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3 years ago

Describe the pair of equations. y = - 1/4x + 10 AND -2x + 8y = 6

Mathematics

1 answer:

Nat2105 [25]3 years ago

4 0

First of all, let's rearrange the second equation so that it comes in the slope-intercept form:

$-2x + 8y = 6\iff x+4y=3 \iff y=-\dfrac{1}{4}x+\dfrac{3}{4}$

Now it becomes evident that the two lines have the same slope of -1/4. When two lines have the same slope, they are parallel.

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Brand A scooter has a top speed that goes 2 miles per hour faster than Brand B. if after hours, Brand A scooter traveled 24 mile

Leni [432]

Your answer would be 22mph

3 0

4 years ago

Read 2 more answers

Please Answer!!!!

ExtremeBDS [4]

First mug holds the most

Solution:

Given that,

You are choosing between two mugs

The volume of cylinder is given as:

$V = \pi r^2h$

Where,

r is the radius and h is the height

One has a base that is 5.5 inches in diameter and a height of 3 inches

$radius = \frac{diameter}{2}$

Therefore,

$r = \frac{5.5}{2}\\\\r = 2.75$

Also, h = 3 inches

Thus volume of cylinder is given as:

$V = \pi \times 2.75^2 \times 3\\\\V = 3.14 \times 22.6875\\\\V = 71.23875 \approx 71.24$

Thus first mug holds 71.24 cubic inches

The other has a base of 4.5 inches in diameter and a height of 4 inches

$Radius = \frac{4.5}{2}\\\\r = 2.25$

h = 4 inches

Therefore,

$V = 3.14 \times 2.25^2 \times 4\\\\V = 3.14 \times 20.25\\\\V = 63.585$

Thus the second mug holds 63.585 cubic inches

On comparing, volume of both mugs,

Volume of first mug > volume of second mug

First mug holds the most

8 0

4 years ago

A board is 48 in long. It must be divided into 4 pieces of equal length, and each cut will cause a waste of 3/16 in. How long wi

NISA [10]

Answer:

12 pieces

Step-by-step explanation:

Total length of the board = 48 in

It must be divided into 4 pieces of equal length

This means, there will be 3 cut to have 4 pieces

Each cut will cause a waste of 3/16 in.

Total waste = 3 cut × 3/16 in

= (3*3)/16

= 9/16 in

Length of board remaining = Total length of the board - Total waste

= 48 - 9/16

= (768-9)/16

= 759/16 in

How long will each piece be after the cuts are made?

Length of each piece after the cut = Length of board remaining / 4

= 759/16 ÷ 4

= 759/16 × 1/4

= 759/64

= 11.859375

Approximately 12 pieces to the nearest whole number

7 0

3 years ago

Is the given function phi(x) = x^2 - x^-1 an explicit solution to the linear equation d^2y/dx^2 - 2/x^2 y = 0? Circle your answe

mart [117]

Answer:

Yes

Step-by-step explanation:

We are given that a function $\phi(x)=x^2-x^{-1}$

We have to find that given function is an explicit solution to the linear equation

$\frac{d^2y}{dx^2}-\frac{2}{x^2}y=0$

If given function is an explicit solution of given linear equation then it satisfied the given differential equation

Differentiate w.r.t x

Then we get $\phi'(x)=2x+x^{-2}$

Again differentiate w.r.t x

Then we get

$\phi''(x)=2-\frac{2}{x^3}$

Substitute all values in the given differential equation

$2-\frac{2}{x^3}-\frac{2}{x^2}(x^2-x^{-1})$

= $2-\frac{2}{x^3}-2+\frac{2}{x^3}=0$

Hence, given function is an explicit solution of given differential equation.

Therefore, answer is yes.

3 0

3 years ago

6. What is the y-value to the solution of y = 5x -4 y = 2x + 8?

Angelina_Jolie [31]

Answer:

y = 16, don't know if I'm 100% right but hope this helps.

Step-by-step explanation:

since they both equal Y they may be equal to each other

Then you would subtract 2x from both sides canceling it out on one side

2x + 8 = 5x - 4

-2x -2x

This would make the equation 8 = 3x - 4

next you add the 4 from both sides

8 = 3x - 4

+4 +4

This will leave you with 12 = 3x

now you divide 3 from both sides and 12/3 = 4 makes X = 4

next you take (4) and plug it in to one of the equations

y = 2(4) + 8

y = 8 + 8

y = 16

8 0

3 years ago