Relating a Polynomial Identity to Pythagorean Triples
In this activity you'll relate polynomial identities with Pythagorean triples. Answer the following questions
based on this triangle with side lengths x^2 – 1, 2x, and x^2 + 1.

Answer:

c=18

Step-by-step explanation:

5/30=3/c

1/6=3/18

1✖️3=3

6✖️3=18

Answer:

$15,000

Step-by-step explanation:

James purchased a total of 5 acres of land for a total price of $75,000. To find the cost of each individual acre, simply divide the total cost with the total amount of acres purchased:

[tex]\frac{total price of land bought}{total amount of acres} = \frac{75000}{5} = 15000[/tex]

The cost per individual acre, assuming all of them cost the same, is $15,000.

~

Answer:

15000

Step-by-step explanation:

Since

5 acres = 75000

therefore,

the cost price per acre would be

total cost price ➗ 5

7500/5= 15000

Answer:

19x

Step-by-step explanation:

product means multiply

19*x

19x

Answer:

The answer is C.

Step-by-step explanation:

if a number and a variable are next to each other, it is assumed they will be multiplied.

Answer:

O a piece of a line with two endpoints

Step-by-step explanation:

O a piece of a line with two endpoints

A piece of a line with two endpoints.

In geometry, a line segment is a part of a line this is bounded by distinct end points and includes every point on the line this is between its endpoints.

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Answer:

-5 ≤x ≤6

Step-by-step explanation:

The domain is the values that x can take

X goes from -5 and includes -5 to x =6 and includes 6

-5 ≤x ≤6

Answer:

See attached!

Step-by-step explanation:

Answer:

C.90 degree

Step-by-step explanation:

45 + 45 + 90 = 180

90 = 45 + 45

Answer:

D

Step-by-step explanation:

The ratio of yellow paint to blue paint is 4:3. We can make the largest amount of green paint by using all of the 20 quarts of yellow paint so we have to solve for x in 4:3 = 20:x, since 4 * 5 = 20, 3 * 5 = x so we use 15 qts of blue paint, therefore we will have 20 + 15 = 35 qts of green paint.

Answer:

D

Step-by-step explanation:

Answer:

x=10

Step-by-step explanation:

The whole figure is symmetric hence x=10

Answer:

Step-by-step explanation:

This problem is on the mensuration of solid shapes, an oblique cylinder.

the expression for the volume of an oblique cylinder is given as

[tex]volume= \pi r^2h[/tex]

Given data

radius r= 5

height h= 12, and

slant length of 13.

Substituting the given data into the expression we can solve for the volume below

[tex]volume= \pi* 5^2*12\\\ volume= \pi*25*12\\\ volume= \pi*300\\\ volume= 300\pi[/tex]

Answer:

300

Step-by-step explanation:

Answer:

(3x-5)(4x+7) / 4x + 17

Step-by-step explanation:

Rewrite the division as a fraction

12 x ^2 + x-35 / 4x+17

Factor by grouping

(3x-5)(4x+7) / 4x + 17

Hope this was the answer you were looking for

A probability outcome gives theoretical probabilities of each possible event in an experiment so option (A) will be correct.

The probability of an event occurring is defined by probability.

Do not take underestimate probability it has several uses in daily life whether forecasts and like that.

Theoretical probability is the probability that shows by the probability formula while experimental probability is an actual probability that can obtain by experiments.

There are various situations in our daily lives where we might need to make predictions about how things will turn out.

Probability outcome which comes out by mathematical formula is always theoretical probability while actual experiment gives us experimental probability hence probability outcome will be the correct answer.

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Answer:

2/8, 3/8, 4/8, 5/8, 7/8. If there are more numbers I apologize, I see 2 boxes that say "obj" instead.

9514 1404 393

Answer:

Step-by-step explanation:

The midpoint divides the segment into two equal lengths:

  AB = BC

  5x -2 = 9x -10

  8 = 4x

  2 = x

  AB = 5(2) -2 = 8

  AC = 2AB = 2(8) = 16

Assuming the cup is a right circular cylinder, it's volume is [tex]V=\pi r^2 h[/tex]

$h=10$, $r=\frac 42$

So the volume is $\pi\cdot(2)^2\cdot10=125.66$

hence you can fill up to 125.66 cubic Inches of milkshake

.

Answer:

  The approximate standard error of the sample proportion is [tex]SE = 0.0454[/tex]

Step-by-step explanation:

From the question we are told that

      The  sample proportion is  [tex]\r p = 0.29[/tex]

       The  sample size is  n =  100

Generally the standard error of the sample proportion is mathematically represented as

         [tex]SE = \sqrt{ \frac{ \r p (1- \r p )}{n} }[/tex]

substituting values    

         [tex]SE = \sqrt{ \frac{ 0.29 (1- 0.29 )}{ 100 } }[/tex]

         [tex]SE = 0.0454[/tex]

Answer:

23 miles per gallon

Step-by-step explanation:

414 miles = 18 gallons

=> 18/18 gallons = 414/18 miles

=> 1 gallon = 23 miles

So, she drove 23 miles per gallon.

Step-by-step explanation:

your required answer is 60°.

Hello,

Here, in the figure;

angle 1= 120°

To find : m. of angle 2.

now,

angle 1 + angle 2= 180° { being linear pair}

or, 120° +angle 2 = 180°

or, angle 2= 180°-120°

Therefore, the measure of angle 2 is 60°.

Hope it helps you.....

Answer:

±7 sqrt(2) = x

Step-by-step explanation:

98 - x^2 = 0

Add x^2 to each side

98 =x^2

Take the square root of each side

±sqrt(98) = sqrt(x^2)

±sqrt(49*2) = x

±7 sqrt(2) = x

Answer:

[tex]\huge \boxed{{x = \pm 7\sqrt{2} }}[/tex]

Step-by-step explanation:

[tex]98-x^2 =0[/tex]

[tex]\sf Add \ x^2 \ to \ both \ sides.[/tex]

[tex]98=x^2[/tex]

[tex]\sf Take \ the \ square \ root \ of \ both \ sides.[/tex]

[tex]\pm \sqrt{98} =x[/tex]

[tex]\sf Simplify \ radical.[/tex]

[tex]\pm \sqrt{49} \sqrt{2} =x[/tex]

[tex]\pm 7\sqrt{2} =x[/tex]

[tex]\sf Switch \ sides.[/tex]

[tex]x= \pm 7\sqrt{2}[/tex]

Answer:

(A) The shape of the distribution of the sample mean is bell-shaped.

(B) The standard error of the distribution of the sample mean is 1.1.

(C) The proportion of the samples that have a mean useful life of more than 36 hours is 0.1814.

(D) The proportion of the sample that has a mean useful life greater than 34.5 hours is 0.6736.

(E) The proportion of the sample that has a mean useful life between 34.5 and 36.0 hours is 0.4922.

Step-by-step explanation:

We are given that Power +, Inc. produces AA batteries used in remote-controlled toy cars. The mean life of these batteries follows the normal probability distribution with a mean of 35.0 hours and a standard deviation of 5.5 hours.

As a part of its quality assurance program, Power +, Inc. tests samples of 25 batteries.

Let [tex]\bar X[/tex] = sample mean life of these batteries

(A) The shape of the distribution of the sample mean will be bell-shaped because the sample mean also follows the normal distribution as it is taken from the population data only.

(B) The standard error of the distribution of the sample mean is given by;

            Standard error =  [tex]\frac{\sigma}{\sqrt{n} }[/tex]

Here, [tex]\sigma[/tex] = standard deviation = 5.5 hours

         n = sample of batteries = 25

So, the standard error =  [tex]\frac{5.5}{\sqrt{25} }[/tex]  = 1.1.

(C) The z-score probability distribution for the sample mean is given by;

                               Z  =  [tex]\frac{\bar X - \mu}{\frac{\sigma}{\sqrt{n} } }[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = population mean life of battery = 35.0 hours

            [tex]\sigma[/tex] = standard deviation = 5.5 hours

            n = sample of batteries = 25

Now, the proportion of the samples that will have a mean useful life of more than 36 hours is given by = P([tex]\bar X[/tex] > 36 hours)

       P([tex]\bar X[/tex] > 36 hours) = P( [tex]\frac{\bar X - \mu}{\frac{\sigma}{\sqrt{n} } }[/tex] > [tex]\frac{36-35}{\frac{5.5}{\sqrt{25} } }[/tex] ) = P(Z > 0.91) = 1 - P(Z [tex]\leq[/tex] 0.91)

                                                               = 1 - 0.8186 = 0.1814

(D) The proportion of the samples that will have a mean useful life of more than 34.5 hours is given by = P([tex]\bar X[/tex] > 34.5 hours)

       P([tex]\bar X[/tex] > 34.5 hours) = P( [tex]\frac{\bar X - \mu}{\frac{\sigma}{\sqrt{n} } }[/tex] > [tex]\frac{34.5-35}{\frac{5.5}{\sqrt{25} } }[/tex] ) = P(Z > -0.45) = P(Z [tex]\leq[/tex] 0.45)

                                                                    = 0.6736

(E) The proportion of the samples that will have a mean useful life between 34.5 and 36.0 hours is given by = P(34.5 hrs < [tex]\bar X[/tex] > 36 hrs)

     P(34.5 hrs < [tex]\bar X[/tex] < 36 hrs) = P([tex]\bar X[/tex] < 36 hrs) - P([tex]\bar X[/tex] [tex]\leq[/tex] 34.5 hrs)

