Which of the following is an even function?
A) f(x) = (x – 1)^2
B) f(x) = 8x
C) f(x) = x^2 – x
D) f(x) = 7

Answer: A

Step-by-step explanation:

Let f(y)=x.

[tex]x=\frac{y+2}{7}\\\\7x=y+2\\\\y=7x-2\\\\f^{-1}(x)=7x-2[/tex]

[tex](-7+9, 1-3)=\boxed{(2, -2)}[/tex]

The answer is (2,-2).

Find the image of the given point under the given translation:

The rule of translation is (x+9, y - 3), P (-7, 1).

Here we need to add 9 from

x value is -7+9=2

y We need to subtract -3 from

y value is (1-3)=-2

So, P’=( 2,-2)

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The equation of the line from give points is y = 2/3x - 5/3.

According to the statement

We have given that the two points which are (-2,-3) and (4,1)

And we have to find the equation of a line that passes through the given points.

So,For this purpose,

First, we need to determine the slope of the line. The slope can be found by using the formula:

[tex]m = \frac{(y_2) -(y_1)}{(x_2) -(x_1)}[/tex]

Where

m is the slope and

Substituting the values from the points in the problem gives:

m = 1 + 3 /4 + 2

m = 4/6

m = 2/3.

And then

Now, we can use the point-slope formula to find an equation for the line. The point-slope formula states:

[tex]y - (y_1) = m(x -x_1)[/tex]

Put the values in it then

y - (-3) = 2/3 (x-(-2))

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

3y + 9 = 2x + 4

3y - 2x = 4 -9

3y -2x = -5

3y = 2x - 5

y = 2/3x - 5/3.

So, The equation of the line from give points is y = 2/3x - 5/3.

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Answer:

the answer is 1,2,4,5 and 7.

Answer: The answer is A,B,D,E,G

Step-by-step explanation: just trust me and enjoy your write answers. Have a nice day.

Answer:

135 is correct answer of this question

Answer:

here's your answer step by step explanation

Step-by-step explanation:

page 6 is missing comment me i will send you page 6

Answer:

j = 7.8.

Step-by-step explanation:

The slope of the line = difference in y-values / corresponding difference in x-values.

Slope = (7-3) / (j-5) = 10/7

so 10(j - 5) = 7*4

10j - 50 = 28

10j = 78

j = 7.8.

Answer:

d

Step-by-step explanation:

the opposite angles of a cyclic quadrilateral sum to 180° , that is

∠ ABD + ∠ ACD = 180°

∠ ABD + 48° = 180° ( subtract 48° from both sides )

∠ ABD = 132°

Answer:

m∠RSU = 10x - 9 = 10(14) - 9 = 140 - 9 = 131

m∠RST = 2x = 2(14) = 28

m∠TSU = 2x + 75 = 2(14) + 75 = 28 + 75 = 103

Step-by-step explanation:

m∠RSU = m∠RST + m∠TSU

10x - 9 = 2x + (2x + 75)

10x - 9 = 2x + 2x + 75

10x - 9 = 4x + 75

-4x +9     -4x  +9

      6x = 84

         x = 14

m∠RSU = 10x - 9 = 10(14) - 9 = 140 - 9 = 131

m∠RST = 2x = 2(14) = 28

m∠TSU = 2x + 75 = 2(14) + 75 = 28 + 75 = 103

Answer:   100 square cm

Step-by-step explanation:   the triangle is 33 cm and the big rectangle is 9x7 square cm. There is a small square that is 2x2 =4 cm so the total is 33 +63 + 4 which is 100 cm.

Answer: 104

Step-by-step explanation:

area of trangle =33 because 6*11/2=33

area of rectangle 9*7=63

area of rectangle  2*2=4

33+63+4=100^2

The algebraic expression of the statement is 4x + 6

The statement is given as:

The sum of four times a number and six

Rewrite as:

The sum of 4 times a number and 6

Let the number be x

So, we have

The sum of 4 times x and 6

Evaluate the product

The sum of 4x and 6

Evaluate the sum

4x + 6

Hence, the algebraic expression of the statement is 4x + 6

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Answer: 9 diagonals

Step-by-step explanation:

The polynomial that should be subtracted from the dividend first is; x³ + 2x²

The long division we are given is;

        __________

x + 2 ) x³ + 3x² + x

Now, when we divide the polynomial by (x + 2), it means that the first quotient will be x².

Then by the multiplication of (x + 2) and x², we get a polynomial which will be subtracted from the dividend. Thus, we have;

(x + 2) * (x²) = x³ + 2x²

Thus, the polynomial to be subtracted is x³ + 2x²

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u = - 4w + 9 is the rearranged equation so that w is the independent variable given that the equation is u - 5= - 4(w - 1). This can be obtained by simplifying the equation and taking w to one side of the equation with other constants.

Simplifying an equation can be done by using the following steps:

Here it is given that the equation is,

⇒ u - 5= - 4(w - 1)

We have to find an equation in which w is taken to one side of the equation with other constants.

First by adding both side of the equation with 5 we get,

⇒ u - 5 + 5 = - 4(w - 1) + 5

By opening the bracket we get,

⇒ u = - 4w + 4 + 5

Finally by adding the constants we get,

⇒ u = - 4w + 9

Hence u = - 4w + 9 is the rearranged equation so that w is the independent variable given that the equation is u - 5= - 4(w - 1).

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Answer:Many

Step-by-step explanation:

As the unknown cancels itself out, it could be absolutely any number. So there are many solutions.

Answer:

a₁ = 5

a₂ = 8

a₃ = 13

a₄ = 20

Step-by-step explanation:

Given sequence formula

aₙ = n² + 4

Requirement of the question

Find the 4 terms in the sequence

Substitute 4 values into the sequence formula

a₁ = (1)² + 4 = 1 + 4 = [tex]\Large\boxed{5}[/tex]

a₂ = (2)² + 4 = 4 + 4 = [tex]\Large\boxed{8}[/tex]

a₃ = (3)² + 4 = 9 + 4 = [tex]\Large\boxed{13}[/tex]

a₄ = (4)² + 4 = 16 + 4 = [tex]\Large\boxed{20}[/tex]

Hope this helps!! :)

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Answer:

Gustavo used a simulation where the data is quantitative’

The probability that the service time will be more than three minutes is 0.3012.

Given that the average wait time at the Rivertown bank's neighborhood branch is 2.5 minutes and has an exponential distribution,

The time it takes to succeed in a continuous sequence of independent trials is described by the exponential distribution, which is a continuous probability distribution.

At the River Town Bank's neighborhood branch, the random variable X service time has an exponential distribution with a mean value of 2.5 minutes. Therefore,

[tex]f(x)=\left\{\begin{array}{ll}\theta e^{-\theta x},& \theta \geq 0,0\leq x\leq \infty\\0&\text{otherwise}\end{array}[/tex]

E(x)=1/θ

θ=1/2.5

θ=0.4

The probability that the service time will be longer than three minutes:

[tex]\begin{aligned}P(X > 3)&=1-P(X\leq 3)\\ &=1-(1-e^{-0.4\times 3}\\ &=e^{-1.2}\\ &=0.3012\end[/tex]

Since the service duration has an exponential distribution and a mean of 2.5 minutes, the needed chance that it will exceed 3 minutes is 0.3012.

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Answer:

$525

Step-by-step explanation:

We can find the original price by using the formula x - 0.36x = 336, where x is the original price, 0.36 is the discount percentage (converted to decimal form), and 336 is the total amount paid after the discount is applied:

[tex]x-0.36x=336\\0.64x=336\\x=525[/tex]

To check and further understand why the formula works, we can simply apply the discount to the original price and subtract the number from the original price:

525 * 0.36 = 189

525 - 189 = 336

Modeling the first formula gives us:

525 - (0.36 * 525) = 336

525 - 189 = 336

Answer: [tex]\Large\boxed{15~dimes~;~9~nickels}[/tex]

Step-by-step explanation:

Given information

Number of coins = 24 coins

Total amount = $1.95

Dime = 10 cents = $0.1

Nickel = 5 cents = $0.05

Set variables

Let d be the number of dimes

Let n be the number of nickels

Set a system of equation

1) d + n = 24

2) 0.1d + 0.05n = 1.95

Multiply 10 on both sides of 2) equation

0.1d · 10 + 0.05n · 10 = 1.95 · 10

d + 0.5n = 19.5

Current system

1) d + n = 24

2) d + 0.5n = 19.5

Subtract 2) equation from the 1) equation

(d + n) - (d + 0.5n) = (24) - (19.5)

Expand the parenthesis

d + n - d - 0.5n = 24 - 19.5

Combine like terms

d - d + n - 0.5n = 4.5

0.5n = 4.5

Divide 0.5 on both sides

0.5n / 0.5 = 4.5 / 0.5

[tex]\Large\boxed{n=9}[/tex]

Substitute the n value into one of the equations to find the d value

d + n = 24

d + (9) = 24

d = 24 - 9

[tex]\Large\boxed{d=15}[/tex]

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Answer:

X=36

Step-by-step explanation:

2x + 3x=5x

if given figure is 180 then

5x=180

X=180/5

X=36

Using a system of equations, it is found that there were 4,000 children tickets sold.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

For this problem, the variables are given by:

The attendance at the amusement park is 5,000 attendees, hence:

x + y = 5000 -> y = 5000 - x.

Considering the cost of parking and that the total money earned by the park is $100,000, we have that:

15x + 40y = 100000

Applying the multiplication of the matrices, these equations are the same that the system gives. Replacing the second equation into the first:

15x + 40(5000 - x) = 100000

25x = 100000

x = 100000/25

x = 4000.

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Answer:

The answer is: (x,y) = (-2,5)

Answer:  C

Step-by-step explanation: the other two options are both wrong, 0.13 is larger than 0.125 and she did order by volume per fish.

Using the z-distribution, the 95% confidence interval to describe the total percentage of students who do not like ice cream is:

(8.34%, 17.66%).

A confidence interval of proportions is given by:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which:

In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

For this problem, the estimate and the sample size are given, respectively, by:

[tex]\pi = 0.13, n = 200[/tex]

Hence the bounds of the interval are:

As a percentage, the interval is:

(8.34%, 17.66%).

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The probability that the machine produces fewer than 3 defective widgets in a production run of 75 items is 0.041.

A probability refers to the ratio of favorable events to the n number of total events.

Also, it means the chance that a particular event (s) will occur expressed on a linear scale from 0 to 1 which can also be expressed as a percentage between 0 and 100%.

Given data

An industrial machine produces 3 widgets.

It has a 0.12 defective rate.

Defective rate fewer than 3

Total Probability = P of 2 defective + P for 1 defective

Total Probability = 2/74 + 1/73

Total Probability ≈ 0.04072565716

Total Probability ≈ 0.041

Therefore, the required probability for fewer than 3 defective rate is 0.041

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a.  The expressions for c and d in terms of a and b are

b.  The inverse of (2,1) is (13/15, -4/15)

The question has to do with binary operation.

A binary operation is a rule of mathematical operation on two sets of elements defined on a given set.

Since The operation * is defined over the set of ordered pairs by (a,b)*(c,d)=(ac-bd,ad+bc) for all (a,b),(c,d)€R given that the inverse of (a,b) is (c,d).

Let (e, e') be the identity element.

We know that for any binary operation * on a given set, a*e = a where e is the identity element.

So,  (a,b)*(e,e') =  (a,b)

So, (a,b)*(c,d) = (ac - bd, ad + bc)

(a,b)*(e,e') = (ae - be, ae' + be')

Since  (a,b)*(e,e') =  (a,b)

(ae - be, ae' + be') = (a, b)

So,

e = a/(a - b) and e' = b/(a + b)

So, (e, e') = (a/(a - b), b/(a + b))

Also, for any binary operation * under a given set a*a⁻¹ = e where a⁻¹ = inverse of a.

Since (c,d) is the inverse of (a,b), we have that

(a,b)*(c,d) = (e, e')

So, (a,b)*(c,d) = (ac - bd, ad + bc)

=  (a/(a - b), b/(a + b))

So,

From (3), c = bd/a + 1/(a - b)

Substituting c into (4), we have

ad + bc = b/(a + b)  

ad + b[bd/a + 1/(a - b)] = b/(a + b)  

ad + b²d/a + b/(a - b) = b/(a + b)  

ad + b²d/a = b/(a + b) -  b/(a - b)]

(a + b²/a)d = b[1/(a + b) -  1/(a - b)]

[(a² + b²)/a]d = b[a - b - (a + b)]/(a - b)(a + b)

[(a² + b²)/a]d = b[a - b - a - b)]/(a - b)(a + b)

[(a² + b²)/a]d = b(-2b)/(a² - b²)

d = -2ab²/[(a² - b²)(a² + b²)]

d = -2ab²/(a⁴ - b⁴)

Substitutind d into c, we have

c = bd/a + 1/(a - b)

c = -2ab³/(a⁴ - b⁴)a + 1/(a - b)

c = -2b³/(a⁴ - b⁴) + 1/(a - b)

So, the expressions for c and d in terms of a and b are

Since (c,d) is the inverse of (a,b) is

So, with a = 2 and b = 1, c = -2b³/(a⁴ - b⁴) + 1/(a - b)

= -2(1)³/(2⁴ - 1⁴) + 1/(2 - 1)

= -2/(16 - 1) + 1/1

= -2/15 + 1

= (-2 + 15)/15

= 13/15

So, with a = 2 and b = 1, d = -2ab²/(a⁴ - b⁴)

= -2(2)(1)²/(2⁴ - 1⁴)

= -4(1)/(16 - 1)

= -4/15

So, the inverse of (2,1) is (13/15, -4/15)

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From my analysis, the answer is likely to be D. I don't have a formula to prove it though.

Answer: 78 degrees.

Step-by-step explanation:

The other guy is wrong don't listen to him.

Answer:

22, 23

Step-by-step explanation:

4x + 3(x + 1) = 157

4x + 3x + 3 = 157

7x + 3 = 157

7x = 154

x = 22

A quantity of 84 shingles are required to cover the surface area of 336 square feet of the first roof.

A quantity of 110 shingles are required to cover the surface area of 220 square feet of the second root.

In this question we must determine both the surface area and the number of shingles to cover two roof configurations as well. In the first case, we calculate the surface area, which is the sum of the area of rectangles:

A = 2 · (8 ft) · (12 ft) + 2 · (6 ft) · (12 ft)

A = 336 ft²

And the number of shingles required to cover the root is:

n = (336 ft²) / (4 ft²)

n = 84

A quantity of 84 shingles are required to cover the surface area of 336 square feet of the first roof.

In the second, we only need to cover the very top surface. The area and the number of shingles are, respectively:

A = 2 · (5 ft) · (22 ft)

A = 220 ft²

n = (220 ft²) / (2 ft²)

n = 110

A quantity of 110 shingles are required to cover the surface area of 220 square feet of the second root.

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