unit 1 test algebra 2

 Unit 1 Test Algebra 2

Answers

Answer 1
6) (-7,4) D or (4)

7) -7,0,5 A or (1)

8) 3x +5 C or (3)

9) 2 B or (2)
Answer 2

6) The solution set of the equation x² + 8x - 15 = 5x + 13 is {-7, 4}.

7) The zeroes of the expression 2x (x - 5) (x + 7) are {-7, 0, 5}.

8) The expression (x + 5) (x + 8) + (x + 5)(2x - 3) can be written as a product of (x + 5) and (3x + 5).

9) There are 2 integer solutions on the interval 0 ≤ x ≤ 10 for the equation x³ - 5x² + 2x + 13 = 5.

We have,

6)

x² + 8x - 15 = 5x + 13

Rearranging the equation:

x² + 8x - 5x - 15 - 13 = 0

x² + 3x - 28 = 0

Now, factorize the quadratic equation:

(x + 7)(x - 4) = 0

Setting each factor equal to zero:

x + 7 = 0 or x - 4 = 0

Solving for x:

x = -7 or x = 4

7)

2x (x - 5) (x + 7) = 0

Setting each factor equal to zero:

2x = 0 or x - 5 = 0 or x + 7 = 0

Solving for x:

x = 0 or x = 5 or x = -7

8)

(x + 5) (x + 8 + 2x - 3)

Simplifying the expression inside the parentheses:

(x + 5) (3x + 5)

9)

x³ - 5x² + 2x + 13 = 5

Substitute each integer value from 0 to 10 into the equation and count the number of solutions.

Substituting each integer value,

x = 0,

x³ - 5x² + 2x + 13 = 5

0 - 0 + 0 + 13 = 5

13 = 5

Not true.

Similarly,

x = 2,

x³ - 5x² + 2x + 13 = 5

8 - 20 + 4 + 13 = 5

25 - 20 = 5

5 = 5

True.

x = 4,

x³ - 5x² + 2x + 13 = 5

64 - 80 + 8 + 13 = 5

85 - 80 = 5

5 = 5

True.

There are two integer solutions:

x = 2 and x = 4.

Therefore,

The solution set of the equation x² + 8x - 15 = 5x + 13 is {-7, 4}.

The zeroes of the expression 2x (x - 5) (x + 7) are {-7, 0, 5}.

The expression (x + 5) (x + 8) + (x + 5)(2x - 3) can be written as a product of (x + 5) and (3x + 5).

There are 2 integer solutions on the interval 0 ≤ x ≤ 10 for the equation x³ - 5x² + 2x + 13 = 5.

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Related Questions

Help with a and b? Thank you

Answers

Step-by-step explanation:

 Given data:

         Cars      Vans    Others

          60          21          3

The data represents the number of cars on a single day.

Find the relative frequency;

It is the number of times an event occurs.

Here the time frame is within a day;

  Relative frequency = [tex]\frac{number of cars + number of vans + others}{number of days}[/tex]  

  Relative frequency  = 60 + 21 + 3  = 84vehicles per day

ii.

Number of vans in a week;

      Number vans  in a week  = 21van per day x 7 days  = 147vans

Which linear inequality is represented by the graph?

1 y 1/2x + 2
2 yx+2
3 y=x+2
4 y2 x + 2

Answers

Answer:

A

Step-by-step explanation:

The linear equation of inequality is y ≤ ( x/2 ) + 2

What is an Inequality Equation?

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the inequality equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

The x intercept of the equation is when y = 0

So , A ( -4 , 0 ) is the x intercept

And , the y intercept is when x = 0

So , B ( 2 , 0 ) is the y intercept

Therefore , the inequality is y ≤ ( x/2 ) + 2 and the graph is plotted

Hence , the inequality is y ≤ ( x/2 ) + 2

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PLEASEE HELP.!! ILL GIVE BRAINLIEST.!! *EXTRA POINTS* DONT SKIP:((

Answers

Answer:

okaaaay. this is 10 units to the y axis...

