Solve the right triangle. Round decimal answers to the nearest tenth.

Answer:

The shortest possible perimeter is: [tex]4\sqrt{15}[/tex]

Step-by-step explanation:

Given

[tex]A = 15[/tex] --- area

Required

Find the shortest possible perimeter

Area is calculated as:

[tex]A=l * b[/tex]

This gives:

[tex]l * b = 15[/tex]

Make l the subject

[tex]l=\frac{15}{b}[/tex]

Perimeter is calculated as:

[tex]P =2(l + b)[/tex]

Substitute [tex]l=\frac{15}{b}[/tex]

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

Rewrite as:

[tex]P =2(15b^{-1} + b)[/tex]

Differentiate and minimize;

[tex]P' =2(-15b^{-2} + 1)[/tex]

Minimize by equating P' to 0

[tex]2(-15b^{-2} + 1) = 0[/tex]

Divide through by 2

[tex]-15b^{-2} + 1 = 0[/tex]

[tex]-15b^{-2} = -1[/tex]

Divide through by -1

[tex]15b^{-2} = 1[/tex]

Rewrite as:

[tex]\frac{15}{b^2} = 1[/tex]

Solve for b^2

[tex]b^2 = \frac{15}{1}[/tex]

[tex]b^2 = 15[/tex]

Solve for b

[tex]b = \sqrt{15[/tex]

Recall that: [tex]P =2(\frac{15}{b} + b})[/tex]

[tex]P = 2 * (\frac{15}{\sqrt{15}} + \sqrt{15})[/tex]

[tex]P = 2 * (\sqrt{15} + \sqrt{15})[/tex]

[tex]P = 2 * (2\sqrt{15})[/tex]

[tex]P = 4\sqrt{15}[/tex]

The shortest possible perimeter is: [tex]4\sqrt{15}[/tex]

Answer:

Step-by-step explanation:

[tex](2x)^{2} +12.6^{2} =21^{2} \\\\4x^{2} +158.76=441\\\\4x^{2}441-158.76\\\\4x^{2} =282.24\\\\x^{2} =70.56\\\\x=8.4[/tex]

hope it helps....

have a great day :)

Answer:

1. possibly congruent

2. possibly congruent

3. congruent

4. similar

Step-by-step explanation:

It is impossible to tell for the first two.  In order to be congruent they must have the measurements (lengthes& angles)  for all coordinating sides and angles.  Since we don't have that info we can only guess and since the look exactly the same we can guess they are congruent.

The third one being on the graph we can tell these are congruent.

the fourth one is obviously not congruent because the side lengths are different.  We are guesing that the coordinating angles are congruent    

the question did not give enough information to properly answer the questions with confidence

Answer:

the wall is 66 inches long

Step-by-step explanation:

hope this helps :)

Answer:

4π

Step-by-step explanation:

Periodic graphs repeat the same pattern.  Here we have a cosine function which clearly repeats itself.  Start at (0, 1) and count the number of squares to the right before the graph looks the same; this occurs at (4π, 1).  x has increased from 0π to 4π.  Thus, the period is 4π.

Answer:

slope:  [tex]\frac{1}{2}[/tex]

y-intercept: (0,-3)  

Step-by-step explanation:

First, place the equation in slope-intercept form to identify the slope and y-intercept easily. Isolate the y in the equation to do this:

[tex]4y = 2x-12\\\frac{4}{4} y = \frac{2}{4} x-\frac{12}{4} \\y = \frac{1}{2} x-3[/tex]

Now that the equation is in slope-intercept form, it is much easier to find the slope and y-intercept of the equation. Remember that the slope-intercept formula is [tex]y = mx + b[/tex].

In an equation written in slope-intercept form, the [tex]m[/tex], or the coefficient of the x-term, represents the slope. So, the slope of his equation is [tex]\frac{1}{2}[/tex]. Also, the [tex]b[/tex], or the constant on the right side of the equation, represents the y-intercept. So, the y-intercept of this equation is (0,-3).  

Step-by-step explanation:

diameter = 2 × radius.

15.5 = 2 × r.

r = 15.5 ÷ 2.

r = 7.75.

volume = πr²

v = π × 7.75².

v = 188.7.

I ain't confident about the volume answer but, the diameter answer is correct.

hope it helps. :)

Answer:

-48 b

Step-by-step explanation:

Answer:

To find an answer in pi square the radius and multiply by pi

Step-by-step explanation:

To

find volume of a sphere = 4/3Πr³

Answer =17,164.2pi Am not sure but i hope its correct.

Answer:

4

Step-by-step explanation:

Answer:

4) volume =288

5) 4=r

Step-by-step explanation:

Question 4

volume=length*width*height

volume= 3*8*12

volume=288

question 5

V=pie r^2*h

144pie=pie r^2 *9

144/9=r^2

16=r^2

4=r

Answer:

hundredths place

Step-by-step explanation:

hope this helps

Answer:

hundredths' place

Step-by-step explanation:

The first digit after the decimal represents the tenths place. (In this case, it's 9) The next digit after the decimal represents the hundredths place. In this case, it's 8 !

