Answer:
1) -5x² + 13x + 6
2) B(x) =(4x + 1 )(2x + 3)
A(x) = (5x +2)(3-x)
Step-by-step explanation:
1) Expand the equation by using distributive property. Then simplify by combining the like terms.
A(x) = (3 -x)2² - (x -3)(7x+ 4) - 18 + 2x²
= (3 - x)4 - [x*7x + x*4 - 3*7x - 3*4] - 18 + 2x²
= 3*4 - x*4 - [7x² + 4x - 21x - 12] - 18 + 2x²
= 12 - 4x - 7x² - 4x + 21x + 12 - 18 + 2x²
= 2x² - 7x² -4x - 4x + 21x + 12 + 12 - 18
= -5x² + 13x + 6
B(x) = (3x + 2)² - (x - 1)²
Identities:
(a + b)² = a² + 2ab + b² ; Here a =3x & b = 2
(m -n)² = m² - 2mn + n² ; Here m = x & n = 1
2) B(x) = (3x)² + 2*3x*2 + 2² - [x² - 2*x*1 + 1]
= 9x² + 12x + 4 - [x² - 2x + 1]
= 9x² + 12x + 4 - x²+ 2x - 1
= 9x² - x² + 12x + 2x + 4 - 1
= 8x² + 14x +3
Product = 8*3 = 24
Sum = 14
Factors = 2 , 12 {2*12 = 24 & 2 +12= 14}
= 8x² + 2x + 12x + 3 {Rewrite the middle term}
= 2x(4x + 1) + 3(4x + 1)
= (4x + 1 )(2x + 3)
A(x) = - 5x² + 13x + 6
= -5x² + 15x -2x + 6
= 5x(-x +3) +2 (-x + 3)
= (5x +2)(3-x)
4) B(x) - 3 = 8x² + 14x + 3 - 3
= 8x² + 14x
= 2x *4x + 2x *7
=2x(4x + 7)
Hence proved.
B(x) = 3
8x² + 14x + 3 = 3
8x² + 14x + 3 - 3 = 0
8x² + 14x = 0
2x(4x + 7) = 0
2x = 0 or 4x + 7 = 0
x = 0 or 4x = -7
[tex]\sf x = \dfrac{-7}{4}[/tex]
x = 0 or [tex]\sf \dfrac{-7}{4}[/tex]
All members of a class of 27 students participated in at least one event on sports day. 20 students participated in individual events and 12 students took part in team events. how many students took part in both individual and team events?
5 students took part in both individual and team events.
What is data?Data is information that has been translated into a form that is efficient for movement or processing. Relative to today's computers and transmission media, data is information converted into binary digital form. It is acceptable for data to be used as a singular subject or a plural subject.
Given:
Total students participated = 27
20 students participated in individual events
12 students took part in team events.
We have N(All students) = 27
N(individual) = 20
N(Team)= 12
So,
[tex]N_{\text{individual \; and \; team}} & = N_{\text{individual}} + N_{\text{team}} - N_{\text{All students}}[/tex]
=20+12-27
=32-27
=5
Hence, 5 students took part in both individual and team events.
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use the accompanying statcrunch session to obtain a simple random sample of 5 high schools in the city of chicago.
Using sampling concepts, one sample of 5 high schools in the city of Chicago is given by:
Englewood Stem, Hyde Park, Lake View, Marshall, Noble - UIC.
What is the missing information?The problem is incomplete, but researching it on a search engine, it gives us a list of 15 high schools in Chicago, and asks us to take a sample of 5.
What is population and sample?Population: Collection or set of individuals or objects or events whose properties will be studied.Sample: The sample is a subset of the population, and a well chosen sample, that is, a representative sample will contain most of the information about the population parameter. A representative sample means that all groups of the population are inserted into the sample.Hence, from the concepts of sample and populations, the sample of 5 means that we have to select 5 schools from the 15 listed, hence they are:
Englewood Stem, Hyde Park, Lake View, Marshall, Noble - UIC.
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For the piecewise-defined function f(x) =
7, x>3
5x-3, XS3
find two x-values that have the same y-value and the sum of the x-values is 10.
.
The two such x-values are 2 and 8.
The piecewise-defined function is :When x is greater than 3, f(x) equals 7.When x is less than or equal to 3, f(x) equals 5x-3.We need to get the same y-values.So, we will equate the two parts of the above piecewise-defined function.7 = 5x-35x = 10x = 2One of the x-values is 2.We are told that the sum of the x-values is 10.So, the second x-value is 10-2 = 8.Thus, the two x-values that have the same y-value and the sum of the x-values is 10 are 2 and 8.To learn more about functions, visit :
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A rectangular auditorium seats 1598 people. The number of seats in each row exceeds the number of rows by 13. Find the number of seats in each row.
find the percent of change when 25 meters change to 30 meters
Answer:
20 %
Step-by-step explanation:
There was a change from 25 m to 30 m. When we find percentage change of something, we first calculate the difference of final and initial value. Then divide it by initial value × 100.
Change:
= 30 m - 25 m
= 5 m
% change:
= 5 m / 25 m × 100
= 100 / 5
= 20 % (ans)
Answer(with steps pls)
Answer:
b. No
Step-by-step explanation:
7/6 can be changed to an equivalent ratio(fraction) by multiplying by the same number on top and on the bottom.
example:
7/6 = 7×3 / 6×3
= 21/18
21/18 is equivalent to 7/6.
7 doesn't even go into 52 for one thing. But 6×8 is 48 so try 8.
7/6 = 7×8 / 6×8
= 56/48
56/48 is equivalent to 7/6, not 52/48
You add 50 grams of solvent to paint. If 50 grams equals 1 part, how many grams
of paint do you need? (Do not label your answer with grams.)
find the rise and the run
Answer:
down below
Step-by-step explanation:
The picture is a little blurry so the graph is hard to read. But I believe the answer is 7/8. The rose would be counting up or down the y axis and the run is counting forward or backward on the x axis.
Hope this helps! :)
Answer:
rise = 7, run = 8
slope = rise/run = 7/8
See attached picture for graph in case you have to plot
Step-by-step explanation:
Take two distinguishable points, (x1, y1) and (x2, y2) on the graph. Find the difference in their y values= y2 - y1. This will be the rise
Find the corresponding difference in the x values, x2 - x1. This will be the run
Divide the y difference by the x difference and you get rise/run which is the slope of the line
Two clear points are (x1 = 0, y1= -7) and (x2=8, y2=0)
(y2 - y1)/(x2 - x1)
= (0 - (-7)/(8 - 0))
= (0+7/(8 - 0) ==> 2 negatives make a positive
= 7/8 and that is rise/run
Rise = 7, run = 8
Picture shows rise and run if you want to graph it
Shawn stated that 5x + 2 is equal to 7x . Is Shawn's claim, correct? EXPLAIN.
Need answer asap
"Shawn stated that 5x+2 is equal 7x" its is an incorrect statement, because we can only add like terms.
Given,
The statement
5x+2 is equal to 7x
Here 5x and 2 are not like terms. So we can't add them together.
So the given statement is incorrect
5x+2 is not equal to 7x
Hence, "Shawn stated that 5x+2 is equal 7x" it is an incorrect statement, because we can only add like terms.
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Please Help Important!!!!!!
Seeing that substituting the value x ≤ -2, did not yield a result that is correct with the equation x5 +7 > x3 we can say that Sam's conjecture is incorrect
Given data
x ≤ -2
x5 +7 > x3
How to test Sam's conjectureSam's conjecture is tested by substituting the value x ≤ -2 into the equation x5 +7 > x3. If the result is in accordance with the equation then Sam's conjecture is correct, however if the result is not in accordance with the equation the Sam's conjecture is incorrect.
The substitution will give
( -2 )^5 + 7 > ( -2 )^3
-32 + 7 > -8
-25 > -8 (since -25 is less than -8, Sam's conjecture is incorrect )
Seeing that substituting the value x ≤ -2, did not yield a result that is correct we can say that Sam's conjecture is incorrect
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Allison is saving money to buy a video game system. in the first week her savings were $8 less than 2/5 the price of the system. in the second week, she saved 50 cents more than 1/2 the price of the system. she was still $37 short. find the price of the system.
Hence , the price of the system $295 .
The linear equations in one variable is associate degree equation that is expressed within the sort of ax+b = zero, wherever a and b square measure 2 integers, and x may be a variable and has just one resolution. as an example, 2x+3=8 may be a equation having one variable in it.Let the price of the system be "x" .
