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3 years ago

5. Consider the following equations.

Mathematics

1 answer:

WITCHER [35]3 years ago

3 0

Answer:

Step-by-step explanation:

In y = mx + b form, the slope can be found in the m position and the y intercept can be found in the b position.

4x - 2y = -6

-2y = -4x- 6

y = (-4/-2)x -(6/-2)

y = 2x + 3....slope here is 2, and y int is 3

3x + y = 3

y = -3x + 3.....slope here is -3, and y int is 3

B. slopes are different, y intercepts are the same

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A slug travels 3 centimeters in 3 seconds. A snail travels 6 centimeters in 6 seconds. Both travel at constant speeds. Mai says,

ollegr [7]

Answer:

Mai is wrong since both travel the same distance in the same amount of seconds

Step-by-step explanation:

3 centimeters in 3 seconds is 1 centimeter a second for the slug

6 centimeters in 6 seconds is 1 centimeter a second for the snail

so both travel the same distance

5 0

3 years ago

Read 2 more answers

Write in slope intercept form an equation of the line that passes through (-2,5),(-1,1)

Juliette [100K]

Answer:

y=-4x-3

Step-by-step explanation:

Hi there!

We are given the following two points: (-2,5) and (-1,1)

We want to write the equation of the line that passes through these two lines in slope-intercept form

Slope-intercept form is given as y=mx+b, where m is the slope and b is the y intercept

First, let's find the slope

The formula for the slope (m) calculated from 2 points is $\frac{y_2-y_1}{x_2-x_1}$ , where $(x_1, y_1)$ and $(x_2, y_2)$ are points

We have everything we need to calculate the slope, but let's label the value of the points to avoid any confusion

$x_1=-2\\y_1=5\\x_2=-1\\y_2=1$

Now substitute into the formula

m= $\frac{y_2-y_1}{x_2-x_1}$

m= $\frac{1-5}{-1--2}$
Simplify

m= $\frac{1-5}{-1+2}$

Subtract

m= $\frac{-4}{1}$

Divide

m=-4

Now substitute -4 as m into the equation:

y=-4x+b

Now we need to find b

As the equation passes through both (-2, 5) and (-1, 1), we can use either point to help solve for b.

Taking (-2,5) for example:

Substitute -2 as x and 5 as y:

5=-4(-2)+b

Multiply

5=8+b

Subtract 8 from both sides

-3=b

Substitute -3 as b.

y=-4x-3

Hope this helps!

See more on this topic here: brainly.com/question/27304092

4 0

2 years ago

What are the zeros of this graph

kotegsom [21]

The zeroes ( where the graph cuts the x axis) ar (-2,0) AND (2,0)

tHE FACTOrIAL FORM IS (x - 2)(x + 2)

Its B

3 0

3 years ago

If 30,000 cm2 of material is available to make a box with a square base and an open top, what is the largest possible volume (in

Cloud [144]

Answer:

The largest possible volume of the box is 2000000 cubic meters.

Step-by-step explanation:

The volume ( $V$ ), in cubic centimeters, and surface area ( $A_{s}$ ), in square centimeters, of the box with a square base are described below:

$A_{s} = l^{2}+h\cdot l$ (1)

$V = l^{2}\cdot h$ (2)

Where:

$l$ - Side length of the base, in centimeters.

$h$ - Height of the box, in centimeters.

By (2), we clear $h$ within the formula:

$h = \frac{V}{l^{2}}$

And we apply in (1) and simplify the resulting expression:

$A_{s} = l^{2}+ \frac{V}{l}$

$A_{s}\cdot l = l^{3}+V$

$V = A_{s}\cdot l -l^{3}$ (3)

Then, we find the first and second derivatives of this expression:

$V' = A_{s}-3\cdot l^{2}$ (4)

$V'' = -6\cdot l$ (5)

If $V' = 0$ and $A_{s} = 30000\,cm^{2}$ , then we find the critical value of the side length of the base is:

$30000-3\cdot l^{2} = 0$

$3\cdot l^{2} = 30000$

$l = 100\,cm$

Then, we evaluate this result in the expression of the second derivative:

$V'' = -600$

By Second Derivative Test, we conclude that critical value leads to an absolute maximum. The maximum possible volume of the box is:

$V = 30000\cdot l - l^{3}$

$V = 2000000\,cm^{3}$

The largest possible volume of the box is 2000000 cubic meters.

4 0

2 years ago

2^7/2^3 basic exponent rules

Stells [14]

Answer:

Step-by-step explanation:

Since they have the same base as 2, by the rule of a^m / a^n = a^m-n.

So 2^7 / 2^3 = 2^ 7-3 = 2^4 = 16

6 0

2 years ago

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