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3 years ago

Write the slope-intercept form of the equation through (4, 2) perpendicular to y=4x-4

Mathematics

1 answer:

Snezhnost [94]3 years ago

5 0

Answer:

y = -1/4x + 3

Step-by-step explanation:

y=mx+b is the slope-intercept form, which your equation y=4x-4 is already in.

To find the perpendicular line, you must take the negative reciprocal of the slope.

y = -1/4x + b

Your "b" will not be the same as the given equation, since the y-intercepts will not be the same. Therefore, you must solve for it using the point given.

Plug in (4, 2) [general: (x, y)] to the corresponding spots in y = -1/4x + b.

(2) = -1/4(4) + b

2 = -1 + b

b = 3

Now that you know m and b, you can plug all the values back into the form y = mx+b.

**Remember that y and x are never plugged back in! You need two variables to have a linear line

y = -1/4x + 3 is the answer.

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Work out the size of one of the exterior angles

hodyreva [135]

Given Information :-

⠀

A polygon with 10 sides ( Decagon )

⠀

To Find :-

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The value of one of the exterior angles

⠀

Formula Used :-

⠀

$\qquad \diamond \: \underline{ \boxed{ \pink{ \sf Exterior ~angle = \dfrac {360^\circ}{no. ~of~sides}}}} \: \star$

⠀

Solution :-

⠀

Putting the given values, we get,

⠀

$\sf \dashrightarrow Exterior ~angle = \dfrac{360 ^\circ}{10} \: \: \\ \\ \\ \sf \dashrightarrow Exterior ~angle = \frac{36 \cancel{0}^\circ}{ \cancel{10}} \: \: \\ \\ \\ \sf \dashrightarrow Exterior ~angle = \underline{ \boxed{ \frak{ \red{36^\circ}}}} \: \star \\ \\$

Thus, the value of the exterior angles of a Decagon is 36°.

⠀

$\underline{ \rule{227pt}{2pt}} \\ \\$

8 0

2 years ago

Read 2 more answers

** WILL GIVE 15 POINTS FOR THIS ONE QUESTION + BRAINLIEST **

densk [106]

Answer:

x + 4y ≤ 15; y ≥ 0

Step-by-step explanation:

The graph doesn't do a very good job of modeling any of the given equations. However, the equations listed above seem the best fit.

The slope of the top (left) line is negative, so the equation will be of the form ...

x + 4y = something

When y=0, x=15, so the "something" is expected to be 15.

However, the line appears to go through points (6, 2) and (-2, 4). Both of these points are on the line x + 4y = 14.

The graph is shaded below the line so the values of x and y that are in the shaded area will add to less than 15 (or 14). Hence, the inequality will be ...

x + 4y ≤ something . . . . . part of the 3rd answer choice

The fact that the shading does not go below y=0 means the other limit is ...

y ≥ 0 . . . . . part of every answer choice.

5 0

3 years ago

Is D the right answer for this? Thank you! - Alyssa

vesna_86 [32]

We start by ordering the values.

5, 7, 8, 10, 13, 14, 17, 17, 21

Now we find the median(middle number).

Median(b): 13
(I added (b) for "base" since we need to take more medians)
The median now divides this data into two halves.

Now we take the medians of the two remaining halves.

Median(Half1): 7.5
Median(Half2): 17

Mark off the minimum and maximum.

Min: 5
Max: 21

Now graph!

Your median(Half1) is incorrect, since your median for the first half is 9. Since our median for the first half is 7.5, the answer would be Answer Choice C.

8 0

3 years ago

Assume that the total revenue received from the sale of x items is given by, R(x)equals34 ln (4 x plus 5 ), while the total c

katen-ka-za [31]

Answer:

63 units

Step-by-step explanation:

The profit function P(x) is given by the revenue function minus the cost function:

$P(x) = R(x) - C(x)\\P(x) = 34ln(x+5)-\frac{x}{2}$

The number of units sold 'x' for which the derivate of the profit function is zero, is the number of units that maximizes profit:

$P(x) = 34ln(x+5)-\frac{x}{2}\\P'(x) =0= \frac{34}{x+5}-\frac{1}{2}\\x+5=68\\x=63\ units$

The number of units that should be manufactured so that profit is maximum is 63 units.

5 0

3 years ago

Write an equation of the line that passes through the given points (1 , 1.5) and (2, 3.5)

Nitella [24]

Answer:

y=2x-0.5

Step-by-step explanation:

typically, the equation of the line is written in slope intercept form, which is y=mx+b, where m is the slope and b is the y intercept

first, we need to find the slope (m) of the line

the formula for slope calculated from two points is given as (y2-y1)/(x2-x1)

we have two points: (1,1.5) and (2,3.5) and we can label them

x1=1

y1=1.5

x2=2

y2=3.5

now plug into the formula:

m=(3.5-1.5)/(2-1)

m=2/1

m=2

the slope of the line is 2

here's our equation so far:

y=2x+b

now we need to find b

since the line will pass through the points (1, 1.5) and (2, 3.5), we can plug either one of them into the equation to solve for

Let's use (1, 1.5)

substitute 1.5 as y and 1 as x

1.5=2(1)+b

1.5=2+b

subtract 2 from both sides

-0.5=b

therefore, our equation is:

y=2x-0.5

hope this helps!

5 0

3 years ago