What is the area of this trapezoid?

Answer:

20[tex]\sqrt{2}[/tex]

Step-by-step explanation:

Using the rule of radicals

[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex]

Simplify

[tex]\sqrt{8}[/tex] = [tex]\sqrt{4(2)}[/tex] = [tex]\sqrt{4}[/tex] × [tex]\sqrt{2}[/tex] = 2[tex]\sqrt{2}[/tex]

Thus

6[tex]\sqrt{8}[/tex] + 8[tex]\sqrt{2}[/tex]

= 6(2[tex]\sqrt{2}[/tex] ) + 8[tex]\sqrt{2}[/tex]

= 12[tex]\sqrt{2}[/tex] + 8[tex]\sqrt{2}[/tex]

= 20[tex]\sqrt{2}[/tex]

Answer:

19,200 square feet

Step-by-step explanation:

Answer:

1. The information from the problem illustrates the number of hours flo and bryan works jointly to mow the lawn.

2. The question demonstrates the numbers of hours worked by the two individuals i.e. flo and bryan to mow the lawn. Find the numbers of hours worked i.e h=? by flo and bryan to mow the lawn.

3. H/3+h/6=1

Take LCM i.e. (2H+H)/6=1

Now add H and and move the 6 on the other side and multiply, that becomes

3H=6

Now take 3 on the other side and divide by 6, which becomes the answer i.e. H=2.

4. Variables are H and values are the hours worked.

5. The problem in this question , why the number of hours are missing which we have to find and gives it a sense that how many hours needed to mow a lawn.

6. The time takes for both of them to mow lawn is 2 hours, which is flo works more than bryan to mow a lawn.

7. If you want to check that your anser is correct put the answer in the equation, if both sides come same then the answer is correct, for instance in the same quwstion where answer is H=2. Now put H in the equation i.e.

H/3+H/6=1

2/3+2/6=1

4+2/6=1

6/6=1

1=1

Hence proved. Enjoy :)

Answer: each side is 20 yds.

Step-by-step explanation:

The formula to find the perimeter of a square is 4 × side so therefore if we divide 80 by 4 we get 20 and 20 *4 is 80.

Answer:

Step-by-step explanation:

P(x) = x^4(x -2)^3(x +1)^2 has zeros at ...

The zeros that have even multiplicity are points where the graph does NOT cross the x-axis. This is true because an even power of a number does not change sign when the sign of the number changes.

Answer: 7.48

Step-by-step explanation:

Let the missing percent be x.

The question implies: 48 = x% of 642

Which means x/100 × 642 = 48

Multiply the numerators = x × 642 = 642x

Multiply the denominators= 100 x 1 = 100

Therefore, 642x /100 = 48

Then, cross multiply:

642x = 100 x 48

642x = 4800

Divide both sides by 642 to get the value of x

x = 4800/642

x = 7.48.

Answer:

10 apples

5+5 is 10

there are 10 apples. since 5 plus 5 is ten.

a. 5²

b. 7⁴

c. 2³

d. 9⁵

Explanation:

An exponent is the number of times a number is multiplied by itself.

a. 5x5  = 5² ( five is multiplied two times)

b. 7 x 7 x 7 x 7  = 7⁴ ( seven is multiplied four times)

c. 2 x 2 x 2  = 2³ ( two is multiplied three times)

d. 9 x 9 x 9 x 9 x 9​ = 9⁵ ( nine is multiplied five times)

Final answer:

Exponential abbreviations express repeated multiplication of the same number as a base raised to a power. For example, 5x5 becomes 5², and 7x7x7x7 becomes 7⁴. This notation simplifies multiplication into a more compact and manageable form.

Explanation:

Writing Multiplications as Exponential Abbreviations

To write the given multiplications as exponential abbreviations, we look for repeated factors and express them as a base number raised to the power of how many times it occurs. Here's how to do it:

This process simplifies multiplication by using exponents to indicate the number of times a base is used as a factor.

Answer:

984 square centimeters

984 cm^2

Step-by-step explanation:

Base: 10 × 24 = 240

Rectangle Sides: 13 × 24 = 312 (×2 = 624)

Triangle Sides: 12 × 10 = 120 (÷2 ×2 = 120)

Add: 240 + 624 + 120 = 984

Answer:

30 are blue or green. If you want a fraction, it's 3/8

Step-by-step explanation:

It already states 20 are blue and 10 are green

20 + 10 = 30

and it's out of 80 marbles, so 30/80 which simplified (both divided by 10) is 3/8

Answer:

30 marbles are either blue or green

Step-by-step explanation:

To get the solution add the blue and green marbles up

20+10 = 30

30 marbles are either blue or green

Answer:

30 ounces is the lowest price

Step-by-step explanation:

30<40

Answer:

3/10

Step-by-step explanation:there are 10 marbles all together three blue ones

Answer:

[tex]\frac{3}{10}[/tex]

Step-by-step explanation:

You have 3 possibilities to get a blue marble out of 10

Step-by-step explanation:

Denominators of both the fractions are 2x and (x - 5)

Therefore,

Lowest common denominator

[tex]= 2x \times (x - 5) \\

= 2 {x}^{2} - 10x[/tex]

There are two ways to solve this problem from the given situation. I'll type out both to help give you a better understanding of this problem.

Method 1: Straightforward, yet complicated

The shaded trapezoid has two base lengths of 25 mm and 50 mm, with a height of 35 mm.

The formula for the area of a trapezoid is the following:

[tex]A=\dfrac{a+b}{2}*h[/tex]

Where a and b are the base lengths and h is the height. Substitute the dimensions of the trapezoid and the formula changes to:

[tex]= \dfrac{25+50}{2}*35[/tex]

Simplifying the equation give us:

[tex]=\dfrac{2625}{2}[/tex]

[tex]=1312.5[/tex]

The trapezoid has an area of 1312.5 mm²

Method 2: Abstract, yet simple

The parallelogram is made up from 2 congruent trapezoids, and one of them is shaded. Thus, we just need to find the area of the parallelogram and divide it by 2 to get the area of a single trapezoid, which will give us the area of the shaded region.

The area formula of a parallelogram is simple, base times height.

The base is 25+50, or 75 mm. The height is 35 mm.

Multiplying these two values gives us 2625 mm². Dividing this by 2 gives us 1312.5 mm². That's the area of a single trapezoid (half the parallelogram), which should also be the area of the shaded region.

This is the same answer we got from method 1.

Conclusion:

The answer is 1312.5 mm²

Both methods give the same answer, which means they each make sure that the other is correct. Let me know if you need any clarifications, thanks!

~ Padoru

Answer:

(20+2) (20-2) = 20² - 2²

20² - 2² = 396

Step-by-step explanation:

from the rule of the difference of two square which states thate

       (a + b)(a − b) = a² − b²

therefore, 22 can also be written as (20 + 2),

while 18 can be written as (20 -2)

therefore by the rule of the difference of two square the product of both expression will give

      (20+2) (20-2) = 20² - 2² = 400 - 4 = 396

Step-by-step explanation:

= (20 + 2) × (20 - 2)

= 22 × 18

= a^2 - b^2 = 396

= (a + b) × (a - b) = 396

From the above, a = 20 and b = 2.

Therefore,

(20^2) - (2^2) = 396.

Answer:

1 - 4x

Step-by-step explanation:

Combine like terms.

To simplify the expression, we can combine like terms.

= 1 + 3x - 7x

= 1 + (3x - 7x)

= 1 + (-4x)

= 1 - 4x

Note that this is not required but its something that should done, which is turn the equation into standard form.

= -4x + 1

Best of Luck!

Answer:

16'.

Step-by-step explanation:

A square has 4 equal  sides so it is 4 * 4' = 16'.

Answer:

$13,200

Step-by-step explanation:

1,100/100 is 11

1200*11=13,200

Answer:

The contractor charges $13,200

For 1,100 square feets

Step-by-step explanation:

To solve the problem we need to understand how to charges

Step one

Given

For each 100 square feet of roofing he charges $1,200

Hence for 1,100 square feet we can see that the charges is 11times

This is because 1100/100= 11

Step two :

Hence he charges 11 times more

Therefore his fee for 1,100 square feet is

1200*11=$13,200

Option B:

[tex]$x=\pm 2\frac{1}{2}[/tex]

Solution:

Given expression:

[tex]$3 x^{2}=18 \frac{3}{4}[/tex]

To find the value of x:

[tex]$3 x^{2}=18 \frac{3}{4}[/tex]

Convert mixed fraction into improper fraction.

[tex]$3 x^{2}= \frac{18\times 4+3}{4}[/tex]

[tex]$3 x^{2}= \frac{75}{4}[/tex]

Divide by 3 on both sides of the equation, we get

[tex]$x^{2}= \frac{25}{4}[/tex]

[tex]$ x^{2}= \frac{5^2}{2^2}[/tex]

Taking square root on both side of the equation.

[tex]$\sqrt{ x^{2}}= \sqrt{\frac{5^2}{2^2}}[/tex]

[tex]$ x=\pm \frac{5}{2}[/tex]

Convert improper fraction into mixed fraction.

[tex]$x=\pm 2\frac{1}{2}[/tex]

Hence option B is the correct answer.

Answer:

211

Step-by-step explanation:

952 + 1520 then divide by 12

Answer:

   x^2 +23x +49

Step-by-step explanation:

You know the area of a rectangle is given by the product of its length and width.

The area of the shaded region is the area of the larger rectangle with the area of the square white space subtracted.

The area of the larger rectangle is ...

  large area = (length)(width) = (x+10)(2x+5)

Multiplying this out, we find the large area to be ...

  large area = 2x^2 +5x +20x +50

  large area = 2x^2 +25x +50

The area of the square can be found the same way:

  square area = (x +1)(x +1) = x^2 +2x +1

__

Then the shaded area is the difference of these:

  shaded area = (large area) - (square area)

  shaded area = (2x^2 +25x +50) - (x^2 +2x +1)

  shaded area = 2x^2 +25x +50 -x^2 -2x -1 . . . . . . eliminate parentheses

  shaded area = x^2 +23x +49 . . . . collect terms

Answer:

what are the numbers if there are more than one number then add all numbers up

Step-by-step explanation: for example

one side of cube :5

another side: 4

another side: 8

another side: 3

add all number up 5+4+8+3=20

Answer:  2.9 inches

Step-by-step explanation:

[tex]Volume_{sphere}=\dfrac{4}{3}\pi r^3\\\\\\Given: V=13.39\\\\\\13.39=\dfrac{4}{3}\pi r^3\\\\\\\dfrac{3}{4\pi}(13.39)=r^3\\\\\\\sqrt[3]{\dfrac{3}{4\pi}(13.39)} = r\\\\\\\large\boxed{2.9=r}[/tex]

Erin's Necklace is 47.6 inch long.

Step-by-step explanation:

Hannah 's necklace is 10 1/5 inches long which means =  (50+1)/5 = 51/5

Erin's necklace is 2 2/3 times = (6+8)/3 = 14/3 longer than Hannah's

Solving for this :

Erin's necklace = [tex]14/3 *51/5[/tex]

⇒ [tex]714/15[/tex]

⇒ 47.6 Inch

Erin's Necklace is 47.6 inch long.

Answer:

13 1/3 or 40/3

Step-by-step explanation:

to find the answer you will divide 2 2/3 and 3/5

2 2/3 divided by 3/5

as my Math Teacher says you should do KFC or Keep Flip Change

the equation now is 2 2/3 times  5/3

now you should write 2 2/3 as a improper fraction

2 2/3= 8/3

8/3 times 5/3= 40/3 or 13 1/3

Answer:

13 1/3

Step-by-step explanation:

i think that is it

Answer:

D. 12 feet

Step-by-step explanation:

Perimeter of a rectangle = 2(L+W)

Where L is length and W is the width.

Given

perimeter = 82 feet

Length is 5 more than 2w

That’s L = 5 + 2w

Now substitute 5 + 2w for L in the formula above

We have

82 = 2 ( 5 + 2w + w)

Simplify the bracket

82 = 2(5 + 3w)

Distribute 2 into (5 + 3w)

82 = 2 x 5 + 2 x 3w

82 = 10 + 6w

Subtract 10 from both sides

82 - 10 = 10 - 10 + 6w

72 = 6w

Divide both sides by 6

72/6 = 6w/6

12 = w

W = 12 feet

The width of the garden is 12 feet.

To find the width of the garden, we can set up an equation using the given information. Let's say the width of the garden is 'w' feet. According to the problem, the length is 5 more than twice the width, so the length would be '2w + 5' feet. The perimeter of a rectangle is equal to twice the sum of its length and width. So, in this case, the perimeter would bec

feet. Simplifying this equation, we get 6w + 10 = 82. Solving for 'w', we subtract 10 from both sides and divide by 6, giving us w = 12 feet. Therefore, the width of the garden is 12 feet.

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Answer:

= 12 square units

Step-by-step explanation:

Please look at the photo attached below, I think it is fit with your question

To find the area, substitute the values given in the question into the formula given below.

Area = base • height

= x • h

= 3 units • 4 units

= 12 square units

Answer:

the answer is 24

Step-by-step explanation:

because if you are in study island it says 24

Answer:

10  2/3

Step-by-step explanation:

Multiply 16 by 2/3

2/3 *16

32/3

Change the improper faction to a mixed number

10 2/3 of an ounce

Answer:

10.666 Ounces

Step-by-step explanation:

16 Ounces ÷ 3 = 5.333 Ounces

5.333 Ounces × 2 = 10.666 Ounces