Abeka Algebra

Which inequalities best describe the domain and range of the part shown?

• Domain: -4 < x < 5 Range: -7 < g(x) < 6

• Domain: -7 < x < 6 Range: -4 < g(x) < 5

• Domain: -4 <= x <= 5 Range: -7 <= g(x) <= 6

• Domain: -7 <= x <= 6 Range: -4 <= g(x) <= 5

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.B.5

James is buying uniforms for the players on a volleyball team. The total cost in dollars can be found using the function c = 34.95u + 6.25, where u is the number of uniforms bought. If there are at least 8 players but not more than 12 players on the volleyball team, what is the domain of the function for this situation?

• 0 < u ≤ 12

• 0 < c ≤ 425.65

• {8, 9, 10, 11, 12}

• {285.85, 320.80, 355.75, 390.70, 425.65}

Which graph best represents a function with a domain of all real numbers less than or equal to 6?

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• 
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Tags

CCSS.8.F.A.1

CCSS.HSF.IF.B.5

Consider the system of equations 3x + 4y = 0 -3x +-4y = 2 Adding the two equations side-by-side and simplifying yields 0 = 2. Which of the following can be concluded about the system of equations?

• It has a unique solution (2, 0).

• It has exactly two solutions (2, 0) and (0, 2).

• It has infinitely many solutions.

• It has no solution.

Answer explanation

Since both sides of the equation do not equal each other, this is how you can tell that a problem has no solution.

Tags

CCSS.8.EE.C.8B

Solve for x.

• 34

• 56

• 42

• 24

Answer explanation

The sum of he measures of the interior angles of a five sided figure is 540 degrees.

4x-13+70+90+2x+10+3x+5=540

Combine like terms

9x+162=540

9x=540-162

9x=378

x=378/9

x=42

y= 3x

y= -x + 4

The solution to the system in an ordered pair is.

• (-2,5)

• (1,3)

• (3, 5)

• (0,0)

Answer explanation

The solution to these equations is the point at which the two lines intersect.

Tags

CCSS.8.EE.C.8B

On a number line, the coordinates of A and B are -3 and b, respectively. If the coordinate of the midpoint M of AB is 5, what is the value of b?

• 12

• 15

• 13

• 4

Answer explanation

If you subtract a point from the midpoint you are able to determine the length of that segment. Midpoint(M) - point of segment (A) = AM

Then use the property of midpoints:

AM=1/2(AxB)

[M is the midpoint of AB]

5-(-3) = 1/2(b-(-3)) [Substitution]

8= 1/2 (b+3)

8= 1/2b + 3/2

multiply both sides of the equation by 2

8x2=2(1/2b) + 2(3/2)

16=b + 3

16-3 = b

13 = b

Tags

CCSS.7.NS.A.1C

Refer to the graph above. The shaded region is the solution set of:

Answer explanation

Locate 2 points on the graph of the line. For example: (-1, 0) & (0,2).

Use these points to figure out the slope of the line. $\frac{y_2-y_1}{x_2-x_1}=\frac{2-0}{0-\left(-1\right)}=\frac{2}{1}$
Then, find the point that is your y-intercept, [meaning where the line intersects the y-axis] (0,2) Now we know the equation is y=2x+2.
Since the line is a solid line and not dotted, we know that it is either $\le or\ge$ .
Finally, we try one of the ordered pairs we picked with both types of inequalities.

The only one that works and matches with the shaded region is $y\le2x+2$

Tags

CCSS.HSA.REI.D.12

Given triangle ABC with vertices A(-2,-2), B(1,2), and C(4,-2) Find the Perimeter.

• 6

• 12

• 16

• 20

Answer explanation

$AB=\sqrt{\left(1-2\right)^2\ +\ \left(2-2\right)^2}$ =5
$BC=\sqrt{\left(4-1\right)^2+\left(-2-2\right)^2}$ =5
$AC=\sqrt{\left(4+2\right)^2+\left(-2+2\right)^2}$ =6
So, 5+5+6=16
The perimeter of the triangle is 16.

Tags

CCSS.HSG.GPE.B.7

What is 2/5 expressed as a percentage?

• 20%

• 50%

• 40%

• 60%