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Complete Question
Lacey and Haley are rewriting expressions in an equivalent, simpler form.
a. Haley simplified x³⋅ x² and got
x⁵
Lacey simplified x³ + x² and got the same result! However, their teacher told them that only one simplification is correct. Who simplified correctly and how do you know?
b. Haley simplifies 3⁵⋅ 4⁵ and gets the result 12^10, but Lacey is not sure.
Is Haley correct? Be sure to justify your answer.
Answer:
a) Haley is correct, Lacey simplified wrongly.
b) Haley is incorrect
Step-by-step explanation:
a. Haley simplified x³⋅ x² and got
x⁵
Lacey simplified x³ + x² and got the same result! However, their teacher told them that only one simplification is correct. Who simplified correctly and how do you know?
For Question a, when it comes to simplifying algebraic expression that has to do with powers, there are certain rules that should be followed.
For example
x^a × x^b = x^(a + b)
For Haley, she simplified x³⋅ x² and got
x⁵
She is correct because this follows the product rule of powers or exponents above
= x³⋅ x² = x³+² = x⁵
For Lacey she is wrong because:
x³ + x² ≠ x⁵
x³ + x² when simplified as quadratic equation = x²(x + 1)
b. Haley simplifies 3⁵⋅ 4⁵ and gets the result 12^10, but Lacey is not sure.
Is Haley correct? Be sure to justify your answer.
For question b, when we have two distinct or different numbers with the same power(exponents) the rule states that:
x^a × y^a = (x × y)^a = (xy)^a
Haley is simplified wrongly. She did not apply the rule above
Haley simplified 3⁵⋅ 4⁵ = (3 × 4) ⁵+⁵
= 12^10, this is wrong.
The correct answer according to the rule =
3⁵⋅ 4⁵ = (3 × 4) ⁵ = 12⁵
Therefore,
3⁵⋅ 4⁵ ≠ 12^10
3⁵⋅ 4⁵ = 12⁵
Haley is wrong.
Solve for x. 7x−9<12 or 14x+8>11
Answer:
For 7x-9<12, the answer is x<3
For 14x+8>11, the answer is x>3/14
Step-by-step explanation: Isolate the variables by dividing each side by factors that do not contain the variable.
I hope this helps you out! :)
9. If H is the midpoint of GI, find GH.
5x + 2
9x - 10
FIND GH
I inserted the graph
Answer:
GH = 17
Step-by-step explanation:
Given that H is the midpoint of segment GI, and GH = 5x + 2, HI = 9x - 10, GH is congruent to HI. This implies GH = HI.
Therefore:
[tex] GH = HI [/tex], which will give us the following equation:
[tex] 5x + 2 = 9x - 10 [/tex]
Solve for x
[tex] 5x + 2 - 9x = 9x - 10 - 9x [/tex] (subtracting 9x from each side)
[tex] -4x + 2 = -10 [/tex]
[tex] -4x + 2 - 2 = -10 - 2 [/tex] (subtracting 2 from each side)
[tex] -4x = -12 [/tex]
[tex] \frac{-4x}{-4} = \frac{-12}{-4} [/tex] (dividing both sides by -4)
[tex] x = 3 [/tex]
GH = 5x + 2
Plug in the value of x
GH = 5(3) + 2 = 15 + 2
GH = 17
Answer:17
Step-by-step explanation: trust me bro
if sugarless gum sells at 2 pieces for $.25, then what would 10 pieces cost?
Answer:
Does this help
Step-by-step explanation:
10 pieces would cost $30
Mabey I am wrong
factorise. 35y²+13y-12
Answer:(
7 y − 3 ) ( 5 y + 4 )
write .11111 as a fraction in simplest form.
Answer:
11111/100000
Step-by-step explanation:
Good luck
If B is the midpoint of AC, and AC=8x-20, find BC.
Answer:
[tex]BC=26[/tex]
Step-by-step explanation:
Start with:
[tex]AB+BC=AC[/tex]
Since [tex]B[/tex] is the midpoint, we also know that:
[tex]AB=BC[/tex]
Knowing this, we can use a system of equations and substitute [tex]AB[/tex] for [tex]BC[/tex] in the equation we started with:
[tex]AB+AB=AC[/tex]
Let's identify our values:
[tex]AB=3x-1\\AC=8x-20[/tex]
Substitute:
[tex]3x-1+3x-1=8x-20[/tex]
Combine like terms:
[tex]6x-2=8x-20[/tex]
Add [tex]20[/tex] to both sides of the equation:
[tex]6x+18=8x[/tex]
Subtract [tex]6x[/tex] from both sides of the equation:
[tex]18=2x[/tex]
Divide by the coefficient of [tex]x[/tex], which is [tex]2.[/tex]
[tex]x=9[/tex]
Substitute [tex]9[/tex] into [tex]3x-1[/tex]
[tex]3(9)-1[/tex]
Solve:
[tex]AB=26[/tex]
Remember that [tex]AB=BC[/tex], thus:
[tex]BC=26[/tex]
For each equation, state whether there is no solution, one solution, or infinitely many solution. Explain your reasoning. A: 3x - 6 = 3(x - 1) - 3 B: 2x + 7 = - 2x + 7 C: 2x + 7 = 2x
Answer:
A: Infinite
B: One
C: No Solution
Step-by-step explanation:
Equation A:[tex]3x-6=3(x-1)-3\\\\3x-6=3x-3-3\\\\\boxed{3x-6=3x-6}[/tex]The sides are the same. This means that the equation has infinite solutions.
Equation B:[tex]2x+7=-2x+7\\\\2x+7-7=-2x+7-7\\\\2x=-2x\\\\2x+2x=-2x+2x\\\\4x=0\\\\\frac{4x=0}{4}\\\\\boxed{x=0}[/tex]The equation has one solution.
Equation C:[tex]2x+7=2x\\\\2x-2x+7=2x-2x\\\\\boxed{7\neq 0}[/tex]
The final result is a contradiction. The equation has no solution.
Write 0.54 as a fraction in simplest form.
Answer:
Convert to a simplified fraction by placing the numbers to the right of the decimal over 100 .
Reduce the fraction.
27 /50
Step-by-step explanation:
Answer:
27/50
Step-by-step explanation:
Take 54 and divide by 100 (54/100). The GCD of 54 is 2. When we divide the numerator and the denominator by 2 we get 27/50
If m/8 =57, find m/1.
Answer:
696
Step-by-step explanation:
[tex]\frac{m}{8} = 87[/tex]
First I would multiply each side by 8 to find what M is (because if you multiple m/8 by 8 the 8s will cancel out).
[tex]m=87*8\\m = 696[/tex]
Because any number divided by 1 would just be itself, 696/1 is just 696.
Answer: m/1= 7.125 or 7.1 (rounded)
Step-by-step explanation:
if m/8=57 then m/1 multiplied by 8 would be 57 . so you do the opposite and divide 57 by 8.
Zoey signed up for a streaming music service that costs $7 per month. The service allows Zoey to listen to unlimited music, but if she wants to download songs for offline listening, the service charges $0.75 per song. How much total money would Zoey have to pay in a month in which she downloaded 45 songs? How much would she have to pay if she downloaded ss songs?
The total money would Zoey have to pay in a month in which she downloaded 45 songs will be $40.75. And she has to pay if she downloaded s songs that will be y = 0.75s + 7.
What is a linear equation?A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
Zoey signed up for a streaming music service that costs $7 per month. The service allows Zoey to listen to unlimited music, but if she wants to download songs for offline listening, the service charges $0.75 per song.
Let x be the number of songs and y be the total amount. Then the equation will be
y = 0.75x + 7
The total money would Zoey have to pay in a month in which she downloaded 45 songs will be
y = 0.75 × 45 + 7
y = 33.75 + 7
y = $40.75
She has to pay if she downloaded s songs that will be
y = 0.75s + 7
More about the linear equation link is given below.
https://brainly.com/question/11897796
#SPJ2
A resort hotel in Scottsdale, AZ charges $1800 to rent a reception hall, plus $58 per person for dinner and open bar. The reception hall can accommodate up to 200 people. a) Write a function, T, to represent the total cost to rent the reception hall if n people attend the reception.
Answer:
T(n) = 1800 + 58n
Step-by-step explanation:
Rent reception = $1800
Charge per person = $58
Number of person who attend reception = n
Total cost = fixed cost + variable cost
Fixed cost = 1800
Variable cost = 58n
Total cost = T(n)
Total cost = fixed cost + variable cost
T(n) = 1800 + 58n
What is the equation for the line that goes through the point (-3,-1) and has the slope of -1/3
[tex]y = {x}^{2} + 4x + 3[/tex]
What is 4(2x+7)=12-2(10-2x)
Answer:
x=-9
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
Step 2: Subtract 4x from both sides.
Step 4: Divide both sides by 4.
If a rocket travels at 30km/s then the distance traveled by it in one hour is _____ A. 1800 km B.1080 km C.108000 km D. 500 km
Answer: C
Step-by-step explanation:
30 km/s x 60 = 1800 (1 minute)
1800 x 60 = 10800 (1 hour)
Answer:
C. 108,000 km
Step-by-step explanation:
use distance = velocity x time
30 km x 3600 sec x 1 hr
sec 1 hr
= 108,000 km
Need help with this one !
Answer:
r=5
Step-by-step explanation:
5x5x5=125
Mr. mehta is trying to subtracting one polynomial from another polynomial, what must he do first?
The first thing he has to do is take that "minus" sign through the parentheses containing the second polynomial. Some students find it helpful to put a " 1 " in front of the parentheses, to help them keep track of the minus sign. Here's what the subtraction looks like, when working horizontally.
how do you find the equation of a line
Choose two statements that are true for this expression.
423 – 7x2 – 30 + 15
A. The term – 3 is a ratio.
B. The entire expression is a difference.
C. There are three terms.
D. There are four terms.
Answer:
Options (A) and (D).
Step-by-step explanation:
Given expression is,
4x³ - 7x² - [tex]\frac{30}{y}[/tex] + 15
Characteristics of the give expression ,
Option (A).
Third term [tex]-\frac{30}{y}[/tex] of the expression is in the form a ratio.
True.
Option (B).
Entire expression is a difference.
False.
Option (C).
There are three terms.
False.
Option (D).
There are four terms in the given expression.
True.
Therefore, Options (A) and (D) will be the correct options.
I will give brainlest!!What is the area of this trapezoid?
Answer:
80
Step-by-step explanation:
The formula for solving the area of a trapezoid is [tex]\frac{a+b}{2} h[/tex]
So plug the numbers in and the answer is 80
hope that helps! have a great day! :)
If the relationship is proportional, what is the missing value from the table? x / y 8 / 6 16 / ? 24 / 18 answers under here! 8,a 9,b 12,c 14,d ADD ANSWER
The correct option is Option C: the missing value is 12.
What is the directly propotional?In directly proportionality, if one quantity increases then the other quantity also increases. if one quantity decreases then other quantity also decreases.
x ∝ y
⇒ x= ky
where k is proportionality constant.
Here the value x1, y1 is given by
x1=8
y1=6
as x1 is directly proportional to y1.
x1 = ky1
⇒8=6k
⇒k= 8/6
⇒k =4/3
If x3= 24 then x3 =ky3
⇒24=(4/3)y3
⇒y3= 24/(4/3)= 18 which is true from the table
Then given in the question x2=16
As x2 is directly proportional to y2.
x2 ∝ y2
⇒ x2 =ky2
where k= 4/3
⇒ 16 = (4/3)y2
⇒ y2= 16/(4/3)
⇒y2= 16*3/4
⇒y2= 12
The correct option is Option C: the missing value is 12.
Learn more about proportionality
here: https://brainly.com/question/24868934
#SPJ2
x2 +__ x + 36 What should go in the blank?
It could be anything in reality. Do you need the zero's solved?Please specify the question properly.
ANS: 12,0,13
find angle PBH and find the value of c
Answer:
Vertically opposite angles are angles that are formed opposite of each other when two lines intersect, and they are always equal.
Thus, Angle PBH is 118 degrees.
-----------------------------------------------
Finding the value of c:
[tex]3c+94=118[/tex]
Subtract 94 from both sides:
[tex]c+94-94=118-94[/tex]
[tex]3c=24[/tex]
Divide both sides by 3:
[tex]\frac{3c}{3}=\frac{24}{3}[/tex]
[tex]c=8[/tex]
|6|+|-2| what's the answer cuz ion know
Answer:
8
Step-by-step explanation:
6|+|−2|
=6+|−2|
=6+2
=8
I will give brainliest!!!!
Answer two questions about Equations AAA and BBB:
A.3x-1=7
B.3x=8
1) How can we get Equation BBB from Equation AAA?
Choose 1 answer:
(Choice A)
A
Multiply/divide both sides by the same non-zero constant
(Choice B)
B
Multiply/divide both sides by the same variable expression
(Choice C)
C
Add/subtract the same quantity to/from both sides
(Choice D)
D
Add/subtract a quantity to/from only one side
2) Based on the previous answer, are the equations equivalent? In other words, do they have the same solution?
Choose 1 answer:
(Choice A)
A
Yes
(Choice B)
B
No
Answer:
1. C
2. A
Step-by-step explanation:
Step 1: Write equation
3x - 1 = 7
3x = 8
Step 2: Use 1st equation and solve
3x = 8
x = 8/3
Step 3: Use 2nd equation and solve
3x = 8
x = 8/3
Both equations have equivalent solutions and the 2nd equation is the simplified version of the 1st.
What is 5 to the power of -3, show how you did it
Answer:5 to the power of -3 is 5 times-5=-25 times -25= 125 times -5 = -625
Step-by-step explanation:
6x-3=2x-1 8 what’s x equal
Answer:
1/2
Step-by-step explanation:
Subtract 2x from both sides
Add 3 to both sides
Then divide both sides by 4
x = (1/2)
Please help me with this one!! If the answer is correct I will mark it the best answer!
Anna and Jon were asked to solve the following inequality:
1- Jon was correct. And did not flip the inequality.
2- Anne was correct. Jon flip the inequality.
3- anne was correct Jon did not perform the inverse operation correctly
4- Jon was correct. Anne did not perform the inverse operation correctly
Answer:
Number two
Step-by-step explanation:
it took the test
The area of the star shaped surface of this block is 1.2m^2. The thickness of the block is 25cm. What is the volume of the block?
Answer:
volume = 0.30 m³
Step-by-step explanation:
GIVEN:
The area of the star shaped surface of this block is 1.2m^2.
The thickness of the block is 25cm.
FIND:
What is the volume of the block?
SOLUTION:
volume = area x length
where area = 1.2 m²; length = 0.25 m
plugin values into the formula:
volume = 1.2 m² x 0.25 m
= 0.30 m³
therefore, the volume of the star shaped block is 0.30 m³
What is the answer to this thing?
Answer:
area=108
Step-by-step explanation:
length times width
8x6=48
10x4=40
5x4=20
---------
Add them all together 48+40+20 =108
How to find the slope
Answer:
by slope what are u meaning by that
Answer:
to find slope it's m= rise/run = y2-y1/ x2-x1
Step-by-step explanation:
m=slope
(x1, x2) = coordinate of the first point in the lines
(y2, y1) = coordinate of the second point in the line.
