The measure of an angle is eight times the measure of its supplementary angle. What is the measure of each angle?

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

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Answer:

= -8x^5 y^4

Step-by-step explanation:

Multiply the numbers: -2 . 4 = -8

-2x^3 yx^2 y^3

Simplify x^3 x^2 : x^5

= -8x^5yy^3

Simplify yy^3 : y^4

= -8x^5 y^4

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:

x^2-12x+31

Step-by-step explanation:

Standard form of the quadratic equation (x-6)^2-5 is x^2-12x+36-5=x^2-12x+31

Answer:

The value of the 2 is two-thousand

Step-by-step explanation:

Answer:

thousands

Step-by-step explanation:

thousands, hundreds tens ones

2                    4              7      3

Answer:

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

Answer:

Dylan must spend 45 minutes of his time on studies.

Step-by-step explanation:

Natasha gets 30 minutes less than Dylan. Total there can be 1 and half hour for studies which means there are 90 minutes for the studies. Dylan must spend half of his time on his studies.

90 minutes * 50% = 45 minutes.

Answer a:

Figure 4 = 5 blocks up, 5 blocks right

Figure 5 = 6 blocks up, 5 blocks right

Answer b: Grows 2 blocks each time, 1 blocks at the top and 1 blocks on the right.

Answer c: Since you add 2 blocks each time, you do the opposite so you subtract 2 blocks. The answer will be 1 block.

Step-by-step explanation:

Answer: x³-21x+20=0

Step-by-step explanation:

To find which polynomial has 1, 4, -5 as the roots, all we have to do is equal each root to 0 and multiply all factors together.

1 is (x-1)=0

4 is (x-4)=0

-5 is (x+5)=0

Now, we just multiply them together.

(x-1)(x-4)(x+5)=0                       [FOIL]

(x²-4x-x+4)(x+5)=0                    [combine like terms]

(x²-5x+4)(x+5)=0                      [FOIL]

x³+5x²-5x²-25x+4x+20=0       [combine like terms]

x³-21x+20=0

Now we know x³-21x+20=0 is the polynomial with those roots.

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:

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%

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.

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Explanation:

These are state abbreviations

Since the given sequence is "AL, AK, AZ, AR, CA", and the states are listed alphabetically so far (in terms of the two letter abbreviations), then the next two would be CO and CT in that order.

Answer:

missing side is √193

= 13.892443989449

A × B = {a, b} × {1, 2, 3} = {{a, 1}, {a, 2}, {a, 3}, {b, 1}, {b, 2}, {b, 3}}

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:

Step-by-step explanation:

If a number can be expressed by sum of two square, only if the number can be represented by 4k + 1 form

1975 = 4*493 + 3

So, 1975 can't be a sum of two squares

Answer:

¼ chance

Step-by-step explanation:

If there is 4 items and 1 blue die and its a ¼ chance if there was more blue then there would be a higher chance for having blue socks

Answer:

((3.55)^2+(4.12)^2+(4.41)^2)/2(3.55)*(4.12)

=358.519825

Step-by-step explanation:

I just used this website called mathpapa.com, extremely useful for algebra calculations. Here's the link if you need it

https://www.mathpapa.com/algebra-calculator.html

Answer:

y=(4-2x)/3

Step-by-step explanation:

3y= 4-2x

y= (4-2x)/3

Answer:

Any number greater than 49.

Step-by-step explanation:

Since 7>0 then multiplying both sides of x>7 by 7 will not effect the direction of the inequality.

If x>7, then 7x>7(7) or 7x>49 after simplifying.

Substituting y for 7 since y=7 gives yx>49.

By commutative property of multiplication we have xy>49.

So any number greater than 49.

Answer:

Step-by-step explanation:

- 22 - □ = 7

=> - 22 - 7 = □

=> - 29 = □

=> □ = - 29 (Ans)

Answer:

x = 7 is the answer for the smaller number

7 + 1 = 8 is the answer for the larger number

Step-by-step explanation:

LET x and  x+1 be the two numbers here, as your hint suggests.

5x + 3(x+1) = 59

5x + 3x+3 = 59

8x = 59-3

8x = 56

/8      /8

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

x = 56/8 ---> x = 7

x = 7 is the answer for the smaller number

7 + 1 = 8 is the answer for the larger number

Check:

5 * 7 + 3 * 8 = 59

35 + 24 = 59

59 = 59 CORRECT

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:

C. TRANSLATE 2 UNITS UP AND 4 UNITS DOWN

Step-by-step explanation:

The transformation that takes place with the following rule (x - 2, y + 4) is translates 2 units left AND 4 units up, the correct option is A.

The transformation of a function may involve any change.

Usually, these can be shift horizontally (by transforming inputs) or vertically (by transforming output), stretching (multiplying outputs or inputs) etc.

If the original function is y = f(x), assuming horizontal axis is input axis and vertical is for outputs, then:

Horizontal shift (also called phase shift):

Left shift by c units:

y=f(x+c) (same output, but c units earlier)

Right shift by c units:

y=f(x-c)(same output, but c units late)

Vertical shift:

Up by d units: y = f(x) + d

Down by d units: y = f(x) - d

Stretching:

Vertical stretch by a factor k: y = [tex]k \times f(x)[/tex]

Horizontal stretch by a factor k: y =[tex]f\left(\dfrac{x}{k}\right)[/tex]

We are given that;

The points (x - 2, y + 4)

Now,

The rule (x - 2, y + 4) means that every point (x,y) of the original figure is moved to a new point (x - 2, y + 4) by subtracting 2 from the x-coordinate and adding 4 to the y-coordinate.

The x-axis is horizontal and positive to the right. Subtracting from the x-coordinate means moving left and adding to the x-coordinate means moving right.

The y-axis is vertical and positive upwards. Subtracting from the y-coordinate means moving down and adding to the y-coordinate means moving up.

Subtracting 2 from the x-coordinate means moving 2 units left and adding 4 to the y-coordinate means moving 4 units up.

Therefore, by transforming functions the answer will be translates 2 units left AND 4 units up.

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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

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

Answer:

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

This is the answer

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