MATHEMATICS HIGH SCHOOL

Use linear combination. To solve system
-2x+7y=10
X-3y=-3

Answers

Answer 1
Answer: -2x + 7y = 10 ⇒ -2x + 7y = 10
   x - 3y = -3   ⇒ -2x + 6y = 6 
                                      y = 4
                         -2x + 7(4) = 10
                           -2x + 28 = 10
                                   -28   -28
                                   -2x = -18
                                    -2      -2
                                       x = 9
                                  (x, y) = (9, 4)
Answer 2
Answer: so
use elimintation
multily second equation by 2
2x-6y=-6
add to first equation

2x-2x+7y-6y=10-6
y=4
subsitute
x-3(4)=-3
x-12=-3
add 12 to both sdies
x=9


x=9
y=4

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The focus of a parabola is (3,-7) and the directrix is y = -4.What is an equation of the parabola?

Answers

Answer:

  (a)  (x -3)^2 = -6(y +5.5)

Step-by-step explanation:

The equation of a parabola can be written as ...

  (x -h)^2 = 4p(y -k)

where (h, k) is the vertex, and p is the distance from the focus to the vertex.

The vertex is half-way between the focus and directrix, so is ...

  (h, k) = (1/2)((3, -7) +(3, -4)) = (3, -5.5)

The focus is at y=-7, and the vertex is at y=-5.5, so the distance between them is ...

  -7 -(-5.5) = -1.5

Then the equation for the parabola is ...

  (x -3)^2 = 4(-1.5)(y -(-5.5))

  (x -3)^2 = -6(y +5.5) . . . . matches the first choice

According to the Central Limit Theorem, a) in a sufficiently large random sample, the distribution of a random variable X, with mean μ and standard deviation σ, is a normal distribution with mean μ and standard deviation σ/sqrt(n)b) The Central Limit Theorem does not apply to heavily skewed distributions.
True or False?

Answers

The statement is True. According to the Central Limit Theorem, in a sufficiently large random sample, the distribution of a random variable X, with mean μ and standard deviation σ, is a normal distribution with mean μ and standard deviation σ/sqrt(n).

1. The Central Limit Theorem states that the distribution of the sample means of a large sample size will approach a normal distribution, regardless of the original distribution of the population from which the sample is drawn.
2. For a sufficiently large sample size, the mean of the sample means will approach the population mean (μ) and the standard deviation of the sample means will approach the population standard deviation divided by the square root of the sample size (σ/sqrt(n)).
3. Therefore, in a sufficiently large random sample, the distribution of a random variable X, with mean μ and standard deviation σ, is a normal distribution with mean μ and standard deviation σ/sqrt(n).

This is the case because the Central Limit Theorem states that the distribution of sample means is approximately normal, regardless of the original distribution of the population from which the sample is drawn.

To know more about central limit theorem, refer here:

brainly.com/question/18403552#

#SPJ11
True so there is the answer

Colin took out a loan with a principal of $32,800. After five years, the interest and principal totaled $48,872. If Colin made monthly payments of $816 for five years until the loan was paid off, how much did Colin pay in service charges?

Answers

Thank you for posting your question here at brainly. I hope the answer will help you. Feel free to ask more questions.

Below are the choices:

a. 
$16,072 
b. 
$88 
c. 
$16,160 
d. 
$163

816 * 5 * 12= 48960 

If the P and I totaled 48872, then... 
48960 - 48872= 88 

The service charges were $88 B.

Answer:

B. 88!!!

Step-by-step explanation:

A number added to itself twelve times is five more than twice the number. What is the number?

Answers

x- \ searching\ number\n\n x+12x=2x+5\n 13x-2x=5\n 11x=5\ |:11\n x=(5)/(11)\n\n The\ number\ is\ (5)/(11),

76 is ,2% of what number ?

Answers

p\%=(p)/(100)\n\n2\%=(2)/(100)=0.02\n\n76:0.02=3800\leftarrow solution

Rewrite f(x) = –2(x − 3)2 + 2 from vertex form to standard form. pleae help.

Answers

f(x) = -2(x - 3)² + 2
f(x) = -2(x - 3)(x - 3) + 2
f(x) = -2[x(x - 3) - 3(x - 3)] + 2
f(x) = -2[x(x) - x(3) - 3(x) - 3(-3)] + 2
f(x) = -2(x² - 3x - 3x + 9) + 2
f(x) = -2(x² - 6x + 9) + 2
f(x) = -2(x²) - 2(-6x) - 2(9) + 2
f(x) = -2x² + 12x - 18 + 2
f(x) = -2x² + 12x - 16
f(x)=-2(x-3)2+2=f(x)=-2(x-3)
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