MATHEMATICS HIGH SCHOOL

13) v2 - 110 + 18 = 0
14) 5x7 - 12x +7 = 0
Solve by factoring
13) v2 - 110 + 18 = 0 14) 5x7 - 1

Answers

Answer 1
Answer:

Answer:

see explanation

Step-by-step explanation:

(13)

v² - 11v + 18 = 0 ← in standard form

(v - 2)(v - 9) = 0 ← in factored form

Equate each factor to zero and solve for v

v - 2 = 0 ⇒ v = 2

v - 9 = 0 ⇒ v = 9

solutions are v = 2, v = 9

(14)

5x² - 12x + 7 = 0

Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 5 × 7 = 35 and sum = - 12

The factors are - 5 and - 7

Use these factors to split the x- term

5x² - 5x - 7x + 7 = 0 ( factor the first/second and third/fourth terms )

5x(x - 1) - 7(x - 1) = 0 ← factor out (x - 1) from each term

(x - 1)(5x - 7) = 0

Equate each factor to zero and solve for x

x - 1 = 0 ⇒ x = 1

5x - 7 = 0 ⇒ 5x = 7 ⇒ x = (7)/(5)

solutions are x = 1, x = (7)/(5)

Related Questions

Which verbal expression best describes the algebraic expression 3x ÷ 5? The quotient of three times some number and five The product of some number and five divided by three The quotient of three and some number times five The sum of three and some number divided by five
Which number line shows the correct placement of -200, 75, and -150?​
Your mother has left you in charge of the annual family yard sale. Before she leaves you to your entrepreneurial abilities, she explains that she has made the job easy for you: everything costs either $1.50 or $3.50. She asks you to keep track of how many of each type of item is sold, and you make a list, but it gets lost sometime throughout the day. Just before she’s supposed to get home, you realize that all you know is that there were 150 items to start with (your mom counted) and you have 41 items left. Also, you know that you made $227.50. Write a system of equations that you could solve to figure out how many of each type of item you sold.A) x + y = 109(1.5)x + 227.50 = (3.5)yB) x + y = 109(3.5)x + 227.50 = (1.5)yC) x + y = 41(1.5)x + 227.50 = (3.5)yD) x + y = 109(1.5)x + (3.5)y = 227.50E) x + y = 150(1.5)x + (3.5)y = 227.50F) x + y = $3.50(1.5)x + (3.5)y = 227.50
Sheri wants to know how the 1,090 students at her school feel about after-school programs She selects each of these samples randomly. Is each a representative sample of the population
Write the expression as either the sine, cosine, or tangent of a single angle. sin(pi/2)cos(pi/7)+cos(pi/2)sin(pi/7)

C(x) = 0.000002x3 − 0.03x2 + 400x + 80,000 where C(x) denotes the total cost incurred in producing x sets. Find the level of production that will yield a maximum profit for the manufacturer. Hint: Use the quadratic formula

Answers

Answer:

The producer will have maximum profit when x is 5000.

Step-by-step explanation:

Given C(x) = 0.000002x³ - 0.03x² + 400x + 80000

To find the level of production that will yield the maximum profit for the manufacturer, firstly, we differentiate C(x) to obtain C'(x), we then set the resulting quadratic expression to zero and solve. Whichever of the two values obtained from the quadratic equation will be tested to see what we want to find.

Differentiate C(x)

C'(x) = 3(0.000002)x² - 2(0.03)x + 400

= 0.000006x² - 0.06x + 400

Set C'(x) = 0

0.000006x² - 0.06x + 400 = 0

Solve using quadratic formula.

x = [-b ± √(b² - 4ac)]/2a

a = 0.000006

b = -0.06

c = 400

x = [-(-0.06) ± √((-0.06)² - 4(0.000006 × 400)]/2(0.000006)

= [0.06 ± √(0.0036 - 0.0096]/0.000012

= (0.06/0.000012) ± i√(0.006)/0.000012

= 5000 ± 6454.97i

x = 5000 + 6454.97i

Or

x = 5000 - 6454.97i

Why is 1/6 greater than 1/8 but less than 1/3

Answers

I would show it in decimals. Seeing it to show how close it is to one would make it a lot easier- 1/6= .16. 1/8=.125 and 1/3=.33 So looking at the decimals you can see how one would be bigger than the other

Does anyone know this

Answers

Answer:

AB-DE

Step-by-step explanation:

hi I m from India nice to meet you bro

Adult male heights are normally distributed with a mean of 70 inches and a standard deviation of 3 inches. The average basketball player is 79 inches tall. Approximately what percent of the adult male population is taller than the average basketball player?0.13%

0.87%

49.87%

99.87%

Answers

Answer: First Option is correct.

Step-by-step explanation:

Since we have given that

Mean (\mu)= 70 inches

Standard deviation (\sigma)= 3 inches

Average basket ball player (\bar{X}) = 79 inches

Since it is normally distributed assume with 5% significance .

So, it becomes,

Z>\frac{\bar{X}-\mu}{\sigma}\n\nZ>(79-70)/(3)\n\nZ>(9)/(3)\n\nZ>3\n\n\therefore\ P(Z>3)=1-0.9987=0.0013

At 0.05 level of significance , 0.0013 = 0.13% of the adult male population is taller than the average basketball player .

Hence, First Option is correct.
Kindly check this link for more details:

Therefore the answer is 0.13% is the approximate percentae of the adult male population who are taller than the average basketball player

An experiment is designed to determine the launch angle that will give a projectile the greatest range (make it go the longest distance). The "launcher" is a slingshot type of apparatus that is spring-loaded and released by a trigger. For each trial, the same painted rock is retrieved and launched. Measurements are taken linearly from the launch site to the landing site. The trials were done on a windless day.Which of the following would be a good hypothesis for this experiment?

If the angle of the launcher is increased, the rock will go further.

Changing the angle of the launcher will vary the distance that the rock can be projected.

Answers

If the angle of the launcher is increased, the rock will go further........
test each

if angle is increased, rock will go further
if the angle starts at 0, then increases to 90 degrees (straight up) the rock will go up then bounce off of the launcher going either front or back, but vastly shorter than if it were pointed straight ahead


2nd one
changing angle change the distance
we see that is true

Boyd charges a $3.50 fee for setting up and taking down the umbrellas. He also charges $2.50 for each hour of use. Suppose h stands for the number of hours you rent. How much will it cost to rent an umbrella for h hours

Answers

2.5h + 3.5

This is because it will cost $2.50 for every hour you use, plus an additionally fee for set up
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