What are the solutions to the equation? x2−12x+36=4 Enter your answers in the boxes. x1= x2=

Answers

Answer 1

The first step getting these answers is to make the equation equal to zero. To do this, you subtract 4 from both sides. After that, you would factor the following equation x^2 - 12x + 32 = 0, To do this you would find number that when multiplied together give you 32 as well as add up to -12. -4 and -8 are the answers that will give you this. Rewrite the equation as (x + -4) (x + -8) = 0. You need to see what numbers would give you zero in both problems. They would be 4 and 8. These are the 2 possible solutions.

Answer 2

Answer:

4 and 8

Step-by-step explanation:

x1 = 4

x2 = 8

Related Questions

The formula for the volume of a sphere is V=4/3 3.14r^3. What is the formula solved for r?

Answers

[tex]V = \frac{4\pi r^{3} }{3} \\ \\ \\ \frac{3V}{4 \pi } = r^{3} \\ \\ \sqrt[3]{ \frac{3V}{4 \pi } } = r [/tex]

HELP ME PLEASEEEEEEEEEEEEEEEEEE

Answers

For this case we have the following solution.
First, let's give the variable a name:
Let
x = gallons of water to be added
For the 10% solution we have:
0.1 * 8 = 0.8
Then, for 5% we have:
(0.8 / x + 8) = 0.05
Rewriting:
(0.8 / x + 8) = (5/100)
Answer:
An equation can be used to find x, the humber of gallons of water he should add is:
(0.8 / x + 8) = (5/100) (option 2).

it rained 3/8 of a inch each day for 3 days straight how much rain fell altogether

Answers

Total of 1 and 1/8 inches total.

Hello!

It rained the same amount on each of the 3 days, so the denominator will remain the same. Multiply the fraction by the amount of days:

3/8 × 3 = 1 1/8

ANSWER:

1 1/8 (or 9/8) inches of rain fell altogether on the 3 days.

a sheep breeding farm counted a total of 40 sheep on their grounds after one year the number of sheep doubled then in the next year the number of sheep doubled again if this trend continues which of the following options represents the number of sheep on the farm by then end of each year

Answers

Answer:
graph (b)

Explanation:
The farm started with 40 sheep and the number doubled each year.
So, the equation modeling this situation would be:
N(x) = 40*(2)^2
By getting the equation, we can notice that we already excluded the third and fourth choices as they have the wrong equations.

Now, we will need to select the right graph which is either graph a or graph b.
To do this, we will get the value of N(x) for different values of x as follows:
At x = 0: N(0) = 40*(2)^0 = 40
At x = 1: N(1) = 40*(2)^1 = 80
At x = 1: N(2) = 40*(2)^2 = 160

Now, taking a look at graph a, we will find that:
N(1) = 120
N(2) = 360
These numbers are not the same as the numbers we calculated, therefore, this graph is wrong

Taking a look at graph b, we will find that:
N(1) = 80
N(2) = 160
These numbers are exactly the same as the ones calculated, therefore, this graph is the correct one.

Hope this helps :)

which of the following is important in a 2 column proof?
A list of all theorems
Staircase LOgic
Order
Detailed explanations for each step

Answers

Answer:

Order.

Step-by-step explanation:

When we are proving a proposition, it's important to have order in our 2-column proof.

So, we must have a left colum for Statements and a right colum for Reasons, that's the order we need to have.

In the statements colum we write our deductions. In the reasons column, we write the justification or reason about our deduction.

Therefore, the right answer is the third choice: Order.

On the map of a town, 1 cm represents 6 miles. Find the distance represented by 4.5 cm. A) 4.5 miles B) 6 miles C) 17 miles D) 27 miles

Answers

The answer is D) 27 miles because 4.5 * 6 = 27

I hope this helps you out!! <3

if 1 cm ...................................................6 miles
4.5 cm.................................................? miles

(6*4.5)/1=27 miles
the choice is D

Alice has 1/5 as many miniature cars as Sylvester has Sylvester has 35 miniature cars how many miniature cars does alic have?

