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Question:

\([6.6 \times 10^{-4} ] \) = `____`

A 0.00066

explanation

Multiplying a decimal value by 10 raised to a power is equivalent to moving the decimal point to the left or right the number of times indicated by the power.
In the case of a negative exponent, the decimal is moved to the left (this is the same as dividing by 10 a number of times).
In the case of a positive exponent, the decimal is moved to the right (this is the same as multiplying by 10 a number of times).
The negative exponent here, −4, indicates that the decimal point is to be moved to the left 4 places, \([6.6 \times 10^{-4} ] \) = 0.00066.

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A line segment is always constrained between ____

Two points

A line segment is specifically constrained by 2 points. If not constrained, it would just be a line, and lines go on in either direction for infinity.

(4x+2)(x+1)= ____

\(4 x^2+6x+2\)

This is a multiplying binomials problem. Multiply the first term in the first binomial by both terms in the second binomial: \(4 x^2+4x\)
Then multiply the second term in the first binomial by each term in the second binomial: 2x+2
Adding them all together you get:
\(4 x^2+4x+2x+2\)
\(4 x^2+6x+2\)

What is the value of this numerical expression?
\( \sqrt{ 6^2+ 8^2 } \)

10

According to the order of operations (PEMDAS; parentheses, exponents, multiplication, division, addition, subtraction), the exponents within the square root must be evaluated first, then the sum can be found, and finally, the square root can be evaluated.
The expression simplifies to: \([ \sqrt{36+64 = \sqrt{100} } = 10 ]\)

A rectangle is cut in half to create two squares that each have an area of 25. What is the perimeter of the original rectangle?

30

The correct answer is (C). The formula to find the area of a square is Side × Side. If each square has an area of 25, then each side of the square must be 5 (because 5 × 5 = 25). So the dimensions of the rectangle are 5 × 10. The perimeter is the sum of all the sides, and is therefore 5 + 10 + 5 + 10 = 30.

What is 12% of \(10^2\)

12

First find 10 x10 = 100 and then multiply by 12%.

Simplify:
\([(7 y^2+3xy-9)\)-\((2 y^2+3xy-5)] \)

\([5 y^2-4]\)

When subtracting polynomials the first step is to distribute the negative sign through the parentheses. This changes the sign on each term inside the parentheses:
\([7 y^2+3xy-9- 2y^2-3xy+5]\)
Arrange like terms next to each other (optional):
\([7 y^2-2 y^2 +3xy-3xy-9+5]\)
Combine like terms to compute the answer: \([5 y^2-4] \).

If two angles in a triangle measure 35 degrees and 47 degrees, what is the value of the third angle?

98 degrees

The interior angles of a triangle must add up to 180 degrees. 180 – 35 – 47 = 98 degrees. Thus, the last angle in the triangle must be 98 degrees.

List A consists of the numbers {2, 9, 5, 1, 13}, and list B consists of the numbers {7, 4, 12, 15, 18}. If the two lists are combined, what is the median of the combined list?

8

Recall that the median of a set of data is the value located in the middle of the data set. In the case of a data set that contains an even number of numbers, the median is the average of the two middle numbers.
Combine the 2 sets provided, and organize them in ascending order: {1, 2, 4, 5, 7, 9, 12, 13, 15, 18}.
Since there are an even number of items in the resulting list, the median is the average of the two middle numbers.
Median = (7 + 9) ÷ 2 = 8.

Choose the answer to the following problem : \( 10^7 \div 10^4\)

\(10^3\)

In a division problem like this, leave the whole number the same and subtract the exponents. \( 10^7 \div 10^4 = 10^{7-4} = 10^3 \)

In the circle seen below, what is the value of x?

8

Given any chord, if a second chord is perpendicular to that chord and also passes through the center of the circle, then the first chord must be bisected. This means the first chord has been divided into two equal halves, meaning x must also be 8.

Solve for : 4w+8 = 6w-4

6

Subtract 6w from both sides of the equation
4w+ 8- 6w = -4
-2w + 8 = -4
-2w= -12
w= 6

The volume of this box is ____.

60

The volume of a cubic rectangle is length* width*height: 3*4*5 = 60.

The equation of a line is given as: y = 3x + 5. Which of the following points does NOT lie on the line?

(3,16)

Points that lie on the line with the equation given must correctly fill in the equation. For example, answer (1,8) gives an X value of 1, from which we can calculate y = 3(1) +5 = 8. Thus, the point (1, 8) must lie on the line. Answer (3,16) does not lie on the line, because if we enter an X value of 3, then y = 3(3) + 5 = 14, which does not match with the point’s value of (3,16). Thus, answer (3,16) does not lie on the line.

Blair’s average (arithmetic mean) on two physics tests is 7. What should Blair’s score be on the next test to have an overall average of 8 for all the tests?

10

The arithmetic mean is defined as the sum of the terms divided by the number of terms. To have an overall average of 8, \([ \frac{\mathrm{7 \times 2+x} }{\mathrm{3} } = 8 ] \) then x=10.