Answer:
Assume x greater-than-or- equal-to 0 and y ... 0 StartRoot x squared y cubed EndRoot + 2 StartRoot x cubed y Superscript 4 Baseline EndRoot + x y StartRoot y EndRoot.
Step-by-step explanation:
Option (b) is correct.
The sum of given expression \sqrt{x^2y^3}+2\sqrt{x^3y^4}+xy\sqrt{y}x2y3+2x3y4+xyy is 2xy\sqrt{y}+2xy^2\sqrt{x}2xyy+2xy2x
Step-by-step explanation:
Given:Expression \sqrt{x^2y^3}+2\sqrt{x^3y^4}+xy\sqrt{y}x2y3+2x3y4+xyy
We have to find the sum of the given expression and choose the correct from the given options.
Consider the given expression \sqrt{x^2y^3}+2\sqrt{x^3y^4}+xy\sqrt{y}x2y3+2x3y4+xyy .
\sqrt{x^2y^3}x2y3 can be written as \sqrt{x^2y^2y}=xy\sqrt{y}x2y2y=xyy
Also, 2\sqrt{x^3y^4}2x3y4 can be written as 2\sqrt{x^3y^4}=2\sqrt{x^2x(y^2)^2}=2xy^2\sqrt{x}2x3y4=2x2x(y2)2=2xy2x
Now, the given expression becomes,
x2y3+2x3y4+xyy
=xy\sqrt{y}+2xy^2\sqrt{x}+xy\sqrt{y}=xyy+2xy2x+xyy .
Now, adding like term, terms having same variable with same degree.
=2xy\sqrt{y}+2xy^2\sqrt{x}=2xyy+2xy2x .
Thus, The sum of given expression \sqrt{x^2y^3}+2\sqrt{x^3y^4}+xy\sqrt{y}x2y3+2x3y4+xyy is 2xy\sqrt{y}+2xy^2\sqrt{x}2xyy+2xy2x
The x- intercepts of a parabola are (0,-6) and (0,4). The parabola crosses the y- axis at -120. Lucas said that an equation for the parabola is y=5x^2+10x-120 and that the coordinates of the vertex are (-1, -125). Do you agree or disagree? List why?
Given:
The x- intercepts of a parabola are (0,-6) and (0,4).
The parabola crosses the y- axis at -120.
Lucas said that an equation for the parabola is [tex]y=5x^2+10x-120[/tex] and that the coordinates of the vertex are (-1, -125).
To find:
Whether Lucas is correct or not.
Solution:
The x- intercepts of a parabola are (0,-6) and (0,4). It means (x+6) and (x-4) are the factors of the equation of the parabola.
[tex]y=a(x+6)(x-4)[/tex] ...(i)
The parabola crosses the y- axis at -120. It means the equation of the parabola must be true for (0,-120).
[tex]-120=a(0+6)(0-4)[/tex]
[tex]-120=a(6)(-4)[/tex]
[tex]-120=-24a[/tex]
Divide both sides by -24.
[tex]\dfrac{-120}{-24}=a[/tex]
[tex]5=a[/tex]
Substituting [tex]a=5[/tex] in (i), we get
[tex]y=5(x+6)(x-4)[/tex]
[tex]y=5(x^2+6x-4x-24)[/tex]
[tex]y=5(x^2+2x-24)[/tex]
[tex]y=5x^2+10x-120[/tex]
So, the equation of the parabola is [tex]y=5x^2+10x-120[/tex].
The vertex of a parabola [tex]f(x)=ax^2+bx+c[/tex] is:
[tex]Vertex=\left(-\dfrac{b}{2a},f(-\dfrac{b}{2a})\right)[/tex]
In the equation of the parabola, [tex]a=5,b=10,c=-120[/tex].
[tex]-\dfrac{b}{2a}=-\dfrac{10}{2(5)}[/tex]
[tex]-\dfrac{b}{2a}=-\dfrac{10}{10}[/tex]
[tex]-\dfrac{b}{2a}=-1[/tex]
Putting [tex]x=-1[/tex] in the equation of the parabola, we get
[tex]y=5(-1)^2+10(-1)-120[/tex]
[tex]y=5-10-120[/tex]
[tex]y=-125[/tex]
So, the vertex of the parabola is at point (-1,-125).
Therefore, Lucas is correct.
