Write the function rule g(x) after the given transformations of the graph of f(x) = 6x.
reflection in the x-axis; vertical compression by a factor of
2
g(x) =

Answer:

y = -5/9x

Step-by-step explanation:

Two points on the line; (4,-2) & (-5,3)

Finding the slope (m):

m = (3-(-2))/(-5-4)

= 5/-9

= -5/9

y = -5/9x + c

Since it passes through the origin, c = 0.

Hence, y = -5/9x

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A linear equation in slope-intercept form for computer; y = -187.5(x) + 1200.

The value of the computer after 6 years will be $75.

Tim spends $1200 on a new computer.

He sells this same computer to that of a friend for $450 after four years.

Let y represent the computer's current value and x depict the number of years.

Create a linear equation in slope-intercept pattern to model the computer's value over time.

y = mx + b

y = 1200,

when x (time) is 0, thus b = 1200

when x = 4, y = 450,

Calculate the slope m.

4m + 1200 = 450

4m = 450 - 1200

m = -750/4

m = -187.5

Put the value of m in linear equation;

y = -187.5x + 1200

Noe, the value of computer after 6 years, put x = 6.

y = -187.5(6) + 1200

y = 75

Thus, the value of the computer after 6 years will be $75.

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Answer: B

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

let the 2 consecutive odd numbers be x and x + 2 , then the sum is

x + x + 2 = 72 , that is

2x + 2 = 72 → B

subtract 2 from both sides

2x = 70 ( divide both sides by 2 )

x = 35

x + 2 = 35 + 2 = 37

the 2 consecutive odd numbers are 35 and 37

The equations that could be used to determine the number of associates assigned to the case and the number of partners assigned to the case is: 800 x + 1800 y = 17600.

Let variable x =represent the number of associates, assigned to the case

Let variable y represent number of partners assigned to the case.

The system of equations re:

800 x + 1800 y = 17600

y = x + 2

Plug equation 2 in equation 1, we get,

800 x + 1800(x+ 2) = 17600

2600 x + 3600 = 17,600

Collect like terms

2400 x = 14,000

Divide both side by 2400x

x = 14,000 / 2400

x = 5.8

x = 6 (Approximately)

So,

y = x + 2

y = 5.8 +3

y = 7.8

y = 8 (Approximately)

Therefore the number of associates assigned to the case were 6, and the number of partners associated to the case were 8.

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Answer:

Exact form: x= -1 ± √2

Decimal Form: x= 0.41421356..., -2.41421356...

Step-by-step explanation:

The roots (zeros) are the x values where the graph intersects the x-axis. To find the roots (zeros) replace  with 0 and solve for x.

Answer:

k = 5

Step-by-step explanation:

f(x) = x + 4

g(x) = x + 9 = (x + 5) + 4 = f(x + 5)

So k = 5

Proved that ∠ 2 = 107° because these two angles are supplementary angles .

Angles that add up to 180 degrees are referred to as supplementary angles. For instance, angle 130° and angle 50° are complementary angles since the sum of these two angles is 180°. If the two additional angles are combined, they create a straight line and an angle.

However, it should be emphasized that the two complementary angles do not necessarily need to be close to one another. As a result, any two angles can be supplementary if their sum is 180 degrees. However, it should be emphasized that the two complementary angles do not necessarily need to be close to one another. So, if two angles are complementary, they can be any two angles.

Given : ∠ 1 and ∠ 2 are supplementary angles

that is ∠ 1 + ∠2 = 180 °

Given ∠ 1 = 73°

thus when we substitute this value in the equation we get ∠ 2 = 180 - 73

∠ 2 = 107 °

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The time taken to create the driveway is 7 hours 42 minutes

The dimensions of the rectangle tile = 3 inch by 5 inches

The area of the rectangle tile = Length × width

= 3×5

= 15 square inches

Time taken to position each rectangle = 6 minutes

The dimensions of the driveway = 2 foot by 4 foot

Convert the dimensions to inches

2 foot by 4 foot = 2×12 inches by 4×12 inches

= 24 inches by 48 inches

The area = Length × Width

= 24×48

= 1152 square inches

Number of tiles needed = Area of the driveway/ Area of the tile

= 1152/15

= 76.8

≈77 tiles

Time taken to create the drive way = Number of tile× Time taken to position each rectangle

= 77×6

= 462 minutes

= 7 hours 42 minutes

Hence, the time taken to create the driveway is 7 hours 42 minutes.

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Zach’s gross income was $79,500.

Given:

Zach's salary = $75,000

His interest income from a CD = $4,500  

Expenses = $5,000

Contribution to an IRA = $4,000

Standard deduction = $5700

Exemption rate = $3,650

Zach’s gross income =  Salary + interest income

                                  = $75,000 + $4,500

                                  = $79,500

Therefore, Zach’s gross income was $79,500.

