A square and a circle are used as sample designs for a tiling project. The length of an edge of a square is two times the length of the radius of a circle.

Find the ratio of the area of the circle to the area of square using the given radii.

Select either Choice 'A' or Choice 'B'

Answer:

y = - [tex]\frac{5}{6}[/tex] x + 2

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (6, - 3) and (x₂, y₂ ) = (0, 2)

m = [tex]\frac{2+3}{0-6}[/tex]= [tex]\frac{5}{-6}[/tex] = - [tex]\frac{5}{6}[/tex], thus

y = - [tex]\frac{5}{6}[/tex] x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (6, - 3), then

- 3 = - 5 + c ⇒ c = - 3 + 5 = 2

y = - [tex]\frac{5}{6}[/tex] x + 2 ← equation of line

The equation of the line in slope-intercept form that passes through the points (6,-3) and (0, 2) is y = -5/6x + 2, where -5/6 is the slope and 2 is the y-intercept.

To write an equation in slope-intercept form (y = mx + b) of the line that passes through two points (6,-3) and (0, 2), first, we need to calculate the slope (m).

The formula to calculate the slope is (y2 - y1) / (x2 - x1). Plugging in the values from the given points, we get the slope as (2 - (-3)) / (0 - 6) = 5 / -6 = -5/6.

Next, substitute one of the points and the slope into the equation to find the y-intercept (b). If we use (0, 2), we get 2 = -5/6 * 0 + b, hence, b=2.

Therefore, the equation of the line in slope-intercept form that passes through these points is y = -5/6x + 2.

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Answer: 1 1/3

Step-by-step explanation: 0.33 repeating and in general is equal to 1/3

Answer:

B is the answer

To solve the mixture problem, we set up an equation based on the total weight and another based on the total cost, then solve the system of equations algebraically to find out how many pounds of peanuts and raisins are needed.

The question involves creating a cost-based blend of two items, peanuts and raisins, to produce a mixture with a target cost per pound. This is a typical algebraic mixture problem, commonly encountered in high school math. To solve this problem, we want to find out how many pounds of peanuts and raisins are needed to make a 50-pound mixture that costs $1.47 per pound when peanuts cost $1.20 per pound and raisins cost $2.10 per pound.

Let's denote the weight of peanuts as P pounds and the weight of raisins as R pounds. The total weight of the mixture is given as 50 pounds, which gives us the equation:

P + R = 50

Next, we need to consider the total cost of the mixture. The cost of the peanuts is P times $1.20, and the cost of the raisins is R times $2.10. Since the mixture should have an overall cost of $1.47 per pound, our cost equation becomes:

1.20P + 2.10R = 1.47 × 50

From our first equation, we can express R as 50 - P, and substitute it into our second equation to find the value of P. After solving these linear equations, we will obtain the exact quantities of peanuts and raisins required to make the desire mixture.

Maricel's code will adjust the shot by 12º

Answer:

The correct angle will be 12.5 degrees.

Answer: 5/11,5

Step-by-step explanation:

Multiply equation one by -4

Multiply equation two by 2

Then, it becomes

-8x - 28y = 28

-8x - 6y = 38

Subtract equation two from equation one .

It becomes -22y = -10

Divide both sides by 22, you have y= 5/11

NOW substitute y=5/11 into equation two to get X.

-4x -3(5/11) =19

-4x = 19 + 15/11

-4x = 20

Divide both sides by -4

X = -5

To solve the system of equations, the elimination method was used, resulting in the solution of the equations as an ordered pair (-6 16/77, 5/11).

To solve the system of equations 2x + 7y = -7 and -4x - 3y = 19, one can use the elimination method. This involves manipulating the two equations to eliminate one of the variables, allowing the other variable to be found. We can multiply the first equation by 2 to align the coefficients of the 'x' terms and then add the equations to cancel out the 'x' terms.

Multiply the first equation by 2: 4x + 14y = -14.

Add this to the second equation: (4x + 14y) + (-4x - 3y) = -14 + 19.

This simplifies to 11y = 5, and solving for 'y' gives y = 5/11.

Substitute 'y' back into the first original equation: 2x + 7(5/11) = -7.

