Mathematics High School

What is the solution set of (x - 2)(x - 3) = 2?

a. {1, 4}
b. {2, 3}
c. {4, 5}

Answers

Answer 1
Step One
Remove the brackets. Use Foil
F: x^2
O: -3x
I: -2x
L:(-2)(-3) = 6

What you have now is
x^2 - 3x - 2x + 6 = 2

Step Two
Combine like terms.
x^2 - 5x + 6 = 2

Step Three
Subtract 2 from both sides.
x^2 - 5x + 6 - 2 = 0
x^2 - 5x + 4 = 0

Step 4
Factor
(x - 4)(x - 1) = 0

Step 5
Find the zeros.
x - 4 = 0
x = 4

x -1 = 0
x = 1

Solution Set
(1,4)

Related Questions

A rectangular sheet of metal has identical squares cut from each corner. The sheet is then bent along the dotted lines to form an open box. The volume of the box is 420 in.3.

The equation 4x3 – 72x2 + 320x = 420 can be used to find x, the side length of the square cut from each corner.

What is the side length of the square that is cut from each corner, to the nearest inch?

Answers

Hello,        

[tex]4x^3-72x^2+320x=420\\ 4(x^3-18x^2+80x-105)=0\\ 4(x^3-3x^2-15x^2+15x+35x-105)=0\\ 4(x^2(x-3)-15x(x-3)+35(x-3))=0\\ 4(x-3)(x^2-15x+35)=0\\ \Delta=15^2-4*1*35=85\\\\ x=3\ or\ x= \dfrac{15+ \sqrt{85}}{2} \ or\ x= \dfrac{15- \sqrt{85}}{2}[/tex]

Answer:

3 in

Step-by-step explanation:

A 4x4 matrix a with real entries and a4 = i, what are the possible characteristic polynomials of a

Answers

If [tex]\mathbf A^4=\mathbf I[/tex], then the characteristic polynomial of [tex]\mathbf A^4[/tex] is

[tex]p_{\mathbf A^4}(\lambda)=\det(\lambda\mathbf I-\mathbf A^4)=\det((\lambda-1)\mathbf I)=(\lambda-1)^4[/tex]

which means [tex]\mathbf A^4[/tex] has eigenvalues [tex]\lambda=1[/tex].


We know that if [tex]\chi[/tex] is an eigenvalue of [tex]\mathbf X[/tex], then [tex]\chi^n[/tex] is an eigenvalues of [tex]\mathbf X^n[/tex].


So if [tex]\lambda=1[/tex] is the only eigenvalue of [tex]\mathbf A^4[/tex], we know that [tex]\pm\sqrt[4]\lambda=\pm1[/tex] are the only possible eigenvalues of [tex]\mathbf A[/tex]. We can construct five possible characteristic polynomials for [tex]\mathbf A[/tex] in that case.

[tex]p_{\mathbf A}(\lambda)=(\lambda-1)^4[/tex]
[tex]p_{\mathbf A}(\lambda)=(\lambda+1)(\lambda-1)^3[/tex]
[tex]p_{\mathbf A}(\lambda)=(\lambda+1)^2(\lambda-1)^2[/tex]
[tex]p_{\mathbf A}(\lambda)=(\lambda+1)^3(\lambda-1)[/tex]
[tex]p_{\mathbf A}(\lambda)=(\lambda+1)^4[/tex]

The Correct Answer Will Get Brainliest.

Ceres is an asteroid with a mass of 8.7 x 10^20 kg that is 2.767 AU from the sun. How many kilometers away is it from the sun?

A: 4.15 x 10^8 km

B: 5.8 x 10^9 km

C: 54.21 x 10^6 km

D: 1.84 x 10^7 km


Answers

For this case the first thing we must know is the following conversion of units:
 1 AU = 1.50 * 10 ^ 8 Km
 Applying the conversion of units we have:
 (2,767) * (1.50 * 10 ^ 8) = 415050000
 Rewriting we have:
 4.15 * 10 ^ 8 Km
 Answer:
 A: 4.15 x 10 ^ 8 km

what is the measure of the angle?

