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Question 1 A)Identify the correct list of coefficients for the quadratic expression: 7x2−4x+127x2−4x+12.(1 point) Responses 7, −4, 127, −4, 127, −4, 127, −4, 12 7x2, −4x, 127x2, −4x, 127x2, −4x, 127x2, −4x, 12 7x2, −4x7x2, −4x7x2, −4x7x2, −4x 7, −47, −47, −47, −4 Question 2 A)Identify the constant in the cubic expression: 6x3+3x2−2x+76x3+3x2−2x+7.(1 point) Responses −2−2negative 2 333 666 777 Question 3 A)Identify the following as an expression or an equation.(4 points) Expression Equation 2x−5=42x−5=4 −3x3=82−3x3=82 21⋅−3x21⋅−3x 5x2−8x+25x2−8x+2 Question 4 A)(3 points) Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. Joseph is selling cellphone data plans. He plans to charge $55 per month for unlimited data, as well as a one-time startup fee of $21. Fill in the expression with the correct numbers to represent the given scenario. Let mm represent the number of months. Response area m+m+ Response area The total cost for 6 months is $Response area. 82553512166 Question 5 A)Select the quadratic equation that is equivalent to: the product of negative six and a number squared, plus the product of five and the same number is thirty-one.(1 point) Responses −6x2+5x+31−6x2+5x+31negative 6 x squared plus 5 x plus 31 −6x2−5x+31−6x2−5x+31negative 6 x squared minus 5 x plus 31 6x2−5x=316x2−5x=316 x squared minus 5 x is equal to 31 −6x2+5x=31

11 answers

Let's break down the questions one by one:

Question 1 A) Identify the correct list of coefficients for the quadratic expression: \(7x^2 - 4x + 12\).

  • The coefficients in the expression \(7x^2 - 4x + 12\) are:
    • Coefficient of \(x^2\): 7
    • Coefficient of \(x\): -4
    • Constant term: 12

So, the correct response is: 7, −4, 12.

Question 2 A) Identify the constant in the cubic expression: \(6x^3 + 3x^2 - 2x + 7\).

  • The constant in this expression is the term without \(x\), which is 7.

So, the correct response is: 7.

Question 3 A) Identify the following as an expression or an equation.

  • \(2x - 5 = 4\) is an equation (because it has an equals sign).
  • \(−3x^3 = 8\) is also an equation (with an equals sign).
  • \(21 \cdot -3x\) is an expression (no equals sign).
  • \(5x^2 - 8x + 2\) is an expression (no equals sign).

So the answers are:

  • \(2x - 5 = 4\): Equation
  • \(−3x^3 = 8\): Equation
  • \(21 \cdot -3x\): Expression
  • \(5x^2 - 8x + 2\): Expression

Question 4 A) Joseph is selling cellphone data plans. He plans to charge $55 per month for unlimited data, as well as a one-time startup fee of $21. Fill in the expression with the correct numbers to represent the given scenario.

Let's let \(m\) represent the number of months. The total cost can be expressed as:

  • The total cost for \(m\) months: \(55m + 21\)

To find the total cost for 6 months:

  • Total cost for 6 months = \(55(6) + 21 = 330 + 21 = 351\)

So:

  • Fill in the expression: 55m + 21
  • The total cost for 6 months is: 351

Question 5 A) Select the quadratic equation that is equivalent to: the product of negative six and a number squared, plus the product of five and the same number is thirty-one.

  • The expression can be formed as: \[-6x^2 + 5x = 31\]

The equation indicates that the product of negative six and \(x^2\) plus the product of five and \(x\) equals thirty-one.

So the correct response is: −6x^2 + 5x = 31.

Question 6 A)A quarterback is standing at the top of the bleachers, trying to throw the football as high into the air as he can. He picks up the football so that it is 47 feet above the ground, and throws the football as high as he can. The height of the football after tt seconds can be modeled by the expression −16t2+32t+47−16t2+32t+47. What does 47 represent in the context of the problem?(1 point) Responses 47 represents the height of the football when the quarterback throws it. 47 represents the height of the football when the quarterback throws it. 47 does not make sense as a value in this problem. 47 does not make sense as a value in this problem. 47 represents the number of footballs they have at practice at a given time. 47 represents the number of footballs they have at practice at a given time. 47 represents the number of seconds the quarterback holds the football before throwing it. 47 represents the number of seconds the quarterback holds the football before throwing it. Question 7 A) Jamie is starting a new marketing strategy that causes her number of clients to grow exponentially. Jamie starts with 50 clients, and each month, her number of clients doubles. The expression 50⋅2m50⋅2m can be used to model the expression. Jamie found that after just 6 months, she had reached 3,200 clients. How did Jamie reach this solution? (1 point) Responses Jamie substituted m=6m=6 into the expression 50⋅62=180050⋅62=1800. Jamie substituted m is equal to 6 into the expression 50 times 6 squared is equal to 1800. Jamie substituted m=6m=6 into the expression 50⋅2⋅6=60050⋅2⋅6=600. Jamie substituted m is equal to 6 into the expression 50 times 2 times 6 is equal to 600. Jamie substituted m=6m=6 into the expression 50⋅26=320050⋅26=3200. Jamie substituted m is equal to 6 into the expression 50 times 2 to the 6th power is equal to 3200. Jamie substituted m=6m=6 into the expression 6⋅250=32006⋅250=3200. Jamie substituted m is equal to 6 into the expression 6 times 2 to the 50th power is equal to 3200. Question 8 A)(4 points) Three classmates are working with three different expressions. Each classmate substitutes in the value x=3x=3 into their expression. Whitney Theo Erin 4x−84x−8 4x2−84x2−8 4x−84x−8 When substituting in the value x=3x=3, Whitney would get a result of , Theo would get a result of , and Erin would get a result of . expression produced the largest value.​​​​​​ Question 9 A) Hank is working on simplifying the algebraic expression 4x−144x−14 when x=5x=5. Her steps are as follows: Step 1: 45−1445−14 Step 2: 20−1420−14 Step 3: 66 In which step did Jenny make a mistake? What should she have done differently? (1 point) Responses Step 2, Jenny should've calculated the value of 4545 to be 1,024. Step 2, Jenny should've calculated the value of 4 to the 5th power to be 1,024. Step 2, Jenny should've added 4 and 5 to get 9. Step 2, Jenny should've added 4 and 5 to get 9. Step 3, 20−1420−14 should be 20÷1420÷14. Step 3, 20 minus 14 should be 20 divided by 14. Step 1, Jenny should've multiplied 4⋅54⋅5 instead of writing 5 as the exponent. Step 1, Jenny should've multiplied 4 times 5 instead of writing 5 as the exponent. Question 10 A)Put the steps in the correct order when multiplying the binomials: (2x−5)(x+7)(2x−5)(x+7). Start with the given expression and end with the simplified trinomial.(4 points) Arrange responses in the correct order to answer the question. Select a response, navigate to the desired position and insert response at that position. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can be moved using the up and down arrow keys or by dragging with a mouse.  (2x−5)(x+7)(2x−5)(x+7)  2x2+9x−352x2+9x−35  (2x)(x)+(2x)(7)+(−5)(x)+(−5)(7)(2x)(x)+(2x)(7)+(−5)(x)+(−5)(7)  2x2+14x−5x−352x2+14x−5x−35

Let's go through each of the questions one by one:

Question 6 A) What does 47 represent in the context of the problem?

In the expression \(-16t^2 + 32t + 47\), the term \(47\) represents the initial height of the football when the quarterback throws it from the top of the bleachers.

So, the correct response is: 47 represents the height of the football when the quarterback throws it.

Question 7 A) How did Jamie reach her solution?

Jamie started with 50 clients, and each month, her number of clients doubles. The expression \(50 \cdot 2^m\) is used to model this growth. After substituting \(m = 6\):

\[ 50 \cdot 2^6 = 50 \cdot 64 = 3200 \]

So, the correct response is: Jamie substituted m=6 into the expression 50⋅2^6=3200.

Question 8 A) Three classmates are substituting \(x = 3\) into their expressions. Let's calculate the results for each classmate:

  • Whitney's expression: \(4x - 8\) \[ 4(3) - 8 = 12 - 8 = 4 \]

  • Theo's expression: \(4x^2 - 8\) \[ 4(3^2) - 8 = 4(9) - 8 = 36 - 8 = 28 \]

  • Erin's expression: \(4x - 8\) (It appears she has the same expression as Whitney) \[ 4(3) - 8 = 12 - 8 = 4 \]

The results are:

  • Whitney: 4
  • Theo: 28
  • Erin: 4

Among the results, Theo produced the largest value.

Question 9 A) In which step did Jenny make a mistake?

Let's review her steps:

  • Step 1: \(4^5 - 14 \to 1024 - 14\)
  • Step 2: \(20 - 14 \to 20 - 14\)

The issue is in Step 1 where Jenny should have correctly calculated \(4^5\) to be \(1024\) instead of moving on to incorrect calculations in subsequent steps.

So the correct response is: Step 1, Jenny should've multiplied \(4^5\) instead of writing \(5\) as the exponent.

Question 10 A) Put the steps in the correct order when multiplying the binomials \((2x - 5)(x + 7)\).

  1. Start with the given expression: (2x - 5)(x + 7)
  2. Expand using the distributive property: (2x)(x) + (2x)(7) + (-5)(x) + (-5)(7)
  3. Combine like terms: 2x^2 + 14x - 5x - 35
  4. Final simplification: 2x^2 + 9x - 35

So, the correct order is:

  1. (2x - 5)(x + 7)
  2. (2x)(x) + (2x)(7) + (-5)(x) + (-5)(7)
  3. 2x^2 + 14x - 5x - 35
  4. 2x^2 + 9x - 35

If needed, you can now arrange these into final responses as follows:

  1. (2x - 5)(x + 7)
  2. \( (2x)(x) + (2x)(7) + (-5)(x) + (-5)(7) \)
  3. \( 2x^2 + 14x - 5x - 35 \)
  4. \( 2x^2 + 9x - 35 \)

Let me know if you need further assistance!

Use the Distributive Property to multiply: −3x(4x−5)−3x(4x−5) .(1 point) Responses −12x+15−12x+15negative 12 x plus 15 −12x2+15x−12x2+15xnegative 12 x squared plus 15 x 12x2−15x12x2−15x12 x squared minus 15 x 7x2+8x

To apply the Distributive Property to the expression \(-3x(4x - 5)\), we multiply \(-3x\) by each term inside the parentheses:

  1. Multiply \(-3x\) by \(4x\): \[ -3x \cdot 4x = -12x^2 \]

  2. Multiply \(-3x\) by \(-5\): \[ -3x \cdot -5 = +15x \]

Now, combine these results: \[ -12x^2 + 15x \]

So, the correct response is: −12x² + 15x (negative 12 x squared plus 15 x).

Maria is designing a garden for flowers and vegetables. The area of the garden covered by flower beds can be represented by the expression 3x2+5x−23x2+5x−2 square feet. The area of the garden covered by vegetable plants can be represented by the expression 2x2−3x+42x2−3x+4 square feet. What is the total area of both flowers and vegetables combined? x2+x2+ x+x+ square feet

To find the total area of the garden covered by both flowers and vegetables, we need to add the two given expressions for the areas:

  1. Area covered by flower beds: \(3x^2 + 5x - 2\)
  2. Area covered by vegetable plants: \(2x^2 - 3x + 4\)

Now, we can add these two expressions together:

\[ (3x^2 + 5x - 2) + (2x^2 - 3x + 4) \]

Now, let's combine like terms:

  1. Combine the \(x^2\) terms: \[ 3x^2 + 2x^2 = 5x^2 \]

  2. Combine the \(x\) terms: \[ 5x - 3x = 2x \]

  3. Combine the constant terms: \[ -2 + 4 = 2 \]

Now, put it all together:

\[ 5x^2 + 2x + 2 \]

Thus, the total area of both flowers and vegetables combined is:

\[ \boxed{5x^2 + 2x + 2} \text{ square feet.} \]

