can someone check my answers? i'm not sure i have them all right. will fan and give a medal for help! attached below

If the surface area of the box in the diagram is 204.25 square feet, what is the value of ‘x’?

Alexandra [31]

Note: Consider x be the breadth of the box.

Given:

The surface area of the box is 204.25 square feet.

Length of the box = 10 ft

Breadth of the box = x ft

Height of the box = 6.5 ft

To find:

The value of x.

Solution:

The surface area of a cuboid is:

$SA=2(lb+bh+hl)$

Where, l is length, b is breadth and h is height of the cuboid.

Putting $SA=204.25, l=10,\ b=x,\ h=6.5$ in the above formula, we get

$204.25=2(10\times x+x\times 6.5+6.5\times 10)$

$204.25=2(10x+6.5x+65)$

$204.25=2(16.5x+65)$

Using distributive property, we get

$204.25=2(16.5x)+2(65)$

$204.25=33x+130$

$204.25-130=33x$

$74.25=33x$

Divide both sides by 33.

$\dfrac{74.25}{33}=x$

$2.25=x$

Therefore, the correct option is B.

7 0

3 years ago

1651 rounded to the nearest thousand

geniusboy [140]

Answer:

2000

nearest thousandth

if the last 3 digits are over 500 then it's rounding up

7 0

2 years ago

Evaluate the expression

nekit [7.7K]

Answer:

2

Step-by-step explanation:

2Y = 10

10 - 6 = 4

x = 2

4/2 = 2

3 0

3 years ago

Read 2 more answers

(1/27)^x-6=27 Could I please have a step by step as well? Much appreciated!

Andrei [34K]

Answer:

$x = 7$

Step-by-step explanation:

1) Use Division Distributive Property: (x/y)^a = x^a/y^a.

$\frac{1}{ {27}^{x - 8} } = 27$

2) Multiply both sides by 27^x - 8.

$1 = {27} \times 27^{1 + x - 8}$

3) Use the product rule: x^a x^b = x^a+b.

$1 = {27}^{1 + x - 8}$

4) Simplify 1 + x - 8 to x - 7.

$1 = {27}^{x - 7}$

5) Use Definition of Common Logarithm: b^a = x if and only if logb (x) = a.

$log_{27}1 = x - 7$

6) Use Change of Base Rule.

$\frac{ log_1 }{ log{27} } = x - 7$

7) Use rule of 1: log 1 = 0.

$\frac{0}{ log_{27}} = x - 7$

8) Simplify 0/log_27 to 0.

$0 = x - 7$

9) Add 7 to both sides.

$7 = x$

10) Switch sides.

$x = 7$

Therefor, the answer is x = 7.

5 0

3 years ago

Marie saved $3,000 dollars last year. She saved $600 in the month of January. What percent of the money she saved last year was

Archy [21]

Answer:

20% of the money was saved from January.

Here is the way to find percentage.

First: work out the difference (increase) between the two numbers you are comparing.

Increase = New Number - Original Number

Then: divide the increase by the original number and multiply the answer by 100.

% increase = Increase ÷ Original Number × 100.

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers