Answers
Given: (a) [tex]2(x+3)=2x+6[/tex] and (b) [tex]4(y-3)=4y-12[/tex].
To find: The expanded form of the given expressions.
(c) [tex]4(m+n)=4m+4n[/tex] (using [tex]a(b+c)=ab+ac[/tex])
(d) [tex]3(5-q)=15-3q[/tex] (using [tex]a(b-c)=ab-ac[/tex])
(e) [tex]5(2c+1)=10c+5[/tex] (using [tex]a(b+c)=ab+ac[/tex])
(f) [tex]3(2x-5)=6x-15[/tex] (using [tex]a(b-c)=ab-ac[/tex])
(g) [tex]7(4b-1)=28b-7[/tex] (using [tex]a(b-c)=ab-ac[/tex])
(h) [tex]3(2x+y-5)=3((2x+y)-5)[/tex]
⇒[tex]3(2x+y-5)=3(2x+y)-15[/tex] (using [tex]a(b-c)=ab-ac[/tex])
⇒[tex]3(2x+y-5)=6x+3y-15[/tex] (using [tex]a(b+c)=ab+ac[/tex])
(i) [tex]2(6a-4b+3)=2((6a-4b)+3)[/tex]
⇒[tex]2(6a-4b+3)=2(6a-4b)+6[/tex] (using [tex]a(b+c)=ab+ac[/tex])
⇒[tex]2(6a-4b+3)=12a-8b+6[/tex] (using [tex]a(b-c)=ab-ac[/tex])
(j)[tex]6(m+n+p)=6((m+n)+p)[/tex]
⇒ [tex]6(m+n+p)=6(m+n)+6p[/tex] (using [tex]a(b+c)=ab+ac[/tex])
⇒ [tex]6(m+n+p)=6m+6n+6p[/tex] (using [tex]a(b+c)=ab+ac[/tex])
(k) [tex]y(y+2)=y^2+2y[/tex] (using [tex]a(b+c)=ab+ac[/tex])
(l) [tex]g(g-3)=g^2-3g[/tex] (using [tex]a(b-c)=ab-ac[/tex])
(m) [tex]n(4-n)=4n-n^2[/tex] (using [tex]a(b-c)=ab-ac[/tex])
(n) [tex]a(b+c)=ab+ac[/tex] (using [tex]a(b+c)=ab+ac[/tex])
(o) [tex]s(3s-4)=3s^2-4s[/tex] (using [tex]a(b-c)=ab-ac[/tex])
(p) [tex]2x(x+5)=2x^2+10x[/tex] (using [tex]a(b+c)=ab+ac[/tex])
(q) [tex]4y(x-3)=4xy-12y[/tex] (using [tex]a(b-c)=ab-ac[/tex])
(r) [tex]5a(2b-5)=10ab-25a[/tex] (using [tex]a(b-c)=ab-ac[/tex])
(s) [tex]4a(3b+2c)=12ab+8ac[/tex] (using [tex]a(b+c)=ab+ac[/tex])
(t) [tex]5p(4p-5q)=20p^2-25pq[/tex] (using [tex]a(b-c)=ab-ac[/tex])
Related Questions
What is slope? Check all that apply.
Answers
Answer:
B, E, and F maybe
Find the explicit formula.
-6, -26,-46,-66, ...
Answers
Answer:
-20
Step-by-step explanation:
as you can see you can still see the 6s, whats the difference between 40 and 20? its 20, its like skip counting but negative, the answer couldve been "20" if it made the number go potitive but its negative so the answer is -20
squares, cubes and circles
Answers
Answer:
Area of the square tile is 49 square inches.
Length of the one side of the square tile is :---
Length=√Area=√49=√7²=7 inches
Solve the system of equations -30 + 7y = -18 and 4x – 4y = 8 by combining
the equations.
Answers
good luck!
A park volunteer plans to work on the park's stone walls for 1 hour every Monday, 1 hour every
Wednesday, and 3 hours on Fridays. The graph shows the number of hours he plans to work for a
given number of weeks. Complete parts a through c.
Answers
Answer:
The answer is below
Step-by-step explanation:
A linear graph has an equation in the form y = mx + b, where y and x are variables, m is the slope of the line and b is the y intercept (that is value of y at x = 0).
a) y represent the number of hours worked and x represent the number of weeks. The points are represented in the form (x, y).
First we can find the slope of the line by picking two points from the graph. Let us use (0, 0) and (2, 10). The slope m is given as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{10-0}{2-0} \\\\m=5[/tex]
The slope and constant of proportionality is 5.
b) The equation can be gotten using the points (0, 0) and (2, 10). Therefore:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\\\\y-0=\frac{10-0}{2-0}(x-0)\\\\y=5x\\\\[/tex]
c) In 16 weeks (i.e. x = 16):
y = 5x
y = 5(16)
y = 80 hours
Find the 8th term of the geometric sequence 5, -15, 45, ...5,−15,45,...
Answers
Answer:
The 8th term of the geometric sequence 5, -15, 45, ... is:
[tex]a_8=-10935[/tex]
Step-by-step explanation:
Given the geometric sequence
5, -15, 45, ...
The first element of the geometric sequence is
[tex]a_1=5[/tex]
A geometric sequence has a constant ratio 'r' and is defined by
[tex]a_n=a_1\cdot r^{n-1}[/tex]
computing the ratios of all the adjacent terms
[tex]\frac{-15}{5}=-3,\:\quad \frac{45}{-15}=-3[/tex]
The ratio between all the adjacent terms is the same and equal to
[tex]r=-3[/tex]
substituting [tex]a_1=5[/tex], and [tex]r=-3[/tex] in the nth term
[tex]a_n=a_1\cdot r^{n-1}[/tex]
[tex]a_n=5\left(-3\right)^{n-1}[/tex]
Determining the 8th term:
We have already got the nth term
[tex]a_n=5\left(-3\right)^{n-1}[/tex]
substituting n = 8 to determine the 8th term
[tex]a_n=5\left(-3\right)^{n-1}[/tex]
[tex]a_8=5\left(-3\right)^{8-1}[/tex]
[tex]a_8=5\left(-3^7\right)[/tex]
[tex]a_8=-5\cdot \:3^7[/tex]
[tex]a_8=-5\cdot \:2187[/tex]
[tex]a_8=-10935[/tex]
Therefore, the 8th term of the geometric sequence 5, -15, 45, ... is:
[tex]a_8=-10935[/tex]
3 multiplied by what gives me 55.50
Answers
Answer:
18.5
Step-by-step explanation:
Divide 55.5 by 3 (working backwards to find your answer)
Then you will get 18.5!
Answer:
18.5
Step-by-step explanation:
divide 55.5 by 3 and you get 18.5.
A must-have for any thrill seeker is a drop tower ride. The Precipice Plummet will stand 420 feet tall. The scale in your architectural diagrams is 1":40'. How tall will your drawing of Precipice Plummet be in inches? (do not include units in your answer, just the number
Answers
The answer is 10.5, but don't put 10.5 if it's just asking for the number and not the unit only put (10)!!!
Pentagon VWXYZ shown on the coordinate grld. A student reflected pentagon VWXYZ across the x -axis Which describes this transformation ?
Answers
Answer:
(x, y) --> (x, -y)
Step-by-step explanation:
Sorry for not explaining it :/ Good Luck!
Answer: I just took the test so the answer would be J. (x,y) --> (-x,y)
Step-by-step explanation: hope this helped thx for the points :D
Identify the translations of the graph of the parent function f(x) = x^2? that result in the graph of g(x) = (x + 2)2 + 6.
Answers
Answer:
x8
Step-by-step explanation: bacause if you see and look really close
The translations of the graph of the parent function [tex]f(x) = x^2[/tex] that result in the graph of [tex]g(x) = (x + 2)^2 + 6[/tex] will be that the parabola moved [tex]2[/tex] units to the left and [tex]6[/tex] units up.
What is translations ?Translation is the act or process of changing completely. In this also the graph changes or transform. i.e. in the graph values of the expression are changing and forming new shape.
We have,
Parent Quadratic equation [tex]f(x) = x^2[/tex]
And,
Translation of graph [tex]g(x) = (x + 2)^2 + 6[/tex]
So,
Parent quadratic function works in the form of [tex]f(x) = a(x-h)^2 + k[/tex]
Here,
"h" tells if the vertex of the parabola is going left or right.
"k" determines if the vertex of the parabola is going up or down.
So, According to the question;
We have,
Translation of graph [tex]g(x) = (x + 2)^2 + 6[/tex]
So,
From equation we find out that the vertex of the parabola moved [tex]2[/tex] units to the left and [tex]6[/tex] units up.
(Always remember if moving left means sign would be of plus because in parent quadratic function is in the form of [tex]f(x) = a(x-h)^2 + k[/tex] we have minus sign in it.)
Hence, we can say that the Translation of the graph of the parent function [tex]f(x) = x^2[/tex] that result in the graph of [tex]g(x) = (x + 2)^2 + 6[/tex] will be that the parabola moved [tex]2[/tex] units to the left and [tex]6[/tex] units up.
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Find two consecutive even integers whose sum is 86. Which of the following equations could be used to solve the problem?
4x = 86
2x + 1 = 86
2x + 2 = 86
x2 + 2= 86
Answers
Answer:
ucg
Step-by-step explanation:
Answer:
2x+1=86
Step-by-step explanation:
I think thats the answer, Im not sure though
John called a plumber to fix a leak in his bathroom. The
plumber charged $30 to come to the house and $25 an hour
while fixing the leak. If the final bill was $105, how many
hours was the plumber at John's house?
Answers
Answer:
3 hours
Step-by-step explanation:
$105 - $30 = $75
$75 ÷ $25 = 3 hours
what is the unit price of $5.36 for 20 oz?
Answers
Answer:
5.36/20
0.268 dollars per oz
plz brainliest :)
do you want an explanation?
In A ABC, m ZA = 36°, m ZB = 45°, and m ZC = 99º. Which statement
is true?
A. CA > BC > AB
B. BC > CA > AB
C. AB > BC > CA
D. AB > CA > BC
Answers
Answer:
The true statement is AB > CA > BC ⇒ D
Step-by-step explanation:
In any triangle, the longest side in length is the opposite to the greatest angle in the measure, and the shortest side in length is opposite to the smallest angle in the measure.
Let us solve the question
∵ ABC is a triangle
∵ m∠A = 36°
∵ m∠B = 45°
∵ m∠C = 99°
→ That means C is the greatest angle and A is the smallest angle
∴ ∠C is the greatest angle and ∠A is the smallest angle
∴ The arrange of the measures of the angles is m∠C > m∠B > m∠A
∵ AB is the opposite side of ∠C
∴ AB is the longest side
∵ BC is the opposite side of ∠A
∴ BC is the shortest side
∵ CA is the opposite side of ∠B
∴ The arrange of the lengths of the sides is AB > CA > BC
∴ The true statement is AB > CA > BC
helpppppp it’s urgenttttttttt!!!!!
Answers
What is the slop in the graph?
Answers
Answer:
-2/5
Step-by-step explanation:
rise/run you count how much it rises and how much it runs
Answer:
-2/5
Step-by-step explanation:
rise over run
A football coach moves 12 m north, then 16 m south, then 22 m north, and finally 6 m
south.
What is the displacement
Answers
Answer: Displacement=12 m north
Step-by-step explanation:
12 m north
Let’s assume
north= positive
south=negative
12+(-16)+22+(-6)=12
10. Use substitution to solve the system of equations below.
- x + 2y = 5
3x - 5y =-11
Answers
Answer:
the answer for y is 4 and x is 3
y=4
x=3
You score a 90% on your quiz. There were 20 total questions. How many did you answer correct?
Answers
Answer:
You would've gotten 2 questions wrong to score a 90%.
Step-by-step explanation:
</3 PureBeauty
Answer:
18
Step-by-step explanation:
20×90/100
here u go fffffcv
X(x+7)=0 solve whatever this id
Answers
Step-by-step explanation:
x(x + 7) = 0
By Zero Product rule,
either x = 0 or (x + 7) = 0.
=> x = 0 or x = -7.
ariana has $1.40 worth of nickels and dimes. she had twice as many nickels as dimes. determine the number of nickels and the number of dimes that ariana has
Answers
Answer:
Ariana has 7 dimes and 14 nickels
Step-by-step explanation:
Nickel = 0.05
Dime = 0.10
1.40 ÷ 2 = 0.70
7 x 2 = 14
because Adriana has twice the nickels as dimes and half of the 1.40 is dimes so the other half is nickels.
nickels x 2 = 14
pls help me for brainlest ASAP
Answers
The slope is 0
Because its not going up, the slope isn’t negative or positive so its moving but it isn’t rising so its 0. If it were going up but not side there would be no slope, but for this its 0
90% OFF original price!
Eric wants to buy a chandelier. The original price is $90. What is the sale price?
$
Answers
90% of $90 is $81, so therefore the sale price (original price - percentage) would be $9.
I’ll give brainiest
Determine if a triangle with side lengths 6, 8, and 12 is acute, right, or obtuse?
Answers
Answer:
obtuse
Step-by-step explanation:
hope this helps
and can you tell me if I was right or wrong?
Please help me with this problem, I'll give brainliest!!
And if you want even more points can you go to my profile, then go to QUESTIONS then if you know the answer to the one underneath this one could you help answer it THANK YOU SO MUCH
Answers
Which is an equation of the line with a slope of 4 and a y-intercept of -2?
Answers
Answer:
y = 4x - 2
Step-by-step explanation:
Y-intercepts cross the y-axis at x = 0. So, we can plug (0 , -2) into an equation with m = 4.
-2 = 4(0) + b
-2 = b
y = 4x - 2
can some one help me solve this −5(p+5over3 )=−4
Answers
Answer:
I did this in my head so I'm not sure but I think it's -1/5=p
What is 287.7 round to the nearest hundredth
Answers
Answer:
287.70 because if u round to the nearest hundreds all u would have to do is add a zero.
I think it's 287.70
A runner has a mass of 89 kg he produces aforce of 84 Newtons between the ground and his running shoes How fast does he accelerate
Answers
Force = mass × acceleration
acc= force / mass
84N/89kg
= 0.94m/s
The acceleration of the runner is 0.9 m/[tex]s^{2}[/tex].
We have a runner has a mass of 89 kg he produces a force of 84 Newtons between the ground and his running shoes.
We have to determine the acceleration of the runner.
What is the formula to calculate the force on a body ?The force on a body is the product of mass and acceleration. Mathematically -
F = ma
According to the question, we have -
Force = 84 N
Mass = 89 Kg
Therefore -
F = ma
84 = 89 x a
a = 84/89 = 0.9 m/[tex]s^{2}[/tex]
Hence, the acceleration of the runner is 0.9 m/[tex]s^{2}[/tex].
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simplify 4a X 6b -3c
Answers
24 abx - 3c