Solve the following quadratic by factoring1) x²+5x+6=0
2) x²+10x+21=0
3) x²+8x+15=0
4) x²+9x+14=0
5) x²-2x35=0

Answers

Answer 1

Answer:

Answer:

Step-by-step explanation:

To solve these quadratic equations by factoring, you need to find two numbers that multiply to the constant term (the number without x^2) and add up to the coefficient of the linear term (the number with x). Here are the solutions for each of the equations:

1. x² + 5x + 6 = 0

We need two numbers that multiply to 6 and add up to 5. The numbers are 2 and 3.

So, we can factor the equation as (x + 2)(x + 3) = 0.

Now, set each factor equal to zero and solve for x:

x + 2 = 0 => x = -2

x + 3 = 0 => x = -3

So, the solutions are x = -2 and x = -3.

2. x² + 10x + 21 = 0

We need two numbers that multiply to 21 and add up to 10. The numbers are 7 and 3.

So, we can factor the equation as (x + 7)(x + 3) = 0.

Now, set each factor equal to zero and solve for x:

x + 7 = 0 => x = -7

x + 3 = 0 => x = -3

So, the solutions are x = -7 and x = -3.

3. x² + 8x + 15 = 0

We need two numbers that multiply to 15 and add up to 8. The numbers are 5 and 3.

So, we can factor the equation as (x + 5)(x + 3) = 0.

Now, set each factor equal to zero and solve for x:

x + 5 = 0 => x = -5

x + 3 = 0 => x = -3

So, the solutions are x = -5 and x = -3.

4. x² + 9x + 14 = 0

We need two numbers that multiply to 14 and add up to 9. The numbers are 7 and 2.

So, we can factor the equation as (x + 7)(x + 2) = 0.

Now, set each factor equal to zero and solve for x:

x + 7 = 0 => x = -7

x + 2 = 0 => x = -2

So, the solutions are x = -7 and x = -2.

5. x² - 2x - 35 = 0

To factor this equation, we need two numbers that multiply to -35 and add up to -2. The numbers are -7 and 5.

So, we can factor the equation as (x - 7)(x + 5) = 0.

Now, set each factor equal to zero and solve for x:

x - 7 = 0 => x = 7

x + 5 = 0 => x = -5

So, the solutions are x = 7 and x = -5.

Related Questions

Will someone PLEASE check my answers asap?? will mark a brainliest!!1) The graph of f(x) = (0.5)x is replaced by the graph of g(x) = (0.5)^x − k. If g(x) is obtained by shifting f(x) down by 3 units, the value of k is ____2) Find an equivalent function to f(x) = 4(7)2x. A) f(x) = 282xB) f(x) = 4(49)xC) f(x) = 196xD) f(x) = 16x(49)x3) The functions f(x) and g(x) are described using the following equation and table:f(x) = −6(1.02)^xx g(x)−1 −50 −31 −12 1Which equation best compares the y-intercepts of f(x) and g(x)?a) The y-intercept of f(x) is equal to the y-intercept of g(x).b) The y-intercept of f(x) is equal to 2 times the y-intercept of g(x).c) The y-intercept of g(x) is equal to 2 times the y-intercept of f(x).d) The y-intercept of g(x) is equal to 2 plus the y-intercept of f(x).4) What is the value of x in the solution to the following system of equations? (5 points)x − y = −3x + 3y = 5For #1 i put in 3 as the answer.For #2 i put B as the answer.For #3 i put B as the answer.For #4 i put 2 as the answer.
Which of the following is a solution to the quadratic equation below? x^2+x-56=0 a.2 b.-55 c.-8 d.28
Robert makes $4.00 an hour when he works overtime.how much does he for 3 1/4 hours of overtime work?
How do u write 6/20 in percentage form?
Find the area of the triangle. Figure is not drawn to scale. Show your work. (Image attached)Thanks so much in advance !! :))

Prices were recorded for all the loaves of bread in a supermarket, the mean price for a loaf of bread was $1.37 with a standard deviation of $0.67, Find the probability that if 13 loaves are selected the mean price is less than $1.00. A 0.0032

B 0.5643

C 0.9105

D 0.0233

Answers

Answer:

$z = (1-1.37)/((0.67)/(√(13))) = -1.991$

And we want this probability:

$P(z<-1.991)$

And using the normal standard distribution or excel we got:

$P(z<-1.991)= 0.0233$

And the best option would be:

D 0.0233

Step-by-step explanation:

For this case we have the following parameters:

$\mu = 1.37, \sigma =0.67$

And we select a sample size of n=13. And we want to find this probability:

$P(\bar X <1)$

We can assume that the distribution for this case is normal and then we can use the z score formula given by:

$z= (\bar X -\mu)/((\sigma)/(√(n)))$

And if we replace the data given we got:

$z = (1-1.37)/((0.67)/(√(13))) = -1.991$

And we want this probability:

$P(z<-1.991)$

And using the normal standard distribution or excel we got:

$P(z<-1.991)= 0.0233$

And the best option would be:

D 0.0233

Christopher is getting a mortgage for a house and will borrow $700,000. For this mortgage, the amortized loan requires annual payments for 22 years at a 4.5% annual interest rate. How much of the first payment (to the nearest cent) is the interest owed for the first year of the loan?

Answers

Answer:

Step-by-step explanation:

How to find the amount of interest owed for the first year of the loan?

To calculate the interest owed for the first year of the loan, we need to consider the loan amount, the annual interest rate, and the loan term.

In this case, borrowing $700,000 for 16 years at an annual interest rate of 7.4%.

The interest owed for the first year can be determined by multiplying the loan amount by the annual interest rate:

Interest = Loan Amount * Annual Interest Rate

Interest = $700,000 * 0.074

Calculating this, we find that the interest owed for the first year is approximately $51,800.30.

Write 3,000,000 in scientific notation.Show your work in the work space below.

Hint: Move the decimal place to the left.

Answers

Answer:

3 × 10^6

Step-by-step explanation:

3 × 1,000,000 = 3 × 10^6

Answer:

3,000,000 = 3 × 1,000,000 = 3 × 106.

Step-by-step explanation:

3,000,000 is a decimal expression, and 3 × 106 is scientific notation.

Hope this helps :))

Solve with completing the square method:
6x²-7x+2=0 and ax²+bx+c=0

Answers

$6x ^2-7x+2=0\n \n a=6 , \ b = -7 , \ c=2 \n \n\Delta = b^(2)-4ac = (-7)^(2)-4*6*2=49-48=1 \n \nx_(1)=(-b-√(\Delta ))/(2a) =(7-√(1))/(2*6)=(7-1)/(12) =(6)/(12)= (1)/( 2)\n \nx_(2)=(-b+√(\Delta ))/(2a) =(7+√(1))/(2*6)=(7+1)/(12) =(8)/(12)= (2)/( 3)$

What is the solution to the system of equations? y = 1/2x-6 and x=-4

Answers

All you have to do is plug -4 for x

y = 1/2 * -4 - 6

y = -8

Solution: (-4, -8)

According to the Fundamental Theorem of Algebra, how many roots exist for the polynomial function? f(x) = (x3 – 3x + 1)2 2 roots 3 roots 6 roots 9 roots

Answers

According to the Fundamental Theorem of Algebra, 6 roots exist for the polynomial function.

What is the fundamental Theorem of Algebra?

Fundamental Theorem of Algebra states that every polynomial equation of degree n with complex number coefficients has n roots, or solutions, in the complex numbers. The roots can have a multiplicity greater than zero.

Given polynomial function

$f(x)=(x^(3)-3x+1 )^(2)$