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Step-by-step explanation:

Mean means the average

So to find the average, add all the numbers then divide by how many numbers there are.

Total=389

Divide by 10 = 38.9

Answer:

assuming the percents are out of 100 the order is

14.8 then 15% then 154/5 then 1450%

if thats not the case let me know and i'll correct it

Step-by-step explanation:

15% of 100 = 15

154/5 = 30.8

1450% of 100 = 1450

We will prove both of the identities by expanding the exponents, only in the first one we need to use a little trick that is multiplying by (-1)^2 = 1.

Let's start with the first one:

(a + b)^2 = (- a - b)^2

We can start with the left side and write:

(a + b)^2 = (a + b)*(a + b)

Now, remember the rule of signs:

(-1)*(-1) = 1

So we can multiply by one the expression above and get:

(a + b)*(a + b) =  (a + b)*(a + b)*1 =  (a + b)*(a + b)*(-1)*(-1)

Now we can reorder the product to get:

(a + b)*(a + b)*(-1)*(-1) = (-1)*(a + b)*(-1)*(a + b) = (-a - b)*(-a - b) = (-a - b)^2

So we proved the first part, now the second one:

(a - b)^2

Let's just expand this:

(a - b)^2 = (a - b)*(a - b) = a*a + a*(-b) + (-b)*a + (-b)*(-b) = a^2 - 2ab - b^2

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Answer:

x-4<16

x<16+4

x<20

S:[20] TRUE

Answer: 5/3

Step-by-step explanation:

The scale factor is the same as the ratio of the length of a side of the image to the length of the corresponding side in the preimage.

We know that N'Q'=10 and NQ=6, so the scale factor is 10/6 = 5/3.

The cube of the number five is written in these following forms:

The cube of a number n is equivalent to multiplying the number n by itself three times.

Hence, in expanded form, the cube of a number n is written as follows:

n x n x n.

In exponential form, the cube of a number n is written as follows:

n³.

In this problem, the number of interest is the number five, hence:

The result of the expression, which is the evaluation, is given by:

5 x 5 x 5 = 25 x 5 = 125.

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 x = 5 is the value of x in exterior angle.

Why is this term "exterior angle" used?

∠QRS is exterior angle .

apply exterior angle theorem in ΔPQR

So, ∠QRS = ∠PQR + ∠RPQ

     8x - 9° = 3x + 12° + 3x - 11°

     8x - 9 = 6x + 1

       8x - 6x = 1 + 9

         2x = 10

            x = 10/2

            x = 5

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Step-by-step explanation:

this is very roughly converted from the original question, I bet. no punctuation marks and, and ...

what I understood of the important information is :

there are 23 boxes of books with 12 books in each.

there are 4 teachers dividing the books evenly among themselves for their cells (classes ?) of students.

so, we need to divide the books by 4 to distribute them evenly into 4 parts.

23×12/4 = 23×3 = 69

each teacher got 69 books.

Answer: 5<x<35

Step-by-step explanation:

An acute angle ranges from 0 to 90 degrees.

[tex]0 < 3x-15 < 90\\\\15 < 3x < 105\\\\5 < x < 35[/tex]

The width of her bedroom is x - 5

It is important to note that the formula for area of a rectangle is expressed as;

Area = lw

Where;

Now, let's substitute the values into the formula, we have;

2x²-7x-15 = (2x+3)w

Divide both sides by the coefficient of w

w = 2x²-7x-15/(2x+3)

Factorize the numerator

w = 2x²- 10x + 3x - 15/(2x+3)

Factor the common terms of the numerator

w = 2x(x - 10) + 3(x - 5)/(2x+3)

enclose the expressions

w = (2x + 3)(x-5)/(2x+3)

Divide the common terms

w = x - 5 feet

Hence, the value is x - 5

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For the given data set, median is better choice for measure than mean because:

Median is usually a better measure of the center when there are extreme values as it is remains unaffected by the precise numerical value. The most common measure of the center is mean.

Adding all numbers in the data and dividing it by the number of values in the set gives mean of a data. Whereas, median is the middle value in a data set, implying that 50% of data points can have a value smaller or equal to the median and 50% of data points can have a value higher or equal to the median.

For a small data set, firstly, count the number of data points and arrange them in increasing order. If the number of data is odd, then add 1 to the number and divide the result by 2 to obtain the rank of the data whose value is the median.

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Answer:

9.

he washes 9 cars on Tuesday.

Step-by-step explanation:

28 * 7 = 196.

448 - 196 = 252

252 / 28 = 9

On solving the linear equation  28x + 196 = 448, we get that Craig washed 9 cars on Tuesday.

