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Anton [14]
3 years ago
8

Edgar builds a sand castle with a rectangular base. The side lengths of the base are 25 in. And 16 in. He wants to surround the

castle's base with a moat that is w inches wide. Write a quadratic function A in standard form to represent the combined area taken up by the castle and the moat.
Mathematics
1 answer:
STALIN [3.7K]3 years ago
7 0

Answer:

A=4w^2+32w+400

Step-by-step explanation:

-Given the castle dimensions is 25in by 16 in.

-And the moat's width is w:

The moat's width will increase the castle's dimension bytwice it's width, 2w:

#The castles area is thus calculated as:

A=lw\\\\=(25+2w)(16+2w)\\\\=400+80w+32w+4w^2\\\\=4w^2+32w+400

Hence, the combined area of the boat is given as A=4w^2+32w+400

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Find x in the triangle below. Round your answer to the nearest tenth.
jonny [76]

Answer:

Step-by-step explanation:

Remark

  • x is opposite the 90 degree angle. It is the hypotenuse.
  • 13 makes up the 57 degree angle. It is the side adjacent.
  • The adjacent side and the hypotenuse define the cos(theta).

Formula

cos(theta) = adjacent side / hypotenuse

Givens

Theta = 57 degrees

Hypotenuse = x

Side adjacent = 13

Solution

  • Cos(57) = 13 / x         Multiply both sides by x
  • x*cos(57) = 13           Divide by cos(theta)
  • x = 13/cos(57)
  • x = 13 / cos(57)
  • cos(57) = 0.5446
  • x = 13/ 0.5446
  • x = 23.87
6 0
3 years ago
Find the slope of the line that goes through (2, -1) and (6, 1).
Arte-miy333 [17]

Answer:

Slope= y=(1/2)x-2

Step-by-step explanation:

7 0
4 years ago
Read 2 more answers
Pls help and show working due ASAP <br> Please
olga2289 [7]

Answer:

Option B

Step-by-step explanation:

In a triangle , sum of measure of any 2 sides is always greater than the measure of the third side. So

5 + 12 > k

=  > 17 > k

Hence the measure of k is less than 17.

In the triangle , measure of the longest side is 12 cm. As we know that sum of measure of any 2 sides of triangle is greater than the measure of third side , the value of k should be more than 7cm because <u>if the value of k would be 7 , then 5 + 7 = 12 and the sum will get equal to the measure of longest side , hence such triangle wont exist.</u>

Atlast , the range of k is :-

7 < k < 17

5 0
3 years ago
What is the answer to this problem. it must be one of the four choices.
Alenkasestr [34]

The correct answer would be B. 2/(x + 8)

When you are completing composite functions, you place the entire second function in for x in the first function. Since the letter f comes first in f o g. then we start with the f(x) equation.

f(x) = 2/x

Now since g comes next, we take the entire equation for g(x) and substitute it in.

f o g = 2/(x + 8)

This is answer B.

3 0
3 years ago
Johnson bought 4 1/4 gallons of ice cream for the celebration the baseball team ate 3/4 of it how many gallons of ice cream did
mezya [45]

Answer:

They ate 0.75. I only wrote it as a decimal.

3÷4= 0.75 Hope it helps :)

Have a good day.

4 0
3 years ago
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