==================================================
Work Shown:
width = w
length = w+9
perimeter = 2*(length + width)
P = 2(w+9+w)
P = 2(2w+9)
P = 4w+18
4w+18 = P
4w+18 = 270
4w = 270 - 18
4w = 252
w = 252/4
w = 63 meters is the width
w+9 = 63+9 = 72 meters is the length
Check:
perimeter = 2*(length + width)
perimeter = 2*(72 + 63)
perimeter = 2*(135)
perimeter = 270
The answer is confirmed.
The age of a father is three times that of his son. In ten year's time their ages will add up to 68 years. If the son is x years old today write down an algebraic expression for: the present age of the father and the son's age in ten year's time and the father's age in 10 year's time.
Answer:
46 and 22
Step-by-step explanation:
let the father b (f) and d son is (s)
so
f=3s.....(1)
(f+10) +(s+10)=68 .... (2)
substitute f=3s in equation (2)
we have
(3s+10)+(s+10)=68
4s+20=68
4s=68-20
4s=48
s=12 .......(3)
substitute (3) in (1)
f=3*12
which f=36
in 10 year time
f+10 =46
s+10=22
PLEASE HELP IM STUCK
Answer: 45
Step-by-step explanation: Given the way the formula is formatted, the first term is 1. The common difference can be found by subtracting a number from the number that follows (ex. 3-2 or 4-3), therefore it's 1. The desired term is what you're trying to find so 44-1=43. When you put it all together, the formula should be 2+1(44-1) which equals 45 when you follow the rules of PEMDAS.
A sample of disinfecting bleach shows a density of 9.4 lb/gal. If 100 pounds of bleach is required for disinfection, how many gallons must be applied
the number of gallons that must be applied is 94 gallons.
What is density?Density is simply defined as the ratio of the mass to the volume occupied by an object or substance.
It is denoted with rho, 'ρ'
The formula for density is given as;
Density = mass/ volume
From the information given, we have that
density = 9.4 lb/galmass = 100 pounds volume is unknownTo determine the volume, we need to make it the subject from the formula
Volume = density × mass
Volume = [tex]\frac{9. 4}{100}[/tex]
Volume = 0. 094
The number of gallons is given as;
= Volume × 1000
= 0. 094 × 1000
= 94 gallons
Thus, the number of gallons that must be applied is 94 gallons.
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Rounding off 6 400mm
The rounding off a given number implies approximating the number to the required value. Thus the answer to the given question is 6 000 mm.
Rounding off a given number implies approximating the number to the required value. This can be done in two major ways: rounding up or rounding down.
Rounding up implies considering the required digit if it is up to or greater than 5, which turns to 1. Rounding down requires no consideration of digits less than 5 which turns to 0.
Thus considering the given question, Since the second digit is 4 which is lesser than 5, then it turns to a zero. So that;
rounding off 6 400 mm would give 6 000 mm.
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assuming that no denominator equals zero, what is the simplest form of x+2/ x^2 +5x+6 divided by 3x+1/x^2-9
Answer:
Step-by-step explanation:
Build Your Math Skills 2B, Round decimals to the nearest hundredth (0.01): 1223.075
Answer: 1223.07
Step-by-step explanation: you don't round up
A dealer buys oranges for 100000, he sold 60% of them for buying price, he sold 50% of the remaining for profit of 60% then he sold the remaining for a loss of 10%. Find the overall profit
Based on the amount of oranges bought, those sold at a profit and those sold at a loss, the overall profit is 14.2%
What is the overall profit?Assume that the buying price was $1 each.
