6-27: On graph to the right, graph each line in the system shown belowWhat is the point of intersection ? Does more one exist? How do you know for sure? y = - x + 2; y = 3x + 6

The inequality  |x+9|<7 can be written as -16<x<-2.

a relationship between two expressions or values that are not equal to each other is called 'inequality.

we have the inequality:|x+9|<7

By Definition of Absolute Value.

-(x+9)<7 and x+9<7

-x-9<7

-x<16

x>-16..(1)

and

x+9<7

x<-2...(2)

-16<x<-2

Hence, the inequality  |x+9|<7 can be written as -16<x<-2.

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A parallelogram is a four-sided shape with two sets of parallel lines and two pairs of congruent sides. It is formed by combining two congruent trapezoids, which results in a quadrilateral with two pairs of opposite sides that are parallel and equal in length. All four angles of the parallelogram are also equal.

1. Draw the two congruent trapezoids.

2. Line up the two trapezoids, making sure that the corresponding sides are parallel and the same length.

3. Connect the two trapezoids with lines to form the parallelogram.

4. Check that the angles of the parallelogram are all equal, and that the two pairs of opposite sides are parallel and the same length.

A parallelogram is a four-sided shape with two sets of parallel lines and two pairs of congruent sides. To make a parallelogram, two congruent trapezoids are combined. This can be done by lining up the two trapezoids, making sure that the corresponding sides are parallel and the same length. Then, the two trapezoids can be connected with lines to form the parallelogram. It is important to check that the angles of the parallelogram are all equal, and that the two pairs of opposite sides are parallel and the same length. If these criteria are met, then the shape is a parallelogram.

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According to the Science and Technology Desk Reference, a US fuel gallon weighs 6.1 pounds. The weight of gasoline may be slightly influenced by the quality of the fuel.

This year, high demand for crude oil and limited supply drove up gas prices. There are other international forces at play even though the Federal Reserve has increased interest rates five times so far in 2022 and plans to do so again soon to push prices down.

|0.1 | 11.8|\s| 1 | 118|\s|10 | 1180|

When you can travel 118 miles on 1 gallon, that is equivalent to a ratio of 1:18.

Just solve for the remaining ratios, 0.1: 11.8; 10: 1180.

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The complete question is

The table shows the distance a small motor scooter can travel using one gallon of gasoline. complete the table to find the number of miles the scooter can travel for other amounts of gasoline.

| Gallons | Miles |

| 0.1 | *Ans* |

| 1 | 118 |

| 10 | *Ans* |

The number of cups of each ingredient Kwame and Olivia could have used is 6 cups and 10 cups respectively.

In mathematics, a combination is a selection of items from a collection, such that the order of selection does not matter. For example, the combination of three fruits from a basket containing apples, oranges, and bananas would be the set {apple, orange, banana}, {apple, banana, orange}, {orange, apple, banana}, {orange, banana, apple}, {banana, apple, orange}, and {banana, orange, apple}. The number of possible combinations is often represented using the combination formula, which is often written as "nCr", where "n" is the total number of items in the collection.

It's not possible to give an exact example of the number of cups of each ingredient each person used, as there are infinitely many ways that Kwame and Olivia could have combined orange juice and mango juice to make 12 and 20 cups respectively.

However, one example of the number of cups of each ingredient each person could have used is:

Kwame: 6 cups orange juice, 6 cups mango juice Olivia: 10 cups orange juice, 10 cups mango juice

This satisfies the constraints that Kwame uses less orange juice than Olivia and his orange-mango juice tastes more like oranges than hers does.

This is an example of the possible combination, but it might not be the only one. Also, it's possible that there are other combinations that could satisfy the given information, but this is one example.

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The fraction that represents the colored part of each shape is i) ½ ii) 8/9 iii) ½ iv) ¼ v) 3/7 vi) ¼ vii) 1 viii) 4/9 ix) ½ x) 1/2.

Fractions refer to the parts of a whole. A fraction is a ratio between specified parts of a figure to all parts of a figure. The numerator indicates the parts of the whole and the denominator indicates the total number of equal parts. In the given shapes, as everything is equally divided, the fraction of shaded region is equal to the number of shaded parts divided by the number of total parts.

i) The number of shaded regions = 2

The total number of regions = 4

Fraction = 2/4 = 1/2

ii) The number of shaded regions = 8

The total number of regions = 9

Fraction = 8/9

iii) The number of shaded regions = 4

The total number of regions = 8

Fraction = 4/8 = ½

iv) The number of shaded regions = 1

The total number of regions = 4

Fraction = 1/4

v) The number of shaded regions = 3

The total number of regions = 7

Fraction = 3/7

vi) The number of shaded regions = 3

The total number of regions = 12

Fraction = 3/12 = 1/4

vii) The number of shaded regions = 10

The total number of regions = 10

Fraction = 10/10 = 1

viii) The number of shaded regions = 4

The total number of regions = 9

Fraction = 4/9

ix) The number of shaded regions = 4

The total number of regions = 8

Fraction = 4/8 = 1/2

x) The number of shaded regions = 1

The total number of regions = 2

Fraction = 1/2

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Therefore , the solution of the given problem of angle comes out to be

x= 48.19° .

