Do these pairs of values (x and y) represent two quantities that are proportional?

X: 4, 6, 10, 14
Y: 2, 3, 5, 7

Answer:

x=10, y=25

Step-by-step explanation:

First, in a trapezoid, the two angles on the same leg (the legs are the opposite sides that are not parallel) add up to 180 degrees. Therefore, 4y as well as (2y+3x) are supplementary. We can write this out as

4y + (2y+3x) = 180

6y+3x = 180

Next, the angles of a triangle add up to 180 degrees. Therefore, as the angles 2y, 4y, and (5x-20) make up a triangle, they add up to 180 degrees. We can write this as

4y + 2y + (5x-20) = 180

6y + 5x -20  =180

Our two equations are thus

6y + 5x - 20 = 180

6y + 3x = 180

If we subtract 6y from both sides in each equation, we can say

5x - 20 = 180-6y

3x = 180-6y

Therefore, we can write

5x-20 = 180-5y = 3x

5x-20=3x

subtract 3x from both sides to make all x variables on the same side

2x-20 = 0

add 20 to both sides to isolate the x and its coefficient

2x = 20

divide both sides by 2 to isolate x

x = 10

Therefore,

x = 10

6y + 3x = 180

6y + 30 = 180

subtract 30 from both sides to isolate the y and its coefficient

6y = 150

y = 25

Answer:

The first and third polynomials have roots in x = 3 and x = -i. (A, C)

Step-by-step explanation:

The quickest form to determine if [tex]x = 3[/tex] and [tex]x = -i[/tex] are roots consist in evaluating each polynomial and proving that result is zero.

A. [tex]f(x) = x^{3}-3\cdot x^{2}+x-3[/tex]

x = 3

[tex]f(3) = 3^{3}-3\cdot (3)^{2}+3-3[/tex]

[tex]f(3) = 27-27+3-3[/tex]

[tex]f(3) = 0[/tex]

x = -i

[tex]f(-i) = (-i)^{3}-3\cdot (-i)^{2}-i-3[/tex]

[tex]f(-i) = i + 3-i-3[/tex]

[tex]f(-i) = 0[/tex]

B. [tex]f(x) = x^{5}+9\cdot x^{4}+28\cdot x^{3} + 36\cdot x^{2}+27\cdot x +27[/tex]

x = 3

[tex]f(3) = 3^{5}+9\cdot (3)^{4}+28\cdot (3)^{3}+36\cdot (3)^{2}+27\cdot (3)+27[/tex]

[tex]f(3) = 2109[/tex]

x = -i

[tex]f(-i) = (-i)^{5}+9\cdot (-i)^{4}+28\cdot (-i)^{3}+36\cdot (-i)^{2}+27\cdot (-i)+27[/tex]

[tex]f(-i) = -i+9 -28\cdot i +36-27\cdot i +27[/tex]

[tex]f(-i) = -56\cdot i +64[/tex]

[tex]f(-i) = 64 -56\cdot i[/tex]

C. [tex]f(x) = x^{5}-9\cdot x^{4}+28\cdot x^{3} - 36\cdot x^{2}+27\cdot x -27[/tex]

x = 3

[tex]f(3) = (3)^{5}-9\cdot (3)^{4}+28\cdot (3)^{3}-36\cdot (3)^{2}+27\cdot (3)-27[/tex]

[tex]f(3) = 0[/tex]

x = -i

[tex]f(-i) = (-i)^{5}-9\cdot (-i)^{4}+28\cdot (-i)^{3}-36\cdot (-i)^{2}+27\cdot (-i)-27[/tex]

[tex]f(-i) = -i - 9+28\cdot i+36-27\cdot i-27[/tex]

[tex]f(-i) = 0[/tex]

D. [tex]f(x) = x^{3}+3\cdot x^{2}+x+3[/tex]

x = 3

[tex]f(3) = (3)^{3}+3\cdot (3)^{2}+(3)+3[/tex]

[tex]f(3) = 60[/tex]

x = -i

[tex]f(-i) = (-i)^{3}+3\cdot (-i)^{2}+(-i)+3[/tex]

[tex]f(-i) = -i+3-i+3[/tex]

[tex]f(-i) = 6-i\,2[/tex]

The first and third polynomials have roots in x = 3 and x = -i. (A, C)

1: 8 faces and 9 with the base 9 vertices and 16 edges

2: 3 faces and 5 with the bases 6 vertices and 9 edges

3: 3 faces and 4 with the base 4 vertices and 6 edges

1: 8 faces and 9 with the base 9 vertices and 16 edges

2: 3 faces and 5 with the bases 6 vertices and 9 edges

3: 3 faces and 4 with the base 4 vertices and 6 edges

Answer:

see explanation

Step-by-step explanation:

The area (A) of a rectangle is calculated as

A = length × breadth

   = (2 + [tex]\sqrt{2}[/tex] )(4-2[tex]\sqrt{2}[/tex] ) ← expand using FOIL

   = 8 - 4[tex]\sqrt{2}[/tex] + 4[tex]\sqrt{2}[/tex] - 4 ← collect like terms

   = 4 units²

--------------------------------------------------------

The opposite sides of a rectangle are congruent , so

perimeter = 2(4 - 2 [tex]\sqrt{2}[/tex]) + 2(2 + [tex]\sqrt{2}[/tex] ) ← distribute parenthesis

                 = 8 - 4[tex]\sqrt{2}[/tex] + 4 + 2[tex]\sqrt{2}[/tex] ← collect like terms

                 = 12 - 2[tex]\sqrt{2}[/tex] units

Answer:

x + 2y = 14

Step-by-step explanation:

That’s the answer

Answer:

D. [tex]\frac{9x^2+14}{18x}[/tex]

Step-by-step explanation:

Find the common denominator, 18x.

Simplify.

Add.

I hope this helps!

Answer: D

Step-by-step explanation:

Common denominator 18x

18x/2=9x.

(9x)(x) = 9x^2

18x/9x=2

(2)(7)=14

(9x^2+14)/18x

Answer:  f(x) will have vertical asymptotes at x=-2 and x=2 and horizontal asymptote at y=3.

Step-by-step explanation:

Given function: [tex]f(x)=\dfrac{3x^2}{x^2-4}[/tex]

The vertical asymptote occurs for those values of x which make function indeterminate or denominator 0.

i.e. [tex]x^2-4=0\Rightarrow\ x^2=4\Rightarrow\ x=\pm2[/tex]

Hence, f(x) will have vertical asymptotes at x=-2 and x=2.

To find the horizontal asymptote , we can see that the degree of numerator and denominator is same i.e. 2.

So, the graph will horizontal asymptote at [tex]y=\dfrac{\text{Coefficient of }x^2\text{ in numerator}}{\text{Coefficient of }x^2\text{ in denominator}}[/tex]

i.e. [tex]y=\dfrac{3}{1}=3[/tex]

Hence, f(x) will have horizontal asymptote at y=3.

Answer:

4

Step-by-step explanation:

4x - 8 + 2y - w

None of the terms can be combined, so there are 4 terms

4x, -8, 2y, and -w

Answer:

Step-by-step explanation:

Answer:

1.417

Step-by-step explanation:

102/72=1.417

Given,

_______________

Find KJ .

_______________

First find the value of x

[tex] \sf \: GK \: = KJ \\\sf 2x + 10 = 3x - 15 \\\sf 2x - 3x = - 15 - 10 \\ \sf - x = - 25 \\ \sf \: - > \boxed{\bf \: x = 25}[/tex]

Now, find the value of KJ.

[tex]\sf3x - 15 \\ \sf= 3(25) - 15 \\ \sf=7 5 - 15 \\ = \boxed{\bf \: 60}[/tex]

-> The value of KJ is 60.

_______________

Hope it helps.

RainbowSalt2222

Answer:

KJ = 60

Step-by-step explanation:

In order to find the length of KJ we must find the value of x

Perpendicular bisectors split lines into two EQUAL parts.

If GJ is bisected then the two parts that make it up are equal to each other.

In other words GK = KJ

If GK = 2x + 10 and KJ = 3x - 15 then

2x + 10 = 3x -15

Solve for x

2x + 10 = 3x -15

Subtract 2x from both sides

10 = x - 15

Add 15 to both sides

x = 25

Now to find KJ we simply plug in the value of x into KJ's given expression

Expression given: 3x - 15

x = 25

KJ = 3(25) - 15

Multiply 3 and 25

KJ = 75 - 15

Subtract

KJ = 60

Answer:  70

Step-by-step explanation:

Antoine's elevation when he is halfway to the top is 70. You cut the diameter (120) in half which gets you 60 and you add the height of the stand holding the wheel (10) which gets you 70.

The his or her elevation should be 70.

