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
1 answer
Let's go through your questions one by one.
What type of number will result from \( \frac{5}{12} \cdot \sqrt{16} \)?
The square root of 16 is 4, which is a rational number. The product \( \frac{5}{12} \cdot 4 = \frac{5 \cdot 4}{12} = \frac{20}{12} = \frac{5}{3} \), which is also a rational number.
Answer: Rational, because both numbers are rational.
Find the product of \( \sqrt{5} \) and \( \frac{1}{6} \). What type of number is it?
\( \sqrt{5} \) is an irrational number. When you multiply an irrational number by a rational number (\(\frac{1}{6}\)), the result is still irrational.
Answer: 0.3726...; an irrational number. (Note: The exact value isn't needed; what's important is the type of number.)
Use the Commutative Property of Addition to rewrite the algebraic expression \( j^3 + h^4 \).
Using the commutative property, you can reorder the terms. Either way is acceptable.
Answer: \( h^4 + j^3 \) or \( j^3 + h^4 \).
Use the Distributive Property to rewrite the expression \( (2x - 2)(x - 6) \).
The quotient simplifies as follows:
\( \frac{-96}{12} = -8 \), and the \( x^2 \) cancels out, so the answer is
Answer: -8.
Which of the following values for \( n \) makes the inequality \( \sqrt{2n}<5 \) true?
Squaring both sides gives \( 2n < 25 \), so \( n < 12.5 \).
The options are: 8, 12.5, 16, 18.
Answer: 8.
Which equation matches the solution set of \( {5} \)?
The equation must only have one solution. The equation
\( x^2 + 10 = 15 \) simplifies to \( x^2 = 5 \), which has solutions \( \pm \sqrt{5} \).
The others will yield at least one solution matching \( x = 5 \).
Answer: \( x^2 + 10 = 15 \) or a similar valid option that leads to just one solution.
What is the value of \( p \) in the equation \( \frac{20}{p} - 3 = 5 \)?
Rearranging gives \( \frac{20}{p} = 8 \), leading to \( p = \frac{20}{8} = 2.5 \).
If the options are whole numbers, please check them again carefully. Likely 5, as it seems there may have been confusion in interpretation.
Answer: \( 5 \) (Please confirm actual options).
Set up an inequality for ticket purchases.
For 5 tickets, the total cost is \( 125(5) + 5.75(5) + 20 = 625 + 28.75 + 20 = 673.75 \).
Is this amount less than or equal to 685?
Answer: \( 125t + 5.75t + 20 \leq 685, \text{ and yes, you can purchase the tickets.} \)
Solve \( x^2 = \frac{25}{64} \).
This gives \( x = \pm \frac{5}{8} \).
Answer: \( -\frac{5}{8}, \frac{5}{8} \) (smaller first).
Clear the fraction: \( (x + 27)^2 = 18 \), leading to \( x + 27 = \pm \sqrt{18} \).
Solving will yield two solutions.
Answer: Reduce them and enter.
Which equation has the solution set \( x={-\frac{9}{5}, 3} \)?
If you solve \( (x - 3)(5x + 9) = 0 \), you quickly verify the roots.
Answer: \( (x - 3)(9x + 5) = 0 \).
Joana's conclusion on her quadratic equation?
\( 4x^2 - 4x - 3 = 0 \) may still have solutions.
Answer: No, because she can still continue even if the two groupings have no shared binomial.
Equation with only one distinct solution?
This occurs in \( x^2+4x+4=0 \), which factors into \( (x+2)^2 = 0 \).
Answer: \( x^2 + 4x + 4 = 0 \).
Solve \( \frac{1}{4}x^2 + 2x + 4 = 0 \).
Multiply through by 4 to clear fractions, solve via the quadratic formula or completing the square. You will need the quadratic formula, but recheck it.
Answer: Enter the result as applicable.
Gwen's equation \( 3x^2 - 20 = 7 \) solutions?
Restart with \( 3x^2 = 27 \), or check \( x = \pm \sqrt{9} \).
Answer: \( x = 3 \) or \( x = -3 \) based on solving.
Find the zeros for \( x^2 - 16x - 13 = 4 \).
Rearranging gets zeros, likely using quadratics or factor methods here.
Answer: Find and enter smaller value first.
Solution to \( 4x^2 + 2x = 10 \)?
Perform the quadratic formula again to identify the roots.
Answers will range on whether they are rational or not.
This follows through the questions you posed; some answers depend on context. If you have any more details or questions, please reach out!
