Roxy is multiplying 1/8 by 4/3 use the drop down

(1) f(x) = (1 - x³) / (x - 1)

(a) The domain is the set of values that this function can take on. If x = 1, the denominator becomes 0 and the function is undefined. Any other value of x is okay, though, since for x ≠ 1, we have

f(x) = (1 - x³) / (x - 1) = - (1 - x³) / (1 - x) = -(x² + x + 1)

which is defined for all x. This also tells us that the plot of f(x) is a parabola with a hole at x = 1. So, the domain is the interval (-∞, 1) ∪ (1, ∞).

(b) The range is the set of values that the function actually does take on. Taking the simplified version of f(x), we can complete the square to write

-(x² + x + 1) = -(x² + x + 1/4 - 1/4) - 1 = -(x + 1/2)² - 3/4

which is represented by a parabola that opens downward, with a maximum value of -3/4. So the range is the interval (-∞, -3/4).

(c) Judging by the plot of f, the limits at both negative and positive infinity are -∞.

(d) Same answer as part (a).

(2) f(x) = x³ - x

(a) The derivative of f at x = 3, and hence the slope of the tangent line to this point, is

[tex]f'(3)=\displaystyle\lim_{h\to0}\frac{f(3+h)-f(3)}h[/tex]

[tex]f'(3)\displaystyle=\lim_{h\to0}\frac{((3+h)^3-(3+h))-24}h[/tex]

[tex]f'(3)=\displaystyle\lim_{h\to0}\frac{(27+27h+9h^2+h^3)-(3+h)-24}h[/tex]

[tex]f'(3)=\displaystyle\lim_{h\to0}\frac{26h+9h^2+h^3}h[/tex]

[tex]f'(3)=\displaystyle\lim_{h\to0}(26+9h+h^2)=\boxed{26}[/tex]

(b) The tangent line at x = 3 has equation

y - f (3) = f ' (3) (x - 3)

y - 24 = 26 (x - 3)

y = 26 x - 54

We also want to find any other tangent lines parallel to this one, which requires finding all x for which f '(x) = 26. We could use the same limit definition as in part (a), but to save time, we exploit the power rule to get

f '(x) = 3 x² - 1

Then solve for when this is equal to 26:

3 x² - 1 = 26   ==>   x² = 9   ==>   x = ±3

The other tangent line occurs at x = -3, for which we have f (-3) = -24, and so the equation for the tangent is

y - f (-3) = 26 (x - (-3))

y + 24 = 26 (x + 3)

y = 26 x + 54

Answer:

The probability will be "0.205".

Step-by-step explanation:

The probability that perhaps the time remains greater than 9.5 days before the next shift will indeed be:

⇒  [tex]P(X>9.5)[/tex]

⇒  [tex]1-P(X<9.5)[/tex]

⇒  [tex]1-(1-exp(\frac{-9.5}{6} ))[/tex]

⇒  [tex]0.205[/tex]

Answer:

An equation is [tex]x+52\°+90\°=180\°[/tex]

Step-by-step explanation:

Let [tex]x[/tex] be the measure of the unknown acute angle.

According to angle sum property of a triangle, sum of all the angles of a triangle is equal to 180°.

One of the acute angles of a right triangle is equal to 52°.

Also, the triangle is a right angled triangle, one of the angle must be equal to 90°.

[tex]x+52\°+90\°=180\°\\x+142\°=180\°\\x=38\°[/tex]

So, an equation is [tex]x+52\°+90\°=180\°[/tex]

Answer:

the answer is 0.4 The reason is because 0.4 x8=0.32

Step-by-step explanation:

Answer:

82.

Step-by-step explanation:

Let the largest number of be 'a'.

Let the middle number be 'b'.

Let the smallest number be 'c'.

