Why must Kyle's and Tynessa's pattern rules be the same, even though their algebraic expressions look different?

Kyles algebraic expression based on his coloring
f(n)=2+2(n+1)

Tynessa's algebraic expression based on his coloring
4+2n

Not question a) tho

Answer:

The center is [tex](-4,5)[/tex] and the radius is [tex]11[/tex].

Step-by-step explanation:

The center-radius form for a circle is:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

where [tex](h,k)[/tex] is the center and [tex]r[/tex] is the radius.

Compare:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

[tex](x+4)^2+(y-5)^2=121[/tex]

[tex]-h=4[/tex] implies [tex]h=-4[/tex].

[tex]-k=-5[/tex] implies [tex]k=5[/tex]

[tex]r^2=121[/tex] implies [tex]r=\sqrt{121}=11[/tex].

The center is [tex](-4,5)[/tex] and the radius is [tex]11[/tex].

The center is (-4.5) and the radius is 11.

The center-radius form for a circle is:

⇒ (x-h)²+(y-k)² = r²

where (h,k) is the center and r is the radius.

Compare:

(x-h)²+(y-k)²

(x+4)+(-5)² = 121

-h = 4 implies h = -4.

-k = -5 implies k = 5

r² = 121 implies r = √121= 11,

The center is (-4.5) and the radius is 11.

The center is a fixed point in the middle of the circle; usually given the general coordinates (h, k). The fixed distance from the center to any point on the circle is called the radius.

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Answer:

v1

Step-by-step explanation:

Answer:

20hrs

Step-by-step explanation:

165-25 = 140

140/7 = 20

= 20hrs.

This is because 20 x $7 = $140 +$25 in account = $165

9514 1404 393

Answer:

  see attached

Step-by-step explanation:

A graph of direct variation is a straight line through the origin. It may have positive, negative, or zero slope. (The slope may not be "undefined.")

The fourth graph or the last one represents a function of direct variation.

Direct Variation is said to be the relationship between two variables in which one is a constant multiple of the other.

In other words, as x increases, y increases, which is evident in the last graph as well.

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Answer:

[tex]x = 5.625[/tex]

Step-by-step explanation:

Step 1:  Make an expression

[tex]\frac{3}{4} = \frac{x}{7.5}[/tex]

Step 2:  Cross Multiply

[tex]\frac{3}{4} = \frac{x}{7.5}[/tex]

[tex]4 * x = 7.5 * 3[/tex]

[tex]4x = 22.5[/tex]

Step 3:  Divide both sides by 4

[tex]4x / 4 = 22.5 / 4[/tex]

[tex]x = 5.625[/tex]

Answer:  [tex]x = 5.625[/tex]

Answer:

x = 6, x = -8

Step-by-step explanation:

Since the Pythagorean Theorem is L^2 + L^2 = H^2, all we have to do is substitute each variable and its equation for our L's.

(x + 2)^2 + (x)^2 = 100

2x^2 + 4x + 4 = 100

2x^2 + 4x - 96 = 0

Using quadratics, sorry, there was no other way, we get:

x = 6 or x = -8.

Check:

6 + 2 = 8^2 = 64

6^2 = 36

64 + 36 = 100 = 10.

-8 works as well.

Therefore, x = 6, x = -8 are correct.

Answer: a= -6 or 8

b=6 or -8

Step-by-step explanation:

From the result in the diagram

X=6 or -8

Remember

A=x+2

Substitute for x=6

A=6+2=8 or

A= -8+2= -6

So how answer for

A= -6 or 8

B=6 or -8

Answer:

y = 5/3 x + 5

Step-by-step explanation:

5x - 3y = -15

Subtract 5x from each side

5x-5x - 3y = -15-5x

-3y = -5x-15

Divide each side by -3

-3y/-3 = -5x/-3 -15/-3

y = 5/3 x + 5

To solve 5x - 3y = -15 for y, you need to isolate y, by adding 5x to both sides and then dividing by -3, yielding the solution y = -5x/3 + 5.

To solve the equation 5x - 3y = -15 for y, we need to isolate y on one side of the equation. Here's a step-by-step process:

Using this method, we can solve any linear equation in two variables for one of the variables. In this case, we have expressed y as a function of x.

Each angle is 40 degrees because a straight line is 180 and there is a 100 so just subtract 100 from 180 then divide 80 by 2 and you're left with 40

Answer:

56232.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

#7 : 6

#8 : 12

#9 : ?

#10 : 110

#12 : ?

Answer:

9.55

Step-by-step explanation:

with a radius of 1 and a volume of 30 the height should be around 9.55

The height of the cylinder is 9.549 in with a volume of 30 cubics in and a radius of 1 in.

It is given that the volume of a cylinder is 30 cubic in and the radius is 1 in.

It is required to find the height of the cylinder.

It is defined as a three-dimensional space enclosed by an object or thing.

We know the volume of a cylinder:

[tex]\rm V = \pi r^2 h[/tex]

Where r is the radius of a cylinder and h is the height of the cylinder.