Solve for 'x', which gives x = -6 16/77.

So, the solution to the system of equations, expressed as an ordered pair, is (-6 16/77, 5/11).

Answer:

(6 + 2) + 7 = 6 + (2 + 7)

Explanation:

(6 + 2) + 7

6 + 2 = 8

8 + 7 = 15

6 + (2 + 7)

2 + 7 = 9

9 + 6 = 15

15 = 15

You will be adding 6, 2 and 7 no matter what. The parenthesis do not make a difference. 6 + 2 + 7 is the same thing as 6 + 2 + 7. 15 = 15.

Answer:

A.

Step-by-step explanation:

A. 15 = 15 (true)

B. -3 = 11 (false)

C. 11 = -3 (false)

Answer:

Contour lines. Hope this helps!

5 jars of jam and 3 packages of bread mix are in gift basket

Solution:

Let "x" be the number of jars of jam

Let "y" the number of packages of bread mix

Cost of 1 jars of jam = $ 6

Cost of 1 package of bead mix = $ 5

There are 8 items in the basket

Therefore,

number of jars of jam + number of packages of bread mix = 8

x + y = 8 ---------- eqn 1

A gift basket that contains jars of jam and packages of bread mix costs $45

Therefore, we frame a equation as:

number of jars of jam x Cost of 1 jars of jam + number of packages of bread mix x Cost of 1 package of bead mix = 45

[tex]x \times 6 + y \times 5 = 45[/tex]

6x + 5y = 45 --------- eqn 2

Let us solve eqn 1 and eqn 2

From eqn 1,

x = 8 - y --------- eqn 3

Substitute eqn 3 in eqn 2

6(8 - y) + 5y = 45

48 - 6y + 5y = 45

y = 48 - 45

Substitute y = 3 in eqn 3

x = 8 - 3

Thus 5 jars of jam and 3 packages of bread mix are in gift basket

[tex]\frac{x^2}{4}-\frac{10x}{2}+25[/tex]

Solution:

Given expression is [tex](\frac{1}{2}x-5)^2[/tex].

Simplify the expression using algebraic formula [tex](a-b)^2=a^2-2ab+b^2[/tex]

[tex](\frac{1}{2}x-5)^2=(\frac{x}{2}-5)^2[/tex]

               [tex]=(\frac{x}{2})^2-2(\frac{x}{2})5+5^2[/tex]

               [tex]=\frac{x^2}{4}-10(\frac{x}{2})+25[/tex]

               [tex]=\frac{x^2}{4}-\frac{10x}{2}+25[/tex]

[tex](\frac{1}{2}x-5)^2=\frac{x^2}{4}-\frac{10x}{2}+25[/tex].

Hence, the simplified form of  [tex](\frac{1}{2}x-5)^2[/tex] is [tex]\frac{x^2}{4}-\frac{10x}{2}+25[/tex].

Answer:

I=60

Step-by-step explanation:

So

P=$250

R=6%

T=4

So to get the answer we would need to multiply everything to get the interest so the answer would be 60 because 250 times 6% equals to 15 then we would multiply 15 by 4 and then get out answer of $60 interest.

Answer:

4/9 or 0.444...

Step-by-step explanation:

[tex] \frac{7}{9} - \frac{1 \times 3}{3 \times 3} [/tex]

[tex] \frac{7}{9} - \frac{3}{9} [/tex]

[tex] \frac{4}{9} [/tex]

Answer: 4/9

Step-by-step explanation: Since our denominators in this problem are 9 and 3, and 9 factors as 3 x 3, they have a common factor of 3 so we find their least common denominator by multiplying the 3 that comes from the 3's that match up times the 3 that doesn't match up so we have 3 x 3 or 9.

In order to get a common denominator of 9 for both our fractions, we multiply top and bottom of the the second fraction by 3 and we have 7/9 - 3/9 which simplifies to 4/9. So 7/9 - 1/3 is 4/9.

I have also attached my work in the image provided.

Answer:

I believe 27%

Step-by-step explanation:

Total juniors = 8

Total students = 30

So 8 out of 30 as a percentage = 26.67

Hope this helps! :)

The width of rectangle is [tex]2\frac{1}{4}[/tex] cm and length is [tex]5\frac{5}{12}[/tex] cm.

