Round the answer to two decimal places

Answer:

9

Step-by-step explanation:

shorter leg = x

longer leg = x + 3

Hypotenuse = x + 6

x² + (x + 3)² = (x + 6)²

x² + x² + 6x + 9 = x² + 12x + 36

2x² + 6x + 9 = x² + 12x + 36

x²  - 6x  - 27 = 0

(x - 9) ( x + 3) = 0

x = 9 or x = -3 (rejected)

The length of the shorter leg of the right angles triangle is 9.

What is a right-angle triangle?

A triangle is said to be right-angled if one of its inner angles is 90 degrees, or if any one of its angles is a right angle. The right triangle or 90-degree triangle is another name for this triangle.

A triangle is said to be right-angled if one of its angles is exactly 90 degrees. The total of the other two angles is 90 degrees. Perpendicular and the triangle's base are the sides that make up the right angle. The longest of the three sides, the third side is known as the hypotenuse

The right triangle's three sides are interconnected. The Pythagorean Theorem explains this connection. This theorem states that in a right triangle,  [tex]h^{2} = x^{2} + y^{2}[/tex];

where, h = hypotenuse; x = perpendicular side; y = base side;

Given that:

shorter leg = x

longer leg = x + 3

Hypotenuse = x + 6

⇒x² + (x + 3)² = (x + 6)²

⇒x² + x² + 6x + 9 = x² + 12x + 36

⇒2x² + 6x + 9 = x² + 12x + 36

⇒x²  - 6x  - 27 = 0

⇒(x - 9) ( x + 3) = 0

⇒x = 9 or x = -3.

x=-3 is not possible;

Hence, The length of the shorter leg = 9.

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The answer is 2 1/4 feet.

Multiply:

1 1/2 x 1 1/2

3/2 x 3/2

9/4

2 1/4

Hope this helps!

Answer: 120 units3

Explanation: When finding the base of a prism, you must always multiply the side with the right angle. So basically, 5 is ignored because it does not have a right angle.

1st step: 3*4=12

2nd step: 12/2=6 (because the tringle which is the base is half a square)

3rd step: 6*20=120

The ending is unit 3 because it is volume. Area is unit 2 and we don't know if the prism is in cm so it is not A, or B, and D is the incorrect answer.

In conclusion:

120 units 3

Hope this helped!

Alin

Answer:

A.

C.

D.

Step-by-step explanation:

Answer:

the first, third, and the 4th

Step-by-step explanation:

Answer:

[tex]k=\frac{153}{124}[/tex]

Step-by-step explanation:

According to the Remainder Theorem; when P(y) is divided by y-a, the remainder is p(a).

The first polynomial is :

[tex]p(y)=ky^3+3y^2-3[/tex]

When p(y) is divided by y-5, the remainder is

[tex]p(5)=k(5)^3+3(5)^2-3[/tex]

[tex]p(5)=125k+75-3[/tex]

[tex]p(5)=125k+72[/tex]

When the second polynomial:

[tex]m(y)= 2y^3-5y+k[/tex] is divided by y-5.

The remainder is;

[tex]m(5)= 2(5)^3-5(5)+k[/tex]

[tex]m(5)= 225+k[/tex]

The two remainders are equal;

[tex]\implies 125k+72=225+k[/tex]

[tex]\implies 125k-k=225-72[/tex]

[tex]\implies 124k=153[/tex]

[tex]k=\frac{153}{124}[/tex]

Answer:

The cost of each kilometer driven is $0.6

Step-by-step explanation:

Let

x ------> the total distance driven on the trip (in kilometers)

y -----> the price of the rental (in dollars)

we have

(110,186) and (170,222) ----> see the table

step 1

Find the slope of the linear function

m=(222-186)/(170-110)

m=36/60

m=0.6 $/km

The slope of the linear equation is equal to the unit rate

so

The cost of each kilometer driven is $0.6

Answer:$120

Step-by-step explanation:

Answer:

[tex]\large\boxed{8425095_{10}=808E87_{16}}[/tex]

Step-by-step explanation:

You divide the given number by 16. Write the result underneath, and the rest of the division on the right.

The number in the hexadecimal system is wrote from the bottom.

10 = A, 11 = B, 12 = C, 13 = D, 14 = E, 15 = F

[tex]\begin{array}{c|c}8425095&7\\526568&8\\32910&14=E\\2056&8\\128&0\\8&8\\0\end{array}\\\\8425095_{10}=808E87_{16}[/tex]

I minimized the steps in the second part. Hope you understand

If you are looking for a line measurement then I suggest using the distance formula.  Which is [tex]\sqrt({x2-x1)^{2} +(y2-y1)^{2}  }[/tex]

Answer:

1/5

Step-by-step explanation:

2/10 chance that a pug would be selected

2/10 is simplified to 1/5

The probability that a randomly selected dog is a pug is 1/5.

Given:

There are 10 dogs at the dog park.

2 dogs are pugs.

We have to find the probability that a randomly selected dog is a pug.

We know, probability is given by:

⇒ Probability = Total number of dogs which are pug / Total number of dogs at the park

⇒ Total number of dogs which are pug = 2

⇒ Total number of dogs at the park = 10

⇒ P(pug) = 2/10

⇒ P(pug) = 1/5

Therefore, the probability that a randomly selected dog is a pug is 1/5.

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The answer is a. If the graphs of the equations were parallel lines then they would have no solutions.

Hope this helps!

If this helps you please make it brainliest.

The statement is NOT true will the graphs of the equations are parallel lines because the system has no solution. Then the correct option is A.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

This system of equations d = 5t + 2 and 2d = 4 + 10t has infinitely many solutions.

The statement is NOT true will the graphs of the equations are parallel lines because the system has no solution. Then the correct option is A.

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Answer:

132

Step-by-step explanation:

858/13=66

66*2=132

Answer: [tex]8.66in^3[/tex]

Step-by-step explanation:

The oy rocket shown is formed by a rectangular prism and a regular pyramid whose base is a square.

The volume of the rectangular prism can be calculated with:

[tex]V_{rp}=l*w*h[/tex]

Where "l" is the length, "w" is the width and "h" is the height.

You can observe that:

[tex]l=8in\\w=1in\\h=1in[/tex]

Then, you can substitute values:

[tex]V_{rp}=(8in)(1in)(1in)=8in^3[/tex]

The volume of the regular square pyramid can be calculated with:

[tex]V_p=\frac{s^2*h}{3}[/tex]

Where "s" is the lenght of a side of the base and "h" is the height of the pyramid.

You can observe in the figure that:

[tex]s=1in\\h=2in[/tex]

Substitute into the formula. Then:

[tex]V_p=\frac{(1in)^2(2in)}{3}=\frac{2}{3}in^3[/tex]

The volume of the toy rocket is the sum of the volume of the rectangular prism and the volume of the regular square pyramid. Then:

[tex]V_{toy}=8in^3+\frac{2}{3}in^3=8.66in^3[/tex]

Answer:

40

Step-by-step explanation:

Let n represent the integer. Then the increase can be written as ...

n + (-12) = 28

We can add 12 to both sides of this equation:

n + (-12) + (+12) = 28 +12

n + 0 = 40 . . . . . . -12 and 12 total to zero; 28 and 12 total to 40.

n = 40

The integer is 40.

Answer: 226200 ft

Step-by-step explanation:

Length=100 ft

Width=58 ft

Height=78 ft

(78x58x100)/2=226200 ft

I know it sounds crazy, but I'm pretty sure that's the answer.

Answer:

[tex]\large\boxed{V=226,200\ ft^3}[/tex]

Step-by-step explanation:

The formula of a volume of a prism:

[tex]V=BH[/tex]

B - area of a base

H - height

We have the triangle in the Base. The fomula of an area of a triangle:

[tex]A_\triangle=\dfrac{bh}{2}[/tex]

b - base

h - height

We have b = 58ft and h = 78ft. Substitute:

[tex]B=\dfrac{(58)(78)}{2}=(29)(78)=2,262\ ft^2[/tex]

The volume:

B = 2,262 ft², H = 100 ft. Substitute:

[tex]V=(2,262)(100)=226,200\ ft^3[/tex]

Since only 12 balls are small, each color has 25, 22 red balls are large - that leaves 3 red balls that are small. 12 small balls total less the 3 red small balls - that leaves 9 green small balls.

Answer:

A.) 12 3/4 cups

B.) 117 1/3

Step-by-step explanation:

Part A

If one serving of ice tea contains 3/4 cup of water, how much does 7 serving have?

To answer this, you must multiply 3/4 and 17

17 is the same as 17/1, so multiply the numerators and denominators

17 x 3 = 51

1 x 4 = 4

51/4 = 12 3/4

So, Leon used 51/4 or 12 3/4 cups of water

Part B

If the cooler has 88 servings of tea, how many cups of water does it have?

To solve this, divide 88 by 3/4

Dividing 88 by 3/4 is the same as multiplying 88 by 4/3.

Again, 88 is the same as 88/1 so multiply the numerators and the denominators.

88 x 4 = 352

1 x 3 = 3

352/3 = 117 1/3

So, there are 352/3 or 117 1/3 cups of water in the cooler

I hope this helps!

To make 17 servings of iced tea, Leon uses 12.75 cups of water. If the water cooler holds 88 servings of iced tea, it contains 66 cups of water.