An angle is a shape in Euclidean geometry comprised of two rays, known as the sides of the loop, that diverge at the apex of both the angle and the vertex, which is situated in the middle. It is possible for two rays to combine to generate an angle inside the plane they are located in. An angle also comes from the collision of two planes. They are known as dihedral angles. There are many options for arranging two line ray with end points in two dimensions to form an angle.

Here,

Given : A right angle triangle,

Where we have to find the value of x angle

thus,

Using trigonometric ratios:

=> Cos x = 18/27

=> Cos x = 6/9

=> Cos x = 2/3

=> x = Cos⁻¹ (2/3)

=> x = 48.19°

Therefore , the solution of the given problem of angle comes out to be

x= 48.19° .

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There are two solutions to the given equation 3x + 4y = 12.

Finding two solutions for the equation 3x + 4y = 12

Putting the value of x = 0 in equation 3x + 4y = 12

⇒3(0) + 4y = 12

⇒ 4y = 12

⇒y = 3

Thus, (0, 3) is a solution to the equation 3x + 4y = 12

Putting the value of y = 0 in the equation 3x + 4y = 12

Thus,

⇒3x + 4(0) = 12

⇒3x = 12

⇒x = 4

Thus, (4, 0) is a solution to equation 3x + 4y = 12

Therefore, (0, 3) and (4, 0) are two solutions to the equation 3x + 4y = 12.

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Class range of 9 can be calculated, this can be shown through below illustrations :Determining the following marks on a test 15 students took: 45, 68, 82, 79, 67, 55, 75, 55, 85, 89, 90, 78, 45, 66, and 49.

To know the maximum and minimum values in the data set, which are 90 and 45, respectively.

Mention the maximum and minimum values. The difference between the maximum and minimum values in a distribution, also called the range, is considered by max - min = 45.

Mention the number of classes, say n = 9, to measure class width i.e. class width = 45 / 9 = 5.

The class width formula gives back the appropriate class width to distribute this data into 9 classes, that is 5.

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Answer:

Step-by-step explanation:

Class range of 9 can be calculated, this can be shown through below illustrations:Determining the following marks on a test 15 students took: 45, 68, 82, 79, 67, 55, 75, 55, 85, 89, 90, 78, 45, 66, and 49.

To know the maximum and minimum values in the data set, which are 90 and 45, respectively.

Mention the maximum and minimum values. The difference between the maximum and minimum values in a distribution, also called the range, is considered by max - min = 45.

Mention the number of classes, say n = 9, to measure class width i.e. class width = 45 / 9 = 5.

The class width formula gives back the appropriate class width to distribute this data into 9 classes, that is 5.

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So, 25 minutes after Baxter began filling the tank, the volume of water in the tank is 255 gallons.

A linear equation can be used to model the situation where water is flowing into a tank at a constant rate. The equation would be in the form:

V = 55 + 8t

Where V is the volume of water in the tank (in gallons), t is the time (in minutes) that has passed since Baxter began filling the tank, and 55 and 8 are the y-intercept and slope respectively

To find the volume of water in the tank 25 minutes after Baxter began filling it, you would substitute 25 for t in the equation above:

V = 55 + 8(25) = 55 + 200 = 255 gallons

So, 25 minutes after Baxter began filling the tank, the volume of water in the tank is 255 gallons.

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1728 is the cubic of the number 12.

Cube of given number = [tex]12^{3}[/tex] which is equal to 1728.

The cubes are made up of values that are obtained by multiplying integers by themselves three or four times. The cube's original number can be found by raising any natural number to the power of three.

Cubes are the numbers that are produced when an integer is multiplied by itself three times. We can find cubes for any number, whether it be an integer or a fraction. In order for the cube of a whole number (x) to produce a perfect cube, the cube root of x3 must equal x. The procedure of locating cubes is thus the opposite of locating the cube root.

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the area of the triangle RMC will be 116.44 unit²

What is are of triangle?

The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle. There are different types of triangles such as isosceles, right-angled, equilateral etc.

The sum of all angles of triangle = 180

In Triangle RMC, RM = 19. MC = 27. and CMR = 27°.

Area is = A*B*sin(M)/2

= 19*27*sin(27)/2

=116.44856

Hence the area of the triangle RMC will be 116.44 unit²

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Draci sets up a room for a banquet with 6 tables.

An equation can be represented by a linear function. The standard form for the linear equation is: y= mx+b , for example, y=15x+7. Where:

m= the slope.

b= the constant term that represents the y-intercept.

The problem is a literal math question, that you can convert into a linear equation. Where:

x= number of tables

y= number of chairs

From the information of the question, you can write:

y=mx+b, where:

y= total number of chairs= 54

m= number of chairs in each table = 9

b=0 , because you have a constant function since Draci places 9 chairs at each table. Thus:

54=9x

x=54/9

x=6

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Answer:

-5x + 13

Step-by-step explanation:

Difference = subtraction

[tex](-2x+9) - (3x-4)\\-2x - 3x + 9 + 4\\-5x + 13[/tex]

The cost of the desktop is $2083.8 and the cost of the laptop is $1783.8.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Kevin bought a desktop computer and a laptop computer. Before finance charges, the laptop cost $350 less than the desktop. He paid for the computers using two different financing plans. For the desktop, the interest rate was 7% per year, and for the laptop, it was 9.5% per year.

The cost will be calculated as:-

305 = 0.06x + 0.095( x + 300 )

305 = 0.06x + 0.095x + 28.5

276.5 = 0.155x

x = $1783.8

Desktop cost = x + 300

Desktop cost = 1783.8 + 300= $2083.8

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Answer:

x = 2, y = 7

Step-by-step explanation:

y - 3x = 1    |*2

2y - x = 12

2y - 6x = 2

2y - x = 12   | - Ist equation

2y-x-2y+6x = 12-2

5x = 10

x = 2

Insert x to first equation:

y - 3*2 = 1

y = 7

Answer:

y = 40x

Step-by-step explanation:

The point (-1,3) would be located at the point (3,-1) after a 270 degree counterclockwise rotation about the point (1,0).

To rotate a point in a 2D space, we can use the rotation matrix formula:

[x'] = [cos(Ф) -sin(Ф)][x]

[y'] [sin(Ф) cos(Ф)][y]

Where x' and y' are the coordinates of the point after rotation, x and y are the coordinates of the point before rotation, and theta is the angle of rotation in radians.

In this case, the point to be rotated is (-1,3) and the point of rotation is (1,0). The angle of rotation is 270 degrees, which is equivalent to 3/2π radians.

Plugging in the values:

[x'] = [cos(3/2π) -sin(3/2π)][-1]

[y'] [sin(3/2π) cos(3/2π)][3]

[x'] = [0 1][-1]

[y'] [-1 0][3]

x' = 3 and y' = -1

Therefore, the point (-1,3) is located at the point (3,-1) after a 270 degree counterclockwise rotation about the point (1,0).

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La fórmula para multiplicar dos números decimales es la misma que para multiplicar números enteros.

Primero, muestra los números en forma de dígitos y coloca un punto decimal entre los números. Luego, multiplica los dígitos del número de la izquierda a la derecha, como si fueran números enteros. Después, añade los resultados, teniendo en cuenta la regla de los puntos decimales. Por último, contar el número de dígitos que hay después del punto decimal, y coloca el punto decimal en el resultado.

En este caso, se multiplican los números 9.7 y 0.08. Primero, se muestran los números en forma de dígitos: 9.7 y 0.08. Luego, se multiplican los dígitos de la izquierda a la derecha, como si

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Answer:

25% sugar syrup means in a mixture of 100g sugar syrup, sugar should be 25g

so, when sugar is 25g , mixture is 100g

when sugar is 1g, mixture is 100/25 = 4g

when sugar is 15g, mixture is 15*4 =60g

So, amount of water to be added=60-15= 45g

Step-by-step explanation:

Answer:

13

Step-by-step explanation:

Since a = 3,  10 x 3 = 30

5c = 5 x 2 = 10

2c = 2 x 2

Now we have 30 - 3 - 10 - 4

30 - 3 = 27 - 10 = 17 - 4 = 13

13 is our total

Answer:

[tex] \sf \: 10a - 3 - 5c - 2c = 13[/tex]

Step-by-step explanation:

Given expression,

→ 10a - 3 - 5c - 2c

Now we have to use,

→ a = 3

→ c = 2

Let's solve the expression,

→ 10a - 3 - 5c - 2c

→ 10(3) - 3 - 5(2) - 2(2)

→ 30 - 3 - 10 - 4

→ 30 - 3 - 14

→ 30 - 17

→ 13 => final value

Therefore, the answer is 13.

Answer: 49

Step-by-step explanation:

78 subtracted by 29 equals 49

Answer:

Step-by-step explanation:

78-29

49

Jerry scored 49 points

Answer: 12 attendees can attend the corporate team-building event, with a budget of $48.

How to calculate event cost?

step1:

First you have to find the unit rate. So for every 11attendees it costs $44, divide them both by the GCF which is 7. 44÷11=4

11÷11=1

So for every 1 attendee it is $4.

Now to figure out how much it would cost for12attendees, figure out what you have to do to 1 to get 12. Multiply it by 12

And whatever you do to one number you have to do for the other.

Step2:

so  $4*12= $48

So for every 12 attendees it costs $48.

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12 attendees can attend the corporate team-building event, with a budget of $48.

step1:

First you have to find the unit rate. So for every 11attendees it costs $44, divide them both by the GCF which is 7. 44÷11=4

11÷11=1

So for every 1 attendee it is $4.

Now to figure out how much it would cost for12attendees, figure out what you have to do to 1 to get 12. Multiply it by 12

And whatever you do to one number you have to do for the other.

Step2:

so  $4*12= $48

So for every 12 attendees it costs $48.

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Answer:

The expression (√2 – √3) (√2 – √3) simplifies to 2 - 2√6 + 3, which can be further simplified to 3 - 2√6.

The formula for finding the base of an isosceles triangle is Base = 2 x (Area) / (Height)

An isosceles triangle is a particular kind of triangle in which the lengths of the two sides are equal. This indicates that the two base angles' lengths are similar (congruent means that they are of the same measure). The third side is referred to as the base, and its opposite angle is referred to as the vertex angle. The legs are the two sides that are of equal length.

The formula for finding the base of an isosceles triangle is - Base = 2 * (Area) / (Height). Where the Area is the total area of the triangle, and "Height" is the height of the triangle as measured from the base to the apex (or the point opposite the base).

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The zeros of function f(x) = x² -x - 2 are: x = 2 and x = -1

Consider given polynomial function  f(x)=x² -x - 2

As we know the zeros of a function are nothing but the values of the variable of the function that makes the function value equal to 0.

To find the zeros of function f(x), we need to equate f(x) to zero then solve it for x.

⇒ f(x) = 0

⇒ x² -x - 2 = 0

using the Quadratic Formula where

a = 1, b = -1, and c = -2

[tex]\Rightarrow x=\frac{-b\pm \sqrt{b^2 -4ac} }{2a}\\\\\\ \Rightarrow x = \frac{1\pm \sqrt{9} }{2}\\\\\\\Rightarrow x = \frac{1\pm 3 }{2}[/tex]

Thus x = 2 and x = -1 are zeros.              

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The complete question is:

What are the zeros of f(x)=x² -x - 2 ?

Answer: I can provide you with the data in tabular format if you want to create the graph with the provided data.

Airtime (min) | Prepaid costs | Contract costs

0 | 41.67 | 108.42

10 | 54.67 | 108.42

20 | 67.67 | 108.42

30 | 80.67 | 108.42

40 | 93.67 | 108.42

50 | 102.14 | 108.42

60 | 114.64 | 108.42

This table shows the airtime (in minutes) used, and the corresponding costs for both prepaid and contract call plans. The prepaid costs are calculated using the formula: R41.67 + R1.30 x airtime used, whereas the contract costs are fixed at R108.42.

It's worth noting that the costs for the contract call plan is fixed and doesn't change with the airtime used, while for the prepaid plan the costs increase as the airtime increases.

Step-by-step explanation:

Answer:

5 days to make a house for both of them

Answer: 6/5 days

Step-by-step explanation:

If a worker can make a house in 2days, it can make 1/2 of the house in 1 day.

Similarly, the other worker can make 1/3 of the house in 1 day.

So, in 1 day, together, they will make 1/2 + 1/3 = 5/6 of the house.

So, it will take them 6/5 days to complete the house together.

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Note that if Triangle PQR is similar to Triangle XYZ, and  If PQ = n + 2, QR = n - 2, and XY = n²- 4, then the value of YZ, in terms of n is: (n-2)²

Where triangle PQR is similar to triangle XYZ, then;

PQ/QR =XY/YZ

Given

PQ = n + 2,

QR = n - 2 and

XY=n² - 4,

Substitute

n+2/n-2 = n²-4/YZ

n+2/n-2 = (n+2)(n-2)/YZ

1/n-2 = n-2/YZ

Cross multiply

YZ = (n-2)(n-2)

YZ = (n-2)²

Hence the value of YZ in terms of n is (n-2)²

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Answer: She makes around $22 dollars per hour.

Step-by-step explanation:

You can divide her wage by the amount of hours she works.