Answer:
2⋅(x 3 −5)
________
5
Step-by-step explanation: I hope this really help!
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "x3" was replaced by "x^3".
STEP
1
:
x3
Simplify ——
5
Equation at the end of step
1
:
x3
(2 • ——) - 2
5
STEP
2
:
Rewriting the whole as an Equivalent Fraction
2.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using 5 as the denominator :
2 2 • 5
2 = — = —————
1 5
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
Adding fractions that have a common denominator :
2.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
2x3 - (2 • 5) 2x3 - 10
————————————— = ————————
5 5
STEP
3
:
Pulling out like terms
3.1 Pull out like factors :
2x3 - 10 = 2 • (x3 - 5)
Trying to factor as a Difference of Cubes:
3.2 Factoring: x3 - 5
Theory : A difference of two perfect cubes, a3 - b3 can be factored into
(a-b) • (a2 +ab +b2)
Proof : (a-b)•(a2+ab+b2) =
a3+a2b+ab2-ba2-b2a-b3 =
a3+(a2b-ba2)+(ab2-b2a)-b3 =
a3+0+0+b3 =
a3+b3
Check : 5 is not a cube !!
Ruling : Binomial can not be factored as the difference of two perfect cubes
Polynomial Roots Calculator :
3.3 Find roots (zeroes) of : F(x) = x3 - 5
Polynomial Roots Calculator is a set of methods aimed at finding values of x for which F(x)=0
Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers x which can be expressed as the quotient of two integers
The Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient
In this case, the Leading Coefficient is 1 and the Trailing Constant is -5.
The factor(s) are:
of the Leading Coefficient : 1
of the Trailing Constant : 1 ,5
Let us test ....
P Q P/Q F(P/Q) Divisor
-1 1 -1.00 -6.00
-5 1 -5.00 -130.00
1 1 1.00 -4.00
5 1 5.00 120.00
Polynomial Roots Calculator found no rational roots
Final result :
2 • (x3 - 5)
————————————
5
Answer:
2⋅(x 3 −5)
________
5
Step-by-step explanation:
The length of a rectangle is 2 m more than twice its width. Find the length and width of the rectangle, if its perimeter is 28 m.
Please use algebra.
Answer:
Length is 10
Width is 8
Step-by-step explanation:
The formula for the perimeter of a rectangle is:
[tex]P=2l+2w[/tex]
We are told that the length l is 2 more than twice the width w. In other words:
[tex]l=2+2w[/tex]
Also, we are given that the perimeter is 28. Therefore:
[tex]P=2l+2w\\28=2(2+2w)+2w[/tex]
Distribute:
[tex]28=4+4w+2w[/tex]
Combine like terms:
[tex]28=4+6w[/tex]
Subtract 4 from both sides:
[tex]6w=24[/tex]
Divide by 6:
[tex]w=4[/tex]
So, the width is 4.
And the length is 2 more than twice the width. Thus:
[tex]l=2+2(4)\\l=2+8=10[/tex]
The length is 10.
And we are done :)
The sum of two numbers is 180. If one number is 40% more than the other, find the numbers
Answer:
We have 2 values to work with, both in terms of x. the first value is just x, our first number. The second value is 40% higher than the original.
x + (x + .4x) = 180
x + 1.4x = 180
2.4x = 180
x = 180/2.4
x = 75 1.4(75) = 105
Check:
75 * .4 = 30
75 + 30 = 105
Answer:
75, 105
Step-by-step explanation:
Let's let the two numbers be a and b.
The sum of them is 180. Thus:
[tex]a+b=180[/tex]
One of the number is 40% more than the other. In other words, let's let a be the bigger number:
[tex]a=1.4b[/tex]
Substitute this into the first equation:
[tex]1.4b+b=180[/tex]
Combine like terms:
[tex]2.4b=180[/tex]
Divide everything by 2.4:
[tex]b=75[/tex]
So, b is 75.
And their sum is 180. Thus, a is 180-75 or 105.
And we're done!
Which is the better buy, 6 bagels for $3.29 or 8 bagels for $4.15? Justify your answer by giving the cost per bagel for each offer in order to get full credit.
Answer: The better buy would be 8 bagels for $4.15
explanation: If you were to buy 6 bagels for $3.29, It would be about $.54 per bagel. but if you were to buy 8 bagels for $4.15, it is about about $.52 per bagel which makes it a better deal.
Name the sets of numbers to which
3/5
belongs
Answer:
Fractions , Rational numbers ,Real numbers
Step-by-step explanation:
-3/5 is arguably a real number
Deshaun and Isabel each have opened a savings account today. Deshaun opened her account with starting amount of $590 and she'll take out $35 each month Isabel opened here with a start of $790 and she'll take out $55 per month (A) For each account write an expression for the amount of zkids in the account after x months (B) Write an equation to show when the two accounts would have the same amount of money
Answer:
Deshaun = $590 - $35x
Isabel : $790 - $55x
$590 - $35x = $790 - $55x
Step-by-step explanation:
For Deshaun :
Amount in her account = $590
Amount she would have withdrawn by month x = $35 × x = $35x
The amount she would have in her account = $590 - $35x
For Isabel :
Amount in her account = $790
Amount she would have withdrawn by month x = $55 × x = $55x
The amount she would have in her account = $790 - $55x
Let x be the time when the money in their account would be equal =
$590 - $35x = $790 - $55x
4√2 + √2 with work
8√3 - 4√3 with work
2√3 x √32 with work
Step-by-step explanation:
4√2 + √2 = 5√2 we add 4 and the invisible 1 in front of √2, the common root stays same
8√3 - 4√3 = 4√3 subtract 4 from 8 the common root stays same
2√3 x √32 ➡ 2√3 x 4√3 too add the expressions we first need to make the roots common then add 4 and 2
Answer:
1. [tex]5\sqrt{2}[/tex]
2. [tex]4\sqrt{3}[/tex]
3. [tex]8\sqrt{6}[/tex]
Step-by-step explanation:
Number 1:
We can treat [tex]\sqrt{2}[/tex] as a variable in which we are multiplying 4 by. Let's call [tex]\sqrt{2}[/tex] x.
This makes our expression [tex]4x + x[/tex]. Combining like terms, we get [tex]5x[/tex]. This means that [tex]4\sqrt{2} + \sqrt{2} = 5\sqrt{2}[/tex].
Number 2:
Again, we can use the same logic as we did in number 1. Let's treat [tex]\sqrt{3}[/tex] as a variable y.
[tex]8y-4y[/tex]
Subtracting a y term from a y term will equal the difference between the coefficients times y. So it's [tex]4y[/tex]. This means that [tex]8\sqrt{3}-4\sqrt{3}=4\sqrt{3}[/tex]
Number 3:
When we multiply radicals, we want to put the radicals in [tex]\sqrt{x}[/tex] form.
[tex]\sqrt{32}[/tex] is already in this form.
However [tex]2\sqrt{3}[/tex] is not.
[tex]2\sqrt{3}[/tex] is the same thing as [tex]\sqrt{3\cdot2^2} = \sqrt{3\cdot4} = \sqrt{12}[/tex].
Now we multiply these radicals by multiply the term inside the square root sign
[tex]\sqrt{32}\cdot\sqrt{12}=\sqrt{32\cdot12} =\sqrt{384}[/tex]
384 is divisible by 64, so:
[tex]\sqrt{384} = \sqrt{64\cdot6} = 8\sqrt{6}[/tex]
Hope this helped!
Match the statement to the property it shows.
If MN = XY, and XY = AB, then MN = AB.
If AB = CD, then CD = AB.
Segment CD is congruent to segment CD.
Answer:
If MN = XY, and XY = AB, then MN = AB. Transitive Property
If AB = CD, then CD = AB. Symmetric Property
Segment CD is congruent to segment CD. Reflexive Property
Step-by-step explanation:
Transitive property states that for all reall numbers a, b, and c, if a = b, b = c, then a = c.
Symmetric Property states that for all real numbers a and b, if a = b, then b = a.
Reflexive Property states that for every real number a, a=a
1. Transitive property
2. Symmetric property
3. Reflexive property
What are equivalence properties ?The equivalence properties are Reflexive property, Symmetric property & Transitive property.
Reflexive Property : For every real number a, a=a
Symmetric Property : For real numbers a & b, if a=b then b=a
Transitive Property : For real numbers a, b, c, if a=b & b=c then a=c
What are the perfect matches ?1. If MN = XY, and XY = AB, then MN = AB ⇒ Transitive property
2. If AB = CD, then CD = AB ⇒ Symmetric property
3. Segment CD is congruent to segment CD ⇒ Reflexive property
Learn more about equivalence properties here :
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In a rectangular field of dimensions 20m x 15m , a triangular park is constructed. If the
dimensions of the park are 5m, 7m and 8m respectively, find the cost of levelling the
remaining field at the rate of Rs 100 per m
m?
Answer:
My answer is 28,250Rs.
Area of a triangle=1/2b×h.
1/2×7×5=17.5.
Area of a rectangle=l×b.
20×15=300.
Area of rectangle-Area of the triangle=300-17.5=282.5m^2.
If 1m^2=100Rs.
then 282.5m^2=282.5×100=28,250Rs.
Sebastien hand-crafts circular braided rugs. The graph shows the prices of various sizes of his rugs. A customer ordered 3 identical rugs for a total of $1,350. Use the graph to determine the radius of each rug in the order. (Enter numerical answer only). Please help.
The correct answer is 6 ft
Explanation:
It is known the customer bought 3 identical rugs, which means the size and radio of each rug was the same. Moreover, the total this customer paid for the rugs was $1350, which is equivalent to $450 for each rug as $1350 ÷ 3 = $450.
Besides this, the black line in the graph shows at $450 (between 400 and 500 in the y-axis) the rugs have a ratio of 6 feet, which is shown in the x-axis as these two values intersect or align to form the black line. This means a carpet with a radius of 6ft costs $450, and therefore each of the rugs the customer bought had a radius of 6ft.
4.32x+1=17.8929 Sole for x
Answer:
x = 3.91039
Step-by-step explanation:
Order of Operations: BPEMDAS
Step 1: Write out equation
4.32x + 1 = 17.8929
Step 2: Subtract 1 on both sides
4.32x = 16.8929
Step 3: Divide both sides by 4.32
x = 3.91039
6. Write 1.12 repeating as a mixed number.
Answer:
3
1 -----
25
Step-by-step explanation:
8(7x-2)=96 What is X
Answer:
x = 2
Step-by-step explanation:
8(7x-2)=96
7x-2 = 96 : 8
7x-2 = 12
7x = 12 +2
7x = 14
x = 14 : 7
x = 2
Answer:
x=2Step-by-step explanation:
[tex]8\left(7x-2\right)=96\\\\\mathrm{Divide\:both\:sides\:by\:}8\\\frac{8\left(7x-2\right)}{8}=\frac{96}{8}\\\\Simplify\\7x-2=12\\\\Add\:2\:to\:both\:sides\\7x-2+2=12+2\\\\Simplify\\7x=14\\\\\mathrm{Divide\:both\:sides\:by\:}7\\\frac{7x}{7}=\frac{14}{7}\\\\Simplify\\x=2[/tex]
Solve in fraction form.
3
Angela has 7 cups of rice and she buys another 2 cup. How much rice does Angela have in all?
Answer:
Hey there!
Angela will have 7+2, or 9 cups of rice.
Let me know if this helps :)
Answer:
7/2
Step-by-step explanation:
What is the approximate value of this square root?
Answer:
12.1
Step-by-step explanation:
To approximate this value, we simply need to know some perfect squares. We know that the value 144 is the perfect square of 12. And we know the value 169 is the perfect square of 13.
Note, that our value, 146 is far closer to 144 than to 169, so we know that we will be close to 12 as our approximation.
The distance from 144 to 146 is 2, while the distance from 169 to 146 is 23.
A rough fractional approximation can be found with 2/23 approximately 0.08.
For the solution then, our approximation of sqrt(146) ~= 12.08 ~= 12.1
Cheers.
Pick any number and add 5 to it. Find the sum of the new number and the original number. Add 5 to the sum. Divide the new sum by 2 and subtract the original number from the quotient. What is the final number?
Answer: The final number is 5
Step-by-step explanation:
Picked number: 10
STEP are all according to what you stated
10+5=15 (first sentence)
15+10=25 (second sentence)
25+5=30 (third sentence)
30÷2-10=5 (fourth sentence)
The final number is 5.
I NEED THIS ANSWER ASAP!!!! The height of tower A is 644 feet more than tower B. The two towers have a combined height of 1590 feet. What are the heights of each tower?
Answer: oop ;-;
Step-by-step explanation: We have two basic equations
A = B + 826 A is 826ft taller than B
A + B = 1516 Combined height is 1516 ft
Replace A with B+826 in 2nd equation and solve for B
B + 826 + B = 1516 Combine like terms
2B + 826 = 1516 Subtract 826 from both sides
2B = 690 Divide both sides by 2
B = 690/2
B = 345 ft
We know that A = B + 826 so you simply need to do
that addition to have the height of both towers.
You have to simplify this expression.
-2x+3-(5-6x)
Answer:
4x−2
Step-by-step explanation:
Answer:
4x -2
Step-by-step explanation:
-2x+3-(5-6x)
Distribute the minus sign
-2x+3-5+6x
-2x+6x +3-5
4x -2
What is this answer ?
Answer:
its a bit cut off can u add the whole screen pls
Step-by-step explanation:
Answer:
KL NM
Step-by-step explanation:
that is the answer
Which table represents a linear function? sorry im dumb ;w;
Answer:
Your answer is the third option
A linear function has to be added or subtracted by the same number every time. The independent variable is x and the dependent variable is y.
So for side "x" 1 is being added to each number and for side "y" is being subtracted by 2
Chocolate and peanut butter cookies are randomly chosen from a cookie jar and placed onto a plate. The first plate had four chocolate chip cookies and one peanut butter cookie. A second plate was prepared with 2 chocolate cookies and p peanut butter cookies. If the probability of drawing a chocolate cookie from each plate is 8/25, how many peanut butter cookies, P, are on the second plate?
Answer:
Step-by-step explanation:
You have r red balls, w white balls in a bag. If you keep drawing balls out of the bag until the bag now only contains balls of a single color (ie you run out of a color) what is the probability you run out of white balls first
Answer:
[tex] \frac{w}{w + r} [/tex]
Given g(x) = x2-4
Find g(-3)
Answer:
-10
Step-by-step explanation:
g(-3)=3×3 -4
=9-4
=5
Answer: 5
Step-by-step explanation:
g(x)=x²-4
g(-3)=(-3)²-4
g(-3)=9-4
g(-3)=5
Hope this helps!! :)
Please let me know if you have any question or need any further explanation
50 divided by a number y
what number sets or set does 11 belong to?
Answer:
Prime number
Step-by-step explanation:
Because it cannot be be multiplied by any other number less then it.
What is the meaning of the
word arch"
The members of a cooking club are making cakes, which they will sell at a street fair for $9 apiece. It cost $50 for a booth at the fair, and the ingredients for each cake cost $4. At some point, the club members will sell enough cakes so that their sales cover their expenditures. How much will the sales and expenditures be?
Answer:
Sales= $90
Expenditures= $90
Step-by-step explanation:
The members of a cooking club are making cakes.
The cakes will be sold at a street fair price of $9 for each cake.
It cost $50 for a booth at the fair.
The ingredients for each cake cost $4
Let y represent the number of cakes that was sold
Since the price of each cake is $9 then,
Sales = $9y
Since the booth cost $50 and ingredients cost $4 then,
Expenditures = $50 + $4y
Sales = Expenditures
9y= 50 + 4y
Collect the like terms
9y-4y= 50
5y= 50
Divide both sides by the coefficient of y which is 5
5y/5= 50/5
y= 10
Sales= 9×10
= $90
Expenditures= $50 + 4(10)
= $50+$40
= $90
Hence the sales is $90 and the expenditures is $90
An instructional video is 1.8 minutes long. How long is the video in seconds? How long is it in hours?
Answer:
108 seconds and 0.03 hours
Analyze the logical statements to fill in the missing information.
1. If a line is horizontal, then it has a slope of 0.
Hypothesis:
Conclusion:
2. A vertical line has an undefined slope.
The statement in equivalent "if-then" form would be:
Hypothesis:
Conclusion:
Answer:
1,2,2,1,2
Step-by-step explanation:
on edg
Conclusion: a slope of 0
Hypothesis: is there is a vertical lineConclusion: then it has an undefined slope.
What is Hypothesis?
A hypothesis, in a scientific context, is a testable statement about the relationship between two or more variables or a proposed explanation for some observed phenomenon.
given:
1. If a line is horizontal, then it has a slope of 0.
Hypothesis: line is horizontal
Conclusion: a slope of 0.
2. . A vertical line has an undefined slope.
Hypothesis: is there is a vertical line
Conclusion: then it has an undefined slope.
Learn more about hypothesis here:
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Isabel need to cut a square piece of wood with the area of 70 in.² approximate the size of the square round to the nearest 10th of a inch
Answer:
8.4 in by 8.4 in
Step-by-step explanation:
The area of a square is the side length squared.
Let s be the side length:
s^2 = 70
s = \sqrt(70) = 8.4 in
Laurissa rolls two number cubes, each with the numbers 1 through 6. Laurissa adds the numbers that appear on the roll Which two sums have an equal chance of occurring?
Answer:
2 and 12;
4 and 10;
5 and 9
6 and 8
Step-by-step explanation:
Given
Roll of two number cubes
Required
Determine the sums which have equal chance
Represent the sample space of both number cubes with S1 and S2
[tex]S_1 = \{1,2,3,4,5,6\}[/tex]
[tex]S_2 = \{1,2,3,4,5,6\}[/tex]
Next, get the outcome of roll two number cubes
Outcome = [tex](1,1)(1,2)(1,3)(1,4)(1,5)(1,6)\ (2,1)(2,2)(2,3)(2,4)(2,5)(2,6)\ (3,1)(3,2)(3,3)(3,4)(3,5)(3,6)[/tex][tex](4,1)(4,2)(4,3)(4,4)(4,5)(4,6)\ (5,1)(5,2)(5,3)(5,4)(5,5)(5,6)\ (6,1)(6,2)(6,3)(6,4)(6,5)(6,6)[/tex]
Next, get the sample space;[tex]S = \{2,3,4,5,6,7, 3,4,5,6,7,8, 4,5,6,7,8,9, 5,6,7,8,9,10, 6,7,8,9,10,11, 7,8,9,10,11,12\}[/tex]
Reorder from lowest to highest[tex]S = \{2,3,3,4,4,4,5,5,5,5,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,9,9,9,9,10,10,10,11,11,12 \}[/tex]
Next, form a frequency table
Sum -- Frequency
2 ---- -- 1
3 ---- -- 2
4 ---- -- 3
5 ---- -- 4
6 ---- -- 5
7 ---- -- 6
8 ----- -- 5
9 - ------ 4
10 --- -- 3
11 --- ---- 2
12 ------ 1
From the above table, we can now determine the two sums that have equal probability;
The two sums that have equal probability have the same frequency;
Hence;
2 and 12 have the same chance of occurring
4 and 10 have the same chance of occurring
5 and 9 have the same chance of occurring
6 and 8 have the same chance of occurring
Answer:
5 and 8
Step-by-step explanation: