Simplify the expression completely:

8x + 4 - 6y - 3x + y =

The angles are equal because the angles are corresponding and the value of x is 7.

When two lines or rays converge at the same point, the measurement between them is called a "Angle."

It is given that:

Two parallel lines are intersected by a transversal.

The angles shown in the picture is called corresponding angles.

The angles are equal to each other

75 = 11x - 2

11x = 77

x = 7

Thus, the angles are equal because the angles are corresponding and the value of x is 7.

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The equation relating N to M be N = 3M and

Kevin needs to read 57 Novels in 19 months.

Given, Kevin needs to read 3 novels each month.

Let N be the number of novels Kevin needs to read in M months.

According to question,

1 month = 3 novels

M months = 3M novels

Now, as he needs to read a total of N novels.

So, N = 3M.

Also, the number of novels he needs to read in 19 months be,

N = 3×19

N = 57 novels.

Hence, the equation relating N to M be N = 3M and the number of novels Kevin needs to read in 19 months be 57.

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Answer:

Assuming this is a triangle, angles would equal up to 180 degrees

Step-by-step explanation:

105 + 25 = 135

180 - 135 = a, a = 45 degrees

The 1/2, 5/12, and 1/2 hour duration it takes Tiffany, Gary, and Noland to walk round the park provides the following;

1) The time in minutes it takes Tiffany to walk round the park is 30 minutes

Gary takes 25 minutes and Noland takes 20 minutes to walk round the park

2) Tiffany will go round 12 times, Gary will go round 12 times and Noland will go round the park 15 times before all three will meet again.

3) The solution to question 2 is arrived at by dividing the least common multiple of 30, 25, and 20, which is 300 by 30, 25, and 20 respectively

The least common multiple also known as the L.C.M. is the least number two or more numbers have as their multiples.

The time it takes Tiffany to walk around the track = 1/2 hour

The time it takes Gary to walk round the park = 5/12 hour

The time it takes Noland to walk round the park  = 1/3 hour

1) The duration in minutes it takes each person to walk round the park are found using the conversion factor for minutes and hours as follows;

60 minutes = 1 hour

Therefore;

1/2 hour = 30 minutes

It takes Tiffany 30 minutes to walk around the track

5/12 hour = 25 minutes

It takes Gary 25 minutes to walk around the track

1/3 hours = 20 minutes

It takes Noland 20 minutes to walk round the park

2) The number of times each person will go round the track before all three meet again is given by the least common multiple of 30, 25, and 20, which is 300

Therefore;

The number of times Tiffany would walk round the park before all three meet again is 300 ÷ 30 = 10

The number of times Gary would walk round the park = 300 ÷ 25 = 12

The number of times Noland walks round the park = 300 ÷ 20 = 15

When all three meet again, Tiffany will halve walked 10 times, Gary would have walked 12 times and Noland would have walked 15 times round the park.

3) The solution for question 2 was arrived at by looking for the lowest common multiple of the durations it takes each of the three persons to walk round the park. The least common multiple provides the time at which all three will have made complete cycles simultaneously.

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Value of x is 2 and y is 0 of the equations 2x + y = 4 and x - y = 2.

A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is used.

Given,

Equation:

2x + y = 4

x - y = 2

From equation 2,

x = 2 + y

Equating in equation 1,

Using substitution method,

2(2+ y) + y = 4

4 + 2y + y = 4

3y = 0

y = 0

x = 2 + y

x = 2+ 0

x = 2

Value of x is 2 and y is 0 of the equations 2x + y = 4 and x - y = 2.

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The next equation will be 6²-4²=2×10.

Here, we have given three equations and we have to find out the next equation.

The first three equations are like this

1. 3²-1²=2×4

2. 4²-2²=2×6

3. 5²-3²=2×8

Now,

As from the equation

On the L.H.S. we can see that every time it is creating a sequence

Like,  every time it is subtracting square value of the one’s from the another number’s square

Which is the value we got from adding 2 in first value.

And on the R.H.S.

We can say that every time 2 multiplies with the next even number than the previous one

So,

The last equation was 5²-3²=2×8

Therefore,

The next equation will be

6²-4²=2×10

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Answer:

x = 60, -70

Step-by-step explanation:

Let's move the constant (-130) to the right by adding it to both sides.

[tex]\sqrt{x} 4(x+5)^{2} =130[/tex]

Now, we can rewrite the equation as (since the square root and square cancel):
2 × | x + 5 | = 130

To get rid of the 2 multiplication, we can divide both sides by 2:

| x + 5 | = 65

This leaves us with 2 equations:

x + 5 = 65

x + 5 = -65

Simplify.

x1 = 60

x2 = -65

Answer: x=2±√3

Step-by-step explanation:

[tex]\displaystyle\\x^2-4x+1=0\\\\ax^2+bx+c=0\\\\a=1\ \ \ \ \ b=-4\ \ \ \ \ c=1\\\\D=b^2-4ac\\\\D=(-4)^2-4(1)(1)\\\\D=16-4\\\\D=12\\\\\sqrt{D} =\sqrt{12}\\\\\sqrt{D}=\sqrt{3(4)} \\\\\sqrt{D}=2\sqrt{3}\\\\ Hence,\\\\x=\frac{-bб\sqrt{D} }{2c} \\\\x=\frac{-(-4)б2\sqrt{3} }{2(1)} \\\\x=\frac{4б2\sqrt{3} }{2} \\\\x=\frac{2(2б\sqrt{3}) }{2} \\\\x=2б\sqrt{3}[/tex]

The value of solution of equation is,

⇒ x = (2 ± √3)

An algebraic equation with the second degree of the variable is called an Quadratic equation.

Given that;

Quadratic equation is,

⇒ x² - 4x + 1 = 0

Now, We can simplify as;

⇒ x² - 4x + 1 = 0

⇒ x = - (-4) ± √(-4)² - 4×1×1 / 2

⇒ x = (4 ± √16 - 4) / 2

⇒ x = (4 ± √12) / 2

⇒ x = (4 ± 2√3) / 2

⇒ x = (2 ± √3)

Thus, The value of solution of equation is,

⇒ x = (2 ± √3)

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Answer: $7.95

Step-by-step explanation:

95.40/12

= $7.95

Answer:

unit rate per book

= $95.40 ÷ 12 books

= $7.95 per book

The  z-score to percentile of 1 = -2.326

In this question, we need to find the z-score to percentile of 1

We know that a Z-scores is a normalized score that used to compare values relative to their population. z-score represents a specific location in the normal distribution, so that there is a certain area that is to the left of that z-score. The percentile associated to a z-score is nothing but the area to the left of that z-score.

the  z-score to percentile of 1 = -2.326

Therefore, the  z-score to percentile of 1 = -2.326

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The equation of the line that passes though the point (-6,-7) and is perpendicular to the line 6x + 5y = 30 is y = (5/6)x -2 .

In the question ,

it is given that

the required line is perpendicular to the line 6x + 5y = 30 ,

rewriting the line we get

5y = -6x + 30

y = (-6/5)x + 6

the slope of perpendicular is -6/5 ,

the slope of the required line will be 5/6 .

The equation of the line passing through (-6,-7) with slope 5/6 is written as

(y - (-7)) = (5/6)(x - (-6))

y + 7 = (5/6)(x + 6)

y + 7 = (5/6)x + 5

y = (5/6)x + 5 -7

y = (5/6)x -2

Therefore  , the equation of the line is y = (5/6)x -2 .

The given question is incomplete , the complete question is

What is an equation of the line that passes through the point (−6,−7) and is perpendicular to the line 6x+5y=30 ?

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Answer:

$129.27 Sale price Including tax

Step-by-step explanation:

Original Price - Discount = Sale Price

130 - 130(0.12) = 114.40

114.40 + 114.40(0.13) = 129.27 Include sale tax

Answer:

The x-intercept is -3

Step-by-step explanation:

Answer:

x = -3, y = 3  ----> (-3,0) and  (0, 3)

Step-by-step explanation:

Required: Find the X-intercept.

1) Let y = 0 to find the x-intercept (s):

0 = x + 3

2) Subtract 3 from both sides.

-3 = x

3) Switch sides.

x = -3

Just to find the y-intercept.

1) Let x = 0 to find the y-intercept (s):

y = 0 + 3

2) Simplify:
y = 3

The proportionality is a relation between two quantities. The equation for the given cases can be written as 3g = 5m,  5m = 3g, 5g = 3m and g = 8 m.

When two quantities have some dependence in their values they can be said to be proportional to each other.

It can be of two types such as direct and indirect.

The direct proportionality means the values of both the quantities are increasing or decreasing at the same time while the indirect proportionality implies that the value of one quantity is increasing while the other is decreasing.

Given that,

The number of gallons of water = g,

The number of minutes = m,

And, the equation for the given condition as,

g = 3 / 5 m

The equation for each minute the washing machine runs, it uses five thirds gallons of water is given as,

g = 5 / 3 m

=> 3g = 5m

The equation for each minute the washing machine runs, it uses three fifths of a gallon of water is given as,

m = 3 / 5 g

=> 5m = 3g

The equation for each gallon of water the washing machine uses, it runs for three fifths of a minute is given as,

g = 3 / 5 m

=> 5g = 3m

The equation for each gallon of water the washing machine uses, it runs for 8 minutes is given as,

g = 8 m

Hence, the equation for the given conditions can be written as,

3g = 5m,  5m = 3g, 5g = 3m and g = 8 m.

