explain why x squared = 16 has two solutions. What are the solutions.

The pairs of prime numbers (p,q) such that  p^2-p=37q^2-q is (43, 7)

The expression is given as:

p^2 - p=37q^2 - q

The boundary or range of numbers of p and q is not given.

So, we make use of numbers between 2 (because 1 is not a prime number) and a very large number (say 1000000)

i.e. 2 ≤ p ≤ 1000000 and 2 ≤ b ≤ 1000000

Using the above range, we have the following program to determine the pairs of prime numbers (p, q).

for a in range(2,1000000):

  for b in range(2,1000000):

      if ((a* *2) - a) == (37 * (b* *2) - b):

          print(str(a)+","+str(b))

The output of the above program is:

(43, 7)

The above represent all pairs of prime numbers (p,q) such that p^2 - p=37q^2 - q

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Answer:

Step-by-step explanation:

that is a regular rhombus, by definition it has perpendicular diagonals, so in the center there are 4 90 ° angles, so your answer is x = 90 °

The mathematical mistake that Riley made is that: "She used the wrong common denominator." (Option A)

A common denominator is a factor that is similar to all the fractions in the sequence of equations.

Hence the correct answer is:

(2(2x² - 6x + 9))/((x-3) (x-2) (x+3))

See the correct sequence of steps below:

Step One - the Expression is given as:

(x/(x-3)(x-2)) + (3/(x+3))

Step 2 - Find the common denominator and rewrite the expression so that the numerators are above the common denominators.

Hence we have:  (x (x+3) + 3(x-3) (x-2))/(x-3)(x-2)(x+3)

Step 3  Apply the Law of Multiplicative Distribution:

Hence we have  (x² +3x+3x²-9x-6x+16)/(x-3)(x-2)(x+3)

Step 4 -  Collect Like Items

This gives us: (x²+3x²)+(3x-9x-6x)+18/(x-3)(x-2)(x+3)

Step 5 Sort for like coefficients

This gives us:  ((1+3)x² +(3-9-6) * x + 18)/(x-3)(x-2)(x+3)

Step 6 -  check for the sum or difference

This gives us: (4x²+(3-9-6) * x+ 18)/(x-3)(x-2)(x+3)

We simplify and factor the expression to get

(2(2x²-6x+6)/(x-3)(x-2)(x+3).

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Answer:4

Step-by-step explanation: 9y-8y+2, when y=2

9(2)-8(2)+2=

18-16+2

=4

Answer:

40

Step-by-step explanation:

the average rate of change of f(x) in the closed interval [ a, b ] is

[tex]\frac{f(b)-f(a)}{b-a}[/tex]

here [ a, b ] = [ 7, 8 ] , then

f(b) = f(8) = 20 ← point (8, 20 ) on graph

f(a) = f(7) = - 20 ← point (7, - 20 ) on graph

average rate of change = [tex]\frac{20-(-20)}{8-7}[/tex] = [tex]\frac{20+20}{1}[/tex] = 40

Answer:

[tex]3(2x + 5)(3x - 1)[/tex]

Step-by-step explanation:

Hello!

We can first factor out the greatest common factor between the coefficients: 3.

Now, let's work with what we have inside the brackets.

Standard form of a quadratic: [tex]ax^2 + bx+ c = 0[/tex]

Given our equation: [tex]6x^2 + 13x - 5[/tex]

We need to find two numbers that add up to b (13) and multiply to ac (-30).

The two numbers are 15 and -2. Expand 13x to 15x and -2x and factor by grouping.

Now, we simply add the other factor, 3, to the final factored form.

Factored Solution: [tex]3(2x + 5)(3x - 1)[/tex]

Answer:

Step-by-step explanation:

Comment

Let the number of pages = x

Play =    1/3x

Actors = 1/4(x - 1/3 x)

Actors = 1/4(2/3x)

Actors = 2/12 x

Producer Director etc = 2 pages

Equation

Actors = 2 pages

2/12 x = 2

Solution

2x/12 = 2               Multiply both sides by 12

12*2x/12 = 2*12     Combine

2x = 24                  Divide by 2

2x/2 = 24/2           Combine

x = 12

Answer

The program had 12 pages.

Answer:

BC = 18 cm

Step-by-step explanation:

As we can see from the diagram:

AB + BC + CD = AD

⇒ 10 cm + BC + 11 cm = 39 cm

⇒ BC + 21 cm = 39 cm

⇒ BC = 39 cm - 21 cm

⇒ BC = 18 cm

Answer:

The offers are equal at $7,000, after $7,000 more money will be made with a straight commission.

Step-by-step explanation:

.05x = .02x + 210  Subtract .02x from both sides.

.03x  = 210   Divide both sides by .03

x  = $7,000.

The measure of arc RT is 156 degree.

Given:

arc TRM=102°

Hence:

arc RST=2×1O2°

arc RST=204°

Measure of arc RT

arc RT= 2(180° - 102°)

arc RT = 2(78°)

arc RT = 156 degrees

Therefore the correct option is B.

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Answer:

t= d/r t=5

Step-by-step explanation:

divide each side by d to isolate t

Answer:

B. quadratic function graph

Answer:

B. More than 90

Step-by-step explanation:

Hope this helps!

20 x (-5) + 10x (-3) + (-5) × (-6)-(3x5) = -115

Answer:

The simplified form of the above expressions solution is -115.

Step-by-step explanation:

The 90 percent confidence interval for the data is given as  396.02, 727.98

The formula is fx/n

= Mean, μ = 562.2

sum up the data and divide by 5

sd =  

Σ(xi - μ)2/N

= (361 - 562.2)² + ... + (631 - 562.2)²/5

= 151806.8/5

= 30361.36

sd = √30361.36

= 174.24511470914

1 - confidence level

= 1 - 0.90

= 0.1

df = 4

Using excel

T.INV.2T(0.1, 4) = ±2.13

562 +- 2.13 x  174.245/√5

562- 165.98, 562+ 165.98

= 396.02, 727.98

Hence the confidence interval can be calculated to be 396.02, 727.98

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Answer:

Step-by-step explanation:

The sum of the exponential expression is e^8x + e^2x

Exponential functions are inverse of logarithmic function

Given the exponential function below;

(e^4x)² + e^2x

Expand

e^8x + e^2x

Hence the sum of the exponential expression is e^8x + e^2x

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the area of the rectangle is 80. 1  cm²

From the given information, let's say one side of rectangle = a

The other side  =  (36 - 2a)/2  

=  18 - a   cm

The angles between the diagonals of the rectangle is 78°

Then, the angle diagonal has with base will give

=  (180° - 78°)/2

= 102/2

= 51°

We have the angle to be 51 degrees, using the tan ratio

Tan θ = opposite/ adjacent

Opposite of angle 51 degrees = a

Adjacent = 18 - a

Thus,

[tex]tan 51 = \frac{a}{18 - a}[/tex]

[tex]1. 2349 = \frac{a}{18-a }[/tex]

cross multiply

[tex]18 -a ( 1. 2349) = a[/tex]

[tex]22. 23 - 1. 2349a = a[/tex]

collect like terms

[tex]a + 1. 2349a = 22. 23[/tex]

[tex]2. 2349 a = 22. 23[/tex]

[tex]a = \frac{22. 23}{2. 2349}[/tex]

a = 9. 95

If a = 9. 95cm

Then, 18 - a = 18 - 9. 95 = 8. 05cm

The formula of area of a rectangle is given as;

Area = width × length

Area = 9.95 x 8.05

Area = 80. 1  cm²

Thus, the area of the rectangle is 80. 1  cm²

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Answer:

  x/6

You're welcome! :)

Answer : 7/6

explanation is long

Answer:

325 adult tickets

Step-by-step explanation:

Let adult tickets be x, student tickets are 75 less than adult tickets, so let student tickets be x-75

The total is 575

x+x-75 = 575

2x = 650

x = 325 adult tickets

Answer:
Alexanders family sprinkler used for 35.25 hours
And the Jenkins family sprinkler was used for 29.75 hours.