Step-by-step explanation:

Let,

Width of rectangle = w

Length of rectangle = [tex]w+3\frac{1}{6}=w+\frac{19}{6}[/tex]

Perimeter of rectangle = [tex]15\frac{1}{3}=\frac{46}{3}[/tex] cm

Perimeter = 2(Length + Width)

[tex]\frac{46}{3}=2(w+\frac{19}{6}+w)\\\\\frac{46}{3}=2(2w+\frac{19}{6})\\\\\frac{46}{3}=4w+\frac{19}{3}\\\\4w+\frac{19}{3}=\frac{46}{3}\\\\4w=\frac{46}{3}-\frac{19}{3}\\\\\ 4w=\frac{46-19}{3}\\\\4w=\frac{27}{3}\\\\4w=9[/tex]

Dividing both sides by 4

[tex]\frac{4w}{4}=\frac{9}{4}\\\\w=\frac{9}{4}[/tex]

Width of rectangle = [tex]\frac{9}{4}=2\frac{1}{4}\ cm[/tex]

[tex]Length = w+\frac{19}{6}=\frac{9}{4}+\frac{19}{6}\\\\Length = \frac{27+38}{12}=\frac{65}{12}\\\\Length=5\frac{5}{12}\ cm[/tex]

The width of rectangle is [tex]2\frac{1}{4}[/tex] cm and length is [tex]5\frac{5}{12}[/tex] cm.

Keywords: rectangle, perimeter

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Final answer:

The width of the rectangle is 9.92 cm (approx.) and the length is 13.09 cm, calculated using the given perimeter and the relationship between the width and length, both rounded to three significant figures.

Explanation:

The question asks to find the width and length of a rectangle given that the length is 3 1/6 cm longer than the width and the perimeter is 15 1/3 cm. To solve this, first express the perimeter as an equation involving width (w) and length (l):

Perimeter (P) = 2l + 2w

Since the length is 3 1/6 cm longer than the width, we can express the length as:

l = w + 3 1/6

Substitute the value of l in the perimeter equation:

15 1/3 = 2(w + 3 1/6) + 2w

Convert mixed numbers into improper fractions for easier computation:

46/3 = 2(w + 19/6) + 2w

Expand and solve for w:

46/3 = (4w + 19/3)

3(46) = 4w(3) + 19

138 = 12w + 19

119 = 12w

w = 119/12

w = 9.916666...

To match our significant figures requirement, we report the width of the rectangle as 9.92 cm to three significant figures. Now calculate the length:

l = w + 3 1/6

l = 9.92 + 3.1666...

l = 13.0866...

Again, matching our significant figures requirement, the length is reported as 13.09 cm to three significant figures.

Answer:

Step-by-step explanation:

31) Y = -3x² + 18 x -25 = -3*x² + -3*-6x -25

  = -3(x² -6x) - 25

( (a-b)² =a² - 2ab + b²;   here a = x; 2ab = -6x = -2*x*3; and so b = 3)

  = -3(x² -6x + 9 - 9) - 25  

 { when we add and subtract 9, the equation will not change}

= -3[(x -3)² - 9] -25

= -3(x - 3)² - (-3)*9 - 25

= -3(x - 3)² + 27 -25

= -3(x - 3)² + 2

32) y= -3x² - 18x - 25

    = -3 (x² + 6x )-25

  = -3 (x² + 6x + 9 - 9) -25

= -3 [ (x+ 3)² - 9] -25

=-3 (x + 3)² - (-3)*9 - 25

= -3(x + 3)² + 27 - 25

= -3(x+3)² +2

Answer:

9076

Step-by-step explanation:

Answer:

The final simplification is (32p^-15).

Step-by-step explanation:

Given:

(2p^-3)^5 we have to simplify.

Property to be used:(Power rule)

Power rule states that: [tex](a^x)^y=a^x^y[/tex] ...the exponents were multiplied.

Using power rule.

We have,

⇒[tex](2p^-3)^5[/tex]          

⇒[tex](2^5)(p^-3^*5)[/tex]     ...taking exponents individually.

