1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Alex787 [66]
3 years ago
6

Write an equation of the line that is parallel to y = 1/2x + 3 and passes through the point (10, -5)

Mathematics
2 answers:
Liula [17]3 years ago
5 0
The correct answer is d
Pavlova-9 [17]3 years ago
4 0
The answer is D) y= 1/2x - 10
You might be interested in
Write the polynomial f(x)=x^4-10x^3+25x^2-40x+84. In factored form
Verizon [17]
<h2>Steps:</h2>

So firstly, to factor this we need to first find the potential roots of this polynomial. To find it, the equation is \pm \frac{p}{q}, with p = the factors of the constant and q = the factors of the leading coefficient. In this case:

\textsf{leading coefficient = 1, constant = 84}\\\\p=1,2,3,4,6,7,12,14,21,28,42,84\\q=1\\\\\pm \frac{1,2,3,4,6,7,12,14,21,28,42,84}{1}\\\\\textsf{Potential roots =}\pm 1, \pm 2,\pm 3,\pm 4,\pm 6, \pm 7,\pm 12,\pm 14,\pm 21,\pm 28,\pm 42,\pm 84

Next, plug in the potential roots into x of the equation until one of them ends with a result of 0:

f(1)=(1)^4-10(1)^3+25(1)^2-40(1)+84\\f(1)=1-10+25-40+84\\f(1)=60\ \textsf{Not a root}\\\\f(2)=2^4-10(2)^3+25(2)^2-40(2)+84\\f(2)=16-10*8+25*4-80+84\\f(2)=16-80+100-80+84\\f(2)=80\ \textsf{Not a root}\\\\f(3)=3^4-10(3)^3+25(3)^2-40(3)+84\\f(3)=81-10*27+25*9-120+84\\f(3)=81-270+225-120+84\\f(3)=0\ \textsf{Is a root}

Since we know that 3 is a root, this means that one of the factors is (x - 3). Now that we know one of the roots, we are going to use synthetic division to divide the polynomial. To set it up, place the root of the divisor, in this case 3 from x - 3, on the left side and the coefficients of the original polynomial on the right side as such:

  • 3 | 1 - 10 + 25 - 40 + 84
  • _________________

Firstly, drop the 1:

  • 3 | 1 - 10 + 25 - 40 + 84
  •     ↓
  • _________________
  •     1

Next, multiply 3 and 1, then add the product with -10:

  • 3 | 1 - 10 + 25 - 40 + 84
  •     ↓ + 3
  • _________________
  •     1  - 7

Next, multiply 3 and -7, then add the product with 25:

  • 3 | 1 - 10 + 25 - 40 + 84
  •     ↓ + 3  - 21
  • _________________
  •     1  - 7 + 4

Next, multiply 3 and 4, then add the product with -40:

  • 3 | 1 - 10 + 25 - 40 + 84
  •     ↓ + 3  - 21 + 12
  • _________________
  •     1  - 7  +  4  - 28

Lastly, multiply -28 and 3, then add the product with 84:

  • 3 | 1 - 10 + 25 - 40 + 84
  •     ↓ + 3  - 21 + 12  - 84
  • _________________
  •     1  - 7  +  4  - 28 + 0

Now our synthetic division is complete. Now since the degree of the original polynomial is 4, this means our quotient has a degree of 3 and follows the format ax^3+bx^2+cx+d . In this case, our quotient is x^3-7x^2+4x-28 .

So right now, our equation looks like this:

f(x)=(x-3)(x^3-7x^2+4x-28)

However, our second factor can be further simplified. For the second factor, I will be factoring by grouping. So factor x³ - 7x² and 4x - 28 separately. Make sure that they have the same quantity inside the parentheses:

f(x)=(x-3)(x^2(x-7)+4(x-7))

Now it can be rewritten as:

f(x)=(x-3)(x^2+4)(x-7)

<h2>Answer:</h2>

Since the polynomial cannot be further simplified, your answer is:

f(x)=(x-3)(x^2+4)(x-7)

6 0
3 years ago
Many utility companies promote energy conservation by offering discount rates to consumers who keep their energy usage below cer
aleksley [76]

Answer:

a. 0.1681 = 16.81% probability that all five qualify for the favorable rate.

b. 0.5283 = 52.83% probability that at least four qualify for the favorable rates

Step-by-step explanation:

For each Puerto Rico resident, there are only two possible outcomes. Either they qualify for discounted rates, or they do not. The probability of a person in the sample qualifying for discounted rates is independent of any other person in the sample. This means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

70% of the island residents of Puerto Rico have reduced their electricity usage sufficiently to qualify for discounted rates.

This means that p = 0.7

Five residential subscribers are randomly selected from San Juan, Puerto Rico

This means that n = 5

a. All five qualify for the favorable rate

This is P(X = 5). So

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 5) = C_{5,5}.(0.7)^{5}.(0.3)^{0} = 0.1681

0.1681 = 16.81% probability that all five qualify for the favorable rate.

b. At least four qualify for the favorable rates

This is

P(X \geq 4) = P(X = 4) + P(X = 5)

So

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 4) = C_{5,4}.(0.7)^{4}.(0.3)^{1} = 0.3602

P(X = 5) = C_{5,5}.(0.7)^{5}.(0.3)^{0} = 0.1681

P(X \geq 4) = P(X = 4) + P(X = 5) = 0.3602 + 0.1681 = 0.5283

0.5283 = 52.83% probability that at least four qualify for the favorable rates

5 0
3 years ago
Would someone that's an expert or just really good with math help me with my three most recent questions please??? I'll mark who
Bogdan [553]
Go on I’m listening!!! What’s the question?
4 0
3 years ago
Please help me guys​
seraphim [82]

Area of pond:

A=\pi r^{2}

r=1,5m

A=3,142*1,5*1,5=7,0695

Area of pond with path

B=\pi r^{2}

r=50 cm+1,5m=0,5m+1,5m=2m

B=3,142*2*2=12,568

Area of path:

12,568-7,0695=5,4985=5,50

8 0
3 years ago
Read 2 more answers
Solve the inequality.
Ray Of Light [21]

Answer:

First, subtract 3 from both sides.

Then, <em>divide</em> both sides by 4.

x>6

4 0
2 years ago
Other questions:
  • Ed is 7 years older than Ted. Ed’s age is also 3/4 times Ted’s age. How old are Ed and Ted?
    9·1 answer
  • What angles are angles with measures that add to equal 180
    15·2 answers
  • Richard walks every day for exercise at a rate of 1 kilometer every 12 min. At this rate ,how many meters can Richard walk in a
    6·2 answers
  • * ANSWER PLS * Convert 55° to radians.
    9·2 answers
  • What is 80% of 22? pls, I need the answer.
    10·2 answers
  • Pleaseeeee help me!!!!! i’ll appreciate it so much!
    8·2 answers
  • What is the y-intercept of the line with the equation y = 4 x + 2? a. -2 b. 4 c. 2 d. Negative one-half
    15·2 answers
  • ANSWER NEEDED QUICK, SHOW YOUR WORK PLEASE)
    9·1 answer
  • Volume of a cylyinder witha heght of 2.3 and a base diameter of 15.2
    7·1 answer
  • Find the solution by graphing the equations pls help
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!