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Answer:

Step-by-step explanation:

12x6 = 72

So 40x2

72 pies she needs 80

So awnser is no she needs 2 more boxes

The adjustment factor (T) which adjusts the exponential smoothing forecast , does this adjustment for a. Trend.

A big part of the Adjusted exponential smoothing forecasting method is the use of an adjustment factor which has the purpose of adjusting the smoothing forecast for a trend.

If this trend is found, then there is a need to smoothen it out of the data so that the model is more trustworthy. It is important that this trend is removed to ensure that the forecast does not have a time bias.

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The Solutions for given inequalities are -2, 5, and -4

Inequalities are algebraic expressions in which both sides are not equal to each other. In inequality, we compare two values with signs like less than (<) (or less than or equal to), greater than (>) (or greater than or equal to), or not equal to sign(≠), etc.

Here we have three inequalities

m -1 < -3, - 4y < - 20, and 5 + b > 1  

We can solve each equation and can give a graph as given below

m -1 < -3  

Add 1 on both sides

=> m - 1 + 1 < -3 + 1

=> m < -2

- 4y < - 20  

Divide both sides with - 4 on both sides

=> - 4y/4 < - 20/4

=>  -y  < - 5

Multiply with -1 on both sides

=> -1(-y) < -5(-1)

=>   y < 5

5 + b > 1  

Subtract - 5 on both sides

=> 5 + b - 5 > 1 - 5

=> b > -4

Therefore,

The Solutions for given inequalities are -2, 5, and -4

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Sale price of the house should be $141509

Amount = $150000

Commission% = 6 %

By formula

Selling price x commission rate = commission paid

SP × 6% = commission paid

(6·SP)/100 =  commission paid …. (1)

Again by formula

Selling price – commission paid = net amount to seller

SP - (6·SP)/100 = 150000   (from equation 1)

SP ( 1 - 0.06) = 150000

SP = 141509.43 ≈ 141509

$141509 should be the sale price of the house.

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Hannah travel for 40 minutes when Hannah travels 5 times as many minutes to work as Raoul does. Together, they travel for 48 minutes.

In mathematics, an equation is a relationship between two expressions that is expressed as an equality on each side of the equal to sign. An equation would be 3y = 16, for instance.

Given,

Let Raoul travel in minutes be x

So, Hannah travel in minutes will be 5x

Together, they travel for 48 minutes.

Equation:

x + 5x = 48

6x = 48

x = 8

Hannah travel in minutes will be 5x.

Total travel by Hannah:

5(8)

40

Hannah travel for 40 minutes when Hannah travels 5 times as many minutes to work as Raoul does. Together, they travel for 48 minutes.

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By solving a system of equations, we can see tha the value of b is 3.81

We know that we have a exponential function of the form:

f(x)=  a*(b)^x

And we know that:

f(5) = 20 and f(9) = 211

Then we can write a system of equations:

20 = a*(b)^5

211 = a*(b)^9

If we take the quotient between the second equation and the first one, we get:

211/20 = (a*(b)^9)/(a*(b)^5)

211/20 = b^(9 - 5)

211 = b^4

(211)^(1/4) = b

3,81 = b

The value of b is 3.81

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Answer:

Step-by-step explanation:

The margin of error is obtained by multiplying the standard error by t*.

The margin of error can be calculated in two ways, depending on whether you have population parameters or sample statistics:

Margin of error (parameter) = critical value x population standard deviation Margin of error (statistic) = Critical value x Sample standard error

A margin of error is a statistical metric that accounts for the difference between actual and projected survey results in a random sample.

In layman's terms, the margin of error measures the degree of unpredictability in data and research results. The margin of error formula is calculated by multiplying a critical factor. The result is then divided by the square root of the sample's number of observations.

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Kayla's expected value for a 2- point shot is 1 point.

What is expected value?

The expected value, also known as expectation, expectancy, arithmetical expectation, mean, average, first or moment, is a generalization of the weighted average in the field of probability theory. Informally, the estimation is the arithmetic mean of a significant number of values of a random variable that were independently chosen. A weighted average of all potential outcomes constitutes the expected value of the a random variable with such a finite number of outcomes. When there is a continuum of potential outcomes, integration defines the expectation. The expectation is provided by Lebesgue integration in the measure theory-based axiomatic foundation for probability.