Step-by-step explanation:

you can use the method “rise over run”. wherever the line touches a new box is where you stop. in this case, you go up two and over one. meaning your slope is 2.

SOMEONE PLZ HELP JSJSJSNSJNSNSNSNSNNS I HAVE 30 MINS LEFT PLZ

Answers

Answer:

the answer is d. x >=4

ASAP HELP BRAINLIEST 100 POINTS PLZ PLZ PLZ HELP



Michelle is having a poster printed from a picture that is 4 inches wide by 6 inches tall. The enlarged poster is 20 inches wide and 30 inches tall. Which proportion can be used to represent the picture sizes?
StartFraction 6 over 4 EndFraction = StartFraction 20 over 30 EndFraction
StartFraction 4 over 6 EndFraction = StartFraction 20 over 30 EndFraction
StartFraction 4 over 6 EndFraction = StartFraction 30 over 20 EndFraction
StartFraction 4 over 30 EndFraction = StartFraction 6 over 20 EndFraction

Answers

Answer:

20 inches wide and 30 inches tall

Step-by-step explanation:

if the height went from 6 to 30 that means it grew by 5 so the poster would be

20 inches wide and 30 inches tall

Answer:

Start Fraction 4/6

End Fraction  20/30

A hierarchy of quadrilaterals is shown. Name the figures that complete the hierarchy. Number the figures in your response to indicate where in the diagram they belong.​

Answers

A hierarchy of quadrilaterals is shown. Name the figures that complete the hierarchy. Number the figures in your response to indicate where in the diagram they belong.

7. A checking account is
overdrawn by $10 on both Friday
and Saturday. By how much was
The account overdrawn?

Answers

20$ because 10+10 is 20
20 dollars? because if you add up the $10 for Friday and Saturday, it makes $20 dollars. I may be wrong tho.

can someone please help me with this question​

Answers

Answer:

16 the answer

Step-by-step explanation:

387/4300 as a percent

Answers

Answer:

9%

Step-by-step explanation:

Convert the fraction to a decimal, then multiply by  

100. Hope this helps!

This would equal nine percent.

Kim sold a house for $230,000 and made a 3% commission. How much money did Kim make in commission for selling the house?

Answers

Answer: kim made $6,900 in commission for selling the house

Step-by-step explanation:i took the test

What is the correct order of the steps used to derive the identity?
A.) 4, 3, 5, 1, 2
B.) 4, 5, 3, 1, 2,
C.) 3, 4, 5, 1, 2
D.) 3, 4, 1, 5, 2

Answers

The correct order of the steps used to derive the identity is (A.) 4, 3, 5, 1, 2

How to determine the correct order of step?

The trigonometry identity is given as:

tan(2x)

When the tangent formula is applied, we have:

[tex]\tan(2x) = \frac{\sin(2x)}{\cos(2x)}[/tex] --- step 4

Expand sin(2x) and cos(2x)

[tex]\tan(2x) = \frac{2\sin(x)\cos(x)}{\cos^(x) - \sin^2(x)}[/tex] --- step 3

The option from the list that obey the above order is (a) 4, 3, 5, 1, 2

Hence, the correct order of the steps used to derive the identity is (A.) 4, 3, 5, 1, 2

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Answer:

A). 4,3,5,1,2

Step-by-step explanation: on edge

Follow my Pinterest 13jadyn13

Answers

You know that seems very interesting

If the average grade of an English class rose from 70 to 80 what is the approximate percent increase

Answers

Answer:

10

Step-by-step explanation:

I need to solve 11-20 ASAP pls

Answers

In num 11 the upper level just next to 26x-3 is 36x-3 and the lower level just next to 36x-3 is 26x-3 In num 20 the lower level of v is 96degrees so they prove the paralysme

(WILL GIVE BRAINLIEST) Solve for x.
-2(-9x+5)-4x=2(x-5)-4

Simplify your answer as much as possible

Answers

Answer:

−2(−9x+5)−4x=2(x−5)−4

Step 1: Simplify both sides of the equation.

−2(−9x+5)−4x=2(x−5)−4

(−2)(−9x)+(−2)(5)+−4x=(2)(x)+(2)(−5)+−4(Distribute)

18x+−10+−4x=2x+−10+−4

(18x+−4x)+(−10)=(2x)+(−10+−4)(Combine Like Terms)

14x+−10=2x+−14

14x−10=2x−14

Step 2: Subtract 2x from both sides.

14x−10−2x=2x−14−2x

12x−10=−14

Step 3: Add 10 to both sides.

12x−10+10=−14+10

12x=−4

Step 4: Divide both sides by 12.

12x

12

=

−4

12

x= -1/3

Step-by-step explanation:

Good luck! Hope this helps! <3

Answer :

[tex]x = - \frac{1}{3} [/tex]

or you can just write x = -0.3

hope this helps!

What happens when there is an unbalanced force acting?

This is for science

Answers

When there is an unbalanced force acting on an object, it changes its speed and/or direction of motion.

Holly and Ethan decide to sell some of their books at a flea market. The booth rental costs $15, and they will sell each book for $1.50. How many books will Holly and Ethan need to sell to make a profit of exactly $30?

Answers

Answer:The answer would be 20 books divide 15 \ 1.50 equals 10 then multiply 10 by 2

Step-by-step explanation:

The number of books sold by Holly and Ethan to get a profit of $30 will be 20.

What is an expression?

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Holly and Ethan decide to sell some of their books at a flea market. The booth rental costs $15, and they will sell each book for $1.50.

The number of books will be calculated as,

1.5x = 30

x = 30 / 1.5

x = 20

Therefore, the number of books sold by Holly and Ethan to get a profit of $30 will be 20.

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Is the following relation a function?


Need answer now

Answers

Answer: No, it is not a function

If you can draw a vertical line through more than one point on the curve, then it's not a function. In this case, we can draw such a line. The graph is said to have failed the vertical line test.

What this means is that some x inputs lead to more than one y outputs. A function is only possible if any x input leads to exactly one y output. The x input must be in the domain.

Answer:

It is not a function.

Step-by-step explanation:

A relation's inputs are not repeated in a function.

Since the graph fails the vertical line test, it is not a function.

See picture.

Hope this helps.

75c- 300 - 35 c =25c + 15c + 200

Answers

Answer:

False

Step-by-step explanation:

40c - 300 = 40c + 200

-300 = 200

false

PLZ HELP! THIS IS THE LAST QUESTION! 75 PTS!!

Answers

Answer:

its b or d

Step-by-step explanation:

Answer:

its b

Step-by-step explanation:

What is the value of the expression
-1s/20r if r= -1/4 and s= 4/5?
Simplify your answer.​

Answers

Answer:

[tex]\frac{4}{25}[/tex]

Step-by-step explanation:

Given expression:

          [tex]-\frac{1s }{20r}[/tex]  

   r  = [tex]-\frac{1}{4}[/tex] , s = [tex]\frac{4}{5}[/tex]

Now;

     [tex]-\frac{1s }{20r}[/tex]    = [tex]-\frac{s}{20r}[/tex]

              Insert the parameters:

                = [tex]-\frac{\frac{4}{5} }{20 x (-\frac{1}{4} )}[/tex]  

               = - [tex]\frac{\frac{4}{5} }{-5}[/tex]  

              -x - = +

                = [tex]\frac{4}{5}[/tex] x [tex]\frac{1}{5}[/tex]

                = [tex]\frac{4}{25}[/tex]

6x^2 – 13x + 6 = 2x^2 solve using quadratic formula

Answers

Answer:

[tex]x=\frac{13\pm\sqrt{73} }{8}[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDASEquality Properties

Algebra I

Standard Form: ax² + bx + c = 0Quadratic Formula: [tex]x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]

Step-by-step explanation:

Step 1: Define equation

6x² - 13x + 6 = 2x²

Step 2: Rewrite in Standard Form

Subtract 2x² on both sides:                    4x² - 13x + 6 = 0

Step 3: Define

a = 4

b = -13

c = 6

Step 4: Solve for x/roots

Substitute:                              [tex]x=\frac{13\pm\sqrt{(-13)^2-4(4)(6)} }{2(4)}[/tex]Exponent:                               [tex]x=\frac{13\pm\sqrt{169-4(4)(6)} }{2(4)}[/tex]Multiply:                                  [tex]x=\frac{13\pm\sqrt{169-96} }{8}[/tex]Subtract:                                 [tex]x=\frac{13\pm\sqrt{73} }{8}[/tex]

And we have our final answer!

2.Yolanda is buying supplies for school. She buys n packages of pels at $1.40 per package and m pads of paper at $1.20 each. What does each term in the expression 1.4n + 1.20m represent? What does the entire expression represent? Interpret the meaning of the term 1.4n. What does the coefficient 1.4 represent? Interpret the meaning of the term 1.20p. What does the coefficient 1.20 represent?

Answers

Answer: 1.4n represents the cost of n packages of pels.

1.20m represents cost of m pads.

Entire expression 1.4n + 1.20m represents total cost of n packages of pels and m pads.

Meaning of 1.4n  =  cost of n packages of pels.

Meaning of 1.20 m = represents cost of m pads.

where , 1.4 = Cost per package of pels

1.2 =Cost per pad of paper

Step-by-step explanation:

Given: Cost per package of pels = $1.40

Cost per pad of paper = $1.20

Number of packages of pels bought = n

Number of pads of paper bought = m

So, 1.4n represents the cost of n packages of pels.

1.20m represents cost of m pads.

Entire expression 1.4n + 1.20m represents total cost of n packages of pels and m pads.

Meaning of 1.4n  =  cost of n packages of pels.

Meaning of 1.20 m = represents cost of m pads.

where , 1.4 = Cost per package of pels

1.2 =Cost per pad of paper

Help me pleaseeeeee!!!!!

Answers

Answer:

A

Step-by-step explanation:

hey can you pls help!!!​

Answers

Answer:

60/4 if i get right can i please get brainliest?

Answer:

60 miles/ 4 gallons

Step-by-step explanation:

60 divided by 4 is 15

PLEASE HELP FAST!!!!Match each description to the expression that can be used to represent it.

Answers

Mayra is the middle child of the family is a, Sakshi is 1 year older than maya is 1+a, and Amul is 2 years younger than Maya is a-2.

Answer:

The first box on the left goes to the middle box on the right! THe second box on the left goes to the first box on the right! And the last box on the left goes to the third box on the right!

Hope this helps and u understand it

Help me I don’t not understand

Answers

Sorry I couldn’t answer S,T, &F. But I hope with the other problems that I solved makes sense, in order for you to solve the other 3.

Tina has two rectangular playpens to keep her new pet dogs. The first rectangle has a width of 6 feet and a length of x - 4 feet. The second rectangle has a width of 8 feet and a length of x + 2 feet. What is the sum of the two perimeters?

Answers

Answer:

4x+24 ft.

Step-by-step explanation:

Perimeter of first rectangular playpen mentioned: 2(6+x-4), which can be simplified to 2(x+2) = 2x + 4.

Perimeter of second playpen mentioned: 2(8+x+2), which can be simplified to 2(x+10) = 2x+20.

Add these two together: 2x+4 + 2x+20 = 4x+24. Don't forget to add units: 4x+24 ft.

2x + 1 = 2x - 1 how many solutions?

Answers

Answer:

the answer is 2

Step-by-step explanation:

Find the slope of the line

Y=1/4x + 2

Answers

Answer: 14

Step-by-step explanation:

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