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3 years ago

Name the constant of variation for y equals 1/4x then find the slope of the (0,0) and (4,1)... please

Mathematics

1 answer:

const2013 [10]3 years ago

4 0

Answer:

Constant of variation: 1/4

Slope of the line: 1/4

Step-by-step explanation:

The constant of variation means the relationship between variables does not change. When we want to identify the constant of variation for an equation, it is helpful to refer to one of the following formulas: xy = k (inverse variation) or y/x = k (direct variation), where k is the constant of variation.

The slope formula states that m = (y2 -- y1) / (x2 -- x1). The slope formula can be read as "slope equals the second y coordinate minus the first y-coordinate over the second x-coordinate minus the first x-coordinate".

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How many gallons of a 50% antifreeze solution must be mixed with 60 gallons of 30% antifreeze to get a mixture that is 40% antif

Mariulka [41]

I don't know what the "six-step method" is supposed to be, so I'll just demonstrate the typical method for this problem.

Let x be the amount (in gal) of the 50% antifreeze solution that is required. The new solution will then have a total volume of (x + 60) gal.

Each gal of the 50% solution used contributes 0.5 gal of antifreeze. Similarly, each gal of the 30% solution contributes 0.3 gal of antifreeze. So the new solution will contain (0.5 x + 0.3 * 60) gal = (0.5 x + 18) gal of antifreeze.

We want the concentration of antifreeze to be 40% in the new solution, so we need to have

(0.5 x + 18) / (x + 60) = 0.4

Solve for x :

0.5 x + 18 = 0.4 (x + 60)

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4 years ago

Which angle is congruent to angle 1? (1 point)

faltersainse [42]

I believe the angle that is congruent to angle 1 is angle 2

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3 years ago

Samantha is measuring the snowfall in a snow Gog for her science project. The first week she measured 3 3/4 inches of snow the s

KATRIN_1 [288]

Samantha measured $13\frac{1}{8}$ inches for the entire month

Step-by-step explanation:

Samantha is measuring the snowfall in a snow Gog for her science project

The first week she measured 3 3/4 inches of snow
The second week she measured twice as much snow, and the third week she measured half as much snow as the first week
It did not snow at all in the fourth week

We need to find how much snowfall Samantha measured for the entire month

∵ She measured $3\frac{3}{4}$ inches of snow in the 1st week

- Change the mixed number to improper fraction

∵ $3\frac{3}{4}=\frac{(3)(4)+3}{4}=\frac{12+3}{4}=\frac{15}{4}$

∴ She measured $\frac{15}{4}$ inches of snow in the 1st week

∵ She measured twice as much snow as the 1st week in the 2nd week

- Multiply the value of the 1st week by 2

∵ $\frac{15}{4}$ × 2 = $\frac{30}{4}$

∴ She measured $\frac{30}{4}$ inches of snow in the 2nd week

∵ She measured half as much snow as the 1st week in the 3rd week

- Multiply the value of the 1st week by 1/2

∵ $\frac{15}{4}$ × $\frac{1}{2}$ = $\frac{15}{8}$

∴ She measured $\frac{15}{8}$ inches of snow in the 3rd week

∵ It did not snow at all in the fourth week

- Add the values of the three weeks above to find the amount

of snowfall she measured for the entire month

∵ The amount of snowfall = $\frac{15}{4}+\frac{30}{4}+\frac{15}{8}$

- To add the fraction you must make all the denominator same number

so multiply the 1st and 2nd fractions by 2 up and down to make all

the denominator equal 8

∴ The amount of snowfall = $\frac{30}{8}+\frac{60}{8}+\frac{15}{8}$

- Add the numerators and put the sum over 8

∴ The amount of snowfall = $\frac{105}{8}$

- You can change the improper fraction to mixed number by divide

105 by 8 and put the reminder over 8

∵ 105 ÷ 8 = 13 and 1/8

∴ The amount of the snowfall = $13\frac{1}{8}$ inches

Samantha measured $13\frac{1}{8}$ inches for the entire month

Learn more:

You can learn more about the fraction in brainly.com/question/1312102

#LearnwithBrinaly

6 0

3 years ago

Without graphing, classify each system of equations as independent, dependent, or inconsistent. Solve independent systems by gra

MArishka [77]

1. Is Dependent.
2. Is Inconsistent

4 0

3 years ago

What are the solutions of the equation x4 + 3x2 + 2 = 0? Use u substitution to solve. x = plus-or-minus i StartRoot 2 EndRoot an

Rom4ik [11]

Answer:

$x=\pm\sqrt{2}i\text{ (or) }x=\pm i$

Step-by-step explanation:

We have been given an equation $x^4 + 3x^2 + 2 = 0$ . We are asked to find the solutions of our given equation using u-substitution.

We can rewrite our given equation as:

$(x^2)^2+3x^2+2 = 0$

Let us assume that $u=x^2$ .

$u^2+3u+2 = 0$

$u^2+2u+u+2 = 0$

$u(u+2)+1(u+2) = 0$

$(u+2)(u+1) = 0$

$(u+2)=0\text{ (or) }(u+1) = 0$

$u=-2\text{ (or) }u=-1$

Upon substituting back the value of u, we will get:

$x^2=-2\text{ (or) }x^2=-1$

$x=\pm\sqrt{-2}\text{ (or) }x=\pm\sqrt{-1}$

$x=\pm\sqrt{-1\cdot 2}\text{ (or) }x=\pm\sqrt{-1}$

Now we will use imaginary unit i. We know that $i^2=-1$ .

$x=\pm\sqrt{i^2\cdot 2}\text{ (or) }x=\pm\sqrt{i^2}$

$x=\pm\sqrt{2}i\text{ (or) }x=\pm i$

Therefore, the solutions for our given equation are $x=\pm\sqrt{2}i\text{ (or) }x=\pm i$ .

5 0

3 years ago

Read 2 more answers