Diane wants to paint the ceiling of her restaurant. The ceiling is in the shape of a square. Its side lengths are 39 feet. Suppose each can of paint will cover 169 square feet. How many cans will she need to paint the ceiling?
The area of the square ceiling is calculated by multiplying the length of one side by itself: 39 feet * 39 feet = <<39*39=1521>>1521 square feet
To determine the number of cans needed, divide the total area to be painted by the area covered by each can: 1521 square feet / 169 square feet = <<1521/169=9>>9 cans
Diane will need 9 cans of paint to cover the ceiling. Answer: \boxed{9}.
Yoko bought 36 books. Yoko bought 9 times as many books as Chris. Let b be the number of books that Chris bought.
(a)Write an equation that relates the number of books that they bought.
Use b,36 , and 9.
(b)Find b.
(a) Since Yoko bought 9 times as many books as Chris, we can write the equation as:
36 = 9b
(b) To find b, divide both sides of the equation by 9:
36/9 = b
4 = b
Therefore, Chris bought 4 books.
for a) blank = blank x blank
For a), given that Yoko bought 9 times as many books as Chris, we can write the equation as:
36 = 9 x b
Here, b represents the number of books that Chris bought.
A circle has a diameter of 26m. What is its circumference?
Use 3.14 for , and do not round your answer. Be sure to include the correct unit in your answer.
The circumference of a circle with diameter d is given by the formula:
Circumference = π * diameter
Given that the diameter is 26m and using π = 3.14, we can calculate the circumference:
Circumference = 3.14 * 26m
Circumference = 81.64m
Therefore, the circumference of the circle is 81.64m.
Find the area of the triangle below.
Be sure to include the correct unit in your answer.
shape: 4 yd, 13yd, and 10yd
To find the area of a triangle, we can use Heron's formula.
Heron's formula states that the area of a triangle with side lengths a, b, and c is:
Area = √(s * (s - a) * (s - b) * (s - c))
Where s is the semi-perimeter of the triangle, calculated as:
s = (a + b + c) / 2
In this case, the sides of the triangle have lengths 4yd, 13yd, and 10yd.
First, we calculate the semi-perimeter:
s = (4 + 13 + 10) / 2
s = 27 / 2
s = 13.5
Now, we can calculate the area using Heron's formula:
Area = √(13.5 * (13.5 - 4) * (13.5 - 13) * (13.5 - 10))
Area = √(13.5 * 9.5 * 0.5 * 3.5)
Area = √(260.625)
Area ≈ 16.135
Therefore, the area of the triangle is approximately 16.135 square yards.
Use the calculator below to approximate 109 as a decimal to the tenths place.
Note that you must do the approximation without using a square root button.
Your answer must be within a tenth of the actual value.
To approximate 109 as a decimal to the tenths place without using a square root button, we can try to find a perfect square close to 109.
The perfect square closest to 109 is 100, which is equal to 10^2.
To find the decimal approximation to the tenths place, we can express 109 as the sum of the perfect square 100 and the remaining value:
109 = 100 + 9
So, we have 109 ≈ 100 + 9.
Now let's rewrite 9 as a decimal approximation to the tenths place, which is 0.9.
Now we can substitute this into the expression:
109 ≈ 100 + 0.9
Adding these two values, we get:
109 ≈ 100.9
Therefore, the decimal approximation of 109 to the tenths place is 100.9.
A machine at a bakery contains flour. When the machine is turned on, it begins to pour the flour out. The machine pours until it is empty, at which time it turns off.
Let y be the amount of flour (in grams) in the machine, and let x be the amount of time (in minutes) from when the machine is turned on. The equation y=-50x+300 models y as a function of x. As shown in the graph below, this model is accurate only from when the machine is turned on until it turns off. (The endpoints of the graph show when the machine is turned on and off.)
Amount of flour in the machine (grams)
y50100150200250300350400450500x123456789100
Amount of time (minutes)
Use the graph to complete each part.
(a)
The machine starts with
The machine continues to pour out flour until it has
Each value in the
(Choose one)
is an amount of flour in the machine.
(b)
The machine is turned on when the amount of time is
The machine stays on until the amount of time is
Each value in the
(Choose one)
is an amount of time since the machine was turned on.
(a) The machine starts with 300 grams of flour.
The machine continues to pour out flour until it has 0 grams left.
Each value in the y-axis is an amount of flour in the machine.
(b) The machine is turned on when the amount of time is 0 minutes.
The machine stays on until the amount of time is 6 minutes.
Each value in the x-axis is an amount of time since the machine was turned on.
Each value in the
(Choose one) domain or range
is an amount of flour in the machine.
Each value in the
(Choose one) domain or range
is an amount of time since the machine was turned on.
Each value in the domain is an amount of flour in the machine.
Each value in the range is an amount of time since the machine was turned on.