Insert grouping symbols <br><br> 2 times 9+7

What are the solutions to the expression x^2-8x=24

labwork [276]

Answer: x= 2(2+sqrt(10)) , x=2(2-sqrt(10)

Step-by-step explanation:

x^2-8x=24 <- subtract 24 from both sides

x^2-8x-24 <- take quadratic formulat (-2+/- Sqrt(b^2 - 4ac)/2a

-(-8) +/- sqrt((-8)^2 - 4(1*-24) all over (2*1) <- simplify

(-(-8) +/- 4sqrt(10) )/2 <- sepereate

(-(-8) +/4sqrt(10) )/2 , (-(-8) - 4sqrt(10) )/2 <- simplify

2(2+sqrt(10)) , 2(2-sqrt(10) =x

6 0

2 years ago

Patrick made a scale drawing of a newly planted hotel the height of the scale drawing is 27 inches what would be the actual heig

Charra [1.4K]

Answer:

0.6858 meters

Step-by-step explanation:

7 0

2 years ago

Read 2 more answers

If you invest $4000 at 9% interest compounded annually, in how many years will you have $20,000. Give your answer the nearest te

Masteriza [31]

Answer:

18.7 years

Step-by-step explanation:

This is a compound interest problem and the following variables have been given;

Principal = 4000; this is the amount o be invested

APR = 9%; this is the compound interest to be earned

Accumulated amount = 20,000

We are required to determine the duration in years. We apply the compound interest formula;

$A=P(1+r)^{n}$

$20000=4000(1+\frac{9}{100})^{n}\\20000=4000(1.09)^{n}\\5=(1.09)^{n}$

The next step is to introduce natural logarithms in order to determine n;

$ln5=nln(1.09)\\n=\frac{ln5}{ln(1.09)}\\n= 18.675$

The number of years required is thus 18.7 years

6 0

3 years ago

The doubling period of a bacterial population is 20 20 minutes. At time t = 100 t=100 minutes, the bacterial population was 9000

Nuetrik [128]

Answer:

The initial population was 2810

The bacterial population after 5 hours will be 92335548

Step-by-step explanation:

The bacterial population growth formula is:

$P = P_0 \times e^{rt}$

where P is the population after time t, $P_0$ is the starting population, i.e. when t = 0, r is the rate of growth in % and t is time in hours

Data: The doubling period of a bacterial population is 20 minutes (1/3 hour). Replacing this information in the formula we get:

$2 P_0 = P_0 \times e^{r 1/3}$

$2 = e^{r \; 1/3}$

$ln 2 = r \; 1/3$

$ln 2 \times 3 = r$

$2.08 \% = r$

Data: At time t = 100 minutes (5/3 hours), the bacterial population was 90000. Replacing this information in the formula we get:

$90000 = P_0 \times e^{2.08 \; 5/3}$

$\frac{9000}{e^{2.08 \; 5/3}} = P_0$

$2810 = P_0$

Data: the initial population got above and t = 5 hours. Replacing this information in the formula we get:

$P = 2810 \times e^{2.08 \; 5}$

$P = 92335548$

3 0

2 years ago

Classify each pair of angles as Complementary, Supplementary or neither.

stellarik [79]

Answer:

Step-by-step explanation:

1. Supplementary

2. complementary

3. neither

4. These two are vertically opposite so neither.

5. Supplementary

6. They add to 90 so they are complementary

7. They add to 180 so they are supplementary.

8. These 2 are equal and vertically opposite. They are neither for this exercise.

9. Complementary: they add to 90.

8 0

2 years ago

Insert grouping symbols 2 times 9+7