Answers

The answer is 7. Since Alice has 1/5 as many cars as Sylvester. You multiply 1/5 by how many cars Sylvester has. Sylvester has 35 cars, so you would do 35 times 1/5 or 35 divided by 5 (multiply by 1/5 and divided by 5 are the same thing) and you would get your answer of 7.

Final answer:

Alice has 1/5 as many miniature cars as Sylvester, who owns 35. By multiplying 35 cars by 1/5, we find that Alice has 7 miniature cars.

Explanation:

The student's question is about finding the number of miniature cars Alice has if she has 1/5 as many as Sylvester, who has 35 miniature cars. To solve this, we use the following mathematical operation:

Alice's miniature cars = 1/5 of Sylvester's miniature cars

Sylvester's miniature cars = 35 cars

To find out how many miniature cars Alice has, multiply the number of Sylvester's miniature cars by 1/5:

35 cars x 1/5 = 7 cars

Therefore, Alice has 7 miniature cars.

what is 5/10 + 25/100

Answers

Turn 5/10 to 50/100. Then add 50/100+25/100 which equals 75/100 ---> 3/5 ---> 0.75

3/4 is your answer and if needed as a decimal it would be 0.75

A cylindrical tank has a height of 12 feet and a diameter of 16 feet. Jane fills the tank with water at a rate of 6 cubic feet per minute. Calculate how long it would take Jane to fill the tank without overflowing it. Explain your reasoning. Round as needed.

Answers

if the diameter is 16 feet, then the radius for the tank will have to be half that,

[tex]\bf \textit{volume of a cylinder}\\\\ V=\pi r^2 h\quad \begin{cases} r=radius\\ h=height\\ -----\\ r=8\\ h=12 \end{cases}\implies V=\pi \cdot 8^2\cdot 12\implies V=\stackrel{ft^3}{768\pi} [/tex]

now, that's how many ft³ of water the tank can hold, since she is filling it up at a rate of 6 ft³ per minute, namely in 1 minute 6 ft³ have gone in, then it'll be

768π/6 how many minutes it'll take.

namely, how many times does 6 go into 768π? well, 768π/6.

Solve the system of equations using the substitution method.

{y=−3x+7
x=−2y−16

Enter your answers in the boxes.

x=

y=

Answers

ANSWER

[tex]x = 6[/tex]

[tex]y = - 11[/tex]

EXPLANATION

The given system of equations is

[tex]y = - 3x + 7...(1)[/tex]

and

[tex]x = - 2y - 16...(2)[/tex]

We substitute equation (1) into equation (2) to get;

[tex]x = - 2( - 3x + 7) - 16[/tex]

[tex]x = 6x - 14- 16[/tex]

We group similar terms

[tex]x - 6x = - 14 - 16[/tex]

[tex] - 5x = - 30[/tex]

Divide both sides by -5.

[tex]x =6[/tex]

Put x=6 into equation (1).

[tex]y = - 3(6) + 7[/tex]

[tex]y = - 18 + 7[/tex]

[tex]y = - 11[/tex]

Answer:

x = 6 and y = -11

Step-by-step explanation:

Given : System of linear equation

y=−3x+7

x=−2y−16

We have to solve the system of equations using the substitution method.

In substitution method, we substitute the value of one variable in term of other and solve for it.

Consider the given system of linear equation

y = −3x + 7 ...(1)

x = −2y − 16 .....(2)

Substitute, (2) in (1), we get,

y = -3(-2y - 16) + 7

Simplify , we get,

y = 6y + 48 + 7

6y - y = - 55

5y = -55

y = -11

Substitute y = -11 in (2), we get,

x = −2(-11) − 16 = 22 - 16 = 6

thus, x = 6

Thus , x = 6 and y = -11

rebekah's baby brother wights 7.71 pounds. Her newborn kitten weights 0.24 pound. How much more does tebekah's baby brother weight that her kitten?

