Mr. Sam's swimming pool is in the shape of a parallelogram, as shown.

What is the area of his swimming pool?
A. 189 ft²

B. 234 ft²
C. 279 ft²


D. 585 ft²

Answer: 2

Step-by-step explanation:

2 times 4 = 8

8 plus 6 = 14

14 divided by 2 = 7

7 squared = 49

49 minus 9 = 40

40 divided by 2 = 20

In this problem we convert the operations into an equation and solve it step by step until we get two possible answers. We pick the one that fits the conditions of the problem, which gives us 9 as the positive number the student had originally thought of.

Let's denote the number you are thinking of as x. Following your sequence of operations we can translate this into an equation:

(((4x + 6) / 2)² - 9) / x = 20

Solving this equation can be done step by step:

Since you mentioned that the number you thought of was positive, we disregard 0.25 (since the squared result after the first operations would be too small to subtract 9 and still divide by the original number to get 20). Therefore, the number you thought of was 9.

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Answer:

2.19

Step-by-step equation:

Answer:

Right angle triangle hypotenuse formula

c = √a²+b²

a=11

b=60

c = √11² + 60²

c = 3611

Step-by-step explanation:

I hope this helps!

(1) The numbers are 8 and 16.

(2) John have 12 nickels and 6 dimes.

Solution:

(1) Let x and y be the two numbers.

Sum of two numbers = 24

⇒ x + y = 24 – – – – (1)

One number = Other number – 8

⇒ x = y – 8 – – – – (2)

Substitute equation (2) in equation (1), we get

⇒ y – 8 + y = 24

⇒ 2y – 8 = 24

Add 8 on both side of the equation, we get

⇒ 2y = 32

Divide by 2 on both sides.

⇒ y = 16

Substitute y = 16 in equation (2)

⇒ x = 16 – 8

⇒ x = 8

Hence the numbers are 8 and 16.

(2) Let n and d be the nickels and dimes respectively.

Nickels + Dimes = 18

⇒ n + d = 18 – – – – (1)

Nickles = Dimes + 6

⇒ n = d + 6 – – – – (2)

Substitute equation (2) in equation (1), we get

⇒ d + 6 + d = 18

⇒ 2d + 6 = 18

Subtract 6 from both side of the equation.

⇒ 2d = 12

Divide by 2 on both side of the equation, we get

⇒ d = 6

Substitute d = 6 in equation (1), we get

⇒ n = 6 + 6

⇒ n = 12

Hence John have 12 nickels and 6 dimes.

Final answer:

The expression given is factored to identify common factors of 30 and 44. By identifying factors like 3, 5 (for 30) and 2, 11 (for 44), it's shown that the expression is indeed divisible by both 30 and 44.

Explanation:

The student asked to prove that the value of the expression: (518−258)(164−213−45) is divisible by 30 and 44. To approach this proof, we will simplify and factor the expression where possible to find common factors of 30 (2*3*5) and 44 (4 × 11).

First, let's factor each part of the expression:

518 = (52)9 = 259

258 = (52)8 = 516

164 = (24)4 = 216

213 remains the same

45 = (22)5 = 210

Now, we rewrite the original expression with these factors:

(259 − 516)(216 − 213 − 210)

Looking at the first parenthesis, we see that 259 and 516 have a common factor of 516, so we can factor it out:

516(25−1)(216−213−210)

Recognizing that 25−1 = 24, and that 24 is divisible by both 3 and 8 (and thus 4), we have a clear division by 30.

For the second parenthesis, we can see that 210 is a common factor:

210(26−23−1)

Again, noticing that 26−23−1 leaves us with numbers of the form 2n − 2n-k − 1, we can confirm divisibility by 2 and potentially by 4 depending on the value of n. Checking the values, 26 − 23 − 1 equals 57, which is also divisible by 3.

So the original expression has factors that include 2, 3, 5, and 11, thereby confirming that the expression is divisible by both 30 and 44.

Answer:

sum was 300000

Step-by-step explanation:

let sum of money is placed  is x rs

Term T = 3 years, rate R = 10%

Then simple interest for for 3 years is

[tex]SI= \frac{PTR}{100}\\ SI=\frac{x\times 3\times 10}{100} \\SI = 0.3x[/tex]

Sum of x will become x+0.3x = 1.3x after 3 years. now this 1.3x is kept for compound interest for two years. ie

[tex]A =P[1+R]^t\\471900=1.3x[1+\frac{10}{100} ]^2\\x=\frac{471900}{1.573} \\x=300000[/tex]

Sum was 300000

At the simple interest rate, the rate is applied only to the initial sum, while

at the compound interest, the rate is applied to the amount in the account.

Reasons:

Let P represent the sum of money invested, we have;

Where;

P = The initial sum invested

r = The simple and compound interest rate applied = 10% = 0.1

t₁ = The number of years the money is placed at simple interest = 3 years

t₂ = The number of years the money is placed at compound interest = 2 years

Therefore;

[tex]\mathbf{(P + P \times 0.1 \times 3) \times (1 + 0.01)^{2}} = 471900[/tex]

Which gives;

[tex]P \cdot (1 + 0.3 ) \times (1 .01)^{2} = 471900[/tex]

[tex]\displaystyle P =\mathbf{\frac{471900}{(1 + 0.3 ) \times (1 .01)^{2} }} \approx 355,847.466[/tex]

The sum of money invested, P ≈ Rs 355,847.466

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Answer:

$67.15

Step-by-step explanation:

79*(1-.15)

= $67.15

Answer:

The least number of people that share a birthday is 1, no matter what the size of the population is.

Step-by-step explanation:

Tricky Question

Suppose there is one person that has their birthday on Feb 02. It's perfectly possible that no one else in the city has their birthday on the same day, i.e. their birthdays are any time except Feb 02. So that person will be the only one who has that as a birthday. It's even possible that no one has a birthday on Feb 02, so the answer will be zero, but it's not possible to talk about sharing if no one is doing it, so the answer is

The least number of people that share a birthday is 1, no matter what the size of the population is.

Note: If this question is talking about probability calculations, then the matter is totally different.

Answer:

length=8+w........1

area=84square feet........2

area of rectangle =length x width

area=(8+w)x W

area=8w+w^2

84=8w+w^2

w^2+8w+(4^2)=84+(4^2)

(w+4)^2=84+16

(w+4)^2=100

√(w+4)^2=√100

w+4=±100

w+4=100 or w+4=-100

w=96 or w=-104

the answer is 96

Answer:

(0,9) for y-intercept

perp.: (-1/2)= m

y - 9 = (-1/2)x - 0

y = (-1/2)x + 9

Step-by-step explanation:

Answer:

The height of the rectangle is 4 cm.

Step-by-step explanation:

You find area by multiplying base and height.

The formula is  A=bh

so 100=25h

25 times 4 is 100

100=25*4

4cm is your answer

5(x-2)-3x+7

5x-10-3x+7

2x-10+7

2x-3

Hope this step by step process helped

Answer:

5x+10

Step-by-step explanation:

you will add 7x_2x=5x

then 4+6=10

Yo sup??

we know that the sum of all the angles of a triangle is 180

therefore

11x+7x+90=180

18x=90

x=5

exterior angle formed on the ground=180-11x

=180-55

=125

Hope this helps

Answer:   [tex]\sqrt{20}[/tex]

Work Shown:

[tex]2\sqrt{5} = \sqrt{4}*\sqrt{5}\\\\2\sqrt{5} =\sqrt{4*5} \text{ use the rule } \sqrt{x}*\sqrt{y} = \sqrt{x*y}\\\\2\sqrt{5} = \sqrt{20}[/tex]

Answer:

900

Step-by-step explanation:

You first split it up with 12x10x25 for the smaller one and you do 20x12x25 for the other

I hope this helps if you need the work i can give it to you

Answer:

←

Step-by-step explanation:

less than as 4.567 is less than 4.576

The correct symbol to use between 4.567 and 4.576 is '<', since 4.567 is less than 4.576.

The question is asking to choose the correct mathematical symbol that makes the given number sentence true. The two numbers are 4.567 and 4.576. In this case,  since 4.576 is greater than 4.567, the correct symbol would be less than ('<'). Thus, the correct number sentence is 4.567 < 4.576.

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Answer: a 3,-2

Step-by-step explanation:

When a point is rotated, it must be rotated around a center.

The coordinate of the image of (-2,-3) is (3,-2)

The point is given as:

[tex](x,y) = (-2,-3)[/tex]

The rule of 90 degrees counterclockwise rotation is:

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

So, we have:

[tex](-2,-3) \to (3,-2)[/tex]

Hence, the coordinate of the image of (-2,-3) is (a) (3,-2)

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Answer:

can you be more clear

Step-by-step explanation:

Answer:

distance is the dependent variable because it depends on the time hiked.

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

Do 25 ^ 2 = 625

Do 20 ^ 2 = 400

Because you're finding something that's nor the hypotenuse you subtract

So you do 625 - 400 = 225

Then you do the square root of 225 to get the answer

Which is 15

Answer:

15

Step-by-step explanation:

Let 'l' be the length of the other leg

Using pythagoras theorem,

25² = 20² + l²

625 = 400 + l²

225 = l²

l = 15

Answer:

528

Step-by-step explanation:

because each class has 22 students and there are 24 classes you multiply them

Answer: 528 children

Step-by-step explanation: 22 children in each class. 24 total classes.

22•24=528

Answer:

C)Rhomus

Step-by-step explanation:

a rhombus is parallel

The correct answer is option C. The shape Amily's riddle best describes is Rhombus.

Let's analyze the riddle step by step to determine which shape Amily is describing.

1. Quadrilateral: The shape has four sides.

2. All sides are parallel: This indicates that opposite sides are parallel to each other, which means the shape is a type of parallelogram.

3. 4 angles, but they are not all equal: This means that although the shape has four angles, they are not all the same measure.

Given these clues, let's evaluate each option:

A) Pentagon: This is a five-sided shape, not a quadrilateral. So, this option is incorrect.

B) Rectangle: A rectangle has four sides and opposite sides are parallel. However, all the angles in a rectangle are equal (each angle is 90 degrees). So, this option is also incorrect.

C) Rhombus: A rhombus has four sides and opposite sides are parallel. Additionally, all sides are of equal length. However, a rhombus can have angles that are not all equal (typically, it has two pairs of equal angles). Given the description, this could be a potential answer, but let’s also consider the last option.

D) Trapezoid: A trapezoid has one pair of parallel sides. However, the riddle specifies that all sides are parallel, which does not match the definition of a trapezoid.

Given that the shape described has all sides parallel and the angles are not all equal, the best match is C) Rhombus.

Answer:

Step-by-step explanation:

A i think sorry if it is wrong

The only ordered pair that can be added to make the relation a function, without repeating an x-value, is option B. (-1,-1).

The question is asking which ordered pair (x,y) makes the given set of ordered pairs a function. A function is defined as a relation where every x-value (input) is associated with exactly one y-value (output). We already have the points (2,3), (–2,5), (4,4), and (-4,5) in our set. To maintain the definition of a function, the x-value of the ordered pair we are going to add cannot be the same as any x-value already present in the set. Looking at our options:

Therefore, the only ordered pair that makes the relation a function is option B. (-1,-1).

Answer: Decolonization as a result of World War II.

Step-by-step explanation:

Answer:

The height of the pyramid is 13.3 inches

Step-by-step explanation:

Let

h ----> the height of the pyramid

b ---> the base of the square pyramid

we know that

Applying the Pythagorean Theorem

[tex]15^2=h^2+(\frac{b}{2})^2[/tex]

see the attached figure to better understand the problem

we have

[tex]b=14\ in[/tex]

substitute

[tex]15^2=h^2+(\frac{14}{2})^2[/tex]

Solve for h

[tex]225=h^2+49\\h^2=225-49\\h^2=176\\h=\sqrt{176}\ in\\h=13.3\ in[/tex]

Final answer:

To solve the equation 5(x+2)=24-2x, distribute, combine like terms, solve for x, and check the solution. The solution x = 2 satisfies the equation, so it is valid.

Explanation:

To solve the equation 5(x+2)=24-2x, we can justify each step as follows:

Distribute the 5 to the terms inside the parentheses: 5x + 10 = 24 - 2x

Combine like terms on both sides of the equation: 5x + 2x = 24 - 10

Combine the x terms: 7x = 14

Divide both sides of the equation by 7 to solve for x: x = 2

Check the solution by substituting it back into the original equation: 5(2+2) = 24 - 2(2)

Simplify the left side: 5(4) = 24 - 4

Multiply: 20 = 20

The solution x = 2 satisfies the equation, so it is valid.

Answer:x-1

Step-by-step explanation:

Angle 3 and angle 4 are supplementary angles and when added together need to equal 180 degrees.

To find angle 4 subtract angle 3 from 180.

Angle 4 = 180 - 101 = 79 degrees.

Answer:

your answer is correct

Step-by-step explanation: because each angle equals the same thing

Answer:

According to the dictionary, it is any of a large group of organic compounds occurring in foods and living tissues and including sugars, starch, and cellulose.

Answer:

Ricky hits 1202 base

Pedro hits = 1485 base

Step-by-step explanation:

Pedro + Ricky = 2687 hits

Let Ricky hits = x

So the Pedro hits will be = x + 283

( x + 283 ) + x = 2687

2 x + 283 = 2687

2 x = 2687 - 283

2 x = 2404

x = 1202

So the Ricky hits 1202 base

Pedro hits (1202 + 283) = 1485 base

Final answer:

To determine the number of hits Ricky and Pedro had, a system of equations was set up and solved. Ricky had 1202 hits, while Pedro had 1485 hits last season.

Explanation:

To solve the problem involving teammates Pedro and Ricky's base hits, we need to set up a system of equations based on the information given:

Pedro and Ricky's hits together total 2687.

Pedro had 283 more hits than Ricky.

Let's denote Ricky's hits as R and Pedro's hits as P. The two equations representing the situation are:

R + P = 2687

P = R + 283

To find the number of hits Ricky had, we can substitute the second equation into the first:

R + (R + 283) = 2687

2R + 283 = 2687

2R = 2687 - 283

2R = 2404

R = 2404 / 2

R = 1202

Now that we have Ricky's hits, we can find Pedro's hits by adding 283 to Ricky's total:

P = R + 283

P = 1202 + 283

P = 1485

Therefore, Ricky had 1202 hits, and Pedro had 1485 hits last season.