Since the diameter is 120 And, elevation of Antoine should be halfway to the top so here we split the diameter into half i.e. half of 120 is 60 and there is the height for stand holding the wheel i.e. 10

So, the elevation should be

= 60 + 10

= 70

Therefore, The his or her elevation should be 70.

Learn more about elevation here: https://brainly.com/question/16616666

Answer:

Below

Step-by-step explanation:

First let's find m

     m = Δy / Δx = y2 - y1 / x2 - x1

         = 1 - 5 / 3 - 1

         = -2

Now to find b, you can sub in the values of (x,y) for (1,5)

5 = (-2)(1) + b

-b = -2 - 5

-b = - 7

b = 7

Final equation

y = -2x + 7

Hope this helped!

Answer:

4x + 2y - 14

Step-by-step explanation:

I hope it is understandable.

Answer:

x = 1.5

Step-by-step explanation:

6 - 2x = 3

→ Minus 6 from both sides to isolate -2x

-2x = -3

→ Divide -2 from both sides to isolate x

x = 1.5

Answer: -3

Add 1 to both sides

[tex]3x-1+1=8+1[/tex]

[tex]3x=9[/tex]

Divide both sides by 3

[tex]3x/3=9/3\\x=3[/tex]

Answer:

9.1 hours

Step-by-step explanation:

Given

Sally

Speed = 66mph

Keith

Speed = 75mph

Time = 8 hours

Required

Determine how long Sally has traveled

To solve this, we make use of Speed formula.

Speed = Distance/Time

Make Distance the subject of formula

Distance = Speed * Time

For Sally:[Substitute 66mph for speed]

Distance = 66 * Time ------ Equation 1

For Keith [Substitute 75mph for speed and 8 hours for Time]

Distance = 75 * 8

Distance = 600m----- Equation 2

From the question, we understand that Keith caught up; this implies that they've both traveled the same distance.

Hence;

Equation 1 = Equation 2

66 * Time = 600

Time = 600/66

Time = 9.1 hours

Hence, Sally has traveled 9.1 hours

Answer:

Hello,

Step-by-step explanation:

3)

[tex]x^2-4x+3=0\\x^2-3x-x+3=0\\x(x-3)-(x-3)=0\\(x-3)(x-1)=0\\\\x-intercepts\ are\ x=3\ or\ x=1[/tex]

4)

[tex]-x^2-8x+12=0\\x^2+8x-12=0\\(x^2+2*4x+16)-16-12=0\\\\(x+4)^2-28=0\\\\\\(x+4-2\sqrt{7} )((x+4+2\sqrt{7} )=0\\\\x-intercepts\ are \ x=-4+2\sqrt{7}\ and\ x=-4-2\sqrt{7}\\\\[/tex]

5)

[tex]f(x)=-3(x-7)(x+4)\\=-3(x^2-3x-28)\\\\=-3(x^2-2*\dfrac{3}{2} *x+\dfrac{9}{4} )+\dfrac{27}{4} +84\\\\=-3(x-\dfrac{3}{2})^2+\dfrac{363}{4} \\\\\\Vertex\ is\ (\dfrac{3}{2},\dfrac{363}{4})[/tex]

Answer:

please mark me brainlist I really need it

Step-by-step explanation:

Say the height of the room is X metres. So the length is 3X, and the breadth is length/2, or 3X/2.

The area of the 4 walls is then 3x^2 + 3X^2 + 3X^2/2 +3X^2/2 = 9X^2

If the cost of plastering is R5/sq m, then 9X^2 * 5 = 720

Solving this gives X = 4 m - a rather high ceiling

The floor area is then (3*4) * (3*4/2) = 72 sq m

Carpeting is then 250*72 = R18000

Answer:

1. GH

2. a

Step-by-step explanation:

Perpendicular: When 2 lines meet at 90 degrees

1. It is line segment GH because AB and GH meet at a 90 degree angle (since there is a box at angle GHF indicating that it is 90 degrees)

2. It has to be a units because it is a rectangle where the top and bottom are congruent and the sides are too

This is a rectangle since AB and CD are parallel and GH can be a transversal line, according to same side interior angles theorem EGH is a also 90 degrees. That means FEG is 90 degrees too because then the quadrilateral will add up to 360 degrees

Answer:

-24

Step-by-step explanation:

-3 multiply 8 = -24

Because when ever you multiply a negative number with a positive number result will always be negative and 3 multiply 8 is 24.

Answer: -24

Step-by-step explanation: When you're asked to multiply

positives and negatives together, the rules are simple.

positive times a positive is a positive

positive times a negative is a negative

negative times a positive is a negative

negative times a negative is a positive

One way that I think will help you is to think

about the problem in terms of the signs.

If the signs are the same, the product will always be positive.

For example, (+3) · (+6) = +18 and (-6) · (-2) = +12.

If the signs are different, the product is negative.

So (+6) · (-4) is -24 and (-10) · (+5) is -50.

So don't get caught up on the signs.

Do the problem first, then determine if the

signs are the same or if they are different.

Answer:

4.44 pints

Step-by-step explanation:

7.4 times 3/5

Answer:

[tex]\huge\boxed{x = 8.2}[/tex]

Step-by-step explanation:

Sin θ = opposite / hypotenuse

Where θ = 34 , opposite = 4.6 and hyp = x

Sin 34 = 4.6 / x

0.6 = 4.6 / x

x = 4.6 / 0.6

x = 8.2

Answer:

x = 8.2

Step-by-step explanation:

Since we have a right triangle, we can use trig functions

sin theta = opp/ hyp

sin 34 = 4.6 /x

x  sin 34 = 46

x = 4.6 /sin 34

x =8.22614159

To the nearest tenth

x = 8.2

Answer:

D

Step-by-step explanation:

Output = 3*input - 2. Observe the graph again

Answer:

a. quarter and eighth notes is the best option

Step-by-step explanation:

you can get help from this attachment

hope it will help you :)

Answer:

-15

Step-by-step explanation:

2x-17=-47

2x=-47+17

2x=-30

x=-30/2

x=-15

Answer:

B

Step-by-step explanation:

The greatest prime factor between 1 and 30 is 29. Remember that a prime number is a number whose only 2 factors is 1 and the number itself. To find out which number is a multiple of 29, all we have to do is divide it by 29, and if the quotient is a whole number then we have found our answer.

A: 1593 / 29 ≈ 54.93

B: 1247 / 29 = 43

We don't need to check C and D because we know that B is the answer.

1247 has the greatest prime factor between 1 and 30

The factor of a number that divides another number perfectly without leaving any remainder.  

For example, the factors of 12 are 1,2,3,4,6 and 12

A prime factor is a number that a prime number

A prime number is a number that can be divided only by 1 and that number

Prime numbers between 1 and 30 are 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29

The greatest prime factor between 1 and 30 is 29

To determine which number has the greatest prime factor, divide each of the numbers in the options by 29.

1593 / 29 = 54.9 (29 is not a prime factor of 1593)

1247/29 = 43 (29 is a prime factor of 1247)

1311 / 29 = 45.2  (29 is not a prime factor of 1311)

943 / 29 = 32.5  (29 is not a prime factor of 943)

To learn more about prime factors, please check: https://brainly.com/question/10371102?referrer=searchResults

Answer: -78 / 35

Step-by-step explanation:

Given

 2/5 + 3/7 + (-6/5) + (-13/7)

Combine terms that have the same denominator

= 2/5 + (-6/5) + 3/7 + (-13/7)

= -4/5 - 10/7

Convert denominator by Least Common Multiple (LCM)

= (-4 × 7) / (5 × 7) - (10 × 5) / (7 × 5)

= -28/35 - 50/35

= -78 / 35

Hope this helps!! :)

Please let me know if you have any questions

Answer:

[tex] \frac{2}{5} + \frac{3}{7} + ( - \frac{6}{5} ) + ( - \frac{13}{7} ) \\ \frac{2}{5} + \frac{3}{7} - \frac{6}{5} - \frac{13}{7} \\ ( \frac{2}{5} - \frac{6}{5} ) + ( \frac{3}{7} - \frac{13}{7} ) \\ \frac{2 - 6}{5} + \frac{3 - 13}{7} \\ \frac{ - 4}{5} + \frac{ - 10}{7} \\ \frac{ - 4}{5} - \frac{10}{7} \\ \frac{ - 28 - 50}{35} \\ \frac{ - 78}{35} \\ - \frac{78}{35} [/tex]

Answer:

6 units to the left of 3

I did the test

Answer:

19)tu=12

20) true

Step-by-step explanation:

19) (22+5x)+(19-2x)=35

   3x+41=35

   3x=-6

  x=-2

TU=22+5*-2

     =12

Answer:

its false

Step-by-step explanation:

Answer:

The answer is false

Step-by-step explanation: