The middle school has 24 students less than 3 times the number of students at one of
the elementary schools.

The two solutions of the system of equations are (4, -1) and (-1, 4).

Here we want to solve the system of equations below:

x + y = 3

x^2 + y^2 = 17

We can isolate x on the first equation to get:

x = 3 - y

And replace that in the other equation to get:

(3 - y)^2 + y^2 = 17

9 - 6y  + y^2 + y^2 = 17

2y^2 - 6y + 9 - 17 = 0

2y^2 - 6y - 8 = 0

y^2 - 3y -4 = 0

Using the quadratic formula we will get the solutions:

[tex]y = \frac{3 \pm \sqrt{(-3)^2 - 4*1*(-4)} }{2} \\\\y = \frac{3 \pm5 }{2}[/tex]

So the two solutions are:

y = (3 + 5)/2 = 4

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

The correspondent values of x are given by evaluating the line.

x + 4 = 3

x = 3 - 4 = -1

So we have the point (-1, 4)

x - 1 = 3

x = 3 + 1

x = 4

So we have the point (4, -1)

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The coordinates of point A are given as follows:

A(19, 23).

The coordinates of point A are obtained applying the proportions in the context of this problem.

The segment AB is represented as follows:

AB = B - A.

Hence the segment 5AB is given as follows:

5AB = 5(B - A) = 5B - 5A.

Then the x-coordinate of A is obtained as follows:

5(16) - 5A = -15

5A = 95

A = 19.

The y-coordinate of A is obtained as follows:

5(30) - 5A = 35

5A = 115

A = 23.

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Answer:

Good luck

:/ :/ :/ :/ :/ :/ :/

Answer:

(-4)^12

Step-by-step explanation:

Hello!

We can use exponent rules to rewrite the equation.

a^b * a^c = a^(b+c)

The value of the equation can be calculated by (-4)^12.

[tex](-4)^{12}[/tex]Answer:

Step-by-step explanation:

using the rule of exponents

[tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex] , then

[tex](-4)^{5}[/tex] × [tex](-4)^{7}[/tex]

= [tex](-4)^{(5+7)}[/tex]

= [tex](-4)^{12}[/tex]

The correct statement is : The probability of landing on purple is equal to the probability of landing on yellow.

Probability is a measure of the likelihood of an event occurring. The probability formula is defined as the possibility of an event happening is equal to the ratio of the number of favorable outcomes and the total number of outcomes. Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes

Given here: A spinner with four different colors purple, yellow, blue and orange.

Now Section 1&8 = Blue

Section 2&3 = yellow

Section 4,5,6 = blue

Section 7 = orange

Total=8

Thus probability for each section are as follows

P(purple)=2/8

           =1/4

P(yellow)=2/8

              1/4

P(Blue)=3/8

P(orange)=1/8

∴ The probability of landing on purple is equal to the probability of landing on yellow.

Hence, The probabilities of all the individual sections are 1/4,1/4,3/8,1/8 for purple, yellow, blue and orange respectively.

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The required scale factor for the resized image is 110.25:1.

The scale factor is defined as the ratio of the modified change in length to the original length.

Here,
The original photo is 4 inches by 6 inches.
The dimensions of the resized image is 3.5 ft by 5.25 ft,
1 feet = 12 inches

As of the definition mentioned above

Scale factor = 3.5 × 12 × 5.25 × 12 / 4×6
Scale factor = 110.25:1

Thus, the required scale factor for the resized image is 110.25:1.

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Answer:

3x = 42

Step-by-step explanation:

The correct equation is

3x = 42

However, because your formatting has been scrambled, I cannot tell you which choice it is

Compare this equation with your original question and see which is the correct choice

3x = 42 means

each kite = 42/3 = $14
but the question is only asking for the equation not the solution

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Lower class limits are 15, 25, 35, 45, 55, 65, 75, Upper class limits are 24, 34, 44, 54, 64, 74, 84, Class width are 10 (all classes have a width of 10), Class midpoints are 19.5, 29.5, 39.5, 49.5, 59.5, 69.5, 79.5, Class boundaries are [15, 25), [25, 35), [35, 44), [45, 54), [55, 64), [65, 74), [75, 84) and Number of individuals included in the summary is 76.

Here are the details for the given frequency distribution:

Lower class limits are the least number among the pair

Here, Lower class limits are 15, 25, 35, 45, 55, 65, 75 respectively.

Upper class limits are the greater number among the pair

Here, upper limit class are 24, 34, 44, 54, 64, 74, 84 respectively.

Class width is the difference between the Lower class limits and Upper class limits which is 10 (all classes have a width of 10).

Class midpoints is the middle point of the lower class limits and Upper class limits which is 19.5, 29.5, 39.5, 49.5, 59.5, 69.5, 79.5 respectively.

Class boundaries are the extreme points of the classes which are  [15, 25), [25, 35), [35, 44), [45, 54), [55, 64), [65, 74), [75, 84) respectively.

Number of individuals = 27 + 33 + 14 + 4 + 6 + 1 + 1

                                     = 76

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Answer:

Step-by-step explanation:

just look at its last number

Answer:

Multiplying by 10 would be the inverse operation

Answer:

Multiplication

Step-by-step explanation:

The inverse operation of division is multiplication and vice versa.

:)

The value of x is -6.05 so that the expression (2.1 - 0.7) + (x + 3.4) is equivalent to -3.95 + 2.7.

We determine the value of x by solving the expression.

In the question;

(2.1 - 0.7) + (x + 3.4) is equivalent to -3.95 + 2.7

Finding the value of the variable is part of solving an algebraic expression. We must perform certain algebraic operations to determine the value of one of the variables in the linear equations before we can substitute that value to determine the value of another variable.

We can write it as

(2.1 - 0.7) + (x + 3.4) = -3.95 + 2.7

Simplify the expression

1.4 + x + 3.4 = -1.25

x + 4.8 = -1.25

Subtract 4.8 on both side, we get

x = -6.05

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The complete equation is:

Enter the value of x so that the expression

(2.1 - 0.7) + (x + 3.4) is equivalent to -3.95 + 2.7.

The  inequality shown on the graph is x > -2 and x < 5 or -2 < x < 5

An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value e.g. 5 < 6, x ≥ 2, etc.

If you examine the graph, you will notice that there is one circle on -2 and another circle on 5. These give you the range of values. Also, notice that circles are not shaded. Thus, this can be written as:

x > -2 and x < 5 or  -2 < x and x < 5

Which can then be combined as:

-2 < x < 5

Note: The reason we did not use ≤ is because the circles are not shaded.

Thus, the inequality is x > -2 and x < 5 or -2 < x < 5

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0.66 litres will be used if she wants to use equal amounts of the solution in 3 experiments.

In mathematics, division is the process of breaking a number into equal parts and determining how many equal parts can be made. For example, dividing 15 by 3 divides 15 into three equal groups of five.

The symbol '÷' or '/' is used to represent division.

Any positive number with no decimal or fractional part is referred to as a whole number. Because these criteria are met, the numbers 1,2,15,500, and 1546 are all whole numbers.

Children will practise dividing whole numbers as they begin to learn their multiplication tables. This is due to the fact that all of the numbers in the times tables are whole numbers!

They will also learn that division is the inverse operation to multiplication, which simply means that division and multiplication perform opposite functions in mathematics.

We have 2 litres of saline water

and want to divide them in 3 experiment equally, i.e.

2 ÷ 3 = 0.6667

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The length of BC in simplest radical form is 2√19

The Pythagorean theorem states that the square of the hypotenuse side of a right angled triangle is equal to the square of the other sides.

It is represented mathematically as;

a² = b² + c²

Given that the parameters;

From the information given, we have that;

Hypotenuse side, a = 20

Adjacent side = 18

Substitute the values

20² = 18² + b²

Find the squares

400 =324 + b²

collect like terms

b² = 400 - 324

b² = 76

Make 'b' the subject of formula

b = 2√19

Hence, the value is 2√19

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The inventory at the beginning of the day, given that 18 were sold earlier that day, is 70 units

The inventory at the beginning of the day can be found by the formula:

= Closing store inventory for the day + Inventory sold during the day

Closing store inventory for the day = 52 units

Inventory sold earlier that day = 18 units

The inventory at the beginning is therefore:

= 52 + 18

= 70 units

In conclusion, the inventory at the beginning of the day was 70 units.

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The value of side length PS is found as 4 units for the given right angled triangles.

For the stated question:

PQ = 3x - 3

QR = 6x - 9

PS = 5x - 6

As, Q is the mid point of PR.

PQ = QR

3x - 3 =  6x - 9

On solving.

x = 2

Then,

PS = 5*2 - 6

PS = 4

Thus, the value of side length PS is found as 4 units for the given right angled triangles.

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The correct question is attached.

A plate of spring roll is price of $7.5.

What is Linear System?

A linear system is a mathematical representation of a system in systems theory that relies on the application of a linear operator. Compared to nonlinear systems, linear systems often have significantly simpler traits and properties.

Let n, b, and c represent the cost per plate of spring roll, chicken tenders , and pretzel dipper, respectively.

One party spends $23 and purchases two plates of chicken tenders and one plate of pretzel dipper.

i.e. 2b + 1c = 23

     2b + c = 23                                        --------------------- 1

Three plates of  spring roll and a plate of chicken tenders are purchased by another group for $30.75.

That is

          3n + 1b = 30.75

          3n + b = 30.75                                          ---------------------- 2

A third party spends $22.25 and purchases one of each appetizer.

That is

             n + b + c  = 22.25                                    --------------------- 3

On solving;

eqn2 - eqn3

            2n - c = 8.5                                           --------------------- 4

on solving;

eqn 1 + eqn 4

             2b+ 2n = 31.5

             b + n = 15.75                                           --------------------- 5

On solving;

eqn 3 - eqn 5

              c = 6.5

Substituting in eqn 4

           2n - 6.5 = 8.5

              n = 7.5

Substituting in eqn 3

           7.5 + b + 6.5  = 22.25

               b = 8.25

Price of spring roll n = $7.5 .

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Answer: 0.3

Step-by-step explanation: 4+5=9. 3/9 times you will pull out grey socks. 3 Divided by 9 is .3333(forever). which is just .3 I think.

The answer to the above graphing problem is that we can easily infer that the graph will initially begin to decline before quickly increasing.

A graph is a mathematical structure that joins a number of points together to represent a certain function. It establishes a pairwise link between the things. The vertices of a network, also known as its nodes, are the edges that link them (lines).

The graph's objective is to graphically portray numerical data for rapid, easy, and clear comprehension. Consequently, graphs are visual representations of data. Data can also be presented as a table, despite the fact that a graphical depiction is simpler to grasp.

Here,

If she first moves in the direction of the petrol station, the graph will be lowering.

As she fills her tank at the gas station, the graph moves upward.

As she approaches the market, the graph will eventually start to decline.

In light of the information,

We can easily deduce that the graph will start out falling, quickly climb, and then keep falling until we reach our target.

As a result, we can quickly deduce that the graph will rapidly increase after initially dropping as the answer to the given graph problem.

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The points with integer coordinates in this rectangular region will be above 50.

You must use graph paper and draw the rectangle. You must draw the picture in order to solve the problem. It is not easy to visualize the rectangle, the coordinates and count the points inside it all at the same time without a picture to help you. You must draw it.


Once you draw it, the vertices are (5,4), (5,-4), (-5,-4) and (-5,4) in the clockwise directions starting from the upper left corner.

Since we are interested in points that are strictly inside the rectangle -4 < y < 4 and -5 < x < 5;
That is y = -3,-2,-1,0,1,2,3 and x = -4,-3,-2,-1,0,1,2,3,4


The points with integer coordinates that are strictly inside the rectangle are then:



(-4,3)   (-3,3),   (-2,3),   (-1,3),   (0,3),   (1,3),   (2,3),   (3,3),  (4,3)
(-4,2)   (-3,2),   (-2,2),   (-1,2),   (0,2),   (1,2),   (2,2),   (3,2),  (4,2)
(-4,1)   (-3,1),   (-2,1),    (-1,1),  (0,1),   (1,1),    (2,1),  (3,1),  (4,1)
(-4,0)   (-3,0),   (-2,0),    (-1,0)   (0,0),   (1,0),    (2,0),   (3,0),  (4,0)
(-4,-1)  (-3,-1),  (-2,-1),  (-1,-1), (0,-1),  (1,-1),  (2,-1),  (3,-1), (4,-1)
(-4,-2) (-3,-2),   (-2,-2), (-1,-2),  (0,-2),  (1,-2),  (2,-2),  (3,-2), (4,-2)
(-4,-3) (-3,-3),   (-2,-3), (-1,-3),  (0,-3),  (1,-3),   (2,-3), (3,-3), (4,-3)

So, The points with integer coordinates in this rectangular region will be above 50.

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The points with integer coordinates in this rectangular region will be above 50.

You must use graph paper and draw the rectangle. You must draw the picture in order to solve the problem. It is not easy to visualize the rectangle, the coordinates and count the points inside it all at the same time without a picture to help you. You must draw it.

Once you draw it, the vertices are (5,4), (5,-4), (-5,-4) and (-5,4) in the clockwise directions starting from the upper left corner.Since we are interested in points that are strictly inside the rectangle -4 < y < 4 and -5 < x < 5;

That is y = -3,-2,-1,0,1,2,3 and x = -4,-3,-2,-1,0,1,2,3,4

The points with integer coordinates that are strictly inside the rectangle are then:

(-4,3)   (-3,3),   (-2,3),   (-1,3),   (0,3),   (1,3),   (2,3),   (3,3),  (4,3)

(-4,2)   (-3,2),   (-2,2),   (-1,2),   (0,2),   (1,2),   (2,2),   (3,2),  (4,2)

(-4,1)   (-3,1),   (-2,1),    (-1,1),  (0,1),   (1,1),    (2,1),  (3,1),  (4,1)

(-4,0)   (-3,0),   (-2,0),    (-1,0)   (0,0),   (1,0),    (2,0),   (3,0),  (4,0)

(-4,-1)  (-3,-1),  (-2,-1),  (-1,-1), (0,-1),  (1,-1),  (2,-1),  (3,-1), (4,-1)

(-4,-2) (-3,-2),   (-2,-2), (-1,-2),  (0,-2),  (1,-2),  (2,-2),  (3,-2), (4,-2)

(-4,-3) (-3,-3),   (-2,-3), (-1,-3),  (0,-3),  (1,-3),   (2,-3), (3,-3), (4,-3)

So, The points with integer coordinates in this rectangular region will be above 50.

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Answer:

1:2.42

Step-by-step explanation:

145/60 = 2.42

Answer: 1 : 29/12

Step-by-step explanation:

60/60 = 1
145/60 = 29/12 in simplest form
therefore 1 : 29/12

The proper interpretation of the slope coefficient b1 in a linear regression line is that, on average, a 1 unit increase in the explanatory variable causes a b1 increase in the response is true since slope is change in dependent variable.

The slope coefficient, bi, for independent variable Xi (where i can be 1, 2, 3, …, k) can be interpreted as the change in the probability that Y equals 1 resulting from a unit increase in Xi when the remaining independent variables are held constant.

The parameters or unknowns in the line are B1 and Bo. The value of y at x=0, or the y-intercept, is called Bo. B1 is the slope, or how much y shifts as x increases by one unit.

The estimated regression coefficient b1 in the multiple linear regression equation measures the relationship between risk factor X1 and outcome after adjusting for X2 (b2 is the estimated regression coefficient that quantifies the association between the potential confounder and the outcome).

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The system of equation: 3(2x-5)=28 represent the dimensions of the play area.

As per the data given,

We have, the width of a rectangle play area is 5 meters less than the length.

Let us assume that the length of the rectangular field = x

So, the value of the width of the rectangular field will be = (x-5)

As we know,

The Perimeter of the rectangular field can be determined by using formula:

Perimeter = 2l+2b, where, l = length of the rectangle, while b = breadth of the rectangle.

From question,

We have a value of the rectangle as 38 m

So, writing the above in form of the equation,

We can write the above as:

2(length + breadth) = 38

=> 3(x+ (x-5) =38

=> 3(x+x-5) =28

=>3(2x+5)=28

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Answer:

Step-by-step explanation:

0-2-0

1-11-11

2-28-56

3-18-54

4-11-44

5-15-75

6-10-60

7-2-14

8-3-24

total number of tickets won - 100

mean number - 336 divided by 100 = 3.36

The area of each box would be proportional to the salaries of each group. Option C.

The use of models to represent data in mathematics is well known. In the case of the data we have, the salaries of the college graduates and the high school graduates have been shown by the use of squares.

We can see that the sizes of the squares respectively show the magnitudes of the salries of the high school graduate and that of the college graduate. The area of the boxes would be proportional to the salaries.

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Answer: Jayda finishes 39 pages in 1 hour

Step-by-step explanation:

156/4 gives us her rate since we have to find 1 hour, not 4 hours.
This is 39

I hope this way able to help you :D

Answer:

Step-by-step explanation:

the domain, range, and x-intercept of the function g(x) = − 4x + 8 are Domain: −∞ < x < ∞; Range: −∞ < y < ∞; x-intercept (2, 0) that is the first option.

A relationship between a group of inputs and one output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.

Given a function  g(x) = − 4x + 8

The domain of a function means all possible inputs or all the numbers that can be put in place of x to get some output

The range of a function means all possible outputs or all the numbers that are the result of all the inputs or values of y

Intercept is the point on a graph whose one coordinate is zero. There are two types of intercepts - X intercept where the y coordinate is zero and Y-intercept where the value of the x coordinate is zero

The domain of the given function is all real numbers or - infinite < x< infinite

The range of the given function is all real numbers or - infinite < x< infinite

The x-intercept of the given function is where y = 0

so,  0 = -4x + 8

-8 = -4x

x = 2

The x-intercept is (2,0)

Therefore, the domain, range, and x-intercept of the function g(x) = − 4x + 8 are Domain: −∞ < x < ∞; Range: −∞ < y < ∞; x-intercept (2, 0) that is the first option.

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