The correct factorization of the expression, [tex]64x^{3} +8[/tex], is 4[tex](2x-1)^{2}[/tex] (8x+2).
According to the question,
We have the following information:
[tex]64x^{3} +8[/tex]
The factors of this expression can be found using identity because 64[tex]x^{3}[/tex] is the whole cube of 4x and 8 is the cube of 2.
So, we have the following expression:
[tex](4x)^{3} + 2^{3}[/tex]
Now, we can use the following identity to factor the given expression:
[tex]a^{3} +b^{3} = (a+b) (a^{2} -ab+b^{2} )[/tex]
We have a = 8x and b = 2:
(8x+2) {[tex](4x)^{2}[/tex]-16x+[tex]2^{2}[/tex]}
(8x+2) (16[tex]x^{2}[/tex]-16x+4)
Taking 4 as the common factor from the second bracket:
4(8x+2) (4[tex]x^{2}[/tex]-4x+1)
Now, finding the factors of second bracket:
4(8x+2) ([tex]4x^{2}[/tex]-2x-2x+1)
4(8x+2) {2x(2x-1)-1(2x-1)}
4(8x+2) (2x-1) (2x-1)
4[tex](2x-1)^{2}[/tex] (8x+2)
Hence, the correct factorization of the expression, [tex]64x^{3} +8[/tex], is 4[tex](2x-1)^{2}[/tex] (8x+2).
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How long is 10:00am to 5:00 pm
Answer:
7 hours.
Step-by-step explanation:
Use a clock and count forward.
Which expression is equivalent to the expression below?
2.1 + (–3.7h) + 1.9h – 1.4
3.5 – 5.6h
−1.1h
0.7 + 1.8h
0.7 – 1.8h
Using the simplification, the equivalent expression of 2.1+(–3.7h)+1.9h–1.4 is 0.7–1.8h.
In the given question we have to find the equivalent expression of the given expression.
The given expression is 2.1+(–3.7h)+1.9h–1.4
Now solving the given expression to find the equivalent expression.
Now solving the expression
=2.1 + (–3.7h) + 1.9h – 1.4
Firstly simplifying the bracket
=2.1–3.7h+ 1.9h – 1.4
=(–3.7h+ 1.9h)+(– 1.4+2.1)
= –1.8h + 0.7
We can write it as
=0.7–1.8h
Hence, the equivalent expression of 2.1+(–3.7h)+1.9h–1.4 is 0.7–1.8h.
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enter an expression in the box to write the equation of a line that passes through the point (-6,2) and is perpendicular to the line y= 3/2x + 4
keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above
[tex]y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{3}{2}}x+4 \qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{3}{2}} ~\hfill \stackrel{reciprocal}{\cfrac{2}{3}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{2}{3}}}[/tex]
so we're really looking for the equation of a line whose slope is -2/3 and that it passes through (-6 , 2)
[tex](\stackrel{x_1}{-6}~,~\stackrel{y_1}{2})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{2}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{2}=\stackrel{m}{- \cfrac{2}{3}}(x-\stackrel{x_1}{(-6)}) \implies y -2= -\cfrac{2}{3} (x +6) \\\\\\ y-2=-\cfrac{2}{3}x-4\implies {\Large \begin{array}{llll} y=-\cfrac{2}{3}x-2 \end{array}}[/tex]
Find the formula, in standard form
y=ax2+bx+c , for a quadratic, that has roots at x=5+4√10 and x=5−4√10 , and has a leading coefficient of 1.
The quadratic equation in standard form that contains the roots 5 + 4√10 and 5 - 4√10 is y = x² - 10 · x - 135.
How to determine quadratic formula in standard form
In this question we must derive a quadratic equation in standard form, that is, a polynomial of the form:
y = a · x² + b · x + c
Where b / a = - r₁ - r₂ and c / a = r₁ · r₂ and r₁ and r₂ are the roots of the polynomial. If we know that a = 1, r₁ = 5 + 4√10 and r₂ = 5 - 4√10, then the quadratic equation is:
y = a · [x² + (b / a) · x + (c / a)]
y = x² + (- 5 - 4√10 - 5 + 4√10) · x + (5 + 4√10) · (5 - 4√10)
y = x² - 10 · x + 25 - 160
y = x² - 10 · x - 135
y = x² - 10 · x - 135 is the quadratic equation in standard form.
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Please help ASAP will mark brainliest
Plot the points ( -3, 7 ) and ( 9, 0)
Find the distance between the points and the midpoint of the line segment joining the points.
Answer: 13.89 units
PLEASE GIVE BRAINLIEST THANK YOU VERY MUCH!!
helpppp please??? brainlesttttt
If x = 2 and t = 4, what is the value of 1/8(x^3− 4)(t² + 8)?
Answer:
64
Step-by-step explanation:
you need to plug the number in subtract and add then multiply the number from the first pair of parenthesis into the main number and after multiply the second pair into it.
1.) Ace wanted to buy a gift for his mother
worth $18.60. He has $7.40 in Savings
and another $6.30 Saved from his
allowance for the past two weeks. How much more
does he need to save this week?
Answer:
$4.90
Step-by-step explanation:
He already has $13.70 (7.40+6.30) saved up so you have to subtract that from 18.60 to find the total Ace needs to save up.
18.60-13.70=4.90
To check your answer, you can add 7.40, 6.30, and 4.90 and see if you get a total of 18.60.
Check: 7.40+6.30+4.90=18.60
rajesh is working out the are of the cirle with radius 10 he writes area=3.142x20 explain why rajesh is wrong
Answer:
100π = 314.1592654
Step-by-step explanation:
area of a circle πr²
π×10²
10×10 =100
100×π
Find the missing number in the following puzzle.
What is [tex]\frac{1000}{\frac{4}{3}\pi }[/tex]
The result of the expression as given in the task content is; 750/π.
What is the result of the quotient?It follows from the task content that the result of the division operation as given in the task content is to be determined.
Given the expression; 1000 ÷ (4/3)π
The expression can therefore be rewritten as follows;
1000 × (3/4) π
Hence, we have;
3000/4π
By further simplifying the expression; we have;
750/π
Hence, the result of the division as given in the task content is; 750/π.
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Bimpe rues 5km per hour faster thean she walk- If she runs for 45 minute and walks for 3 hour.
! BE A GOOD NAJM/ NAJMAH, AL
Answer:
See below
Step-by-step explanation:
I think you may have left some info out of your question post, but here is something that may help you:
x = walk speed km/hr
x + 5 = run speed km/hr
45 min = 3/4 hr = .75 hr
(.75)(x+5) + 3 * x = total distance in km
3.75x + 3.75 = total distance
WILL GIVE BRAINLIEST PLEASE HELP!!!!
A cat runs 10 meters north, sees a dog and runs 2 meters back south. It then runs 6 meters west. What is the displacement of the cat and the total distance it ran?
Answer:
The cat is at at 8 north 6 west
Step-by-step explanation:
The cat ran a total of 14 meters
A gallon of water contains 128 fluid ounces. A rain barrel can hold 6,400 ounces of rainwater.
Estimate how many gallons of water can the barrel hold?
Answer:
50 gallons
Step-by-step explanation:
6400 ÷ 128
= 50
Select all of the solutions for the linear inequality graphed below:
The solutions to the inequality whose graph is as represented in the attached image are;
A) (-4, 0)C) (0, 0)E) (-2,0)Graphical solution of inequalities.It follows from the task content that the graphical solutions for the inequality are represented on the graph and the points which are solutions for the inequality are to be identified.
Therefore, the points which are solutions for the inequality are points which are located in the shaded region of the graph.
Hence, such points include;
A) (-4, 0)C) (0, 0)E) (-2,0)The answer choices B, D and F represents points on the border line of the inequality graph and since the line is broken, they are not solutions to the inequality.
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15. Given the following measurements in
parallelogram ABCD, find the PERIMETER of
CED
AC 34 in. AB = 26 in. BD = 28 in.
P =
20 points for whoever answers
The Perimeter of CED AC is 34 in. AB is 26 in. BD is 28 in. P is 57 in.
Explain about the parallelogram?A parallelogram is the name given to a quadrilateral in geometry. In a parallelogram, the opposing sides are parallel and of equal length. The rhombus, rectangle, and square are just a few shapes that are parallelograms.
Having two sets of parallel sides makes a quadrilateral a parallelogram. A parallelogram has opposite sides that are the same length and angles that are the same size. Additionally, the internal angles on the same transverse side are supplementary. 360 degrees are equal to the total of all internal angles.
Two parallel pairs of sides make up a parallelogram, a quadrilateral. Four right angles form a parallelogram called a rectangle. Rhombus: An equal-length parallelogram with four sides.
The diagonals of a parallelogram bisect each other AC = 2 CE
Substitute AC= 34 into AC = 2 CE 34 = 2CE
Calculate 34 = 2 CE CE = 17
The diagonals of a parallelogram bisect each other BD = 2DE
Substitute BD= 28 into BD = 2DE 28 = 2DE
Calculate 28 = 2 DE DE = 14
Opposite sides of parallelogram are congruent AB = CD
Substitute AB = 26 into AB = CD CD = 26
Perimeter of a triangle PΔCDE = CE + CD + DE
Substitute CE = 17 DE = 14 CD = 26 PΔCDE = CE + CD + DE
PΔCDE = 17+ 26 + 14
PΔCDE = 57
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2
Linda paid $5.50 for 4 pounds of
strawberries. How much did she pay
per pound of strawberries?
Answer:
$ 1.38
Step-by-step explanation:
5.50 ÷ 4 = 1.375. rounded to 2 dp: 1.38
A doctor wants to estimate the mean HDL cholesterol of all 20- to 29-year-old females. How many subjects are needed to estimate the mean HDL cholesterol within 4 points with 99% confidence assuming S=13.8 based on earlier studies? Suppose the doctor would be content with 90 confidence. How does the decrease in confidence affect the sample size required?
The way the decrease in confidence affect the sample size required is: A. Decreasing the confidence level decreases the sample size needed.
How to find the sample size ?Using this formula to find the decrease in sample size
n = [zs/E]^2
Where:
n = Sample size
zs = z-score
E= margin of error
Confidence coefficient for 99% = 2.58
Hence,
2.58 × 13.8/sqrt(n) = 0.04
2.598 × 13.4 /0.04 = sqrt(n)
( 2.598× 13.8 /0.04)^2 = n
n=803,371.6
So,
Confidence coefficient for 90% = 1.64
n= (1.64× 13.8/0.04)^2
n =320,129.64
Therefore the correct option is A.
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The complete question is:
A doctor wants to estimate the mean HDL cholesterol of all 20- to 29-year-old females. How many subjects are needed to estimate the mean HDL cholesterol within 4 points with 99% confidence assuming S=13.8 based on earlier studies? Suppose the doctor would be content with 90 confidence. How does the decrease in confidence affect the sample size required?
How does the decrease in confidence affect the sample size required
A. Decreasing the confidence level decreases the sample size needed.
B. The sample size is the same for all levels of confidence.
C. Decreasing the confidence level increases the sample size needed.
2
Select the correct answer from each drop-down menu.
Julia and Kellen are participating in a read-a-thon to raise money for charity. The money each of them raises will be a mix of fixed and per-page
donations.
Function / models the total amount, in dollars, that Julia will raise if she reads x pages:
j(x) = 1.65x + 17.31.
Function k models the total amount, in dollars, that Kellen will raise if he reads x pages:
k(x) = 0.90x+9.28.
The function
If they both re
h(x)=0.75x+26.59
h(x) = 0.75x+8.03
h(x) = 2.55x+8.03
h(x) = 2.55x+26.59
represents the difference between the amounts Julia and Kellen will raise when they both read x pages.
ence will be $
Reset
Next
Mrs. Reed is buying seeds to start a vegetable garden. She purchases 12 packets of bean seeds, 15
packets of carrot seeds, and 2 packets of corn seeds. Choose Yes or No to tell if each statement about
the purchase is correct.
Step-by-step explanation:
Mrs. Reed is buying seeds to start a vegetable garden. She purchases 12 packets of bean seeds, 15
packets of carrot seeds, and 2 packets of corn seeds. Choose Yes or No to tell if each statement about
the purchase is correct.
Please help: Which numbers are in order from least to greatest?
A.
0.561, 8.627, 5.325
B.
4.057, 4.122, 5.008
C.
1.742, 1.558, 1.671
D.
6.705, 6.527, 6.211
x-intercept of (y+12) = 3(x - 9)
Answer: purple is the greatest
(b)
The table below shows the cost price, selling price and profit or loss as a percentage of the cost
price.
Complete the table below, inserting the missing values at (i) and (ii).
(i)
(ii)
Cost Price
$55.00
(c) The table shows some rates of exchange :
Calculate the value of
(i) EC $ 1 in TT $......
(ii) US $80 in EC $ .
(iii) TT $648 in US $. .....
Selling Price
$44.00
$100.00
US $1.00 = EC $2.70
TT $1.00 = EC $ 0.40
Percentage
Profit or Loss
25% profit
(4 marks)
. (1 mark)
. (1 mark)
...... (3 marks)
Total 12 marks
Answer:
US$1.00=EC$2.70 TT$1.00=EC$0.40 calculate the value of : 1.EC$1in TT$ 2.US$80inEC$ 3.TT$648 in US$
Step-by-step explanation:
that what i've got is that I hope that helps you
Is the function that cuts through the points (2, 3) and (-1, 6) increasing or decreasing? a. increasing c. neither b. decreasing d. cannot be determined Please select the best answer from the choices provided A B C D Mark this and return
Helppp!!! I need help I don’t know how to do this pleasee
Answer:10.85
Step-by-step explanation:
First you have to multiply a, 3 5/6, by b, 5 2/3. Which is 21.7222222, if you simplify it, you would get 21.7. Then you divide the total by 2 and you get 10.85.
