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

Answers

Answer 1

A negative number * another negative number gives a positive value

A positive number * another positive number also gives a positive value

The solutions are -4, 4

Hope this helps :)

Related Questions

Information about a play took up 1/3 of the pages in the program. Information about the actors took up 1/4 of the remaining pages. Information about the director, the producer, and the designer took up 2 pages, the same number of pages devoted to the actors. How many pages were there in the program?

Answers

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.

Proofs and congruent triangles 2 forgot to put images last time 50 points ( serious answer or 1 star and report ) ( YOU NEED TO CHECK MY ANSWERS PLEASE )

Answers

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

Determine what type of model best fits the given situation:

Answers

Answer:

B. quadratic function graph

A school play sold 575 tickets total They were either adult or student tickets there were 75 fewer student tickets sold than adult tickets how many adult tickets were sold

Answers

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

Which expression is equivalent to √2+4?
OA. (2+4)²
OB. (2+4)²
OC. 6
D. 62

Answers

Option A, root(2+4) = root 6. Can be written as (2+4)^1/2

Find all primes p, q such that p^2-p=37q^2-q

Answers

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

How to determine the pairs of numbers?

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

Answers

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

Write the equation of a parabola whose directrix is

y

=

−

1.5

y

=

-

1.5

and has a focus at

(

−

4

,

−

2.5

)

(

-

4

,

-

2.5

)

.

Answers

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]

What is the measure of arc RT

Answers

The measure of arc RT is 156 degree.

Measure of arc RT

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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The function y=f(x)is graphed below. What is the average rate of change of the function f(x) on the interval 7≤x≤8?

Answers

Answer:

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

_+_+_= 30
Use only
1,3,5,7,9,11,13,15
You can repeat it

Answers

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)

Please help ASAP! Clear explanations are greatly appreciated!

Answers

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

What is a system of equations?

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:

Variable x: Her normal hours.Variable y: Her time and a half hours.

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:

x + 8y = 375.x + 4y = 330.

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

x + 8y = 375.-2x - 8y = -660.

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

x = 660 - 375 = €285.

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factor 18x^(2)+39x-15

Answers

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.

[tex]f(x) = 18x^2 + 39x - 15[/tex][tex]f(x) = 3(6x^2 + 13x - 5)[/tex]

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]

a = 6b = 13c = -5

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.

Factor by Grouping[tex]6x^2 + 13x - 5[/tex][tex]6x^2 -2x + 15x - 5[/tex][tex]2x(3x- 1) +5(3x - 1)[/tex][tex](2x +5)(3x - 1)[/tex]

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

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

101.19 / 4 using long division

Answers

25.3 is the answer to your problem

What is the angle for x

Answers

Answer:

X = 90°

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 °

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

Answers

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

Answer:

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

Step-by-step explanation:

Hello!20 x (-5) + 10x (-3) + (-5) × (-6)-(3x5).. given expression [tex] - 100 + 10( - 3) + ( - 5)( - 6) - 15 \\ - 100 - 30 + ( - 5)( - 6) - 15 \\ - 100 - 30 + 30 - 15 \\ - 130 + 30 - 15 \\ - 100 - 15 \\ - 115[/tex]

riley makes a mistake in step 2 while doing her homework. What was her mistake? StartFraction x Over x squared minus 5 x + 6 EndFraction + StartFraction x Over x + 3 EndFraction Step 1: StartFraction x Over (x minus 2)(x minus 3) EndFraction + StartFraction 3 Over x + 3 EndFraction Step 2: StartFraction x Over (x minus 2) (x + 3) EndFraction + 3 (x minus 2) Over (x minus 2) (x + 3) EndFraction Step 3: StartFraction x + 3 x minus 6 Over (x minus 2) (x + 3) EndFraction Step 4: StartFraction 4 x minus 6 Over (x minus 2) (x + 3) EndFraction She added the two fractions incorrectly. She used the wrong common denominator. She did not distribute the negative correctly. She did not multiply the first fraction by a factor. Mark this and return

Answers

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

What is a Common Denominator?

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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A town planner is interested in getting some demographic data about the households in the city. The city has ten wards that vary in size. Which sampling method is most appropriate?

Answers

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

What is the Sampling Method used?

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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Evaluate the following expression when y=2.

9y−8y+2

Answers

Answer:4

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

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

18-16+2

simplify. ((x/4)+(x/3))/(x/2)

Answers

Answer:

x/6

You're welcome! :)

Answer : 7/6

explanation is long

Which of the following sets of numbers could not represent the three sides of a triangle?

Answers

Answer:

Step-by-step explanation:

E and F are two events and that P(E)=0.2 and P(F/E)=0.6 what is P(E and F)

Answers

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

How to solve Conditional Probability?

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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Express the following

Answers

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

Simplifying exponential function

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 alexander family and jenkins family each used their sprinklers last summer. the water output rate for the alexander familys sprinkler was 20 L per hour. theh water output rate fro the jenkins familys sprinkler was 25 L per hour. the familes used their sprinklers for a combined total of 65 hours, resulting in a total water output of 1450 L. How long was each sprinkler used?

Answers

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.

1. Based on the circular
angle below. What is the
best measurement
the angle?
for
a. less than 90°
b. more than 90°
C. more than 180°
d. less than 60°

Answers

Answer:

B. More than 90

Step-by-step explanation:

Hope this helps!

Using the following table, construct and interpret a 90% confidence interval for the population standard deviation of the carbon in metric tons.
Nation
Brazil
Germany
Mexico
Emissions
Canada
361
844
398
Great Britain 577
631

Answers

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

First we have to find the mean

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

Answers

Answer:

t= d/r t=5

Step-by-step explanation:

divide each side by d to isolate t

The diagonals of a rectangle enclose an angle of measure 78 degree
. If the perimeter of the rectangle is 36cm, what is its area?

Answers

the area of the rectangle is 80. 1 cm²

What is the area of a rectangle?

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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WHICH LINE IS PERPENDICULAR TO THE LINE WITH EQUATION Y = -1/2X?

Answers

Answer:

y=-1/4x+3 is the answer.

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You are offered two different sales jobs. The first company offers a straight commission of 5% of the sales.
The second company offers a salary of $ 210 per week plus 2% of the sales. How much would you have to
sell in a week in order for the straight commission offer to be at least as good?

Answers

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.

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