A circular playground has an area of about 1500 square feet. If the committee decides to double the radius, what is the approximate area of the new playground?

Answer:

21 feet (20.977)

Step-by-step explanation:

1. Draw a picture, it makes it much easier. Draw a right triangle with the vertical labeled 25 and the horizontal labeled X, then label the angle adjacent to the horizontal and hypotenuse 40°

2. Use tangent because X is opposite of 40 and 25 is adjacent to angle 40. the equation would be Tan40/1 = X/25

3. You then cross multiply to get 25Tan(40) = X

4 You then plug it into a calculator and get the full answer of 20.97749078, but I always round up to either 20.98 or 21 feet, whatever your teacher allows

Answer:

  [tex]\sqrt{a^2+b^2+16}\text{ units}[/tex]

Step-by-step explanation:

The distance is found using the distance formula:

  [tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}[/tex]

Then the distance from the given point to the origin is ...

  [tex]d=\sqrt{(a-0)^2+(-b-0)^2+(-4-0)^2}\\\\=\boxed{\sqrt{a^2+b^2+16}\ \dots\text{ units}}[/tex]

The width of the canyon is 315 ft.

An isosceles triangle is a triangle that has two sides of equal length. Sometimes it is specified as having exactly two sides of equal length, and sometimes as having at least two sides of equal length, the latter version thus including the equilateral triangle as a special case.

Given that, Jim owns a restaurant on the edge of a canyon. He wants to install a cable car over the canyon. He needs to know the width of the canyon. (please refer to the figure attached)

m ∠ ABC = 180°-80°  (Linear pair)

m ∠ ABC = 100°

In Δ ABC,

∠ A + ∠ B + ∠ C = 180°  (sum of interior angles of a triangle)

∠ A = 180°-(100°+40°)

∠ A = 40°

Since, ∠ A = 40° and ∠ C = 40°

Therefore, ∠ A = ∠ C

Therefore, AB = BC (Side opposite to equal angles are equal)

That means,  Δ ABC is an isosceles triangle

∵ BC = 315 ft

∴ AB = 315 ft

AB is the width of the canyon.

Hence, The width of the canyon is 315 ft.

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Answer:

3(2s + 6t + w)

Step-by-step explanation:

Since the highest GCF is 3, I divided 6s, 18t, and 3w. This equals to 3(2s + 6t + w)

Answer:

3(2s+6t+w)

Step-by-step explanation:

Answer:

B (-2, 0)

Step-by-step explanation:

put the first equation in for y in the second equation - watch the negative

2x - (x +2) = -4

2x - x -2 = -4

x = -2

plug this x back in to find y

y = -2 + 2 = 0

Answer:

B

Step-by-step explanation:

plug in the answers given into both equations to see if the statements true

y=x+2

0=(-2)+2

0=0

2x-y=-4

y=2x+4

0=2(-2)+4

0=0

Answer: 7.6, 22/7, 1.01

Step-by-step explanation:

Answer:

NOTE: Standard form is Ax+By=C

Distribute -1

5a -a +3b

Rewrite

5a +3b = -a

Multiply every term by -1 so -a will be positive

-5a -3b = a

Answer:

18 servings each pint being 1/3 serving size that 3 servings per pint 3×6 =18

[tex]\boxed{-2\left(z+5\right)+20>6\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:z<2\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:2\right)\end{bmatrix}}[/tex]

Solution:

Given inequality is:

[tex]-2(z+5)+20>6[/tex]

We have to solve the given inequality

[tex]-2\left(z+5\right)+20>6\\\\\mathrm{Subtract\:}20\mathrm{\:from\:both\:sides}\\\\-2\left(z+5\right)+20-20>6-20\\\\\mathrm{Simplify}\\\\-2\left(z+5\right)>-14[/tex]

[tex]Multiply\ both\ sides\ by\ -1\ \left(reverse\:the\:inequality\right)[/tex]

Whenever we multiply or divide an inequality by a negative number, we must flip the inequality sign

[tex]\left(-2\left(z+5\right)\right)\left(-1\right)<\left(-14\right)\left(-1\right)\\\\\mathrm{Simplify}\\\\2\left(z+5\right)<14\\\\\mathrm{Divide\:both\:sides\:by\:}2\\\\\frac{2\left(z+5\right)}{2}<\frac{14}{2}\\\\\mathrm{Simplify}\\\\z+5<7\\\\\mathrm{Subtract\:}5\mathrm{\:from\:both\:sides}\\\\z+5-5<7-5\\\\simplify\ the\ above\\\\\boxed{z < 2 }[/tex]

Thus the solution to inequality is:

[tex]-2\left(z+5\right)+20>6\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:z<2\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:2\right)\end{bmatrix}[/tex]

Answer:

20%

Step-by-step explanation:

If there are 25 marbles in the bag and 5 of them are red then you just divide 25 by 5 which is 5 which is 1/5 the 25 witch 20%

Answer:

20%

Step-by-step explanation:

Nice seeing you a year later <3

1 second = 2 megabytes

[tex]1\frac{1}{2}\ seconds=3\ megabytes[/tex]

2 seconds = 4 megabytes

Step-by-step explanation:

Given,

Time taken to download 5 megabytes = [tex]2\frac{1}{2}=\frac{5}{2}[/tex] seconds

[tex]\frac{5}{2}\ seconds = 5\ megabytes[/tex]

Multiplying both sides by [tex]\frac{2}{5}[/tex] to find unit rate

[tex]\frac{2}{5}*\frac{5}{2}\ second = \frac{2}{5}*5\\1\ second = 2\ megabytes[/tex]

1 second = 2 megabytes

[tex]1\frac{1}{2}\seconds = \frac{3}{2}\ seconds[/tex]

[tex]\frac{3}{2}\ seconds = \frac{3}{2}*2[/tex]

[tex]\frac{3}{2}\ seconds = 3\ megabytes[/tex]

[tex]1\frac{1}{2}\ seconds=3\ megabytes[/tex]

2 seconds = 2*2 megabytes

2 seconds = 4 megabytes

Keywords: fraction, multiplication

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Answer:

mean = -0.25

Step-by-step explanation:

Explanation:-

mean:- The sum of all the observations and then divided the number of observations and it is denoted by 'μ'

given data is -15 , -12 , 8 and 9

Given observations is '4' so n = 4

[tex]mean= \frac{-15-12+8+9 }{4}[/tex]

[tex]mean= \frac{-27+17}{4}[/tex]

[tex]mean = -0.25[/tex]

The mean of given data is - 0.25

The mean of -15, -12, 8, and 9 is calculated by summing the numbers to get -10 and then dividing by 4, leading to a mean of -2.5.

The mean of a set of numbers is calculated by summing up all the numbers and then dividing the total by the count of the numbers. In this case, to find the mean of -15, -12, 8, and 9, you would add these four numbers together and then divide by 4, because there are four numbers in this set.

The calculation would look like this:

(-15) + (-12) + 8 + 9 = -10

To find the mean, you would then divide -10 by the number of values in the set, which is 4:

Mean = -10 / 4 = -2.5

Therefore, the mean of the numbers -15, -12, 8, and 9 is -2.5.

Mega Moving truck is 632.102 cubic feet greater than 2-bedroom  moving truck.

Solution:

Volume of the mega moving truck = length × width × height

                                                          [tex]$=22 \frac{1}{4}\times7 \frac{7}{12}\times 8 \frac{5}{12}[/tex]

Convert mixed fraction into improper fraction.

                                                          [tex]$= \frac{22\times4+1}{4}\times \frac{7\times12+7}{12}\times \frac{8\times12+5}{12}[/tex]

                                                          [tex]$= \frac{89}{4}\times \frac{91}{12}\times \frac{101}{12}[/tex]

Volume of the mega moving truck = 1420.137 cubic ft

Volume of the 2-bedroom  moving truck = length × width × height

                                                          [tex]$=14 \frac{1}{2}\times7 \frac{7}{12}\times 7\frac{1}{6}[/tex]

Convert mixed fraction into improper fraction.

                                                          [tex]$= \frac{14\times2+1}{2}\times \frac{7\times12+7}{12}\times \frac{7\times6+1}{6}[/tex]

                                                          [tex]$= \frac{29}{2}\times \frac{91}{12}\times \frac{43}{6}[/tex]

Volume of the 2-bedroom  moving truck = 788.035 cubic ft

Difference between them = 1420.137 – 788.035

                                           = 632.102 cubic ft

Hence Mega Moving truck is 632.102 cubic feet greater than 2-bedroom  moving truck.

Answer:

35 lbs

Step-by-step explanation:

because 160-120=40-5=35. sorry if wrong

Maggie wants to the middle of the healthy range weight 130lbs should she gain.

Given that,

Maggie weighs for her height = 105lbs

Recommended weight = 120lbs

Limit for weighs not more than = 160lbs

We have to find ;

If she wanted to be in the middle of the healthy range how much weight should she gain.

According to the question,

If she wanted to be in the middle of the healthy range = Limit for weighs not more than - Recommended weight

= 160lbs - 120lbs

= 40lbs

Then,

Recommended weight - limit for weighs not more than

= 120lbs - 105lbs

= 15lbs

Difference between the weight = 40-15 = 25lbs

Therefore ,

Maggie weighs for her height + Difference between the weight = 105lbs + 25lbs = 130lbs

Hence , Maggie wants to the middle of the healthy range weight 130lbs should she gain.

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Answer:

27 paper fortune tellers

Step-by-step explanation:

fortune tellers = time

3 = 6

6 = 9

9 = 12

12 = 15

15 = 18

18 = 21

21 = 24

24 = 27

27= 30

so 30 fortune tellers will be made in 30 minutes

hope this helps!!!

Answer:

Actually, it's 25 paper fortune tellers.

Step-by-step explanation:

15 = 18

15 divided by 3 = 18 divided by 3

5 = 6

5 x 5 = 6 x 5

25 = 30

Answer:

Her weekly allowance is $8.

Step-by-step explanation:

Let the weekly allowance of Ming is $x.

If she spends half of her weekly allowance playing mini-golf and to earn more money her parents let her wash the car for $5, then the remaining amount of money that she has = [tex](\frac{x}{2} + 5)[/tex] dollars.

Now, given that [tex](\frac{x}{2} + 5) = 9[/tex]

⇒ [tex]\frac{x}{2} = 4[/tex]

⇒ x = $8

Therefore, her weekly allowance is $8. (Answer)

Answer:

300mb

Step-by-step explanation:

We can read the atmospheric pressure at an altitude of 22 kilometers can be read by tracing directly from the graph.

22 kilometers is half way between 20 kilometers and 24 kilometers on the vertical axis.

The reading is shown in the attachment.

From the reading the atmospheric pressure is about 300mb

The correct answer is A

Answer:

43.7 ft

Step-by-step explanation:

Radius of the semicircular garden is 8.5 ft .

Diameter = 8.5 × 2 = 17 ft

Circumference of the garden = [tex]\frac{1}{2}[/tex] × π × diameter = [tex]\frac{1}{2}[/tex] × π × 17 = 26.7 ft (rounded up to the nearest tenth of a foot)

Distance around the gardent = Circumference + diameter = 26.7 ft + 17 ft =  43.7 ft

Answer:

160+192+144=496

Step-by-step explanation:

120% of 160=Friday

75% of (1.2*160)=Sat

160=Thursday

Answer:

160+192+144=496

Step-by-step explanation:

120% of 160=Friday

75% of (1.2*160)=Sat

160=Thursday

Step-by-step explanation:

Answer:

Cost per Apple is $0.75

Step-by-step explanation:

Step 1:  Divide cost by the apples

$6.00 / 8 = x

$0.75 = x

Cost per Apple is $0.75

Answer:

0.75

Step-by-step explanation:

Just divide $8.00 by $6.00

Answer:

The answer is -5.

Answer:

XAE and EAY form a linear pair.

done

DE and XY are perpendicular.

XAE and DAY are vertical angles.

Step-by-step explanation:

This answer explains the mathematical concepts related to angles and lines i.e., vertical angles, perpendicular lines, complementary angles, and linear pair. Vertical angles are equivalent, perpendicular lines intersect at right angles, complementary angles sum to 90 degrees, and a linear pair of angles sum to 180 degrees.

Without the actual diagram presented in your question, I can only provide some general insights into your question which is related to angles and lines. Firstly, vertical angles are the angles opposite each other when two lines intersect. They are always equal.

Secondly, two lines are perpendicular if they intersect at a right angle(90 degrees). In terms of angles, two angles are complementary when they add up to 90 degrees. Finally, a linear pair refers to two angles that are adjacent (share a common vertex and side but have no common interior points) and whose non-common sides are opposite rays, i.e., they add up to 180 degrees.

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Answer:

Step-by-step explanation:

[tex]\frac{1}{4}*\frac{10}{9}=\frac{1*5}{2*9}=\frac{5}{18}[/tex]

The simplified fraction is 9/40.

