The length of a rectangular room is 5 feet greater than its width. Which of the following equations represents the area (A) of the room?
A=w+(w+5)
A=2w+2(w+5)
A=5(w+8)
A=w(w+5)
Correct Answer : D
To find the area of the room, we form an equation of find an equation relating the length and width of the rectangle. If we let the width of the room to be w, then
Width of the rectangle= w
Length of rectangle=(w+5)
Area of the rectangle, A= Length*width=(w+5)*w
A=w(w+5)
Thus, the area of the rectangular room is w(w+5).
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Correct Answer is B
Explanation
we find the value of x by applying the absolute conditions to the given equation.
First, add 2 to both sides of equation
The absolute conditions are:
If   , a>0, then u=a or u=-a
In this case a=10, which is greater 0.
The first condition becomes
Add 2 to both sides of the equation
Divide both sides by 4
The second condition becomes
Add 2 to both sides of the equation
Divide both sides by 4
Then, the value of x is 3 or -2.
Correct Answer is A
Explanation
Using a calculator to evaluate 15÷27 results in 0.5555555556. To two decimal places, the answer becomes 0.56.
Thus, 0.56 is the decimal equivalent of 15/27.
Correct Answer is A
Explanation
we need to find the portion of pizza shared by other three friends.
Two friends eat half of the pizza, which is ½
And the remaining amount of pizza,Â
Now, the other three friends share ½ amongst themselves equally. Then, each friend gets
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Correct Answer is D
Explanation
To find the area of the room, we form an equation of find an equation relating the length and width of the rectangle. If we let the width of the room to be w, then
Width of the rectangle= w
Length of rectangle=(w+5)
Area of the rectangle, A= Length*width=(w+5)*w
A=w(w+5)
Thus, the area of the rectangular room is w(w+5).
Correct Answer is D
Explanation
To find the amount of vanilla in mL, use dimensional analysis of the units of measurements.
Two ways to convert between teaspoon and mL are:
Since we are required to find the amount in mL, we use a cionverstioon that will result in mL. Inspecting the above options, we use the second option and set up an equation in way the unwanted units cancel out and leave the wanted unit we are looking for. Then,
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Correct Answer is D
Explanation
Percentages are fractions with denominator equal to 100. To convert a percent to decimal form, divide the value by 100.
The decimal form of 98.2% is 0.982.
Correct Answer is B
Explanation
We use the calculator to find the positive square root of 19, which is then multiplied by 3.
Using the calculator,
Multiplying the square root above with 3 becomes
The approximate value of 3 times the square root of 19 is 13.1.
Correct Answer is D
Explanation
In this task, we use the relation from the given scenario to compare the number of dimes to quarters.
If we let p be number of pennies in the bottle. Then,
Number of quarters in the bottle = 2p
Number of nickels in the bottle = 3p
Number of dimes in the bottle =6(3p)=18p
Now relating dimes to quarters, we have
Thus, there are 9 times as many dimes as quarters in the box.
Correct Answer is D
Explanation
We are asked to find the number of cups of flour that will be used to make 90 cookies.
First, we convert 2 ¼ into improper fraction as:
Letting x to be the number of cups of flour, we set up a proportion equation with number of cookies on numerator and number of cups of flour on the denominator becomes:
Solve the value of x by cross-products
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Thus, the number of cups of flour needed to make 90 cookies is 81/16 cups, which is equal to 5 1/16 cups.
Correct Answer is B
Explanation
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First, express Japheth’s uncle’s age in terms of Japheth’s age as follows
Japheth’s age=k
Japheth’s uncle’s age, u = 3k-10.
Thus, the relationship between Japheth’s uncle’s age to that of Japheth is u=3k-10.
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