Find all solutions to the equation
in the interval [0, 21). Enter the
solutions in increasing order.
sin 2x = 2 sin x
x = [?],[1]
TT
Remember: sin 20 = 2 sin 0 cos 0
Answer:
[tex]x=0, \\x=\pi[/tex]
Step-by-step explanation:
Recall the trigonometric identity [tex]\sin 2x=2\sin x\cos x[/tex].
Therefore, given [tex]\sin 2x=2\sin x[/tex], rewrite the left side of the equation:
[tex]2\sin x\cos x=2\sin x[/tex]
Subtract [tex]\sin x[/tex] from both sides:
[tex]2\sin x\cos x-2\sin x=0[/tex]
Factor out [tex]2\sin x[/tex] from both terms on the left:
[tex]2\sin x(\cos x-1)=0[/tex]
We now have two cases:
[tex]\begin{cases}2\sin x=0, x=k\pi\text{ for }k\in \mathbb{Z}\\\cos x-1=0,x=k2\pi\text{ for }k\in \mathbb{Z}\end{cases}[/tex]
Since the problem stipulates that [tex]x[/tex] is in the interval [tex][0, 2\pi)[/tex], we have:
[tex]\text{For }x\in [0, 2\pi):\\\sin x=0\rightarrow \boxed{x=0, x=\pi}\\\cos x-1=0\rightarrow \boxed{x=0}[/tex]
Recall that square brackets mean inclusive and parentheses mean exclusive. Therefore, [tex]2\pi \notin [0, 2\pi)[/tex].
A solid wooden block in the shape of a rectangular prism has a length, width and height
Step-by-step explanation:
Volume of the block
[tex] = lbh[/tex]
[tex] = \frac{3}{8} \times \frac{1}{8} \times \frac{5}{8} [/tex]
[tex] = \frac{3 \times 5}{ {8}^{3} } [/tex]
[tex] = \frac{15}{512} [/tex]
The interior angles of a hexagon are in the ratio 1:2:3:4:5:9 Find the angles. This is an example of a concave hexagon. Write in an equation.
Answer:hope this helps.. please mark as brainliest.....
9514 1404 393
Answer:
30°, 60°, 90°, 120°, 150°, 270°
Step-by-step explanation:
Let x represent the smallest angle. Then the sum of angles of the hexagon is ...
x + 2x + 3x + 4x + 5x + 9x = 720°
24x = 720°
x = 30°
The angles are ...
30°, 60°, 90°, 120°, 150°, 270°
Which of the following are true statements? Check all that apply. (WILL GIVE BRAINLIEST)
A. log(M/N) = (logM)/(logN) B. logM+logN=log(MN)
C. log(M/N)=logM-logN
D. logM-logN=log(M-N)
Answer:
B and C are the correct answers
Step-by-step explanation:
Hope this helps!
The statement B and C are true according to logarithm rules.
What are logarithms?In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a number x to the base b is the exponent to which b must be raised, to produce x.
A) log(M/N) =log M/log N
Quotient rule is log (x/y)=log x-log y
So, which in not true
B) logM+logN=log(MN)
Product rule is log(xy)=logx+logy
So, the statement is ture
C) log(M/N) =log M - log N
Quotient rule is log (x/y)=log x-log y
So, the statement is ture
D) log M - log N=log(M-N)
Quotient rule is log (x/y)=log x-log y
So, which in not true
Therefore, the statement B and C are true according to logarithm rules.
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if you roll a single die and get 4 fives in a row what is the probability that you would get a 5 on the next roll
Answer
(1/6)⁴ = 1/1296
Step-by-step explanation:
robabilty of getting a 5 in a throw of dice is 1/6 . So, the required probability of getting 4 5’s in rolling a dice 4 times is (1/6)4
(a) Expand and simplify (4 + root3)(4 – root3).
Step-by-step explanation:
just use (a+b)(a-b) = [tex]a^{2} - b^{2}[/tex][tex](4+\sqrt{3}) (4-\sqrt{3)} = 4^{2} - (\sqrt{3} )^{2} = 16 - 3 = 13[/tex]
answer is 13
52.3 X 16.0 please help me thank you so much !
Answer:
836.8
Step-by-step explanation:
which equation represents a line parallel to the y-axis?
Answer:
B. x=4
Step-by-step explanation:
I hope this helps!
If ABC~ ADEF and the scale factor from AABC to A DEF is 2, what are the
lengths of DE, EF, and DF, respectively?
E
B
4
2
6
A А
A. 4, 8, 12
B. 2, 8, 12
C. 8, 16, 24
D. 1, 2, 3
Answer:
A. 4, 8, 12
Step-by-step explanation:
there is a scale factor f=2 to "go" from one triangle to the other.
that means all sides of the target triangle are created out of their corresponding side of the source triangle by multiplying them by the scale factor.
so,
2×f = 2×2 = 4
4×f = 4×2 = 8
6×f = 6×2 = 12
The lengths of DE, EF, and DF are 4, 8 and 12 respectively, (option 1)
What are similar triangles?Two triangles are said to be similar if their corresponding sides are in equal ratio and corresponding angles are congruent.
Given that, Δ ABC~ Δ DEF and the scale factor from Δ ABC to Δ DEF is 2
Since, the scale factor is 2, therefore each side of Δ ABC is increased by 2 in Δ DEF
Therefore,
DE = 2AB
EF = 2BC
DF = 2AC
Therefore,
DE = 4
EF = 8
DF = 12
Hence, the lengths of DE, EF, and DF are 4, 8 and 12 respectively, (option 1)\
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Because psychologists generally use college students as research participants, the research does NOT involve Group of answer choices random sampling. convenience sampling. confounds. random assignment.
Answer: random sampling
Step-by-step explanation:
Because psychologists generally use college students as research participants, the research does not involve random sampling.
Random sampling is when each sample has an equal chance of being selected. Since the psychologists are targeting a particular set of students, the random sampling might not be applicable in this case.
The yearly cost in dollars y, for a member at a video game arcade based on total game tokens purchased, x, is y=1/2x+6. A nonmember pays $20 per game token, but no yearly fee. Which equation represents the yearly cost for a nonmember at the same video game arcade based on the total number of game tokens purchased in a year?
Answer:
y = 20x
Step-by-step explanation:
For members
y = 1/2x + 6
Where,
y = yearly cost in dollars
x = total game tokens purchased
1/2 = cost of each game token
6 = yearly fee
For non members: without yearly fee
A nonmember pays $20 per game token
y = 20x represents the yearly cost for a nonmember at the same video game arcade based on the total number of game tokens purchased in a year
Answer:
B,C,E
Step-by-step explanation:
Got it right on Edge
This graph shows a proportional relationship.
What is the constant of proportionality?
Answer:
[tex]m = \frac{3}{4}[/tex]
Step-by-step explanation:
Given
See attachment
Required
The constant of proportionality
Select two points on the graph
[tex](x_1,y_1) = (0,0)[/tex]
[tex](x_2,y_2) = (4,3)[/tex]
So, the constant of proportionality (k) is:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{3-0}{4-0}[/tex]
[tex]m = \frac{3}{4}[/tex]
At a local Brownsville play production, 420 tickets were sold. The ticket
prices varied on the seating arrangements and cost $8, $10, or $12. The
total income from ticket sales reached $3920. If the combined number
of $8 and $10 priced tickets sold was 5 times the number of $12 tickets
sold, how many tickets of each type were sold?
Answer:
jsdcjdvnjkdnjnjdanskcbanknqnjfkrbgiyrwhgondfkv
Step-by-step explanation:
define supplementary angles
A pair of angles is known as supplementary angles when the sum of the angles is 180°
Step-by-step explanation:
Supplementary angles are those angles that measure up to 180 degrees. hope it helps.stay safe healthy and happy....7x+14
2x2 + x-6
What is the GCF
i will solve it first i need full form
Answer:
When i tried solving it, there was no GCF except for 1.
However, the GCF of the numerator is 7
I need help please!!!
Answer:
40 degrees
Step-by-step explanation:
What is the coefficient of x^3 in the expansion of (2x−3)^5?
Help please!!
Answer:
1....................
Answer:
1Step-by-step explanation:
COEFFICIENT....
justbrainlyuser
Instructions: Problem 3 ! Find the missing angle in the image below. Do not include spaces in your answers
Answer:
155
Step-by-step explanation:
first add 72 and 83 = 155. Then use 180-155=25. then subtract 25 from 180.
Estimate the difference 5,290-436
Answer:
it will be
=> 4854
Step-by-step explanation:
hope it's helpful for you xd
Evaluate
-2 x 3/12 x 5/10 x 7/15
[tex]\displaystyle\Large \boldsymbol -2 \cdot \frac{3}{12} \cdot \frac{5}{10} \cdot \frac{7}{15} =-2 \cdot \frac{3 \!\!\!\!\diagup \cdot1}{3 \!\!\!\!\diagup\cdot 4} \cdot \frac{5 \!\!\!\!\diagup\cdot 1}{5 \!\!\!\!\diagup\cdot 2} \cdot \frac{7}{15} =\\\\\\-\frac{2 \!\!\!\!\diagup\cdot 7 }{2 \!\!\!\!\diagup\cdot 4 \cdot 15} =\boxed{-\frac{7}{60}}[/tex]
what is the quotient of 3/4 ÷ 5/12
Answer:
1 4/5
Step-by-step explanation:
3/4 ÷ 5 /12
Copy dot flip
3/4 * 12/5
Rewriting
3/5 * 12/4
3/5 * 3
9/5
1 4/5
The amount of potential energy, P, an object has is equal to the product of its mass, m, its height off the ground, h, and the gravitational constant, g. This can be modeled by the equation P = mgh.
What is the equivalent equation solved for h?
StartFraction StartFraction p Over m EndFraction Over g EndFraction equals h. = h
StartFraction p Over m g EndFraction equals h.= h
Pmg = h
StartFraction p Over StartFraction m Over p EndFraction EndFraction equals h. = h
The equivalent equation solved for h is [tex]\frac{P}{mg} = h[/tex]
Subject of FormulaFrom the question, we are to determine the equivalent equation solved for h
From the given information,
The amount of potential energy, P, is modeled by the equation
P = mgh
To determine the equivalent equation solved for h, we will make h the subject of the equation,
From,
P = mgh
Divide both sides of the equation by mg
That is,
[tex]\frac{P}{mg} = \frac{mgh}{mg}[/tex]
∴ [tex]\frac{P}{mg} = h[/tex]
Hence, the equivalent equation solved for h is [tex]\frac{P}{mg} = h[/tex]
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Answer
B
Step-by-step explanation:
Edge 2022
what is the slope of the line shown below?
Johan published a monthly poetry magazine. In March he printed 1400 copies of magazine. In April he increased his print run by 15%
Answer:
1610
Step-by-step explanation:
Answer:
1610
Step-by-step explanation:
you can easily get the solution without a calculator:
1400
+ 140 (+10%)
+ 70 (+5%)
= 1400 + 210
which equation is represented by the table
Answer:
B. b=3a+2
Step-by-step explanation:
I just substituted all of the a values in and I got the b values.
Answer:
Your answer is B, b = 3a+2
Step-by-step explanation:
for example:
3(2) + 2 = 8
Insert a number from column a into the variable and it will come out as the number in column b if it's the correct equation.
What is the answer for this question
i think the answer is c :)
Answer:
(C.) sqrt(75)
Step-by-step explanation:
the simplification looks like this
1. 5 * sqrt( 3 )
2. sqrt(5 * 5 * 3)
3. sqrt(25 * 3)
4. sqrt(75)
How many numbers? How many numbers are there from 421 to 430? How many numbers are there from 567 to 573? How many numbers are there from 890 to 898?
what method you used to find out the numbers between one number and another
Answer:
9,6,8 but if you mean like all the numbers its infinite because you can add decimals and the number will never end
What is the domain of the function on the graph?
•all real numbers
•all real numbers greater than or equal to -2
•all real numbers greater than or equal to -5
•all real numbers greater than or equal to 0
Answer:
all real numbers
Step-by-step explanation:
got it right
Answer:
A
Step-by-step explanation:
it is all real numbers
brainiest please
Find the slope between the points (−3,−5) and (10,-5)
. Enter DNE if the slope between the points is undefined.
Answer:
0
Step-by-step explanation:
[tex] m = \dfrac{y_2 - y_1}{x_2 - x_1} [/tex]
[tex] m = \dfrac{-5 - (-5)}{-3 - 10} [/tex]
[tex] m = \dfrac{0}{-13} [/tex]
[tex] m = 0 [/tex]
from -3 to 10 are 13 steps to the right and from -5 to -5 0 steps up or down.
devide the steps up by the steps to the right
0 / 13 = 0
in this case it's obvious, but I hope you see the method how to do this. you would normally get a more interesting fraction as a slope.
