h(x) = -x² + 3x + 10

Answers

Answer 1

Answer:

x = 5 or x = -2 or 3 - 2 x (derivative)

Step-by-step explanation:

Solve for x over the real numbers:

-x^2 + 3 x + 10 = 0

Multiply both sides by -1:

x^2 - 3 x - 10 = 0

x = (3 ± sqrt((-3)^2 - 4 (-10)))/2 = (3 ± sqrt(9 + 40))/2 = (3 ± sqrt(49))/2:

x = (3 + sqrt(49))/2 or x = (3 - sqrt(49))/2

sqrt(49) = sqrt(7^2) = 7:

x = (3 + 7)/2 or x = (3 - 7)/2

(3 + 7)/2 = 10/2 = 5:

x = 5 or x = (3 - 7)/2

(3 - 7)/2 = -4/2 = -2:

Answer: x = 5 or x = -2

____________________________________

Find the derivative of the following via implicit differentiation:

d/dx(H(x)) = d/dx(10 + 3 x - x^2)

Using the chain rule, d/dx(H(x)) = ( dH(u))/( du) ( du)/( dx), where u = x and d/( du)(H(u)) = H'(u):

(d/dx(x)) H'(x) = d/dx(10 + 3 x - x^2)

The derivative of x is 1:

1 H'(x) = d/dx(10 + 3 x - x^2)

Differentiate the sum term by term and factor out constants:

H'(x) = d/dx(10) + 3 (d/dx(x)) - d/dx(x^2)

The derivative of 10 is zero:

H'(x) = 3 (d/dx(x)) - d/dx(x^2) + 0

Simplify the expression:

H'(x) = 3 (d/dx(x)) - d/dx(x^2)

The derivative of x is 1:

H'(x) = -(d/dx(x^2)) + 1 3

Use the power rule, d/dx(x^n) = n x^(n - 1), where n = 2.

d/dx(x^2) = 2 x:

H'(x) = 3 - 2 x

Simplify the expression:

Answer:  = 3 - 2 x


Related Questions

How do you write 30,8608

Answers

Answer:

it should be 308,608. the comma is after every three in this scenario.

Step-by-step explanation:

30,8608 is this supposed to be a joke?

A sandman earns a commission of 26%. One week he had sales of $24400. Find the commission for the week.

Answers

Answer:

6344

Step-by-step explanation:

Find 26% of 24400

24400 * 26%

24400 * .26

6344

if given the diameter how can you find the radius

Answers

Answer:

Divide the diameter by 2.

Step-by-step explanation:

The radius of any circle is always the end to the center.

The diameter is a point of the circle to the opposite side.

This means that the diameter is twice the size of the radius, so to find the radius from the diameter, divide the diameter by 2.

Hope this helped!

Answer:

Divide the diameter by 2. d/2=r

Step-by-step explanation:

If a diameter has been given instead of a radius, you can find the radius by dividing the diameter by 2, for example.

If the diameter was 10, the radius would 10/2=5.

I need help please help meee I don’t understand

Answers

Answer:

204

Step-by-step explanation:

To simplify the shape, you can do multiple things. I've opted to shave down both prongs to take it from a 'T' shape to a rectangular prism.

For height of the prongs, take 4 from 6.

6 - 4 = 2

Divide by 2 as there are 2 prongs.

2 / 2 = 1

Remember L * W * H

6 * 3 * 1 = 18

Remember that there are two prongs!

3 + 4 = 7

6 * 7 * 4 = 168

168 + 2(18) = 204

Find (fºg)(2) and (f+g)(2) when f(x)= 1/x and g(x) = 4x +9

Answers

[tex](f\circ g)(2)=\dfrac{1}{4\cdot2+9}=\dfrac{1}{17}\\\\(f+g)(2)=\dfrac{1}{2}+4\cdot2+9=\dfrac{1}{2}+17=\dfrac{1}{2}+\dfrac{34}{2}=\dfrac{35}{2}[/tex]

An investigator claims, with 95 percent confidence, that the interval between 10 and 16 miles includes the mean commute distance for all California commuters. To have 95 percent confidence signifies that

Answers

Answer:

Hello the options to your question is missing below are the options

 A) if sample means were obtained for a long series of samples, approximately 95 percent of all sample means would be between 10 and 16 miles

