Fill in the table using the function rule y=5x-2

The types of variation and their constants are;

1) Direct variation with constant of variation as -1/4

2) Direct variation with constant of variation as ³/₂

A variation is defined as a relation that exists between a set of values of one variable and then a set of values of other variables.

In variation, if the variables change proportionately that is they either increase together or decrease together, then they are said to vary directly.

1) We are given the equation;

4y = -x

Now, y is the output while x is the input and so we make y the subject to get; y = -¹/₄x

Now, writing the relationship between y and x as a variation, we will have; y ∝ x

For this to be equal, there has to be a constant of proportionality which means; y = kx

Comparing with our equation tells us that;

This is a direct variation with constant of variation as -1/4

2) We are given the equation;

3x = 2y - 7

Rearranging gives;

2y = 3x + 7

y = ³/₂x + 7

Now, the greater the value of x, the greater the value of y and as such this is also a direct variation with the constant of variation being 3/2.

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The maximum weight that could be supported by a beam that is 6 inches wide, 2 inches high, and 24 feet long is 3.33.

G = C×(w×h²/l)

Where,

C = constant

C = G×l/(w²h²)

Weight (w) = 6 in

Height (h) = 2 in

Length (l)= 10 ft

Maximum ton (G) = 8 t

C = 8×10/(6×2²)

C = 80/24

C = 10/3

G = (10/3)×(w×h²/l)

So, Maximum weight

G = (10/3)×(6×2²/24)

G = 10/3 t

G = 3.33 tones

The maximum weight is 3.33 tones.

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When a person from this group is selected at random, the probability that this person has type AB blood is 3/40

Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1. In this case, 0 denotes the impossibility of the event and 1 represents certainty.

It should be noted that in this case, the number of people with AB blood is 15 and there are 200 people. The probability will be:

= Number of AB blood type / Total number of people

= 15 / 200

= 3/40

The probability is 3/40.

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Answer:

£27839

Step-by-step explanation:

O×M=N (original x multiplier = original value)

£28000×0.97%=£27160< 1st year decrease

£27160x1.025=£27839<2nd year increase

The measurements 15, 17, 22 do not form a right triangle.

In this question, we have the measurements 15, 17, 22

We check whether the measurements 15, 17, 22 is Pythagorean triple.

22^2 = 484

15^2 = 225

17^2 = 289

15^ + 17^2 = 225 + 289

                = 514

                ≠ 484

i.e., 15^ + 17^2 ≠ 22^2

This means, these measurements do not form a right triangle.  

Therefore, the measurements 15, 17, 22 do not form a right triangle.

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Answer:

(4)

Step-by-step explanation:

Let's make the smaller number equal to x. Since they are consecutive odd numbers, the larger number is x+2.

Twice the smaller number is 2x. Three times the larger number is 3(x+2). If twice the smaller is subtracted from three times the larger, then the expression should be: 3(x+2) - 2x

Then, since the result of this is four more than the smaller, this expression is x+4.

Finally, we put it all together, so we get: 3(x+2) - 2x = x + 4. Option 4 is our correct answer.

Hence, the option (4) is correct.

What is the equation?

The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

Here given that,

Two numbers are consecutive odd integers. If twice the smaller is subtracted from three times the larger, the result is four more than the smaller.

Let us assume the smaller number is [tex]x[/tex].

The larger number is  [tex](x+2)[/tex].

Two numbers are consecutive odd integers. If twice the smaller is subtracted from three times the larger than it is

[tex]3(x+2)-2x[/tex]

So, the result is four more than the smaller.

i.e., [tex]3(x+2)-2x=x+4[/tex]

Hence, the option (4) is correct.

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Answer:

Step-by-step explanation:

domain: 1,2,3,4

Range: 8,6,4,2

D=-2

[tex]a_{n}=a_{1}+(n-1)-2[/tex] formula

The value of the translated function g(x) will be x²+1.

A function is defined as the expression that set up the relationship between the dependent variable and the independent variable.

Given that the function is f(x) = x². The function g(x) in the form of  a(x–h)²+k will be written as below,

The function is translated to the 1 unit up which means that the value of k will be equal to the positive 1.

The function is,

g(x) = a(x–h)²+k

g(x) = 1(x-0)² + 1

g(x) = x² + 1

Therefore, the value of the translated function g(x) will be x²+1.

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Answer:

y=-1/4x+4

Step-by-step explanation:

The graph starts on 4 so that is your y-intercept

Use slope formula to get the slop (y2-y1 over x2-x1)

Use 2 coordinates for formuls (In your case (0,4) and (4,3))

3-4=-1 4-0=4

slope is -1/4

y= -1/4x+4

The coordinates of F' when reflected in the line y=x is F'(1,-7)

Given:

When point F is reflected in the line y = x, the image is located at F"(-7, 1).

The x-coordinate and y-coordinate are reversed when a point is reflected over the line y = x. The x-coordinate and the y-coordinate switch places and become negated if you reflect over the line y = -x (the signs are changed). The point is on the line y = x. (y, x).

so the point  F"(-7, 1) after reflection changes to:

F'(1,-7)

Hence we get the value of F' as (1,-7).

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In actuality, "absolute value" refers to thinking of all numbers as positive and removing all negative signs from front of them (or zero). Symbol for absolute value. -71<181<|9|<1-10| set of absolute values

Without taking into account direction, absolute value describes how far a number is from zero on the number line. A number's absolute value can never be negative. Look at some illustrations. 5 is the sum of its absolute values. There are 5 units between 5 and 0.

The non-negative value of a real number x, regardless of its sign, is its absolute value (or modulus), | x |. For instance, 5 has an absolute value of 5, and 5 has a value of 5.

The exact distance of an integer or number from zero on a number line is its absolute value. As a result, the absolute value is never negative and is always positive.

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The measures of the remaining three angles of the decagon are 40, 50 and 130 degrees.

A decagon is a polygon with 10 sides. In a regular decagon, the interior angles add up to 1440 degrees, and the exterior angles add up to 360 degrees.

Therefore, seven of the angles of a decagon have measures whose sum is 1220. Of the remaining 3 angles, exactly two are complementary and exactly two are supplementary.

Complementary angles sum up to 90 degrees while supplementary angles sum up to 180 degrees.

Therefore,

1440 - 1220 = 220

Let the angles be a, b and c.

Therefore,

a + b + c  =220

a + b = 90

b + c = 180

Hence,

a = 220 - 180

a = 40°

b = 90 - 40

b = 50°

c = 180 - 50

c = 130°

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Answer:  The correct answer is $15.06 is remaining after 71 minutes

Step-by-step explanation:

What we need to find out:

What we know:

If we convert the minutes (m) and remaining credits (c) to (x,y) data sets, they would look like the following:

  x       y

 41    19.26       (41, 19.26)

 57   17.02       (57, 17.02)

Plugging the x, y values into a linear equation, we get:

y - 19.26 = (17.02 - 19.26) / (57 - 41) * (x-41)

Solve the equation for y by adding 19.26 to both sides:

y − 19.26 + 19.26 = −0.14x + 5.74 + 19.26

y = −0.14x + 25

Resulting standard slope-intercept format:

y = −0.14x + 25

Now plug in 71 for the x value (minutes):

y = (-0.14*71) + 25

y = 15.06

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The quotient of 5 divided by 3/10 is equal to 50/3

When we want to divide by a fraction, we just need to replace that division by the product with the inverse of the fraction.

So, if we want to divide A by the fraction (b/c), then we can write:

A÷(b/c)

That will be equal to A*(c/b), so:

A÷(b/c) =  A*(c/b)

Here we want to divide 5 by 3/10, then we need to solve:

5÷(3/10)

Using the above rule we will get:

5÷(3/10) = 5*(10/3) = 50/3

That is the quotient.

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Answer:

$208

Step-by-step explanation:

$79.50 x 24 = 1908

$1908 + 400 = 2308

$2100/2308 = 9%

Carey will pay a total interest of $1,508 over the course of the installment plan for the computer system.

Interest is a financial concept that represents the cost of borrowing money or the return on invested capital. It is a fee charged for the use of borrowed funds or the compensation received for lending money or investing in assets.

Total number of monthly payments

= 12 months/year x 2 years

= 24 months

and, Monthly payment amount = $79.50

Total amount paid in monthly installments

= Monthly payment amount x Total number of monthly payments

= $79.50 x 24

= $1,908

Next, we can subtract the initial down payment from the total amount paid to find the interest paid:

Total interest paid = Total amount paid - Down payment

= $1,908 - $400

= $1,508

Therefore, Carey will pay a total interest of $1,508 over the course of the installment plan for the computer system.

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Answer:

16

Step-by-step explanation:

(8+2) + (6 − 4) × 3

= 10+6

=16

The value of the side CB in the right angled triangle is found as 4√2 units.

