Question 2 of 5
Which two ratios represent quantities that are proportional?

Answer: [tex]4004.76\ ft[/tex]

Step-by-step explanation:

Given

inclination is [tex]\theta=75^{\circ}[/tex]

Mountain is [tex]h=3900\ ft[/tex] high

Cable is tied [tex]x=910\ ft[/tex] from the base of the mountain

From the figure, length of the shortest path is [tex]l[/tex]

It is given by using Pythagoras theorem

[tex]\Rightarrow l^2=3900^2+910^2\\\Rightarrow l=\sqrt{(3900)^2+(910)^2}\\\Rightarrow l=4004.76\ ft[/tex]

Answer:

y² = (1/16)x³

Step-by-step explanation:

Given that :

y² varies directly as the cube of x

y² α x³

y² = kx³ - - - (1)

Where, k = constant of f proportionality

We can obtain the value of k ; when x= 4 and y = 2

2² = k4³

4 = 64k

k = 4/64

k = 1/16

Putting k = 1/16 in (1)

y² = (1/16)x³

First subtract the amount the bow takes from the total:

70 - 32 = 38 inches

The width is 14 on top and bottom so subtract 14 x 2 = 28 from 38:

38-28 = 10

Divide 10 by the 2 sides:

10/2 = 5

The height is 5 inches.

Answer:

y=(4-2x)/3

Step-by-step explanation:

3y= 4-2x

y= (4-2x)/3

Replace x with -11 and solve:

Y = (-11)^2 + 11

(-11)^2 = 121

Y = 121 + 11

Y = 132

Answer: 132

Answer:

132

Step-by-step explanation:

y = x^2 +11

Let x = -11

y = (-11)^2 +11

  = 121+11

  = 132

Answer:

[tex](x,y) = ( 5 , - 7)[/tex]

Step-by-step explanation:

we would like to solve the following system of linear equation by substitution:

[tex] \displaystyle \begin{cases} y = x - 12\\ 8x + 8y = - 16\end{cases}[/tex]

notice that, we're already given the value of y therefore simply substitute it to the II equation

[tex]8x + 8(x - 12) = - 16[/tex]

distribute:

[tex]8x + 8x - 96= - 16[/tex]

simplify addition:

[tex]16 x- 96= - 16[/tex]

isolate -96 to left hand side and change its sign:

[tex]16 x= - 16 + 96[/tex]

simplify addition:

[tex]16 x= 80[/tex]

divide both sides by 16 and that yields:

[tex] \boxed{x= 5}[/tex]

now substitute the got value of x to the first equation:

[tex]y = 5- 12[/tex]

simplify subtraction:

[tex]y = - 7[/tex]

hence,

the solution is (x,y)=(5,-7)

Solve by substitution :

y = x - 12

8x + 8y = -16

y = x - 12 ------- eq(1)

8x + 8y = -16 ------- eq(2)

Finding x ⤵

Putting y = x - 12 in eq(2) we get

Finding y ⤵

Putting x = 5 in eq(1) we get

Hence, x is 5 and y is -7

Answer: Choice A

4^2 + b^2 = 5^2

This is due to the pythagorean theorem.

Answer:

576xxxycm

Step-by-step explanation:

1cm×12x×x+48xy=576xxxycm

Answer:

f(3) = 2

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Functions

Step-by-step explanation:

Step 1: Define

Identify

f(x) = 2x - 4

Step 2: Evaluate

Answer:

n(AuB)=n(A)+n(B)=18

This is the answer

Answer:

55 Gallons

Step-by-step explanation:

143 - (8)(11)

143 - 88

143 -  88

55 gallons

Answer:

-2, 6, 20 ,...

Step-by-step explanation:

3n² +5n -2

if n=0 , then 3*0² +5*0 -2= -2

if n=1, then 3*1² +5*1 -2 = 3+5-2 = 6

if nu 2, then 3*2² +5*2 -2 = 12 +10 -2 = 20

Answer:

missing side is √193

= 13.892443989449

Answer:

the answer is 5×3+11×5 feet

Answer:

4th option

Step-by-step explanation:

An equilateral triangle has 3 congruent sides

Divide the perimeter by 3 for length of side

[tex]\frac{15x^3+33x^5}{3}[/tex]

= [tex]\frac{15x^3}{3}[/tex] + [tex]\frac{33x^5}{3}[/tex]

= 5x³ + 11[tex]x^{5}[/tex] ← length of 1 side

The options for the box and whisker plots aren't given ; however using technology, a box and whisker plot could be generated from the data.

Answer:

Step-by-step explanation:

Given :

45, 44, 47, 49, 45, 47, 42, 39, 45, 42, 44

Using technology, the box and whisker plot generated for the data is attached below.

The 5 - number summary is also given below :

Minimum: 39

Median: 45

First quartile: 42

Third quartile: 47

Interquartile Range: 5

Maximum: 49

Outliers: none

Answer:

Step-by-step explanation:

Answer:

[tex] ({a + b})^{2} [/tex]

[tex](a + b)(a + b)[/tex]

[tex] {a}^{2} + 2ab + {b}^{2} [/tex]

hope this help you

Answer:

Below.

Step-by-step explanation:

If the length is x then the width is x-9 inches.

Perimeter

= 2L + 2W = 86

2x + 2(x - 9) = 86

4x - 18 = 86

4x = 104

x = 26

So the length is 26 inches and the width is 17 inches.

Answer:

Option C,

y² = 18x, since the graph opens right

Answered by GAUTHMATH

1. The equation is 18 = 3 × x

2. a) The independent variable is the of ounces of lemon juice in the lemonade

b) A = a × b

c) First quadrant

The procedure to find the above answers are presented here as follows;

1. The following is the table of values of the data

[tex]\begin{array}{ccc} Lemon \ juice \ ounces \ (x)& & Water \ in \ ounces \ (y)\\2&&6\\3&&9\\4&&12\\5&&15\end{array}[/tex]

The given data in the table shows that the Lemon juice ounces, x, and the Water in ounces, y, have a direct proportionality relationship which is given as follows;

y ∝ x

∴ y = k × x

Where;

k = The constant of proportionality

k = y/x

Therefore;

k = 6/2 = 9/3 = 12/4 = 15/5 = 3

k = 3

y = k × x

∴ y = 3 × x

Therefore;

The equation to represent how much lemon juice, x, is needed when Waheeda uses y = 18 ounces of water  is given by placing y = 18 in y = 3 × x as to get;

18 = 3 × x

∴ x = 18/3 = 6; 6 ounces of lemon juice is needed with 18 ounces of water

2. The independent variable is the input or causing variable that determines the output variable

Therefore, the independent variable is the number of ounces of lemon juice required to be mixed with a given number of ounce of water to make lemonade

b) Let a represent the selling price for a glass of lemonade, let b represent the number of glasses of lemonade she sells, and let A represent the amount she earns, we have;

A = a × b

c) The given x and y values in the data are both positive values, which indicate that the data would appear in the first quadrant

Learn more about dependent and independent variable here;

https://brainly.com/question/18456313

Answer:

900 is the correct awnser

here it is :)

do check properly, I have given step by step instructions:)

do give feedback on my answer, would appreciate it!

Answer:

900000

Step-by-step explanation:

[tex]30*10^{4}[/tex]

=3*10000

=30000

=30*30000

=900000

Answer: 18

Step-by-step explanation: Factor of 18 are: 1, 2, 3, 6, 9, 18

Factor of 36 are : 1, 2, 3, 4, 6, 9, 12, 18, 36

Hope that helps

Answer:

18

Step-by-step explanation:

listing the factors

factors of 18 are 1, 2, 3, 6, 9, 18

factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36

The common factors are 1, 2, 3, 6, 9, 18

with GCF being 18

Answer:

Y/X = 2/3 x^2 + 16/3

Y= 2/3 x^3 + 16/3 x

Just replace y with y/X and X with x^2

Answer:

50%

Step-by-step explanation:

1. determine the monthly interest rate

monthly interest rate = interest / loan amount

monthly interest = 25 / 600 = 4.17%

2, multiply the monthly interest rate by 12 to determine the annual interest rate

Annual interest = 4.17 x 12 = 0.5 = 50%

Answer:

Not sure if this will help but that looks like a bisection of angles BAC and TSR.

When figures are translated, rotated or reflected, the resulting figures are congruent to the original figure because the transformations are rigid. However, when a figure is dilated, the resulting figure is not congruent to the original figure.

ABCD and A'B'C'D are congruent because A'B'C'D is the result of rotating ABCD 180 degrees about the origin.

I've included the missing graph as an attachment.

Using points A and A' as our references.

We have:

[tex]A = (-1,1)[/tex]

[tex]A' = (1,-1)[/tex]

The rule of rotation 180 degrees about the origin is:

[tex](x,y) \to (-x,-y)[/tex]

So, we have:

[tex](-1,1) \to (-(-1),-1)[/tex]

[tex](-1,1) \to (1,-1)[/tex]

The above rule is applicable to other points in ABCD and A'B'C'D'

Since the rule of transformation is rotation (a rigid transformation), then ABCD and A'B'C'D are congruent.

Read more at:

https://brainly.com/question/9475847

Answer:

Step-by-step explanation:

If you drew out the bell curve and put the values where they go, this would be a no-brainer that doesn't even need math to solve. However, we will use the formula and then the table for z-scores to find this answer.

We are looking for the probability that the number of calls falls between 19 and 67. The standard deviation is 8 and the mean is 43. The probability we are looking for is P(19 < x < 67), therefore we look for the probability first that number of calls is greater than 19:

[tex]z=\frac{19-43}{8}=-3[/tex] and from the table and to the right of the z-score, the probability that the number of calls is greater than 19 is .99865 (or 99.8%). Likewise,

[tex]z=\frac{67-43}{8}=3[/tex] and from the table and to the right of the z-score, the probability that the number of calls is greater than 67 is .00315.

Take the difference of these to get the probability that the number of calls falls between these 2:

.99865 - .00135 = .9973 or 99.7%

Answer:add a screenshot

Step-by-step explanation:

I can't see the our glasses