find the product of following:(i) (x+3) (x+2) (ii) (2x-1) (2x-7)
Answers
Part (i)
Answer: x^2 + 5x + 6-----------------
Work Shown:
(x+3)(x+2)
y(x+2) ..... Let y = x+3
y*x + y*2 ... distribute
x(y) + 2(y)
x(x+3) + 2(x+3) .... plug in y = x+3
x*x + x*3 + 2*x + 2*3 ... distribute
x^2 + 3x + 2x + 6
x^2 + 5x + 6
=====================================================
Part (ii)
Answer: 4x^2 - 16x + 7-----------------
Work Shown:
We could follow the same set of steps as shown back in part (i), but I'll show a different approach. Feel free to use the method I used back in part (i) if the visual approach doesn't make sense.
The diagram below is a visual way to organize all the terms. Many textbooks refer to it as "the box method" which helps multiply out any two algebraic expressions.
Each inner cell is found by multiplying the corresponding outer terms. For instance, in the upper left corner we have 2x*2x = 4x^2. The other cells are filled out the same way.
The terms in those four inner cells (gray boxes) are:
4x^2-14x-2x7The like terms here are -14x and -2x which combine to -16x, since -14+(-2) = -16.
We end up with the answer 4x^2-16x+7
Related Questions
Kedwin can watch movies at home in two ways. He can order unlimited online movies for $10 a month. He could also go to the local movie rental store and rent 5 movies for $4.00. The system representing this scenario is graphed below.
How many movies does Kedwin need to rent each month to make the online option a better deal?
a. 10 movies per month
b. 10.40 movies per month
c. 12.5 movies per month
d. 13 movies per month
Answers
Answer:
I believe the answer is D.)13 movies per month.
Step-by-step explanation:
Answer:
D. 13 movies per month.
Step-by-step explanation:
Isaac is purchasing two pairs of shoes—one pair for $37.00 and the second pair for $42.00. The state sales tax applied to Isaac’s bill is 7%. How much is Isaac’s total bill? If Isaac uses a coupon entitling him to a 25% discount off the purchase price before tax, how much will his bill be? Assume that a 7% sales tax is applied to the discounted price. Using words, explain how you found the discounted price.
Answers
7.11 and 9.48
Step-by-step explanation:
.12 is equal to 7.11
with out coupon
.12 is equal to 9.48
with the coupon
Thomas can process a pile of paperwork in 4 hours less time than Frank. Together they can process the pile in 2.1 hours. How long would it take Frank to do the job alone?
Answers
Answer:
F = 7 hours
Step-by-step explanation:
Let the time taken by Frank to work alone be F.
Translating the word problem into an algebraic equation;
Thomas alone takes (F - 4) hours.
Combine time = 2.1 hours
Their individual work rate expressed in piles per hour are;
Frank = 1/F
Thomas = 1/(F - 4)
Combined rate = 1/F + 1/(F - 4)
Simplifying the equation, we have;
Combined rate = (F - 4 + F)/F(F - 4)
Combined rate = (2F - 4)/F(F - 4)
Combined rate = (2F - 4)/(F²- 4F)
Now to find the time taken when they work together is;
(2F - 4)/(F²- 4F) = 1/2.1
Cross-multiplying, we have;
2.1*(2F - 4) = F² - 4F
4.2F - 8.4 = F² - 4F
Rearranging the equation, we have;
F² - 4.2F - 4F + 8.4 = 0
F² - 8.2F + 8.4 = 0
Solving the quadratic equation by factorization;
Factors = -7 and -1.2
F² - 7F - 1.2F + 8.4 = 0
F(F - 7) - 1.2(F - 7) = 0
(F - 7)(F - 1.2) = 0
Therefore, F = 7 or 1.2 hours
The time taken by Frank alone would be 7 hours.
The measures of the angles of a triangle are shown in the figure below. Solve for x.
