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3 years ago

write an equation of the line with the same slope as the line given by 5x+2y=8 and as the same y-intercept as 3x-7y=10

2 answers:

5 0

The slope of the first equation would be -5/2 because
2y=-5x+8
y=-5x/2+4
The y intercept of the 2nd equation is when x=0, so -7y=10
y=-10/7
The equation of the line would be y=-5x/2-10/7
Or in standard form....
5x/2+y=-10/7
5x+27=-20/7

vampirchik [111]3 years ago

4 0

$5x+2y=8\ \ \Rightarrow\ \ 2y=-5x+8\ \ \Rightarrow\ \l_1:\ y=- \frac{5}{2}x+8\\ \\ l_2:\ y=ax+b\ \ \ and\ \ \ l_2\ ||\ l_1\ \ \ \Leftrightarrow\ \ \ a=- \frac{5}{2} \\ \\l_2:\ y=- \frac{5}{2}x+b\\ \\3x-7y=10\ \ \ and\ \ \ x=0 \ \ \ \Rightarrow\ \ \ 3\cdot0-7y=10 \ \ \Rightarrow\ \ \ y=- \frac{10}{7} \\ \\b=- \frac{10}{7}\ \ \ \Rightarrow\ \ \ l_2:\ y=- \frac{5}{2}x- \frac{10}{7}\\ \\ l_2:\ \frac{5}{2}x+y=- \frac{10}{7}\ \ /\cdot14\\ \\l_2:\ 35x+7y=-20$

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3 years ago

A group of scientists are studying a new species of insects. They observe the patterns of 6 insects. The scientists find that th

Stels [109]

Answer:

(B) $477=6(1+0.20)^t$

Step-by-step explanation:

we can use formula

$P(t)=P_0(1+r)^t$

where

Po is the initial population

r is the growth rate

t is the time in months

We are given

initial population of insects

so, Po=6

The scientists find that the insect population, x, is growing exponentially 20% per month

so, r=0.20

now, we can plug these values

$P(t)=6(1+0.20)^t$

there to be a population of 477 insects

so, P(t)=477

now, we plug it

and we get

$477=6(1+0.20)^t$

4 0

3 years ago

Suppose that you toss a fair six-sided {1,2,3,4,5,6} die and let X represent the outcome obtained. Find the expected volume of a

timofeeve [1]

Answer:

The expected volume of the box is 364 cubic inches.

Step-by-step explanation:

Since the die is fair, then P(X=k) = 1/6 for any k in {1,2,3,4,5,6}. Let Y represent the volume of the box in cubic inches. For how the box is formed, Y = X²*24. Thus, the value of Y depends directly on the value of X, and we have

(When X = 1) Y = 1²*24 = 24, with probability 1/6 (the same than P(X=1)

(When X = 2) Y = 2²*24 = 96, with probability 1/6 (the same than P(X=2)

(When X = 3) Y = 3²*24 = 216, with probability 1/6 (the same than P(X=3)

(When X = 4) Y = 4²*24 = 384, with probability 1/6 (the same than P(X=4)

(When X = 5) Y = 5²*24 = 600, with probability 1/6 (the same than P(X=5)

(When X = 6) Y = 6²*24 = 864, with probability 1/6 (the same than P(X=6)

As a consequence, the expected volume of the box in cubic inches is

E(Y) = 1/6 * 24 + 1/6*96 + 1/6*216+ 1/6*384+ 1/6*600+1/6*864 = 364

3 0

3 years ago

Which addition expression

mina [271]

Answer:(9+41)+-1-71)

Step-by-step explanation:

6 0

3 years ago

The total profit for a company in February was 15% higher than it was in January. The total profit for the two months was $122,9

stepladder [879]

Answer:

The profit for January is $57,200.

Step-by-step explanation:

The total profit for the two months would be the result of adding up the profit in January plus the profit in February:

Total profits=Profit in January+Profit in February

Also, you can say that profits in January can be represented by x and you know that the profit for a company in February was 15% higher than it was in January which can be expressed as: 1.15x. Moreover, you know that the total profit for the two months was $122,980. Now, you can replace the values on the formula:

122,980=x+1.15x

Now, you can solve for x:

122,980=2.15x

x=122,980/2.15

x=57,200

According to this, the answer is that the profit for January is $57,200.

7 0

3 years ago