From the question given above,

The sum of the three numbers is 223. This can be written as:

a + b + c = 223 .... (1)

The largest number is 13 more than the smallest number. This can be written as:

a = c + 13 ..... (2)

The sum of the largest number and the smallest number is 7 more than twice the middle number. This can be written as:

a + c = 2b + 7..... (3)

Summary:

a + b + c = 223 .... (1)

a = c + 13 ..... (2)

a + c = 2b + 7..... (3)

Substitute the value of a in equation 2 into equation 3. This is illustrated below:

a + c = 2b + 7

a = c + 13

c + 13 + c = 2b + 7

2c + 13 = 2b + 7

Make b the subject

2c + 13 – 7 = 2b

2c + 6 = 2b

2(c + 3) = 2b

Divide both side by 2

b = 2(c + 3) / 2

b = c + 3 ..... (4)

Substitute the value of a in equation 2 and the value of b in equation 4 into equation 1. This is illustrated below:

a + b + c = 223

a = c + 13

b = c + 3

(c + 13) + (c + 3) + c = 223

c + 13 + c + 3 + c = 223

3c + 16 = 223

Collect like terms

3c = 223 – 16

3c = 207

Divide both side by 3

c = 207/3

c = 69

The smallest number (c) is 69

Substitute the value of c into equation 2 to obtain the largest number (a). This is illustrated below:

a = c + 13

c = 69

a = 69 + 13

a = 82

Therefore, the largest number (a) is 82

Answer:

The vertex is (-5, -1)

Step-by-step explanation:

Standard vertex form is a(x - b)^2 + c where (b, c) is the vertex.

Answer:

First, let's write our equation in a general way.

We know that:

1 cubic foot weighs 80 pounds.

The container weighs 40 pounds.

Then, if i put n cubic feet of sand in the container, the total mass will be one time the mass of the container plus n times the mass of one cubic foot of sand.

We can write this as:

w(n) = 40lb + n*80lb

This is a linear equation, where the y-axis will represent the mass in pounds and the x-axis will be the number of cubic feet of sand in the container in units, a graph of this is shown below.

You can see that it is really steep, this is because for really small increments in n, the weight increases a lot.

Answer

ok, Just plot the points at (0,40) and (2,200) :))

Answer:

39pounds 6oz

Step-by-step explanation:

15x2=30

1x30=30pounds

5x30=150oz

30p+150oz=39.37500

37500p=6oz

39pounds and 6 oz

Answer:

[tex]-8,+735[/tex]

Step-by-step explanation:

The lowest point in New Orleans is 8 feet below sea  level.

This can be represented numerically using [tex]-8[/tex]

(negative sign denotes below sea level)

The highest point in Chicago is 735 feet above sea  level.

This can be represented numerically using [tex]+735[/tex]

(positive sign denotes above sea level)

Answer:

This is correct but if some people are confused it’s a negative integer and a positive integer

Step-by-step explanation:

Answer:

1.954

so 4 is in the thousandths

Step-by-step explanation:

Answer:

-5

Step-by-step explanation:

-3+-2=-5

this is the answer

Answer:

|0.05|

Step-by-step explanation:

no absolute value can be negative

Answer:

0.05

Step-by-step explanation:

The lines outside the number mean absolute value. The absolute value of a number is how far it is from 0, so it's always positive. Basically, you just swap the sign of whatever number you are looking at. In this case, absolute value of -0.05 would simply be 0.05. Hope this helped!

Answer:

x=25

Step-by-step explanation:

First, we add all like terms. Then, we solve for x.

[tex]70+x + 55 + 30 = 180\\x+70 + 55 + 30 = 180\\x+155=180\\x=25[/tex]

We can rearrange some things because order does not matter with addition. Next, we just use basic equation solving techniques.

Answer:

25. Hope this helps :)

Step-by-step explanation:

180-70=110

110-55=55

55-30=25

Your missing answer would be 25

X=25

Answer: is it a function-yes

why: none of the y values are the same

Step-by-step explanation:

Answer:

W>16

Step-by-step explanation:

The formula for calculating the perimeter of a rectangle:

P = 2L+2W

L is the length of the rectangle

W is the width of the rectangle:

Given

P = 96m

If the length of a rectangle is 2 times the width, then L = 2W

Substitute into the formula:

Since the perimeter is less than 96m

96 < 2(2W)+2W

96 < 4W+2W

96 < 6W

Divide both sides by 6:

96/6 < 6W/6

16 < W

W>16

Hence the possible values of the width are all values greater than 16.

Answer:

Step-by-step explanation:

We need to calculate the speed of Jasmine first as shown:

Speed = Distance/Time

Given:

Distance = 12miles

Time = 20mins

Time = 20/60 hr

Time = 1/3 hr

Speed = 12/(1/3)

Speed = 12 * 3/1

Speed = 38mi/hr

From the formula:

S = d/t

To get the equation needed, substitute s = 36 into the formula:

36 = d/t

d = 36t

Hence the required equation is d = 36t where d is the distance in miles and time in hour

Answer:

36

Step-by-step explanation:

Answer:

15 cups of flour

Step-by-step explanation:

Answer:

x=1/15

Step-by-step explanation:

SOLVE:

1 (divide) 2 7/9 = x+ 4 2/5x

1 (divide) 25/9 = x + 4 2/5x

1 * 9/25 + 5 2/5x

9/25 = 5 2/5x

divide both sides by 5 2/5 or you can multiply by the reciprocal

5 2/5x = 27/5x

then once you do that you get x= 1/15

CHECK ANSWER:

Insert 1/15 instead of x

1 (divide) 2 7/9 = (1/15) + 4 2/5 (1/15)

9/25 = 9/25 Yes it is a true statement.

ANSWER:

x= 1/15

Answer:

24x+10y=98

2sunny days

5rainy days

Step-by-step explanation:

x=number of sunny days

y=number of rainy days

(2*24)+(10*5)=98

vualah :)

Answer:

ava ran the fastest

Step-by-step explanation:

Answer:

According to the question 25% of the students wore jackets.

Thus 25% of 12 wore jackets

The number of students can be found easily by multipling 12 with 25//100

12*25/100

12*1/4

12/4

thus, 3 students

Therefore, option 3 is correct

Answer:

6 ,16

Step-by-step explanation:

he doubled it

Answer:

8^5 + 2 = Trisha's Tokens

Step-by-step explanation:

Answer:

42

Step-by-step explanation:

8 x 5 +2

Answer:

2 1/4

Step-by-step explanation:

Answer: Can u post a question?

Step-by-step explanation:

Penjelasan langkah demi langkah:

1)

[tex]= 243^{\frac{2}{3} }\\= (\sqrt[3]{243})^2\\= 7^2\\= 49[/tex]

2) √32 +3√18-2√50

= √16*2 +3√9*2-2√25*2

= 4√2 + 3(3√2)-2(5√2)

= 4√2 + 9√2-10√2

= 13√2-10√2

= 3√2

3) 1000 ⅔×64⅙

 [tex]= (\sqrt[3]{1000}) ^2 \times (2^6)^{1/6} \\= 10^2 \times 2\\= 100 \times 2\\= 200[/tex]

4) 3/4+√2

[tex]3/4+\sqrt{2} \\= \frac{3+4\sqrt{2} }{4 }[/tex]

5) 2√3×√18

= 2√3×√9*2

= 2√3×3√2

= (2*3)(√3*√2)

= 6√6

6) 12/3+√3

= 4+√3

7) √1000—2√40

= 10 -2 (√4*10)

= 10-2(2√10)

= 10 - 4√10

8) 2- ¹+3-¹

[tex]= \frac{1}{2} + \frac{1}{3}\\ = \frac{3+2}{6}\\ = \frac{5}{6}[/tex]

9)

[tex]\frac{5}{\sqrt{5} }\\ merasionalisasikan\\= \frac{5}{\sqrt{5} }\times \frac{\sqrt{5} }{\sqrt{5} }\\= \frac{5\sqrt{5} }{\sqrt{25} }\\= \frac{5\sqrt{5} }{5}\\ = \frac{\sqrt{5} }{1}[/tex]

Jika pernyataannya opsional, penyebutnya adalah 1

10) 2√3×√18

= 2√3×√9*2

= 2√3×3√2

= (2*3)(√3*√2)

= 6√6

Answer:

AB, BC, AC

Step-by-step explanation:

Hopefully I helped!! :)