Find the area of the following figure.

252 [tex]cm^{2}[/tex]

400 [tex]cm^{2}[/tex]

312 [tex]cm^{2}[/tex]

300 [tex]cm^{2}[/tex]

Answer: In the two similar triangles, Angle 1 and Angle 4 are alternate interior angles.

Vertical angles prove that Angle 3 is congruent to angle 6.

The triangles are similar because alternate interior angles are congruent.

Step-by-step explanation:

Given:

The equation is:

[tex]3x-8y=k[/tex]

It cuts the x-axis and y- axis at the point A and B respectively.

The area of ∆AOB =12 sq.units.

To find:

The value of k.

Solution:

We have,

[tex]3x-8y=k[/tex]

Substituting [tex]x=0[/tex] to find the y-intercept.

[tex]3(0)-8y=k[/tex]

[tex]0-8y=k[/tex]

[tex]y=\dfrac{k}{-8}[/tex]

[tex]y=-\dfrac{k}{8}[/tex]

Substituting [tex]y=0[/tex] to find the x-intercept.

[tex]3x-8(0)=k[/tex]

[tex]3x-0=k[/tex]

[tex]x=\dfrac{k}{3}[/tex]

Area of a triangle is:

[tex]A=\dfrac{1}{2}\times base\times height[/tex]

The height of the ∆AOB is [tex]OB=\dfrac{k}{8}[/tex] because distance cannot be negative and the base of the ∆AOB is [tex]OA=\dfrac{k}{3}[/tex]. So, the area of the ∆AOB is:

[tex]A=\dfrac{1}{2}\times \dfrac{k}{8}\times \dfrac{k}{3}[/tex]

[tex]A=\dfrac{k^2}{48}[/tex]

It is given that, the area of ∆AOB = 12 sq.units.

[tex]\dfrac{k^2}{48}=12[/tex]

[tex]k^2=576[/tex]

[tex]k=\pm \sqrt{576}[/tex]

[tex]k=\pm 24[/tex]

Therefore, the value of k is either 24 or -24.

Answer:

Step-by-step explanation:

8 exponent 2 + 2 = 64 + 2 = 66

Answer:

8^2+2

=8*8+2 [8^2=8*8]

=64+2

=66

Step-by-step explanation:

The square of a number is equal to the number my multiplied by itself 2 times i.e. n*n=n^2. Using BODMAS (Brackets of Division, Muliplication, Addition and Subtraction), we should multiply 8 first, then add 2 to it.

Answer:

Mean = 109.4

Step-by-step explanation:

Mean = (Sum of all values)/(Number of values)

Mean = (100 + 121 + 105 + 113 + 108)/(5)

Mean = (547)/5

Mean = 109.4

Answer:

109

Step-by-step explanation:

Mean is just finding the average of the data set.

100+121+105+113+108=547, first add up all the numbers

547/5=109.4, then divide that sum by the amount of numbers in the set

Answer:a symbol, usually a letter, used to represent a number.

Step-by-step explanation:

a math process (like adding, subtracting, multiplying, or dividing)

Answer:

200

Step-by-step explanation:

[tex]\mathbb{ANSWER:}[/tex]

[tex]\sf \frac{-3-\sqrt{2} }{3\sqrt{17} }[/tex]

[tex]\sf = \frac{-3-\sqrt{2} }{3\sqrt{17} } \cdot \frac{\sqrt{17} }{\sqrt{17} }[/tex]

[tex]\sf = \boxed{\sf \frac{-3\sqrt{17} - \sqrt{34} }{51} }[/tex]

Answer:

x = 8

Step-by-step explanation:

The measures of the angles in a triangle add up to equal 180°

That being said we can create an equation to solve for x

( note that this is a right triangle indicated by the square. A right triangle has a right angle which has a measure of 90° )

180 = 90 + 5x + 5 + 5x + 5

now we solve for x using basic algebra

step 1 combine like terms

90 + 5 + 5 = 100

5x + 5x = 10

now we have 180 = 100 + 10x

step 2 subtract 100 from each side

180 - 100 = 80

100 - 100 cancels out

now we have 10x = 80

step 3 divide each side by 10

10x / 10 = x

80 / 10 = 8

we're left with x = 8

Answer:

this pdf is not downloading .

no idea what to do now .

can you give question on comments

1.) 3x

2.) area

3.) six

4.) 3/2

:)

Answer:

The height of the pyramid can be represented as

3x

The

area

of an equilateral triangle with length

The area of the hexagon base is

six

The volume of the pyramid is

3/2

Step-by-step explanation:

Answer:   6  1/8

Step-by-step explanation:

Each x on the line represents one piece of string that long. For example, since there is one x at 1/8, she cut one piece of string 1/8 ft long. So you take all the values and add them up:

1/8+2/4+2/4+2/4+2/4+5/8+3/4+3/4+7/8

then find a common denominator (so make everything over 8)

1/8+4/8+4/8+4/8+4/8+5/8+6/8+6/8+7/8    =      41/8

when you divide this, you will get 5 1/8

since theoriginal problem says she still has 1 foot leftover, you add one to get the total value when she started.

So, Emma had 6 1/8 ft string originally

Answer:A≈50.27in²

Step-by-step explanation:

Given:

The base of the prism is a right triangle with legs 1 m and 2 m.

The height of the prism is 17 m.

To find:

The volume of the given prism.

Solution:

The area of a triangle is:

[tex]Area=\dfrac{1}{2}\times base\times height[/tex]

So, the area of base of the prism is:

[tex]Area=\dfrac{1}{2}\times 1\times 2[/tex]

[tex]Area=1[/tex]

Now, the volume of the prism is:

[tex]V=Bh[/tex]

Where, B is the base area and h is the height of the prism.

Substituting [tex]B=1,h=17[/tex], we get

[tex]V=(1)(17)[/tex]

[tex]V=17[/tex]

The volume of the prism is 17 cubic m. Therefore, the correct option is (d).

Answer:

1050 ways

Step-by-step explanation:

Total Number of red balls = 5

Total Number of blue balls = 5

Total Number of white balls = 7

Number of red balls selected = 3

Number of blue balls selected = 4

Number of red balls selected = 5

Using the multiplication and combination relation :

nCr * nCr * nCr

Red balls = 5C3

Blue balls = 5C4

White balls = 7C5

Using calculator:

5C3 * 5C4 * 7C5 = 10 * 5 * 21

(10 * 5 * 21) = 1050 ways

Answer:

B.

Step-by-step explanation:

Answer:

x = number of wheelbarrow = 40

y = number of wagon = 30

Step-by-step explanation:

Let

x = number of wheelbarrow

y = number of wagon

x + y = 70 (1)

x + 4y = 160 (2)

subtract (1) from (2) to eliminate variable x

4y - y = 160 - 70

3y = 90

y = 90/3

y =30

Substitute y = 30 into (1)

x + y = 70 (1)

x + 30 = 70

x = 70 - 30

x = 40

x = number of wheelbarrow = 40

y = number of wagon = 30

Answer:

10k+15/5

Step-by-step explanation:

Answer:

58 percent is one of them

Step-by-step explanation:

105 freshman divided by 180 students total

Step-by-step explanation:

a. false

b.true

c.false

d. false

Answer:

a. False

b. True

c. True

d. False

Step-by-step explanation:

The formula for the area of a trapezoid treats the distance between the parallel sides as the height. Doing this lists the height as 4m.

You can separate a trapezoid into a rectangle with a width of 3 and a height of 4, as well as a right triangle with a width of 2 and a height of 4.

This expression is the written out portion of separating the trapezoid into a triangle and rectangle.

(3 * 4) represents the rectangle and (1/2 * 2 * 4) represents the triangle.

The area as found by the accurate expression in part C is 16.

Answer:

the total number of boxes being loaded is 1,200 trucks

Step-by-step explanation:

Given that

There are 48 boxes that should be loaded onto a truck

And, still it is required to lead 96% of the boxes onto the truck

We need to find out the total number of boxes that should be loaded

So

Since 48 boxes represent the 4% of the boxes that are loaded

So,

The total number of boxes would be

= 48 × 100 ÷ 0.04

= 1,200 trucks

Hence, the total number of boxes being loaded is 1,200 trucks

Answer:

6 gallons and 2 pints

Thank for posting the pic, it makes sense now!

Answer:

110°

Step-by-step explanation:

Since angle B is 30° and the ratio of a to b is 2:1, multiply 30 by 2 to get the measure of angle a = 60°.

Since angles a is 60° And the ratio of a to c is 3:1, divide 60 by 3 to get the measure of angle c = 20°.

add them up:

60 + 30 + 20 = 110°

Answer:

(x - 3)(x - 12)

Step-by-step explanation:

Assuming you require to factor the expression

x² - 15x + 36

Consider the factors of the constant term (+ 36) which sum to give the coefficient of the x- term (- 15)

The factors are - 3 and - 12, since

- 3 × - 12 = + 36 and - 3 - 12 = - 15 , then

x² - 15x + 36 = (x - 3)(x - 12) ← in factored form

Answer:

0.

Step-by-step explanation:

There is a total of 20 red + 14 blue + 10 purple + 28 green + 8 yellow beads which equal 80 total beads. However, she does not have any pink beads, so the probability of picking one is 0 pink beads / 80 total beads = 0.

Answer:

Step-by-step explanation:

hello : x = -0.75

Answer:

56.25 π cm^2

Step-by-step explanation:

The circumference of a circle is given by C = 2 π r

15 π = 2 π r

Divide each side by π

15 = 2r

Divide by 2

15/2 = 2r/2

7.5 = r

We want to find tha area

A = π r^2

A = π (7.5)^2

A = π 56.25

A = 56.25 π