Here V = 30 cubic in and r = 1 in

[tex]\rm 30 = \pi\times 1^2\times h[/tex]  or

πh = 30

h = 9.549 in

Thus, the height of the cylinder is 9.549 in with a volume of 30 cubics in and a radius of 1 in.

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Answer:

The original price was reduced 35%

Step-by-step explanation:

we know that

Jeans are reduced from $28.00 to $18.20

In this problem

The original price of 28.00 represent 100%

so

using proportion

Find out what percentage represent the difference between the original price and the new price

[tex]\frac{28}{100}=\frac{28-18.20}{x}\\\\x=100(9.8)/28\\\\x=35\%[/tex]

therefore

The original price was reduced 35%

Answer:

Number of hour worked by Dewey = 27 hours

Number of hour worked by Huey =  20hours

Number of hours worked by Louie = 40 hours

Step-by-step explanation:

Let x be number of hours worked by Dewey

Number of hour worked by Huey = x - 7

Number of hours worked by Louie = 2*(x-7) = 2*x -2*7 = 2x- 14

Together they worked 87 hours

x + x-7 + 2x-14 = 87

4x - 21 = 87

4x = 87 +21

4x = 108

x = 108/4

x = 27 hours

Number of hour worked by Dewey = 27 hours

Number of hour worked by Huey = x - 7 = 27 - 7 = 20hours

Number of hours worked by Louie = 2x - 14 = 2*27 - 14 = 54 - 14 = 40 hours

Answer:

21.6 Kilometers

Step-by-step explanation:

We know that every hour has 60 minutes, so the car travels at [tex]\frac{72}{60}[/tex] kilometers per minute.  Multiplying this by 18 gives [tex]18*\frac{72}{60}=21.6[/tex] kilometers.

Answer: Sales tax would be $5.40

Step-by-step explanation: The sales value itself of the dress (that is, without tax) is $65.49.

The amount charged as sales tax in Pearland is given as 8.25% (or 0.0825).

Hence if she is shopping in Pearland, the AMOUNT OF SALES TAX she would pay can be calculated as,

Sales tax = Sales price x 0.0825

Sales tax = 65.49 x 0.0825

Sales tax = 5.402925

Approximately to two decimal places, the sales tax becomes $5.40

The material needed to make 1 kite is 144 square inches and for 3 kites she need 432 square inches of the material.

Step-by-step explanation:

Diagonals of the kite = 16 inches and 18 inches

Area of the kite = (16 x 18) /2

= 144 square inches

Area of 3 kites = 3 x 144

= 432 square inches.

The material needed to make 1 kite is 144 square inches and for 3 kites she need 432 square inches of the material.

Answer:

the first one is 144 and the second one is 432

Step-by-step explanation:

Answer:

I think u=11

Step-by-step explanation:

A=6a^2

726 divided by 6= 121

square root of 121=11

answer=11

Answer:

57

Step-by-step explanation:

when you multiply 7x25 you get 675 then divide by 12 you get 56.25 meaning you need one more so you get 57

8, 24, 25

[tex]8^2+24^2\neq 25^2[/tex]

Answer:

D

Step-by-step explanation:

Answer:

B) (-2,1)

Step-by-step explanation:

The solution is where the two lines intersect, in this case at (-2,1)

Hope this helps! :)

Answer:

B) (-2, 1)

Step-by-step explanation:

2 units left from the origin

So x = -2

1 unit up

So y = 1

Answer:

Second

Step-by-step explanation:

This question is asking for the largest magnitude. The second is of so. The deeper you go the more negative the number gets as thats how far you are off sea-level.

Answer:

the second one

Explanation: If you got this you are right

Answer:

A. 210 ft

Step-by-step explanation:

The area of the circle is  36π mm²

A circle can be described as a round figure whose circumference (the distance round the circle) is equidistant from the centre. An image of a circle is attached.

The area of a circle = πr²

π= pi = 22/7

r = radius = 6mm

The radius of a circle is the distance from the centre of the circle to any point on the circle's circumference.

Area of the circle = π x 6² = 36π mm²

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The area of the circle with a radius of 6mm is 36π mm².

The area (\(A\)) of a circle is given by the formula:

[tex]\[ A = \pi r^2 \][/tex]

where [tex]\(r\)[/tex] is the radius.

Given a radius of [tex]\(6 \, \text{mm}\),[/tex] substitute this value into the formula:

[tex]\[ A = \pi \times (6 \, \text{mm})^2 \][/tex]

[tex]\[ A = \pi \times 36 \, \text{mm}^2 \][/tex]

So, the area of the circle is[tex]\(36\pi \, \text{mm}^2\)[/tex] , and the units are square millimeters[tex](\(\text{mm}^2\)).[/tex]

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Answer:

(-10, -3)

Step-by-step explanation:

()  excludes -10 and -3 so it only includes the numbers in between.

The set builder notation is {x: x ∈ Z⁻, -10 < x < -3} and the set is {-9, -8, -7, -6, -5, -4}

It is given the set of numbers that are greater than -10 and less than -3.

Since they are negative integers, so all the required numbers also belong to the same category of numbers.

