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Find the range of the relation.

A. {-4, 4}

B. { -4, -2, 0, 2, 4 }

C. { -7, -4, -2, -1, 0, 2, 4, 5 }

D. { -7, -4, -1, 2, 5 }

Answer:

32

Step-by-step explanation:

Step-by-step explanation:

If he doubles the amount of money he has now, he will have enough to buy the game with $8 left over. 2x=56+8 ; 2x=64 ; x=64/2 ; x=32. Skylar has $32 right now.Nov 12, 2020©

The distance between pair of parallel lines with the following equation

y=x+2 y=x-4  is  [tex]3{\sqrt 2 }[/tex]

​

Parallel lines are any two or more lines that lie in the same plane but never cross one another. Both have the same slope and are equally distant from one another. No matter how far we extend a parallel line, it will always remain straight.

The fundamental characteristics listed below make it simple to recognize parallel lines.

The slope of a line which is perpendicular to both the lines will be -1. Check what are the y-intercept of any of the two lines and write the equation of the perpendicular line through it.

The y-intercept of the line y = x − 4 is (0,−4).

So, the equation of a line with slope −1 and a y-intercept of −4 is y = −x −4.

The perpendicular intersects or meets the line y = x - 4 at (0, 4).

Now, to find the point of intersection of the perpendicular & the other line, solve the two equations. Solve the right sides & solve for x.

x + 26 = -x - 6

     2x = -6                                       (combine them like terms)

       x = -3                                       (divide both the side by 2)

Find y:

y = -3 - 4

  = -7

So, the point of intersection is (−3,−7).

Use the Distance Formula to find the distance between the points (-3, -7) and (0,−4).

[tex]{\displaystyle d={\sqrt {\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}}[/tex]

  [tex]={\sqrt {\left(0-(-3\right)^{2}+\left(-4-(-7\right))^{2}}}[/tex]

  [tex]={\sqrt {3^2 +3^2}}[/tex]

  [tex]=3{\sqrt 2 }[/tex]

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The following set of numbers, 15, 36, and 39, can be the measures of the sides of a right triangle.

A triangle is a polygon with three sides and three vertices.

To know if a set of number is a valid measure of the sides of a triangle, it must follow the Triangle Inequality Theorem which states that the sum of any two sides must be greater than the third side, such that a + b > c, a + c > b, and b + c > a.

let a = 15, b = 36, and c = 39

a + b > c     15 + 36 > 39     51 > 39     True

a + c > b     15 + 39 > 36     54 > 36     True

b + c > a     36 + 39 > 15     75 > 15     True

To know what type of triangle based on the length of its side:

1. Take the sum of the squares of the two smaller sides.

15^2 + 36^2 = 1521

2. Compare it to the square of the largest side.

39^2 = 1521

1521 = 1521

If the sum of the squares of the 2 is larger than the square of the 3rd, it is an acute triangle.

if they are equal, it is a right triangle

if they are smaller, then it is an obtuse triangle.

Hence, 15, 36, and 39 can be the measure of the sides of a right triangle.

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The exterior angle (∠ 5) is larger than either remote interior angle (∠ 7 and ∠ 8).

According to the exterior angle inequality theorem, the measure of any exterior angle of a triangle is greater than the measure of either of the opposite interior angles. The adjacent interior angle and the exterior angle are supplementary. A triangle's exterior angles add up to 360º.

A triangle's exterior angle is always greater than its two remote interior angles.

By the Exterior Angle Inequality Theorem, the exterior angle (∠ 5) is larger than either remote interior angle (∠ 7 and ∠ 8).

m ∠ 7 < m ∠ 5 and m ∠ 8 < m ∠ 5 .

Therefore, the correct answer is ∠ 7 and ∠ 8.

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Answer:

5(2.47y−2.03)

Use the distributive property to multiply 5 by 2.47y−2.03.

12.35y−10.15

Step-by-step explanation:

The value of x in the question is 4

The given parameters are

PQT = 60

PQS = 4x + 14

The line bisects PQT

So, we have

PQS = 1/2 * PQT

This gives

4x + 14 = 1/2 * 60

Evaluate

4x + 14 = 30

Evaluate the like terms

4x = 16

Divide by 4

x = 4

Hence, the value of x in the question is 4

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Answer: Small box has the lowest amount when divided, that box has the best value.

Step-by-step explanation:

Given data,

Big box = 500 g

It cost is $8.00

Small box = 300 g

It cost is $ 5.40

First switch the box that's in kilograms into grams.

One kilogram=1000 grams.

Then,    Big box = 500 g = $ 8.00

            Small box = 300 g = $ 5.40

Next divide the amount in each box by the cost of each box.

           Big box = 500/8

           Big box  = 62.5

           Small box = 300/540

           Small box  = 0.5555

Therefore,

So, since small box has the lowest amount when divided, that box has the best value.

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Answer:

A=h(b+c) solve for c

First, multiply h to b and c

A = hb + hc

Then, transfer hb to the other side and change its sign from positive to negative.

A – hb = hc

To get c, Divide both sides by h

(A – hb)/h = hc/h

(A - hb)/h = c  OR c = (A – hb)/h

Example. Let us assume the following. A = 500 ; h= 10;b= 20; c= ?

c = (A – hb)/h

c = (500 – (10*20))/10

c = (500 – 200)/10

c =  300/10

c = 30

To check; use the original equation given.

A = h(b+c)

A = 10(20+30)

A = 200 + 300

A = 500. same as the figure given in the example.

[tex]\displaystyle\\Answer:\ b=\frac{A-hc}{h}[/tex]

Step-by-step explanation:

[tex]\displaystyle\\A=h(b+c)\\A=hb+hc\\A-hc=hb+hc-hc\\A-hc=hb\\Divide\ both\ parts\ of\ the\ equation\ by\ h(h\neq 0):\\\frac{A-hc}{h}=b\\ Hence,\\b=\frac{A-hc}{h}[/tex]

Answer:

Step-by-step explanation:

A sloping line on a speed-time graph represents an acceleration . The sloping line shows that the speed of the object is changing. The object is either speeding up or slowing down. The steeper the slope of the line the greater the acceleration.

By the use of arithmethic, the final temperature in Sudbury is - 1 °C.

In this problem we know that initial temperature and two consecutive changes in time. A temperature rise represents a positive change, whereas a temperature fall represents a negative change, then the final temperature is equal to sum of the initial temperature and its two changes:

T = T' + ΔT₁ + ΔT₂

T = 4 °C + 5 °C - 10 °C

T = 9 °C - 10 °C

T = - 1 °C

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Answer:

The solution below is wrong. The correct solution is [tex]x = \frac{-b (+-)\sqrt{73} }{16}[/tex]

Step-by-step explanation:

Rearrange the numerals :

[tex]9x + 2 = 8x^2 + 6x\\8x^2 + 6x - 9x - 2 = 0\\8x^2 - 3x - 2 = 0\\[/tex]

Use quadratic formula :

Solution 1: (Note: the -b"+"....  is actually "±" as the system has some problem of adding "±" symbol)

[tex]x = \frac{-b+\sqrt{b^2 - 4ac}}{2a} \\x = \frac{-(-3)+\sqrt{(-3)^2 - 4(8)(-2)}}{2(8)} \\x= \frac{3+\sqrt{9 + 64 }}{16} \\\\x= \frac{3+\sqrt{73 }}{16} \\\\[/tex]

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The value of the expression 8 x `1000 is 8000

The expression is given as

8 x `1000

The above expression implies that we multiply 8 by 1000

This can be done directly using a calculator, and it can be solved step by step

The step by step procedure is as follows

Express 1000 as 10 x 100

So, we have

8 x `1000 = 8 x `10 x 100

Evaluate 8 x 10

8 x `1000 = 80 x 100

Evaluate 80 x 100

8 x `1000 = 8000

Hence, the value of the expression 8 x `1000 is 8000

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The coordinate points  of g(x) are (-1, 2), (0, 0), (1, 2).

We know that the points (-1, 1), (0, 0), and (1, 1) belong to f(x) graph, where:

f(x) = x^2

Notice that the inputs in these points are x = -1, x = 0, x = 1.

Function g(x) is:

g(x) = 2x^2

Using the given inputs, we have:

g( -1) = 2*(-1)^2 = 2

g(0) = 2*0^2 = 0

g(1) = 2*(1)^2 = 2

Then the coordinate points  of g(x) are (-1, 2), (0, 0), (1, 2).

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Answer:

[tex]\frac{8\sin 72^{\circ}\sin 34^{\circ}}{\sin 116^{\circ}}[/tex]

Step-by-step explanation:

In triangle ABD,

[tex]\sin 72^{\circ}=\frac{BD}{8} \implies BD=8 \sin72^{\circ} [/tex]

In triangle BCD,

∠CBD=34° (isosceles triangle)

∠DCB=116° (sum of angles in a triangle)

[tex]\frac{BC}{\sin 34^{\circ}}=\frac{8\sin 72^{\circ}}{\sin 116^{\circ}} \\ \\ BC=\frac{8\sin 72^{\circ}\sin 34^{\circ}}{\sin 116^{\circ}}[/tex]

Answer:

4.59 cm to nearest hundredth.

Step-by-step explanation:

Consider triangle ABD.

sin 72 = DB / 8

DB = 8 sin 72

      = 7.608 cm.

Imagine a line from point C perpendicular to DB at point E.

As triangle CDB is isosceles ( DC = BC), this line will cut DB in 2

so, DE = 1/2 * 7.608 = 3.804.

Now consider triangle DCE which is a right-angled triangle at E.

cos 34 = 3.804 / DC

DC = 3.804 / cos 34

      = 4.588 cm

BC = DC = 4.588.

AA=60+1.50x and BB=30+2.50x are the two required situations and  the number miles driven, x,x, that would make the cost of each company the same is 30.

Two expressions with equal sign is called as Equation.

Company A charges an initial fee of $60 for the rental plus $1.50 per mile driven= 60+1.50x

Company B charges an initial fee of $30 for the rental plus $2.50 per mile driven=30+2.50x.

60+1.50x=30+2.50x

60-30=2.50x-1.50x

30=x

Therefore, AA=60+1.50x and BB=30+2.50x are the two required situations and  the number miles driven, x,x, that would make the cost of each company the same is 30.

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The number of days Bilquis can afford to rent while staying within her budget is 2 days.

The question has the following data

amount charged =  $48

Rent per mile = $0.08

The mile to drive = 175 miles.

Amount to spend = 110 dollars

The inequality would be written as

48x + 0.08(175) ≤ 110

we are to solve for the value of x

this would be

48x + 14 ≤ 110

48x ≤ 110 - 14

48x ≤ 96

We have to divide through by 48

x ≤ 96 / 48

x ≤ 2

Hence we can say that the number of days Bilquis can afford to rent while staying within her budget is 2 days.

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Step-by-step explanation:

this is the solution above

If the coordinates are rotated 90 degrees clockwise, the resulting expression will be;

B' = (0, -5)

K' = (-3, 0)

U' = (2, -2)

Y' = (-3, 4)

When a coordinate (x, y) is rotated 90 degrees clockwise around the origin is (-y, x)

Given the coordinates points

B = (5, 0)

K = (0, 3)

U = (2, -2)

Y = (4, 3)

If the coordinates are rotated 90 degrees clockwise, the resulting expression will be;

B' = (0, -5)

K' = (-3, 0)

U' = (2, -2)

Y' = (-3, 4)

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Answer: x=8 ==> A

Step-by-step explanation:

15x-6=114     ==> both angles are congruent angles, so they're equal

15x-6+6=114+6

15x=114+6

15x=120

15x/15=120/15

x=120/15

x=8 ==> A

Answer:

m = 6

Step-by-step explanation:

➟ m² = 36

in order to find the value of m take square root from both side

➟ [tex] \sf \: \sqrt{ {m}^{2} } = \sqrt{36} [/tex]

Calculate the values

➟ m = 6

∴ the value of m is 6

Answer:

x+6/4=13

Step-by-step explanation:

the result is 11.5

   The function y = 6x - x² + 1 already defined is a quadratic function.

 A function is the definition of a mathematical expression or equation that helps us to give a visual representation, through graphs to analyze the behavior of the same, a function is not real when it cuts the vertical axis at a same point of x.

      The given function is given by means of the expression

y=6x -x²+1

y = -x² + 6x + 1 , it is a quadratic function because of its exponent "2".

 Where we can separate each of the terms or parts:

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When both bags weigh over 50 pounds when the passenger approaches the check in counter, the person will pay an extra charge.

It should be noted that one will pay for an excess luggage when the luggage is heavier than the allowance when the person checks in.

It should be noted that every airline has a restriction on how heavy the luggage can be.

Therefore, when both bags weigh over 50 pounds when the passenger approaches the check in counter, the person will pay an extra charge.

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The value of x is 15.

(3 - x/2) - (1 - x/3) = 7 - (x - x/2)

(6 - x/2) - (3 - x/3)  = 7 - (2x - x/2)

(6 - x/2) - (3 - x/3) =14 - 2x +x /2

by solving these equations we get ,

18 - x -6 = 42 - 3x

12 - 42 = - 2x

where, x = 15 .

therefore the value of x is 15.

In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

examples of equation and expression.

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The number of miles that Maria ran is 25.6 mile.

From the information given, she runs for 4 hours at a speed of 6.4 miles per hour.

It should be noted that distance is calculated as the speed multiplied by the time taken.

In this case,the distance will be:

= Speed × Time

= 6.4 × 4

= 25.6 miles

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Answer: 19 ==> 1st option

Step-by-step explanation:

f(x) = 5x + 1

f(-4)=5(-4) + 1

f(-4)=-20 + 1

f(-4)=-19 ==> 1st option

By applying the triangle midpoint theorem to the triangle, the value of x is equal to: D. 12.

In Geometry, two (2) triangles are similar when the ratio of their corresponding sides are equal in magnitude and their corresponding angles are congruent.

In Mathematics, two geometric figures are considered to be congruent only when their corresponding side lengths are congruent and the magnitude of their angles are congruent.

Triangle midpoint theorem states that the line segment which connects the midpoints of two (2) sides of a triangle must be parallel to the third side, and it's congruent to one-half of the third side.

By applying the triangle midpoint theorem to the triangle, we have:

8x = 2(2x + 24)

8x = 4x + 48

8x - 4x = 48

4x = 48

x = 48/4

x = 12.

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The value of f(x)= (x-3).g(x)+8

A division algorithm is an algorithm which, given two integers N and D, computes their quotient and/or remainder, the result of Euclidean division.

dividend= divisor x quotient+ remainder

given that, f(x) has remainder 8 and divided by x-3

as per division algorithm we can say that

dividend= divisor x quotient+ remainder

f(x)= (x-3).g(x)+ 8

if we need to find f(3) then put 3 in the place of x

that gives you f(3) = (3-3).g(x)+ 8

                        f(3)= 8

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The answer to f(x)= (x-3). g(x)+8

An algorithm for dividing two integers, N and D, into their quotient and/or remainder, or the product of Euclidean division, is known as a division algorithm.

Dividend equals Divisor x Quotient plus Remainder.

Given that, f(x) is divided by x-3 and has a remainder of 8.

The division algorithm allows us to state that

Dividend equals Divisor x Quotient plus Remainder.

f(x)= (x-3) (x-3).

g(x)+ 8

If we need to find f(3), we should substitute 3 for x.

giving you f(3) = (3-3).

g(x)+ 8

f(3)= 8

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