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Greeley [361]
3 years ago
12

The line goes through the ordered pair (10, 6) It has a y-intercept of -2.

Mathematics
1 answer:
VLD [36.1K]3 years ago
6 0

Answer: the x-intercept would be (2,-2)

Step-by-step explanation:

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Use the factor theorem to determine whether or not the first polynomial is a factor of the second
krok68 [10]

Answer/Step-by-step explanation:

Based on the factor theorem, a polynomial, x - a, is said to be a factor of another polynomial, f(x), if an only if f(a) = 0.

Using this theorem, let's determine whether each of the given first polynomial, is a factor of the second polynomial.

1. x - 1; x² + 2x + 5

By the factor theorem, x - 1 will be a factor of f(x) = x² + 2x + 5, if and only if f(1) = 0.

f(1) = 1² + 2(1) + 5

= 1 + 2 + 5

= 8

Since f(1) ≠ 0, therefore the first polynomial, x - 1, is NOT a factor of the second polynomial, x² + 2x + 5.

2. x + 1; x³ - x - 2

By the factor theorem, x + 1 will be a factor of f(x) = x³ - x - 2, if and only if f(-1) = 0.

f(1) = -1³ - (-1) - 2

= -1 + 1 - 2

= -2

Since f(-1) ≠ 0, therefore the first polynomial, x + 1, is NOT a factor of the second polynomial, x³ - x - 2.

3. x - 4; 2x³ - 9x² + 9x - 20

By the factor theorem, x - 4 will be a factor of f(x) = 2x³ - 9x² + 9x - 20, if and only if f(4) = 0.

f(4) = 2(4)³ - 9(4)² + 9(4) - 20

= 128 - 144 + 36 - 20

= 0

Since f(4) = 0, therefore the first polynomial, x + 4, is a factor of the second polynomial, 2x³ - 9x² + 9x - 20.

4. a - 1; a³ - 2a² + a - 2

By the factor theorem, a - 1 will be a factor of f(a) = a³ - 2a² + a - 2, if and only if f(1) = 0.

f(1) = 1³ - 2(1)² + 1 - 2

= 1 - 2 + 1 - 2

= -2

Since f(1) ≠ 0, therefore the first polynomial, a - 1, is NOT a factor of the second polynomial, a³ - 2a² + a - 2.

5. y + 3; 2y³ + y² - 13y + 6

By the factor theorem, y + 3 will be a factor of f(y) = 2y³ + y² - 13y + 6, if and only if f(-3) = 0.

f(-3) = 2(-3)³ + (-3)² - 13(-3) + 6

= -54 + 9 + 39 + 6

= 0

Since f(-3) = 0, therefore the first polynomial, y + 3, is a factor of the second polynomial, 2y³ + y² - 13y + 6.

7 0
3 years ago
Which operation would you do first?
svp [43]

Answer:

Addition +

Step-by-step explanation:

You are correct because according to PEMDAS, you have to do what is inside the parentheses first, which just happens to be addition.

7 0
3 years ago
5. A company sells small, colored binder clips in packages of 20 and offers a money-back guarantee if two or more of the clips a
SOVA2 [1]

Answer:

a) Binomial.

b) n=20, p=0.01, k≥2

The probability hat a package sold will be refunded is P=0.0169.

Step-by-step explanation:

a) We know that

  • the defective probability is constant and independent.
  • the sample size is bigger than one subject.

The most appropiate distribution to represent this random variable is the binomial.

b) The parameters are:

  • Sample size (amount of clips in the package): n=20
  • Probability of defective clips: p=0.01.
  • number of defective clips that trigger the money-back guarantee: k≥2

The probability of the package being refunded can be calculated as:

P(x\geq2)=1-(P(x=0)+P(x=1))\\\\\\P(x=k) = \dbinom{n}{k} p^{k}q^{n-k}\\\\\\P(x=0) = \dbinom{20}{0} p^{0}q^{20}=1*1*0.8179=0.8179\\\\\\P(x=1) = \dbinom{20}{1} p^{1}q^{19}=20*0.01*0.8262=0.1652\\\\\\P(x\geq2)=1-(0.8179+0.1652)=1-0.9831=0.0169

6 0
3 years ago
Is 180 divisilbe by 9
Darina [25.2K]
9 is divisible by 9, Therefore, 180 is divisible by 9 and the answer to the question, "Is 180 Divisible By 9?" is Yes.
7 0
3 years ago
Read 2 more answers
Before starting his job, Clayton had been on an airplane 3 times. Since then, he has flown 6 times each year.
xz_007 [3.2K]

Answer:

f = 6y + 3

Step-by-step explanation:

<u>The equation to reflect this condition is:</u>

  • f = 6y + 3

<u>Where</u>

  • 3 - is constant, the initial number of flights
  • 6 - coefficient, number of flights per year
  • y- number of years
  • f- total number of flights
8 0
3 years ago
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