Linear equation is an equation containing one unknown variable with power one and constants.

The standard form of an linear equation in one variable x is :

ax + b = 0 , where a, b are constants

x= -b/ a is solution if this equation or we can solve this equation by adding or subtracting , multiplying or dividing same number to both sides.

Given that Craig washes cars and earns $ 28 for each car . He washed 7 cars on Monday.

Let on Tuesday he washed x cars

Total money earned on Tuesday and Monday by Craig = $448

Money earned on Monday = $ 7× 28 = $ 196

Money earned on Tuesday  = $ x×28 = $ 28x

⇒ 28x + 196 = 448

Subtracting 196 from both sides we get

⇒ 28x + 196 -196 = 448 - 196

⇒ 28 x = 252

Dividing both sides by 28

⇒ x = 252/28 = 9

Therefore, Craig washed 9 cars on Tuesday.

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Answer: No Solution

Step-by-step explanation:

||3x - 1| + 5| <1  ⇒

[tex]\left \{ {{|3x - 1| + 5 < 1} \atop {|3x - 1| + 5 > -1 }} \right.[/tex]    ⇒

[tex]\left \{ {{|3x - 1| < -4} \atop {|3x - 1| > -6} \right.[/tex]        ⇒

The first equation does not make sense because absolute value and as it is a system of equations, the whole system does not have a solution.

ΔDEF ≅ Δ RPQ by ASA rule and line segment RF ≅ line segment HR.

In triangle DEF and triangle PQR,

We can see that:

DF = RQ = 5cm

0∠D = ∠Q = 60°

∠F = ∠R = 80°

So, we get that:

ΔDEF ≅ Δ RPQ ( ASA rule.)

Also, we are given that:

quadrilateral RAUF ≅ Quadrilateral HBQR

This means that:

line segment RF ≅ line segment HR.

Therefore we get that, ΔDEF ≅ Δ RPQ by ASA rule and line segment RF ≅ line segment HR.

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Answer:

[tex]\boxed{\sf{r < -4\quad r\geq 2}}[/tex]

Step-by-step explanation:

Isolate the term of r.

First, subtract by 5 from both sides.

r+5-5<1-5

Solve.

r<-4

Add by 1 from both sides.

r-1+1≥1+1

Solve.

Add the numbers from left to right.

r≥2

Therefore, the correct answer is r<-4 and r≥2.

I hope this helps, let me know if you have any questions.

Answer:

40°

Step-by-step explanation:

By the exterior angle theorem, [tex]m\angle 1=100^{\circ}[/tex]. Applying the theorem again, we get [tex]m\angle 2=40^{\circ}[/tex]

Using the Law of Detachment, the conclusion is that it is not safe to be out in the open, as the conclusion is true, since the conditional and the hypothesis are true.

The Law of Detachment is a logic axiom which states that if a conditional and the hypothesis are true, then the conclusion is also true.

Supposing a conditional statement p -> q, we have that:

For this problem, the sentence is:

"If there is lighting, then it is not safe to be out in the open."

Hence p and q are given as follows:

Marla sees lighting from the soccer field, hence the statement p is correct, and we know that the conditional is true, hence the conclusion that it is not safe to be out in the open can be reached.

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4.25 light years is 2.4984x10¹³ miles

What is light years?

A light-year, sometimes spelt light year, is a huge measure of length used in astronomy that is comparable to approximately 9.46 trillion kilometers (9.461012 kph) or 5.88 trillion miles (5.881012 mi). A light-year, as defined by the International Astronomical Union (IAU), is the distance that light travels in a vacuum in one Julian year (365.25 days). The phrase light-year is frequently misconstrued as a unit of time since it contains the time-measurement word "year." The light-year is most commonly used in non-specialist contexts and popular scientific publications to indicate distances to stars and other cosmic distances.

1 light years is = 5.8786x10¹² miles

4.25 light years = 5.8786x10¹²x4.25 = 2.4984x10¹³ miles

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Answer:

September2020

13outcomes

The domain for the given graph would be [-5,10] and range for the graph would be [0.4,5.6]. in both the case whether increasing or decreasing graph.

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). The entire range of independent variable values is the domain of a function.

The range of a function is the set of outputs the function achieves when it is applied to its whole set of outputs. In the function machine metaphor, the range is the set of objects that actually come out of the machine when you feed it all the inputs.

Graphs can also be used to determine the domain and range of functions. The domain of a graph consists of all the input values shown on the x-axis because the domain refers to the set of possible input values. The range represents the set of possible output values shown on the y-axis.

Here, The domain would be [-5,10] as the graph is depicting.

The range would be[0.4,5.6].

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(66 inches) because i don't know

but my answer is correct