There are (4^9)^5 ⋅ 4^0 books at the library. What is the total number of books at the library?

A pipe is leaking at 1.5 cups per day about how many gallons per week is the pipe leaking

yawa3891 [41]

1 U.S. CUP - 0.0625 U.S. GALLONS

So? Convert the cups to gallons.

7 DAYS/PER WEEK

1.5 x 7 = 10.5

So... half a cup is about 0.03125 gallons.

0.03125 + (10 x 0.0625) = ???

Drum roll please...

Plot twist: You can do it yourself.

:P

3 0

2 years ago

(3x² - 4x+8) + (-7² - 27-8)

iragen [17]

Answer:

3x^ - 4x - 76

Step-by-step explanation:

4 0

2 years ago

Help please, stuck on this one!

allochka39001 [22]

Answer:

AFCE = 30

P+Q = 11

Step-by-step explanation:

From the picture, you can see the figure can be decomposed into two identical large triangles with area 20, and 4 identical longer ones, that have to cover the remaining area 40, thus 10 each.

From that you can count the area.

Second puzzle is just trial and error.

4 0

2 years ago

What is the area of a sector with a central angle of 210 degrees and a diameter of 4.6m?

WINSTONCH [101]

Sector area = (central angle / 360) * PI * radius^2
sector area = (210 / 360) * PI * 2.3^2
sector area = (7 / 12) * PI * 5.29
sector area = 9.6944313302 
sector area = 9.7 square meters (rounded)

Source:
http://www.1728.org/radians.htm

8 0

2 years ago

Patrick has just finished building a pen for his new dog. The pen is 3 feet wider than it is long. He also built a doghouse to p

zalisa [80]

General Idea:

(i) Assign variable for the unknown that we need to find

(ii) Sketch a diagram to help us visualize the problem

(iii) Write the mathematical equation representing the description given.

(iv) Solve the equation by substitution method. Solving means finding the values of the variables which will make both the equation TRUE

Applying the concept:

Given: x represents the length of the pen and y represents the area of the doghouse

Statement 1: "The pen is 3 feet wider than it is long"

$Length \; of\; the \; pen = x\\ Width \; of\; the\; pen=x+3$

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Statement 2: "He also built a doghouse to put in the pen which has a perimeter that is equal to the area of its base"

$Area \; of\; the\; Dog \; house=y\\ Perimeter \; of\; Dog\; house=y$

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Statement 3: "After putting the doghouse in the pen, he calculates that the dog will have 178 square feet of space to run around inside the pen."

$Area \; of \; the\; Pen - Area \;of \;the\;Dog \;House=\;Space\;inside\;Pen\\ \\ x \cdot (x+3)-y=178\\ Distributing \;x\;in\;the\;left\;side\;of\;the\;equation\\ \\ x^2+3x-y=178\Rightarrow\; 1^{st}\; Equation\\$

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Statement 4: "The perimeter of the pen is 3 times greater than the perimeter of the doghouse."

$Perimeter\; of\; the\; Pen=3\; \cdot \; Perimeter\; of\; the\; Dog\; House\\ \\ 2(x \; + \; x+3)=3 \cdot y\\ Combine\; like\; terms\; inside\; the\; parenthesis\\ \\ 2(2x+3)=3y\\ Distribute\; 2\; in\; the\; left\; side\; of\; the\; equation\\ \\ 4x+6=3y\\ Subtract \; 6\; and \; 3y\; on\; both\; sides\; of\; the\; equation\\ \\ 4x+6-3y-6=3y-3y-6\\ Combine\; like\; terms\\ \\ 4x-3y=-6 \Rightarrow \; \; 2^{nd}\; Equation\\$

Conclusion:

The systems of equations that can be used to determine the length and width of the pen and the area of the doghouse is given in Option B.

$178=x^2+3x-y\\ \\ -6=4x-3y$

8 0

3 years ago

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