The student is asking how to calculate the total amount of water needed for 17 servings of iced tea, with each serving using 3/4 cup of water. To find the total, we multiply the number of servings by the amount of water per serving:

17 servings times  3/4 cup/serving = 12.75 cups

For part B, to find out how many cups are in 88 servings:

88 servings times  3/4 cup/serving = 66 cups

Answer:

The number of paper clips that Crystal has is 3 and the number of paper clips that Gayle has is 14

Step-by-step explanation:

Let

x----> the number of paper clips that Crystal has

y --->   the number of paper clips that Gayle has

we know that

[tex]y=x+11[/tex] ----> equation A

[tex]x=42/y[/tex] ----> equation B

substitute equation A in equation B

[tex]x=\frac{42}{x+11} \\ \\x^{2} +11x=42\\ \\x^{2} +11x-42=0[/tex]

Solve the quadratic equation by graphing

The solution is [tex]x=3\ paper\ clips[/tex]

see the attached figure

Find the value of y

[tex]y=3+11=14\ paper\ clips[/tex]

therefore

The number of paper clips that Crystal has is 3

The number of paper clips that Gayle has is 14

Answer:

Hi! Next time attach all possible answers in media form. Check attachment for the answer. Please mark brainliest I'm trying to get to next rank, have a good day. Message me if you ever need more help.

Answer: The Electronic Funds Transfer Act is a federal law that protects consumers engaged in the transfer of funds through electronic methods. This includes the use of debit cards, automated teller machines and automatic withdrawals from a bank account.

Step-by-step explanation:

Answer: It limits liability if their debit card is stolen and used

Answer:

In 9 years, the account will be worth $1699.48

Step-by-step explanation:

Compound interest is interest calculated on the initial principal and also on the accumulated interest of previous periods of a deposit or loan. Ian invested $1.315 in savings account which earns 2.86% interest compunded quaterly.

The ammount of money the account will be worth is given by the formula:

[tex]A = P(1 + \frac{[\frac{r}{4}}{100} )^4n[/tex]

where r: Rate of annual interest = 2.86%

n: the number of years = 9

P= Principal ammount = $1315

Then A= $1699.48

I would personally choose B.

Answer:

(5,151) and (16,316) are days with equal attendance for both plays.

Step-by-step explanation:

https://brainly.com/question/8102047

The correct answer is 5,101

Answer:

h = 15 feet

Step-by-step explanation:

A right triangle is formed by the slant height, the radius of the base and h, with the slant height being the hypotenuse.

Using Pythagoras' theorem in the right triangle.

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

Since base diameter = 16 then radius = 8

h² + 8² = 17²

h² + 64 = 289 ( subtract 64 from both sides )

h² = 225 ( take the square root of both sides )

h = [tex]\sqrt{225}[/tex] = 15

The height of the given cone will be 15 feet.

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. The theorem can be used to determine how steep mountains or slopes are. To calculate the distance between an observer and a location on the ground when the observer is looking down from a tower or structure. It is mostly utilized in the construction industry.

Given, A right cone has a slant height of 17 feet, and the diameter of the base is 16 feet.

Since slant height and radius of the base makes a right-angle triangle with the base of radius and hypotenuse of the slant.

Thus, from the Pythagorean theorem:

hypotenuse² = height² + base²

In our case,

Hypotenuse = slant height = 17 feet

Base = radius of base of the cone = 16/2 = 8

Thus,

17² = height² + 8²

height² = 17² - 8²

height² = 225

height = 15 feet

Therefore, the height of the given cone will be 15 feet.

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Answer:

Step-by-step explanation:

find the volume of each figure

The correct answer is C. -3/2

Answer:

number of students with blue eyes and blond hair= 42

Number of students with grey eyes and brown hair= 5

Difference of number of kids with grey eyes and brown hair and the number of students with green eyes and black hair =6

Difference of the number of students with green eyes and blond hair and the number of students with grey eyes= 14

Answer:

15

Step-by-step explanation:

The angle in total is 90* because its a right angle.

The equation is 4x+30=90

subtract 30 from both sides

4x=60

divide 4 from both sides

x=15

hope this helped!

Answer:

15

Step-by-step explanation: 90-30=60   60÷4=15

Answer:

[tex]3 ^{1}/_{6}[/tex]

Step-by-step explanation:

6 goes into 19 3 times with a remainder of 1.

So your base number is going to be 3 with your remainder of 1 going into your numerator over the denominator of six.

ANSWER

[tex]3 \frac{1}{6} [/tex]

EXPLANATION

The given expression is :

[tex] \frac{19}{6} [/tex]

This is an improper fraction because the numerator is greater than the denominator.

To express this as a mixed number find the number of times the denominator will divide the numerator exactly and express the remainder over the denominator in simplest form.

[tex] \frac{19}{6} = 3 \frac{1}{6} [/tex]

The answer is A, A is the answer

The sampling interval would be 20, the correct option is B.

It is a type of sampling technique in which each sample has an equal probability of being chosen.

The total number of residents in the building is 80.

Random sampling is done and the residents are interviewed.

The percentage of the residents that are being interviewed is 25%.

The sampling interval has to be calculated.

The sampling interval is given by = 25 % of 80

= 25 * 80 / 100

= 20

The number of residents that were interviewed is 20.

The sampling interval is 20 people.

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Answer:

The answer would be A.

Step-by-step explanation:

This is because when you divde 120 by 10, you will be given an answer of 12. This shows that 10% of 120 is 12.

Answer:

A. What is 10% of 120?

Step-by-step explanation:

did it on edge and the other person is correct :] Hope this helps