Question 1 Factoring is the process of reversing the distributive property so that a polynomial can be written as the product of simpler polynomials. True False

a)  Verified

b)  4 + √7 and 4 - √7

Given a cubic function with three roots, one of the roots is given as x = 2. The other two roots can be found by using the factor theorem. Using factor theorem, we have(f(x) = x³ - 10x² + 27x - 18)(x - 2) is a factor of f(x)if and only if f(2) = 0.So, we have f(2) = 2³ - 10(2²) + 27(2) - 18 = 0. Therefore, (x - 2) is a factor of f(x) and we can find the other two roots by factorizing the cubic function. Using long division method, we get f(x) = (x - 2)(x² - 8x + 9) Now, to find the other two roots, we solve the quadratic equation x² - 8x + 9 = 0 using the quadratic formula. x = (-b ± √(b² - 4ac))/2a. We have a = 1, b = -8 and c = 9. Substituting the given values in the above formula, we get x = (8 ± √(8² - 4(1)(9)))/2= (8 ± √28)/2= 4 ± √7. Therefore, the three roots of the cubic function are 2, 4 + √7 and 4 - √7.

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Answer:

7x = 7

with solution of x = 1

This is the first choice

Step-by-step explanation:

Choice 1
7x = 7 => x = 7/7 = 1

Choice 2
7x = 7x provides no additional info and therefore there are an infinite number of solutions; any value of  will satisfy

Choice 3
x + 1 = x + 1; infinite solutions for reasons cited under choice 2

Choice 4
x + 1 = x + 2
Eliminating x from both sides gives 1 = 2
Such an equation will have no solution; no value of x can satisfy the equation

Correct answer: Choice 1: 7x = 7

the selling price as a percent of cost is 120.52%, b- the selling price is $508.20 and the markup is 20.95% of cost.

(a) To find the selling price as a percent of cost, we need to first find the selling price and then divide it by the cost and multiply by 100%.

The markup on cost is 21%, which means the dealer sells the part for:

420 + 0.21*420 = $508.20

So the selling price is $508.20 and the cost is $420.

The selling price as a percent of cost is:

508.20/420 * 100% = 120.52%

So the selling price is 120.52% of the cost.

(b) The selling price is $508.20.

(c) The markup is the difference between the selling price and the cost, expressed as a percentage of the cost:

Markup = (Selling price - Cost)/Cost * 100%

= (508.20 - 420)/420 * 100%

= 20.95%

So the markup is 20.95% of the cost.

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The percentage interest rate added to the account at the end of the year is 1.3%

Tax is the compulsory levy paid by citizens to the government for buying goods and services.

Amount Samia invest = £3,000

Amount of interest = x

Rate of tax = 20%

Amount of tax = £7.80

So,

20% of x = £7.80

0.2x = £7.80

x = £7.80/0.2

x = £39

Percentage of interest rate:

x% of £3000 = £39

x% × 3000 = 39

x% = 39/3000

x% = 0.013

x% = 1.3%

Hence, 1.3% is the percentage of Samia investment added to the account.

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binomial distribution

Question: Suppose that 20% of all copies of grade 7 Science textbook fail a certain binding strength test. Let X denote the number among 15 randomly selected copies that fail the test.b. What is the probability that at least 8 fail the test?To find the probability that at least 8 fail the test, we will use the binomial probability formula.The binomial distribution is a statistical distribution that describes the probability of success or failure in an experiment or survey with two possible outcomes.Suppose a trial consists of n independent experiments, each of which has two possible outcomes: either success with probability p or failure with probability q = 1 – p. If X is the number of successes in n trials, then X is said to follow a binomial distribution with parameters n and p. The probability that X = x is given by;P(X = x) = nCxpx(1-p)n-xwhere nCx = n! / x! (n-x)! is the binomial coefficient which counts the number of ways that x successes can be chosen from n trials.Using the formula, we have;P(X >= 8) = P(X = 8) + P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14) + P(X = 15)Here n = 15, p = 0.2 and q = 0.8P(X >= 8) = P(X = 8) + P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14) + P(X = 15)= 15C8 (0.2)^8 (0.8)^7 + 15C9 (0.2)^9 (0.8)^6 + 15C10 (0.2)^10 (0.8)^5 + 15C11 (0.2)^11 (0.8)^4 + 15C12 (0.2)^12 (0.8)^3 + 15C13 (0.2)^13 (0.8)^2 + 15C14 (0.2)^14 (0.8)^1 + 15C15 (0.2)^15 (0.8)^0= 0.0094 + 0.0267 + 0.0524 + 0.0864 + 0.1174 + 0.1312 + 0.1184 + 0.0352= 0.5771Therefore the probability that at least 8 fail the test is 0.5771 (rounded to four decimal places).Answer: 0.5771

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Answer:

45

Step-by-step explanation:

Step-by-step explanation:

let f(x) be y

y=x+2

make x the subject of the formula

x=2-y

Answer:

Step-by-step explanation:

Answer:

1a) x=40°

2a) x=30°

Step-by-step explanation:

Use the fact that the sum of the angles of a triangle is always 180°.

