Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.

There are two mystery numbers. The sum of 6 times the first number and 4 times the second number is -2. The sum of 6 times the first number and 2 times the second number is 8. What are the two numbers?

The graph that beast describes the slope of -2/3 passing through points (-1, 0) is in option c

Information given in the question include

a linear function graph

The data is plotted as a linear function

A linear function consists of functions where the variables has exponents of 1. The graph of linear functions is a straight line graph and the relationship is expressed in the form.

y = mx + c

The slope is represented as m, The slope by definition is the ratio change of the output values to the input values

the slope, m = -2/3

negative slopes slants from top left to bottom right as in a and c

from the graph, option c has points (-1, 0) and (0, -2/3)

m = (-2/3 - 0) / (0 - -1)

m = (-2/3) / (0 + 1)

m = -2/3

This matches with option C

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Step-by-step explanation:

9)=

By the question:-

x + y = 130-i

x - y = 34-ii

Now,

Add i and ii,

x + y + x -y = 164

or, 2x = 164

so, x = 82

Now,

x -y = 34

or, 82 - y = 34

so, y = 48

The numbers are 82 and 48.

10) =

Let adults ticket be x and childs ticket be y.

x + y = 800

x = 800 - y - eqn i

4.5x + 6y = 4500

Substituting x's value from eqn i,

4.5(800-y) + 6y = 4500

or, 3600 - 4.5y + 6y = 4500

or, 1.5y = 900

so, y = 600

Now,

x + y = 800

or, x + 600 = 800

so, x = 200

Hence, 600 adult tickets were sold and 200 child tickets were sold.

11)=

Let cost of one small box be x and one medium box be y.

So,

4x + 2y = 54-eqn i

x + 2y = 33-eqn ii

subtracting eqn i from ii,

x + 2y - 4x - 2y = - 21

or, -3x = - 21

so, x = 7

Now,

x + 2y = 33

or, 2y = 33 - 7

or, y = 26/2

so, y = 13

So, cost of one small box is $7 and medium box is $13.

Answer:

given point is (-3,-2)

The rule for a rotation by 270° about the origin is (x,y)→(y,−x).

So,

(-3,-2)==============(-2,3).

there fore,

(-2,3) is the image point of (-3,-2)after the transformation r(x-axis) and rotation 270°.

The percentage of people over speeding on this road on purpose is 9%

Percent of people speeding on this road noticed the sign = Percentage of people who notice the speed limit at the beginning of the road - Percentage of people who notice the sign and follow the speed limit

= 84% - 75%

= 9%

In conclusion, the percentage of people who intentionally speed on purpose is 9%

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Answer: 16

Step-by-step explanation:

There are 9 numbers from the range with the difference of 4 in the digits

The properties of the numbers are given as

Difference: Largest - Smallest = 4

Range: 10 to 99

The numbers with above properties are as follows

15, 26, 37, 48, 59, 62, 73, 84 and 95

When these numbers are counted, we have

Frequency = 9

This means that there are 9 of such numbers from 10 to 99

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The slope of the line that is parallel to the line -7x-5y=-6 is -7/5

It is possible to determine a line's direction and steepness by looking at its slope. Finding the slope of lines in a coordinate plane can aid in anticipating whether the lines are parallel, perpendicular, or none at all without actually using a compass.

Any two unique places along the line may be used to determine the slope of any line. When two different places on a line are considered, the slope of a line formula compares the vertical change to the horizontal change in each case. We shall comprehend how to discover the slope in this piece, along with some of its uses.