Sol- The expected value is calcuated using the formula:

EV= x.P(x)

where x is the weight/value of the event, and P(x) is the probability of the event occurring.

For a 2-point shot, we have:

X=2

P(x) = 50/100 = 0.5

There for the expected value will be -

EV = 2×0.5 = 1

Thus,

The expected value will be 1 point.

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The complete ratio is24:8=3:1.

What is ratio?

By comparing two amounts of the same units, the ratio can be used to calculate how much of one item is included in the other. There are two different categories for ratios. The first is a part to part ratio, whereas the second is a part to whole ratio. The relationship between two separate entities or organisations is shown by the part-to-part ratio. For instance, a class has a 12:15 boy-to-girl ratio, whereas the part-to-whole ratio describes how one group compares to another. For instance, five people enjoy reading books out of every ten persons. Since the ratio of the component to the total is 5:10, 5 out of every 10 persons enjoy reading.

Here the given ratio 24:8=3:?

Let us take missing part as x then,

=> 24:8=3:x

=>24/8=3/x

=>x = 3*8/24

=> x=1

Hence the complete ratio is 24:8=3:1

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The equation of ellipse in standard form is:

[(2x + 18)² /8²] + [(y + 5)² /8²] = 1

The equation of the ellipse in general conic form is,

4x² + y² + 72x+10y + 285 = 0

comparing given equation with Ax^2+Bxy+Cy^2+Dx+Ey+F=0 we get,

A = 4, B = 0, C = 1, D = 72, E = 10, F = 285

Consider given equation of conic,

4x² + y² + 72x+10y + 285 = 0

4x² +72x + y² + 10y = - 285

4x² +72x + 324 + y² + 10y = - 285 + 324

(2x + 18)² + y² + 10y + 25 = - 285 + 324 + 25

(2x + 18)² + (y + 5)² = 64

(2x + 18)² + (y + 5)² = 8²

(2x + 18)² /8² + (y + 5)² /8² = 1

Therefore, the equation of ellipse in standard form is:

[(2x + 18)² /8²] + [(y + 5)² /8²] = 1

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A line that represent the "rise" and the "run" of the line is shown in the image attached below. Also, a slope of this line in simplest form is equal to 0.25.

Mathematically, the slope of a line is also referred to as pitch or gradient and can be calculated by using this formula:

Slope, m = V/H

Where:

From the graph of this line, we would choose the following data points to represent both the rise and run:

Rise (x, y) = (-5, 0)

Run (x, y) = (7, 3)

Substituting the selected data points into the slope formula, we have;

Slope (pitch), m = (3 - 0)/(7 - (-5))

Slope (pitch), m = (3 - 0)/(7 + 5)

Slope (pitch), m = 3/12

Slope (pitch), m = 0.25

At point (-5, 0), the equation of this line would be calculated by using the point-slope form:

y - y₁ = m(x - x₁)

Where:

Substituting the parameters into the formula, we have;

y - 0 = 0.25(x - (-5))

y - 0 = 0.25(x + 5)

y = 0.25x + 1.25

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Adjacency matrices have to be symmetric. This is true.

An adjacency matrix is a square matrix used to represent a finite graph in graph theory and computer science. The matrix's elements indicate whether or not two vertices in the graph are adjacent. The adjacency matrix of a finite simple graph is an a-matrix with zeros on its diagonal.

An adjacency matrix is a method of representing a graph as a boolean (0 or 1) matrix. Any graph's adjacency matrix is symmetric, for the obvious reason that there is an edge between Pi and Pj if and only if Pj and Pi have an edge (the same one).

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The amount it would cost Rachel to shelve her book collection is $51.80.

The first step is to determine the total width of the 79 books in the collection.

Total width = width of one book x total number of books

Total width = 1.5 x 79

Total width = 118.50 inches

The second step is to calculate the number of shelves that would be needed for the book collection.

Number of shelves that would be needed = total width of the collection / width of one shelf

Number of shelves that would be needed = 118.50 / 34.50

Number of shelves that would be needed = 3.4 ≈ 4

Total cost to shelve the book collection = cost of one shelf x total number of shelves needed

Total cost to shelve the book collection = 4 x $12.95 = $51.80

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Answer: 1: Congruent angles

2: Corresponding Angles

3: 7

Step-by-step explanation:

I'm not entirely sure if I got all of these correct due to the fact I'm not the best when it comes to math, but when I searched the word bank options and looked at the images, I made sure they looks the most similar.

Has 5 1/2 cups or 11/2

Needs 1 3/4 or 7/4

Divide how much she has by how much she needs

(11/2) / (7/4)

Is also the same as

(11/2) * (4/7)

Which equals

= 44/14

= 22/7

or 3 1/7