What type of number will result from 5/12

Question

⋅ 16−−√?
?(1 point)
Responses

Radical, because one factor is a radical.
Radical, because one factor is a radical.

Irrational, because one factor is irrational.
Irrational, because one factor is irrational.

Rational, because both numbers are rational.
Rational, because both numbers are rational.

Irrational, because both factors are irrational.

Find the product of 5–√
and 1/6
. What type of number is it?(1 point)
Responses

0.37; a rational number
0.37; a rational number

0.3726 . . . ; an irrational number
0.3726 . . . ; an irrational number

2.40; a rational number
2.40; a rational number

2.4027 . . . ; an irrational number
2.4027 . . . ; an irrational number

Use the Commutative Property of Addition to rewrite the algebraic expression:
j^3+h^4
(1 point)
_____

Use the Distributive Property to rewrite the expression (2x − 2)(x − 6).(1 point)
Responses

3x2−10x−8
3 x squared minus 10 x minus 8

2x2+10x−10
2 x squared plus 10 x minus 10

2x2−14x+12
2 x squared minus 14 x plus 12

x2−8x+12

What is (a2−11)+(3a2−4a+6)?
(1 point)
Responses

4a2−4a−5
4 A squared minus 4 A minus 5

3a2−4a−5
3 A squared minus 4 A minus 5

−4a2+4a+5
negative 4 A squared plus 4 A plus 5

−5

Multiply the polynomials (2r − 5)(r + 4).(1 point)
r2
+
r+

What is the quotient of −96x212x2?
(1 point)

Which of the following values for n makes the inequality 2n−−√<5
true?(1 point)
Responses

8
8

12.5
12.5

16
16

18

Which equation matches the solution set of {5}?(1 point)
Responses

x+x−9=1+x
x plus x minus 9 is equal to 1 plus x

3x/5+4=7
3 x over 5 plus 4 is equal to 7

x2+10=15
x squared plus 10 is equal to 15

2x−20=30

What is the value of p in the following equation? 20/p−3=5
(1 point)
Responses

7
7

5
5

1
1

3

Get ready for an amusement park day of fun! You and your family want to spend the day
at a theme park. You have pooled your money together and have $685. The tickets to the
park are $125 each and there is an online processing fee of $5.75 per ticket. You also need
to pay $20 for parking. If you have a family of five, do you have enough money to purchase
these tickets? Find an inequality to determine how many tickets can be purchased. Then find
how many tickets you are able to purchase based on your inequality. (1 point)
Responses

125t + 5.75t + 20 ≤ 685, and yes, you can purchase the tickets.
125t + 5.75t + 20 ≤ 685, and yes, you can purchase the tickets.

125t + 5.75t ≤ 685, and yes, you can purchase the tickets.
125t + 5.75t ≤ 685, and yes, you can purchase the tickets.

125t + 5.75t + 20 ≤ 685, and no, you cannot purchase the tickets.
125t + 5.75t + 20 ≤ 685, and no, you cannot purchase the tickets.

125t ≤ 685, and yes, you can purchase the tickets

Solve x^2=25/64.
There are two real solutions. Enter the lesser number first.
Leave the answers in simplest fraction form.(1 point)

Solve the following quadratic equation. Round to the nearest hundredth if necessary: (x+27)^2/−6=−3
.

Enter the smaller of the 2 values first.

(1 point)

Which of the following equations has the solution set x={−9/5, 3}?
(1 point)
Responses

(x−3)(9x+5)=0
open paren x minus 3 close paren times open paren 9 x plus 5 close paren is equal to 0

−3x(5x+9)=0
negative 3 x open paren 5 x plus 9 close paren is equal to 0

(x−3)(5x+9)=0
open paren x minus 3 close paren times open paren 5 x plus 9 close paren is equal to 0

(x+3)(9x−5)=0

Joana solved the equation 4x2−4x−3=0
. She followed the steps to solve a quadratic equation by grouping. However, in Step 3 she noticed that the two groupings did not share a common binomial, as shown in her work below. She concluded that the quadratic equation has no solutions. Is Joana’s conclusion correct? Review Joana’s work to answer the question.

Step 1: 4x2+2x+(−6x)−3=0

Step 2: (4x2+2x)+(−6x−3)=0

Step 3: x(4x+2x)+(−3(2x+1))=0
(1 point)
Responses

No, because she did not factor out the GCF from the first grouping.
No, because she did not factor out the GCF from the first grouping.

No, because she can still continue the steps even if the two groupings have no shared
binomial.
No, because she can still continue the steps even if the two groupings have no shared binomial.

Yes, because there are no factors of −12 that add up to −4.
Yes, because there are no factors of −12 that add up to −4.

Yes, because the two groupings do not share a common binomial.

Which equation has only one distinct solution?(1 point)
Responses

x2+4x+4=0
x squared plus 4 x plus 4 is equal to 0

x2+5x+4=0
x squared plus 5 x plus 4 is equal to 0

x2−4=0
x squared minus 4 is equal to 0

x2−5x+4=0

Solve the following quadratic equation: 1/4x^2+2x+4=0
(1 point)
x=

Gwen was asked to solve the equation 3x^2−20=7
. What is/are the correct solution(s)?(1 point)
Responses

x=−3
x is equal to negative 3

x=−3, x=3
x=−3, x=3

x=9, x=−9
x=9, x=−9

x=3

Find the zeros of the quadratic equation: x^2−16x−13=4

Enter the smaller of the 2 values first.