     P([tex]\bar X[/tex] < 36 hours) = P( [tex]\frac{\bar X - \mu}{\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]\frac{36-35}{\frac{5.5}{\sqrt{25} } }[/tex] ) = P(Z < 0.91) = 0.8186

     P([tex]\bar X[/tex] [tex]\leq[/tex] 34.5 hours) = P( [tex]\frac{\bar X - \mu}{\frac{\sigma}{\sqrt{n} } }[/tex] [tex]\leq[/tex] [tex]\frac{34.5-35}{\frac{5.5}{\sqrt{25} } }[/tex] ) = P(Z [tex]\leq[/tex] -0.45) = 1 - P(Z [tex]\leq[/tex] 0.45)

                                                                    = 1 - 0.6736 = 0.3264                              

Therefore, P(34.5 hrs < [tex]\bar X[/tex] < 36 hrs) = 0.8186 - 0.3264 = 0.4922.

Answer:15x^2-3x

Step-by-step explanation:

Answer:

https://brainly.com/question/17155330

Step-by-step explanation:

Question:

Marcelina uses a blend of white corn and yellow corn to make tortilla chips at her restaurant. She needs to buy 50kg of corn in total for her next order. White corn costs $0.30 per kilogram, yellow corn costs $0.15 per kilogram, and she wants to spend $12 total.

What does point F represent in this context?

Answer:

Marcelina spends less that the intended amount of money and buy less than enough corn

Answer:

6+2+9+5+2+3+6+3 = 36

Step-by-step explanation:

If you like my answer than please mark me brainliest

Answer:

=4-7

=5

:same will be 5 years older than Sabrina

9514 1404 393

Answer:

  a.  55%

Step-by-step explanation:

The percentage increase is calculated from ...

  % increase = (amount of increase)/(original amount) × 100%

  = (2219 -1432)/1432 × 100% = 787/1432 × 100% ≈ 54.96%

The number of births increased by about 55% during those 10 years.

Answer:

Step-by-step explanation:

2219-1432/1432 x 100% = 787/1432 x 100 = 54.9581~~ 55%

Hence the area of the second rhombus is 45 square meters

The area of a rhombus is expressed as

A = base * height

For the rhombus with an area of 5 square meters and a side length of 3 meters

Height = Area/length

Height = 5/3 metres

Since the length of a similar rhombus is 9meters, the scale factor will be expressed as;

k = ratio of the lengths = 9/3

k = 3

Height of the second rhombus = 3 * height of the first rhombus

Height of the second rhombus = 3 * 5/3

Height of the second rhombus = 5 meters

Area of the second rhombus = length * height

Area of the second rhombus = 5 * 9

Area of the second rhombus = 45 square meters

Hence the area of the second rhombus is 45 square meters

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The correct option is option B;

(B) 45 square meters

The known parameters in the question are;

The area of the rhombus, A₁ = 5 m²

The length of one of the sides of the rhombus, a = 3 m

The length of a side in a similar rhombus, b = 9 m

The unknown parameter;

The area of the second rhombus

Strategy or method;

We have that two shapes are similar if their corresponding sides are proportional

From the above statement we get that the ratio of the areas of the two shapes is equal to the square of the ratio of the lengths of the corresponding sides of the two shapes of follows;

[tex]\begin{array}{ccc}Length \ Ratio&&Area \ Ratio\\\dfrac{a}{b} &&\left (\dfrac{a}{b} \right)^2 \\&&\end{array}[/tex]

Let the area of the second rhombus be A₂, we get;

[tex]Area \ ratio = \dfrac{A_1}{A_2} = \left( \dfrac{a}{b} \right)^2[/tex]

Where;

a = 3 m, b = 9 m, and A₁ = 5 m², we get;

[tex]Area \ ratio = \dfrac{5 \ m^2}{A_2} = \left( \dfrac{3 \, m}{9 \, m} \right)^2 = \dfrac{1}{9}[/tex]

Therefore;

9 × 5 m² = A₂ × 1

A₂ = 45 m²

The area of the second rhombus, A₂ = 5 m².

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Answer:

see below

Step-by-step explanation:

Difference is subtract

(8-2)

Then add this to x

(8-2) +x

6+x

Answer:

Probability of Type 1 error = 0.033

Probability of type II error = 0.952

Step-by-step explanation:

H0: Individual does not have disease

H1: individual has disease

Type 1 error occurs when we fail to accept a correct null hypothesis and accept an alternate Instead

Type ii error occurs when we accept a false null hypothesis instead of the alternate hypothesis

Probability of people with disease = 98.4%

Probability of people without disease = 3.3%

1.probability of type 1 error = 3.3/100

= 0.033

2. Probability of type ii error = (1-98.4%) = 1-0.948

= 0.052