Answers

Remember that the x-axis is a straight angle, so is measure is 180°. To find the measure of our angle, we are going to add the right angle, 180°, and the smaller angle 55°:

Measure of the angle=55°+180°=235°

We can conclude that the measure of the angle in the picture is 235°

Classify each polynomial and determine its degree. The polynomial 3x2 is a with a degree of . The polynomial x2y + 3xy2 + 1 is a with a degree of .

Answers

Answer:

The polynomial 3x2 is a  

monomial

with a degree of  

2

.

 

The polynomial x2y + 3xy2 + 1 is a  

trinomial

with a degree of  

✔ 3

.

Step-by-step explanation:

this the answer on the edge

What is the first step to simplify the expression: [–23 – [5 · (2 – 4)]] ÷ 32

Answers

Hello there, and thank you for posting your question here on brainly.

Short answer: 2 - 4

Why?

When you have an equation with parenthesis, you do those first. When you have parenthesis inside of parenthesis, you do that first.

Hope this helped you! ♥

Answer:

According to PEDMAS , We first simplify the PARENTHESES

[5 · (2 – 4)] = [5· -2] = -10

Step-by-step explanation:

 Given expression  [–23 – [5 · (2 – 4)]] ÷ 32

We have to find the  first step to simplify the given expression.

We apply PEDMAS

P stands for PARENTHESES

E  stands for EXPONENTS

D stands for DIVIDE

M  stands for MULTIPLY

A stands for ADDITION

S stands for SUBTRACTION.

So, according to PEDMAS , We first simplify the PARENTHESES

Thus, [5 · (2 – 4)] = [5· -2] = -10

Need help with these 2 problems I’m pretty sure I got the first one right but I don’t know how to do the second one please and thank you!!

Answers

Since APR interest is a simple interest rate, we are going to use the formula for calculating simple interest: [tex]A=P(1+rt)[/tex]
where 
[tex]A[/tex] is the final amount after [tex]t[/tex] years
[tex]P[/tex] is the initial investment 
[tex]r[/tex] is the interest rate in decimal form 
[tex]t[/tex] is the number of years 

Mathematical steps for solving the problem:
We can infer from our problem that you are going to invest $800-$640=$160 in your savings account, so [tex]P=160[/tex]. To convert the interest rate to decimal form, we are going to divide the rate by 100%
[tex]r= \frac{4.5}{100} =0.045[/tex]. Since you are leaving the money in your savings account for a year, [tex]t=1[/tex]. Lets replace those values in our formula:
[tex]A=P(1+rt)[/tex]
[tex]A=160[1+(0.045)(1)][/tex]
[tex]A=160(1+0.045)[/tex]
[tex]A=160(1.045)[/tex]
[tex]A=167.2[/tex]

We can conclude that  your total savings after buying the refurbished laptop are: $167.2

Drag and drop the symbols to enter the equation of the circle in standard form with center and radius given. Center (5, -3), radius = 1

Answers

Hi there!

The standard form of the equation of a circle is:
[tex](x - a) {}^{2} + (y - b) {}^{2} = r {}^{2} [/tex]


With (a, b) representing the centre and r representing the radius of the circle. 
Since the centre of the circle is (5, -3) and the radius is 1, we get the following equation:

[tex](x - 5) {}^{2} + {(y + 3)}^{2} = 1[/tex]

A Student said the volume of a cylinder with a 3-inch diameter is two times the volume of a cylinder with the same height and a 1.5-inch radius. What is the error?

Answers

They would be the same because the formula is volume equals pi radius squared times height. So you would use the radius of 1.5 instead of the diameter of 3

The square root of the quotient of a number and 6 is 9. find the number

Answers

sq root (x / 6) = 9
We square both sides:
(x / 6) = 81
x = 486


What is the standard deviation of the following data set rounded to the nearest tenth?


51.8, 53.6, 54.7, 51.9, 49.3


A.3.4

B.3.3

C.1.9

D.1.8

Answers

51.8, 53.6, 54.7, 51.9, 49.3
the standard deviation of the data set will be found as follows:
Var=∑(x-μ)²/(n)
μ-mean
μ=(51.8+53.6+54.7+51.9+49.3)/5
μ=261.3/5=52.26
Next:
∑(x-μ)²=(51.8-52.26)²+(53.6-52.26)²+(54.7-52.26)²+(51.9-52.26)²+(49.3-52.26)²
∑(x-μ)²=16.852
thu
Var(x)=16.852/(5)=3.3704

Hence the standard deviation will be:
σ=√3.3704=1.835865~1.8

Answer: D] 1.8

Answer:

1.8

Step-by-step explanation:

If Kareem’s living room has an area of 225 square feet, how much will he spend to carpet his living room?

Answers

Answer: $ 568.99

Because 18.99+22 x 225/9 = 568.99

Answer: 568.99

Step-by-step explanation: your mom

A class is trying to eliminate t from the parametric equations x=t^2+3 and y=4t. Beth says that she can write t=sqrt(x-3) to eliminate the parameter. Why is this wrong?

She should have added 3 to x, not subtracted.
She should always solve for t as a function of y.
She should have taken both the positive and negative square root.
She should first substitute y for t before solving.

Answers

C, She should have taken both the positive and negative square roots,

Because when a number is squared, even if it is negative it can become positive,

so taking square should include + and - to the answer.

Beth says that she can write that she should have taken both the positive and negative square root to eliminate the parameter. Therefore, option (c) is correct.

What is an equation?

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

We have to find the error which is done by Beth to eliminate the parameter. So, we will take the first equation and do all the steps to find the error and get the desired result.

Given that, x=t²+3 and y=4t

Try find the expression of "t" in terms of "x". We will use equation (1) and we have

x-3=t²

t=√(x-3)

Thus, Beth says that she can write that she should have taken both the positive and negative square root to eliminate the parameter. Therefore, option (c) is correct.

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Find the exact values of cos (3pi/4radians) and sin (3pi/4 Radians)

Answers

[tex]\cos\dfrac{3\pi}{4}=\cos\left(\pi-\dfrac{\pi}{4}\right)=-\cos\dfrac{\pi}{4}=-\dfrac{\sqrt2}{2}[/tex]

[tex]\sin\dfrac{3\pi}{4}=\sin\left(\pi-\dfrac{\pi}{4}\right)=\sin\dfrac{\pi}{4}=\dfrac{\sqrt2}{3}[/tex]

Look at the picture.

[tex]\dfrac{\pi}{2} < \dfrac{3\pi}{4} < \pi\\\\therefoere\\\\\cos\dfrac{3\pi}{4} < 0\ and\ \sin\dfrac{3\pi}{4} > 0[/tex]



If 30 fair dice are rolled find the approximate probability that the average number ofo dots is between 2 and 4

Answers

The probability that the average number of dots is between 2 and 4 when rolling 30 fair dice is 0.9441.

what is probability?

Probability is the branch of mathematics that deals with the study of random events or phenomena. It involves the quantification of uncertainty and the measurement of the likelihood of occurrence of an event.

The average number of dots on a fair die is

= (1+2+3+4+5+6)/6

= 3.5.

We can model the sum of the numbers on the 30 dice as a normal distribution with mean

= (30)(3.5) = 105

and, standard deviation √(30)(35/12) ≈ 9.13.

Let X be the sum of the numbers on the 30 dice, and let Y be the average number of dots. Then Y = X/30.

We want to find P(2 ≤ Y ≤ 4). This is equivalent to P(60 ≤ X ≤ 120), since Y = X/30.

Using the normal distribution, we can standardize X to get:

Z = (X - 105) / 9.13

Then we can compute the probability as:

P(60 ≤ X ≤ 120)

= P[(60 - 105) / 9.13 ≤ Z ≤ (120 - 105) / 9.13]

≈ P(-4.93 ≤ Z ≤ 1.64)

Using a standard normal distribution table or calculator, we can find that P(-4.93 ≤ Z ≤ 1.64) ≈ 0.9441.

Therefore, the approximate probability that the average number of dots is between 2 and 4 when rolling 30 fair dice is 0.9441.

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according to the U.S. census bureau, the population of Hawaii in 2010 was 1,360,301 and it was growing at an annual rate of 1.2%. Predict the population in Hawaii in 2032

Answers

By applying the formula for the compound interest, [tex]FV_{N} = PV_{N} * (1+r)^{N} [/tex], because of the same logic we could calculate population in 2032. According to the formula, we can write that: 1,360,301 * (1+0.012) ^ [tex] {22} [/tex]   = 1,768,505. 

this will be worth ten points

Answers

First, you can write that 1260 ÷ 15 = 84.

To prove this one way, you can show the multiplication of the quotient and divisor.  If the division was correct, it would end up as the value of the dividend:

84 * 15 = 1260
1260 = 1260

To prove this another way, you can show 84 being added 15 times and seeing if it totals 1260:

84 + 84 + 84 + 84 + 84 + 84 + 84 + 84 + 84 + 84 + 84 + 84 + 84 + 84 + 84 = 1260
1260 = 1260

Answer:

1260/15=84

Step-by-step explanation:

1200/15=80 and 60/15=4

80 + 4 = 84.

Another way is 15 + 15 + 15 and keep counting 84 times and you would get 84

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The perimeter of a rectangular garden is 43.8 feet. Its length is 12.4 feet. What is the width

Answers

perimeter of rectangle =2(l+b)

43.8 =2(12.4 + w)

21.9=12.4 +w

21.9-12.4 = w

w=9.5 feet
The width is 9.5.

  First you know what the length is. You must find the measurement of both combined.
   12.4 x 2 = 24.8   (Length)

  Subtract this number from the perimeter.  43.8 - 24.8 = 19.

  19 is your width multiplied by two. The total measurement of both, to find just the width divide by 2.

  19 / 2 = 9.5 (WIDTH)

simplify
3 (2x+4y-2z)+7 (x+y-4z)

Answers

6x+12y-6z+7x7y-28z= 13x+19y-34z

How many cubes are needed to build this structure?


8


7


10


9

Answers

Hello!

I believe that 8 cubes are needed to build the given figure

I hope this helps!

Answer:

Option A. 8 cubes

Step-by-step explanation:

In the given structure we can count the cubes by dividing the figure in three sub parts.

Two in L shape and one below on L shape figure.

Two L shape figure contains 2×3 = 6 cubes

Cubes hidden under one L shape = 2

Then total cubes = 6 + 2 = 8

Option A. 8 cubes is the answer.

A number from 1-100 is randomly selected. What is the probability that it is a perfect square, given that is an odd number?

Answers

Those numbers are 1-9-25-49-81
Probability is
5/100=1/20

A lawn roller is 1 m wide and 80 cm high. What area is covered in each revolution

Answers

The area for each revolution is given by:
 A = 2 * pi * r * l
 Where,
 r: roller radius
 l: roller width
 We have then:
 A = 2 * 3.14 * (0.80 / 2) * 1
 A = 2.512 m ^ 2
 Answer:
 The area that is covered in each revolution is:
 A = 2.512 m ^ 2

Ernie is making a cylinder-shaped container to store his pens. The container has a base on one end and an opening on the other end. He is going to spray paint the outside of the container. The container has a diameter of 3 inches and a height of 18 inches.

Answers

For this case we must calculate the surface area of the container to know the amount of paint that Ernie must use.
 We have then:
 A = pi * r ^ 2 + 2 * pi * r * h
 Where,
 r: cylinder radius
 h: cylinder height
 Substituting values:
 A = 3.14 * (3/2) ^ 2 + 2 * 3.14 * (3/2) * 18
 A = 176.625 in ^ 2
 Answer:
 The amount of paint needed is:
 A = 176.625 in ^ 2

What are the zeros of f(x) = x2 – 10x + 25?

A. x = –5 and x = 10
B. x = –5 only
C. x = –5 and x = 5
D. x = 5 only

Answers

That factors into
(x-5) * (x-5)

The answer is 5

The zeros of a function are also known as the roots of the function

The correct option for  the zeros of f(x) = x² - 10·x + 25 is the option D.

D. x = 5 only

The reasons why the selected option is correct are given as follows:

The given equation is presented as follows;

f(x) = x² - 10·x + 25

Solution:

The zeros are the values of x when the equation is equal to zero which is given as follows;

x² - 10·x + 25 = 0

By observation, we have;

Given that the coefficient of x² is one, and we have that 25 = (-5) × (-5), and -10 = -5 + (-5), therefore, we can write;

0 = x² - 10·x + 25 = (x - 5)·(x - 5)Which gives, either x = 5 , or x = 5

Therefore, the zeros of the function is 5 only, and the correct option is option D.

