Answer:
9x³y²
Step-by-step explanation:
To simplify, factorize 81 in powers of 2 ; x⁶ in powers of 2 and y² in powers of 2.
[tex]\sf \sqrt{81x^6y^2}=\sqrt{9^2 * x^{3*2}*y^2}[/tex]
[tex]\sf = \sqrt{9^2* (x^3)^2)* y^2}\\\\ = 9 * x^3*y^2\\\\=9x^3y^2[/tex]
Multiply. Write your answer in simplest form.
√5• √18
The answer to the question is 3√10.
The concept used here is radical expressions
Radicals, like fractions, are often simplified till you have got the littlest attainable elements.
Be conscious of what numbers square measurewithin the unconventional sign and that square measure not! Unless you'll be able to take the rootof the individual prime numbers, they have to stay beneath the unconventional.The same methodworks for variables beneath the unconventional.
On multiplying 5 and 18 we get expression as -√90
90 can be rewritten as 9×10
9 can further be written as 3²
On simplifying we get √9×10
Since 9 is the square root of 3 we can take 3 outside the square root sign.
So the final answer is 3√10.
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2x−y+2z=−6−3y+z=−22x−3z=4
Enter your answer, in the form (x,y,z), in the boxes in simplest terms.
Answer:
1/2
Step-by-step explanation:
Point Form:
(
3
4
,
−
2
,
1
2
)
Equation Form:
x
=
3
4
,
y
=
−
2
,
z
=
1
2
Given a∥b , and c is not parallel to a or b, which statements must be true? Select each correct answer. Responses m∠1=m∠5 the measure of angle 1 equals the measure of angle 5 m∠5=m∠12 the measure of angle 5 equals the measure of angle 12 m∠4=m∠5 the measure of angle 4 equals the measure of angle 5 m∠7=m∠11
The correct answers of the statement are as follows;
m∠1=m∠5 the measure of angle 1 equals the measure of angle 5m∠4=m∠5 the measure of angle 4 equals the measure of angle 5How to find angles in parallel lines?Line a and b area parallel lines.
c is not parallel to a or b.
When parallel lines are cut by a transversal, angle relationships are formed. The angle relationship includes corresponding angles, alternate angles, vertically opposite angles etc.
Therefore, let's select the correct answer in the options.
m∠1 = m∠5
Therefore, the measure of angle 1 is equals to the measure of angle 5 because they are corresponding angles.
m∠4 = m∠5
Therefore, the measure of angle 4 is equals to the measure of angle 5 because they are alternate angles.
Hence, the correct answers of the statement are as follows;
m∠1=m∠5 the measure of angle 1 equals the measure of angle 5m∠4=m∠5 the measure of angle 4 equals the measure of angle 5learn more on parallel lines and angles here: https://brainly.com/question/11546031
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Can someone please help i don’t understand at all :/
Using the Segment Addition Postulate, considering the congruent segments and the trisection, the missing lengths of the segments are given by the following items:
CH = 4.HI = 4.ID = 4.CB = 12.AC = 6.AE = 12.A to F = 4.GE = 4.FB = 8.DG = 8.What is the segment addition postulate?The segment addition postulate is a geometry axiom that states that a line segment, divided into a number of smaller segments, has the length given by the sum of the lengths of the segments.
For this problem, two other concepts are important, given by the bullet points below:
Congruence: Congruent segments have the same length.Trisection: A trisection of a segment divides the segment into three segments of equal lengths.CD = 12, hence, considering the trisection: (12/3) = 4.
CH = 4.HI = 4.ID = 4.CD is also congruent to CB, hence:
CB = 12.
CE = 6, and AE = 2CE, hence:
AC = 6.AE = 12.Due to the postulate, since DG = 8 and GE = 12, and the entire lengths are of 12, and considering the congruence:
A to F = 4.GE = 4.FB = 8.DG = 8.More can be learned about the segment addition postulate at https://brainly.com/question/2134445
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Zack is planting a garden
that is in the shape of a triangle. The
base of the triangle is 12 feet and the
height is 11 feet. What is the area of
the garden?
Carolyn and Gershon are competing to see who can raise the most money for cancer research. Carolyn’s parents gave her $100, and she raised $15 a day. Gershon’s parents gave him $50, and he raised $15 a day. If they continued at the same rate, who won the contest?
Carolyn will win the contest as the money raised by her is more than the money raised by Gershon.
We are given that:
For Carolyn:
Money given by parents = $ 100
Money she raises every day = $ 15
For Gershon:
Money given by parents = $ 50
Money he raises every day = $ 15
Let the number of days a contest lasts be x.
So, the equations for both will be:
For Carolyn:
100 + 15 x
For Gershon:
50 + 15 x
By comparing, we get that:
Money raised by Carolyn > Money raised by Gershon.
Therefore, we get that, Carolyn will win the contest as the money raised by her is more than the money raised by Gershon.
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what is the answer to -5 - (-9) =
Answer: 4
Step-by-step explanation:
= Multiply -1 by -9 to change 9 to a positive number
= Add -5 to 9 (-5 + 9 = 4)
= 4
Which expression is equivalent to
√81/100
A. √9/10
B. 9/10
C. 9/50
D. 9√10/10
===================================================
Work Shown:
[tex]\sqrt{\frac{81}{100}}\\\\\\\frac{\sqrt{81}}{\sqrt{100}}\\\\\\\frac{\sqrt{9^2}}{\sqrt{10^2}}\\\\\\\frac{9}{10}\\\\\\[/tex]
Therefore, [tex]\sqrt{\frac{81}{100}}=\frac{9}{10}\\\\\\[/tex]
--------------------
Explanation:
I broke up the single square root to make a fraction of square roots. Then I rewrote 81 as 9^2, and 100 as 10^2. This is so the square roots cancel out with the squares.
The general rule is that [tex]\sqrt{\text{x}^2} = \text{x} \ \text{ , where x} \ge 0[/tex]
5. The sequence of numbers below is missing the
fourth value. Which of the following is the form
of the missing value in its lowest terms?
3/11, 6/16,9/21,__, 15/31, 18/36
a. 12/25
b. 4/13
c 6/13
d. 1/2
E.7/26
Answer: A i think
Step-by-step explanation:
Please answer this question.
Answer:
I have attached as an image. Kindly check.
Step-by-step explanation:
Simplify each expression. (16)³/₄
The simplified expression is 8
To find the simplified form of the mentioned expression, we will first simplify the value in bracket. Then, multiply the powers to solve it.
As per the known fact, 4² and 2⁴ result to give the number 16.
Expression = (2⁴)³/₄
Now, again as per the known fact, the exponents can be multiplied.
Exponents = 4×(3/4)
Cancelling 4 as it is common in both numerator and denominator
Exponents = 3
Putting the resultant exponent back to the expression -
Expression = 2³
Taking cube -
Expression = 2×2×2
Performing multiplication
Expression = 8
Hence, the simplified form of expression is 8
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(x+y) 4
Binomial expansion
The binomial expansion for ( X + Y )⁴ is X⁴ + 4 X³(Y) + 6 X²(Y²) + 4 XY³ + Y⁴.
Use the binomial expansion theorem to find each term. The binomial theorem states ( a + b )ⁿ = ⁿ∑ _{k = 0} n C k ⋅ ( a^(n - k) × b^{k} ) .
⁴∑ _{k = 0} = ( 4 ! / [ ( 4 − k ) ! k ! ] ) × ( X )^{4 - k} × ( Y )^{k}
Expanding the summation.
( X + Y )⁴ = ( 4! / ( 4 − 0 )! 0! ) × ( X )⁴⁻⁰ × ( Y )⁰ + ( 4! /( 4 − 1 )! 1! ) × ( X )⁴⁻¹ × ( Y )¹ + ( 4! / ( 4 − 2 )! 2! ) × ( X )⁴ ⁻ ² × ( Y )² + ( 4! /( 4 − 3 )! 3! ) × ( X )⁴ ⁻ ³ × ( Y )³ + 4! / ( 4 − 4 )! 4! × ( X )⁴ ⁻ ⁴ × ( Y )⁴
Simplify the exponents for each term of the expansion.
( X + Y )⁴ = 1 × ( X )⁴ × ( Y )⁰ + 4 × ( X )³ × ( Y )¹ + 6 × ( X )² × ( Y )² + 4 × ( X )¹ × ( Y )³ + 1 × ( X )⁰ × ( Y )⁴
Therefore,
( X + Y )⁴ = X⁴ + 4 X³ (Y) + 6 X² (Y²) + 4 X Y³ + Y⁴
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if -12r+16= -8 what is the value of r
Answer:
r = 2
Step-by-step explanation:
-12r + 16 = -8
Subtract 16 from both sides to isolate the r term.
-12r + 16 - 16 = -8 - 16
-12r = -24
Divide both sides by negative twelve.
-12r/-12 = -24/-12
Solve.
r = 2
Answer:
r=2
Step-by-step explanation:
sub 16 frome each side: -12r=-24
divide both sides by -12: r=2
would have made it more detailed but im lazy rn, have a good day
Find the slope of the following graph and write your result in the empty box
Answer:
The slope is 2.
Step-by-step explanation:
You can use the slope formula or pick two points, count up from one point then to the right. Use rise/run if you use the counting method.
The slope formula is y2-y1/x2-x1
Use the points (20, 20) and (30, 40)
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Hope this helps!
Please mark as brainliest if correct!