The amount earned from 60% of them is:
= 60% x 100,000 x 1
= $60,000
The profit from selling 50% of the remaining is:
= (50% x 40,000) x 1.60
= $32,000
The loss from selling the other 50%:
= (50% x 40,000) x 0.90
= $22,222.22
Total selling price:
= 60,000 + 32,000 + 22,222.22
= $114,222.22
Total profit:
= (114,222.22 - 100,000) / 100,000
= 14.2%
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According to USA Today, the average cost of a private university is $50,000 with a population standard deviation of $2,500. 100 universities are randomly selected and the average income of those 100 universities was $49,450. Using the 5 step hypothesis testing process, can you support the claim that the average cost of private universities are decreasing? Use a .01 significance level. (Use the z or t value of -2.2) What is your conclusion based on p-value?
Using the z-distribution, it is found that since the p-value is less than 0.05, there is evidence to support the claim that the average cost of private universities are decreasing.
What are the hypothesis tested?At the null hypothesis, it is tested if the average cost is still of $50,000, that is:
[tex]H_0: \mu = 50000[/tex]
At the alternative hypothesis, it is tested if the average cost is decreasing, that is:
[tex]H_1: \mu < 50000[/tex]
What is the test statistic?The test statistic is:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.[tex]\sigma[/tex] is the standard deviation of the population.n is the sample size.The parameters for this problem are:
[tex]\overline{x} = 49450, \mu = 50000, \sigma = 2500, n = 100[/tex]
Hence:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{49450 - 50000}{\frac{2500}{\sqrt{100}}}[/tex]
z = -2.2.
What is the p-value and the conclusion?Using a z-distribution calculator, for a left-tailed test, as we are testing if the mean is less than a value, with z = -2.2, the p-value is of 0.0139.
Since the p-value is less than 0.05, there is evidence to support the claim that the average cost of private universities are decreasing.
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The table represents the amount of storage space, in megabytes, used by music files on Zayd’s computer.
A 2-column table with 5 rows titled Zayd's Music Storage. The first column is labeled Number of Files with entries 10, 20, 30, 40, 50. The second column is labeled Space Used (Megabits) with entries 15, 30, 45, 60, 75.
Which statement best describes the relationship between storage space and number of music files?
As the number of files remains constant, the storage space used decreases.
As the number of files remains constant, the storage space used increases.
As the number of files increases, the storage space used decreases.
As the number of files increases, the storage space used increases.
Answer:
As the number of files increases, the storage space used increases.
Find the extremum of f(x,y) subject to the given constraint, and state whether it is a maximum or a minimum. f(x,y)=xy; 6x y=
There is a maximum value of 6 located at (x, y) = (1, 6).
The function given to us is f(x, y) = xy.
The constraint given to us is 6x + y = 12.
Rearranging the constraint, we get:
6x + y = 12,
or, y = 12 - 6x.
Substituting this in the function, we get:
f(x, y) = xy,
or, f(x) = x(12 - 6x) = 12x - 6x².
To find the extremum, we differentiate this, with respect to x, and equate that to 0.
f'(x) = 12 - 12x ... (i)
Equating to 0, we get:
12 - 12x = 0,
or, 12x = 12,
or, x = 1.
Differentiating (i), with respect to x again, we get:
f''(x) = -12, which is less than 0, showing f(x) is maximum at x = 1.
The value of y, when x = 1 is,
y = 12 - 6x,
or, y = 12 - 6*1 = 6.
The value of f(x, y) when (x, y) = (1, 6) is,
f(x, y) = xy,
or, f(x, y) = 1*6 = 6.
Thus, there is a maximum value of 6 located at (x, y) = (1, 6).
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The provided question is incomplete. The complete question is:
"Find the extremum of f(x, y) subject to the given constraint, and state whether it is a maximum or a minimum. f(x, y)=xy; 6x+y=12.
Given: y varies directly with x and has a constant rate of change of 7. when the value of y is 12, then the value of x would be _____.
Answer:X=12/7
Step-by-step explanation:
Y [tex]\alpha[/tex] X
⇒Y=KX
Where K is the constant
From the question,k=7
⇒ When Y=12,
y=KX
12=7X
X=12/7
Sasha solved an equation, as shown below:
Step 1: 8x = 56
Step 2: x = 56 – 8
Step 3: x = 48
Part A: Is Sasha's solution correct or incorrect? If the solution is incorrect, explain why it is incorrect and show the correct steps to solve the equation. (6 points)
Part B: How many solutions does this equation have? (4 points)
I know part A, but what about Part B?
Part A: Sasha's solution of the equation incorrect. The solution x = 7.
Part B: The equation have They are unique solutions.
According to the question,
Sasha solved an equation, as shown below:
Step 1: 8x = 56
Step 2: x = 56 – 8
Step 3: x = 48
Step 2 is incorrect, the correct steps to find x, we would divide both sides by 8 so,
8 / 8x = 8 / 56
x = 7.
An equation can have infinitely many solutions only if the system of an equation has infinitely many solutions when the two lines are coincident, and they have the same y-intercept. If the two lines have the same y-intercept and the slope, they are actually in the same exact line. Then the have infinitely many solutions.
But, the given equation have unique solutions. Thus, x=7.
Hence, Part A: Sasha's solution incorrect. The solution x = 7.
Part B: They are unique solutions solutions.
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Which of the following equations have complex roots?
A. 3x^2-1=6x
B. 3x^2+2=0
C. 2x^2-1=5x
D. 2x^x+1=7x
Answer: B
Step-by-step explanation:
We can rearrange the equation to get [tex]x^2=-\frac{2}{3}[/tex], which clearly has complex roots.
Amanda increased the amount of protein she eats every day from 48 g to 54 g. what percentage did Amanda increase the amount of protein she eats
Step-by-step explanation:
I just answered this. how often did you post that question ?
she added 54-48 = 6g.
how many % of 48g are these 6g ?
100% = 48
1% = 100%/100 = 48/100 = 0.48g
how many % are 6g ?
as many as how often 1% (0.48g) fits into 6g :
6 / 0.48 = 12.5%
What type of quadrilateral is created by the points:
L (-5,4), M (2,2), N (0,-3), S (-7,-1)
Given same lengths and slopes of the opposite sides and nature of the angle between adjacent sides, we have;
The type of quadrilateral is a parallelogram How can the type of quadrilateral be found?The given points are;
L(-5, 4), M(2, 2), N(0, -3), S(-7, -1)
Lengths of the sides are;
Length of LM = √((2-(-5))²+(2-4)²) ≈ √(53)
Length of MN = √((2-0)²+(2-(-3))²) ≈ √(29)
Length of NS = √((0-(-7))²+((-3)-(-1))²) ≈ √(53)
Length of LS = √(((-7)-(-5))²+((-1)-4)²) ≈ √(29)
Therefore;
The lengths of opposite sides are the same.Slope of LM = (2-4)/(2-(-5)) = -2/7
Slope of MN = (2-(-3))/(0-2) = 5/2
Slope of NS = ((-3)-(-1))/(0-(-7)) = -2/7
Slope of LS = ((-1)-4)/(-7-(-5)) = 5/2
Therefore;
The opposite sides are parallel, and The the adjacent sides are not perpendicularThe quadrilateral created by the points L(-5, 4), M(2, 2), N(0, -3), S(-7, -1) is therefore;
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Help me, 50 pts, I'll give brainliest, *take your time answering if you need *
1. how many groups of 5/7 are in 1
2. 8 divided by 5/7
3. The tape diagram shows that Ehecatl's hair, which is now 12cm long is 60% as long as it was before his haircut.
Complete the table to show different percentages of Ehecatl's hair length before the haircut. (table is the file)
There are 1.40 groups of 5/7 in 1.
8 divided by 5/7 is 11 1/5.
Here is the completed table:
Length (cm) Percentage
12 60% of Ehecatl's old hair
4 20% of Ehecatl's old hair
20 100% of Ehecatl's old hair
How do we carry out division?Division is the process of grouping a number into equal parts using another number. The sign used to denote division is ÷. Division is one of the basic mathematical operations.
In order to determine how many groups of 5/7 are in 1, divide 1 by 5/7
1 ÷ 5/7
1 x 7/5 = 7/5 = 1.40
8 ÷ 5/7
8 x 7/5
= 56 / 5
= 11 1/5
What are the lengths of Ehecatl's hair ?
The first step is to determine the length of her hair before she cut it
Length of the hair before it was cut = new length / 60%
12 / 0.6 = 20
60% x 20 = 12cm
20% x 20 = 4cm
100% x 20 = 20cm
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given the graph of the function f(x)=1/x2 write the equation g(x)
horizontal compression by 1/5
vertical stretch by a factor of 7
reflection in y-axis
translation 10 units left and 1 unit down
Answer:g(x)
Step-by-step explanation:1/5 g (x)
40 cm³ of water is poured into an empty measuring cylinder. A stone of mass 129g is put into the cylinder. If the density of the mixture of the stone is 8.6g/cm³, find the new reading of the cylinder.
Step-by-step explanation:
I assume the measuring cylinder measures the cm³ of its normally liquid content.
because for anything else we would need more information about the dimensions of the cylinder.
and so, originally the cylinder shows 40 cm³.
after dropping the stone in, how many cm³ of water is the cylinder then showing ?
let's first mention some facts we are going to use :
water weighs 1 kg (1000 g) per liter.
and 1 liter fits exactly into a cube of
10 cm × 10 cm × 10 cm = 1000 cm³
so, 1 cm³ water weighs exactly 1 g and has therefore a density of 1 g / cm³.
the stone has a density of 8.6 g / cm³, is therefore heavier than water and sinks (and replaces water correspondingly).
how many cm³ does the stone have (and replaces water) ?
well, it has 129 g, and 8.6 g of the stone fill a cm³.
so, it has
129 / 8.6 = 15 cm³
therefore, as these 15 cm³ of stone replace 15 cm³ of water, this is the same as putting 40 + 15 = 55 cm³ of water into the measuring cylinder.
and the cylinder reads now 55 cm³.
FYI : but there is still only 40 cm³ of water in there.
this is actually used to calculate the density of objects (by first weighing and then dropping them into the water to see how much water they replace).
Answer: 55 cm³.
Step-by-step explanation:
[tex]\displaystyle\\m_{stone}=129\ g\ \ \ \ \ \rho_{stone}=8,6\ \frac{g}{cm^3} \ \ \ \ \ V_{water}=40\ cm^3\ \ \ \ \ V=?.\\ \boxed {\rho=\frac{m}{V} }\\V=\frac{m}{\rho} \\V=V_{water}+V_{stone}\\V_{stone}=\frac{m_{stone}}{\rho_{stone}} \\V_{stone}=\frac{129}{8,6}\\V_{stone }=15\ cm^3.\\V=40+15\\V=55\ cm^3.[/tex]
hey can you help me with this one ?