Answers
Answer:
x = 25
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Geometry
All angles in a triangle add up to 180°Step-by-step explanation:
Step 1: Set Up Equation
29° + (4x + 9)° + (x + 17)° = 180°
Step 2: Solve for x
Combine like terms: 5x + 55 = 180Isolate x term: 5x = 125Isolate x: x = 25Gary's pay is $15 per hour. He receives a 6% pay raise.
Answers
The question is incomplete, the complete question is;
Gary's pay is $15 per hour. He receives a 6% pay raise.
Which method can Gary use to correctly calculate his new hourly pay rate?
Choose Yes or No for each method.
Answer:
Multiply 15 by 0.06 and add the result to 15 is the correct method
Step-by-step explanation:
Now when you are told to obtain the percentage, it simply means to multiply the given percentage by the number.
Here is what i mean;
6% of 15 simply means
6/100 * 15
Or
0.06 * 15 = 0.9
Since his basic pay of $15 was increased by this percentage, we have to add $0.9 so we have;
15 + 0.9 = $ 15.9
Find the solution of
−
6
(
2
x
+
1
)
=
54
.
Answers
Answer:x-5
Step-by-step explanation:
-6(2x+1)=54
Distribute:
-12x-6=54
Add 6 on both sides:
-12x-6+6=54+6
-12x=60
Divide 12 on both sides:
-12x/-12=60/-12
x=-5
write an equation in slope intercept form given slope and point for following (9,-4) slope 2/3 please helpppp
Answers
Answer:
y=2/3x -10
Step-by-step explanation:
y= m x + b
m=slope
slope = 2/3
b= y-intercept
plot point (9,-4) and count down two, left three, until reach y axis.
HELPPPPPPP PLEASE I HAVE TO SUBMIT IN 20 MINS!!!!!!
Answers
5. 4-2sqrt(10) and 4+2sqrt(10)
6. (x-8)^2 -62
Find cot 0 if tan 0 = 2
Answers
Answer:
1/2
Step-by-step explanation:
cot0=1/tan0
plug in tan0=2
cot0=1/2
3.41 rounded to the nearest tenth please help
Answers
Anything under 5 it stays the same and anything over 5 it goes up one
Answer:
3.4
Step-by-step explanation:
tell whether the ordered pair is a solution to the system of inequalities
Answers
Answer:
Yes, it is
Step-by-step explanation:
The solution to the inequality are the sets of points that lie where we have the shaded part
The coordinates (3,0) lie on the shaded part and thus will be a solution to the set of inequalities
WHATS THE SLOPE BETWEEN THE POINTS (-2,8) AND (4,20)
Answers
Answer:
m = 12 / 6 = 2 / 1 = 2
Step-by-step explanation:
2.) You’ll then have 12/6. Divide it out and you get 2/1 or 2.
Answer: Slope is 2/1 or 2
find the next 2 terms in this sequence
Answers
Hope this helps
1 2/3 - (-5 2/3) plsssssssssssssss helppppppppppppppppp
Answers
Answer:
[tex]7\frac{1}{3}[/tex]
Step-by-step explanation:
Answer:
i think its 7 1/3 but i may be wrong check that befoer u answer- i did this stuff like 2 years ago
Step-by-step explanation:
If this is this then what is what
Answers
Answer:I feel like I should understand this
Step-by-step explanation:
WILL GIVE BRAINLLIEST
9 is 10% of what number
Answers
Answer: the answer is 90 bro
Step-by-step explanation:
Plz help my teacher isn’t emailing my back
Answers
Answer:
ugh'
Step-by-step explanation:
12 and 4 i could be wrong sozStep-by-step explanation:
What is RU?
A.20
B.30
C.12
D.15
Answers
Answer:
a
Step-by-step explanation:
The segment RT is a perpendicular bisector and means Δ RSU is isosceles, then the 2 legs are congruent, that is
RS = RU , substitute values
8x = 6x + 5 ( subtract 6x from both sides )
2x = 5 ( divide both sides by 2 )
x = 2.5
Thus
RU = 6x + 5 = 6(2.5) + 5 = 15 + 5 = 20 → a
please help me on this! will give you brainliest, ty:,
Answers
Answer: 4^9
Step-by-step explanation:
4^-7 is just 1/4^7 so this is equal to 4^2 divided by 1/4^7. Dividing by a fraction is the same thing as multiplying by its reciprocal (just flip the fraction). So this whole equation is equal to 4^2 multiplied by 4^7. And when you multiply two exponents with the same base, the exponents are just added. So, your answer should be 4^9. Hope this helps! :)
can anyone answer this?
Answers
#13 slope =1/2 (up 1 over 2) y intercept= 1 because it starts at y(0,1)
#14 y=1/2x+1
#15 this slope means that the savings account saves on average $2000 dollars every 2months.
I hope this helps if it did please help me out by marking this comment as the brainiest answer. Helps me out a lot goodluck
What's the answer? I need help asap
Answers
The two triangles are congruent through AA (angle-angle proportionality theorem) therefore all the sides are congruent to each other.
In this case:
2y = 5y - 7
2y - 5y = -7
-3y = -7
y = -7/-3
y = 7/3
X ≤ 2 x ≥ 2 -4 < x ≤ -2 -4 < , x, ≤ -2 -4 ≤ x ≤ -2 What is the domain of the function?
Answers
Answer:
really hard and strong but am interested
12 - x
If x = 7, what is the value of the expression above?
Answers
Answer:
5
Step-by-step explanation:
12-7=5
Answer:
5
Step-by-step explanation:
We know that x is equal to 7. That means we can replace x with this value. This makes our new expression:
12 - 7
12-7 is equal to 5, so this expression will equal 5 when x = 7.
Write the expanded form of the following:
a) 21.061
b) 0.358
c) 506.0201
d)126.00
Answers
Answer:
a) 21.061
20+1+0.0+0.06+0.001
b)0.358
0+0.3+0.05+0.008
c)506.0201
500+0+6+0.0+0.02+0.000+0.0001
d)126.00
100+20+6
Happy New year ✨
*
4/3*3.14*2.6*2.6*2.6
Answers
Answer:
73.58
Step-by-step explanation: This is just a guess so I may be wrong. So when I put this into the calculator, it is showing a big number: 73.58485333 so what I did was round it to the nearest hundredths which is 73.58 so hope this helps somebody :)
689858/9375 or 73.584853
Step by step explanation:
4/3*3.14*2.6*2.6*2.6 - original equation
4/3*157/50*13/5*13/5*13/5 - convert decimals into fractions
2/3*157/25*13/5*13/5*13/5 - reduce the numbers with the GCF (greatest common factor) 2
689858/9375 - multiply the fractions
Karen and James both had 30 stocking stuffer items on their shopping list. After black Friday shopping Karen had finished 35% of her shopping After black Friday shopping James had finished 60% of his shopping HOW MANY MORE items has James purchased than Karen?
Answers
Answer: 7.5 items
Step-by-step explanation:
Both Karen and James had 30 stocking items.
Karen bought 35% of her items;
= 35% * 30
= 10.5 items
James has bought 60%;
= 60% * 30
= 18 items
= 18 - 10.5
= 7.5 items
A pound of apple costs $2.50. Represent the cost of n pounds.
Answers
Answer:
2.50n
Step-by-step explanation:
If im reading this right you're trying to represent the number of n pounds, so 2.50 * n
say you had 3 pounds:
2.50 (3) = 7.50
Solve for y
*show your work *
6y - 3x = 12
1/2 x + 1/4 y = 2
Answers
Step-by-step explanation:
if negative sign is there we must add and if positive sign is there subtraction should be written there.....
helpppp i need the answer fast it’s timed
Answers
bruh, who else has exams?
Answers
Answer:
I have exams too well cba's
Step-by-step explanation:
Answer:
Girl I have exams I don't like them
Step-by-step explanation: