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kramer
3 years ago
5

Solve each system by elimination 6x+3y=21 -12x+y=-7

Mathematics
2 answers:
Olenka [21]3 years ago
5 0

Answer:

x=1,y=5

Step-by-step explanation:

6x+3y=21....(1)

-12x+y=-7.....(2)

From (2) make y the subject of formula

y=-7+12x...(3)

Substitute (3) into (1)

6x+3(-7+12x)=21

6x-21+36x=21

Collect like terms

6x+36x=21+21

42x=42

Divide both sides by 42

x=1

Substitute the value of x into (3)

y=-7+12(1)

y=-7+12

y=5

Therefore x=1,y=5

AnnyKZ [126]3 years ago
4 0

Answer:

(x,y)=(1,5)

Step-by-step explanation:

6x+3y=21/*2

-12x+y=-7

12x+6y=42 (1)

-12x+y=-7 (2)

(1)+(2): 7y=35

-12x+y=-7

y=35/7

-12x+y=-7

y=5

-12x+5=-7

y=5

-12x=-7-5

y=5

-12x=-12

y=5

x=-12/(-12

y=5

x=1

(x,y)=(1,5)

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A certain standardized test's math scores have a bell-shaped distribution with a mean of 530 and a standard deviation of 119. Co
kumpel [21]

Answer:

a) 68.2%

b) 31.8%

c) 2.3%

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 530

Standard Deviation, σ = 119

We are given that the distribution of math scores is a bell shaped distribution that is a normal distribution.

Formula:

z_{score} = \displaystyle\frac{x-\mu}{\sigma}

a) P(test scores is between 411 and 649)

P(411 \leq x \leq 649)\\\\= P(\displaystyle\frac{411 - 530}{119} \leq z \leq \displaystyle\frac{649-530}{119})\\\\= P(-1 \leq z \leq 1)\\\\= P(z \leq 1) - P(z < -1)\\= 0.841 - 0.159 = 0.682 = 68.2\%

b) P(scores is less than 411 or greater than 649)

P(x < 411 < x, x > 649)\\=1 = P(411 \leq x \leq 649)\\=1 - 0.682\\=0.318 = 31.8\%

c) P(score greater than 768)

P(x > 768)

P( x > 768) = P( z > \displaystyle\frac{768 - 530}{119}) = P(z > 2)

= 1 - P(z \leq 2)

Calculation the value from standard normal z table, we have,  

P(x > 768) = 1 -0.977 = 0.023 = 2.3\%

5 0
3 years ago
Using plane K, name a point that is not on the line.
yuradex [85]

Answer:

  H

Step-by-step explanation:

Plane K is shown with two lines. Points on one of them are A, B, G. Points on the other one are G, M, N.

The point in plane K that is not shown on any line is point H.

3 0
1 year ago
1,5,9,13 generalize the pattern by finding the nth term
ladessa [460]

Answer:

an= a1 +(n-1)*4

Step-by-step explanation:

a1 = 1, a2 =5, a3 = 9, a4= 13,... an= ?

we see that each term is getting bigger so usually that will happen because of addition or multiplication-in our case add 4 to previous term

a1 = 1,

a2 = a1+(2-1) 4 = 1+4 = 5,

a3 = a1 + (3-1)*4 = a1+8 = 1 + 8 = 9,

a4= a1 + (4-1)*4 = a1 + 12 = 1+12= 13,

...

an= a1 +(n-1)*4

7 0
2 years ago
Helppppp please can someone please answer this
oksian1 [2.3K]
20 and 24 are the answers
4 0
3 years ago
Convert into decimals (use your calculator): a) 6/38 b) 45/55 c) 4/28 d) 35/28 e) 1030/2030
Delicious77 [7]

Answer:

a.\hspace{3} \frac{6}{38} = 0.15789474\\\\b.\hspace{3} \frac{45}{55} = 0.81818181\\\\c.\hspace{3} \frac{4}{28} = 0.14285714\\\\d.\hspace{3} \frac{35}{28} = 1.25\\\\e.\hspace{3} \frac{1030}{2030} = 0.50738916

Step-by-step explanation:

Rational numbers, expressed as decimal numbers, are obtained from the operation of division between the integer of the numerator and the integer of the denominator. Then:

a.\hspace{3} \frac{6}{38} = 6\div38 = 0.15789474\\\\ b.\hspace{3} \frac{45}{55} = 45\div55 = 0.81818181\\\\c.\hspace{3} \frac{4}{28} = 4\div28 = 0.14285714\\\\ d.\hspace{3} \frac{35}{28} = 35\div28 = 1.25\\\\ e.\hspace{3} \frac{1030}{2030} = 1030\div2030 = 0.50738916

3 0
3 years ago
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