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Trinh drew a triangle that had coordinates (1, –2), (4, –2), and (1, –4). She translated the figure 4 units left and 5 units up. What are the coordinates of the new figure?
(–4, 2), (–1, 2), and (–4, 0)
(–3, –2), (0, –2), and (–3, –4)
(–3, 3), (0, 3), and (–3, 1)
(1, 3), (4, 3), and (1, 1)

Answers

(-4, 2), (-1, 2), and (-4, 0
THE FIRST ONE IS RIGHT so yeah please mark me brainlest

Which value is the 10th term in the sequence:-62,-47,-32,-17,-2?

Answers

The answer is 13
Sure!!!

complete the general solution to y=cos^-1(1) for K a whole number

Answers

I think that would be 0 +/- 360n  in degrees ans 0 +/- 0 + 2npi  in radians

Answer:  

If the equation is exactly the one you posted then the unique answer is:

[tex]y = 0[/tex]

or  what is the same:

[tex]y=0K[/tex]

Explanation:

If your equation is exactly the one you posted then it has only one solution: y = 0

Because the range of [tex]y=\cos^{-1}(x)[/tex] is the interval [tex][0, \pi][/tex]

The meaning of [tex]\cos^{-1}(1)[/tex] is to find the angle whose cosine is 1.

In the range of the function arccosine the only angle whose cosine is 1 is the angle 0.

But if your equation was the following one:

[tex]\cos(y)=1[/tex]

Then in that case we would have infinite solutions since it will be the set:

[tex]y=\cos^{-1}(1)+2K\pi[/tex]  where K is an integer, since the period of cosine is [tex]2\pi[/tex]

So, in such a case the solution set would be:

[tex]y=0+2K\pi=2K\pi[/tex]  

But for the equation you posted, the unique solution is: y = 0 or what is the same y = 0K

How to find the length of a rectangle when given the height?

Answers

Height usually refers to three dimensional objects, so I assume you mean height.

The formula for area is:

Area = length • width

If you were given the width and area of the rectangle you would be able to find the length by doing inverse operations. In this case, the opposite of multipication is division

Example: 56 = l • 8

56 / 8 = 7

56 = 7 • 8

The length is 7.

I hope this helps!

The length of a rectangle can be found by dividing the area of the rectangle by its height if the area is known. Without the area, additional information is necessary to calculate the length.

To find the length of a rectangle when given the height, we typically need additional information such as the area or the aspect ratio of the rectangle. However, without that information, directly calculating the length is not possible. Let's explore a scenario where we have the area of the rectangle. In such a case, if we are given the area (A) of the rectangle and the height (h), we can use the formula for the area of a rectangle which is A = length times height. Solving for the length (l), we rearrange the formula to get l = A/h. For instance, if the area of the rectangle is 150 square centimetres and the height is 10 centimetres, the length would be 150 cm2 / 10 cm = 15 cm. It's also important to consider proportions when scaling shapes.

Which summation formula represents the series below? 12 – 24 + 48 – 96

Answers

The summation formula for the series given by:
 12 – 24 + 48 – 96
will be calculated as follows:
first term,a=12
common ratio=+/-2
thus the sum will be:
(i=1)Σ[12(-2)^(i-1)]

Thus the answer:
(i=1)Σ[12(-2)^(i-1)]

Answer: B

Step-by-step explanation:

A bag contains 2 blue, 4 green, and 3 white chips. What is the probability of drawing a white chip then another white chip without replacement?


A.) 7/9


B.) 8/81


C.) 2/3


D.) 1/12

Answers

total number of chips: 2 + 4 +3 = 9

total white chips = 3
 probability of picking white first = 3/9 = 1/3

after taking one chip there would be 9-1 = 8 chips left

and 3-1 2 white chips left

probability of picking 2nd white chip = 2/8 = 1/4

probability of picking both =  1/3 x 1/4 = 1/12
 answer is D


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