PLS HELP WHY NOBODY ANSWERING ME ?
Answer:
10×5.6=56 5.6×10=56
Step-by-step explanation:
apple trees 10× 5.6 acres of land = 56 apple trees
Do y’all need any help
Answer:
Yes
Step-by-step explanation:
Math, due tomorrow and i can't find the rate of enlargement of my dilation in transformation....
Part A
Write - 1/33 as a decimal.
Answer:
0.030303...
Step-by-step explanation:
i put the dots because this is a repeating decimal
Answer:
0.03030303030303.
PLEASE HELP ME ASAP
Answer:
[tex] \sf \: x ≤ \frac{11}{6} \: or \: x> \frac{11}{3} [/tex]
Step-by-step explanation:
First question
6x-2≤9
Step 1: Add 2 to both sides.
6x−2+2≤9+2
6x≤11
Step 2: Divide both sides by 6.
6x/6 ≤ 11/6
x≤11/6
Second question
4+3x>15
Step 1: Simplify both sides of the inequality.
3x+4>15
Step 2: Subtract 4 from both sides.
3x+4−4>15−4
3x>11
Step 3: Divide both sides by 3.
3x/3 > 11/3
x> 11/3
I need help with this don’t bs please
Answer: download the app photo math and rewrite your equation and replace your variables with your numbers so the app can understand it. then just take a pic with it on the app and it will give you the answer. its a super useful app!
Step-by-step explanation:
Solve by factoring. Check your answers. x²=5 x+14
The factoring of the expression x² = 5 x + 14 is (x+2)(x-7)
By ordering the values, we get:
x²- 5x - 14 = 0
To solve this exercise, we have to follow the rules of factoring:
1. Looking for the a and b number that state the following equations:
a + b = -5a * b = -14Analyzing that (a*b) is a negative number, it means that (a) and (b) have different signs, and due to the results of (a+b) is negative the higher number has to be the negative one.
The number could be:
a = 2
b = -7
Confirming:
a + b = 2 + (-7) = -5
a * b = 2 * (-7) = -14
2. Rewriting the factored expression (x+a)(x+b) with the obtained values, we get:
(x+2)(x-7)
What is factoring?Is a technique that consist of decomposition of a factor into a product of another factor, which when multiplied together give the original number.
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Rio has 3/4 liters of milk. He uses 1/3 of the milk to make tea. How much milk does Rio use for the tea?
Answer:
5/12
I'm assuming this means how much milk is left because it tells how much milk was used in the question
Step-by-step explanation:
Convert to common denominator and you get 9/12 of milk - 4/12 of milk and you get 5/12
A classmate writes the matrix at the right to represent a system and says that the solution is x=2, y=0. Explain your classmate's error and describe how to correct it.
A classmate writes the matrix at the right to represent a system and says that the solution is x = 2, y = 0. Classmate's error and how to describe it is mentioned as follows:
Given:
x = 2
y = 0
From this we can say that The second row of the matrix doesn't have a coefficient in the y column. The equation represented by second row is 0 = 0 and not y = 0.
Thus it is concluded that the equation represented by second row is 0 = 0 not y = 0.
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3
4
14. Vincent found a recipe for banana
macadamia nut bread that uses cup
of macadamia nuts. If he wants to make
only half of the recipe, how many cups of
macadamia nuts should Vincent use?s was
We'll use 3/8 cup of macadamia nuts.
Describe ratios.
A ratio is defined as a/b where b is not equal to 0. Since a and b are separate portions of the two values, the total combined amount is expressed as (a + b).
Given:
3/4 cup of macadamia nuts are used in a banana macadamia nut bread recipe that Vincent created. We are aware of this based on the information provided.
The quantity of nuts needed if he decides to make only half the recipe is:
used macadamia nuts = 1/2 * 3/4
used macadamia nuts =3/8
Therefore, there will be 3/8cup of Macadamia nuts utilized.
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The correct question is given below
"Vincent found a recipe for banana macadamia nut bread that uses 3/4 cup of macadamia nuts. If he only wants to make half the recipe, how many cups of macadamia nuts should be use?"
Solve each equation. Round to the nearest ten-thousandth. Check your answers.
5-3x=-40
After solving the equation, x = 15 is the value of x in 5-3x = -40 .
⇒ 5 - 3x = -40
⇒ - 3x = -40-5
⇒ - 3x = -45
⇒ 3x = 45
⇒ x = 45/3
⇒ x = 15
How to solve an equation?To solve linear equations, utilize the steps that are provided below.
Remove parentheses from each side of the equation and combine similar terms to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.The common denominator can be multiplied by each side of the equation to eliminate fractions.Lets take an example of solve z for 7z – (3z – 4) = 12
Here is no multiplication or division, so this will be easy to solve
⇒ 7z – (3z – 4) = 12
⇒ 7z – 3z + 4 = 12
⇒ 4z = 12 – 4
⇒ 4z = 8
⇒ z = 8/4
⇒ z = 2
See, that was so simple, using the mentioned methods, every linear equation can be solved easily.
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anyone know the answer?
alexander and sophia are selling books alexander has sold 3/8 of the 48 books that he started with sophia has sold 5/7 of the 38 books the she started with
Based on the fraction of their books that they have sold, the number of books that Alexander is left with is 30 books and the number of books that Sophia is left with is 11 books.
How many books are left?Alexander has sold 3/8 of the 48 books and so to find the number of books left, the formula is:
= 48 - (3/8 x 48 books)
= 48 - 18
= 30 books
The number of books that Sophia is left with is:
= 38 - (5/7 x 38)
= 38 - 27
= 11 books
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if the diameter of a circle is 18 feet, which is closest to the circumference
If the diameter of the circle is 18 feet, the circumference of the circle is 56.55 feet.
The circumference of a circle or ellipse in geometry is its perimeter. That is, if the circle were opened up and straightened out to a line segment, the circumference would be the length of the arc.
The diameter of a circle is 18 feet.
D = 18 feet
Now, the radius of the circle is half the diameter of the circle.
Therefore,
Diameter = 2 × Radius
Radius = Diameter / 2
D = 2r
r = D / 2
r = 18 feet / 2
r = 9 feet
Now, the circumference of a circle is given as:
Circumference = π × diameter
Circumference = π × 2r
Circumference = 2πr
Circumference = 2 × π × 9 feet
Circumference = 2 × 3.14159 × 9
Circumference = 56.55 feet
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pls help with this question attached
The value of equation P (x) = [tex]2[/tex] + [tex]\frac{x}{2}[/tex] + [tex]x^{2}[/tex] - [tex]\frac{x^{2} }{3}[/tex] when x = (-1) is P(-1) = [tex]\frac{13}{6}[/tex]
P (x) = [tex]2[/tex] + [tex]\frac{x}{2}[/tex] + [tex]x^{2}[/tex] - [tex]\frac{x^{2} }{3}[/tex]
If the value of x = -1
P (-1) = 2 + [tex]\frac{-1}{2}[/tex] + [tex](-1)^{2}[/tex] - [tex]\frac{(-1)^{2} }{3}[/tex]
P (-1) = 2 - [tex]\frac{1}{2}[/tex] + 1 - [tex]\frac{1}{3}[/tex]
The above equation consist of fractional numbers as well as the whole numbers to therefore it is not possible to apply the operations in this particular conditions.
Equation is statement which equates two algebraic expressions.On taking LCM for the denominators of the fractional numbers (2 , 3), we get 6 as the Least Common Multiple.
To apply the sum and difference operation, we need to make the denominators of all the terms same.
[tex]2 * \frac{6}{6} = \frac{12}{6}[/tex][tex]\frac{1}{2} * \frac{3}{3} = \frac{3}{6}[/tex][tex]1 * \frac{6}{6} = \frac{6}{6}[/tex][tex]\frac{1}{3} * \frac{2}{2} = \frac{2}{6}[/tex]P (-1) = [tex]\frac{12}{6} - \frac{3}{6} + \frac{6}{6} - \frac{2}{6}[/tex]
P (-1) = [tex]\frac{12-3+6-2}{6}[/tex]
P (-1) = [tex]\frac{13}{6}[/tex]
Value of the equation P when 'x' is replaced by (-1) will be [tex]\frac{13}{6}[/tex]
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which is a true statement? y=6x+3 the slope is 6 and the point passes through (-2,-9)__x+3=12 the slope is 1/3 the point passes through (-3,5)___ 4x-5y=35 the slope is 4/5 the point passes through (-3,5)__y=-2x-4 the slope is -2 the point passes through (-1,-6)
Answer:
y=6x+3
Step-by-step explanation:
Draw it on a graph, then use rise over run, 6/1 and you get 6.
Solve each equation. If necessary, round to the nearest ten-thousandth. log x²=2
The solution of the given equation by rounding off it to the nearest ten-thousandth is 2.7182.
What is a round-off of the digit?
In mathematics, a round-off is defined as an approximation of the given number to a fewer number of significant digits by taking into consideration some rules.
For eg: 13.58 ~ 13.6
Solving the given equation: log x² = 2
We are given a logarithmic expression: log x² = 2 —- 1
We know that log x² = 2 log x and log (ab) = log a + log b
Using in equation 1, we have,
2 log x = 2
log x = 1
Using exponential on both sides, we have
e^(log x) = e^1
x = e
x = 2.7182
Hence, the solution of the given equation rounded off to the nearest ten-thousandth is 2.7182.
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