What is the mathematical reasoning for Step 3?
A 2-column table with 5 rows. First column is labeled Reason with entries Given, Step 1, Step 2, Step 3, Step 4. Second column is labeled Step with entries three-fourths x (negative 8 x + 6), (three-fourths x) (negative 8 x) + (three-fourths x) (6), three-fourths times (negative 8) times x times x + three-fourths times 6 times x, (three-fourths times (negative 8)) times (x times x) + (three-fourths times 6) times x, negative 6 x squared + 9 over 2 x.
associative property
commutative property
distributive property
simplify
Answers
Based on the operation in step 3, the mathematical reasoning that we see is the Associative property.
What is the reasoning in step 3?Step 2 was:
= 3/4x (-8x) + (3/4x) (6)
Step 3 then became:
3/4 x (-8) × x × x + 3/4 x 6x
This shows the associative property because the numbers were regrouped but because they are being multiplied by each other, the result will not change.
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3. Distributive Property
Related Questions
A typist can type 45 words per minute. How many minutes will it take him the type a 2500 word report?
Answers
Answer:
55.56 or 55 5/9
Step-by-step explanation:
To find the time it takes to type a report, you need to divide the number of words in the report by the words the typist can type in a minute.
2500/45 = 55.56
It takes 55.56 minutes or 55 5/9 minutes to type a 2500 word report.
Answer:
55 minutes and 33 seconds.
Step-by-step explanation:
To solve this we can set up a proportion.
1/45=x/2500
Cross multiply.
1*2500=45*x
45x=2500
Divide both sides by 45.
x=55.5*
.5* minutes is about 33 seconds. (0.55555*60)
So, it will take him around 55 minutes and 33 seconds.
please answer this problem step by step
Answers
The intervals of each behavior of the function are given as follows:
Decreasing: (-∞, -3).Constant: (-3, 3).Increasing: (3, ∞).How to classify the function as increasing, decreasing or constant?The function is increasing when the graph moves right and up.The function is decreasing when the graph moves right and down.The function is constant when the graph of the function is an horizontal line.More can be learned about functions at https://brainly.com/question/24808124
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What is the value of the expression?
3 • [(30 - 8) ÷ 2 + 2]
Answers
Answer: 39
Step-by-step explanation:
30-8=22
22/2=11
11+2=13
13 times 3 =39
What is 9/14 closer to 0, 1, or 1/2?
Answers
Answer = 1/2
9/14 = 0.64
The goal is to get to 14/14 to get to a whole 1.
A half of 14 is 7 so the half would be 7/14
9/14 is 5 less than getting to the whole and is 2 more from being a half
Therefore it’s closer to 1/2
Which is the product in the expression 5(z+6)-25+x
Answers
Find the x-intercepts of the parabola with vertex (1,20) and y-intercept (0,16), Write your answer in this form: (X1,Y1), (X2,Y2). If necessary, round to the nearest hundredth.
Answers
ANSWER
\((-1.24,0),(3.24,0)\)EXPLANATION
We want to find the x intercepts of the parabola with vertex (1, 20) and y intercept (0, 16).
To do this, first find the equation of the parabola.
The vertex form of the equation of a parabola is:
\(\begin{gathered} y=a(x-h)^2+k \\ \text{where (h, k) = vertex} \end{gathered}\)Therefore, we have:
\(y=a(x-1)^2+20\)To find the value of a, substitute the values of x and y of the y intercept into the equation:
\(\begin{gathered} 16=a(0-1)^2+20 \\ 16=a(-1)^2+20 \\ 16=a+20 \\ \Rightarrow a=16-20 \\ a=-4 \end{gathered}\)Therefore, the equation of the parabola in vertex form is:
\(y=-4(x-1)^2+20\)Now, write it in standard form:
\(\begin{gathered} y=-4(x^2-2x+1)+20 \\ y=-4x^2+8x-4+20 \\ y=-4x^2+8x+16 \end{gathered}\)To find the x intercepts, find the values of x when y = 0:
\(\begin{gathered} -4x^2+8x+16=0 \\ \text{Solve using Quadratic formula:} \\ x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ a=-4;b=8;c=16 \\ x=\frac{-8\pm\sqrt[]{8^2-4(-4)(16)}}{2(-4)}=\frac{-8\pm\sqrt[]{64+256}}{-8} \\ x=\frac{-8+\sqrt[]{320}}{-8};x=\frac{-8-\sqrt[]{320}}{-8} \\ \Rightarrow x=\frac{-8+17.89}{-8};x=\frac{-8-17.89}{-8} \\ x=-1.24;x=3.24 \end{gathered}\)Therefore, the x intercepts are:
\((-1.24,0),(3.24,0)\)how do I simplify this in exponential expression
Answers
how to convert pounds to rands
Answers
Answer:
To convert pounds to rands, you need to know the current exchange rate between the two currencies. Once you have the exchange rate, you can multiply the number of pounds by the exchange rate to get the equivalent amount in rands.
For example, if the exchange rate is 1 GBP = 20 ZAR and you want to convert 100 pounds to rands, you would multiply 100 by 20, which equals 2000 rands.
Step-by-step explanation:
algebra domain and range please help
Answers
Answer:
Option 2.
Step-by-step explanation:
Find the domain by finding where the function is defined. The range is the set of values that correspond with the domain.
Domain: \((- \infty} ,0)\) ∪ \((0, \infty} )\)
Range: \((- \infty} ,0)\)∪\((0, \infty} )\)
Walmart was having a sale on video games. They offered a 15% discount on a game that was originally priced at $30. After the sale, the discounted price of the game was increased by 10%. What is the new price of the game after this increase?
Answers
Answer:
28.05$
Step-by-step explanation:
The game got a discount of 15%.
New price is (30$) ( 0.85 ) = 25.5$ (since the discount is 15% you only pay for the 85% of the original price)
Then an increase of 10%. this is:
New price: 25.5$ (1.10) = 28.05
New price is 28$ with 5 cents
(ie) The Actual width (w) of the is 66 cm
use the scale drawing to find the
Actual length (1) of the rectangle?
Inside the rectangle
Width 18mm
Length 24mm
what's the actual length
of the rectangle
O
Answers
Answer:
Since I was given the scale of width(mm) and the actual width(cm) , also the length in (mm) and we looking for actual which must in cm.
We use the above information in cross multiplecation which gave us the actual length of 88 cm
At the beginning of 2002, an ice cream shop claimed to have "nearly 1,020 different ice cream flavors." Assuming that you could choose from 1,020 different flavors, that you could have your ice cream in a cone, a cup, or a sundae, and that you could choose from a dozen different toppings, how many different desserts could you have?
Answers
Answer:
36720 different desserts
Step-by-step explanation:
(1020x3)x12=36720
Yesterday, Charmaine went on a bike ride. Her average speed was 10 miles per hour. Today, she went on another ride, this time averaging 13 miles per hour. In
the two days, she biked for a combined total time of 12 hours.
Let x be the number of hours she biked yesterday. Write an expression for the combined total number of miles she biked in the two days.
total number of miles biked
Answers
4. P/E Ratios. Favorita Candy’s stock is expected to earn $2.40 per share this year. Its P/E ratio is 18. What is the stock price? (LO7-1)
Answers
Answer:
2.4*18 = $43.2
stock price is $43.2
Step-by-step explanation:
find the surface area .NO FILES #2
Answers
Answer:
486
Step-by-step explanation:
The solid is a cube. The faces of a cube are 6 congruent squares.
side = 9 ft
surface area = 6 * side²
SA = 6 * (9 ft)²
SA = 486 ft²
A local dry-cleaning company bought new equipment and its estimated useful life is 4 years. Using the straight-line depreciation method, what is the rate of depreciation each year?
Answers
Answer:
$2,500 or 25%
Step-by-step explanation:
Let's use the same example:
Cost of Equipment = $10,000
Useful Life = 4 years
Depreciation Rate = (Annual Depreciation / Cost of Equipment) * 100
Annual Depreciation = Cost of Equipment / Useful Life
Annual Depreciation = $10,000 / 4 years
Annual Depreciation = $2,500
Depreciation Rate = ($2,500 / $10,000) * 100
Depreciation Rate = 0.25 * 100
Depreciation Rate = 25%
What does x equal in the picture below?
Answers
All of the outside angles added together are 360 so it would be 7x+49+6x+33+83=360
13x+165=360
13x=195
x=15
GET 5 STARS, THANKS, AND BRAILIEST!!!
Solve by elimination:
x + 3y = 1
-3x -3y = -15
Group of answer choices
(-2 , -7)
(2 , 7)
(-7 , 2)
(7 , -2)
Answers
Answer:
(7, -2)
Step-by-step explanation:
x + 3y = 1
-3x - 3y = -15
(x-3x) + (3y-3y) = 1-15
-2x + 0 = - 14
-2x = - 14
x = 7
x + 3y = 1
7 + 3y = 1
3y = 1-7
3y = -6
y = -2
Answer:
D: (7 , -2)
Step-by-step explanation:
Multiply each equation by the value that makes the coefficients of x
opposite.
(3)⋅(x+3y)=(3)(1)
−3x−3y=−15
Simplify
3x+9y=3
−3x−3y=−15
Add the two equations together to eliminate x
from the system.
3x+9y= 3
+ −3x−3y=−15
_____________
6y=−12
Divide each term by 6 and simplify.
y=−2
Substitute the value found for y into one of the original equations, then solve for x.
x=7
The solution to the independent system of equations can be represented as a point.
(7,−2)
The result can be shown in multiple forms.
Point Form:
(7,−2)
Equation Form:
x=7, y=−2
I hope this helps!!!!!!!
27,813 students took the ACET this year. If only 2,836 students were admitted into the Ateneo among those students, what is the Ateneo’s acceptance rate? a. 7.5% b. 10.2% c. 13.4% d. 9.0%
Answers
If only 2,836 students were admitted into the Ateneo among 27,813 students, who took the ACET this year, the Ateneo’s acceptance rate is b. 10.2%.
How the rate is determined:The rate is the ratio of one value, expression, measurement, or quantity compared to another.
The rate represents the quotient of the numerator and the denominator.
The rate is expressed as a percentage by multiplication with 100.
The number of students who took the ACET this year = 27,813
The number of students who were admitted into the Ateneo = 2,836
The percentage or rate admitted = 10.19667% (2,836 ÷ 27,813 × 100)
= 10.2%
Thus, we can conclude that the acceptance rate or percentage is Option B.
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2 numbers that equal 17 and 5
Answers
Answer:
3 +2 = 5 and 12 + 5 = 17
Step-by-step explanation:
i hope this helps im not sure if its frght or if it helps sorry if its wrong.
1 Apply Ana is bowling. She pays $4 per game and $7 to rent shoes. After three games, each additional game is free. Is the total cost to bowl a function of the number of games played?
Answers
Answer:
game is free. Is the total cost to bowl a function of the
Step-by-step explanation:
Solve for q 10/9=3/q q=
Answers
Answer:
q = 27/10
Step-by-step explanation:
10/9 = 3/q
To find q, we must seperate it from the other numbers,
First we divide both sides by 3,
(10/9)/3 = (3/q)/3
10/27 = 1/q
Now we find the reciprocal of both sides to get the answer,
27/10 = q
q = 27/10
5y - 30 = 15x solve for y
Answers
Answer:
y=6-3x
Step-by-step explanation:It should be that but im not 100% sure
amina and cara take a math test amina scores 40 marks,cara scores 60 marks write the ratio of amin to cara's marks
-they are given $20 to share,they share the money in the ratio of their marks how much does amina recieves
Answers
Answer
8
Step-by-step explanation:
Ratio: 40 : 60
Total amount - $20
40/100 x 20
= 8 (ANS)
i hope my answer is correct if not i apologize.
Use the following clues to find the secret number
I am a 3-digit number.
All of my digits are odd.
I am less than 600.
I am greater than 400.
If you add my digits you get 15.
My last digit is 7
What am I?
Answers
Bookwork code: N84
Look at the poster below showing the price of pencils in a stationery shop.
Annabel wants to buy exactly 76 pencils. What is the lowest amount she can
pay?
Give your answer in pounds (£).
spar
..
Pencils for sale!
30p each
Pack of 10
pencils for £2
Answers
Based on mathematical operations, the lowest amount that Annabel can pay for pencils is $15.20
How is the lowest amount determined?The lowest amount that Annabel can pay for pencils can be determined using the mathematical operations of multiplication and division.
Multiplication and division are two of the four basic mathematical operations, including addition and subtraction.
If Annabel chooses to purchase the first pencil at 30p each, she would pay £22.80 (£0.30 x 76).
If Annabel chooses to purchase the second pencil class of a pack of 10 pencils for £2, she would pay £15.20 [£2 x (76 ÷ 10)].
Pencils for sale
30p each
Pack of 10 pencils for £2
Thus, if Annabel wants to buy the pencils, she can either pay £15.20 or £22.80, but using mathematical operations, the lowest amount she can pay is £15.20.
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Which expressions are equivalent to -2(2h+10)+4h−2(2h+10)+4hminus, 2, left parenthesis, 2, h, plus, 10, right parenthesis, plus, 4, h ?
Answers
Answer:
The answer is "-4(h+9)"
Step-by-step explanation:
Given:
\(\bold{ -2(2h+10)+4h-2(2h+10)+4-2(2h+10)+4h}\)
\(\to -4h-20+4h-4h-20+4-4h-20+4h \\\\\to -4h -60+4 \\\\\to -4h-36\\\\\to -4(h+9)\)
Answer:
−20−4h+4h or −20 (If you are on khan then its A and B)
Step-by-step explanation:
100% correct
Complete this sequence of numbers such that the difference between any two adjacent numbers is the same : 3/k, _, _, 9/2k.
Answers
The completed sequence is: 3/k, 3/k, 3/k, 9/2k.To complete the sequence of numbers with a constant difference between adjacent numbers, we can calculate the common difference by subtracting the first term from the second term.
Let's denote the missing terms as A and B.
The given sequence is: 3/k, A, B, 9/2k.
The common difference can be found by subtracting 3/k from A or B. Therefore:
A - 3/k = B - A = 9/2k - B.
To simplify, we can equate the two expressions for the common difference:
A - 3/k = 9/2k - B.
Next, we can solve for A and B using this equation.
Adding 3/k to both sides gives:
A = 3/k + 9/2k - B.
Now, we can substitute the value of A into the equation:
3/k + 9/2k - B - 3/k = 9/2k - B.
Simplifying further, we have:
9/2k - 3/k = 9/2k - B.
Cancelling out the common terms, we find:
-3/k = -B.
Multiplying both sides by -1, we get:
3/k = B.
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A 6-foot sub valued at $30 is divided among five players (P1, P2, P3, P4, P5) using the last-diminisher method. The players play in a fixed order, with P1 first, P2 second, and so on. In round 1, P1 makes the first cut and makes a claim on a piece. For each of the remaining players, the value of the current claimed piece at the time it is their turn is given in the following table: P2 P3 P4 P5
Value of current claimed piece $6.00 $8.00 $7.00 $6.50 a. Which player gets his or her share at the end of round 1? b. What is the value of the share to the player receiving it? c. How would your answer change if the values were as follows? P2 P3 P4 P5 Value of current claimed piece $6.00 $8.00 $7.00 $4.50
Answers
a.P5 is the last player in the fixed order, they will make the last cut and get their share at the end of round 1. b. P5's share is worth $1.50. c.the value of P5's share would still be $1.50.
a. The last-diminisher method means that each player takes turns making a cut and claiming a piece. The player who gets their share at the end of round 1 is the player who makes the last cut. Since P5 is the last player in the fixed order, they will make the last cut and get their share at the end of round 1.
b. The value of the share to P5 is the total value of the sub divided by 5, minus the sum of the values of the pieces claimed by the other players before them. The total value of the sub is $30, so the value of P5's share is:
($30/5) - ($6 + $8 + $7) = $1.50
So P5's share is worth $1.50.
c. If the values were as follows:
P2 P3 P4 P5
Value of current claimed piece $6.00 $8.00 $7.00 $4.50
Then the player who gets their share at the end of round 1 would still be P5, since they have the lowest value of the current claimed piece. The value of P5's share would be:
($30/5) - ($6 + $8 + $7) = $1.50
So the value of P5's share would still be $1.50.
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Robert's book bag is weighing him down. His bag alone weighs 4 pounds. His library book
weighs 2 pounds. The math book is 4 times the weight of the library book, and his science
book is 2 times the weight of the math book. How much does his book bag weigh with all
these books? What is the heaviest book in his book bag?
Answers
The library book weighs 2 pounds.
The math book is 4 times the weight of the library book, so it weighs 4 * 2 = 8 pounds.
The science book is 2 times the weight of the math book, so it weighs 2 * 8 = 16 pounds.
To find the total weight of Robert's book bag, we add the weights of all the books and the bag:
4 pounds (bag) + 2 pounds (library book) + 8 pounds (math book) + 16 pounds (science book) = 30 pounds.
Therefore, Robert's book bag weighs 30 pounds with all these books.
To determine the heaviest book in his book bag, we compare the weights of the books:
The bag weighs 4 pounds.
The library book weighs 2 pounds.
The math book weighs 8 pounds.
The science book weighs 16 pounds.
From these options, the science book is the heaviest, weighing 16 pounds.
Answer:
1) 30 pounds is the weight of the bag all together
2) science book is the heaviest book
Step-by-step explanation:
bag=4 pounds
library book=2 pounds
maths book=2×4=8 pounds
science book=8×2=16 pounds
4+2+8+16=30 pounds all together
heaviest book= science book (16 pounds)