Ms. Baube launched a water balloon from the roof of the gym. Mr. Howard filmed the launch and gave her the data for the balloon's flight. How high was the roof of the school?

Answer:

52 m

Step-by-step explanation:

a^2 + b^2 = c^2

a^2 + 39^2 = 65^2

a^2 + 1521 = 4225

4225 - 1521 = 2704

Square root of 2704 = 52

Answer:

52m

Step-by-step explanation:

as this is a right angled triangle (has a 90° angle), you can use the Pythagoras theorem to work out the missing side.

Pythagoras theorem:

[tex]a^{2} + b^{2} = c^{2}[/tex]

side A squared (labeled on diagram below)

+ side B squared

= side C squared

for this example though, we don't know the length of side B so we need to swap around the formula.

[tex]c^{2} - a^{2} = b^{2}[/tex]

replace the letters for their numbers,

[tex]65^{2} - 39^{2} = b^{2}[/tex] (calculate)

[tex]65^{2} - 39^{2} = 2704[/tex]  

2704 = b² but we want b by itself so we will square root b² (2704)

[tex]\sqrt{2704} = 52[/tex]

∴ side B = 52m (remember we were calculating in meters)

I hope this was helpful :-)

Answer:

80 feet

Step-by-step explanation:

Kindly refer to the attached image for explanations

The mapping rule for a 90° clockwise rotation is (x, y) → (–y, –x), so R ( 2, -5) becomes (-5, -2).

Point C is the image of R.

The point C is the image of R.

Here,

Point R was rotated about the origin (0,0) by 90° clockwise.

We have to find the image of R.

What is 90 degree Clockwise rotation?

To rotate the figure 90 degrees clockwise about a point, every point (x,y) will rotate to (y, -x).

Now,

By figure;

Point R is ( 2, -5 )

Now, Point R was rotated about the origin (0,0) by 90° clockwise.

The image of point (x, y) = (y, -x)

Hence, the image of R = (-5, -2 ) = Point C

So, by graph;

Point C is image of Point R.

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Answer: 9y = 2x is the constant proportionality of 9

Step-by-step explanation:

Answer:

9y = 2x is the constant proportionality of 9

Step-by-step explanation:

Answer:

12y + 11

Step-by-step explanation:

To add them you would add like terms. That means you would add those with y together and those without together.

8y + 4y + 6 + 5 = 12y + 11

If you want to solve for y, subtract 11 from both sides then divide both sides by 12.

Answer:

Step-by-step explanation:

hello :

(8y + 6) + (4y + 5)=12y+11

Answer:

  4 cm

Step-by-step explanation:

The ratios of sides in a 30-60-90 triangle are ...

  1 : √3 : 2

The hypotenuse is double the length of the shortest side, so is 4 cm in your triangle.

Final answer:

In a 30-60-90 triangle, if the shortest side is 2 cm, the hypotenuse is twice that length, resulting in a hypotenuse of 4 cm.

Explanation:

The 30-60-90 right triangle has sides in a specific ratio. The lengths of the sides opposite the 30°, 60°, and 90° angles are in the ratio 1:√3:2. If the shortest side is 2 cm, which is opposite the 30° angle, the hypotenuse is twice the length of the shortest side because it is opposite the 90° angle. Therefore, the length of the hypotenuse is 4 cm.

Answer:

?

Step-by-step explanation:

Answer:

x=85

Step-by-step explanation:

The angles are vertical angles, therefore they are congruent. This means we can set them equal to each other.

x+5=90

Solve for x by isolating x. To do this, subtract 5 from both sides

x+5-5=90-5

x=85

So, x=85, and the second choice is correct.

Answer:

It is 85.

Step-by-step explanation:

The angles are vertical from each other so they are equal. 85+5=90.

Answer:

168 leagues in 12 days

Step-by-step explanation:

84 : 6

if doubled, 6 x 2 = 12  and 84 x 2 = 168

168 : 12

Answer:

Step-by-step explanation:

The  " -200 "   decreases the amount owed by $200 every month

So...he pays $200 per month

Answer:

the third one down is the answer

Option C is correct, x² - 10x + 25 = 0 is the polynomial for the solution set of {5}.

Polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables

The polynomial with a solution set of {5} for the equation

x²-5x+25=0

x is the variable of the given polynomial

We know that (a-b)²=a²+b²-2ab

x²-5x+25 can be converted to (x-5)²

(x-5)² = 0

Expanding the square, we get:

x² - 10x + 25 = 0

Hence, x² - 10x + 25 = 0 is the polynomial for the solution set of {5}.

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Answer:

a

Step-by-step explanation:

Answer:

1,875 cm^3

Step-by-step explanation:

To find the volume of the big square you would multiply 20x5x20= 2,000

to find the volume of the little square you would multiply 5x5x5= 125

Then to find the Volume of the square with the hole in it you would subtract 2,000 and 125 which = 1,875 cm^3

Answer:

Could you provide more detail so that I can help. Perhaps a screenshot or photo of the problem?

Step-by-step explanation:

Answer:

1. 1.685

2. 16.828

Step-by-step explanation:

1. log_5 15

To evaluate this logarithm you use the following formula:

[tex]Log_ab=\frac{log_{10}b}{log_{10} a}[/tex]

by replacing you obtain:

[tex]log_5 15=\frac{log_{10} 15}{log_{10}5}=\frac{1.176}{0.698}=1.685[/tex]

hence, the answer is 1.685

2. -3ln(1/e4/5)

to solve this logarithm you use the following properties:

[tex]ln(a^m)=m\ ln(a)\\\\ln(\frac{a}{b})=ln(a)-ln(b)\\\\ln(e^m)=m[/tex]

[tex]ln(1)=0[/tex]

By applying all these properties you obtain:

[tex]-3ln(\frac{1}{\frac{e^4}{5}})=-3[ln(\frac{1}{e^4})-ln(5)]=-3[ln(1)-ln(e^4)-ln(5)]\\\\-3ln(\frac{1}{\frac{e^4}{5}})=-3[0-4-1.609]=16.828[/tex]

hence, the answer is 16.282

We are to find how long will it take to return to the ground?

Answer:

t = 0.48 sec

Step-by-step explanation:

We are given;

initial velocity; vi = 40 ft/s

hi = 70 ft

acceleration due to gravity; a = 32 ft/s²

Now, we are given that the rocket's height as a function of time is;

h = -12at² + vit + hi

At ground, h = 0

Plugging in the relevant values to obtain ;

0 = -12(32)t² + 40t + 70

-384t² + 40t + 70 = 0

The roots of the equation gives; t = 0.48 sec

Answer:

D. the diagonals bisect each other

Final answer:

The property of all squares is that their diagonals bisect each other. Other options are incorrect as squares have parallel and congruent sides as well as congruent angles. Therefore, the correct answer is D.

Explanation:

The question asks which of the following is a property of all squares. The correct answer is option D: The diagonals bisect each other. In every square, this property holds true, as squares are a type of rectangle, and in rectangles, the diagonals are congruent and bisect each other. We know that a square has four equal sides and four equal angles, which are right angles.

This implies that not only are the diagonals congruent, but they also divide the square into four congruent right triangles, bisecting one another at their midpoint. Options A, B, and C describe properties that are incorrect for squares, as all sides of a square are parallel and congruent, and all angles are congruent as well.

Answer:

1.5

Step-by-step explanation:

0,1,1,2,3,4 - rearrange in order

2+1=3

3/2=1.5

I hope this helps!

Answer:

1.5

Step-by-step explanation:

Arrange the data in order from least to greatest

2,3,1,1,0,4

Least to greatest:

0,1,1,2,3,4

Then, find the number in the middle

In this case, there is 2 numbers in the middle, so we will take the average of those 2

1,2

To find the average, add up the numbers and divide by the number of terms

1+2=3

3/2=1.5

1.5 is the median

Answer:

Yes. 1/10 is equal to 0.10. So 6/10 is equal to 0.60.

Answer:

A and E

Step-by-step explanation:

Answer:

a and e

Step-by-step explanation:

i got it right :)

Answer:

S is the center of the circle shown below. The correct answer choice is A.

Step-by-step explanation:

Answer:    

Answer is B

Answer:

B

Step-by-step explanation:

Answer:

400

Step-by-step explanation:

Is means equals and of means multiply

68 = 17% * what number

Change to decimal form

68 = .17 * what number

Divide each side by .17

68/.17 = .17/.17 what number

400 = what number

The number is 400

68 is approximately 17 percent of 400.

To find out what number 68 is 17% of, we can use the following formula:

(17 / 100) x = 68

Let's solve for x:

(17 / 100) x = 68

To isolate x, we can multiply both sides of the equation by (100 / 17):

x = (68 × 100) / 17

x ≈ 400

Therefore, 68 is approximately 17% of 400.

To understand this calculation, think of the percentage as a proportion or ratio. In this case, we are trying to find the ratio of 68 to the unknown number. The result, 0.17, represents how much of the unknown number 68 comprises. By multiplying this ratio by the unknown number, we obtain the value of x, which is approximately 400. Thus, 68 is roughly 17% of 400, indicating that 68 represents 17% of the value 400.

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Answer:true

Step-by-step explanation:

Answer:

Approximately: 9.63

Step-by-step explanation:

Answer:

this might be it : 12xy+228y

Step-by-step explanation:

you multiply 2 by 3 and get 6 and then multiply by 2 again and add they y

and then multiply 52 by 2 and gte 104 and them multiply by 2 and get 228 and add they y

Answer:

6xy² + 10y²z

Step-by-step explanation:

I did it and I got it right

Answer: The answer is A

Step-by-step explanation:

Because it said, 2 unshaded parts and 3 shaded parts. And you have to multiply by 2 for 2 and 3