[tex] \bf{= \frac{64 {x}^{3} - 1 }{4x - 1} }\\ \\ \bf{= \frac{( \cancel{4x - 1})(16 {x}^{2} + 4x + 1) }{ \cancel{4x - 1}}} \\\\ \bf{= 16 {x}^{2} + 4x + 1}[/tex]
Answer:
[tex]16x^2+4x+1[/tex]
Step-by-step explanation:
Given expression:
[tex]\dfrac{64x^3-1}{4x-1}[/tex]
Step 1Factor the numerator of the given expression.
Rewrite 64 as 4³ and 1 as 1³:
[tex]\implies (4^3)x^3-1^3[/tex]
[tex]\textsf{Apply the exponent rule} \quad a^b \cdot c^b=(ac)^b:[/tex]
[tex]\implies (4x)^3-1^3[/tex]
[tex]\textsf{Apply the Difference of Cubes Formula} \quad x^3-y^3=\left(x-y\right)\left(x^2+xy+y^2\right):[/tex]
[tex]\implies (4x)^3-1^3=(4x-1)\left((4x)^2+4x(1)+(1)^2\right)[/tex]
[tex]\implies (4x)^3-1^3=(4x-1)\left(16x^2+4x+1\right)[/tex]
Step 2Replace the numerator in the given expression with the factored numerator from step 1:
[tex]\implies \dfrac{64x^3-1}{4x-1}=\dfrac{(4x-1)\left(16x^2+4x+1\right)}{4x-1}[/tex]
Cancel the common factor (4x - 1):
[tex]\implies 16x^2+4x+1[/tex]
Write an equation of the line in slope-intercept form.
Hello and Good Morning/Afternoon
Let's take this problem step-by-step:
What does this problem want us to find:
[tex]\hookrightarrow \text{The slope-intercept form}: y= mx + b[/tex]
m : slope b: y-interceptLet's find the slope:
(x₁, y₁) ⇒ 0,3)(x₂, y₂) ⇒ (4,2)[tex]m = \dfrac{y_2-y_1}{x_2-x_1} = \dfrac{2-3}{4-0} =-\dfrac{1}{4}[/tex]
Let's find the y-intercept:
⇒ the value of the y-coordinate when the x-coordinate value is '0'
⇒ thus it is '3'
Our equation is:
[tex]y=-\dfrac{1}{4} x+3[/tex] <===== Answer
Hope that helps!
#LearnwithBrainly
Greetings from Brasil...
One way to solve this question is through a determinant.
| X Y 1 |
| X₁ Y₁ 1 | = 0
| X₂ Y₂ 1 |
as
(X₁; Y₁) = (0; 3)
(X₂; Y₂) = (4; 2)
then
| X Y 1 |
| 0 3 1 | = 0
| 4 2 1 |
4Y + X - 12 = 0Which expression has the same value as 12 − 6 ÷ 3
a. 12 − (6 ÷ 3)
b. 12 ÷ 6 − 3
c. (12 − 6) ÷ 3
d. 12 − 3 ÷ 6
33.
Find the value of the expression: (5 + 7)2
a. 24 c. 144
b. 74 d. 54
Answer: a. 24
Step-by-step explanation:
We will simplify using PEMDAS.
Given:
(5 + 7)2
Add:
(12)2
Multiply:
24
a. 24
Hello!
[tex](5+7)2[/tex]
[tex]5+7=12\\12*2=24[/tex]
Your answer would be A. 24
Hope this helps!
Which statement is true?
Solve for z.
−1.2z−8.2>−9.7
Show the solution
Hello!
Inequality: [tex]-1.2z-8.2 > -9.7[/tex]
To solve, we need to add 8.2 to both sides of the inequality:
[tex]-1.2z-8.2+8.2 > -9.7+8.2\\-1.2z > -1.5[/tex]
Now to get our solution, we will need to divide both sides by -1.2:
[tex]\frac{-1.2z}{-1.2} > \frac{-1.5}{-1.2}\\[/tex]
Final answer:
[tex]\fbox{z} < \fbox{1.25}[/tex]
Hope this helps!
86.
A 6-sided number cube is rolled. Find the probability of each
event. Write each answer as a fraction, a decimal, and a percent.
P(5)
a. 1, 1.0 , 100% c. 0, 0.0, 0%
_ _
b. 1/6, 0.16, 16.6% d. 1/8, 0.125, 12.5%
A bee flies 6 feet per second directly to a flowerbed from its hive. The bee stays at the flowerbed for 14 minutes, and then flies directly back to the hive at 4 feet per second. It is away from the hive for a total of 19 minutes. A. what equation can you use to find the distance of the flowerbed from the hive? B. How far is the flowerbed from the hive? Let d be the distance of the flowerbed from the hive.
Answer:
5 minutes
Step-by-step explanation:
d / r = t
The bee is flying for 19 - 14 minutes
(d / 6) + d / 4) = 5
Answer: 25 feet
Step-by-step explanation:
19 - 14 = 5
total travel time = 5 min
av. between 6 and 4
= 6+4÷2 = 5
5 feet per sec × 5 min = 25 feet
What is -9 ÷ 2/3 ?
Answer I got: -27/3
Is it right?
Answer:
-27/2
Step-by-step explanation:
A lizard can lose its tail to escape a predator, and the tail will grow back at a constant rate. After 6 weeks, a lizard's tail has regrown to 3 3/4 inches long. Find the number of inches the tail grew each week.
Answer:
15/24 or 5/8 inches each week
Explanation and Checking part below :)
Step-by-step explanation:
3 3/4 ÷ 6
1. Turn the mixed number into an improper fraction.
15/4 ÷ 6/1
2. Use the KCF (keep,change,flip) method (multiply the reciprocal).
15/4 × 1/6 = 15/24
3. Simplify if needed to.
15/24 ----> simplified is 5/8
Check:
5/8 × 6 = 30/8
30/8 = 3 6/8 -----> Simplified to 3 3/4
what is 2 to the power of -1 + 1/2?
Answer:
The answer is 1
Step-by-step explanation:
2^-1 is basically turning it into 1/2. And the rest is history
Answer:
1
Step-by-step explanation:
can you pls make me BRAINLYS
The library loans 4 times as many non-fiction books as it does
fiction books. Write a rule for the relationship between the two
variables. Use n for non-fiction and f for fiction.
The rule for the relationship between the nonfiction and fiction books as an expression is n = 4f.
We have,
Let's write a rule for the relationship between the number of non-fiction books (n) and the number of fiction books (f) based on the given information.
We are told that the library loans 4 times as many non-fiction books as it does fiction books.
This means that the number of non-fiction books (n) is equal to 4 times the number of fiction books (f).
Mathematically, we can express this relationship as:
n = 4f
Where:
n = Number of non-fiction books
f = Number of fiction books
Thus,
The rule for the relationship between the nonfiction and fiction books as an expression is n = 4f.
Learn more about expressions here:
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Evaluate: 42 − 12 ÷ 6
—————————————————
(6 − 3) × 4 − 7
Answer:
42 - 12 ÷ 6 = 40
(6 - 3) x 4 - 7 = 5
Step-by-step explanation:
First of all, when coming over to an equation with a division or multiplication sign, we first solve the division or multiplication first, then the subtraction or addition. So, 12 ÷ 6 = 2. Then, 42 - 2 = 40. And in the other one we must first solve what's in the parenthesis. So, 6 - 3 = 3. Then, we multiply, 3 x 4 = 12. Then subtract. 12 - 7 = 5.
Hope this helps :)
Please answer need the extra credit
*count a pair of shoes as a singular unit *
Mary oversees shoe suppliers from 3 places. she is trying to supply for
retail stores.
supplier A has 4 crates of shoes plus six loose pairs
supplier B has 6 crates of shoes, but one pair is missing
supplier C has 10 crates plus five loose pairs
assume each crate contains an equal number of shoes, write an expression describing the total number of shoes available.
write another expression describing the number of shoes available for each retail store if the shoes are divided equally among stores.
Use a proportion to convert 10,000 kilometers to miles. Round to the nearest whole number.
Answer Choices:
A. 16,100 miles
B. 5,000 miles
C. 6,211 miles
D. 10,000 miles
* Note * Whoever answers this first will get brainly, and please show your work or I won't get any credit.
Which of the following points best represents the location of -1 5/8 on the number line?
Answer:
A
Step-by-step explanation:
Looking at the number line, you will notice that A, B, and C are less than 0.
Eliminate D, which is greater than 0.
Further still, as negative numbers get 'smaller', they go from -1 to -∞.
i.e.: -1 > -2 > -3
if you forget the above fact, looking at the number line, you can see that A is between -1 and -2, and [tex]-1\frac{5}{8}[/tex] is between -1 and -2 just as [tex]1\frac{5}{8}[/tex] is between 1 and 2.
Then, simply counting the ticks from -1 to -2, you can see that A falls on the 5th tick, while -2 falls on the 8th tick from -1.
Hope this helped.
Answer:
A
Step-by-step explanation:
-1 5/8 would be between -2 and -1
Consider the blueprint an artist creates of the outline of a mural, where 1 unit represents 1 foot. The artist edits the blueprint of the art mural by transforming triangle LMN on the coordinate plane.
If the artist dilates triangle LMN by a scale factor of 3 about the origin, creating triangle L′M′N′, what are the coordinates of N′?
Responses
(−9,−3)
(−3,−3)
(−1,−13)
(−13,−1)
Answer:
-9-3 i think
Step-by-step explanation:
Multiply or Divide. Write fractions in simplest form.
Answer: -7/26
Step-by-step explanation:
The school asked students to help decide what to name the school gym. Each student was given a list of six names and asked to choose one. What type of graph would be the most appropriate to graph the results?
A. bar graph
B. line graph
C. histogram
D. circle graph
Answer:A
Step-by-step explanation:
This would be the easies to understand in my opion so that is what i would use try this one. Can i get a brainliss??????
Which expression has the same value as 36 ÷ 6 ⋅ 2
a. (36 ÷ 6) ⋅ 2
b. 36 ⋅ 6 ÷ 2
c. 36 ÷ (6 ⋅ 2)
d. 36 ÷ 2 ⋅ 6
The ratio of red flowers to yellow flowers is 4 to 5. If there are 48 red flowers, what is the number of yellow flowers? if you answer this i will give you 100 points and write out how you did it
Answer:
60
Step-by-step explanation:
I believe if you have 48 red flowers you divide 48 by 4 which gives you 12.12*5 is 60 correct me if I'm wrong.
Which statement is the best comparison between the populations of the two continents in 2008
Answer:
Africa population is 2X larger than North America
Step-by-step explanation:
9.67x10⁸ = 967000000 which is 2 times more than north america which is 529 million
Answer:
Africa's population was about 2 times larger than North America's population in 2008
Step-by-step explanation:
9.67*10^8 = 967000000 = 971 million
971 million = Africa
529 = north America
Write an equation with a slope: -3/4 and y-intercept: -1/4
Answer:
y = (-3/4)x - 1/4
Step-by-step explanation:
Use the slope-intercept formula y = mx + b. Here m = -3/4 and b = -1/4, and so: y = (-3/4)x - 1/4
The equation of the line with slope -3/4 and y-intercept is -1/4 is y=-3/4x-1/4.
What is slope intercept form of line?The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of the line is the ratio of the rise to the run, or rise divided by the run.
It describes the steepness of line in the coordinate plane.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
Given that the slope is -3/4 and y-intercept is -1/4.
We have to find the equation of line with slope -3/4 and y-intercept is -1/4.
m=-3/4 and b = -1/4
Now plug in these values in slope intercept form y=mx+b
y=-3/4x-1/4
Hence, y=-3/4x-1/4 is the equation of the line with slope -3/4 and y-intercept is -1/4.
To learn more on slope intercept form click:
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8(5-2x)=24
Solve x. Pls show working
distribute the terms
-16x+40=24
subtract 40 from both sides
-16x - -16
divide both by 16
x = 1
Find the value of the expression: 3 ⋅ (2 + 6)2
a. 114 c. 48
b. 192 d. 144
Answer:
48
Step-by-step explanation:
first, we will use the distribution property: a (b + c): (ab + ac)
[3(2) + 3(6)] 2
now we will multiply
(6+18)2
(24)2
=48
Evaluate using the order of operations
Answer:
Step-by-step explanation:
First, you have to solve it with parenthesis, where the answer is one, then multiply them by 6= 6. The answer is 4.
Please answer need the extra credit
*count a pair of shoes as a singular unit *
Mary oversees shoe suppliers from 3 places. she is trying to supply for
retail stores.
supplier A has 4 crates of shoes plus six loose pairs
supplier B has 6 crates of shoes, but one pair is missing
supplier C has 10 crates plus five loose pairs
assume each crate contains an equal number of shoes, write an expression describing the total number of shoes available.
write another expression describing the number of shoes available for each retail store if the shoes are divided equally among stores.
Answer: 20c + 10.
Step-by-step explanation:
(c represents crates)
I wrote each equation separately first.
Supplier A: 4c + 6
Supplier B: 6c - 1
Supplier C: 10c + 5
We can add all the cs from each supplier giving us 4c + 6c + 10c which equals 20c. Now we can add the extra shoes as, 6 + (-1) + 5 equaling 10. I wrote -1 because we are missing that shoe, but you can write it as 6 - 1 + 5 instead. Together the two numbers make the equation 20c + 10. Hope that helps : )
I swear if you answer this correctly, you saved my life.
Answer:
[tex] \frac{5.5}{0.5} = 11 \\ \\ 5) - 2.5 \times 1 \times \frac{1}{4} = - \frac{25}{10} \times \frac{5}{4 \\ } \\ = - \frac{25 \times 5}{10 \times 4} = - \frac{25}{8} = - 3 \times \frac{1}{8} [/tex]
Aman had to sell his television at a loss of 12%. If the selling price was
Rs.7040, what was its cost price? Explain step by step please.
this is the explanation i hope it will be good
Lauren's graduation picnic will cost $34 if it has 17 attendees. At most how many attendees can there be if Lauren budgets a total of $38 for her graduation picnic? Solve using unit rates.
___attendees
Complete the inequality statement. 40 cm ___ 4 m
>
=