B.the unknown population mean is definitely between 10 and 16 miles

C.if these intervals were constructed for a long series of samples, approximately 95 percent would include the unknown mean commute distance for all Californians

D.the unknown population mean is between 10 and 16 miles with probability .95

Answer : if these intervals were constructed for a long series of samples, approximately 95 percent would include the unknown mean commute distance for all Californians  ( c )

Step-by-step explanation:

95%  confidence

interval = 10 to 16 miles

To have 95% confidence signifies that if these intervals were constructed for a long series of samples, approximately 95 percent would include the unknown mean commute distance for all Californians

confidence interval covers a range of samples/values in the interval and the higher the % of the confidence interval the more precise the interval is,

A box contains 40 identical discs which are either red or white if probably picking a red disc is 1/4. Calculate the number of;
1. White disc.
2. red disc that should be added such that the probability of picking a red disc will be 1/4

Answers

The wording in this question is off... I am assuming you’re asking for the number of white discs and red discs if the probability of picking a red disc is 1/4.
If the probability of picking a red disc is 1/4, there are 10 red discs and 30 white discs.

1. Which word best describes how you feel when working on a math assessment? ( point)
bored
excited
anxious
confident​

Answers

Answer:

math is really a difficult subject for me. sometimes i feel confident when i get my answers correct, but sometimes i feel bored when i dnt get my answer. Sometimes i feel anxious , sometimes i feel excited to solve the problems.

The mathematics assessment defines as "the process of gathering evidence about a content performance of capacity to use, as well as comportment away from traditional maths, as well as of making presumptions from that proof for a range of functions". In several inferences could be derived from the information in the Educational section. In order to enhance a program that promotes learning outcomes, assessment involves the use of empirical evidence on student learning. As just a result, students' learning is improved.As per my opinion, the given question is an opinion question and in the education sector some student likes math and some aren't. In this, I will select the "excited and confident" choice because I love maths.

Learn more:

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A population consists of 100 elements. We want to draw a simple, random sample of 20 elements from this population. On the first selection, the probability of any particular element being selected is ____.

Answers

Answer:

1/5

Step-by-step explanation:

Probability is the likelihood or chance that an event will occur.

Probability = expected outcome of event /total outcome

Since the population consists of 100 elements, the total outcome of event = 100.

If random sample of 20 element is drawn from the population, the expected outcome = 20

On the first selection, the probability of any particular element being selected = 20/100 = 1/5

How do you evaluate this?

Answers

[tex]_6C_3=\dfrac{6!}{3!3!}=\dfrac{4\cdot5\cdot6}{2\cdot3}=20[/tex]

Please help. I’ll mark you as brainliest if correct!

Answers

Answer:

(DNE,DNE)

Step-by-step explanation:

-24x-12y = -16. Equation one

6x +3y = 4. Equation two

Multiplying equation two with +4 gives

4(6x +3y = 4)

24x +12y = 16...result of equation two

-24x -12y= -16...

A careful observation to the following equation will help us notice that the both equation are same thing.

Multiplying minus to equation one gives

-(-24x-12y=-16)

24x+12y = 16.

Since the both equation are same, there is no solution to it.

Use the graph showing Phillip's account balance to answer the question that follows. ^

What is the interest rate on Phillip's account?

A - 3.3%

B - 6.7%

C - 9.0%

D - 15.3%

Answers

Answer:

A - 3.3%

Step-by-step explanation:

From the graph

Where x= 0

Amount =$ 450

It shows that$450 is the capital

Then

When x= 3

Amount=$494.55

So interest generated within 3 years

= $494.55-$450

=$ 44.55

When x= 9

Amount = $583.65

So interest generated within 9 years

= $583.65-$450

=$ 133.65

PRT/10= Interest

450*x*3/100= 44.55

1350x= 4455

X= 4455/1350

X= 3.3

So the rate is =3.3%

Karim has two investments, one in Company A, and another in Company B. Karim purchased 3,000 shares in company A at $2.65 per share. Since purchasing the shares, the price per share increased to $2.95 per share, after which point Karim decided to sell, realizing a profit. At the same time, Karim purchased 2,000 shares in Company B at $1.55 per share. Since purchasing the shares, the share price fell to $1.30 per share, after which Karim decided to sell the shares, suffering a loss. Karim is required to pay tax at a rate of 28% on the combined profit from both investments. Calculate how much tax Karim must pay.

Answers

Answer:

A:$2478

B:$728

Total:$3206

Step-by-step explanation:

2.95x3000=8850

1.30x2000=2600

8850x0.28=2478

2600x0.28=728

2478+728=3206

An economist is interested in studying the spending habits of consumers in a particular region. The population standard deviation is known to be $1,000. A random sample of 50 individuals resulted in an average expense of $15,000. What is the width of the 99% confidence interval for the mean of expense? a. 364.28 b. 728.55 c. 329.00 d. 657.99

Answers

Answer:

The  width is  [tex]w = \$ 729.7[/tex]

Step-by-step explanation:

From the question we are told that

   The population standard deviation is  [tex]\sigma = \% 1,000[/tex]

    The  sample size is  [tex]n = 50[/tex]

    The sample mean  is  [tex]\= x = \$ 15,000[/tex]

Given that the confidence level is  99% then the level of significance is mathematically represented as  

               [tex]\alpha = 100 - 99[/tex]

=>            [tex]\alpha = 1\%[/tex]

=>             [tex]\alpha = 0.01[/tex]

Next we obtain the critical value of  [tex]\frac{\alpha }{2}[/tex] from the normal distribution table, the value is

             [tex]Z_{\frac{\alpha }{2} } = Z_{\frac{0.01 }{2} } = 2.58[/tex]

Generally margin of error is mathematically represented as

             [tex]E = Z_{\frac{\alpha }{2} * \frac{\sigma }{\sqrt{n} }[/tex]

substituting values

              [tex]E = 2.58 * \frac{1000 }{\sqrt{50} }[/tex]

              [tex]E = 2.58 * \frac{1000 }{\sqrt{50} }[/tex]

               [tex]E = 364.9[/tex]

The width of the 99% confidence interval is mathematically evaluated as

         [tex]w = 2 * E[/tex]

substituting values

          [tex]w = 2 * 364.9[/tex]

          [tex]w = \$ 729.7[/tex]

Find the polynomial for the area.
The area is​

Answers

Answer:  ¹/₂( x² - 10y² + 10xy - xy )

Step-by-step explanation:

From the diagram area of the triangle = ¹/₂ ˣ base ˣ height

where the base = x + 10y and the height = x - y

Therefore putting these into the formula above

Area  =   ¹/₂ [( x + 10y )( x -y )]

         =   ¹/₂( x² - xy + 10xy - 10y²)units²

         = ¹/₂( x² - 10y² + 10xy - xy )

     

Match the base to the corresponding height.
Base (b)
Height (h)
b
h
h
b

Answers

The base 1 is matched with height 2, base 2 is matched with height 3 and base 3 is matched with height 1. The base to the corresponding height is matched in the attached figure.

What is a triangle?

Triangle is the closed shaped polygon which has 3 sides and 3 interior angles. The height of the triangle is the dimension of the elevation from the opposite peak to the length of the base.

Thus, the base 1 is matched with height 2, base 2 is matched with height 3 and base 3 is matched with height 1. The base to the corresponding height is matched in the attached figure.

In the given figure, three triangles is shown with base and height. Here,

The base 1 is matched with height 2, as the height shown in figure 2 is the dimension of the elevation from the opposite peak to the length of the base 1.Similarly, base 2 is matched with height 3.Base 3 is matched with height 1.

Thus, the base 1 is matched with height 2, base 2 is matched with height 3 and base 3 is matched with height 1. The base to the corresponding height is matched in the attached figure.

Learn more about the base and height of the triangle here;

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Explain how to solve the inequality (x + 1)(x – 2) ∙ (x – 3) > 0. Explain in your own words, each step necessary to solve the inequality, making sure to follow the proper order of operations. Is this inequality accurate? Explain why or why not.

Answers

Answer:

[tex]x > -1[/tex] or

[tex]x > 2[/tex] or

[tex]x > 3[/tex]

Step-by-step explanation:

Given

[tex](x + 1)(x - 2) (x - 3) > 0[/tex]

Required

Solve; with steps

[tex](x + 1)(x - 2) (x - 3) > 0[/tex]

Start by splitting the inequality as follows

[tex]x + 1 > 0[/tex] or [tex]x - 2 > 0[/tex] or  [tex]x - 3 > 0[/tex]

Solve the inequalities one after the other

Solving: [tex]x + 1 > 0[/tex]

Subtract 1 from both sides

[tex]x + 1 - 1 > 0 - 1[/tex]

[tex]x > -1[/tex]

Solving: [tex]x - 2 > 0[/tex]

Add 2 to both sides

[tex]x - 2 +2 > 0 +2[/tex]

[tex]x > 2[/tex]

Solving: [tex]x - 3 > 0[/tex]

Add 3 to both sides

[tex]x - 3 +3> 0+3[/tex]

[tex]x > 3[/tex]

Hence, the solution to the inequality is

[tex]x > -1[/tex] or

[tex]x > 2[/tex] or

[tex]x > 3[/tex]

The perimeter of a rectangular garden is 43.8 feet. It's length is 12.4t . What is it's width ?

Answers

Answer:5

Step-by-step explanation:

PLZ HELPPPPPP. 25 POINTS.

A store sells books for $12 each. In the proportional relationship between x, the number of books purchased, and y, the cost per books in dollars" to "y, the total cost of the books in dollars, the constant of proportionality is 12. Which equation shows the relationship between x and y?

A. y=12/x

B. y=12x

C. y=12+x

D. y=12−x

Answers

Answer:

b

Step-by-step explanation:

because its right dummy

Twice the difference of a number and 9 is 3. Use the variable b for the unknown number.

Answers

Answer:

b = 10.5

Step-by-step explanation:

2(b-9) = 3

then:

2*b + 2*-9 = 3

2b - 18 = 3

2b = 3 + 18

2b = 21

b = 21/2

b = 10.5

check:

2(10.5 - 9) = 3

2*1.5 = 3

Let REPEAT TM = { | M is a TM, and for all s ∈ L(M), s = uv where u = v }. Show that REPEATTM is undecidable. Do not use Rice’s Theorem.

Answers

Answer:

Step-by-step explanation:

Let REPEAT [tex]_{TM[/tex]= { | M is a TM, and for all s ∈ L(M), s = uv where u = v }

To prove that REPEAT [tex]_{TM[/tex]  is undecidable.

Let  REPEAT [tex]_{TM[/tex] {| M is a TM that does not accept M}

Then, we form a TM  u for L by applying TM v as a subroutine.

Assume Repeat   is decidable

Let M be the algorithm that  TM which decides the REPEATU = on input "s" simulate the M

Accept; if M ever enters the accept state

Reject; if M ever enters the reject state

U does not decide the REPEAT as it may loop over s

so REPEAT is undecidable

It takes amy 8 minutes to mow 1/6 of her backyard. At that rate how many more minutes will it take her to finish mowing her backyard

Answers

Answer:

40 minutes

Step-by-step explanation:

If it takes her 8 minutes to mow 1/6 of it, we can find the total amount of time it  will take by multiplying 8 by 6, since 1/6 times 6 is 1 (1 represents the whole lawn mowed)

8(6) = 48

The question asks for how many more minutes it will take, so subtract 48 by 8.

48 - 8 = 40

= 40 minutes

Answer:

40 minutes

Step-by-step explanation:

We can use ratios to solve

8 minutes          x minutes

------------------- = ----------------

1/6 yard                 1 yard

Using cross products

8 * 1 = 1/6 x

Multiply each side by 6

8*6 = 1/6 * x * 6

48 = x

48 minutes total

She has already done 8 minutes

48-8 = 40 minutes

2/3a - 1/6 =1/3 please help me

Answers

Answer:

[tex]a = \frac{3}{4}[/tex]

Step-by-step explanation:

Let's convert everything to sixths to make it easier to work with.

[tex]\frac{4}{6}a - \frac{1}{6} = \frac{2}{6}[/tex]

Add 1/6 to both sides:

[tex]\frac{4}{6}a = \frac{3}{6}[/tex].

Dividing both sides by 4/6:

[tex]a = \frac{3}{6} \div \frac{4}{6}\\\\a = \frac{3}{6} \cdot \frac{6}{4}\\\\a = \frac{18}{24}\\\\a = \frac{3}{4}[/tex]

Hope this helped!

please help !! Solve –2.5x ≤ 25

Answers

Answer:

x ≥-10

Step-by-step explanation:

–2.5x ≤ 25

Divide each side by -2.5, remembering to flip the inequality

–2.5x/-2.5 ≥ 25 /-2.5

x ≥-10

Answer:

[tex]x\leq -10[/tex]

Step-by-step explanation:

[tex]-2.5x\leq 25[/tex]-----> Multiply by -1:

[tex]2.5x\geq -25[/tex]-----> Divide by 2.5:

[tex]x\geq -10[/tex]

Hope this helps!

If A = {2,4,6,8,10) and B = [4,8,10), then which of the following statements is false?

A n B = B
B C B
A C B​

Answers

A C B because all elements of A are not found in B

22 tons is equivalent to ______ kilograms.

Answers

22 tons is equivalent to


ANSWER: 19958.064 kilograms

Hope it helps:))

Answer:

20000 kg

Step-by-step explanation:

Recall that 1 kg = 2.2 lb approximately.  Then:

22 tons        1 kg        2000 lb

------------ * ------------ * --------------  =  20000 kg

      1           2.2 lb          1 ton

Lauren is a college sophomore majoring in business. This semester Lauren is taking courses in accounting, economics, management information systems, public speaking, and statistics. The sizes of these classes are, respectively, 375, 35, 45, 25, and 60.Required:Find the mean and the median of the class sizes. What is a better measure of Lauren's "typical class size"—the mean or the median?

Answers

Answer:

Mean = 108

Median = 45

The better measure of Lauren's "typical class size" is the Mean

Step-by-step explanation:

1. Calculating mean and median.

The mean is an important measure of central tendency, and it is the average of the measurement of a given set of data. It is calculated as follows:

[tex]Mean\ (\overline {X}) &= \frac{\sum X}{N}[/tex]

where X = individual data sets

N = total number of data

[tex]Mean= \frac{375\; +\ 35\ +\ 45\ +\ 25\ +\ 60}{5} \\=\frac{540}{5} \\= 108[/tex]

The Median divides the measurements into two equal parts, and in order to calculate the median, the distribution has to first be arranged in ascending or descending order. Arranging this series in descending order:

375, 60, 45, 35, 25

The formula for calculating median is given by:

[tex]M_{d} = \frac{N\ +\ 1}{2} th\ data\\\\=\frac{5\ +\ 1}{2}th\ data\\\\=\frac{6}{2} th\ data\\= 3rd\ data\\M_{d} = 45[/tex]

from the list or arranged data in descending order (375, 60, 45, 35, 25), the third data is 45.

Therefore, Median = 45

2. The better measure of typical class size is Mean because the mean depends on all the values of the data sets, whereas the median does not. When there are extreme values (outliers) the effect on the median is very small, whereas it is effectively captured by the mean.

Fill in the following blanks to prove that n 2^1 n < 2^n n+1 < 2^(n+1) is Box 3 Options: True | False Next, assume that Box 4 Options: 1 < 2^1 k + 1 < 2^(k+1) k < 2^k as we attempt to prove Box 5 Options: k < 2^k k + 1 < 2^(k+1) 2 < 2^1 Therefore, we can conclude that Box 6 Options: k < 2^k k + 1 < 2^(k+1) 2^1 < 2^k k + 2 < 2^(k+2)

Answers

Answer:

see below

Step-by-step explanation:

n < 2^n

First let n=1

1 < 2^1

1 <2  This is true

Next, assume that

(k) < 2^(k)

as we attempt to prove that

(k+1) < 2^(k+1)

.

.

.

Therefore we can conclude that

k+1 < 2^(k+1)

Answer:

Step-by-step explanation:

Hello, please consider the following.

First, assume that n equals [tex]\boxed{1}[/tex]. Therefore, [tex]\boxed{1<2^1}[/tex] is [tex]\boxed{\text{True}}[/tex]

Next, assume that [tex]\boxed{k<2^k}[/tex], as we attempt to prove [tex]\boxed{k+1<2^{k+1}}[/tex]

Since .... Therefore, we can conclude that [tex]\boxed{k+1<2^{k+1}}[/tex]

The choice for the last box is confusing. Based on your feedback, we can assume that we are still in the step 2 though.

And the last step which is not included in your question is the conclusion where we can say that we prove that for any integer [tex]n\geq 1[/tex], we have [tex]n<2^n[/tex].

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Compute (3/4)*(8/9)*(15/16)*(24/25)*(35/36)*(48/49)*(63/64)*(80/81)*(99/100) Express your answer in the simplest way possible. (Suggestion: First, try computing 3/4*8/9 then 3/4*8/9*15/16 and so on. Look for patterns.

Answers

Answer:

[tex](\frac{3}{4})*(\frac{8}{9})*(\frac{15}{16})*(\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49})*(\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}) = \frac{11}{20}[/tex]

Step-by-step explanation:

Given

[tex](\frac{3}{4})*(\frac{8}{9})*(\frac{15}{16})*(\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49})*(\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100})[/tex]

Required

Simplify

For clarity, group the expression in threes

[tex]((\frac{3}{4})*(\frac{8}{9})*(\frac{15}{16}))*((\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]

Evaluate the first group [Divide 8 by 4]

[tex]((\frac{3}{1})*(\frac{2}{9})*(\frac{15}{16}))*((\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]

[Divide 9 by 3]

[tex]((\frac{1}{1})*(\frac{2}{3})*(\frac{15}{16}))*((\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]

[tex]((\frac{2}{3})*(\frac{15}{16}))*((\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]

[Divide 15 by 3]

[tex]((\frac{2}{1})*(\frac{5}{16}))*((\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]

[Divide 16 by 2]

[tex]((\frac{1}{1})*(\frac{5}{8}))*((\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]

[tex](\frac{5}{8})*((\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]

Evaluate the second group [Divide 35 and 25 by 5]

[tex](\frac{5}{8})*((\frac{24}{5})*(\frac{7}{36})*(\frac{48}{49}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]

[Divide 49 by 7]

[tex](\frac{5}{8})*((\frac{24}{5})*(\frac{1}{3})*(\frac{4}{7}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]

[Divide 24 by 3]

[tex](\frac{5}{8})*((\frac{8}{5})*(\frac{1}{1})*(\frac{4}{7}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]

[tex](\frac{5}{8})*((\frac{8}{5})*(\frac{4}{7}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]

Merge the first and second group

[tex]((\frac{5}{8})*(\frac{8}{5})*(\frac{4}{7}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]

[tex](1*(\frac{4}{7}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]

[tex](\frac{4}{7})*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]

Evaluate the last group [Divide 99 by 9]

[tex](\frac{4}{7})*((\frac{63}{64})*(\frac{80}{9})*(\frac{11}{100}))[/tex]

[Divide 63 by 9]

[tex](\frac{4}{7})*((\frac{7}{64})*(\frac{80}{1})*(\frac{11}{100}))[/tex]

[Divide 64 and 80 by 8]

[tex](\frac{4}{7})*((\frac{7}{8})*(\frac{10}{1})*(\frac{11}{100}))[/tex]

[Divide 10 and 4 by 2]

[tex](\frac{4}{7})*((\frac{7}{4})*(\frac{5}{1})*(\frac{11}{100}))[/tex]

[Divide 100 by 5]

[tex](\frac{4}{7})*((\frac{7}{4})*(\frac{1}{1})*(\frac{11}{20}))[/tex]

[tex](\frac{4}{7})*((\frac{7}{4})*(\frac{11}{20}))[/tex]

[tex](\frac{4}{7})*(\frac{7}{4})*(\frac{11}{20})[/tex]

[tex]1*(\frac{11}{20})[/tex]

[tex]\frac{11}{20}[/tex]

Hence;

[tex](\frac{3}{4})*(\frac{8}{9})*(\frac{15}{16})*(\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49})*(\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}) = \frac{11}{20}[/tex]

Two sides of a triangle are equal length. The length of the third side exceeds the length of one of the other sides by 3 centimeters. The perimeter of the triangle is 93 centimeters. Find the length of each of the shorter sides of the triangle

Answers

Answer:

30 cm

Step-by-step explanation:

let x be the lenght of the two sides of equal lenghts, so the other is x+3

and the perimeter is x+x +x +3

P=3x+3

P=3(x+1)

93=3(x+1)

31=x+1

x=30

so the shorter sides are of 30 centimeters and the longest is 33

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