what are the values of a, b, and c in the quadratic equation –2x^2 4x – 3 = 0? a = 2, b = 4, c = 3 a = 2, b = 4, c = –3 a = –2, b = 4, c = 3 a = –2, b = 4, c = – 3

Answers

Answer 1

Answer: a=-2
b= either negative or positive 4 (you didn't include a plus or minus sign in your question)
c=-3
It should be the last answer choice.

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Can someone help me please

Fourteen is 50% less than what number?

Answers

21 since 14 x 1.5 is 21

Tony’s class needs more than $500 for the school dance. So far, they have raised $200. They plan to have a car wash, charging $8 a car, to raise more money. Tony solved the inequality 8x + 200 Greater-than-or-equal-to 500, and determined that if they wash 37 cars, they will have enough money. Is he correct? Explain.

Answers

no, tony is not correct. solving the inequality tells us that x is greater than or equal to 37.5. since the class must wash a whole number of cars, they need to wash at least 38 cars.

Answer:

Sample Response: No, Tony is not correct. Solving the inequality tells us that x is greater than or equal to 37.5. Since the class must wash a whole number of cars, they need to wash at least 38 cars.

Select the factors of x^2 -10x+25? A.(x+5)(x+5) B.(x-5)(x-5) C.(x+25)(x+1) D.(x-25)(x-1)

Answers

The correct answer is option B which is the factors are (x-5)(x-5).

What is a quadratic equation?

It is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.

The quadratic equation will be solved as follows:-

x² -10x + 25 = x² -5x - 5x + 25

= x ( x- 5 ) - 5 ( x-5 )

= ( x - 5 ) ( x - 5 )

The factors of the equation are 5 and 5.

Therefore the correct answer is option B which is the factors are (x-5)(x-5).

To know more about quadratic equations follow

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a²-2ab+b²=(a-b)²

x²-10x+5=x²-2×5×x+5²=(x-5)²=(x-5)(x-5)

B.(x-5)(x-5)

Find the product.
8y 3(-3y 2)

Answers

8y³(-3y²)
-24y³⁺²
-24y⁵

1. Which of the following is the factored form of the expression: 3x2 – 4x? A. x(3x - 4)
B. x(3 – 4x)
C. (3x -1) (x -1)
D. (3x +1)(x -1)

2. Which is a completely factored form of the expression: x2 + 21x +20 ?

A. (x + 5)(x + 4)
B. (x + 10)(x + 2)
C. (x + 20)(x + 1)
D. (x + 21)(x - 1)

3. Which expression is factored form of 4x2 -9?

A. 2(x - 3)2
B. (x - 3)2
C. 2(x + 3)(x - 3)
D. (2x + 3)(2x - 3)

4. Below are factored forms of the expression: 12x3 – 36x2 . Which expression has the greatest common factor as the first term?

A. 3x (4x2 – 12x)
B. 4x2(3x -9
C. 12x2(x – 3)
D. 12x(x2 - 3x)
5. Adele’s lawn has an area of (x2 -5x -6) square feet and a length of (x + 1) feet. What is the width of the lawn in feet?

A. (x -6)
B. (x +6)
C. (x2 -4x -5)
D. (x2 -6x -7)

6. The expression below represents the area, in square meters, of a rectangle:
X2 + 5x -24
Which of the following pairs of expressions could represent the length and width, in meters, of the rectangle?

A. (x – 3) and (x + 8)
B. (x – 4) and (x + 6)
C. (x – 6) and (x + 4)
D. (x – 8) and (x + 3)

7. What is the complete factorization of 32 – 8z2?

A. -8(2 + z)(2 –z)
B. 8(2 + z)(2 – z)
C. -8(2 + z)2
D. 8(2 – z)2

8. What is the greatest common factor of: 12x2 , 24x2y2 , and 46xy?

A. 4x
B. 3x
C. 6x
D. 2x
9. Which expression is equivalent to: 2x2 -3x -35?

A. (2x + 7)(x - 5)
B. (2x - 7) (x + 5)
C. (2x - 5)(x + 7)
D. (2x + 5)(x - 7)

10. What are the factors of 81x2 + 36x + 4?

A. (9x + 2)(x +2)
B. (9x +2)(9x +2)
C. (9x -2)(9x -2)
D. (9x +2)(9x -2)

11. The top of a rectangular table has an area of: 18x2+ 69x +60.
The width of the table is 3x + 4. What is the length of the table?
(Show proof by multiplying – show your work)

12. Simplify: (x2 +2x)(5x -3)
A. 11x2 -3
B. 6x3 -6x
C. 5x3 + 7x2 – 6x
D. 5x3 – 13x2 -6x

13. Factor by grouping: 30g5 +24g3h – 35g2h2 - 28h3 Show your work!

14. Which is the correct way to factor the polynomial : x2 -16?

A. (x -4)(x -4)
B. (x -4)(x +4)
C. (x +4)(x -2)(x +2)
D. Not factorable

15. The area of a square painting is: 81p2 + 90p +25. What is the length of one side? Prove by multiplication – show your work.

Answers

1. $3x^2-4x=x(3x-4)$ - A.

2. $x^2 + 21x +20=(x-x_1)(x-x_2)$

Find the roots:

$D=21^2-4\cdot 20=441-80=361, \ √(D)=19,\n \nx_1=(-21-19)/(2)=-20, \ x_2=(-21+19)/(2)=-1$ ,

then

$x^2 + 21x +20=(x+20)(x+1)$ - C.

3. $4x^2 -9=(2x)^2-3^2=(2x-3)(2x+3)$ - D.

4. $12x^3-36x^2=12x^2(x-3)$ - C.

