Equivalent expressions are expressions that have the same value, and can be used interchangeably.
The result of the sum [tex]2 (\sqrt[3]{16x^3y}) + 4 (\sqrt[3]{54x^6y^5})[/tex] is [tex]4x\sqrt[3]{2y} + 8x^2y\sqrt[3]{2y^2})[/tex]
The expression is given as:
[tex]2 (\sqrt[3]{16x^3y}) + 4 (\sqrt[3]{54x^6y^5})[/tex]
Rewrite the expression as:
[tex]2 (\sqrt[3]{16x^3y}) + 4 (\sqrt[3]{54x^6y^5}) = 2 (\sqrt[3]{2^4x^3y}) + 4 (\sqrt[3]{3^3 \times 2x^6y^5})[/tex]
Evaluate the roots
[tex]2 (\sqrt[3]{16x^3y}) + 4 (\sqrt[3]{54x^6y^5}) = 2 (2x\sqrt[3]{2y}) + 4 (3x^2y\sqrt[3]{2y^2})[/tex]
Open the brackets
[tex]2 (\sqrt[3]{16x^3y}) + 4 (\sqrt[3]{54x^6y^5}) = 4x\sqrt[3]{2y} + 12x^2y\sqrt[3]{2y^2})[/tex]
The above expression cannot be further simplified.
Hence, the result of the sum [tex]2 (\sqrt[3]{16x^3y}) + 4 (\sqrt[3]{54x^6y^5})[/tex] is [tex]4x\sqrt[3]{2y} + 8x^2y\sqrt[3]{2y^2})[/tex]
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The sum of the expression is [tex]4 (\sqrt[3]{x^3y} +12x^2y(\sqrt[3]{ 2 y^2})\\[/tex].
We have to determine, the sum of the given expression.
According to the question,
Expression; [tex]2(\sqrt[3]{16x^3y} +4(\sqrt[3]{56x^6y^5})[/tex]
To determine the sum of the given expression following all the steps given below.
Rewrite the expression term in the form of their cubes,
[tex]\rm = 2(\sqrt[3]{16x^3y} +4(\sqrt[3]{56x^6y^5})\\\\ = 2(\sqrt[3]{2^4x^3y} +4(\sqrt[3]{3^3 \times 2 \times x^6y^5})\\\\= 2\times 2(\sqrt[3]{x^3y} +4\times 3(\sqrt[3]{ 2 \times x^6y^5})\\\\= 4 (\sqrt[3]{x^3y} +12x^2y(\sqrt[3]{ 2 y^2})\\\\=4 (\sqrt[3]{x^3y} +12x^2y(\sqrt[3]{ 2 y^2})\\[/tex]
Hence, The sum of the expression is [tex]4 (\sqrt[3]{x^3y} +12x^2y(\sqrt[3]{ 2 y^2})\\[/tex].
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The function D(t) defines a traveler’s distance from home, in miles, as a function of time, in hours. D(t) = StartLayout enlarged left-brace 1st Row 1st column 300 t 125 , 2nd column 0 less-than-or-equal-to t less-than 2. 5 2nd Row 1st column 880, 2nd column 2. 5 less-than-or-equal-to t less-than-or-equal-to 3. 5 3rd Row 1st column 75 t 612. 5, 2nd column 3. 5 less-than t less-than-or-equal-to 6 EndLayout Which times and distances are represented by the function? Select three options. The starting distance, at 0 hours, is 300 miles. At 2 hours, the traveler is 725 miles from home. At 2. 5 hours, the traveler is 875 miles from home. At 3 hours, the distance is constant, at 880 miles. The total distance from home after 6 hours is 1,062. 5 miles.
The distance in given time t is determined by substituting the value of time and solving the equation.
At 2 hours, the traveler is 725 miles from home.
At 3 hours, the distance is constant, at 880 miles.
The total distance from home after 6 hours is 1,062.5 miles.
Given that,
The function D(t) defines a traveler’s distance from home, in miles, as a function of time, in hours.
D(t) = 300t + 125
We have to determine,
Which times and distances are represented by the function?
According to the question,
The function D(t) defines a traveler’s distance from home, in miles, as a function of time, in hours.
D(t) = 300t + 1251. The starting distance at 0 hours is ;
At [tex]0 \leq t < 2.5[/tex]
Then,
[tex]\rm D(t) = 300t + 125 ;\\\\\ D(0) = 300(0) + 125 = 125 \ miles[/tex]
The starting distance, at 0 hours, is 125 miles.
2. The distance at 2 hours is,
[tex]\rm D(t) = 300t + 125 ;\\\\\ D(2) = 300(2) + 125\\\\ D(2) =600+125\\\\ D(2) = 725 \ miles[/tex]
At 2 hours, the traveler is 725 miles from home.
3. The distance at t = 2.5 hours is,
At 2.5 ≤ t ≤ 3.5
D(2.5) = 880 miles (Fixed)
At 2.5 hours, the traveler is 880 miles from home.
4. The distance at t = 3 hours is,
2.5 ≤ t ≤ 2.5
D(3) = 880 miles
At 3 hours, the distance is constant, at 880 miles.
5. The distance at t = 6 hours is,
3.5 < t ≤ 6
[tex]\rm D(t) = 300t + 125 ;\\\\\ D (6)= 75(6) + 612.5\\\\ D(6) = 450 + 612.5\\\\D(6) = 1062.5 miles[/tex]
The total distance from home after 6 hours is 1,062.5 miles.
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please I need help immediately
Answer:
Step-by-step explanation:
4x+6<= -54
4x <= -60
x <= -15 [The point -15 is included, so it must be a solid dot]
----------------
5x + 7 > -18
5x > -25
x > -5 [The point -5 is NOT included, so it should be an empty dot.]
Solution C seems the best.
Nathan uses ¼ cup of water for every ½ cup of lemon juice to make lemonade. Enter the number of cups of water Nathan uses for 1 cup of lemon juice. LEAVE THE UNITS OFF, JUST WRITE THE NUMBER.
I think it should be 1/2 cup water. Sorry if I'm wrong
Find the perimeter of the figure below, in centimeters.
Answer
64.8
Step-by-step explanation:
brainliest pls
Answer:
64.8 cm.
Step-by-step explanation:
Add up the sides:
Perimeter = 2(8.7) + 2(5.5) + 2(5.5) + 2(10.8) + 2(1.9)
= 17.4 + 11 + 11 + 21.6 + 3.8
= 64.8 cm.
write 9^3 x 27^2 as a single power of 3
Answer:
3^12
Step-by-step explanation:
9³=(3²)³=3^6
27²=(3³)²=3^6
So together, it is 3^12
Answer:
3^12
Step-by-step explanation:
9^3 x 27^2
Rewrite 9 as 3^2 and 27 as 3^3
3^2^3 * 3^3^2
We know that a^b^c = a^(b*c)
3^(2*3) * 3^(3*2)
3^6 * 3^6
We know that a^b * a^c = a^(b+c)
3^(6+6)
3^12
Can someone help me understand this pls? (Provide an explanation)
Question:
Is triangle AFD congruent to triangle BEC?
Answer: is not congruent
To be congruent, it has to be same size and shape. It can face in any directions. Both the shapes have to be equal in all side lengths and equal angles.
Looking at the triangle you can understand that it is not congruent as the triangles have a size difference of being big and small. But if you still desire detailed explanation then here:
There is four rules for a triangle to be congruent. If one of these rule matches then you can say the triangle is congruent.
1. The three sides are equal
2. Two angles are the same and a corresponding side is the same
3. Two sides are equal and the angle between the two sides is equal
4. Two angles are equal and the side between them is equal
There are no angles, so find if all the three sides are equal. Even if one side is not equal, you can say it is not congruent. So if you just measure any side length of the smaller and big triangle, the length is not equal. None of the side lengths in either of the triangle is equal.
A cell phone company charges a 20$ flat fee plus $0.05 for every minute used for calls
Answer:
In both the cases, the given total amount is given as:
T = 10 + 0.05 m (when minutes talked m < 600)
T = 40 + 0.15 k (when minutes talked k > 600)
Step-by-step explanation:
What are the coordinates of the point on the directed line segment from (-4,-1) to (6,4) that partitions the segment into a ratio of 3 to 2?
Using proportions, it is found that the coordinates of the desired point are (2,2).
The first point is A(-4, -1).The second point is B(6, 4).The desired point is C(x,y).The point C partitions the segment AB into a ratio of 3 to 2, hence:
[tex]C - A = \frac{3}{5}(B - A)[/tex]
This proportion is applied using both the x and y coordinates of the points, hence:
[tex]x - (-4) = \frac{3}{5}[6 - (-4)][/tex]
[tex]x + 4 = 6[/tex]
[tex]x = 2[/tex]
[tex]y - (-1) = \frac{3}{5}[4 - (-1)][/tex]
[tex]y + 1 = 3[/tex]
[tex]y = 2[/tex]
The coordinates of the desired point are (2,2).
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Joseph invests money in an account paying a simple interest of 2.9% per year. If he invests $60 and no money will be added or removed from the investment, how much will he have in one year, in dollars and cents?
Nikita began with the figure shown.
A.
B
She completed the following actions to construct the angle bisector of ZABC, but made a mistake in one of the steps. Select the step in which
her mistake was made.
Step 1: She placed the compass on point B and drew an arc which intersects ray BA at point D and ray BC at point E.
Step 2: Next, she placed the compass on point D and drew an arc on the interior of ZABC.
Step 3: Then, she placed the compass on point C and drew an arc on the interior of ZABC, which intersects the previous arc.
Step 4: She labeled the intersection of the two arcs as point F and drew the ray BF, which represents the angle bisector
of ZABC.
The angles formed by the angle bisector BF are ∠FBA and ∠FBC.
The step in which the mistake was made is step 3; Then, she placed the compass on point C and drew an arc on the interior of ∠ABC which intersects the previous arc.
Reasons:
The steps to draw an angle bisector are;
Place the compass at the vertex of the angle and draw an arc intersecting the the two rays forming the angle at points D and E
Place the compass at point D and draw an interior arc to the given angle
Place the compass at point E and draw a second interior arc intersecting the previous arc
The point of intersection of the two arcs can be labelled F and joined to the vertex of the given angle to complete the angle bisection
Therefore, the step in which the mistake was made is; Step 3 where the compass is placed at point C rather than point E to draw the second arc of the angle bisector
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Answer:
Step three
Step-by-step explanation:
she placed the point on C when it was supposed to be on E
Pls help peeps would be appreciated
Answer:
A.
Because it has it two sides equal
What three consecutive numbers add up to 75?
Answer:
24,25,26
Step-by-step explanation:
Answer:24, 25, 26
Step-by-step explanation:
Divide the 75 by 3 because that is how many numbers you need. Then subtract 1 to get 24, add 1 to get 26, and also use 25.
Which statement about f ( x ) = x 2 + 5 x − 84 is true?
Answer:
It is False
Step-by-step explanation:
Calculate the slope of the following points. (0, 4) and (5, 9). Show all work.
Answer:
1
Step-by-step explanation:
Subtract the y values and put them in the numerator (top of fraction). 9-4=5.
Subtract the x values and put them in the denominator (bottom) 5-0=5.
Put the numbers in the fraction and simplify. 5/5 = 1.
Write an equation of a line that is perpendicular to the given line and passes through the given point.
y = 6x - 7
(12,-4)
• y = 6x +5
• y = -6x-5
• y = -1/6 x + 6
•y = -1/6 - 2
Answer:
• y = -6x-5
Step-by-step explanation:
Find the value of x, y, and z, in the rhombus below.
Answer:
x = 19, y = -7, z = -18
Step-by-step explanation:
Since its a rhombus and 1 side = 29, all sides = 29. Just solve each side.
2x - 9 = 29
2x = 38
x = 19
-3y + 8 = 29
-3y = 21
y = -7
-2z - 7 = 29
-2z = 36
z = -18
The value of the variables x, y, and z will be 19, -7, and -18, respectively.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
All the sides of the rhombus are congruent with each other.
Then the equations are given below.
2x - 9 = 29
-3y + 8 = 29
-2z - 7 = 29
Simplify the first equation, then we have
2x - 9 = 29
2x = 38
x = 19
Simplify the second equation, then we have
-3y + 8 = 29
3y = - 21
y = -7
Simplify the third equation, then we have
-2z - 7 = 29
2z = - 36
z = - 18
The value of the variables x, y, and z will be 19, -7, and -18, respectively.
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Which congruence criteria is met in the following scenario?
SAS
SSS
None, because SSA is not a triangle congruence criteria.
ASA
AAS
None, because SSA is not a triangle congruence theorem.
Draw the graph of y= -6
Answer:
See attachment.
Step-by-step explanation:
PLZ HELP
If a triangle has one interior angle measuring 102°, what is a possible pair of measurements for the other two
interior angles?
Answer:
39
Step-by-step explanation:
There is a possibility that this triangle is isosceles. Angles in triangles add up to 180. 102-180=78. Since we are assuming this triangle is isosceles, we can just divide 78 by 2 and get 39 which might be the other two angles. They might both be 39 degrees.
Since triangle angles must add up to 180 degrees, the other angles must add up to 78 degrees. One possible pair could be if you divided 78 in half, which is 39. There could also be tons of more I can provide a list of below:
39,39
40,38
35,43
Write an explicit formula for a_nth term of the sequence 18, 6, 2, ...
Answer:
Step-by-step explanation:
Evaluate -1 - [-z] where z = -2
[tex]\huge\textbf{Hey there!}[/tex]
[tex]\huge\textsf{-1 - [-z]}\\\\\huge\textsf{= -1 - [- -2]}\\\\\huge\textsf{= -1 - - 2}\\\\\huge\textsf{= -1 + (-2)}\\\\\huge\textsf{= -1 - 2}\\\\\huge\textsf{= -3}\\\\\\\huge\textbf{Therefore, your answer is: \boxed{\mathsf{-3}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Answer:
-3
Step-by-step explanation:
Evaluate - 1 - ( - z ) where z = -2
you can find this out because when there are two minuses by each other it equals a positive but then z = -2 so that adds another minus so it narrows it down to -1+-2 which equals 3
Please help, super hard question for me!
Give two systems of equations, each containing two equations, that would be easier to solve by substitution than by elimination. Then give two systems that would be easier to solve with elimination. Finally, explain how you decide whether to use elimination or substitution to solve a system.
I will give brainliest to best answer
AND DON’T ANSWER THEN DELETE FOR POINTS
Answer:
Step-by-step explanation:
When using the substitution method we use the fact that if two expressions y and x are of equal value x=y, then x may replace y or vice versa in another expression without changing the value of the expression.
Solve the systems of equations using the substitution method
{y=2x+4
{y=3x+2
We substitute the y in the top equation with the expression for the second equation:
2x+4 = 3x+2
4−2 = 3x−2
2=== = x
To determine the y-value, we may proceed by inserting our x-value in any of the equations. We select the first equation:
y= 2x + 4
We plug in x=2 and get
y= 2⋅2+4 = 8
The elimination method requires us to add or subtract the equations in order to eliminate either x or y, often one may not proceed with the addition directly without first multiplying either the first or second equation by some value.
Example:
2x−2y = 8
x+y = 1
We now wish to add the two equations but it will not result in either x or y being eliminated. Therefore we must multiply the second equation by 2 on both sides and get:
2x−2y = 8
2x+2y = 2
Now we attempt to add our system of equations. We commence with the x-terms on the left, and the y-terms thereafter and finally with the numbers on the right side:
(2x+2x) + (−2y+2y) = 8+2
The y-terms have now been eliminated and we now have an equation with only one variable:
4x = 10
x= 10/4 =2.5
Thereafter, in order to determine the y-value we insert x=2.5 in one of the equations. We select the first:
2⋅2.5−2y = 8
5−8 = 2y
−3 =2y
−3/2 =y
y =-1.5
Answer:
1. No, because a system of linear equations in two variables may have, zero, or infinietley solutions.
2. true because the answer of a system is the intersect, not where the lines cross a grid.
3.a. y=2x+4
y=3x+2
2x+4=3x+2
4-2=3x-2
2=x
b.y=2x+4
y=2*2+4=8
c. 2.2.5-2y=8
5-8=2y
=3=2y
-3/2=y
y=1.5
Step-by-step explanation:
answers for teh complete assigment
Select an the correct answers.
Which two tables represent the same function?
Answer:
4th is right
Step-by-step explanation:
fourth is right, x + 8 = y
you have it correct
How do you write 750% as a fraction or mixed number
Answer:
750/100 or 7 1/2 whichever way u need
Step-by-step explanation:
A sequence of numbers is shown below :
1 5 9 13 17
explain why 95 will not be a term in this sequence
Answer:
95 is not a term here as the next verse should be 98 as it is a 94 term in this pattern
95 will not be a term in the sequence 1, 5, 9, 13, 17, ....., as the value of n for the nth term is not integer.
What is arithmetic sequence ?An ordered group of numbers with a shared difference between each succeeding word is known as an arithmetic sequence.
The given sequence of numbers is,
1, 5, 9, 13, 17, .....
The first term of the given sequence a₁ =1,
From the given sequence, the common difference pair of two consecutive terms d = 4,
Let nth term of the sequence aₙ= 95,
By arithmetic sequence formula,
aₙ = a₁ + (n-1).d
Substitute the value of aₙ and d,
95 = 1 + (n-1).4
94 = (n-1). 4
(n-1) = 23.5
n = 24.5
The value of n can't be decimal, so 95 can't be a term of the given sequence.
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Is this triangle a right triangle? Explain.
Answer:
hmm
Step-by-step explanation:
I can't see any triangle there..a right angled triangle is meant to look like this
What is m<1?
60
120
66
114
Answer:
60 Is the correct answer
Answer:
114
Step-by-step explanation:
all angles of a triangle add up to 180
180-80-34 = 66
66 is the angle right next to 1
180 degrees will be the product of both of those angles
180-66 = 114
114 degrees
help me out plzzzzzz
Answer:
A=4, B=3, C=2, D=7 or A=2, B=7, C=4, D=3
Step-by-step explanation:
To factor this, you are looking for factors of 8×21 = 168 that have a sum of 34.
168 = 1×168 = 2×84 = 3×56 = 4×42 = 6×28 = 7×24 = 8×21 = 12×14
The sums of these factor pairs are 169, 86, 59, 46, 34, 31, 29, 26. The factor pair whose sum is 34 is 6×28. This means we can rewrite the expression as ...
8x² +28x +6x +21
Factoring by pairs gives ...
4x(2x +7) +3(2x +7)
(4x +3)(2x +7) ⇒ A=4, B=3, C=2, D=7 or A=2, B=7, C=4, D=3
Answer:
......................
Y=x2+3x+1
when х= 5, y=?
Answer:
y = 41
Step-by-step explanation:
Substitute x = 5 into the equation
y = 5² + 3(5) + 1 = 25 + 15 + 1 = 41
simplify: 2x^2+15x-30
A= 2x^2
B= 15x
C= -30
(x-5)(x-6)
I dunno, its my question, just answering it for fun