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HSPT Math : Algebra

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Example Question #561 : Algebra

If X< 4 , then

|X - 12| + |X- 4|

can be rewritten as which of the following?

Possible Answers:

-2X + 16

2X-16

Correct answer:

-2X + 16

Explanation:

If X < 4 , then

X - 4 < 0 , so

|X- 4| = -(X-4)= -X + 4 .

Also,

X - 12 < 4 - 12 = -8 < 0 , so

|X- 12| = -(X-12)= -X + 12

Therefore,

|X - 12| + |X- 4|

= (-X + 4)+ (-X + 12)

= -2X + 16

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Example Question #4 : Solve Multi Step Problems With Positive And Negative Rational Numbers: Ccss.Math.Content.7.Ee.B.3

Define an operation $\bigstar$ on the set of real numbers as follows:

$a \bigstar b = \frac{a+b}{ab}$ .

$a \bigstar (-1) = 1$ . What is the value of ?

Possible Answers:

a= -2

$a = - \frac{1}{2}$

$a = \frac{1}{2}$

a= 2

Correct answer:

$a = \frac{1}{2}$

Explanation:

$a \bigstar b = \frac{a+b}{ab}$

and

$a \bigstar (-1) = 1$

$\frac{a+(-1)}{a(-1)}=1$

$\frac{a-1}{-a} = 1$

$\frac{a-1}{-a} \cdot (-a) = 1 \cdot (-a)$

a- 1 = -a

a- 1 + a +1 = -a + a +1

2a= 1

$2a \div 2 = 1 \div 2$

$a = \frac{1}{2}$

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Example Question #561 : Algebra

Solve for :

4x+6=30

Possible Answers:

x=9

x=6

x=20

x=30

Correct answer:

x=6

Explanation:

The first step to solve for is to undue the by subtracting it from both sides of the equation.

This results in having

4x=24 .

Then you must undue 4*x by dividing by on each side resulting in an answer of

24/4=6 .

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Example Question #1 : Solve Multi Step Problems With Positive And Negative Rational Numbers: Ccss.Math.Content.7.Ee.B.3

Define an operation $\bigstar$ on the set of real numbers as follows:

$a \bigstar b = \frac{ab}{a+b}$

$a \bigstar 1= -1$ . What is the value of ?

Possible Answers:

a = -2

a = -0.5

a = -1

No real value of makes this true.

Correct answer:

a = -0.5

Explanation:

$a \bigstar b = \frac{ab}{a+b}$ , so

$a \bigstar 1 = \frac{a \cdot 1 }{a+1} = \frac{a }{a+1}$

Set this equal to :

$\frac{a }{a+1} = -1$

$\frac{a }{a+1} \cdot (a+1) = -1 \cdot (a+1)$

a = -a - 1

a + a = -a - 1 + a

2a = - 1

$2a \div 2= - 1 \div 2$

a = -0.5

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Example Question #1171 : Concepts

is a number less than 24.

Which of the following gives a solution of the equation

| x + 15 | + C = 24

in terms of ?

Possible Answers:

x = C -9

x = C +9

x = C+39

x = C -39

Correct answer:

x = C -39

Explanation:

| x + 15 | + C = 24

| x + 15 | + C - C = 24 - C

| x + 15 | = 24 - C

C < 24 , so 24 - C is positive, so solutions exist; either

x + 15 = 24 - C or x + 15 = - ( 24 - C) .

We examine both cases.

x + 15 = 24 - C

x + 15 - 15= 24 - C - 15

x = 9 - C = -C + 9

x + 15 = - ( 24 - C)

x + 15 = C -24

x + 15 - 15 = C -24 - 15

x = C -39

Only x = C -39 is among the choices.

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Example Question #1171 : Concepts

x+y = -17

y+z = -34

x+z = 45

Evaluate .

Possible Answers:

y = 31

y = -48

insufficient information is given to determine the value of

y = 14

Correct answer:

y = -48

Explanation:

(x+y) + (y+z)+ (x+z)= -17 + (-34)+ 45

2x+ 2y+2z = - 6

$(2x+ 2y+2z) \div 2 = - 6 \div 2$

x+y+z = -3

(x+y+z )- (x+z ) = -3 - 45

y = -48

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Example Question #1771 : Hspt Mathematics

Axes 4

In the above diagram, which of the four points is the -intercept of the line of the equation 4x+5y = -40 ?

Possible Answers:

Correct answer:

Explanation:

The -coordinate of the -intercept of the line of an equation can be found by setting y= 0 and solving for :

4x+5y = -40

$4x+5 \cdot 0 = -40$

4x+ 0 = -40

4x= -40

$4x\div 4 = -40 \div 4$

x = -10

The -intercept is the point (-10, 0) , which is ten units left of the origin. This is the point marked in the diagram.

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Example Question #566 : Algebra

Axes 4

Refer to the above diagram. Which line has the same slope of the line of the equation 4x+6y =17 ?

Possible Answers:

Correct answer:

Explanation:

Rewrite the equation in slope-intercept form y = mx+b as follows:

4x+6y =17

4x+6y - 4x =17 - 4x

6y =- 4x+ 17

$\frac{1}{6} \cdot 6y =\frac{1}{6} \cdot (- 4x+ 17)$

$y = -\frac{4}{6}x+ \frac{17}{6}$

$y = -\frac{2}{3}x+ \frac{17}{6}$

The slope of this line is the coefficient of , which is $-\frac{2}{3}$ .

The slope of a line is its ratio of rise to run. The slopes of the four lines in the diagram are given below, with their justification shown.

Axes 4

Of the four lines, the line marked also has slope $-\frac{2}{3}$ .

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Example Question #567 : Algebra

Axes 4

Refer to the above diagram. Which line is perpendicular to the line of the equation 8x - 12y = 71 ?

Possible Answers:

Correct answer:

Explanation:

Rewrite the equation of the perpendicular line in slope-intercept form y = mx+b as follows:

8x - 12y = 71

8x - 12y- 8x = 71 - 8x

- 12y =- 8x+ 71

$-\frac{1}{12} \cdot (- 12y )= -\frac{1}{12} \cdot (- 8x+ 71)$

$y = \frac{8}{12}x - \frac{71}{12}$

$y = \frac{2}{3}x - \frac{71}{12}$

The slope of the line is the coefficient of , which is $\frac{2}{3}$ . The slope of a line perpendicular to this is the opposite of the reciprocal of $\frac{2}{3}$ , which is $-\frac{3}{2}$ .

The slope of a line is its ratio of rise to run. The slopes of the four lines in the diagram are given below, with their justification shown.

Axes 4

Of the four lines, the line marked has slope $-\frac{3}{2}$ .

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Example Question #568 : Algebra

Axes 4

Refer to the above diagram. Which of the above points is on the line of the equation y = 2x+ 7 ?

Possible Answers:

Correct answer:

Explanation:

All four points on the diagram have -coordinate , so set x= -1 in the equation to find the corresponding -coordinate:

y = 2x+ 7

y = 2(-1)+ 7 = -2 + 7 = 5

The correct point is the one with coordinates (-1, 5) . This point is one unit left and five units up from the orgin - the point at this location is .

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HSPT Math : Algebra

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #561 : Algebra

Example Question #4 : Solve Multi Step Problems With Positive And Negative Rational Numbers: Ccss.Math.Content.7.Ee.B.3

Example Question #561 : Algebra

Example Question #1 : Solve Multi Step Problems With Positive And Negative Rational Numbers: Ccss.Math.Content.7.Ee.B.3

Example Question #1171 : Concepts

Example Question #1171 : Concepts

Example Question #1771 : Hspt Mathematics

Example Question #566 : Algebra

Example Question #567 : Algebra

Example Question #568 : Algebra

All HSPT Math Resources

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