So for 1a), x + x+40 + x+20 = 180

Simplify to

3x + 60 = 180

3x = 120

x = 40

apply the same logic to all the others.

For circles, the sum of the angles is 360°, so for 2b)

5x+3x+4x = 360 =>

12x = 360

x = 30°

113,950,000,000 ([tex]1.1395x10^7[/tex] is scientific notation, so you need to move the decimal to the left 7 places and add the relevant commas to get 113,950,000,000 in standard notation).

Notation is a method of representing information, usually in a concise and organized way. It can be used to represent mathematical equations, algorithms, music, dance, and other concepts. Notation is often used as a shorthand for communicating ideas to others, as it allows for a more precise and efficient way of conveying information. Notation also allows for the precise and consistent representation of a concept, allowing for greater accuracy and understanding.

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Answer:

Step-by-step explanation:

I think y ≤ 3 - 3x

Answer:

-128.31

First choice

Step-by-step explanation:

Using a calculator:

7.05(−18.2) = 7.05 x -18.2 = -128.31

Answer:

y=30x+50

Step-by-step explanation:

3x30+50=140

5x30+50=200

Answer:

5 cubed is 5 x 5 x 5 = 125.

10 squared is 10 x 10 = 100.

So, 5 cubed - 10 squared = 125 - 100 = 25.

We can also express 25 as a power of 5 by noting that 25 = 5 squared. Therefore:

5 cubed - 10 squared = 5 squared x 5 - 10 squared = 5^(2+1) - 10^(2) = 5^3 - 10^(2) = 125 - 100 = 25.

So, the answer is 5 squared or 5^2.

Step-by-step explanation:

Answer:

25

Step-by-step explanation:

5 cubed - 10 squared

[tex]5^{3} - 10^{2} \\ = 125 - 100\\= 25[/tex]

Hope this helps!

Brainliest and a like is much appreciated!

Answer:

288π in³

Step-by-step explanation:

V-sphere = 4/3πr³

D = 12in   r = D/2 = 12/2 = 6 in

V = (4/3)(6)³π = (4/3)(216)π = 288π in³

Answer:

x = 4

Step-by-step explanation:

log a + log b = log ab

log(base b) x = y, then b^y = x

log₂2x + log₂4 = 5

log₂ (2x × 4) = 5

log₂ 8x = 5

8x = 2^5

8x = 32

x = 4

Answer:

3(a−1)

———

a+1

Step-by-step explanation:

For (a), the probability that John wins on the third round given that he only won two rounds of the three is 5/6.

For (b), the suitability of modelling X after the geometric distribution is appropriate because the geometric distribution is the probability distribution of the number of Bernoulli trials needed to get one success. The probability of John winning on the fifth round is $(\frac{2}{5})^4(\frac{5}{6})=\frac{50}{648}$

For (c), any necessary assumptions required in order to suitably model Y after the binomial distribution is that the trials (i.e. rounds of play) are independent, and that the probability of success is the same for each trial. The parameters of this binomial distribution are: n = 10, p = 1/5.

For (d), assuming the assumptions in Question 2(c) hold, the expected value of Y (E(Y)) is 8 and the variance of Y (Var(Y)) is 2.4.

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The true statement is that (x + 3) is a factor of f(x) = x³ + 3x² - x - 3 since f(-3) = 0.

A polynomial is an expression that consists of variables, terms, exponents and constants.

The factors are the polynomials which are multiplied to produce the original polynomial.

The factorisation of a polynomial is breaking the polynomial as a products.

Therefore,

f(x) = x³ + 3x² - x - 3

Hence, let's use the factor (x + 3)

Therefore,

f(-3) = (-3)³ + 3(-3)² - (-3) - 3

f(-3) = -27 + 27 + 3 - 3

f(-3) = 0

Therefore, the factor is (x + 3) since f(-3) = 0

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Using Pythagorean theorem, the triangle is an acute triangle.

What is Pythagorean theorem?

The Pythagorean theorem is a fundamental result in Euclidean geometry that describes the relationship between the three sides of a right-angled triangle.

In equation form, this can be written as:

[tex]c^2 = a^2 + b^2[/tex]

where c is the length of the hypotenuse, and a and b are the lengths of the other two sides (also known as the legs) of the right-angled triangle.

If the triangle is not a right triangle, then the inequality [tex]c^2 < a^2 + b^2[/tex]holds for an acute triangle and [tex]c^2 > a^2 + b^2[/tex] holds for an obtuse triangle.

Using this formula, we can check if the given triangle is right, acute, or obtuse:

a = 43, b = 96, and c = 89

[tex]c^2 = 89^2 = 7921[/tex]

[tex]a^2 + b^2 = 43^2 + 96^2 = 1849 + 9216 = 11065[/tex]

Since [tex]c^2 < a^2 + b^2[/tex], we can see that:

[tex]c^2 < a^2 + b^2[/tex]

So the triangle is an acute triangle.

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Answer:

(2x - 3) (x + 3)

Step-by-step explanation:

Let's check

(2x - 3) (x + 3)

2x² + 6x - 3x - 9

2x² + 3x - 9

So, (2x - 3) (x + 3) is the correct answer.

After approximately 9.95 years, the employee will be earning $10.00 per hour.

What is property of logarithms?

The properties of logarithms are a set of rules that can be used to manipulate logarithmic expressions, including the product, quotient, power, and change of base properties.

We are given that the employee's hourly wage after t years is given by the equation [tex]y=7.03(1.03)^t[/tex]. We need to find the amount of time t after which he will be earning $10.00 per hour. So we set y = $10.00 and solve for t as follows:

$10.00 = $[tex]7.03(1.03)^t[/tex]

Divide both sides by $7.03:

1.4246 = [tex]1.03^t[/tex]

Take the natural logarithm of both sides:

ln(1.4246) = ln([tex]1.03^t[/tex])

Using the property of logarithms that ln([tex]a^b[/tex]) = b * ln(a), we can simplify the right-hand side:

ln(1.4246) = t * ln(1.03)

Solve for t:

t ≈ 9.95 years

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Each year, the wild turkey population, which was once 250, drops by 2.2%. There will be around 209 turkeys left after 8 years.

Wild turkey populations are declining at a 2.2% annual pace. The initial population of 250 turkeys is anticipated to drop to around 209 turkeys after 8 years. Using the exponential decay formula, we can determine the rate of decline annually: P is the population at a certain moment, P0 is the starting population, r is the rate of reduction expressed as a decimal, and t is the time in years. P = P0 (1 - r)t. The answer to the r equation is r = (1 - (P/P0)(1/t)) = 0.022. As a result, the population is declining by 2.2% annually.

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The answer of the given question based on the theorem  For any integer , is odd if and only if + 1 is even the answer is for any integer , is odd if and only if + 1 is even.

A theorem is  statement in mathematics that has been proven to be the true based on logical reasoning and the mathematical principles. In other words,  theorem is a proposition that can be demonstrated or proved to be true through  logical argument.

Proof:

(⇒) Suppose is odd.

Thus, for some integer , = 2 + 1.

Now + 1 = (2 + 1) + 1 = 2 + 2 = 2( + 1).

Therefore, + 1 is even.

(⇐) Suppose + 1 is even.

Then, for some integer , + 1 = 2.

Thus, for some integer , = 2 - 1 = 2( - 1) + 1 .

Since 2 | 2( + 1), 2 | ( + 1).

Therefore, is odd.

Thus, we have shown that for any integer , is odd if and only if + 1 is even.

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The area of a parallelogram can be obtained from the formula for a rectangle by using the same base and height, leading to the formula Area of parallelogram = base x height.

By moving the red triangle to the green triangle, we create a rectangle with the same base and height as the original parallelogram. Therefore, the area of the original parallelogram is equal to the area of the rectangle, which is given by the formula:

Area of rectangle = base x height

We can conclude that the formula for the area of a parallelogram is also given by:

Area of parallelogram = base x height

This is because a parallelogram can be divided into two congruent triangles, and the area of each triangle is half the area of the parallelogram. Therefore, the area of a parallelogram is equal to the base times the height, which is the same as the formula for the area of a rectangle.

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The principal is $467.69 rupees (rounded to two decimal places).

The concept of simple interest is a type of interest calculation based on a fixed percentage rate applied to an initial amount of money, called the principal, for a specific period of time

To find the principal, we can use the formula:

Total Interest = (Principal x Rate x Time) / 100

Where,

Rate = Annual Rate of Interest

Time = Period in years

Plugging in the given values, we get:

1222 = (Principal x 6.5 x 4) / 100

Simplifying the equation:

1222 = (26 x Principal) / 10

Multiplying both sides by 10/26:

Principal = $467.69

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[tex]1\dfrac{1}{2} = \dfrac{3}{2} = 1.5[/tex]

[tex]20 (10) (5-1.5) = 200(3.5) = 700 \ cubic \ feet[/tex]

Answer:

(B) 700 cubic feet

Step-by-step explanation:

The height of water in the pool is 5 - 1 1/2 = 3 1/2 feet.

The volume of water needed to fill the pool up to 3 1/2 feet is:

20 feet x 10 feet x 3 1/2 feet = 700 cubic feet

Therefore, the answer is (B) 700 cubic feet.

Answer:

-5

Step-by-step explanation:

3n-6=-21

    +6   +6

3n=-15 --> divide both sides by 3

n=-5