Answer:
[tex]a = 8[/tex] or [tex]a = -\frac{14}{3}[/tex]
Step-by-step explanation:
[tex]13(a+4)+24(a+5) = 3(a^{2} +9a+20)[/tex]
[tex]3a^{2} -10a-112=0[/tex]
[tex](3a+14)(a-8)=0[/tex]
[tex]a = 8[/tex] or [tex]a = -\frac{14}{3}[/tex]
[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
[tex]\qquad \sf \dashrightarrow \: \cfrac{13}{a + 5} + \cfrac{24}{a + 4} = 3[/tex]
[tex]\qquad \sf \dashrightarrow \: \cfrac{13(a + 4) + 24(a + 5)}{(a + 5)(a + 4)} = 3[/tex]
[tex]\qquad \sf \dashrightarrow \: \cfrac{13a + 52+ 24a + 120}{a {}^{2} + 5a + 4a + 20} = 3[/tex]
[tex]\qquad \sf \dashrightarrow \: \cfrac{ 37a + 172}{a {}^{2} +9a + 20} = 3[/tex]
[tex]\qquad \sf \dashrightarrow \: 3( {a }^{2} + 9a + 20) = 37a + 172[/tex]
[tex]\qquad \sf \dashrightarrow \: 3 {a}^{2} + 27a + 60 = 37a + 172[/tex]
[tex]\qquad \sf \dashrightarrow \: 3 {a}^{2} + 27a - 37a + 60 - 172 = 0[/tex]
[tex]\qquad \sf \dashrightarrow \: 3 {a}^{2} - 10a - 112= 0[/tex]
[tex]\qquad \sf \dashrightarrow \: 3 {a}^{2} - 24a + 14a - 112 = 0[/tex]
[tex]\qquad \sf \dashrightarrow \: 3a(a - 8) + 14(a - 8) = 0[/tex]
[tex]\qquad \sf \dashrightarrow \: (a - 8) + (3a + 14) = 0[/tex]
So, required values of " a " are :
[tex]\qquad \sf \dashrightarrow \: a = 8 \: \: \: or \: \: \: a = - \cfrac{ 14}{3} [/tex]
Julie spent 6 hours on the phone in 2 days. How many hours will she spend on the phone in a week?
The model of a trinomial is shown.
An algebra tile configuration. 0 tiles are in the Factor 1 spot and 0 tiles are in the Factor 2 spot. 24 tiles are in the Product spot: 1 is labeled + x squared, 7 are labeled negative x, the 2 tiles below + x squared are labeled + x, and the 14 tiles below the negative x tiles are labeled negative.
What are the factors of the trinomial? Select two options.
x – 14
x + 7
x – 7
x – 2
x + 2
The factors of the trinomial based on the information given include:
C. x – 7
E. x + 2
What is a trinomial?It should be noted that a trinomial is an algebraic expression that has three non-zero terms. Here, the examples of a trinomial expression: x + y + z is a trinomial in three variables x, y and z. Also, 2a² + 5a + 7 is a trinomial in one variables.
In this case, the algebra tile configuration has 0 tiles are in the Factor 1 spot and 0 tiles are in the Factor 2 spot. 24 tiles are in the Product spot: 1 is labeled + x squared, 7 are labeled negative x. Here, the trinomial is x² - 5x - 14.
The factors will be:
x² - 5x - 14.
x² + 2x - 7x - 14
x(x + 2) - 7(x + 2)
= (x + 2)(x - 7)
A polynomial with three terms is called a trinomial.
In conclusion, the correct options are C and E.
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Solve the following initial value problem.
d²s
dt²
= -36cos(6t+n), s'(0) = 100, s(0) = 0
S=
(Type an exact answer, using * as needed.)
For starters,
[tex]\cos(6t+\pi) = \cos(6t) \cos(\pi) - \sin(6t) \sin(\pi) = -\cos(6t)[/tex]
Now by the fundamental theorem of calculus, integrating both sides gives
[tex]\displaystyle \frac{ds}{dt} = s'(0) + \int_0^t 36 \cos(6u) \, du = 100 + 6 \sin(6t)[/tex]
Integrating again, we get
[tex]\displaystyle s(t) = s(0) + \int_0^t (100 + 6\sin(6u)) \, du = \boxed{100t - \cos(6t) + 1}[/tex]
Alternatively, you can work with antiderivatives, then find the particular constants of integration later using the initial values.
[tex]\displaystyle \int \frac{d^2s}{dt^2} \, dt = \int 36\cos(6t) \, dt \implies \frac{ds}{dt} = 6\sin(6t) + C_1[/tex]
[tex]\displaystyle \int \frac{ds}{dt} \, dt = \int (6\sin(6t) + C_1) \, dt \implies s(t) = -\cos(6t) + C_1t + C_2[/tex]
Now,
[tex]s(0) = 0 \implies 0 = -1 + C_2 \implies C_2 = 1[/tex]
and
[tex]s'(0) = 100 \implies 100 = 0 + C_1 \implies C_1 = 100[/tex]
Then the particular solution to the IVP is
[tex]s(t) = -\cos(6t) + 100t + 1[/tex]
just as before.
How much work can a 500 w Electric mixer do in 2.5 minutes
Answer:
Work(W)=7.5*10⁴J
Step-by-step explanation:
Greetings !
[tex]firstly \: recall \: the \: work \: power \: equation \\ w = pt \\ substitute \: known \: variables \: to \: the \: equation \\ w = (500)(150) \\ change \: 2.5min \: to \: second = 150second \\ solve \: for \: work \\ w = 7.5 \times 10 {}^{4} j[/tex]
400 people were surveyed for this grab how many more people prefer vanilla than do strawberry
Using proportions, it is found that 68 more people prefer vanilla than do strawberry.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
Researching this problem on the internet, it is found that, out of 400 people:
35% preferred vanilla.18% preferred strawberry.Hence the amounts are:
V = 0.35 x 400 = 140.S = 0.18 x 400 = 72.The difference is:
140 - 72 = 68.
68 more people prefer vanilla than do strawberry.
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Name the rule for this sequence.
27, 21, 15, 9, 3,...
A) divide the previous term by 0.06
B) divide the previous term by 0.6
C) add 6 from the previous term
D) subtract 6 from the previous term
Answer:
D) subtract 6 from the previous term
Step-by-step explanation:
27-6=21, 21-6=15, 15-6=9, and 9-6=3
What is the equilibrium expression for the reaction below?
N₂(g) +
3H₂(g)2NH₂(g)
OA.
B.
OC.
OD.
3 [N₂] [H₂]
2 [NH]
[NH₂7²2
[N₂][H₂]
[NH₂]
[N₂] [H₂]
[N₂] + 3 [H₂]
2[NH₂]
The equilibrium expression is written as [NH3]^2/[N2] [H2]^3.
What is equilibrium constant?A reaction involves the conversion of reactants to products. Now we know that the number that shows us the extent to which we can convert the reactants to products is given by the equilibrium constant. If the equilibrium constant is large and positive, then the reaction tends towards the conversion of reactants to products. on the other hand, when the reaction has a small equilibrium constant, then the reaction tends towards the reactants.
Thus, the magnitude of the equilibrium constant tells us how easily reactants are converted into products and this is necessary when we are trying to predict the direction in which a reaction will go or make calculations.
Given a reaction; N₂(g) + 3H₂(g) ----> 2NH3(g) we can now write the expression for the equilibrium of the reaction as;
K = [NH3]^2/[N2] [H2]^3
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One rectangular solid with a square base has twice the height of another rectangular solid with a square base with the same side length. which statements about the two rectangular solids are true? check all that apply.
The correct statements about the solids are:
(A) The bases are congruent.(D)The volume of the first solid is twice as much as the volume of the second solid.(E) If the dimensions of the second solid are x by x by h, the first solid has 4xh more.What are solids?Solid geometry or stereometry is the standard name for the geometry of three-dimensional Euclidean spaces in mathematics. Stereometry is concerned with the volume measurements of various solid forms, such as pyramids, prisms, and other polyhedrons; cylinders; cones; truncated cones, and balls bordered by spheres.To find which statements are correct:
Congruent base: This is used to indicate that the triangles' bases are the same and that they have the same shape.
The volume of the first triangle is: [tex]2x^{2} h[/tex]
The volume of the second triangle is: [tex]x^{2} h[/tex]
Therefore, the correct statements about the solids are:
(A) The bases are congruent.(D)The volume of the first solid is twice as much as the volume of the second solid.(E) If the dimensions of the second solid are x by x by h, the first solid has 4xh more.Know more about solids here:
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The complete question is given below:
One rectangular solid with a square base has twice the height of another rectangular solid with a square base with the same side length. Which statements about the two rectangular solids are true? Check all that apply.