So, it is represented by Z⁻

Then, the set builder notation is

{x: x ∈ Z⁻, -10 < x < -3} and

The set is {-9, -8, -7, -6, -5, -4}

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The line with equation 3x – 2y = 12 has the value of slope (m) equal to [tex]\frac{3}{2}[/tex] and y - intercept equal to -6.

What is the slope intercept form of a line ?

The equation of line that can be written as y = mx + c, where m is the slope and c is the line's y-intercept, is known as a slope intercept form.

The equation of a line is given which is 3x – 2y = 12.

This can be also written as :

3x - 2y - 12 = 0

We know that general equation of a line is given by ax + b + c = 0.

So , the given equation is :

3x – 2y = 12

dividing by 12 on both sides we get "

[tex]\frac{3x}{12}[/tex] - [tex]\frac{2y}{12}[/tex] = [tex]\frac{12}{12}[/tex]

[tex]\frac{x}{4}[/tex] - [tex]\frac{y}{6}[/tex] = 1

or

[tex]\frac{x}{4}[/tex] + (- [tex]\frac{y}{6}[/tex]) = 1

This is the slope intercept form of the given equation.

So , using the slope intercept form of line ,

y = mx + c

y = [tex]\frac{3}{2}[/tex] x - 6

If we compare : we get

c = y intercept = -6

and

Slope (m) = [tex]\frac{3}{2}[/tex]

Therefore , the line with equation 3x – 2y = 12 has the value of slope (m) equal to [tex]\frac{3}{2}[/tex] and y - intercept equal to -6.

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Final answer:

The line 3x – 2y = 12 has a slope of 3/2 and a y-intercept of -6, corresponding to choice A.

Explanation:

The equation of the line is given as 3x – 2y = 12. To find the slope and the y-intercept, we should rewrite this equation in slope-intercept form, which is y = mx + b, where 'm' is the slope and 'b' is the y-intercept. To do this, solve the given equation for y:

So, we have the slope (m) as 3/2 and the y-intercept (b) as -6, which corresponds to choice A.

Answer:

(x + 2/3)^2 + (y + 3/4)^2 = 5^2

Step-by-step explanation:

Apply the general formula for a circle:  (x - h)^2 + (y - k)^2  = r^2, where (h, k) is the center and r is the radius.  Since the center is (-2/3, -3/4), and r = 5, we get:

(x + 2/3)^2 + (y + 3/4)^2 = 5^2

Answer:

About 1691.886 gallons.

Step-by-step explanation:

The firs step is to find the volume of the pool in cubic feet. The formula for the volume of a cylinder is [tex]\pi r^2 h[/tex], which in this case is [tex]\pi \cdot 6^2 \cdot 2\approx 226.188[/tex] cubic feet. Multiplying this by 7.48, you get a total of about 1691.886 gallons of water. Hope this helps!

Answer:

Angela eats more cake

Angela ate 1/8 more cake

1/4 of the chocolate

3/8 of the Vanilla

no more Strawberry

Step-by-step explanation:

Angela: 4/8 + 2/8 + 4/8 = 10/8 = 1 1/4

David: 2/8 + 3/8 +4/8 = 9/8 = 1 1/8

Chocolate: 4/8 + 2/8 = 6/8,  8/8 - 6/8 = 2/8 or 1/4

Vanilla: 2/8 + 3/8 = 5/8, 8/8 - 5/8 = 3/8

Strawberry: 4/8 + 4/8 = 8/8, 8/8 - 8/8 = 0

Final answer:

Angela ate more cake than David by 0.125 of a cake after calculating fractions consumed by each. The remaining amounts of cake are 1/4 of chocolate, 3/8 of vanilla, and none of the strawberry cake is left.

Explanation:

To find out who eats more cake, Angela or David, we need to calculate the fractions of each cake they consumed. Firstly, we can simplify the fractions of the cake Angela and David ate by converting them to have the same denominator or to represent them as decimals. The total amount of each cake consumed needs to be added up individually for Angela and David.

Angela's Cake Consumption:

Chocolate Cake: 4/8 (simplified to 1/2 or 0.5)

Vanilla Cake: 2/8 (simplified to 1/4 or 0.25)

Strawberry Cake: 2/4 (simplified to 1/2 or 0.5)

Total cake eaten by Angela = 0.5 (chocolate) + 0.25 (vanilla) + 0.5 (strawberry) = 1.25

David's Cake Consumption:

Chocolate Cake: 1/4 (or 0.25)

Vanilla Cake: 3/8 (simplified to 0.375)

Strawberry Cake: 1/2 (or 0.5)

Total cake eaten by David = 0.25 (chocolate) + 0.375 (vanilla) + 0.5 (strawberry) = 1.125

Angela ate more cake than David by 0.125 of a cake.

Amount of Each Cake Left:

Chocolate Cake: 1 - (0.5 + 0.25) = 1/4 or 0.25 left

Vanilla Cake: 1 - (0.25 + 0.375) = 3/8 or 0.375 left

Strawberry Cake: 1 - (0.5 + 0.5) = 0 left