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3 years ago

What is point-slope form? When can you use point-slope form? How is it useful?

1 answer:

6 0

The formula for point slope form is y=mx+b. You can use it to plot lines, find the slope, find the y intercept, and you can also change it into other forms like point-slope and standard form.

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If we transform y=x^2 by 5 units to the left and 8 units ups, what is the vertex of the resulting parabola?

sertanlavr [38]

Answer: y = (x + 5)² + 8

<u>Step-by-step explanation:</u>

y = x²

left 5 units: y = (x + 5)²

up 8 units: y = (x + 5)² + 8

7 0

3 years ago

Read 2 more answers

How many 4 digit numbers consisting of only the digits 2,4,6 and 8 are divisible by 4

Blababa [14]

Answer:

digits used once: 12
repeated digits: 128

Step-by-step explanation:

In order for a number to be divisible by 4, its last two digits must be divisible by 4. This will be the case if either of these conditions holds:

the ones digit is an even multiple of 2, and the tens digit is even
the ones digit is an odd multiple of 2, and the tens digit is odd.

We must count the ways these conditions can be met with the given digits.

Since we only have even numbers to work with, the ones digit must be an even multiple of 2: 4 or 8. (The tens digit cannot be odd.) The digits 4 and 8 comprise half of the available digits, so half of all possible numbers made from these digits will be divisible by 4.

<h3>digits used once</h3>

If the numbers must use each digit exactly once, there will be 4! = 24 of them. 24/2 = 12 of these 4-digit numbers will be divisible by 4.

<h3>repeated digits</h3>

Each of the four digits can have any of four values, so there will be 4^4 = 256 possible 4-digit numbers. Of these, 256/2 = 128 will be divisible by 4.

7 0

1 year ago

Read 2 more answers

A rancher wishes to build a fence to enclose a 2250 square yard rectangular field. Along one side the fence is to be made of hea

Bess [88]

Answer:

The least cost of fencing for the rancher is $1200

Step-by-step explanation:

Let <em>x</em> be the width and <em>y </em>the length of the rectangular field.

Let <em>C </em>the total cost of the rectangular field.

The side made of heavy duty material of length of <em>x </em>costs 16 dollars a yard. The three sides not made of heavy duty material cost $4 per yard, their side lengths are <em>x, y, y</em>. Thus

$C=4x+4y+4y+16x\\C=20x+8y$

We know that the total area of rectangular field should be 2250 square yards,

$x\cdot y=2250$

We can say that $y=\frac{2250}{x}$

Substituting into the total cost of the rectangular field, we get

$C=20x+8(\frac{2250}{x})\\\\C=20x+\frac{18000}{x}$

We have to figure out where the function is increasing and decreasing. Differentiating,

$\frac{d}{dx}C=\frac{d}{dx}\left(20x+\frac{18000}{x}\right)\\\\C'=20-\frac{18000}{x^2}$

Next, we find the critical points of the derivative

$20-\frac{18000}{x^2}=0\\\\20x^2-\frac{18000}{x^2}x^2=0\cdot \:x^2\\\\20x^2-18000=0\\\\20x^2-18000+18000=0+18000\\\\20x^2=18000\\\\\frac{20x^2}{20}=\frac{18000}{20}\\\\x^2=900\\\\\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}\\\\x=\sqrt{900},\:x=-\sqrt{900}\\\\x=30,\:x=-30$

Because the length is always positive the only point we take is $x=30$ . We thus test the intervals $(0, 30)$ and $(30, \infty)$

$C'(20)=20-\frac{18000}{20^2} = -25 < 0\\\\C'(40)= 20-\frac{18000}{20^2} = 8.75 >0$

we see that total cost function is decreasing on $(0, 30)$ and increasing on $(30, \infty)$ . Therefore, the minimum is attained at $x=30$ , so the minimal cost is

$C(30)=20(30)+\frac{18000}{30}\\C(30)=1200$

The least cost of fencing for the rancher is $1200

Here’s the diagram:

3 0

2 years ago

How do you solve negative exponents?

JulsSmile [24]

Negative Exponent Rule:
this says that negative exponents in the numerator get moved to the denominator and become positive exponents. Negative exponents in the denominator get moved to the numerator and become positive exponents.
Like this||

4 0

2 years ago

Read 2 more answers

It would be nice if I get some help with these 2 things

Stella [2.4K]

Thing 1
A. You can set up a proportion by dividing how much of something there is by the original. (This probably doesn't make much sense but I hope you can understand it from the answer to the problem below!)
B.First, do 168/21 to see how many more times he put flour in.
168/21= 8
Then to find out the milk in the same proportion do the number (in this case 8) times the original of the thing you wan to find out.
8x9=72
72 tablespoons of milk are needed for 168 cups of flour in this adapted recipe.

Thing 2
24/36=8y
To solve any equation, you want to have letters on one side and numbers on the other, so...
-8 from both sides...
(24/36)-8=y
24/36=0.6
y=(0.6-8)
y=-7.4

Hope this helps :)

5 0

3 years ago