Answer:
10 31/36 m
Step-by-step explanation:
formula for area of a triangle base times height times 1/2
we turn the height and base into improper fractions
3 5/6= 23/6
5 2/3=17/3
Now we multiply together to find area
23/6x17/3= 391/18
391/18x1/2=391/36
10 31/36
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The table and corresponding frequency polygon show information about the
waiting times of some patients at a dentist.
What fraction of patients waited for more than 7 minutes?
Frequency
10
5
5
Waiting time (a minutes)
10
P
Waiting time
(a minutes)
5< x≤6
6<257
7<#58
8< x≤9
9< x≤ 10
The fraction of the patients that have a waiting time of more than 7 minutes found by using the area under the curve is 269/312
What is a fraction in mathematics?A fraction indicates the quantitative comparison showing the number of times one quantity is contained in another quantity.
The area under the frequency curve is found as follows;
Dividing the area into composite shapes of a rectangle, triangle and trapezoid, we get;
(9.2 - 5.5) × 4 + (4 + 2)×3/2 + (2.5 + (9.2 - 5.5)) × 1/2 + (2.5 + 1.2) × 2/2 + 1.2 × 1/2 = 31.2
The area for those that have a waiting time of more than 7 minutes is therefore;
(9.2 - 5.5) × 4 + (4 + 2)×3/2 + (2.5 + (9.2 - 5.5)) × 1/2 = 26.9
The fraction that have a waiting time of more than 7 minutes is therefore;
26.9/31.2 = 269/312 ≈ 0.862
The fraction of the patients that have a waiting time of more than 7 minutes is 269/312
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F(n)= 3n -4 find term 3 of the explicit arithmetic sequence
The third term will be 5 in the explicit arithmetic sequence.
What is an arithmetic sequence?An arithmetic sequence is defined as an arrangement of numbers that is in a particular order.
The formula to find the general term of an arithmetic sequence is,
aₙ = a₁ + (n-1)d
The explicit formula of an arithmetic sequence is given in the question as:
F(n) = 3n -4 ....(i)
To determine the term 3.
Substitute the value of n = 3 in equation (i),
T₃ = 3(3) - 4
T₃ = 9 - 4
Apply the subtraction operation,
T₃ = 5
Therefore, the third term will be 5 in the explicit arithmetic sequence.
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I understand it but it won't give me the marks for explaining. What should I try?
Answer:
B is never true
Step-by-step explanation:
you can't get a negative number when you have a even power
The burner is the engine of the balloon. What is the role of a resistor in an engine?
A ballast resistor is utilized inside the ignition system of automobile engines or balloons. it acts as a resistor for the ignition ballast.
Between the main source of both the ignition coil & the coil stud, there's an ignition ballast resistor. It lowers the ignition coil's risk of failure.
An ignition ballast resistance assists in lowering the coil voltage & coil current when the generator revs the engine.
Minimal current consequently results in a low-temperature increase. Additionally, the ignition coil lives a long time as a result.
However, an ignition system requires a greater voltage that is also the same as the power source's voltage. Therefore, a resistor for the ignition ballast is connected to the jumper wire. The jumper wire additionally supplies the ignition with the necessary voltage when starting the engine.
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1. Kevin took $45 with him to spend on snack for himself and his friends at the movie theater. The price for each bucket of popcorn was $4. The price of each drink was half the price of a bucket of popcorn.
(a) Sketch the graph that represents the situation and label the intercepts. Use one axis to represent the number of buckets of popcorn and the other axis to represent the number of drinks.
(b) Explain your graph.
The equation of the relationship is 2x + 4y = 45 and the graph is attached
How to sketch the graph?From the question, we have the following parameters:
Amount = $45Price of each bucket of popcorn = $4Price of each drink = Half the price of each bucket of popcornThis means that
Price of each drink = Half $4
Evaluate
Price of each drink = $2
Represent the number of drinks with x and the number of bucket of popcorn with y
So, we have the following representation
Total amount of popcorn + Total amount of drinks = Total amount
This gives
2x + 4y = 45
Next, we sketch the graph
See attachment for the graph of the equation
The explanation of the graphThe graph is represented by a straight line
This means that it is a linear equation
Also, the graph touches the axes at (0, 11.25) and (22.5, 0)
This means that the highest number of drinks and buckets are 11.25 and 22.5 respectively
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