Which lines are parallel
FM and GB
MB and FG
MB and GB
FM AND FG

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.

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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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.

Alternate interior angles are congruent if the two parallel lines are intersected by the transversal.

When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate angles, vertically opposite angles etc.

The parallel lines in the diagram has two red arrows on it.

The transversal line is the one that cut the other two parallel lines.

The angles formed are 9x + 5 and 10x - 5.

Therefore, if the two parallel lines are intersected by the transversal then alternate interior  angles are congruent.

Hence,

9x + 5 = 10x - 5

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Answer:

50

Step-by-step explanation:

          i^2 = -1

First simplify the radicals. Then use FOIL method

[tex]\sf (3 + \sqrt{-16})(6-\sqrt{-64}) = (3 +\sqrt{i^2*4^2})(6-\sqrt{i^2*8^2})[/tex]

                                     = ( 3 + 4i)(6 -8i)

                                     = 3*6 - 3*8i + 4i*6 - 4i*8i

                                     = 18 - 24i + 24i - 32i^2

                                      = 18 - 24i + 24i - 32*(-1)

                                       = 18 - 24i +24i + 32

                                       = 18 + 32 - 24i + 24i

Combine like terms,

                                       = 50

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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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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 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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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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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:

September2020

13outcomes

In case whereby the factors of 45= 3x3x5  and 75=3x3x5 given the factors, that both 45 and 75 share are 3, 5 , which are two factors

The factors of the two given numbers 45 and 75 can be seen as those whole numbers that when it is been used to divide the numbers 45 and 75 will have no remainders.

For instance , if we divide 45 by 3 then we will have 15 which do no have any remainder, same with when we divide 45 by 5 , it will have no remainder, same thing can be done to 75, we can divide it by 3 as wel as 5 without getting any remainder.

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(66 inches) because i don't know

but my answer is correct

Answer: Slope 0.5298 ± 0.2372

Y-intercept 1.429 ± 1.198

X-intercept -2.697

Step-by-step explanation: I hope that helped

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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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]

[tex] - 2x + 2 = 180 \\ - 2x = 180 - 2 \\ - 2x = 178 \\ \frac{ - 2x}{ - 2} = \frac{178}{ - 2} \\ x = - 89[/tex]

ATTACHED IS THE SOLUTION of X

Answer:

1 5/7

Step-by-step explanation:

12/7 x 5/5 = 60/35 or 1 5/7

Answer:

k = 5

Step-by-step explanation:

f(x) = x + 4

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

So k = 5

The equation of the line in the point-slope form is y + 3 = 1/2(x - 5)

From the question, we are to determine the equation of the given line in point-slope form

First, we will determine the slope of the line

Using the points (1, -5) and (3, -4)

From the formula,

Slope = (y₂ - y₁) / (x₂ - x₁)

Slope = (-4 - -5) / (3 - 1)

Slope = ( -4 + 5) / 2

Slope = 1/2

Now,

For the point-slope form of the line

Using the point-slope form of the equation of a straight line,

y - y₁ = m(x - x₁)

Where m is the slope

The given point is (5, -3)

Thus,

The point-slope form of the line is  

y - -3 = 1/2(x - 5)

y + 3 = 1/2(x - 5)

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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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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: 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

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

Answer:

INVALID or 16

Step-by-step explanation:

The answer would be invalid due to the double addition signs.

However, if you meant to put a 2 in between those signs, it would be:

4+2+2+2+2+2+2

6+2+2+2+2+2

8+2+2+2+2

10+2+2+2

12+2+2

14+2

16

Answer:

Step-by-step explanation:

14

The equation of the polynomial is P(x) = (x - 4)(x - 6)(x + 3)²

Polynomial expressions are mathematical statements that are represented by variables, coefficients and operators

The given parameters are

The sum of multiplicities of the polynomial equation must be equal to the degree.

This means that the multiplicity of the zeros 4 and 6 is 1

The equation of the polynomial is then calculated as

P(x) = (x - zero)^ multiplicity

So, we have

P(x) = (x - (-3))² * (x - 4) * (x - 6)

This gives

P(x) = (x - 4)(x - 6)(x + 3)²

Hence, the equation is P(x) = (x - 4)(x - 6)(x + 3)²

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Answer:

x-4<16

x<16+4

x<20

S:[20] TRUE

Incomplete question.No requirement of question

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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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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