What are the answers to questions one and three

Answer:

h(x) = (x-6)(x+2)

k(x) is not further factorable

Step-by-step explanation:

h(x) = x²-4x-12

      = (x-6)(x+2)

k(x) = x²-4x+8

not further factorable

Answer:

c

Step-by-step explanation:

Answer:

$746.24

Step-by-step explanation:

3.2/100 = 0.032

5,830 X 4 = 23,320

23,320 X 0.032 = 746.24

Answer:

f(x)= -(x-2)^2+2

Step-by-step explanation:

the same valuve needs the be added to both sides

f(x)+?= -x^2+4x+?-2

to complete the square -x^2+4x-4= -(x-2)^2 add the -4 to the expression

f(x)+?= -x^2+4x-4-2

since -4 was added to the right side, also add -4 the the left side

f(x)-4= -x^2+4x+?-2

now factor out the negative sign from the expression

f(x)-4= -(x^2-4x+4)-2

using a^2-ab+b^2=(a-b)^2

f(x)-4= -(x-2)^2-2

move the constant the the right side and change its sign

f(x)= -(x-2)^2-2+4

now calculate the sum

f(x)= -(x-2)^2+2

Answer:

8

Step-by-step explanation:

Mary needs 8 boxes to put 96 muffins in dozens so 96÷12 gives you 8

9514 1404 393

Answer:

  (4x^2 +21x +18)/(3x^2 +34x -24)

Step-by-step explanation:

I find it helpful to keep in mind the form ...

  a/b + c/d = (ad +bc)/(bd)

When we apply that to this case, we get ...

  [tex]\dfrac{x+3}{x+12}+\dfrac{x+2}{3x-2}=\dfrac{(x+3)(3x-2)+(x+12)(x+2)}{(x+12)(3x-2)}\\\\=\dfrac{(3x^2+7x-6)+(x^2+14x+24)}{(x+12)(3x-2)}=\boxed{\dfrac{4x^2+21x+18}{3x^2+34x-24}}[/tex]

Answer:

Y=-1/4x-4

Step-by-step explanation:

To find the slope, you would need to use the equation y2-y1/x2-x1 by the coordinates. You would get -3-(-2)/-4-(-8). This would result in -1/4. Now that you have your slope, you plug in one of the coordinates. If you used  (-8,-2), you would get -2=-8(-1/4)+b. Simplify the equation to get -2=2+b, which simplifies to -4=b, and b is the y intercept.

Answer:

-1.0

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Answer:

2.83 inches

Step-by-step explanation:

Let y equal the length of the drawing in inches. Use a proportion to solve for the missing length.

Answer: 2x+52=2(x+26)

3x-35=-105

Step-by-step explanation:

Answer:

[tex]\frac{2x}{5}- \frac{3y^{2} }{4}[/tex]

Step-by-step explanation:

(2/5x-3/4y^2) & (2/5x+3/4y^2) is [tex]\frac{2x}{5}- \frac{3y^{2} }{4}\\[/tex]

Answer:

t=x+3

y = (x+3)^2 + 5

y = x^2+6x + 9 + 5

y= x^2 + 6x + 14

Answer:

5 times x-3?

Step-by-step explanation:

Sorry if its wrong i didn't really understand what you wanted.

Answer:

Explained below.

Step-by-step explanation:

The random variable X is defined as the number of stars in a given volume of space.

[tex]X\sim \text{Poisson}\ (\lambda=1)[/tex]

The probability mass function of X is:

[tex]p_{X}(x)=\frac{e^{-\lambda}\lambda^{x}}{x!}[/tex]

(7)

Compute the probability of exactly two stars in 16 cubic light-years as follows:

[tex]P(X=2)=\frac{e^{-1}\times 1^{2}}{2!}=\frac{e^{-1}}{2}=\frac{0.36788}{2}=0.18394\approx 0.184[/tex]

(8)

Compute the probability of three or more stars in 16 cubic light-years as follows:

[tex]P(X\geq 3)=1-P(X<3)\\\\=1-P(X=0)-P(X=1)-P(X=2)\\\\=1-\sum\limits^{2}_{x=0}[\frac{e^{-1}\times 1^{x}}{x!}]\\\\=1-0.36788-0.36788-0.18394\\\\=0.0803[/tex]

(9)

In 16 cubic light years there is only 1 star.

Then in 1 cubic light years there will be, (1/16) stars.

Then in 4 cubic light years there will be, 4 × (1/16) = (1/4) stars.

(10)

In 16 cubic light years there is only 1 star.

Then in 1 cubic light years there will be, (1/16) stars.

Then in t cubic light years there will be, [t × (1/16)] stars.

Answer:

219.42858852

Step-by-step explanation:

Answer:

I think it B or C but hope I can help :)

Step-by-step explanation:

Answer: what grade is this

Step-by-step explanation:

Answer:

-3

Step-by-step explanation:

Answer:

42 squared is 1764

Step-by-step explanation:

Answer: (x + 42)(x - 42)

Step-by-step explanation:

factorise: x^2 - 42^2

. x^2 - 42^2 have ^2 in common (so you can ignore that).

. put in brackets (x - 42)(x + 42)

. +/- any order really doesn't matter :D

Answer:

[tex]m = \frac{2}{3}[/tex]

Step-by-step explanation:

Use the following equation:

slope [tex](m) = \frac{y^2 - y^1}{x^2 - x^1}[/tex]

Set the variables with the points:

[tex](x_1 , y_1) = (-16 , -6)\\(x_2 , y_2) = (-4 , 2)\\[/tex]

Plug in the corresponding numbers to the corresponding variables in the equation:

[tex]m = \frac{2 - (-6)}{-4 - (-16)}[/tex]

[tex]m = \frac{2 - (-6)}{- 4 - (-16)} = \frac{2 + 6}{16 - 4} = \frac{8}{12}[/tex]

slope [tex]m = \frac{8}{12}[/tex] [tex]= \frac{2}{3}[/tex]  (simplified)

~

Answer:

2/3

Step-by-step explanation:

Answer: h/3 + 7.5 = w

Answer:

(0,4)

Step-by-step explanation:

Alan's method is correct coz to find we add all the given value and divide by the numbers present

Answer:

The answer is: -190

Step-by-step explanation:

First, you need to input the -3 into the h(x) equation as follows:

h(-3) = 10(-3) - 15, then solve.

h(-3) = -30 - 15

h(-3) = -45.

Then you do the same for g(-5).

So, g(-5) = 30(-5) + 5

g(-5) = -150 + 5

g(-5) = -145.

Now you add the -45 and -145.

h(-3) + g(-5) = -45 - 145

h(-3) + g(-5) = -190.

Step-by-step explanation:

the answer is C

2/5(2x+3)

I hope it helps

Answer:

No, triangle B is a reflection of triangle A.

Step-by-step explanation:

The points of triangle A are reflected across the dotted line. So as a result triangle B is a reflection of triangle A.

Answer:

No

Step-by-step explanation:

Its a reflection because even if you did rotate it it would never be in that orientation.

Answer:

For #5 all you have to do is set down to points in order for it to count. The answer is: (0,2) and (3,6)

Step-by-step explanation:

In order to find where exactly you must plot the points, we plug in what we know. In our equation, the 2 is our y intercept, this means that the point is (0,2) (Side Note: here's another example, (0,6) the 6 would be our y intercept)

From the point (0,2) we use the other value given. The other value given in this case, is our slope. When dealing with slope, we use Rise over Run or Rise/Run. This means that from the 2 on the graph, you rise 3 which would be 5 and you run to the right for 4. This now gets you the points (3,6)

Hope this helps with plotting the other questions! :)

(SIDE NOTE: IF THEY GIVE THE VALUE WITH X AS JUST A NUMBER, YOU CAN PLACE A 1 UNDER IT TO TURN IT INTO A FRACTION. FOR EXAMPLE 3X CAN BE TURNED INTO 3/1 WHICH WOULD THEN BE RISE 3 AND RUN 1.

(sooory about the caps, it's just to get your attention.)

If PV = 800, then P can be written as a function of V,

P(V) = 800 / V

(a) The average rate of change of P as V increases from 200 to 250 in³ is then

(P (250) - P (200)) / (250 in³ - 200 in³) = (3.2 lb/in² - 4lb/in²) / (50 in³)

... = -0.016 (lb/in²)/in³

(Or -0.016 lb/in⁵, but I figure writing the rate as (units of pressure) per (unit volume) makes more sense.)

(b) We can also write V as a function of P :

V(P) = 800 / P

Take the derivative:

V'(P) = - 800 / P²

which immediately demonstrates that V'(P) ∝ 1 / P², as required. (The fish-looking symbol, ∝, means "is proportional to".)

If differentiating is supposed to be more involved, you can use the limit definition:

[tex]V'(P)=\displaystyle\lim_{h\to0}\frac{V(P+h)-V(P)}h[/tex]

[tex]V'(P)=\displaystyle\lim_{h\to0}\frac{\frac{800}{P+h}-\frac{800}P}h[/tex]

[tex]V'(P)=\displaystyle\lim_{h\to0}\frac{\frac{800P-800(P+h)}{P(P+h)}}h[/tex]

[tex]V'(P)=\displaystyle800\lim_{h\to0}\frac{-\frac h{P(P+h)}}h[/tex]

[tex]V'(P)=\displaystyle-800\lim_{h\to0}\frac1{P(P+h)}=-\dfrac{800}{P^2}[/tex]

Part(a): The average rate of change of [tex]\frac{dP}{dV}[/tex] is [tex]-0.0164 lb/in^{2}[/tex]

Part(b): The required answer is [tex]\frac{dV}{dP} \infty \frac{1}{P^{2}}[/tex]

Part(a):

Given,

[tex]PV=800[/tex]

Differentiating the above equation with respect to [tex]V[/tex].

[tex]\frac{dP}{dV}=-\frac{P}{V}[/tex]

Now, at [tex]V=200 in^{3}[/tex] and [tex]P=4 lb/in^2[/tex]

At [tex]V=250 in^3[/tex] and [tex]P=\frac{80}{25} lb/in^2[/tex]

Hence, we can write,

[tex]\frac{dP}{dV}[/tex] at [tex]V=200[/tex] we get,

[tex]\frac{-1}{200}=\frac{-1}{50}[/tex]

Again [tex]\frac{dP}{dV}[/tex] at [tex]V=250[/tex] we get,

[tex]\frac{-80}{25\times 250}[/tex]

So, the average rate of change of [tex]\frac{dP}{dV}[/tex] is,

[tex]\frac{-\frac{1}{50}- \frac{8}{25\times25} }2\\=-\frac{1}{100}-\frac{1}{625}\\=-0.0164 lb/in^2[/tex]

Part(b):

Given,[tex]PV=800[/tex] then,

[tex]V=\frac{800}{P}[/tex]

Now,[tex]\frac{dV}{dP} =-\frac{800}{P^2}[/tex]

Then the above implies,

[tex]\frac{dV}{dP} \infty \frac{1}{P^{2}}[/tex]

Learn more:https://brainly.com/question/12817429

Answer:

X=2

Step-by-step explanation:

3x-15=7-8x

3x+8x=7+15

11x=22

x=[tex]\frac{22}{11}[/tex]

x=2

Answer:

324

Step-by-step explanation:

3x3 = 9

9-15 = -6

8x8=64

7-64=-54

-54 x -6 = 324