For the given question,

The diagram is given;

AB = 7 units.

AG = 3 units.

GB = 7 - 3 = 4 units.

GC = 4 units.

In right angled triangle GCB, apply Pythagorean theorem.

CB² = GB² + GC²

CB² = 4² + 4²

CB² = 2(4)²

Taking square root both side.

CB = 4√2

Thus, the value of the side CB in the right angled triangle is found as 4√2 units.

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Answer:

1  :  4

Step-by-step explanation:

There are 4 squares and 16 triangles.

That is,

Squares : Triangles

          4  :  16

To write it in its simplest ratio, divide both by 4.

Squares : Triangles

         1  :  4

on dividing 100 by 200 we get answer as 0.5 or we can also write it as 1/2 in fraction.

What is division?

Multiplication is the opposite of division. If 3 groups of 4 add up to 12, then 12 divided into 3 groups of equal size results in 4 in each group.

The fundamental goal of division is to produce equal groups or to ascertain how many individuals are in each category following a fair distribution.

To divide 12 donuts into three similar groups in the aforementioned case, you would need to put four doughnuts in each group. Consequently, 12 divided by 3 will equal 4.

We need to find 100/200,

on solving this division problem we get answer as 1/2 (in fraction) or 0.5 (in decimal).

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The integer in the set S:{−24, 2, 20, 35} that will make the inequality five-sixths m minus five is less than one-half m plus 3 false is 35

Inequalities are created through the connection of two expressions. It should be noted that the expressions in inequality aren't always equal. Inequalities imply that the expressions are not equal. They are denoted by the symbols ≥  <  >   ≤.

In this case, based on the information we will replace m with 35. This will be illustrated thus:

= 5/6(35 - 5) < 1/2(35 + 3)

= 5/6(30) < 1/2(38)

= 25 < 19

In this case, 25 isn't less than 19. Therefore, 35 is the correct integer.

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Answer:

9. 4/5

10. 3/4

11. 1/4

12. 1/8

13. 1/11

14. 1/9

15. 9/10

16. 1/10

Step-by-step explanation:

ur welcome

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:

instead of X, we replace 9.

So we have: f(9)=4*9^2-2*9+4.

Again, f(9)= 4*81-18+4=324-14=310.

An inequality that can be solved to show the number of chairs c Mrs. Smith can buy 8c ≤ 56

In this question we have been given Mrs. Boyer is buying folding chairs that are on sale for $8.

She has $56

We need to find an inequality that can be solved to show the number of chairs c Mrs. Smith can buy.

A price of one chair is $8

So, the price of 'c' number of chairs would be 8c

But she has $56

So, to find the number of chairs she can buy, we need to divide 56 by 8

We can write is as 8c = 56

⇒ c = 7

But she might buy less that 7 chairs.

So, we write above relation in inequality form as,

8c ≤ 56

Therefore, an inequality that can be solved to show the number of chairs c Mrs. Smith can buy 8c ≤ 56

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The equivalent equation to the given equation i.e, x = x² - 20  is   x² - x - 20 = 0

What is a Quadratic equation ?

A second-degree equation of the form ax² + bx + c = 0 is known as a quadratic equation in mathematics. Here, x is the variable, c is the constant term, and a and b are the coefficients. Since x is a second-degree variable, this quadratic equation has two roots, or solutions.

The given expression is,

x = x² - 20

We have to make the equation in quadratic form i.e, ax² + bx + c = 0

so, first take x to the right side

0 = x² - 20 - x

Now swap the equation,

x² - 20 - x = 0

put 'x' term in middle and constant term at last like this,

x² - x - 20 = 0

Hence, The equivalent equation to the given equation i.e, x = x² - 20 is  x² - x - 20 = 0

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Answer:

4 1/6 = 25/6

Why?:

Multiply the denominator with the mixed number 4.

Add the numerator 1 and get 25.

Then, you keep the denominator (Which is 6) on the bottom.

And finally, you get

25/6

Answer:

25/6

Step-by-step explanation:

first start by multiplying 6 and 4, which leads you to 24

then add the 1 from the numerator and you get 25 as your numerator.

for the denominator, leave six as it is so it becomes 25/6

Step-by-step explanation:

r - 535 = 175

r = 175 + 535 = 710

Answer:

take - 535 to the other side (over equal to side)

which makes it +535

r = 175 + 535

r = 710