Answers

Rebekah's baby weighs 7.47 more than her kitten

7.71 - .24 = 7.47. The answer is 7.47 pounds.

Maritza is buying a multipack of 3 pairs of socks for $25.98. She will save $6.24 by buying the multipack instead of buying 3 individual pairs of the same socks.

If each pair of socks costs the same amount, how much does each pair of socks cost when bought individually?

Answers

Each pair of the sock will cost $6.58

25.98-6.24=19.74
19.74/3=6.58

£850 is invested for 2 years at 6% per annum compound interest. a) Work out the total interest earned over the first 2 years.

Answers

The correct answer to 850 for 2 years at 6% interest is 955

Answer:

6% annum for 850 would be 955

7+11v=9v-9 how do you solve by steps

Answers

You're solving this equation for the variable 'v', so the main goal is to isolate it on one side of the equation.

7 + 11v = 9v - 9 Subtract 7 from both sides
7 - 7 + 11v = 9v - 9 - 7 Simplify
11v = 9v - 16 Subtract 9v from both sides
11v - 9v = 9v - 9v - 16 Simplify
2v = -16 Divide both sides by 2
[tex] \frac{2v}{2} [/tex] = -[tex] \frac{16}{2} [/tex] Simplify
v = -8

Check your answer by plugging the value (-8) into the original equation.

7 + 11(-8) = 9(-8) - 9 Simplify the mulitiplication steps
7 + (-88) = -72 - 9 Rewrite 7 + (-88) as 7 - 88
7 - 88 = -72 - 9 Simplify both sides
-81 = -81

The check worked out, so your answer is v = -8 .

An employee has an annual salary of $51,300. They receive $2,830 in health insurance and $4,600 in paid time off per year. They drive their personal vehicle for work which costs them $600 per month, but the company reimburses them $0.54 per mile for the total work miles driven. If the employee drives 36,000 miles for work for the year, what will be their total employment compensation?
a.
$70,740
b.
$70,970
c.
$77,570
d.
$78,170

Answers

The answer is B:$70,970

The total employment compensation of the employee is b. $70,970.

What are Arithmetic operations?

Arithmetic operations are the basic part of mathematics which combines the basic operations like addition, subtraction, multiplication and division.

Given that,

Annual salary of the employee = $51,300

Health insurance per year = $2,830

Paid time off per year = $4,600

Monthly expense for personal vehicle = $600

Yearly expense = 12 × $600 = $7200

Reimbursement for the vehicle = $0.54 per work mile

Reimbursement for vehicle for 36,000 miles for work for the year = $0.54 × 36,000 miles = $19,440

Total employment compensation = ($51,300 + $2,830 + $4,600 + $19,440) - $7200

= $70,970

Hence the employment compensation is $70,970.

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Find a ⋅ b.

a = 7i - 4j, b = 4i + 3j

A) <28, -12>
B) 16
C) -40
D) <11, -1>

Answers

Answer:

B) 16

Step-by-step explanation:

The dot product of a pair of vectors is the sum of the products of their corresponding parts. It is a scalar.

... a · b = (7i -4j) · (4i +3j) = 7·4 + (-4)·3

... = 28 -12 = 16

If the newspaper plans to select an ad at random each week to be published free, what is the probability that the ad for a specific week will be a help dash wanted help-wanted ad

Answers

1/7
1 divided by 7
0.14285714285%
But to round..
0.14%

Answer:Theres a article about that ont he internet

Step-by-step explanation:

The human population doubles approximately every 50 years. If there were 2.5 million people in 1950, how many people are forecasted to populate the earth in 2050?

