = 72 milligrams

This week's proportions as doctor indicated;

Medication B = 8 milligrams

Let, Medication A = x milligrams

As we are instructed to mix the Medication in the proper proportions,

So,

According to the question,

90/72 = x/8

10/8 = x/8

⇒ x = 10 milligrams

Here,  the Medication A mixed is 10 milligrams.

Therefore, the Medication A mixed this week should be 10 milligrams.

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Answer:

you can buy 98 beds and buy dresses by rest of the money

Answer:

2.48 seconds

Step-by-step explanation:

See attached

Answer:

34.562

Step-by-step explanation:

To find the perimeter of a circle, it's 2 * the radius * pi. In this case, we have a semicircle, so it would be the circle's perimeter divided by 2, or just the radius * pi.

The radius, 11, times pi (3.142), is 34.562.

Brainliest, please :)

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

we find the volume as if it were a parallelepiped and we remove the volume of the missing part.

8 * 6 * 10 = 480 cm³

480 - 2 * 3 * 10 = 420cm³

Step-by-step explanation:

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There are 25773 foxes in the region in the year 2008

The given parameters are:

Let the number of years after 2000 be x.

So, the function is

f(x) = a * (1 + r)^x

This gives

f(x) = 15000 * (1 + 0.07)^x

In 2008, we have:

x = 8

So, the equation becomes

f(8) = 15000 * (1 + 0.07)^8

Evaluate

f(8) = 25773

Hence, there are 25773 foxes in the region in the year 2008

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A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of the line will be y =4x+5. Thus, the correct option is C.

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of a line is given by,

y =mx + c

where,

x is the coordinate of the x-axis,

y is the coordinate of the y-axis,

m is the slope of the line, and

c is the y-intercept.

Given the slope of the line is 4 and it goes through (-1,1), therefore, the equation of the line will be,

y = mx + c

y = 4x + c

Substitute the value of points,

1 = 4(-1) + c

1 = -4 + c

5 = c

Hence, the equation of the line will be y =4x+5. Thus, the correct option is C.

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Step-by-step explanation:

1) zeros of the given function:

6x²-3=0; ⇔ 6(x²-0.5)=0; ⇔ x²=0.5; ⇔

[tex]\left[\begin{array}{ccc}x=-\sqrt{0.5} \\x=\sqrt{0.5} \end{array}[/tex]

2) relationship:

if to see the equation x²-0.5=0 (ax²+bx+c=0 is standart form!), then the sum of the zeros is '0' (it is 'b' of the standart form), the product of equation roots is '-0.5' (it is 'c' of the standart form).

[tex]{\large{\textsf{\textbf{\underline{\underline{Given :}}}}}}[/tex]

★ The polynomial

f(x) = 6x² - 3

[tex]{\large{\textsf{\textbf{\underline{\underline{To \: find :}}}}}}[/tex]

★ Zeroes of the polynomial f(x) = 6x² - 3

[tex]{\large{\textsf{\textbf{\underline{\underline{Solution :}}}}}}[/tex]

We have,

[tex]f(x) = \tt 6 {x}^{2} - 3[/tex]

Which can also be written as

[tex] \implies f(x) = \tt {(\sqrt{6} x)}^{2} - { (\sqrt{3}) }^{2} [/tex]

Using a² - b² = (a - b) (a + b)

[tex] \implies f(x) = \tt ( \sqrt{6} x - \sqrt{3} )( \sqrt{6} x + \sqrt{3} )[/tex]

To find the zeroes, solve f(x) = 0

[tex] \longrightarrow \tt ( \sqrt{6} x - \sqrt{3} )( \sqrt{6} x + \sqrt{3} ) = 0[/tex]

either [tex] \tt \sqrt{6} x - \sqrt{3} = 0 \: or \: \sqrt{6} x + \sqrt{3} = 0[/tex]

[tex] \implies \tt \sqrt{6} x = \sqrt{3 \: } \: or \: \: \sqrt{6} x = - \sqrt{3}[/tex]

[tex] \implies \tt x = \dfrac{ \sqrt{3} }{ \sqrt{6} } \: or \: x = - \dfrac{ \sqrt{3} }{ \sqrt{6} }[/tex]

[tex] \implies \tt x = \dfrac{ \sqrt{3} }{ \sqrt{2 \times 3} } \: or \: x = - \dfrac{ \sqrt{3} }{ \sqrt{2 \times 3} }[/tex]

[tex]\implies \tt x = \dfrac{ \cancel{ \sqrt{3} }}{ \sqrt{2} \: \cancel{\sqrt{3}} } \: or \: x = - \dfrac{ \cancel{ \sqrt{3} }}{ \sqrt{2} \: \cancel{\sqrt{3}} }[/tex]

[tex]\implies \tt x = \dfrac{1}{ \sqrt{2} } \: \: or \: \: - \dfrac{1}{ \sqrt{2} }[/tex]

Hence, the zeroes of f(x) = 6x² - 3 are:

[tex] \tt \alpha =\sf \boxed {{ \red{ \dfrac{1}{ \sqrt{2} } } }}\: \: and \: \: \beta =\sf \boxed {{ \red{ - \dfrac{1}{ \sqrt{2} } } }}[/tex]

• Verification

Sum of zeroes = [tex] ( \alpha + \beta )[/tex]

[tex] = \tt \dfrac{1}{ \sqrt{2} } + \bigg(- \dfrac{1}{ \sqrt{2} } \bigg)[/tex]

[tex] = \tt \dfrac{1}{ \sqrt{2} } + - \dfrac{1}{ \sqrt{2} } [/tex]

[tex]= \tt 0[/tex]

and, [tex]\tt - \dfrac{Coefficient \: of \: x}{Coefficient \: of \: {x}^{2} }[/tex]

[tex] \tt = - \dfrac{0}{6} [/tex]

[tex] \tt = 0[/tex]

[tex] \therefore \tt \: Sum \: of \: zeroes = {\boxed{ \red{\dfrac{ \tt Coefficient \: of \: x}{ \tt Coefficient \: of \: {x}^{2}}}}}[/tex]

Also,

Product of zeroes = [tex] \alpha \beta [/tex]

[tex] = \dfrac{1}{ \sqrt{2} } \times - \dfrac{1}{ \sqrt{2} } [/tex]

[tex] = - \dfrac{1}{ 2 } [/tex]

and, [tex]\tt - \dfrac{Constant \: term}{Coefficient \: of \: {x}^{2} }[/tex]

[tex] \tt = \dfrac{ - 3}{6} [/tex]

[tex] \tt = \dfrac{ - 1}{2} [/tex]

[tex] \therefore \tt \: Product \: of \: zeroes = {\boxed{ \red{\dfrac{ \tt Constant \: term}{ \tt Coefficient \: of \: {x}^{2}}}}}[/tex]

[tex]\rule{280pt}{2pt}[/tex]

Step-by-step explanation:

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Answer:

thats not even understandable

The solution set is {3, -3} and is represented by the number line shown below.

It is the representation of numbers in real order.

The difference between the consecutive numbers in a number line is always positive.

We have,

To solve the equation -2|x| = -6,

We can begin by dividing both sides by -2:

|x| = 3

This means that the absolute value of x is equal to 3.

The solutions to this equation are x = 3 and x = -3.

The number line that represents these solutions is:

<--(+)===================(+)--->

   -3                                       3

The open circles indicate that the solutions are not included in the solution set since the absolute value of x cannot be negative.

Therefore,

The solution set is {3, -3} and is represented by the number line shown above.

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The width of the pool is 10 feet.

The area of rectangle is product of length and breadth.

Let the width be x.

length = 24 + 2x. and breadth =  12 + 2x

We know, area= 1408 ft².

(12 + 2x)(24 + 2x) = 1408

12*24 + 12*2x + 24*2x + (2x)² = 1408

288 + 72x + 4x² = 1408

4x² + 72x + 288 - 1408 = 0

4x² + 72x - 1120 = 0

x² + 18x - 280 = 0

x² - 10x + 28x - 280 = 0

x(x - 10) + 28(x - 10) = 0

(x - 10)(x + 28) = 0

So, x=10, -28.

Hence, the width be 10 feet.

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Answer:

below

Step-by-step explanation:

Measure of each angle is 27 and 63 degrees.

Answer: A. [tex]\frac{12}{13}[/tex]

Step-by-step explanation:

The best way to remember this is SOH-CAH-TOA. For sin, it would be the opposite angle over the hypotenuse. The opposite angle of ∠C is 24 and the hypotenuse is 26. But that isn't in the answer choices, so you'll simplify the fraction.

[tex]\frac{24}{26} =\frac{12}{13}[/tex], therefore, the answer is A.

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