5. $x^2 -5x -6=(x-x_1)(x-x_2)$

Find the roots:

$D=(-5)^2-4\cdot (-6)=25+24=49, \ √(D)=7,\n \nx_1=(5-7)/(2)=-1, \ x_2=(5+7)/(2)=6$ ,

then

$x^2 -5x -6=(x-6)(x+1)$ and the width of the lawn is x-6 - A.

6. Since $x^2 + 5x -24=(x+8)(x-3)$ the length and width are x+8 and x-3 - A.

7. $32 -8z^2=8(4-z^2)=8(2^2-z^2)=8(2-z)(2+z)$ - B.

8. $12x^2=2\cdot 2\cdot 3\cdot x\cdot x, \n24x^2y^2=2\cdot 2\cdot 2\cdot3\cdot x\cdot x\cdot y\cdot y , \n 46xy=2\cdot 23\cdot x\cdot y$ .

So the greatest common divisor is $2\cdot x=2x$ - D.

9. $2x^2 -3x -35=2(x-x_1)(x-x_2)$

Find the roots:

$D=(-3)^2-4\cdot (-35)\cdot 2=9+280=289, \ √(D)=17,\n \nx_1=(3-17)/(2\cdot 2)=-(7)/(2), \ x_2=(3+17)/(2\cdot 2)=5$ ,

then

$2x^2 -3x -35=2(x+(7)/(2))(x-5)=(2x+7)(x-5)$ - A.

10. $81x^2 + 36x + 4=(9x)^2+2\cdot 9x\cdot 2+2^2=(9x+2)^2$ - B.

11. $18x^2+ 69x +60=3(6x^2+23x+20)=3\cdot 6(x+(5)/(2))(x+(4)/(3))=(6x+15)(3x+4)$ , the length is 6x+15.

12. $(x^2 +2x)(5x -3) =x^2\cdot 5x-x^2\cdot 3+2x\cdot 5x-2x\cdot 3=5x^3-3x^2+10x^2-6x=5x^3+7x^2-6x$ - C.

13. $30g^5 +24g^3h- 35g^2h^2 - 28h^3=(30g^5 +24g^3h)-(35g^2h^2+ 28h^3)=6g^3(5g^2+4h)-7h^2(5g^2+4h)=(5g^2+4h)(6g^3-7h^2)$ .

14. $x^2 -16=(x-4)(x+4)$ - B.

15. $81p^2 + 90p +25=(9p)^2+2\cdot 9p\cdot 5+5^2=(9p+5)^2$ , the length of one side is 9p+5.

Answer:

yes that is right

Step-by-step explanation:

usa test prep

Allie deposited $300.00 into a new savings account that earns 13% interest compounded quarterly. How long will it take for the balance to grow to $995.00? Round your answer to the nearest month. years and months

Answers

Answer:

9 years 4 months

Step-by-step explanation:

To find out how long it will take for Allie's initial deposit of $300to grow to $995 in a savings account with a 13% annual interest rate compounded quarterly, we can use the compound interest formula:

$\boxed{\begin{array}{l}\underline{\textsf{Compound Interest Formula}}\n\nA=P\left(1+(r)/(n)\right)^(nt)\n\n\textsf{where:}\n\phantom{ww}\bullet\;\;\textsf{$A$ is the final amount.}\n\phantom{ww}\bullet\;\;\textsf{$P$ is the principal amount.}\n\phantom{ww}\bullet\;\;\textsf{$r$ is the interest rate (in decimal form).}\n\phantom{ww}\bullet\;\;\textsf{$n$ is the number of times interest is applied per year.}\n\phantom{ww}\bullet\;\;\textsf{$t$ is the time (in years).}\end{array}}$

In this case:

A = $995
P = $300
r = 13% = 0.13
n = 4 (quarterly)

Substitute the values into the formula and solve for t:

$995=300\left(1+(0.13)/(4)\right)^(4t)$

Simplify the expression inside the bracket:

$995=300\left(1.0325\right)^(4t)$

Divide both sides of the equation by 300:

$(995)/(300)=\left(1.0325\right)^(4t)$

Take natural logs (ln) of both sides of the equation:

$\ln\left((995)/(300)\right)=\ln\left(1.0325^(4t)\right)$

$\textsf{Apply the power law:} \quad \ln x^n=n \ln x$

$\ln\left((995)/(300)\right)=4t\ln\left(1.0325\right)$

Divide both sides of the equation by 4ln(1.0325) to isolate t:

$(\ln\left((995)/(300)\right))/(4\ln\left(1.0325\right))=t$

$t=(\ln\left((995)/(300)\right))/(4\ln\left(1.0325\right))$

Evaluate using a calculator:

$t=9.37184241...$

Therefore, it will take 9.37 years for the balance to grow to $995.00.

To determine the number of months, subtract 9 from the value of t and multiply by 12:

$\textsf{Months}=12(9.37184241...-9)=4.46210895...$

Therefore, it will take 9 years and 4 months (rounded to the nearest month) for the balance to grow to $995.00.

Additional comments

In the case of quarterly compounding, the interest is calculated and added to the account balance every three months (once every quarter). So, even though it will take 9 years and 4 months for the balance to reach $995.00, Allie's account will not show this exact amount at that specific time. It will show a balance of $979.61 at 9 years and 3 months, and a balance of $1,011.45 at 9 years and 6 months, so technically, the account balance will still show as $979.61 at 9 years and 4 months.

Answer:

9 years and 4 months

Step-by-step explanation:

In order to calculate the number of years and months it will take for Allie's savings account balance to grow to $995.00, we can use the following compound interest formula:

$\sf A = P\left(1 + (r)/(n)\right)^(nt)$