To simplify the complex fraction 1/4 over 10/9, you can multiply both the numerator and the denominator by the reciprocal of the denominator of the complex fraction, which is 9/10. This is sometimes referred to as the skillfully chosen factor. By doing so, you are simplifying the expression by getting rid of the complex fraction structure.

Here's the step-by-step simplification:

Multiply both the numerator (1/4) and the denominator (10/9) by 9/10.

Simplifying the numerator: (1/4) * (9/10) = 9/40.

Simplifying the denominator: (10/9) * (9/10) = 1 because the nines and tens cancel out.

Now you have a simple fraction: 9/40 over 1, which is just 9/40.

The simplified fraction is 9/40. When multiplying fractions, you multiply the top numbers and divide by the bottom numbers in the fractions.

Answer: Dilation by a scale factor of 0.75

Step-by-step explanation:

Answer:

5 pounds of shrimp and 5 pounds of crawfish were purchased in the mixture.                                          

Step-by-step explanation:

We are given the following in the question:

Bobby buys 10 pounds seafood for $30.

Let x pounds of shrimp be purchased and y pounds of crawfish.

Thus, we can write,

[tex]x + y =10[/tex]

Cost of shrimp = $5 per pound

Cost of crawfish = $1 per pound

Total money spent = $30

Thus, we can write the equation,

[tex]5x + y = 30[/tex]

Solving the two equation by elimination method,

[tex]5x + y-(x+y) = 30-10\\4x = 20\\x = 5\\y = 10 - x = 10 - 5 = 5[/tex]

Thus, 5 pounds of shrimp and 5 pounds of crawfish were purchased in the mixture.

x = 5

Solution:

Given equation is [tex]x+1=\sqrt{5x+11}[/tex].

[tex]\Rightarrow x+1=\sqrt{5x+11}[/tex]

Squaring on both sides of the equation to remove the square root.

[tex]\Rightarrow (x+1)^2=(\sqrt{5x+11})^2[/tex]

[tex]\Rightarrow (x+1)^2=5x+11[/tex]

Using algebraic identity: [tex](a+b)^2=a^2+2ab+b^2[/tex]

[tex]\Rightarrow x^2+2x(1)+1^2=5x+11[/tex]

[tex]\Rightarrow x^2+2x+1=5x+11[/tex]

Combine all terms in one side of the equation.

[tex]\Rightarrow x^2+2x+1-5x-11=0[/tex]

Arrange like terms together.

[tex]\Rightarrow x^2+2x-5x+1-11=0[/tex]

[tex]\Rightarrow x^2-3x-10=0[/tex]

Now solve by factorization.

[tex]\Rightarrow x^2-5x+2x-10=0[/tex]

[tex]\Rightarrow (x^2-5x)+(2x-10)=0[/tex]

Take common terms on left side of the term.

[tex]\Rightarrow x(x-5)+2(x-5)=0[/tex]

Now, take (x – 5) common on both terms.

[tex]\Rightarrow (x+2)(x-5)=0[/tex]

⇒ x + 2 = 0 (or) x – 5 = 0

⇒ x = –2 (or) x = 5

If we put x = –2 in the given equation,

[tex]-2+1=\sqrt{5(-2)+11}[/tex]

[tex]\Rightarrow-1=1[/tex]

It is false. So, x = –2 is not true.

If we put x = 5 in the given equation,

[tex]5+1=\sqrt{5\times5+11}[/tex]

[tex]5+1=\sqrt{36}[/tex]

[tex]\Rightarrow6=6[/tex]

It is true. So, x = 5 is true.

Hence x = 5 is the solution.

Answer:

Step-by-step explanation:

A linear expression has the highest power of the variable to 1, i.e ax+b

Then only the first option is in a linear expression format

9x-2

The linear expression from the given options is 9x - 2.

Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.

Given are four expressions consisting of variable x.

Linear expressions are those expressions for which the highest degree of the variable in the expression is 1.

Look at the expressions with the power of the variable equals one and no other term in the expression has power of the variable more than 1.

The expression is 9x - 2.

In 3x² + 4x - 5, the highest degree of the variable is 2.

In 5x³ + 6x² - 7x + 8, highest degree of the variable is 3.

In 4x⁴ - 5x³ + 6x² - 7x + 8, highest degree of the variable is 4.

Hence the linear expression is 9x - 2.

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Answer:

200

Step-by-step explanation:

200 × 33% = 66 so

200 is answer

Answer:

A) 200

Step-by-step explanation:

33% of x is 66

33/100 = 66/x

33x = 6600

x = 6600/33

x = 200