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Factor out x from the expression

answer : x×(x-2y)

The solution to the first system of equations is given as follows:

(0, -0.6).

The solution to the second system of equations is given as follows:

(0.64, 1.18).

The first system of equations is given as follows:

Multiplying the first equation by -2, the system is given as follows:

Adding the two equations, the solution for y is given as follows:

15y = -9

y = -9/15

y = -0.6.

Hence the solution for x is of:

7x - 10(-0.6) = 6

7x + 6 = 6

x = 0.

The second system of equations is given as follows:

Multiplying the first equation by 3 and the second by 2, we have that:

Adding them, the solution for y is obtained as follows:

22y = 26

y = 26/22

y = 1.18.

The solution for x is of:

6x + 12(1.18) = 18

x = (18 - 12 x 1.18)/6

x = 0.64.

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The mechanic that would charge less for a 50-hour repair is Mechanic A.

Mathematically, the point-slope form of any straight line can be modeled by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

For the table for Mechanic B, an equation which represent its data points is given by:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - 300 = (600 - 300)/(20 - 10)(x - 10)

y - 300 = 300/10(x - 10)

y = 30x - 300 + 300

y = 30x.

When x = 50 hours, the charges for Mechanic A is given by:

y = 25x + 100

y = 25(50) + 100

y = $1,350

When x = 50 hours, the charges for Mechanic B is given by:

y = 30x

y = 30(50)

y = $1,500

In conclusion, we can logically deduce that Mechanic B charges a higher fee than Mechanic A.

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Answer:

a) linear function

b) quadratic function

Step-by-step explanation:

a) j(n) is a linear function since 5 is added everyday.

b) t(n) would be a quadratic function because the total amount of jumping jacks wouldn't have the same number that is beiung added.

day 1 = 5

day 2 = 15

day 3 = 30

day 4 = 50

day 5 = 75

This is showing that at first 10 jumping jacks are added but then for day 2 15 are added, for day 3 20 are added and so on.

Answer:

The house's value decreased by $46580

The current value of the house is $227420

Step-by-step explanation:

How much did the house's value decrease in dollars?

17% = 0.17

$274,000 x 0.17 = $46580

So, the house's value decreased by $46580

What is the current value of the house?

$274,000 - $46580 = $227420

So, the current value of the house is $227420

Applying the corresponding angles theorem, the values of x and y are:

x = 13

y = 24

The Corresponding Angles Theorem states that if two lines are cut by a transversal and the pairs of corresponding angles are congruent, then the two lines are parallel.

From the diagram given, we have:

63 + (5x - 8) + (7x - 31) = 180 [corresponding angles theorem]

63 + 5x - 8 + 7x - 31 = 180

12x + 24 = 180

12x = 180 - 24

12x = 156

x = 13

5x - 8 + 4y + 27 = 180

Plug in the value of x:

5(13) - 8 + 4y + 27 = 180

65 - 8 + 4y + 27 = 180

84 + 4y = 180

4y = 180 - 84

4y = 96

4y/4 = 96/4

y = 24

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The solution of the given inequalities is given below:

a. x < 5 or x < -3

b. x ≥ 4

The solution of an inequality is the value that will make the inequality true.

The solution of the given inequalities is determined as follows:

a. x² - 2x - 15 < 0

x² - 5x + 3x - 15 < 0

x(x - 5) + 3(x - 5) < 0

x - 5 < 0

x < 5

or

x + 3 < 0

x < -3

b. |3x-2| ≥ 10

3x - 2 ≥ 10

3x ≥ 10 + 2

3x ≥ 12

x ≥ 4

The solutions are shown in the number lines attached.

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(a) The Total Surface Area of a pyramid = (1/2) × Base Perimeter × Slant Height + Base area

(b) The Lateral Surface Area of a pyramid = (1/2) × Base Perimeter × Slant Height

A pyramid's surface area is a measurement of the entire area occupied by all of its faces. Check out the pyramid shown below to view all of its faces as well as its peak, altitude, slant height, and base.

The whole area of a pyramid's faces makes up its surface area. There are two different types of surface areas in a pyramid: the total surface area(TSA) and the lateral surface area (LSA).

(a) The total surface area of the pyramid is measured as:

The Total Surface Area of a pyramid = lateral surface area of pyramid + Base area

The Total Surface Area of a pyramid = (1/2) × Base Perimeter × Slant Height + Base area

(b) The lateral surface area of the pyramid is measured as:

The Lateral Surface Area of a pyramid = The total area of the pyramid's side faces (triangles)

The Lateral Surface Area of a pyramid = (1/2) × Base Perimeter × Slant Height

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The time when h(t) = 169 is 4.13am.

For (a), one possible formula for h(t) is the sinusoidal function, h(t) = Asin(Bt + C) + D, where A is the amplitude (maximum height - minimum height), B is the angular frequency (2 pi/period), C is the phase (starting point), and D is the minimum height. In this case, A = 3, B = 2pi/24, C = 0, and D = 170. Therefore, the formula for h(t) is h(t) = 3sin(2pit/24) + 170.

For (b), we need to solve for t when h(t) = 169. We can rearrange the equation to 3sin(2pit/24) = -1 and solve for t. Using a calculator, we can find that t = 8.21 hours. As 8.21 hours after midnight is 4.13am, the time when h(t) = 169 is 4.13am.

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The value of PR when the Pythagorean formula is used would be = 33.

A kite is a type of quadrilateral that has 2 pairs of equal-length sides and these sides are adjacent to each other.

The value of PR can be determined with the use of the Pythagorean formula = c² = a² +b²

where c = 65

a = 56

b = PR = X

b = c² - a²

b² = 65² - 56 ²

b² = 4225 - 3136

b² = 1089

b= √ 1089

b = 33.

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Complete question:

Quadrilateral QRST is a kite. What is PR?

The cruise ship will be 70 units (could be nautical miles, kilometers or any other unit) away from the iceberg.

What is the slope intercept?

The slope-intercept form of a linear equation is y = mx + b, where x and y are the coordinates of a point on the line, m is the slope of the line (the steepness of the line), and b is the y-intercept (the point where the line crosses the y-axis).

To determine how close the cruise ship will get to the iceberg, we need to find the point of intersection between the ship's path (y = x + 40) and the location of the iceberg (x = 40, y = 10).

Substituting x = 40 into y = x + 40, we get:

y = 40 + 40

y = 80

So the point of intersection is at (40, 80).

We can then use the distance formula to find the distance between the point of intersection and the location of the iceberg:

d = √((40 - 40)^2 + (80 - 10)^2)

d = √((0)^2 + (70)^2)

d = 70

So the cruise ship will be 70 units (could be nautical miles, kilometers or any other unit) away from the iceberg.

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The length of the arc SU is given by 1.63978 units.

The circumference (or) perimeter of a circle = 2πr units. The area of a circle = πr2 square units. Where r is the radius of the circle. The circumference of the circle or the perimeter of the circle is the measurement of the boundary of the circle. Whereas the area of the circle defines the region occupied by the circle.

Given here: The angle ∠STU=94 and ST=17

Thus ST forms the radius of the circle.

Now we know the angle subtended by the arc is given by

SU=2πr×94°/360

  =2×3.14×0.2611

  =1.63978 units

Hence, The length of the arc SU is given by 1.63978 units.

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As per the concept of compounding interest, the amount he deposited on each year is $471.55

Compounding interest in math is the term defined as the interest on a deposit calculated based on both the initial principal and the accumulated interest from previous periods.

Here we know that the final amount is 12,400.00 and the time period is 13 years and interest rate is 6.05%.

Here we have identified that the compounding frequency is monthly basis.

Then the amount is calculated by using the compound interest formula

A = P(1 + r/n)ⁿˣ

Here we have to convert R as a percent to r as a decimal

r = R/100

r = 6.05/100

r = 0.0605 per year,

Now we have to solve the equation for P

P = A / (1 + r/n)ⁿˣ

P = 12,400.00 / (1 + 0.0605/12)⁽¹²ˣ¹³⁾

P = 12,400.00 / (1 + 0.0050416666666667)¹⁵⁶

P = $5,658.58

Here we know that the principal amount for one year for each month the amount is calculated as,

=> 5,658.58/12 = 471.55

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Answer:$742; $38,584

Step-by-step explanation: 14% of $5,300 is $742 (0.14 x 5300). There are 52 weeks in a year so $742 x 52 weeks = $38,584.

The linear model for the price of a home P=2,000t+97,000

if 1980 -> t=0 then, 1986 -> t=6 (six years later).