⇒[tex]32(p^-^1^5)[/tex]         ...[tex]2^5=2*2*2*2*2=32[/tex]

⇒[tex]32p^-^1^5[/tex]

So our final values are 32p^-15

Answer:

work is shown and pictured

Answer:

1 4/12

Step-by-step explanation: What you need to do first is make them improper fractions with the same denominator.

1 1/6 = 7/6       1 4/12 = 16/12.       Now you can make them have the same denominator. 7/6 = 14/12 and 16/12. So 1 and 4/12 is bigger.

Answer:

X=9

Step-by-step explanation:

In the picture above.

Answer:

[tex]y=-2x+3[/tex]

Step-by-step explanation:

Given the slope of line [tex]m[/tex] is [tex]-2[/tex].

And y-intercept is [tex](0,3)[/tex]

We can write the equation of line by using the slope-intercept form.

The slope-intercept from is

[tex]y=mx+b[/tex]

Where [tex]m[/tex] is the slope of line. And [tex]b[/tex] is the y-intercept.

In our problem y-intercept is given as [tex]b=3[/tex].

Plugging these we get,

[tex]y=-2x+3[/tex]

Answer:

Step-by-step explanation:

the average can be found by adding up all ur numbers and dividing by how many numbers u have

so her average test score is : (88 + 80) / 2 = 168/2 = 84 <==

To find Maddie's average test score, add up her scores (88+80=168) and divide by the number of tests (2). This gives us an average of 84.

The subject of this question is Mathematics, specifically the concept of calculating averages. To calculate Maddie's average test score, you'll need to add up the scores she received and then divide the sum by the number of tests she took.

In this case, Maddie earned an 88 on her first test and an 80 on her second test. You would add these two scores together (168), then divide by 2 (since she took 2 tests), which gives us an average of 84.

So, Maddie's average test score is 84.

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Answer:

Step-by-step explanation:

0.4 × 3.2

Convert to fraction

0.4 = 4/10 = 2/5 & 3.2 = 32/10 = 16/5

0.4 × 3.2 = 2/5 × 16/5 = 32/25 = 1.28

Without conversion you press ur calculator and you get 1.28

Answer: x=13

Step-by-step explanation:

Replace u wit y = 3x+14

6x-6(3x+14)=-24

6x-18-84 = -24

6x-102=-24

Add -102 on both sides

6x=78

Divide 6 on both side and have your answer

Answer:

Step-by-step explanation:

I've already answered this question.

Frank will plant a total of 5y + 9 vegetable seeds across his two gardens.

Frank has two gardens where he plans to plant vegetable seeds. In one garden, he will plant y vegetable seeds. In the other garden, he will plant 4y+9 seeds. To find the total number of seeds Frank is going to plant, we need to add together the number of seeds for each garden.

The total number of seeds is:

Total seeds = y + (4y + 9)

Combine like terms:

Total seeds = y + 4y + 9

Total seeds = 5y + 9

Thus, Frank will plant a total of 5y + 9 vegetable seeds across both gardens.

The percent increase is 0.53%

The percentage increase in the number of Greywolf is 90% and this can be determined by using the unitary method.

Given :

The following steps can be used in order to determine the percentage increase in the number of Greywolf:

Step 1 - The unitary method can be used in order to determine the percentage increase in the number of Greywolf.

Step 2 - According to the given data, there are previously 20 Greywolf in a wildlife park which is 100%.

Step 3 - So, let the percentage of 38 Greywolf be 'x'. So, the value of 'x' can be calculated as:

[tex]x = \dfrac{38}{20}\times 100[/tex]

[tex]x = 190\%[/tex]

Step 4 - So, the percentage increase in the number of Greywolf is:

[tex]{\rm Percentage \; Increase} = 190-100[/tex]

[tex]{\rm Percentage \; Increase} = 90\%[/tex]

The percentage increase in the number of Greywolf is 90%.

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Answer: area for circle is  πr² so πr² =28.26 and we can sub 3.14 as pi

3.14*r²=28.26 we can divide by 3.14 to get r² on it's own

r²=28.26/3.14

then we root both sides to get r on it's own

28.26/3.14=9 √9=3

and the diameter is double the radius 3*2=6 so the diameter is 6

Step-by-step explanation: