Rewrite each algebraic expression in an equivalent form with the fewest
number of terms possible.
a. 6(x + 7)(x + 2)
b. (2y – 5)
c. (5x + 4y)(2x - y)
d. (3x + 7)(3x – 7)
e. (t + 2) – (4t +9) – t
Answers
Answer:
Step-by-step explanation:
The terms will be multiplied in order to get the simplified polynomials.
a. 6(x + 7)(x + 2)
[tex]6(x + 7)(x + 2)\\=6[x(x+2)+7(x+2)]\\=6(x^2+2x+7x+14)\\=6(x^2+9x+14)\\=6x^2+54x+84[/tex]
The simplified form of 6(x + 7)(x + 2) is [tex]6x^2+54x+84[/tex]
b. (2y – 5)^2
Using the formula: [tex](a-b)^2 = a^2+b^2-2ab[/tex]
[tex]=(2y)^2+(5)^2-2(2y)(5)\\=4y^2+25-20y[/tex]
The simplified form is: [tex]4y^2-20y+25[/tex]
c. (5x + 4y)(2x - y)
[tex]=5x(2x-y)+4y(2x-y)\\=10x^2-5xy+8xy-4y^2\\=10x^2+3xy-4y^2[/tex]
The simplified form of (5x + 4y)(2x - y) is [tex]10x^2+3xy-4y^2[/tex]
d. (3x + 7)(3x – 7)
Using the formula: [tex](a+b)(a-b) = a^2-b^2[/tex]
[tex]= (3x)^2-(7)^2\\= 9x^2-49[/tex]
The simplified form of (3x + 7)(3x – 7) is [tex]9x^2-49[/tex]
e. (t + 2) – (4t +9) – t
[tex]=t+2-4t-9-t\\=t-4t-t+2-9\\= -4t-7[/tex]
The simplified form of (t + 2) – (4t +9) – t is [tex]-4t-7[/tex]
Hence,
a. The simplified form of 6(x + 7)(x + 2) is [tex]6x^2+54x+84[/tex]
b. The simplified form is: [tex]4y^2-20y+25[/tex]
c. The simplified form of (5x + 4y)(2x - y) is [tex]10x^2+3xy-4y^2[/tex]
d. The simplified form of (3x + 7)(3x – 7) is [tex]9x^2-49[/tex]
e. The simplified form of (t + 2) – (4t +9) – t is [tex]-4t-7[/tex]
Related Questions
Find the value of : 0.678 multiplied by 9.01/0.0234
Answers
Answer:
261.06 (Approx)
Step-by-step explanation:
Given:
Two number = 0.678,9.01/0.0234
Find:
Multiply
Computation:
⇒ 0.678,9.01/0.0234
⇒ 0.678 x [9.01/0.0234]
⇒ 6.10878 / 0.0234
⇒ 261.058874
261.06 (Approx)
PLEASE HELP VERY URGENT!
The graph shows the distance Kerri drives on a trip. What is Kerri's speed?
Driving Time and Distance
A. 25 miles per hour
B. 60 miles per hour
C. 75 miles per hour
D. 50 miles per hour
Answers
Answer:
Kerri's speed = 50 mile per hour. Therefore option (D) is true.
Step-by-step explanation:
Given the distance-time graph
It is clear from the distance-time graph that:
at Time = 1 hour, Distance = 50 milesat Time = 2 hours, Distance = 100 milesso the two points on the distance-time graph is:
(1, 50)(2, 100)Finding the slope between the points to determine the speed.
Please note that the slope between the points represents the speed or rate of change.
Speed = Rate of change = y₂-y₁ / x₂-x₁
= 100 - 50 / 2-1
= 50 / 1
= 50 miles per hour
Thus, Kerri's speed = 50 mile per hour. Therefore option (D) is true.
Please help me. Solve for x state the properties used. 5(x - 2) - 6 = 24
Answers
Answer:
x = 8
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Step-by-step explanation:
Step 1: Define Equation
5(x - 2) - 6 = 24
Step 2: Solve for x
Add 6 to both sides: 5(x - 2) = 30Divide 5 on both sides: x - 2 = 6Add 2 to both sides: x = 8Step 3: Check
Plug in x into the original equation to verify it's a solution.
Substitute in x: 5(8 - 2) - 6 = 24Subtract: 5(6) - 6 = 24Multiply: 30 - 6 = 24Subtract: 24 = 24Here we see that 24 does indeed equal 24.
∴ x = 8 is the solution to the equation.
please help me on this , tyyy :]
Answers
9514 1404 393
Answer:
(a) 1, 2
(b) 4
Step-by-step explanation:
(a) 9x +81 = 9·x +9·9 = 9(x +9) . . . . . . matches first and second choices
__
(b) 10 +14y -5 -y = (14y -y) +(10 -5) = 13y +5 . . . . . . matches fourth choice only
In Siberia, a record high temperature of 98 F has been reported. The record low temperature is 192 degrees lower than the record high temperature. What was the coldest Siberia temperature?
Answers
Answer:
Lo: - 94o F
Step-by-step explanation:
Hi: 98oF
Difference: 192 degrees lower
Low: ?
Formula
98 - 192 = -94
That seems incredibly cold. I've lived through a day that was - 60oF and that was enough. (about - 51o C)
If you think in Celcius
The formula is
C = 5/9(F - 32)
C = 5/9 (-94 - 32)
C = 5/9 (-126)
C = -60
I think Siberia must be much colder than -60.
How can I divide 18/15 without any leftovers
Answers
Answer:
You can turn the leftovers into a decimal. the answer you would get would be 1.2.
Step-by-step explanation:
Hope this helps and have a nice day!
Answer:
Calculate out how many times the denominator goes into the numerator. To do that, divide 18 by 15 and keep only what is to the left of the decimal point:
18 / 15 = 1.2000 = 1
Multiply the answer from Step 1 by the denominator and deduct that from the original numerator.
18 - (15 x 1) = 3
Keep the original denominator and use the answers from Step 1 and Step 2 to get this:
1 3/15
Minimize the fraction part from Step 3 by dividing the numerator and denominator by 3, which is the greatest common factor, to get the final answer. 18/15 as a Mixed Number is:
1 1/5
Which would also equal to 1.2000.
Hope this kinda helped and made some sense.
(☞ﾟヮﾟ)☞BRAINIEST☜(ﾟヮﾟ☜)
Step-by-step explanation:
What is the slope of a line that is parallel to the given equation?
y -- 2 = 5 (x + 1)
Answers
Answer: Slope = 10.000/2.000 = 5.000
x-intercept = 7/-5 = -1.40000
y-intercept = 7/1 = 7.00000
Step-by-step explanation:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
y-2-(5*(x+1))=0
STEP
1
:
Equation at the end of step 1
(y - 2) - 5 • (x + 1) = 0
STEP
2
:
Equation at the end of step 2
y - 5x - 7 = 0
STEP
3
:
Equation of a Straight Line
3.1 Solve y-5x-7 = 0
Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).
"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.
In this formula :
y tells us how far up the line goes
x tells us how far along
m is the Slope or Gradient i.e. how steep the line is
b is the Y-intercept i.e. where the line crosses the Y axis
The X and Y intercepts and the Slope are called the line properties. We shall now graph the line y-5x-7 = 0 and calculate its properties
Graph of a Straight Line :
Calculate the Y-Intercept :
Notice that when x = 0 the value of y is 7/1 so this line "cuts" the y axis at y= 7.00000
y-intercept = 7/1 = 7.00000
Calculate the X-Intercept :
When y = 0 the value of x is 7/-5 Our line therefore "cuts" the x axis at x=-1.40000
x-intercept = 7/-5 = -1.40000
Calculate the Slope :
Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is 7.000 and for x=2.000, the value of y is 17.000. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 17.000 - 7.000 = 10.000 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)
Slope = 10.000/2.000 = 5.000
Geometric figure: Straight Line
Slope = 10.000/2.000 = 5.000
x-intercept = 7/-5 = -1.40000
y-intercept = 7/1 = 7.00000
The sum of three consecutive numbers is 72 what is the smallest of the numbers
Answers
Answer:
23
Step-by-step explanation:
Suppose,
the first number = x
the second number = x+1
the third number = x+1+1 = x+2
Question wise,
x+x+1+x+2 = 72
3x+3 = 72
3x = 72-3 = 69
x = 69/3 = 23
so the numbers are,
23,(23+1)=24 and (23+2)=25
Do the bois got me? Please bois
Answers
Answer:
the 2
second one
Step-by-step explanation:
Answer:
DFA BFC
Step-by-step explanation:
Third time posting. Explain it too
Answers
Answer:
D. x-5 / x+4
Step-by-step explanation:
(-3x³ +9x² +30x) / (-3x³ -18x² - 24x)
=-3x (x²-3x-10) / -3x(x²+6x+8)
=-3x(x+2)(x-5) / -3x(x+2)(x+4)
=x-5 / x+4
Answer:
oooooooof
Step-by-step explanation:
-3 5/6 make it a decimal
Answers
Answer:
-3.56 i think .
Step-by-step explanation:
What is the equation in slope-intercept form of a line that passes through the point (4, 5) and has a slope of 1/2?
Answers
Answer:
1/2x + 5
Step-by-step explanation:
The y intercept is 5 & the slope is already given!
Can someone please help me on this question?
Answers
A veterinarian is interested in the average number of pets her clients own. Over the course of a month, she questions each client she meets with and records their responses. The veterinarian calculates the average and draws a conclusion from her data.
What kind of statistical study did the veterinarian conduct?
A.
theoretical study
B.
survey
C.
experiment
D.
observational study
Answers
Answer:b
Step-by-step explanation:
Plato
Eliza is planning a 5-day trip. She has budgeted $38.25 a day for food and the hotel will cost a total of $349.75. She also is bringing $495.00 for spending money. What is the average cost per day for Eliza’s trip?
Answers
Answer:
$207.20
I hope this can help in any way!
PLEASE HELP FAST FIND THE DOMAIN AND RANGE OF EACH GRAPH ILL GVIE 30 POINTS!
Answers
Answer:
1. domain (-3,5] range (3,4]
2. domain [-2,4] range [5,4]
3. domain (1,4) range (-1,-4)
Step-by-step explanation:
im in algebra two so you can trust my answer. happy holidays and stay safe!
Step-by-step explanation:
1).domain [-3,5)
range( -4,3]
2)domain[-2,4)
range:[-2,5)
3) domain[1,4]
range [-4,-1]
Jack can type 35 words per minute. How long would it take Jack to type a 490 word essay?
Answers
Miguel took 7 hours to read a 259-page book and Julissa took 5 hours to read a 175-page book. Who read more pages per hour?
Answers
J: 175/5= 35 pages per hour
Answer: Miguel
Write a real-world problem where you would
want to compare rates of change for two different functions.
Answers
Answer and Step-by-step explanation:
Let us assume two boys are jogging.
Boy 1 jogging speed is 10 kilometres per hour
Boy 2 jogging speed is 20 kilometres per hour
This can be represented in terms of distance, d and time, t. When we do this, we have:
d = 10t boy 1
d = 20t boy 2
This implies that boy 1 rate of change is 10 kilometers for every one hour and boy 2 is 20 kilometers for every 1 hour.
From here, we can conclude that the rate of change of boy 2 is twice the rate of change of boy 1.
Which is the input value produces the same output value for the two functions on the graph ?
Answers
Answer:
X = - 2
Hope it's help you.... ^_^
HELPPP ASAP!!! Fernando, sixty-six, developed tremors a few years ago. Now he is becoming unsteady on his feet. Which of
the following would explain these symptoms?
O Alzheimer's
O frontal lobe dementia
O andropause
O Parkinson's
Answers
Answer:
The answer is Parkinson's Disease
Step-by-step explanation:
It is correct on Odyssey Ware
A bag of flour contains 24 cups. Each sponge cake that Gilda makes uses 3 cups of
flour. How many cakes can she make with one bag of flour?
8
3
24
1
Answers
Answer:
8
Step-by-step explanation:
This is the answer because:
1) Since there are 24 cups in one bag and she uses 3 cups per cake, all we have to do is divide:
24 ÷ 3 = 8
Therefore, the answer is 8.
Hope this helps! :D
HELP ME PLEASE!!!!!!
Answers
1-0 divided by 3-0
Slope is 1/3
the slope represents the relationship between x and y
b) (6,2) and (-3,-1)
-1-2 divided by -3-6
Slope is 1/3
c) yes, the two triangles represent the same slope as all of the four points used are collinear (on the same line), making all the slopes equal.
Four friends had dinner at a restaurant. The bill was $55.40, and they added a 20% tip. The 4 friends shared the total cost equally. How much money did each person pay?
Answers
Answer:
$16.62 each
Step-by-step explanation:
First, find 20% of the bill to figure out how much the tip is worth:
20% over 100% = $x over $55.40 ---> 20 * 55.4 / 100 = 11.08
Now that we know the tip is $11.08, next add it on to the bill:
$11.08 + $55.40 = $66.48
Now divide this by 4 to split the bill evenly between the 4 friends:
$66.48 / 4 = $16.62
I don’t know how to do this I’m so confused
Answers
Answer:
You have to graph it
Step-by-step explanation:
Step-by-step explanation:
take the value in that BIG curly bracket as X terms....then substitute one by one to the equation given below to get Y values...after that u have cordinates then u can draw the graph..
[tex]x \: \: \: y \\ - 2 = - 8 \\ - 1 = - 10 \\ 0 = - 12 \\ 1 = - 14 \\ 2 = - 16[/tex]
this is for the first equation..so the coordinated are...
(-2,-8), (-1,-10), (0,-12), (1,-14), (2,-16)
use the same methord to find the others
what is the value of 5 + -2
Answers
Answer:
3
Step-by-step explanation:
5 is greater than 2 and two is negative so the answer is positive
Which represents z = 3 (cosine (StartFraction 7 pi Over 6 EndFraction) + I sine (StartFraction 7 pi Over 6 EndFraction) )?
Answers
Answer:
The first one
Step-by-step explanation:
Answer:
A on edge
Step-by-step explanation:
The distance between Prague and Vienna is 254 km. The local time in Prague is the same as the local time in Vienna. Calculate the average speed of the train
Answers
Answer: 56.44 km/h
Step-by-step explanation:
Speed = Distance / Time
Time = 1950 - 1520 = 4 hours 30 minutes = 4.5 hours
Speed = 254/4.5
= 56.44 km/h
pllsss I needddd helpp
Answers
Help Me! ASAP! Determine whether each equation has no solution, one solution or infinitely many solutions. Choose No Solution, One solution, or Infinitley Many Solutions for each equation.
Answers
Answer:
Step-by-step explanation:
(1). One solution
(2). Infinitely Many Solutions
(3). One solution
(4). No Solution
Answer:
1. 1 solution, 2. Infinite solutions, 3. 1 solution, 4. No solution
Step-by-step explanation: