Answers
Answer:
(10 - 3x)(10 + 3x)
Explanation:
This type of question yields what is called a difference of squares, which is recognizable because of the subtraction (-) operation between the two terms of the binomial. When questions like this are seen, the formula for difference of squares can be implemented. This formula is:
(a² - b²) = (a - b)(a + b)
With this, we can square root both terms of the original binomial and plug our variables for a and b into the formula.
Let 100 = a², let 9x² = b²
√(100) = 10
√(9x²) = 3x
Those values are now a and b, respectively, so when we place them in their spots in the formula, the completed factoring is: (10 - 3x)(10 + 3x)
To check this answer for accuracy, we can use the FOIL method and combine like terms to see if it gives us the original equation. FOIL stands for Firsts, Outsides, Insides, and Lasts, instructing us which terms should be multiplied together so:
Firsts: 10(10) = 100
Outsides: 10(3x) = 30x
Insides: -3x(10) = -30x
Lasts: -3x(3x) = -9x²
We place them in the same equation and combine like terms:
100 + 30x - 30x - 9x²
100 + 0 - 9x²
100 - 9x²
We are back to our original equation so the answer of (10 - 3x)(10 + 3x) is accurate.
Related Questions
The mean of 3 consecutive terms in an arithmetic sequence is 10, and the mean of their squares is 394. What is the largest of the 3 terms?
Answers
a, a+b, a+2b
mean of the numbers is:
(a+a+b+a+2b)/3=10
(3a+3b)/3=10
a+b=10
thus second term is 10
The sum of square will be:
((10 - b)² + 10² + (10 + b)²) / 3 = 394
(100 - 20b + b² + 100 + 100 + 20b + b²) / 3 = 394
(300 + 2b²) / 3 = 394
(150+b²)=591
b²=441
b=-21,21
thus the numbers will be:
10-21, 10, 10+21
=-11,10,31
Suppose q and r are independent events, and P(Q)= 0.39, P(R)= 0.85. Find P(q and r)
Answers
P (q and r) = 0.3315
Explanation:
We are given that:
P (q) = 0.39
P (r) = 0.85
Since the two events are independent, therefore, the formula that we will use to get P (q and r) is as follows:
P (q and r) = P (q) * P (r)
Based on the givens:
P (q and r) = 0.39 * 0.85 = 0.3315
Hope this helps :)
Answer:
0.3315
Step-by-step explanation:
which of the following functions is continuous between x=-3 and x=0? choices on attachment
Answers
A: f(x) = (-x + 1)/(x + 2)
Now we don't actually need to know what the graph of this function looks like to see which values it is continuous for, instead we should look at which values of x will make this function undefined - in this case that would be x = -2. The reasoning behind this is that a number divided by 0 would be undefined, so when we search for which value of x would make the denominator of the equation 0, we get:
x + 2 = 0
x = -2
Since x = -2 is within the interval [-3, 0] we cannot say the function is continuous over this interval
B: f(x) = -2/(x + 1)
Using the same method as above we get:
x + 1 = 0
x = -1
x = -1 is again within the interval [-3, 0] and so the function is not continuous within this interval
C: f(x) = 3x/(x - 2)
x - 2 = 0
x = 2
x = 2 is outside the interval of [-3, 0] and so the function is continuous within this interval and C is the correct answer.
Just for the sake of it however we can look at D as well:
D: f(x) = 1/(2x + 1)
2x + 1 = 0
x = -1/2
-1/2 is within [-3, 0] and so D is not continuous over this interval
Can please help!
10. Write an inverse variation to model the situation and answer the question. Two rectangular fields have the same area. One measures 75 yd by 60 yd. If the other has a length of 72 yd, what is its width?. Show your work
Answers
equation is: width = area / length
width = 62.5 yd
Explanation:
For the first rectangle:
We have:
length = 75 yd and width = 60 yd
Therefore:
area = length * width
area = 75 * 60
area = 4500 yd²
For the second rectangle:
We have:
area = area of first rectangle = 4500 yd²
length = 72 yd
area = length * width
width = area / length ............> The required equation
width = 4500 / 72
width = 62.5 yd
Hope this helps :)
How can we get the answer for...Decrease £8 by 20%
Answers
8-1.6= 6.4
therefore the answer is £6.40
You start a business making painted flower containers. You spend 300$ on paint and 5$ on each container. You charge 20$ for each container. How many containers do you have to sell to break even?
Answers
300/15 = 20
Please help me with this!
Answers
D. 2x + 3
_____
You can check this result:
for x=1: 2·1 + 3 = 5
for x=4: 2·4 + 3 = 11
These values correspond to those in the table.
(1,5)
(2,7)
(3,9)
(4,11)
When you see 3 and 9, you sometimes immediately think it is 3x=y, but you have to look at the other coordinates as well. This can be show in option a, 5x=y. This can not be the anser because 3×5=15≠9. We can eliminate that answer. Option B says that you are adding 2, but when you add 2 to 4, it equals 6 and not 11. The same for C, 4 added to 4 equals 8, not 11.
The one left, D, is the answer. When you put each x value in, you do get the corresponding y value as well. To even make sure, I made a graph with 2x+3=y as the function to see if those values/coordinates would pop up.
give the length and width in whole inches of three different rectangles that each have an area of 48 in. squared
Answers
The reason is that to find the area of a rectangle you multiply two dimensions.
2 in x 12 in
3 in x 8 in
4 in x 6 in
On all these either one could be the length and the other the width.
Through music we can communicate more then what can be expressed with words alone
True or false
Answers
A diner has a breakfast special. A customer can chose scrambled, fried, or poached eggs. The breakfast comes with a side of bacon, sausage, or fruit salad. The customer can choose coffee, tea, or milk. How many different combinations of eggs, side, and drink does a customer have to choose from?
Answers
So, there are 27 combinations.
A diner has a breakfast special. A customer can chose scrambled, fried, or poached eggs. The breakfast comes with a side of bacon, sausage, or fruit salad. The customer can choose coffee, tea, or milk. How many different combinations of eggs, side, and drink does a customer have to choose from?
Solution:
Number of ways the customer can choose eggs=3
Number of ways the customer can choose side=3
Number of ways the customer can choose drinks=3
So, total number of combinations for choosing eggs and side and drinks
=3(for eggs) and 3(for sides) and 3(for drinks)
=3 * 3 *3
=27
A customer has 27 combinations of eggs, side, and drink available.
This is right or wrong, please anyone
Answers
You added when you were supposed to divide.
24/30 = 0.8
I hope that this is right and sorry if I'm wrong
I was sick the day that the class went over how to do this and I don’t know how to do it.
Answers
Jamelia estimates the square root of 72 in the following way:
√72 = 2√36 = 2*6 = 12
(a) Explain why her reasoning is incorrect.
(b) Estimate the square root of 72 to the nearest tenth. Show your work.
Answers
we have that
√72
√72-----> √(2*36)=√2*√36 is not 2*√36------> this is the error
√2*√36=√2*√6²-----> √2*(6)----> 6√2
alternative method
72 is equal to-------> 2³*3²
therefore
√72-----> √[2³*3²]----->√ 2³*√3²-------> (2√2)*(3)-----> 6√2
Part b)Estimate the square root of 72 to the nearest tenth
we know that
√2 is equal to 1.41
so
√72=6√2------> 6*1.41-----> 8.46----> 8.5
the answer Part b) is 8.5
The owner of a bookstore predicts that 30% of the books she sells each week are self-help books. To test this prediction, the owner randomly selects 150 books out of the total number of books sold for a week and records the type of each book. The table shows the results of samples taken for 2 separate weeks. Sample Fiction History Cooking Self-help Total week 1 50 29 37 34 150 week 2 55 31 34 30 150 Based on these samples, is the owner's prediction correct? Select from the drop-down menus to correctly answer the question. The owner's prediction is . Based on the samples, about of the books sold each week are self-help books.
Answers
34 out of the 150 sold in week 1 were self-help books.
34 out of the 150 sold in week 2 were self-help books.
This gives us 68 self-help books out of 300 books sold.
68/300 = 0.2267 ≈ 0.23 = 23%
Based on the samples, the owner's prediction of 30% is not correct; approximately 21.34% of the books sold each week are self-help books.
The bookstore owner predicts that 30% of the week's book sales are self-help books. To evaluate this prediction, we need to look at the number of self-help books sold in the samples provided for two separate weeks. In week 1, 34 out of 150 books sold were self-help books, which is 22.67%. In week 2, 30 out of 150 books sold were self-help books, which is 20%. To determine the average percentage of self-help books sold over the two weeks, we average these two percentages: (22.67% + 20%) / 2, which gives us 21.34%.
dividing whole numbers 22 divided by 300
Answers
Answer:
22 divided by 300 will be equal to 0.07333.
Step-by-step explanation:
Dividing 22 by 300
[tex]\frac{22}{300}=\frac{2\times 11}{2\times 2\times 5\times 5\times 3}[/tex]
[tex]\frac{22}{300}=\frac{11}{2\times 5\times 5\times 3}=\frac{11}{150}[/tex]
[tex]\frac{11}{150}=\frac{11}{15}\times \frac{1}{10}[/tex]
The value of [tex]\frac{11}{15}=0.7333[/tex]
[tex]\frac{22}{300}=\frac{11}{150}=0.7333\times \frac{1}{10}=0.07333[/tex]
So, the value of 22 divided by 300 will be equal to 0.07333.
Dividing 22 by 300 gives a quotient of 0.0733, representing the proportion of 22 out of 300.
Explanation:To perform the division of the whole numbers 22 and 300, you simply divide 22 by 300 using long division or a calculator. However, since 300 is larger than 22, the result will be a decimal or fraction that is less than 1. Mathematically represented as:
22 ÷ 300 = 0.0733
In a real-world scenario, this number could be interpreted as the proportion or percentage of a whole that the number 22 represents out of 300.
Learn more about Division of Whole Numbers here:https://brainly.com/question/29885808
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Find the Distance, d, across the lake
Answers
You have to use similar figures to work this out.
15 ft / 8 ft has to equal d ft / 6 ft
So, you divide 15 by 8, which equals 1.875
You then times 1.875 by 6 = 11.25
The Distance, d, across the lake is 26.25 feet.
Similar TrianglesWhen two triangles have all the corresponding angles equal to each other, then their sides are in a ratio.
Given to us,AB = 8 feet,
BC = 15 feet,
BP = 6 feet,
PQ = d,
AP = AB + BP = 8 + 6 = 14 feet
In the figure, [tex]\triangle ABC \sim \triangle APQ[/tex]
[tex]\dfrac{BC}{AB}=\dfrac{PQ}{AP}[/tex]
[tex]\dfrac{15}{8}=\dfrac{d}{14}[/tex]
[tex]d = \dfrac{15\times 14}{8}[/tex]
[tex]d = 26.25[/tex]
Hence, the Distance, d, across the lake is 26.25 feet.
Learn more about Similar triangles:
https://brainly.com/question/25882965
What is the volume of the triangular prism ?
Answers
The volume of the rectangular pyramid is 640 cm³.
What is the volume of a pyramid?The volume of a pyramid is [tex]\frac{1}{3} Ah[/tex] where A is the area of the base of the pyramid and h is the height.
Area of the base = area of a rectangle with dimensions 12cm*10cm
Area of the base =12*10 =120 cm²
Height of the pyramid =16cm
So, the volume of the pyramid = [tex]\frac{1}{3}*120*16[/tex] cm³
The volume of the pyramid =640 cm³
Hence, the volume of the rectangular pyramid is 640 cm³.
To get more about pyramids visit:
https://brainly.com/question/12903285
It says in abc, What is m
Answers
Make ∠A + B + C = 180.
x + (4x) + (5x - 13) = 180
Add all like terms.
10x - 13 = 180
Add 13 to both sides.
10x = 193
Divide both sides by 10.
x = 19.3
Now plug in x into m∠C, (5x - 13).
5(19.3) - 13 = 83.5
The m∠C is 83.5°.
A sample of 81 was taken from a population with a standard deviation of 45 kilograms. If the sample mean was 112 kilograms, the mean of any other sample of 81 will be within what range 99.7% of the time?
A. 97 kilograms to 127 kilograms
B. 102 kilograms to 122 kilograms
C. 92 kilograms to 132 kilograms
D. 107 kilograms to 117 kilograms
Answers
Population Standard Deviation = s = 45
Sample Mean = x = 112
Since, population standard deviation is known, we will use z distribution to find the confidence interval.
The critical z value for 99.7% is 2.968
So, the confidence interval will be:
[tex](112-2.968* \frac{45}{ \sqrt{81} }, 112-2.968* \frac{45}{ \sqrt{81} }) \\ \\ (97.16, 126.84)[/tex]
Rounding of to nearest integers the confidence interval will be 97 to 127.
So, option A gives the correct answer
the goalie ate half of a pizza that had a diameter of 20 inches! what was the area of pizza that she ate? what was the length of crust she ate?
Answers
Since it’s diameter you divide it by 2 so it would 10. 10= radius, now does you multiply it by its self so 10•10= 100. Now multiply it but pie which it 3.14. 100•3.14= 314. 314 should be your answer!
Sorry if you get this wrong :( but I’m learning this and I usually get these right but best of luck! :)
A college entry exam has 38 questions worth 200 points. The test consists of multiple-choice questions, x, worth 4 points each and essay questions, y, worth 10 points each. Which system of equations can be solved to find the number of multiple-choice questions on the test?
Answers
There are no options listed in the question to choose from, but the equations should look like the following:
x= # multiple choice questions
y= # essay questions
QUANTITY EQUATION:
x + y= 38
VALUE EQUATION:
4x + 10y= 200
If we solved these two equations by elimination or substitution, we would find the number of multiple choice (x) and the number of essay (y) questions on the test.
ANSWER: x + y= 38; 4x + 10y= 200
Hope this helps! :)
Answer:
Let's use the variables x and y to represent the number of multiple-choice and essay questions on the test, respectively.
The total number of questions is 38, so we can write:
x + y = 38
The total number of points is 200, so we can write:
4x + 10y = 200
This gives us a system of equations:
x + y = 38
4x + 10y = 200
We can solve this system of equations to find the number of multiple-choice questions on the test.
Fernando poured water from one-pint bottles into a three-gallon bucket. How many pints of water could the bucket hold?
Answers
One gallon holds eight pints. 8 x 3 = 24
13 percent of what is 78
Answers
"what" is the unknown, so use x for what.
"of" in math usually means a multiplication.
"is" means "="
13% * x = 78
0.13x = 78
x = 78/0.13
x = 600
Answer: the number is 600
Please help......
1. Write an approximate equation of the line of best fit in slope-intercept form.
2. Use the equation from part B to predict the resting heart rate of a person who exercises 30 minutes per day. Show your work.
3. Explain how you found your answer to part C.
Answers
find the slope:
slope = change in Y over change in x = 69 - 72 / 6-0 = -3 / 6 = -1/2
equation would be y = -1/2x + 72
2. y = -1/2x+72 = -1/2(30) +72 = -15 +72 = 57 beats per minute
3. replaced x in the equation with 30 to find the beats per minute for exercising 30 minutes
HELP NEEDED
Use the functions h(x) = 5x − 2 and t(x) = 4x + 6 to complete the function operations listed below.
Part A: Find (h + t)(x). Show your work.
Part B: Find (h ⋅ t)(x). Show your work.
Part C: Find h[t(x)]. Show your work.
Answers
h(x) = 5x − 2 and t(x) = 4x + 6
so
(h + t)(x) = 5x − 2 + 4x + 6
(h + t)(x) = 9x +4
Part B: Find (h ⋅ t)(x). Show your work.
h(x) = 5x − 2 and t(x) = 4x + 6
so
(h ⋅ t)(x) = (5x − 2) (4x + 6)
(h ⋅ t)(x) = 20x^2 + 30x - 8x - 12
(h ⋅ t)(x) = 20x^2 + 22x - 12
Part C: Find h[t(x)]. Show your work.
h(x) = 5x − 2 and t(x) = 4x + 6
so
h[t(x)] = 5(4x + 6) − 2
h[t(x)] = 20x + 30 - 2
h[t(x)] = 20x + 28
hope all help.
A prism is filled with 44 cubes with 1/2 units side lengths. What is the volume of the prism in cubic units?
Answers
First, we need to find the volume of one cube. It would be LWH.
0.5 x 0.5 x 0.5 = 0.125
Now, just multiply that volume by 44.
0.125 x 44 = 5.5
Plzz help me im giving 12 points
Answers
30m + 50 = 20m + 100
This is the new equation needed to solve for m.
first we must isolate "m".
30m + 50 = 20m + 100
- 50 - 50
30m = 20m + 50
-20m -20m
10m = 50
divide both sides by 10 to isolate "m".
m = 5
hope this helps!
Jerome bought a book on sale at the store. The sale price of the book was $8.96. Write and solve an equation to determine the regular price of the book to the nearest cent
Answers
The regular price of the book is $8.96.
Explanation:To determine the regular price of the book, we can set up an equation using the sale price and the regular price. Let's say the regular price is 'x'.
So the equation becomes:
8.96 = x
To solve for 'x', we can simply state that the regular price of the book is $8.96.
How many pounds of peanuts will each person get if 3 people share 1/5 pounds of peanuts equally?
Answers
1 person = 1/5 ÷ 3 = 1/5 x 1/3 = 1/15 pound
Answer: 1 person gets 1/15 pounds of peanuts.
you need to count all of the loaves of bread in the front area . there are 22 loaves of white bread, 17 loave of wheat bread, and 19 gourmet breads.what is the total number of loabes?
Answers
36-22=14
the answer is 14