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3 years ago

What is the solution of the system? Use any method. 3x + 2y = 7 y = –3x + 11

Mathematics

1 answer:

Gnom [1K]3 years ago

6 0

Answer:

$(5,-4)$

Step-by-step explanation:

SOLVE BY SUBSTITUTION:

STEP 1: Replace all occurrences of $y$ with $-3x+11$ in each equation.

$-3x+22=7\\y=-3x+11$

STEP 2: Solve for $x$ in the first equation.

$x=5\\y=-3x+11$

STEP 3: Replace all occurrences of $x$ with $5$ in each equation.

$y=-4\\x=5$

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Will mark brainliest and rate 5/5 if question is answered right.

Roman55 [17]

Answer:

a) A = 36π in² ≈ 113.09 in²

b) $0.98 per slice

c) $0.09 per square inch

Step-by-step explanation:

a) area = πr²

r= diameter/2 = 12/2 = 6

A = π(6)²

A = 36π in² ≈ 113.09 in²

b) s = price per slice

s = 9.75 ÷ 10

s = $0.975 ≈ $0.98

c) price per square inch = price ÷ area

= 9.75 ÷ 113.09

= $0.086 ≈ $0.09 per square inch

4 0

3 years ago

What is the range of the function graphed below? PLEASE ANSWER ASAP

jenyasd209 [6]

<h3>Answer: Choice C) $-\infty < y < 2$ </h3>

This is a more complicated way to write $y < 2$

The range is the set of all possible y outputs of a function. So we use the graph to see what y values are possible. The graph shows that y can be anything smaller than y = 2. We can't actually reach y = 2 itself due to a horizontal asymptote here.

In interval notation, the answer would be $(-\infty, 2)$ with the curved parenthesis to indicate "do not include y = 2 as part of the range".

6 0

3 years ago

Find the smallest positive integer solution to the following system of congruences: x = 0 (mod 5) x = 8 (mod 11) The solution is

igomit [66]

Answer:

The smallest positive integer solution to the given system of congruences is 30.

Step-by-step explanation:

The given system of congruences is

$x=0(mod5)$

$x=8(mod11)$

where, m and n are positive integers.

It means, if the number divided by 5, then remainder is 0 and if the same number is divided by 11, then the remainder is 8. It can be defined as

$x=5m$

$x=11n+8$

$5m\cong 11n+8$

Now, we can say that m>n because m and n are positive integers.

For n=1,

$5m=11(1)+8=19$

$5m=19$

19 is not divisible by 5 so m is not an integer for n=1.

For n=2,

$5m=11(2)+8$

$5m=30$

$m=6$

The value of m is 6 and the value of n is 2. So the smallest positive integer solution to the given system of congruences is

$x=5(6)=30$

Therefore the smallest positive integer solution to the given system of congruences is 30.

8 0

3 years ago

An urn contains green and red balls. six balls are randomly drawn from the urn in succession, with replacement. that is, after e

ANEK [815]

0.022 might be the answer.

7 0

3 years ago

In a study of 30 high school students, researchers found a high correlation, 0.93, between amount of exercise and weight lost. W

zloy xaker [14]

Answer:

Option A is true

The researchers proved that exercise causes weight loss only for high school students.

Step-by-step explanation:

We are told that the researchers found a high correlation, 0.93, between amount of exercise and weight lost.

Now, looking at each of the options;

- A is True because due to the high correlation, the research proves that exercise causes weight loss but only for high school students.

- B is not true because we are told the correlation is very high at 0.93. Thus, it is untrue that there is no proven causation.

-C is not true because there's no where that the researchers have completely proved that exercise causes weight loss generally. It is only peculiar to the high school students studied.

-D is not true because the 93% is just a correlation and not a percentage of those who lost weight

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3 years ago