MATHEMATICS HIGH SCHOOL

What are the solutions of this quadratic equation? x^2+13=8x+37

Answers

Answer 1

Answer:

The solutions of the quadratic equation x² + 13 = 8x + 37 are x = 4 + 2√10 and x = 4 - 2√10.

What is a quadratic equation?

The quadratic equation is defined as a function containing the highest power of a variable is two.

The given equation as:

x² - 8x + 13 = 37

Subtracting 37 from both sides, we get:

x² - 8x - 24 = 0

Now, we have the equation in standard form, so we can use the quadratic formula to find the solutions:

x = (-b ± √(b² - 4ac)) / 2a

Here, a = 1, b = -8, and c = -24.

Substitute these values into the quadratic formula, and we get:

x = (-(-8) ± √((-8)² - 4(1)(-24))) / 2(1)

x = (8 ± √(64 + 96)) / 2

x = (8 ± √160) / 2

x = (8 ± 4√10) / 2

Simplifying, we get:

x = 4 ± 2√10

Therefore, the solutions of the quadratic equation x² + 13 = 8x + 37 are x = 4 + 2√10 and x = 4 - 2√10.

Learn more about quadratic function here:

brainly.com/question/14083225

#SPJ3

Answer 2

Answer:

Answer:

$x\in\left\{4-2√(10)\ ,\ \,4+2√(10)\,\right\}$

Step-by-step explanation:

$x^2+13=8x+37\n\nx^2-8x-24=0\n\na=1\,,\ \ b=-8\,,\ \ c=-24\n\nx_1=(-(-8)-√((-8)^2-4\cdot1\cdot(-24)))/(2\cdot1)=\frac{8-√(64+96)}2=\frac{8-√(160)}2 =\n\n=\frac{8-4√(10)}2=\frac{2(4-2√(10))}2=4-2√(10) \n\nx_2=(-(-8)-√((-8)^2-4\cdot1\cdot(-24)))/(2\cdot1)=\frac{8+4√(10)}2=4+2√(10)$

Related Questions

What is the 13th term of this arithmetic sequence? 132, 135, 138, 141,
Johnny heads to the store with $20. He spends $7 on a t-shirt, then buys some candy bars for $1.50 each. How many candy bars could he buy if he spent all of his money?
You are challenged to a lucky draw game. If you draw a face card (K, Q, J) from a standard deck of cards, you earn 10 points. If you draw any other card, you lose 2 points. What is the expected value that you can get if you draw another card?
The following contingency table shows opinion about global warming (nonissue vs. serious concern) among registered voters, broken down by political party affiliation (Democratic, Republican, and Independent). Use the table to answer a) through c) below. Opinions on Global Warming Nonissue Serious Concern Total 500 500 200 1200 Democratic 80 Political Party Republican 300 Independent110 490 42 200 90 Total 710 a) What is the probability that a randomly selected registered voter who is a Republican believes that global warming is a serious issue? 0.400 (Round to three decimal places as needed.) b) What is the probability that a randomly selected registered voter is a Republican given that he or she believes global warming is a serious issue? 0.167(Round to three decimal places as needed.)
Prove that

Roseanna did not pay last month's credit card bill in full. Her daily balances for her last billing cycle are listed. What was Roseanna's average daily balance to the nearest cent? (Hint: Find the average or mean of these numbers.)For seven days she owed $456.11

For three days, she owed $1,077.00

For six days, she owed $900.08

For nine days, she owed $2,113.15

For five days, she owed $2,310.15

Answers

Average daily balance = (456.11 + 1,077.00 + 900.08 + 2,113.15 + 2,310.15)/(7 + 3 + 6 + 9 + 5) = 6,856.49/30 = 228.55

Therefore, Roseanna's average daily balance = $228.55

Answer:

$228.54

Step-by-step explanation:

Given : Roseanna did not pay last month's credit card bill in full. Her daily balances for her last billing cycle are listed.

To Find: What was Roseanna's average daily balance to the nearest cent?

Solution:

For seven days she owed $456.11

For three days, she owed $1,077.00

For six days, she owed $900.08

For nine days, she owed $2,113.15

For five days, she owed $2,310.15

Mean = $\frac{\text{Sum of amount owned}}{\text{Total no. of days}}$

Mean = $(456.11+1077+900.08+2113.15+2310.15)/(7+3+6+9+5)$

Mean = $(6856.49)/(30)$

Mean = $228.5496$

Hence Roseanna's average daily balance to the nearest cent is $228.54

125apples were shared between jerry and kay. kay received 20% less than jerry.

Answers

if that is the case, then Jerry got 60% and Kay received 40%, because together they make the 100%, or in equations:
kay + jerry = 100%
kay = jerry - 20%
substitute:
jerry - 20% + jerry = 100%
2*jerry = 120%
jerry = 60%
kay = jerry - 20% = 60% - 20%
kay = 40%
if you want to know the amount of apples each has:
kay = 40%(125) = 0.4(125)
jerry = 60%(125) = 0.6(125)

A man walks due west for 4 km. He thenchanges direction and walks on a bearing of
197° until he is south-west of his starting point.
How far is he then from his starting point? with workings

Answers

Answer:

Step-by-step explanation:

Let the starting point be B and the stopping be C as shown in the diagram below.

therefore, the angle at A will be (197-90)degree = 107degree

the angle at B is 45degree, since it is directly south west of C.

therefore the angle at C will be A+B+C=180 degree(sum angle of a triangle)

107+45+C=180

therefore, C=180-107-45=28degree

therefore, using sine rule gives;

sinA/a =sinC/c

sin107/a=sin28/4

0.9563/a=0.4695/4

0.9563/a=0.11736

therefore, a =0.9563/0.11736=8.148=8.1km(approx.)

How much will my 84% class grade be affected by a 60% test grade?

Answers

Answer:yes

Step-by-step explanation:

yes

Answer:

You haven't given enough information.

50.4%

72%

Step-by-step explanation:

84% × 60%

$(63)/(125)=0.504$

0.504 = 50.4%

84% + 60% = 144%

144% ÷ 2 = 72%

Brian invests £600 into his bank account. He receives 3.2% per year compound interest. How much will Brian have after 6 years? Give your answer to the nearest penny where appropriate.

Answers

Answer:

Step-by-step explanation:

We would apply the formula for determining compound interest which is expressed as

A = P(1 + r/n)^nt

Where

A = total amount in the account at the end of t years

r represents the interest rate.

n represents the periodic interval at which it was compounded.

P represents the principal or initial amount deposited

From the information given,

P = £600

r = 3.2% = 3.2/100 = 0.32

n = 1 because it was compounded once in a year.

t = 6 years

Therefore,.

A = 600(1 + 0.032/1)^1 × 6

A = 600(1.032)^6

A = £724.82

The function f(x)=60(1.5)xf(x)=60(1.5)x models an animal population after x years.How does the average rate of change between Years 3 and 6 compare to the average rate of change between Years 0 and 3?

The average rate of change is 1.5 times as fast.

The average rate of change is 3 times as fast.

The average rate of change is 3.375 times as fast.

The average rate of change is 2.25 times as fast.