The two points are (t, price) -> (0,97000) and (6,109000)

we want an equation in the form y=mx+b,

the y-intercept(b) is the y=p value when x =tis 0: so b=

m is the slope: m={{y2-y1}/{x2-x1}}={{t2 - t1}/{P2 - P1}}

given two points

(t, P) = (0, 97k) and (6, 109k)

slope = (97 - 109)/(0 - 6)=2

P - 97 = 2(t - 0) < point-slope form

P = 2t + 97 < in thousands

P = 2,000t + 97,000

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Answer:

$460

Step-by-step explanation:

Therefore the regular price of the sofa is $460

This data will be considered as Qualitative sample.

Qualitative data is the data that is not represented by numbers, On the other hand, the quantitative data is represented by numbers and it is classified as discrete and continuous.

Qualitative sample

In qualitative research, only a sample  of a population is selected for any given study. The study's research objectives and the characteristics of the study population determine which and how many people to select.

Quantitative sample

The quantitative research sampling method is the process of selecting representable units from a large population. Quantitative research refers to the analysis wherein mathematical, statistical, or computational method is used for studying the measurable or quantifiable dataset.

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There are 5 short answer questions on the test.

Algebra is a common thread that runs through practically all of mathematics. It involves the study of variables and the rules for manipulating them in formulas.

let us assume,

x = the number of multiple choice questions worth 3 points each

y = the number of short answer questions worth 8 points each

since the test has total of 25 questions we have

x + y = 25

the algebra test is worth 100 points

3×x + 8×y = 100

by solving the system of equations

x + y = 25

3×x + 8×y = 100

we find

x = 20

y = 5

there are 5 short answer questions on the test.

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Answer:

The answer is

[tex]48[/tex]

Step-by-step explanation:

Greetings!!

N.B

Theorem 1: Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.

Thus,

[tex]50 + 82 + x = 180 \\ 132 + z= 180 \\x = 180 - 13 \\ x = 48[/tex]

Hope it helps!!!

Note that after 15 minutes, Liam is 25 blocks away from his house. This prompt is a distance - time graph problem.

A distance-time graph depicts how far an object has moved in a given amount of time. It is a basic line graph that depicts distance versus time findings. The Y-axis represents distance. The X-axis represents time.

It should be noted that a distance-time graph depicts how the distance and speed of an item vary over time. The movement of three items over time is depicted in this graph. The slope, or steepness, of each line shows the speed of the item. In general, the quicker the item, the steeper the slope.

Note that by the 13th minute, Liam had already covered 25 blocks but remained stationary at that location for 3 minutes.

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Considering the attached image. This transformation can be described by (x' , y') = (x' -y')

Transformation refers to movements objects make especially as described on a coordinate plane

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. the four ways include

Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.

Examining the preimage and the image of the attached picture show that the translation involved is reflection

And the transformation rule for reflection over y axis is

(x, y) → (x, -y)

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Answer:

-1.5 or 1 1/2

Step-by-step explanation:

from the graph you see on Y-axis when Y =2, x=0. so you got a point: (0,2)

then on the right lower quadrant, when x = 2, y = -1, another point (2,-1)

slope = (y2 -y1)/(x2-x1) = [2-(-1)] / (0-2) =-1.5

the way the slope's direction is, you know the slope must be negative.

Answer: Image attached below

Simply draw a dashed line at 6 and shade below the line

Inequalities are relationships between numbers or expressions that show whether a value is greater, less, or equal to another value.

Graph of y = 6

The first step of graphing any inequality is to graph it as though it were an equation. So, first graph the line y = 6. This line is a horizontal line at the y-value 6.

Then, go back to the inequality. The inequality states that y is less than 6. Since there is no "or equal to" sign, the line should be dotted. If there were an "or equal to" sign, then the line should have been solid. This is because the solutions to the inequality do not include 6.

Shading

Whenever you graph an inequality, the portion of the graph that satisfies the inequality should be shaded. In this case, the inequality is looking for all y-values less than 6. So, the portion of the graph under the line should be shaded in.

So the dimensions of the box are:

Length: 20m

Width: 10m

Height: 10m

We can use the information provided in the problem to set up a system of equations. Let H be the height, L be the length, and W be the width.

From the problem, we know:

L = 2H (the length is twice the height)

W = L - 10 (the width is 10 meters less than the length)

2HW + 2LW + 2LH = 10WH (the surface area is 10 times the width times the height)

We can substitute the first and second equations into the third one to obtain:

2H(2H-10) + 2(2H)(2H-10) + 2(2H)(2H) = 10H(2H-10)

Solving this equation we get H = 10m

With this value we can solve for the other dimensions:

L = 2H = 2 * 10 = 20m

W = L - 10 = 20 - 10 = 10m

So the dimensions of the box are:

Length: 20m

Width: 10m

Height: 10m

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So the dimensions of the box are:

Length: 20m

Width: 10m

Height: 10m

We can use the information provided in the problem to set up a system of equations. Let H be the height, L be the length, and W be the width.

From the problem, we know:

L = 2H (the length is twice the height)

W = L - 10 (the width is 10 meters less than the length)

2HW + 2LW + 2LH = 10WH (the surface area is 10 times the width times the height)

We can substitute the first and second equations into the third one to obtain:

2H(2H-10) + 2(2H)(2H-10) + 2(2H)(2H) = 10H(2H-10)

Solving this equation we get H = 10m

With this value we can solve for the other dimensions:

L = 2H = 2 * 10 = 20m

W = L - 10 = 20 - 10 = 10m

So the dimensions of the box are:

Length: 20m

Width: 10m

Height: 10m

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To flush twice the volume of water contained in the system, you would need to flush 18.2 gallons x 2 = 36.4 gallons of water through the system.

To calculate the volume of water contained in the system, you would use the formula for the volume of a cylinder: V = πr^2h, where r is the radius of the pipe (half the diameter), h is the length of the pipe, and π is approximately 3.14.

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A system of equations that could be used to find the number of adults and the number of children in the theatre is:

x + y = 362

y = x + 140

In order to write a system of linear equations to describe this situation, we would assign variables to the number of adults and number of cats respectively, and then translate the word problem into algebraic equation as follows:

Since the total number of adults and children at this theatre is 362, a linear equation which represents this situation is given by;

x + y = 362

Additionally, there are 140 more adults than children;

y = x + 140

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Answer:

-299 ft

Step-by-step explanation:

Start: -184 ft

Climb: + 53 ft

Descent: - 168 ft

-184 ft + 53 ft - 168 ft = -299 ft

Answer: -299 ft

The interval of times that represents the middle 99. 7% of his finishing

times in the 400 meter race = (57, 63)

We know that the empirical rule or 68-95-99.7 rule states that for a normal distribution, 68% of observations falls within the first standard deviation (µ ± σ), 95% within the first two standard deviations (µ ± 2σ), and 99.7% within the first three standard deviations (µ ± 3σ).

Here, mean (μ) = 60 seconds, standard deviation (σ) = 1 second

To  determine the interval of times that represents the middle 99. 7% of his finishing times in the 400 meter race.

the 99.7% are within three standard deviations would be,

μ ± 3σ

= (60 - 3(1), 60 + 3(1))

= (57, 63)

The required interval is:  (57, 63)

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For the given graphs, 3) graph represents a function.

Despite the fact that the offered collection of points does in fact depict a relation (since xs and ys are connected), the set they provided me with has two points with the same x-value: (2, 3) and (2, 3). This relation cannot be a function because x = 2 offers me two possible destinations, or two possible y-values.

The only thing I have to do to determine whether the relation they have given me is a set of points is to look at the points' x-values; if any x appears more than once, the relation is not a function.

As, there exist an image for all the elements of the given graph and there exist unique pre-image for the range.

Domain = [-6, 6]

Range = [-3, 3]

For the second graph, the image for every co-domain is 4. So, it is not a function.

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The All the expressions that are equivalent to "3.5 - (4.7)" are (b) -4.7 + 3.5 and (e) 3.5+ (-4.7)  .

to find the equivalent expressions , we solve the expressions :

the main expression is 3.5 - (4.7) = -1.2 ;

Simplifying the expressions :

(a) 4.7 - (3.5) = 1.2    False

(b) -4.7 + 3.5 = -1.2   True

(c) 3.5 + 4.7 =  8.2  False

(d) 3.5 - (-4.7) = 3.5 + 4.7 = 8.2   False

(e) 3.5 +(-4.7) = 3.5 - 4.7  = -1.2   True

So , the only value of the expressions that matches with the main expressions are (b) -4.7 + 3.5 and (e) 3.5+ (-4.7)  .

The given question is incomplete , the complete question is

Select ALL of the expressions that are equivalent to "3. 5 - (4. 7)"

(Select all that apply. )

(a) 4.7 - (3.5)

(b) -4.7 + 3.5

(c) 3.5 +4.7

(d) 3.5 - (-4.7)

(e) 3.5 + (-4.7)

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