Answers

From 1950 to 2050 is 100 years, so that would make the population doubling twice in that amount of time. So in 2000 the population would go from 2.5 million to 5 million. And in 2050 the forecast for population would be 10 million.
2.5 x 2 = 5
5 x 2 = 10

which set of three numbers could be the side lengths of a triangle A.5,5,14 B.3,3,2 C.3,3,8 D. 5,5,10

Answers

Answer:

B. 3, 3, 2

Step-by-step explanation:

The triangle inequality requires the sum of the lengths of the two shortest sides exceed the length of the longest side. That is the case only for the lengths of selection B:

2 + 3 > 3

Which list of decimals is ordered from least to greatest? A) 0.11, 0.101, 0.21 B) 0.27, 0.35, 0.41 C) 0.35, 0.056, 4.2 D) 1.09, 0.91, 1.90. I need it quick

Answers

I think B would be your answer. Hope this helps. :)

The answer is B) 0.27, 0.35, 0.41

tim has 30 grapes. he keeps 9 grapes for himself. then he gives 7 grapes each to some of his friends. to how many friends does tim give grapes?

Answers

30 - 9 is 21 grapes shared. 21 divided by 7 is 3 friends.

He hands out grapes to 3 friends
30-9 he kept = 21
21÷7 he gives out per friend =3

if the circumference of a circle measures 3π cm, what is the area of the circle in terms of π?

Answers

the circumference equation is 2pi r and the circumference for this problem is 3pi so that would mean that the radius is 1.5

with that info, we can find out the area of the circle which is pi r squared.
1.5*1.5=2.25

AREA=2.25pi

The area of the given circle, in terms of pi, is:

A = (9/4)pi cm^2

How to find the area of the circle?

We know that for a circle of radius R, the circumference is:

C = 2*pi*R

And the area is:

A = pi*R^2

In this case, we know that:

C = 3pi cm = 2pi*R

Then we must have:

3cm = 2R

(3/2)cm = R

Now we can replace this on the area equation:

A = pi*((3/2)cm)^2 = pi*(9/4) cm^2

If you want to learn more about circles, you can read:

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One number is 33 more than another number. The quotient of the larger number and smaller number is 5 and the remainder is 1. Find the numbers.

Answers

The two numbers are 41 and 8. You can set up the problem as two equations. First, x = 33 + y for "one number (x) is (=) 33 more (33 +) than another number (y)." You can set up the other equation as (x-1)/5y or (x-1) = 5y. You can substitute 33 + y for every x in the second equation and solve for y. You would get y = 8, then you can use the y value in the first equation to solve for x to get x = 41.

Final answer:

The two numbers in question are 8 and 41.

Explanation:

Step-by-Step Solution to Find the Two Numbers

Let the smaller number be x. Thus, the larger number would be x + 33. According to the problem, the larger number divided by the smaller number gives a quotient of 5 and a remainder of 1. We can represent this information using the following equation:

(x + 33) = 5x + 1

This equation states that when the larger number is divided by the smaller number, we obtain a quotient of 5 and a remainder of 1.

Now, let's solve the equation for x:

Subtract 5x from both sides of the equation: (x + 33) - 5x = 1Simplify the equation: -4x + 33 = 1Subtract 33 from both sides: -4x = -32Divide both sides by -4: x = 8

Since we have found the smaller number to be 8, the larger number is:

8 + 33 = 41

Therefore, the two numbers are 8 and 41.

The modulus operator would confirm our solution since 41 % 8 does indeed yield a remainder of 1, as stated in the problem.

Measure the length of the top of your desk in centimeters.describe how you found the length

Answers

Simply take a ruler with centimeters on it and measure your desk.Tell the teacher you counted how many centimeters.

When constructing an inscribed equilateral triangle, how many arcs will be drawn on the circle?

a. 3

b. 4

c. 5

d. 6

Answers

The answer is A(3). 3 arcs will be drawn

It can be done with 2 arcs. In the attached, I started with diameter AD, then drew arcs at B and C of the same radius as the circle from a center at A. Triangle BCD is the inscribed equilateral triangle.

Perhaps a more usual method would be to start at D, draw an arc at E, then from there at B. Resetting the compass to have radius, DB, a third arc can be drawn at C using either B or D as the center. This method would give you
.. selection A: 3 arcs

If you didn't want to reset the compass, you could draw two more arcs, say from B to A, then from A to C. This method would give you
.. selection B: 4 arcs.

how do you solve x^2+4x-5=0

Answers

Try this option:
1. root1*root2=-5; root1+root2=-4.
2. root1=-5; root2=1.
answer:1;-5.

Actually the answer is (-1,5)

x^2 – 4x – 5 = 0

x^2 – 4x = 5

x^2 – 4x + 4 = 5 + 4

(x – 2)^2 = 9

x – 2 = ± 3

x = 2 + 3 and x = 2 – 3

x = 5 and x = –1

{–1, 5}

The radioactive isotope radium has a half-life of 1,600 years. The mass of a 100-gram sample of radium will be______ grams after 200 years.

Answers

To solve this we are going to use the half life equation [tex]N(t)=N_{0} e^{( \frac{-0.693t}{t _{1/2} }) } [/tex]
Where:
[tex]N_{0} [/tex] is the initial sample
[tex]t[/tex] is the time in years
[tex]t_{1/2} [/tex] is the half life of the substance
[tex]N(t)[/tex] is the remainder quantity after [tex]t[/tex] years

From the problem we know that:
[tex]N_{0} =100[/tex]
[tex]t=200[/tex]
[tex]t_{1/2} =1600[/tex]

Lets replace those values in our equation to find [tex]N(t)[/tex]:
[tex]N(200) =100e^{( \frac{(-0.693)(200)}{1600}) } [/tex]
[tex]N(200)=100e^{( \frac{-138.6}{1600} )} [/tex]
[tex]N(200)=100e^{-0.086625} [/tex]
[tex]N(200)=91.7[/tex]

We can conclude that after 1600 years of radioactive decay, the mass of the 100-gram sample will be 91.7 grams.

Tell what each of the residual plots below indicates about the appropriateness of the linear model

Answers

The closer the points are/more uniform they are to the residual line, the better the fit. The more skewed and scattered they are, the model is a worse fit.

Final answer:

Residual plots can indicate the appropriateness of a linear model by examining patterns and deviations of the residuals.

Explanation:

A residual plot is a graph that shows the difference between the observed and predicted values in a linear regression model. It helps to assess the appropriateness of the linear model by examining the patterns and deviations of the residuals. In the first graph, there seems to be a systematic pattern and non-randomness in the residuals, indicating that the linear model may not be appropriate. However, in the second graph, the residuals are randomly scattered around zero with no evident pattern, suggesting that the linear model is more appropriate.

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Is the quotient of 5 and 1 / 2 greater than or less than 5? Explain your answer.

Answers

the qoutient of 5 and 1/2 is 2.5 so it is less than

The quotient of 5 divided by 1/2 is greater than 5 because dividing by a number less than 1 results in a larger number. In this case, it is equivalent to multiplying 5 by 2, yielding 10.

To determine if the quotient of 5 and 1/2 is greater than or less than 5, we consider the operation of division. Dividing by a number less than 1 will result in a larger number, while dividing by a number greater than 1 will result in a smaller number. The number 1/2 is less than 1, so when 5 is divided by 1/2, the quotient is greater than 5. It is equivalent to multiplying 5 by 2 (since dividing by a fraction is the same as multiplying by its reciprocal), which is 10. Therefore, 5 divided by 1/2 equals 10, which is greater than 5.

Can you please help me ?

Answers

What you can do for this case is to use the following trigonometric definition.
Tan (x) = a / b
Where,
a: opposite side of the triangle.
h: adjacent side of the triangle.
Clearing x:
x = Atan (a / b)
Substituting:
x = Atan (a / b)
x = Atan (5.74 / 4)
x = 55.12874356
Whole degree
x = 55
Answer:
x = 55 (option 3)

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