Mod 12 Exam
Determine whether or not the triangle with the given side lengths is a right triangle.
51 feet, 14 feet, 49 feet
Don't forget to explain your reasonings

Answer:

1441.08 cubic inches

Step-by-step explanation:

Blue

V = L * W * H

L = 15

W = 9

H = 9

V = 9 * 9 * 15 =                       1215 CU IN

YELLOW

Diameter = 6

Height = 8

radius = d/2

radius = 6/2

radius = 3

Volume = pi*r^2 * h

Volume = 3.14*3^2 * 8

Volume =                                226.08    Add

                                               1441.08

Answer:

120

Step-by-step explanation:

Answer: 156mm sq for the rectangle and 100mm sq for the triangle

Answer:

12 cubic centimeter blocks are in the bottom layer

Step-by-step explanation:

(38+45)+9*2+3-59+((4/2)*3+8*5)=

83+18+3-59+(6+40)=

83+18+3-59+(6+40)=

83+18+3-59+46=

(83+18+3+46)-59=

150-59=91

I'm not sure if this is correct but it should be. Is it 4/2*3 or (4/2)³?If it is (4/2)³ the result would be 93.

Answer:

B

Step-by-step explanation:

18:48

divide both sides by 6

3:8

Answer: 24

Step-by-step explanation:

m - 15 + 15 = 9 + 15

m = 24

Answer:

6cm

Step-by-step explanation:

correct for 100 points i swear

Answer:

I think the answer is 7x+ 6a

Step-by-step explanation:

3 (x - 6) + 5 (a + 1) - 2 (4x + 2)

3 (-6x) + 5 (1a) -2 (6x)

3x + 6a + 4x

= 7x+ 6a answer!

Answer:

82 degrees

let the point where the lines cross be E

ABD angle is 108 / 2 = 54 degrees

CAB angle is 56 / 2 = 28 degrees

the missing angle in ABE triangle is 180-54-28=98 degrees. angle x is 180 - 98 = 82

Answer:

$75000

Step-by-step explanation:

Given data

Let her yearly earnings be x

so

40% of x= $30000

40/100*x=30000

0.4x=30000

x=30000/0.4

=$75000

Hence the total amount made per years is

$75000

Answer:

a) Smallest line that can be made with each color = 300 cm

b) Total strips should be used = 47 strips

c) Total strips used of blue color = 20

  Total strips used of green color = 15

  Total strips used of red color = 12

Step-by-step explanation:

Given - To decorate a wall, there are 15 cm blue, 20 cm green, and 25 cm red strips of paper. On the wall you want to build three lines of the same size, one of each color and without cutting any strip.

To find - a) How long is the smallest line that can be made with each color?

              b) How many strips should be used?

              c) How many of each color?

Proof -

a)

For the smallest line that can be made with each color, we just have to find the lcm (least common multiple) of the 3 srtips.

Firstly,

Decompose the 3 strips to its prime factors , we get

15 = 3×5

20 = 2²×5

25 = 5²

So,

The Lcm(15, 20, 25) = 3×2²×5² = 3×4×25 = 300

∴ we get

Smallest line that can be made with each color = 300 cm

b)

Now,

Total strips used = 300 cm

Strips used by 15 cm blue = [tex]\frac{300}{15}[/tex] = 20 strips

Strips used by 20 cm green = [tex]\frac{300}{20}[/tex] = 15 strips

Strips used by 25 cm red = [tex]\frac{300}{25}[/tex] = 12 strips

So,

Total strips should be used = 20 + 15 + 12 = 47 strips

c)

Total strips used of blue color = 20

Total strips used of green color = 15

Total strips used of red color = 12

Answer:

Use rules of logarithms to expand.

Undefined!

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

(9 + 3 )× 3 / 2 = 12×3 / 2 = 6×3 = 18

Answer:

I think that J would be the answer , It is more reliable than the left ones .

Hope it was helpful , good luck ^^

Answer:

4/5

Step-by-step explanation:

Convert 1 3/5 into improper fraction

1 3/5 -> 8/5

1/2x8/5= 8/10

8/10= 4/5

Given:

Focus of a parabola = [tex]\left(1,\dfrac{1}{2}\right)[/tex]

Directrix: [tex]y=3[/tex]

To find:

The equation of the parabola.

Solution:

The equation of a vertical parabola is:

[tex]y-k=\dfrac{1}{4a}(x-h)^2[/tex]            ...(A)

Where, [tex](h,k)[/tex] is center, [tex](h,k+a)[/tex] is focus and [tex]y=k-a[/tex] is the directrix.

On comparing the focus, we get

[tex](h,k+a)=\left(1,\dfrac{1}{2}\right)[/tex]

[tex]h=1[/tex]

[tex]k+a=\dfrac{1}{2}[/tex]           ...(i)

On comparing the directrix, we get

[tex]k-a=3[/tex]              ...(ii)

Adding (i) and (ii), we get

[tex]2k=\dfrac{7}{2}[/tex]

[tex]k=\dfrac{7}{4}[/tex]

Putting [tex]k=\dfrac{7}{4}[/tex] is (i), we get

[tex]\dfrac{7}{4}+a=\dfrac{1}{2}[/tex]

[tex]a=\dfrac{1}{2}-\dfrac{7}{4}[/tex]

[tex]a=\dfrac{-5}{4}[/tex]

Putting [tex]a=\dfrac{-5}{4},h=1,k=\dfrac{7}{4}[/tex] in (A), we get

[tex]y-\dfrac{7}{4}=\dfrac{1}{4\times \dfrac{-5}{4}}(x-1)^2[/tex]

[tex]y-\dfrac{7}{4}=\dfrac{-1}{5}(x^2-2x+1)[/tex]

[tex]y-\dfrac{7}{4}=-\dfrac{1}{5}(x^2)-\dfrac{1}{5}(-2x)-\dfrac{1}{5}(1)[/tex]

[tex]y=-\dfrac{1}{5}x^2+\dfrac{2}{5}x-\dfrac{1}{5}+\dfrac{7}{4}[/tex]

On further simplification, we get

[tex]y=-\dfrac{1}{5}x^2+\dfrac{2}{5}x+\dfrac{35-4}{20}[/tex]

[tex]y=-\dfrac{1}{5}x^2+\dfrac{2}{5}x+\dfrac{31}{20}[/tex]

Therefore, the equation of the parabola is [tex]y=-\dfrac{1}{5}x^2+\dfrac{2}{5}x+\dfrac{31}{20}[/tex].

Note: Option C is correct but the leading coefficient should be negative.

Answer:

25+25-25=25+0=25 is your answer

Answer:

25 +25-25=25

Have a nice day!

Answer:

its most likely A

Step-by-step explanation:

Considering it goes at a steady rate with the second variable being reasonably scattered, the level of pure water would obviously go down not up,considering you are adding frogs. than again i havent really reached this degree of mathematics. But through reasoning i beleive it's A

Answer:

Expected population=  1,904,308 people

Step-by-step explanation:

Giving the following information:

Present Value (PV)= 1,350,000

Number of periods (n)=  10 years

Growth rate (g)= 0.035 per year

To calculate Future Value (FV), we need to use the following formula:

FV= PV*(1 + i)^n

FV= 1,350,000*(1.035^10)

FV= 1,904,308 people

Answer:

Step-by-step explanation:

Adjecent angle: Two angles that have the same vertex and one side in common.

Vertcial angle: Pairs of opposite angles formed by intersecting lines-- vertical angles have the same measure.

The answer is in the screenshot I hope I helped.

If you want to you can give me brainliest. (Your choice :D NO Pressure)

Answer:

1/1

Step-by-step explanation:

Answer:

1. E

2. A

3. B

4. I

Step-by-step explanation:

EABI, try it out, comment if i get it right, i am so f**cking tired right now so sorry if its wrong

Answer:

7.2

Step-by-step explanation:

a^2 + b^2 = c^2

a^2 +12^2 = 14^2

a^2 = 14^2 - 12^2

a^2 = 196 - 144

a^2 = 52

a =  square root of 52 = 7.2

Answer:

4250 children.

Step-by-step explanation:

72 - 38 = 34

34 degrees = 578 people

/34                   /34

1 degree = 17 people

72 + 38 = 110

360 - 110 = 250

17 * 250 = 4250 children.

Y = ½(Z)

Step-by-step explanation:

Y = ½(Z)

Answer:

bar graph or line plot

Step-by-step explanation: