Determine all the zeros for the function f(x) = (x2 + 3x - 10)(x - 4).

Answer:

f’(2) = -21/128

f’(-1) = -42

Step-by-step explanation:

We are given a function:

[tex]\displaystyle \large{f(x)=\frac{6}{x^7}}[/tex]

We want to evaluate f’(2) and f’(-1). Keep in mind that f’(x) denotes or means the derivative of f(x). So what we are going to do first is to find the derivative of given function.

Derive the function, there are two ways to derive it, either using power rules or quotient rules. For this, I’ll demonstrate two methods.

Power Rules

If [tex]\displaystyle \large{f(x)=x^n}[/tex] then [tex]\displaystyle \large{f\prime (x)=nx^{n-1}}[/tex] where n is any real numbers.

Since the function is written in a fraction form, we’ll have to convert it to the x^n form using law of exponent.

[tex]\displaystyle \large{f(x)=\frac{6}{x^7} \to f(x)=6\cdot \frac{1}{x^7}}[/tex]

Law of Exponent I

[tex]\displaystyle \large{\frac{1}{a^n} = a^{-n}}[/tex]

Therefore:

[tex]\displaystyle \large{f(x)=6x^{-7}}[/tex]

Then derive the function using power rules:

Property of Differentiation I

[tex]\displaystyle \large{y=kf(x) \to y\prime = kf\prime (x)}[/tex] where k is a constant.

[tex]\displaystyle \large{f\prime (x)=6\cdot -7x^{-7-1}}\\\displaystyle \large{f\prime (x)=6\cdot -7x^{-8}}\\\displaystyle \large{f\prime (x)=-42x^{-8}}[/tex]

Quotient Rules

[tex]\displaystyle \large{y=\frac{f(x)}{g(x)} \to y\prime = \frac{f\prime (x)g(x)-f(x)g\prime (x)}{[g(x)]^2}}[/tex]

If f(x) = k or a constant then:

Property of Differentiation II

[tex]\displaystyle \large{y=k \to y\prime = 0}[/tex] for k is a constant.

[tex]\displaystyle \large{y=\frac{k}{g(x)} \to y\prime = \frac{0\cdot g(x)-kg\prime (x)}{[g(x)]^2}}\\\displaystyle \large{y\prime = \frac{-kg\prime (x)}{[g(x)]^2}}[/tex]

Therefore:

[tex]\displaystyle \large{f\prime (x)=\frac{-6\cdot 7x^{7-1}}{[x^7]^2}}\\\displaystyle \large{f\prime (x)=\frac{-42x^6}{x^{14}}}\\\displaystyle \large{f\prime (x)=-42x^{6-14}}\\\displaystyle \large{f\prime (x)=-42x^{-8}}[/tex]

Laws of Exponent used above:

[tex]\displaystyle \large{(a^n)^m = a^{nm}}\\\displaystyle \large{\frac{a^n}{a^m} = a^{n-m}}[/tex]

Therefore the derivative of function is:

[tex]\displaystyle \large{f\prime (x) = -42x^{-8}}[/tex] or [tex]\displaystyle \large{f\prime (x)=-\frac{42}{x^8}}[/tex]

Next is to substitute x = 2 and x = -1 in the derivative.

[tex]\displaystyle \large{f\prime (2)=-\frac{42}{2^8}}\\\displaystyle \large{f\prime (2) = -\frac{42}{256}}\\\displaystyle \large{f\prime (2)= -\frac{21}{128}}[/tex]

And:

[tex]\displaystyle \large{f\prime (-1)=-\frac{42}{(-1)^8}}\\\displaystyle \large{f\prime (-1) = -\frac{42}{1}}\\\displaystyle \large{f \prime (-1) = -42}[/tex]

Therefore, f’(2) = -21/128 and f’(-1) = -42.

Answer:

a = 7

Step-by-step explanation:

3x + 4 = 57 ÷ 3

3x + 4 = 19

3x = 15

x = 5

2x + 2 =  2(5) + 2 = 10 + 2 = 12

19 - 12 = 7

a = 7

hope this helps!! p.s. i really need brainliest :)

Answer: 3005

Step-by-step explanation: multiply 5 by 20 and it will give 100 then times 30 Equals 3000 and plus gives 3005 . Please mark brainliest

Answer:3005

Step-by-step explanation :multiply 5 by 20 and it will give 100 then multiply by 30  that Equals 3000 and plus 5 that gives you 3005

Answer:

9n/60

Step-by-step explanation:

add 1/12 + 1/15 which = 5/60 + 4/60.

= 9/60

YAY!!!!!!!

The fraction of the exams that Mr Tough and Mrs Nice grade in 1 hour if they work together is 3/20

In Maths, a fraction is used to represent the portion/part of the whole thing. A fraction has two parts, namely numerator and denominator. There are proper fractions, improper fractions and mixed fractions.

Example: 2/5, 1/4 etc.

We will this equation,

rate × time = work done

For this problem:

             Mr Tough's rate:

                          Mr Tough's rate × 12 hours = final exam

                          Mr Tough's rate = 1/12

             Mrs.Nice's' rate:

                            Mrs .Nice's' rate × 15 hours = final exam

                            Mrs .Nice's' rate = 1/15

To make this into a solvable equation,  find the total time (T) needed for Mr Tough and Mrs.Nice to grade the final exam. This time is the sum of the rates of Mr Tough and Mrs.Nicea, or:

Total time:

T(1/12 hours + 1/15 hours) = final exam

T =  final exam / (1/12 + 1/15)

Simplifying we get,

T =  final exam / (0.15)

Now, to finish in 1 hour we will find what fraction of the final exam they can grade, so taking T = 1 hour,

1 hour =  final exam / (0.15)

By further simplifying,

final exam = 1 × 0.15

                 = 0.15

                 = 15/ 100

                 = 3/20

Therefore, 3/20 fraction of the final exam they can grade if they work together for 1 hour.

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The volume of the chocolate is the amount of choclate used in the cherries

The amount of chocolate used is 17.24 cubic centimeters

Start by calculating the volume of the cherries using:

V = 4/3 π(D/2)^3

The diameter of the cherry is 2.8 cm.

So, we have:

V = 4/3π(2.8/2)^3

Evaluate

V = 11.49

Next, calculate the volume of the cherry and the chocolate.

V = 4/3π(0.5+2.8/2)^3

V = 28.73

Calculate the difference (d) between both volumes

d = 28.73 - 11.49

d = 17.24

Hence, the amount of chocolate used is 17.24 cubic centimeters

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Answer:$940

Step-by-step explanation:

29%=$272.60

100%=

100%*$272.60/29%=$940

$940

Answer:

[tex]\lim_{x \to 0} \frac{12xe^x-12x}{cos(5x)-1}=-\frac{24}{25}[/tex]

Step-by-step explanation:

Notice that [tex]\lim_{x \to 0} \frac{12xe^x-12x}{cos(5x)-1}=\frac{12(0)e^{0}-12(0)}{cos(5(0))-1}=\frac{0}{0}[/tex], which is in indeterminate form, so we must use L'Hôpital's rule which states that [tex]\lim_{x \to c} \frac{f(x)}{g(x)}=\lim_{x \to c} \frac{f'(x)}{g'(x)}[/tex]. Basically, we keep differentiating the numerator and denominator until we can plug the limit in without having any discontinuities:

[tex]\frac{12xe^x-12x}{cos(5x)-1}\\\\\frac{12xe^x+12e^x-12}{-5sin(5x)}\\ \\\frac{12xe^x+12e^x+12e^x}{-25cos(5x)}[/tex]

Now, plug in the limit and evaluate:

[tex]\frac{12(0)e^{0}+12e^{0}+12e^{0}}{-25cos(5(0))}\\ \\\frac{12+12}{-25cos(0)}\\ \\\frac{24}{-25}\\ \\-\frac{24}{25}[/tex]

Thus, [tex]\lim_{x \to 0} \frac{12xe^x-12x}{cos(5x)-1}=-\frac{24}{25}[/tex]

given ,

a circle of radius 12 inches

and [tex]\theta[/tex] = 45°

now we know that ,

[tex]\\{Area \: of \: sector = \frac{\theta}{360\degree} \times \pi \: r {}^{2} } \\ \\ [/tex]

let's now plug in the values of radius and theta as 12 inches and 45° respectively ,

[tex]\\\dashrightarrow \: \frac{45}{360} \times \frac{22}{7} \times 12 \times 12 \\ \\ \dashrightarrow \: \frac{1}{8} \times \frac{22 \times 12 \times 12}{7} \\ \\ \dashrightarrow \: \frac{22 \times 12 \times 12}{56} \\ \\ \dashrightarrow \: \frac{3168}{56} \\ \\ \dashrightarrow \: 56.57 \: inches {}^{2} (approx.)[/tex]

hope helpful :D

Answer:

㏒₆ (18) - ㏒₆ (6) = ㏒₆ (3)Here subtraction of logarithm given. So we have to use the property of logarithm of quotient.The property says that㏒ₐ (M) - ㏒ₐ (N) = ㏒ₐ (M/N)So for subtraction we have to divide them. That is logarithm of difference becomes the quotient.So we can write,㏒₆ (18) - ㏒₆ (6) = ㏒₆ (18/6) If we divide 18 by 6 we will get 3.So, ㏒₆ (18) - ㏒₆ (6) = ㏒₆ (3)

Step-by-step explanation:

Answer:Quotient Property

Step-by-step explanation:The property used to rewrite the expression is the quotient rule of logarithms, which states that log_b(x/y) = log_b(x) - log_b(y).

The miles Peyton's family had travelled when he fell asleep is 770 miles

Percentage can be described as a fraction out of an amount that is usually expressed as a number out of hundred. The sign used to represent percentages is %.

Miles when Peyton fell asleep = 77% x 1000 = 770 miles

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Answer:

4

Step-by-step explanation:

had to look it up but do 20 x 0.2 (1/5) and u get 4

Answer:

In physics the standard unit of weight is Newton, and the standard unit of mass is the kilogram. On Earth, a 1 kg object weighs 9.8 N, so to find the weight of an object in N simply multiply the mass by 9.8 N. Or, to find the mass in kg, divide the weight by 9.8 N.Divide the object's weight by the acceleration of gravity to find the mass.

Step-by-step explanation:

this is what i think

Answer:

Width = 12in, Length = 17in

Step-by-step explanation:

We can create two expressions from the given statements:

1) L (length) = 5 + W (width)

and

2) 58 = 2L + 2W (the equation for rectangular perimeter)

Substituting L from the first equation into the second equation yields:

58 = 2(5+W) + 2W

Distributing the 2 and solving for W yields:

12in = W

Plug this back into the first expression,

L = 5 + 12

L = 17in

Answer:

width = 12 in

length = 17 in

Step-by-step explanation:

Let width of rectangle = x

⇒ length of rectangle = x + 5

Given:

Perimeter = 2 × width + 2 × length

⇒ 58  = 2x + 2(x + 5)

⇒ 58  = 2x + 2x + 10

⇒ 58  = 4x + 10

⇒ 48  = 4x

⇒ x = 12

Therefore,

width = x = 12 in

length = x + 5 = 12 + 5 = 17 in

Answer:

4squared is 16 so 16×16=256

hope it help

Answer:

4^2=16 multiplyin 16 by 16 gets you 256

Step-by-step explanation:

Answer:

B A C A B

Step-by-step explanation:

i took this test before

Answer:

The answer is (-6 + √41), (-6 – √41)

Step-by-step explanation:

We are given an equation

Subtract 5 from both side we get,

x² + 12x – 5 = 5 – 5

x² + 12x – 5 = 0

we get the equation in the form of

Here, a = 1, b = 12, c = (-5)

Now, Add and subtract (b/2a)² we get,

x² + 12x + (12/2)² – (12/2)² – 5 = 0

x² + 12x + (6)² – (6)² – 5 = 0

(x + 6)² – 36 – 5 = 0

(x + 6)² – 41 = 0

Now, add 41 both side we get,

(x + 6)² – 41 + 41 = 0 + 41

(x + 6)² = 41

√(x + 6)² = √41

x + 6 = ±√41

x = -6 + √41, -6 – √41

Thus, The roots of the equation is

(-6 + √41) and (-6 – √41).

-TheUnknownScientist 72

Answer: 8/12

Step-by-step explanation:

1/4 times 3 will give you 3/12 and add 5/12

Answer:

$710,000

Step-by-step explanation:

The computation of the owner’s equity at the end of the year is given below:

We know that

The accounting equation equals to

Total assets = Total liabilities + owners equity

where,

Total assets = $800,000 + $150,000 = $950,000

And, the total liabilities = $300,000 - $60,000 = $240,000

So, the owners equity at the end of the year would be

= $950,000 - $240,000

= $710,000

The net square pyramid and its given dimension as shown has a total surface area of 1040 ft².

Surface area of a square pyramid = A + 1 / 2 ps

where

Therefore,

A = l²

where

A = 20² = 400 ft²

p = 4l = 4 × 20 = 80 ft

s = 16 ft

Therefore,

Surface area = 400 + 1 / 2 × 80 × 16

Surface area = 400 + 1280 / 2

Surface area = 400 + 640

Surface area = 1040 ft²

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[tex]\left(2+\sqrt{10} \right)\left(2-\sqrt{10} \right)\\\\=2^2-\left(\sqrt{10} \right)^2\\\\=4-10\\\\=-6[/tex]

Answer:

T. Perimeter

Step-by-step explanation:

Answer:

[tex]\frac{2}{k+2}[/tex]

Step-by-step explanation:

Simplify the expression and you will get this.

hope this helps

Answer:

Step-by-step explanation:

Holding the perimeter fixed, the shape with greatest area is square ( all sides of the same) length) For your name example a square with a perimeter of 20 cm has sides of 5 cm and area of 5 times 4=20 cm) ^3 hope this helps

Answer:

54.03% probability that a randomly selected road has between 128 and 136 potholes per 10 miles.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean  and standard deviation, the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

Find the probability that a randomly selected road has between 128 and 136 potholes per 10 miles.

This probability is the pvalue of Z when X = 136 subtracted by the pvalue of Z when X = 128. So

X = 136

has a pvalue of 0.8849.

X = 128

has a pvalue of 0.3446.

0.8849 - 0.3446 = 0.5403

54.03% probability that a randomly selected road has between 128 and 136 potholes per 10 miles.

Radius of Circular Base Of Cone= 8m

Total Surface Area= 350m²

Considering Slant Height as l

We know,

Total Surface Area= Curved Surface Area of Cone+ Area of circular Base

i.e.,

[tex]350 { \text{m}}^{2} = \pi \times r \times l + \pi \times {r}^{2} [/tex]

[tex]350 = \pi \times r(l \times r) \\ \\ \implies 350 = 3.142 \times 8(l + 8) \\ \\ \implies \frac{350}{3.142 \times 8} = l + 8 \\ \\ \implies 13.924 = l + 8 \\ \\ \implies l = 13.924 - 8 \\ \\ \therefore l = 5.924 \: \text{cm}[/tex]

So, Slant Height= 5.924 cm

Answer:

Step-by-step explanation:

Use distributive property: a*(b - c) = (a*b) -(a*c).

Here, a = 2 ; b = 9p  & c = 1/2

[tex]2*(9p - \dfrac{1}{2})=2*9p-2*\dfrac{1}{2}\\\\\\ = 18p - 1[/tex]

The solution set 3 and 7 are the true values of the absolute value equation

The absolute value equation that has a solution set of 3 and 7 is [tex]|x - 5| = 2[/tex]

The solution sets of the absolute value equation are given as:

x = {3, 7}

Calculate the mean of the solutions

[tex]x_1 = \frac{7 +3}{2}[/tex]

[tex]x_1 = 5[/tex]

Calculate the difference of the solutions divided by 2

[tex]x_2 = \frac{7 - 3}{2}[/tex]

[tex]x_2 = 2[/tex]

The absolute value equation is the represented as:

[tex]|x - x_1| - x_2 = 0[/tex]

Substitute known values

[tex]|x - 5| - 2 = 0[/tex]

Add 2 to both sides

[tex]|x - 5| = 2[/tex]

Hence, the absolute value equation that has the a solution set of 3 and 7 is [tex]|x - 5| = 2[/tex]

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Answer:

12x−9y−12z

Step-by-step explanation:

1. 16x−12y−3z−4x−(−3y)−9z

2. Combine 16x and −4x to get: (12x−12y−3z+3y−9z)

3. Combine −12y and 3y to get: (12x−9y−3z−9z)

4. Combine −3z and −9z to get: (12x−9y−12z)

Answer: 12x−9y−12z Step-by-step

explanation: 1. 16x−12y−3z−4x−(−3y)−9z 2. Combine 16x and −4x to get: (12x−12y−3z+3y−9z)3. Combine −12y and 3y to get: (12x−9y−3z−9z) 4. Combine −3z and −9z to get: (12x−9y−12z)