Given, line is -7x-5y=-6

We have to write the given line in slope-intercept form

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

The slope-intercept form is y= mx +c

By using the slope-intercept form,

Slope=(-7/5)

The lines that are parallel to y= (-7/5)x+(6/5) have the same slope of -7/5

Therefore, the slope of the line that is parallel to the line -7x-5y=-6 is -7/5

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Answer:

450

Step-by-step explanation:

You can easily calculate 337.5 is 75 percent of what number by using any regular calculator, simply enter 337.5 × 100 ÷ 75 and you will get your answer which is 450

Answer:

Use AAA congurency rule

Step-by-step explanation:

1 angle=52

2 angle=58

3 angle=78

Answer:  C.  174 + 10x - 6x = 102 + 10x

Each school give 12 correct answers

Step-by-step explanation:

174 + 10x - 6x = 102 + 10x

x =  number of correct answers AND,

x = number of incorrect answers

Solve for x:

174 - 102 = 10x + 6x -10x

72 = 6x

x = 12

Each school give 12 correct answers

If price p(x) =26(4)^{-x/5}, the revenue when 15 units are sold is equal to $6.09.

From the information provided, the amount of revenue with respect to price that's being generated in this scenario can be calculated by using the following function (expression):

R(x) = x × P(x)

Where:

Since the revenue function, we would simply substitute the value of the unit price and evaluate as follows:

Revenue, R(x) = x × 26(4)^{-x/5}

Substituting the given parameters into the formula, we have;

Revenue, R(x) = 15 × 26(4)^{-15/5}

Revenue, R(x) = 15 × 26(4)^{-3} or (15 × 26)/4³

Revenue, R(x) = 15 × 26(0.015625) or 390/64

Revenue, R(x) = 6.09375 ≈ $6.09.

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Complete Question:

The revenue function is given by R(x)=x⋅p(x) dollars where x is the number of units sold and p(x) is the unit price. If p(x)=26(4)^{-x/5}, find the revenue if 15 units are sold. Round to two decimal places.

Answer:

33 degrees

Step-by-step explanation:

The square in the corner of these two vectors signifies that this is a right angle, which will always equal 90 degrees, so if you subtract angle 2's value of 57 degrees, you will be left with angle 1 as 33 degrees.

The volume of the flower box is 7560 cubic inches

The given parameters in the question are:

Length = 5 ft

Upper and lower bases = 18 inches and 10 inches

Height  = 9 inches

The volume of the box can be calculated using the following volume equation

Volume = 0.5 * Height * Length * (Sum of the bases)

Substitute the known values in the above equation So, we have the following equation

Volume = 0.5 * 9 inches * 5 feet * (18 inches + 10 inches)

Convert feet to inches

Volume = 0.5 * 9 inches * 60 inches * (18 inches + 10 inches)

Evaluate

Volume = 7560 cubic inches

Hence, the volume is 7560 cubic inches

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The least number of items that can be produced so that the average cost is no more than $24 is 95.

According to the question,

We have the following information:

The function C(x)=−21x+2025 represents the cost to produce x items.

Cost should be no more than $24.

So, we have the following inequality to find the number of items:

-21x+2025 ≤24

Subtracting 2025 from both sides:

-21x≤24-2025

-21x ≤ -2001

Dividing both sides by -21:

x ≤ 2001/21

x ≤95.28

Hence, the least number of items that can be produced so that the average cost is no more than $24 is 95.

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According to the solving the Angle m = 124

An angle with something like a vertex point at 180 degrees is considered to be a straight angle in geometry. Basically, it produces a straight line with sides that are turned away from the vertex. "Flat angles" is another term for it.

A straight line appears to have a straight angle. Here's an illustration of a straight angle. a straight line that has a half circle in the middle and at the top to symbolize a straight angle.

The sum of all angles in triangle  = 180.

Angle A = 56

Angle B = 68

Angle C =

A + B + C = 180

56 + 68 + C = 180

124 + C = 180

C = 180 - 124

C = 56

if Angle C = 56

so we know the property of straight angle:

= Angle m + 56 = 180

Angle m = 180 - 56

Angle m = 124

According to the solving the Angle m = 124

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A factor is a number that divides another number, leaving no remainder

The formula to find the measure of an interior angle of a hexagon is [(n - 2)×180]/n. Hence, option C is correct.

In geometry, a polygon is any enclosed curve made up of a collection of continuous line segments (sides) without any intersections.

Triangles (three sides), polyhedral (four sides), and pentagons are the three simplest polygons (five sides). Convex polygons are those in which none of the elongated sides overlap the polygon; concave polygons are those in which they do.

Equilateral refers to a polygon with equal angles. Equiangular shapes have equal internal angles on all sides. Regular polygons are any equilateral and equiangular polygons.

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Answer:Answer: SAS

Step-by-step explanation:

⇒ ∠AEC is the angle vertical opposite to ∠BEC

The solution of the system equation is C) There is no solution

What is system equation?

  A set of one or more equations comprising numerous variables is referred to as a system of equations. The variable mappings that satisfy all of the component equations in a system of equations, or the points where the components of this system of equations intersect, are the solutions to that system. A system of equations in algebra is made up of two or more equations that are solved together. the process of eliminating, substituting, and graphing solutions to a system of equations or inequalities in two variables

Here the given equations are ,

=> y+7=3x-------> 1

=> y = 3x-7 ------> 2

and 6x-2y =12------> 3

Now put value of 2 into 3 then,

=> 6x-2(3x-7)=12

=> 6x-6x+14=12

=>14=12

The statement is false for any real number.

Therefore the correct option for the given system equation  is C) There is no solution.

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The simple interest that Oliver needs to pay is $ 90

Simple interest is nothing but interest on a loan at a rate. The formula for Simple interest is given below

Simple interest, I = ptr

where p = principal amount

t = time period in years

r = rate of interest in decimals

Here we have

Oliver borrowed $1,500 to purchase a riding lawn mower  

The rate of interest r = 12%

=> 12/100 = 0.12 (in decimals )

The time period given = 6 months = 0.5 years   [ 6/12 = 0.5 ]  

From the above formula,

The simple interest, I = ptr

=> I = $1,500(0.12) (0.5) = $ 90

Therefore,

The simple interest that Oliver needs to pay is $ 90  

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Answer: y= 3 times 2 to the power x. Second answer

Step-by-step explanation:

if you plug in 0 for x, y= 3x 1= 3

if you plug in 1 for x y= 3 x 2 = 6

Look at the x values and y values

(0,3) and (1, 6) on the graph. It matches answer number 2. Remember, 2 raised to the power 0 = 1 and 3 times 1 = 3. And 2 raised to the power 1 =2 and 3 times 2 = 6.

The first table A shows the relationship between the number of sets of markers bought by the teacher and the total cost of the markers.

From given question, the cost per set of markers = $3

The teacher had a $2-off coupon to use toward the total cost of the markers bought.

It is given that the number of sets of markers bought by the teacher is x, and y is the total cost of the markers.

so, we get a linear equation as:

3x - 2 = y

From table A we can see that the data satisfied the given equation,

3x - 2 = y

when x = 3, y = 3(3) - 2 = $7

when x = 9, y = 3(9) - 2 = $25

when x = 12, y = 3(12) - 2 = $34

when x = 24, y = 3(24) - 2 = $70

Therefore, the first table A shows the relationship between the number of sets of markers bought by the teacher and the total cost of the markers.

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The length of the square for the 2.25 inches King's height will be 0.75. The correct option is A.

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, a chessboard is made using the ratio of square length to the king's height, 1.5 inches to 4.5 inches. If a chessboard is made with a king's height of 2.25 inches.

The square length will be calculated as,

Square length / Kings Height = 1.5 / 4.5

Square length = (King's height x 1.5 ) / 4.5

Square length = ( 1.5 x 2.25 ) / 4.5

Square length = 0.75 inches

Therefore, the length of the square for the 2.25 inches King's height will be 0.75. The correct option is A.

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The factoring is the representation of a polynomial in multiplication term thus the factoring of (1/3)b - 1/3 will be 1/3(b - 1).

An algebraic factor is the multiplication of two algebraic terms.

That term could be in form of summation multiplication or in subtraction.

The root of the quadratic equation formed by the algebraic factor is always real.

As per the given polygon,(1/3)b - 1/3

Take 1/3 as common in the whole polygon,

1/3(b - 1).

Since the terms 1/3 and (b - 1) both are in the multiplication of each other.

Hence "The factoring is the representation of a polynomial in multiplication term thus the factoring of (1/3)b - 1/3 will be 1/3(b - 1)".

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