It is given that in the first week her savings were $8 less than 2/5 the price of the system which can be represented by equation
First week savings = (2/5)x -8
It is also given that in the second week, she saved 50 cents more than 1/2 the price of the system which can be represented by equation
Second week savings = (1/2)x +0.5
savings + short = price of system
(2/5)x -8 + (1/2)x +0.5 + 37 = x
(2/5)x + (1/2)x + 29.5 = x
4x + 5x/ 10 + 29.5 = x
9x/10+ 29.5 = x
0.9x + 29.5 = x
29.5 = x - 0.9x
29.5 = 0.1x
$ 295 = x
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Bamboo the elephant weighed 235 lb at birth. Each month Bamboo has gained 180 lb.
If Bamboo now weighs 1495 lb, how old is she?
please help yall
Answer:7lb
Step-by-step explanation:
7x180=1260lb
1260+235=1495lb
what is the solution to this problem? 2 | x+5 | =4
Answer:
x = -7
x = -3
Step-by-step explanation:
Given the following question:
[tex]2\left|x+5\right|=4[/tex]
To find the answer to this question we have to remember to apply the absolute value. The absolute value means we have to convert any negative within the lines into positive.
[tex]2\left|x+5\right|=4[/tex]
[tex]\frac{2\left|x+5\right|}{2}=\frac{4}{2}[/tex]
[tex]\left|x+5\right|=2[/tex]
Apply absolute value:
[tex]x+5=-2[/tex]
[tex]x+5=2[/tex]
Solve each equation:
[tex]x+5=-2[/tex]
[tex]5-5=0[/tex]
[tex]-2-5=-7[/tex]
[tex]x=-7[/tex]
[tex]x+5=2[/tex]
[tex]5-5=0[/tex]
[tex]2-5=-3[/tex]
[tex]x=-3[/tex]
Your answers are "x = -3 and x = -7."
Hope this helps.
Answer:
x = -3
x= -7
Step-by-step explanation:
l x + 5 l = 4/2
(x + 5) = 2 or - (x + 5) = 2
- (x + 5) - 5 = 2 - 5
x = -3
- x - 5 = 2
- x - 5 + 5 = 2 + 5
-x = 7
x = -7
5/6=1/3+d
omg help mee
Answer:
[tex]d=1/2[/tex]
How to solve:
Group.Find d.Step-by-step explanation:
[tex]\frac{5}{6}=\frac{1}{3}+d\\\frac{1}{3}+d=\frac{5}{6}[/tex]
Group
[tex]\frac{1}{3}+d=\frac{5}{6}\\\frac{1}{3}+d-\frac{1}{3}=\frac{5}{6}-\frac{1}{3}\\d+\frac{1}{3}+\frac{-1}{3}=\frac{5}{6}-\frac{1}{3}\\d+\frac{1-1}{3}=\frac{5}{6}-\frac{1}{3}\\d+\frac{0}{3}=\frac{5}{6}-\frac{1}{3}\\d+0=\frac{5}{6}-\frac{1}{3}\\d=\frac{5}{6}-\frac{1}{3}\\d=\frac{5}{6}+\frac{-1\cdot 2}{3\cdot 2}\\d=\frac{5}{6}+\frac{-1\cdot 2}{6}\\d=\frac{5}{6}+\frac{-2}{6}\\d=\frac{5-2}{6}\\d=\frac{3}{6}\\d=\frac{1\cdot 3}{2\cdot 3}\\d=\frac{1}{2}[/tex]
Hope it helps.
In which place is the digit in the number 5,341 that would it be changed to 5,841 how to how do the values of two numbers compare
We get that, the digit is in the 3rd place (hundreds).The difference between the numbers is 500.
We want to change the digit in the number 5,341 into 5,841.
We also need to find the difference between the numbers.
The number 3 is in the 3rd place (hundreds) of the number 5,341 as a digit will be replaced by 8 to form the number 5,841.
This means that 300 is replaced by 800 because the third place in both the numbers is of hundreds.
The difference between 800 and 300 is:
800 - 300 = 500.
Subtraction of 5,341 from 5,841 also yields 500.
Therefore, we get that, the digit is in the 3rd place (hundreds).The difference between the numbers is 500.
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ever since renata moved to her new home, she's been keeping track of the height of the tree outside her window. the variable hhh models the height of the tree (in centimeters), ttt years since renata moved in. h
The tree was 210 cm tall.
Let 'h(t) ' models the height of the tree in centimeters and 't' denotes the number of years since Renata moved in.
Given, h(t) = 210 + 33t
This is a linear function in 't'.
This function says that in each year the tree grows 33 cm tall.
We need to find the height of the tree when Renata moved in.
When Renata moved in, the number of years, t = 0
Applying this into h(t) , we get,
h(t) = 210 + 33 x 0 = 210 cm
Therefore the tree was 210 cm tall when Renata moved in.
The question was incomplete. Find the complete question here:
Ever since Renata moved to her new home, she's been keeping track of the height of the tree outside her window. h(t) models the height of the tree (in centimeters), t years since Renata moved in. h(t)=210+33t
How tall was the tree when Renata moved in?
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Please help!! State which property of equality justifies the statement:
If 7x=28, then x=4.
The property of equality justifies the given statement is Transitive property of equality.
Given,
The statement:
If, 7x = 28,
then, x = 4
We have to find the property of equality that justifies this statement:
The transitive property of equality formula is given as follows:
If y = z and x = y, x must be z. Where items belong to the same category as x, y, and z. For instance, if a line segment's measurement is represented by "x," then its measurement should also be represented by "y" and "z."
The property of equality that justifies this statement If, 7x = 28,
then, x = 4 is transitive property of equality.
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Maria wanted to bring back 5 million grains of sand from her trip to the beach. Each grain of sand weighs approximately 6.7 x 10^-7 kg. How heavy is the bag of sand that Maria brings home?
a
Multiply (5,000,000 x 6.7 x 10^-7) = (5 x 10^6) x (6.7 x 10^-7) = (5 x 6.7) x (10^(6 + - 7)) = 33.5 x 10^-1 = 3.35 kg
b
Multiply 5 x (6.7 x 10^-7) = 33.5 x 10^-7 = 3.35 x 10^-6 kg
c
Multiply (5,000,000 x 6.7 x 10^-7) = (5 x 10^6) x (6.7 x 10^-7) = (5 x 6.7) x (10^(6 + 7)) = 33.5 x 10^13 = 3.35 x 10^14 kg
d
Divide (5,000,000 / 6.7 x 10^-7) = (5 x 10^6) / (6.7 x 10^-7) = (5 / 6.7) x (10^(6 - 7)) = .74 x 10^-1 = 0.074 kg
PLEASE HELP
Answer:
3.35
Step-by-step explanation:
5,000,000*6.7 * 10^-7
= 5 * 10^6 * 6.7*10^-7
= 33.5 * 10^-1
= 3.35
The weight of 5 million grains of sand is 3.35 kg.
Option A is the correct answer.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Weight of each grain of sand = 6.7 x [tex]10^{-7}[/tex] kg
Weight of 5 million grains of sand.
= 5,000,000 x 6.7 x [tex]10^{-7}[/tex] kg
= 5 x [tex]10^6[/tex] x 6.7 x [tex]10^{-7}[/tex]
= 33.5 x [tex]10^{-1}[/tex] kg
= = 3.35 kg
Thus,
The weight of the total grain of sand is 3.35 kg.
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you are about to buy a calculator for $10, and the sales-person tells you that the model you want to buy is on sale for $5 at the store’s other branch, which is a 20 minute drive away.
Answer:
The question is incompleye. Do elaborate?
Look at the equations below. Tell whether each equation is True or False.
a. 2^9/2^-5=2^14
b. (5^0)^3 = 5^3
c. 4^5 x 2^5 = 8^10
d. 3^-9x3^7= 1/3^2
Answer: A. is true.
Step-by-step explanation: The left side 16384 is equal to the right side 16384, which means that the given statement is always true.
Use the function: f(x)=√√2x-5 to answer the following:
a) f(7)
b) f(x + 1)
c) f(-x)
d) the domain of f(x).
Answer:
the answer is a because if you calculate it correctly that the answer I got
The average of five numbers is 72, two of them are 70 and 74. Find the average of the other three numbers.
The average of the other 3 numbers is 72.
Average or mean is a measure of central tendency which calculates the central point of a data-set.
Average of a set of numbers is calculated by taking the sum of the numbers and dividing it by the total frequency of the numbers.
If 3 numbers a , b and c are taken then the average is equal to
(a+b+c) ÷3
Given average of 5 numbers is 72.
Therefore the sum of the numbers is 72 × 5 = 360
Two of the numbers are 70 and 74 .
Sum of the remaining 3 numbers = 360 - (70 + 74) = 360 - 144 = 216
Average of the 3 numbers = 216 ÷ 3 = 72
Therefore the average of the remaining 3 numbers is 72.
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I will Mark Brainlist ...Find the length of p. Please Help its Math question i will Mark Brainlist !!
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Here we go ~
Let's use Trigonometric ratios to find p :
[tex]\qquad \sf \dashrightarrow \: \cos(60) = \cfrac{6}{p} [/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{1}{2} = \dfrac{6}{p} [/tex]
[tex]\qquad \sf \dashrightarrow \: p = 6 \times 2[/tex]
[tex]\qquad \sf \dashrightarrow \: p = 12 \: \: units[/tex]
two sides of a right triangle measure 222 units and 444 units. 2\text{ units}2 units4\text{ units}4 units what is the area of the square that shares a side with the third side of the triangle?
With the help of Pythagoras Theorem for triangles, we get that the possible areas of the square are: 12 sq. units and 20 sq. units, according to the cases mentioned.
What is Pythagoras Theorem?According to the Pythagoras Theorem, in a right angled triangle, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.
Given:
Sides of a right triangle are 2 and 4 units.
To find: Area of a square that shares a side with the third side of the triangle.
Finding:
There can the following cases:
If 2 and 4 units are the lengths of the perpendicular sides.
Then, by Pythagoras Theorem, -
[tex]H^{2} = 2^{2}+4^{2}\\ H^{2} = Side^{2}\\H=Side \\H= \sqrt{4+16} \\H= \sqrt{20} \\H= 2\sqrt{5}[/tex]
Hence, the area of the square = side² = 20 units²
If 4 units is the length of hypotenuse.
Then, by Pythagoras Theorem,
[tex]4^{2} = 2^{2} + A^{2} \\16 - 4 = A^{2} \\= \sqrt{12}\\[/tex]
side of triangle = [tex]\sqrt{12}[/tex]
Hence, the area of the square = side² = 12 units²
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Tom drives 8 1/2 miles every 1/30 hour. How many miles can he drive in 3 hours
In 3 hours Tom drives 243 miles.
What is speed?The rate at which an object's position changes in any direction. Speed is defined as the ratio of distance traveled to time spent traveling. Because it has only one direction and no magnitude, speed is a scalar quantity.So, to find how many miles Tom can drive in 3 hours:
Given: Tom drives 81/2 miles every 1/30 hour.
81/2 miles = 40.5 miles1/30 hours = 30 minutesSo, in 30 minutesTom drives 40.5 miles.
Then, in 1 hour Tom will drive 40.5 + 40.5 = 81 miles.Miles Tom will drive in 3 hours = 81 × 3 = 243 miles.Therefore, Tom drives 243 miles in 3 hours.
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201.96+38.7+0.84
Eh this question I been on it for like 3 hours
I need help
Answer:
241.5
Step-by-step explanation:
201.96+38.7+0.84
operation of 12 less than x
Given that 5x8y = 29
Find y when x = -1
Give your answer as an improper fraction in its simplest form.
okay this is another question for you my good friend jdoe0001
The independent variable: lengths of the sides
The dependent variable: the perimeter of a square,
K(5) = 20.
What is the Dependent and Independent variable of a Function?The dependent variable of a function is the output of a function that changes as a result of any change in the independent variable, which is the input of the function.
The input (independent variable) determines the output (dependent variable) of a function.
Therefore, we can make the following deductions:
The independent variable, x, represents lengths of the sides, and the dependent variable is the perimeter of a square, because the perimeter of the square depends on the length of the side of the square.
The function that relates to the variables is: K(x) = 4x
So, K(5) = 4(5) = 20.
This means, if 5 is the length of one of the sides of the square, then 20 is the perimeter of the square.
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what is 2.3,3.3% and 2/3 in oder greatest to least.
2.3,3.3% and 2/3 in order of greatest to least is 3.3% > 2/3 > 2.3.
What is descending order?Arrangement in a series that begins with the greatest or largest and ends with the least or smallest.
Now the given numbers are,
2.3,3.3% and 2/3
Converting them into decimals we get,
2.3 = 2.300
3.3% = 0.033
2/3 = 0.667
Arranging them from greatest to least we obtain,
0.033 > 0.667 > 2.3
Thus, the given numbers from greatest to least are,
3.3% > 2/3 > 2.3
Hence, 2.3,3.3% and 2/3 in order of greatest to least is 3.3% > 2/3 > 2.3.
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