Alex has a workshop with an area that can be modeled by the expression 4x2+7x−34x2+7x−3 square feet. He agrees to rent out part of his workshop to his friend Matt. Alex agrees to let Matt use a space in his workshop that is 2x2+7x−52x2+7x−5 square feet. What is the expression that models the remainder of Alex's workshop space once he rents Matt his portion? (1 point) Responses 6x2+14x−86x2+14x−8 square feet 6 x squared plus 14 x minus 8 square feet 2x2−82x2−8 square feet 2 x squared minus 8 square feet 2x2+22x2+2 square feet 2 x squared plus 2 square feet 2x2−14x−82x2−14x−8 square feet 2 x squared minus 14 x minus 8 square feet

To find the expression that models the remainder of Alex's workshop space after renting out part of it to Matt, we need to subtract the area that Matt is renting from the total area of the workshop.

  1. Total area of the workshop: \[ 4x^2 + 7x - 3 \]

  2. Area Matt is renting: \[ 2x^2 + 7x - 5 \]

Now, we can subtract Matt's area from Alex's total area:

\[ (4x^2 + 7x - 3) - (2x^2 + 7x - 5) \]

Now, distribute the negative sign across the second expression:

\[ 4x^2 + 7x - 3 - 2x^2 - 7x + 5 \]

Next, combine like terms:

  1. Combine the \(x^2\) terms: \[ 4x^2 - 2x^2 = 2x^2 \]

  2. Combine the \(x\) terms: \[ 7x - 7x = 0 \]

  3. Combine the constant terms: \[ -3 + 5 = 2 \]

Putting it all together:

\[ 2x^2 + 0 + 2 = 2x^2 + 2 \]

So, the expression that models the remainder of Alex's workshop space once he rents Matt his portion is:

\[ \boxed{2x^2 + 2} , \text{square feet.} \]

When simplified, which expressions produce the trinomial 4x2−20x−244x2−20x−24 ? Select the TWO that apply.(2 points) Responses 4(x2−20x−24)4(x2−20x−24)4 times open paren x squared minus 20 x minus 24 close paren 4(x−6)(x+1)4(x−6)(x+1)4 open paren x minus 6 close paren open paren x plus 1 close paren −4(x2+5x+6)−4(x2+5x+6)negative 4 times open paren x squared plus 5 x plus 6 close paren 4(x2−5x−6)

To determine which expressions simplify to the trinomial \(4x^2 - 20x - 24\), let's analyze the provided options step-by-step:

  1. First Option: \(4(x^2 - 20x - 24)\)

Distributing \(4\): \[ 4(x^2 - 20x - 24) = 4x^2 - 80x - 96 \] This does not match \(4x^2 - 20x - 24\).

  1. Second Option: \(4(x - 6)(x + 1)\)

Using the distributive property (FOIL method): \[ 4[(x - 6)(x + 1)] = 4[x^2 + 1x - 6x - 6] = 4[x^2 - 5x - 6] \] Distributing \(4\): \[ 4x^2 - 20x - 24 \] This matches \(4x^2 - 20x - 24\).

  1. Third Option: \(-4(x^2 + 5x + 6)\)

Distributing \(-4\): \[ -4(x^2 + 5x + 6) = -4x^2 - 20x - 24 \] This does not match \(4x^2 - 20x - 24\).

  1. Fourth Option: \(4(x^2 - 5x - 6)\)

Distributing \(4\): \[ 4(x^2 - 5x - 6) = 4x^2 - 20x - 24 \] This matches \(4x^2 - 20x - 24\).

Now summarizing the results:

  1. First Option: \(4(x^2 - 20x - 24)\) - does not match.
  2. Second Option: \(4(x - 6)(x + 1)\) - matches.
  3. Third Option: \(-4(x^2 + 5x + 6)\) - does not match.
  4. Fourth Option: \(4(x^2 - 5x - 6)\) - matches.

Thus, the two options that produce the trinomial \(4x^2 - 20x - 24\) when simplified are:

  • \(4(x - 6)(x + 1)\)
  • \(4(x^2 - 5x - 6)\)

So, the correct responses are:

  • \(4(x - 6)(x + 1)\)
  • \(4(x^2 - 5x - 6)\)