A) The bases are congruent.
B) The solids are similar.
C) The ratio of the volumes of the first solid to the second solid is 8:1.
D)The volume of the first solid is twice as much as the volume of the second solid.
E) If the dimensions of the second solid are x by x by h, the first solid has 4xh more
surface area than the second solid.
Which choice is equivalent to the expression below?
5x√2-3√2+x√2
Answer:
You did not list any choices but if you simplify that the answer is 6√2x-3√2
Step-by-step explanation:
If they want you to factor it instead of simplifying the answer is 3√2(2x-1)
Answer:
[tex]6x\sqrt{2} - 3\sqrt{2}[/tex]
Step-by-step explanation:
So you haven't provided any options, but I'm assuming they want it in most simplified form.
To do this, we simply combine like terms, and in this case you can see the [tex]\sqrt{2}[/tex] as a variable, if it makes it easier to think about why we can combine terms. So just like how we can do: [tex]2y + y = 3y[/tex] we can do the same thing here, since sqrt(2) constant and it's in each expression.
So if it makes a bit easier to represent, I'll rewrite the equation such that sqrt(2) = y
[tex]5xy-3y+xy[/tex]
So in here, think of y as the variable and the 5x, -3, and x as the coefficients.
In doing this we can combine the terms by adding them, since they all have the same "variable" (sqrt(2))
[tex](5x-3+x)y[/tex]
Simplify this expression to get
[tex](6x-3)y[/tex]
Now just plug the sqrt(2) back in as y and you get the expression
[tex](6x-3)\sqrt{2}[/tex]
Since we can't combine the 6x and -3 in any way, we we can just distribute this back into the sqrt(2)
[tex]6x\sqrt{2} - 3\sqrt{2}[/tex]
What is the end behavior of the function f of x equals negative 4 times the cube root of x? as x → –[infinity], f(x) → –[infinity], and as x → [infinity], f(x) → [infinity]. as x → –[infinity], f(x) → [infinity], and as x → [infinity], f(x) → –[infinity]. as x → –[infinity], f(x) → 0, and as x → [infinity], f(x) → 0. as x → 0, f(x) → –[infinity], and as x → [infinity], f(x) → 0.
The end behavior of the function is as:
as →∞, f(x)→+∞ and as x→-∞, f(x)→+∞
What is end behavior?The x-axis "endpoints" of a function's graph are referred to as its "end behavior" in this context.
How do determine the end behavior of a function?choosing the polynomial function's greatest degree. The highest degree term will dominate the graph since it will expand more quickly than the other terms as x gets very big or very small.
Function f(x)=2∛x has the following graph:
The behavior of the function at its conclusion is because it leads to infinity.
as x→∞, f(x)→+∞ and as x→-∞, f(x)→+∞
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A pyramid has the same volume as a cube of side 10.0 cm
The height of the pyramid is the same as the side of the square base
Calculate the height of the pyramid
Textbook says the answer is 14.4 cm but i don't understand how
Please explain with step by step explanation
The height of the pyramid is 14.4 cm.
How to find the height of the pyramid?volume of a pyramid = 1 / 3 Bh
where
B = base areah = height of the pyramidTherefore,
volume of the cube = L³
where
L = side length of the cubeHence,
volume of the cube = 10³
volume of the cube = 1000 cm³
The volume of the pyramid is the same with the volume of the cube.
Hence,
1000 = 1 / 3 Bh
The height of the pyramid is the same as the square base.
Therefore,
1000 = 1 / 3 (h²)h
1000 = 1 / 3 h³
cross multiply
3000 = h³
h = ∛3000
h = 14.4224957031
Hence, the height of the pyramid is 14.4 cm.
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