Step-by-step explanation:

Lets start with 2 assumptions, what if we only used the Alexander's family sprinklers, We can define X as the variable
[tex]20x=1450[/tex]
[tex]x= 72.5[/tex]
If we just used the Alexanders it would of took 72 hours and 30 minutes.

Now lets look at the Jenkins family sprinkler, lets define it as Y.
[tex]25y=1450[/tex]
[tex]y = 58[/tex]
With only the Jenkins it would of took 58 hours.

Now, if they just of shared the work equally among the two sprinklers, the Alexanders family doing 725 L and the Jenkins with the other half.
It would of took the Alexanders
[tex]20x= 725[/tex]
[tex]x=36.25[/tex]

Jenkins
[tex]25y=725[/tex]
[tex]y=29[/tex]

Making it a combined time of 65.25 hours. 15 minutes long of our 65 hour time.

Now the Jenkins sprinkler generates 5 more L than Alexanders per hour. Which means it would only take the Jenkins family 1 hours to make 25 liters but Alexanders would take [tex]\frac{5}{4}[/tex] hours. We know that 1 hour contains 60 minutes, which means [tex]\frac{1}{4}[/tex] of a hour contains 15 minutes.

So it would take Alexanders family sprinkler 15 minutes more to produce the same amount per hour that the Jenkins does.

So from this we can conclude that if the Jenkins family sprinkler was used more we can cut the extra 15 minutes off, making the answer That the

Alexanders family sprinkler used for 35.25 hours
And the Jenkins family sprinkler was used for 29.75 hours.

Answer:

y=0.5x²-4x-10.

Step-by-step explanation:

1) according to the definition of parabola:

d1=d2, then

[tex]2) \ |y+1.5|=\sqrt{(x+4)^2+(y+2.5)^2} ;[/tex]

3) after evolution:

-(2y+4)=(x+4)²; ⇔

[tex]y=-\frac{1}{2}x^2-4x-10.[/tex]

Answer

1 possible solution:

(5x7) in the first blank

(-3!) in the second blank

(-1) in the third blank

Step-by-step explanation:

(5x7) + -(3!) + -(1)          3! equals 3x2x1 or 6

35 + (-6) + (-1)

Using a system of equations, it is found that her normal week is of €285.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

For this problem, the variables are given as follows:

The first equation, considering the first sentence, is given by:

x + 8y = 375.

The second equation, considering the second sentence, is given by:

x + 4y = 330.

Then the system is:

Multiplying the second equation by -2, the system is:

Adding the equations, we have that her normal week is given by:

x = 660 - 375 = €285.

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The best sampling method that Is most appropriate for the town planner is called Stratified Sampling.

The best sampling method that I would recommend for the town planner is called Stratified Sampling.

The reason for using stratified sampling is because it is a method of sampling that involves dividing a population into smaller groups–called strata and in this case, the rows of houses can be used as a strata.

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The probability of E and F expressed as P(E and F) equals;0.12

We are given;

P(E) = 0.2

P(F|E) = 0.6

Now, P(F/E) is known as conditional probability and it means the probability of event F given the probability of another event E. This can be expressed as; P(F|E) = P(E and F)/P(E)

Thus;

P(E and F) = 0.2 * 0.6

P(E and F) = 0.12

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Answer:

Step-by-step explanation:

Q3 asks for reasons of statements in a theorem proof.

1 Given is correct

2 Definition of right angle is correct

3 should be sum of interior angles in a triangle

4 is substitution

5 subtracting 90degree from left and right hand side

6 is definition of complementary

Answer:

y=-1/4x+3​ is the answer.

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