Answer:

-64

Step-by-step explanation:

we should put -2 for j and -1 for k,

Answer:

the answer is 64

Answer:

22

Step-by-step explanation:

6^2=36

36*2=72

6*8=48

72-48=24

24-2=22

I hope this is right

Answer:

30ft

Step-by-step explanation:

Given data

Volume= 360 ft^3

Area= 12 ft^2

We know that the expression for volume is

Volume= Area*Height

Substitute

360= 12*h

h= 360/12

h= 30 ft

Hence the height of the prism is 30ft

Answer:

A or b

Step-by-step explanation:

Answer:

c= 3/4 but in decimal form it will be 0.75

Step-by-step explanation:

Answer:

The answer is 3/4.

Check the pic for explanation

thank you:)

if it is correct please mark me brainliest

Answer:

1.55 feet.

Step-by-step explanation:

From the question given above, the following data were obtained:

Angle R = 24°

Hypothenus = RS = 3.8 feet

Opposite = ST = x

The value of x can be obtained by using the sine ratio. This is illustrated below:

Sine R = Opposite / Hypothenus

Sine 24 = x / 3.8

Cross multiply

x = 3.8 × Sine 24

x = 3.8 × 0.4067

x = 1.55 feet

Thus, the Lenght ST is 1.55 feet.

Answer:

C: 1

this answer is c because the line is one the Y intercept of 1

Answer:

Y-intercept is (0,8)

Step-by-step explanation:

Firstly, we need to get the equation of the line segment

We have the general equation as;

y = mx + b

m is the slope and b is the y-intercept

So for the slope between (9,6) and (-2,-1); we have

m = (y2-y1)/(x2-x1)

m = (-1-6)/(-2-9) = -7/-11 = 7/11

Mathematically, when two lines are perpendicular, their slopes have a product of -1

Let the slope of the second line be m

m * 7/11 = -1

7m = -11

m = -11/7

The equation of the second line is;

y = mx + b

y = -11x/7 + b

The line passes through the point (3.5,2.5)

So,

2.5 = -11/7(3.5) + b

2.5 = -5.5 + b

b = 2.5 + 5.5

b = 8

so the y-intercept of the perpendicular bisector is 8

Answer:

give the full questions

Answer:

Its height would be 7 meters.

Answer:

D

Step-by-step explanation:

As,

-10 is always greater than -13

Hence, -13 < -10

Step-by-step explanation:

We can set up an average equation in the form, where x is the last score in the fourth quarter:

[tex]\frac{85 + 88 + 92 + x}{4} = 90[/tex]

[tex]85 + 88+92 + x =360\\\\x = 95[/tex]

She needs at least a 95 on the last quarter to average 90 in all four quarters.

Answer:

I agree with Cheryl.

24 ÷ 3 = 8

3 ÷ 24 = [tex]\frac{1}{8}[/tex]

Commutative property works for multiplication because when you multiply two numbers, you have repeated addition. No matter which way you add up the numbers, you will get the same result. When you divide, you are breaking up a certain number by a certain number. If they are not the same number, you will get a different result.

Answer:

i actually dont know my guy, sorry im also stuck on this one.

Step-by-step explanation:

jp

it 2 my favorite person on the world!

u sure are funny

Answer:

1+1=11

Step-by-step explanation:

I'm sure EVERYONE knows that lol

b is cheaperrrrrrrrrrrrrrrrrrrrrrrrrrrrr

Answer:

Subtract 2 pi*r^2 from either side of the equation giving you 

S - 2 * pi *r^2 = 2 * pi * r * h

Divide by 2 pi * r on either side of the equation which would give us

h = ( S - 2 pi r^2) / 2 pi r

We have made h the height of the surface cylinder when the formula of the surface area of a cylinder was presented to us.

The formula for h is [tex]\frac{s-2\pi r^{2} }{2\pi r}[/tex]

Given the formula for Surface area of cyclinder

S A = 2pir^2 + 2pirh,

where r is the radius of the base of the cylinder and h is the height of the cylinder.

We need to find h from the given formula

What is Surface area of cyclinder?

Surface Area = 2pir^2 + 2pirh,

Surface Area(S) = 2pir^2 + 2pirh,

S = 2×pi×r×r + 2×pi×r×h

Take  2×pi×r common

S = (2×pi×r)(r + h)

Divide both sides by 2×pi×r

S/(2×pi×r) = r + h

Shift r to left side to get h

S/(2×pi×r) - r =h

Therefore h = ( S - 2 pi r^2) / 2 pi r

To learn more about surface area problems click here :

https://brainly.com/question/16226827

#SPJ2

Answer:

The second option

Step-by-step explanation:

Since root 16 is an integer (4), the second option produces the fraction 4/5 which is rational.

Answer:

area of rectangle is Length×breadth.....so area=l×b