(1 point)
x=

, x=

Which of the following is a solution to the quadratic equation 4x2+2x=10
? (1 point)
Responses

−2+41√/4
the fraction with numerator negative 2 plus square root of 41 and denominator 4

−1−41√/4
the fraction with numerator negative 1 minus square root of 41 and denominator 4

−2+92√/8
the fraction with numerator negative 2 plus 9 square root of 2 and denominator 8

−1−92√/8

PLEASE DOUBLE CHECK

Answer 1

Sure! Let’s go through each question one by one:

1. What type of number will result from \( \frac{5}{12} \cdot \sqrt{16} \)?

   • Calculation: \( \sqrt{16} = 4 \).
   • So, \( \frac{5}{12} \cdot 4 = \frac{20}{12} = \frac{5}{3} \) which is a rational number.
   • Response: Rational, because both numbers are rational.

2. Find the product of \( \sqrt{5} \) and \( \frac{1}{6} \). What type of number is it?

   • Calculation: \( \sqrt{5} \cdot \frac{1}{6} = \frac{\sqrt{5}}{6} \).
   • Since \( \sqrt{5} \) is irrational, the entire product is irrational.
   • Response: \( 0.3726 \ldots \); an irrational number.

3. Use the Commutative Property of Addition to rewrite the algebraic expression: \( j^3 + h^4 \).

   • The property states that \( a + b = b + a \).
   • Rewritten: \( h^4 + j^3 \).

4. Use the Distributive Property to rewrite the expression \( (2x - 2)(x - 6) \).

   • Apply distributive property: \( 2x^2 - 12x - 2x + 12 = 2x^2 - 14x + 12 \).
   • Response: \( 2x^2 - 14x + 12 \).

5. What is \((a^2-11)+(3a^2-4a+6)\)?

   • Combine like terms: \( (1a^2 + 3a^2) + (-4a) + (-11 + 6) = 4a^2 - 4a - 5 \).
   • Response: \( 4a^2 - 4a - 5 \).

6. Multiply the polynomials \( (2r - 5)(r + 4) \).

   • Distribute: \( 2r^2 + 8r - 5r - 20 = 2r^2 + 3r - 20 \).

7. What is the quotient of \( -96x^2 / (12x^2) \)?

   • Calculation: \( -96/12 = -8 \).
   • Response: \( -8 \).

8. Which of the following values for \( n \) makes the inequality \( \sqrt{2n} < 5 \) true?

   • Solve: \( 2n < 25 \) leads to \( n < 12.5 \).
   • Response: 12.5.

9. Which equation matches the solution set of {5}?

   • We can quickly check each option:
     • \( x + x - 9 = 1 + x \) simplifies to \( x = 5 \).
     • The others do not equal 5.
   • Response: \( x + x - 9 = 1 + x \).

10. What is the value of \( p \) in the equation \( \frac{20}{p} - 3 = 5 \)?

    • Solve: \( \frac{20}{p} = 8 \) leads to \( 20 = 8p \) thus \( p = 2.5 \).
    • None of the options provided correspond to correct values based on the solution.

11. Get ready for an amusement park day of fun! Inequality:

    • Total cost: \( 125t + 5.75t + 20 \leq 685 \).
    • \( 130.75t + 20 \leq 685 \), leads to \( 130.75t \leq 665 \), thus \( t \leq 5.08 \).
    • You can purchase 5 tickets.
    • Response: \( 125t + 5.75t + 20 \leq 685, \text{ and yes, you can purchase the tickets} \).

12. Solve \( x^2 = \frac{25}{64} \):

    • Taking the square root gives \( x = \pm \frac{5}{8} \).
    • Ordered: \( \frac{-5}{8}, \frac{5}{8} \).

13. Solve \( (x + 27)^2 / -6 = -3 \):

    • Re-arranging will give \( (x + 27)^2 = 18 \), \( x + 27 = \pm \sqrt{18} \), \( x = -27 \pm 3\sqrt{2} \).
    • Choose the smaller one first.

14. Which of the following equations has the solution set \( x={-\frac{9}{5}, 3} \)?

    • The correct equation matching these roots is:
    • Response: \( (x - 3)(5x + 9) = 0 \).

15. Joana solved the equation \( 4x^2 - 4x - 3 = 0 \).

    • Joana's conclusion is No, because she can still continue the steps even if the two groupings have no shared binomial.

16. Which equation has only one distinct solution?

    • \( x^2 + 4x + 4 = 0 \) can be factored as \( (x + 2)^2 = 0 \).
    • Response: \( x^2 + 4x + 4 = 0 \).

17. Solve \( \frac{1}{4}x^2 + 2x + 4 = 0 \):

    • This doesn't yield real solutions due to the discriminant being negative.

18. Gwen was asked to solve the equation \( 3x^2 - 20 = 7 \):

    • Rearranging yields \( 3x^2 - 27 = 0 \), or \( x^2 = 9 \) thus \( x = 3 \text{ and } -3 \).
    • Response: \( x = -3, x = 3 \).

19. Find the zeros of the quadratic equation \( x^2 - 16x - 13 = 4 \):

    • Rewrite as \( x^2 - 16x - 17 = 0 \).
    • Response: Solve using \( x = 8 ± \sqrt{73} \) (values in simplest forms).

20. Which of the following is a solution to the quadratic equation \( 4x^2 + 2x = 10 \)?

    • Arranging gives the standard quadratic form, use the quadratic formula to find roots.

Please feel free to ask for more information or clarifications on any specific question!