This is my question. These are the options below, does anyone know the simplest form?
Answers
Answer:
B. [tex]2ab^5\sqrt{2ab}[/tex]
Step-by-step explanation:
To simplify, first, simplify the integers. The integers include the number 8. To simplify 8, find out what is the largest perfect square that is a factor of 8. In this case, that is 4. Then, divide 8 by that number. This equals [tex]\sqrt{4} *\sqrt{2}[/tex]. Since the square root of 4 is 2, it can be taken out of under the radical. So, the new expression is [tex]2\sqrt{2a^3b^11}[/tex].
Next, simplify the exponents. To simplify exponents under a radical divide the exponent by the root. For example, 3 divided by 2 is 1 with a remainder of 1. So, take the answer out from under the radical and then leave the remainder in the radical. This looks like[tex]\sqrt{a^3} = a\sqrt{a}[/tex]. Then, do this for the other variable, [tex]\sqrt{b^11} = b^5\sqrt{b}[/tex]. Finally, put everything for the final answer, [tex]2ab^5\sqrt{2ab}[/tex].
Related Questions
Which expression is equivalent to 2(14x-3y+28+12.2-5y-17.5)
Answers
Answer:
28x-16y+45.4
Step-by-step explanation:
Add up all the variables inside the bracket by first grouping like terms
Then, multiply through by 2 ✅✅
really need help to do step by step
Answers
8. x = -32
Step-by-step explanation:
1/4x + 10 = 2
Step 1. Subtract 10 from both sides
1/4x = -8
Step 2. Solve for x
Since we’re trying to isolate the variable, convert 1/4 to a decimal
1/4 = 0.25
Then solve for x
x = -8/0.25
x = -32
Answer:
x/4+10=2
x/4=2-10
x/4=-8
x=-8 x 4
x=-32
Step-by-step explanation:
what is twelve less than a variable
Answers
Answer:
x-12
Step-by-step explanation:
Let the variable be x
12 less than
x-12
X-12
all I've found is 1 but how do I work that out properly beaides guess and check
Answers
Answer:
1
Step-by-step explanation:
(1-x)/x=0
or, 1-x=0
or, -x=-1
or, x=1
Answer:
F(x) = 0 when x=1
Step-by-step explanation:
We need the numerator to equal zero
1-x = 0
Add x to each side
1-x+x = 0+x
1 =x
The denominator cannot equal zero( The denominator does not equal zero when x =1)
F(x) = 0 when x=1
Algebra 1
Simplify 9) y(x + 4) - 6(x + 4)
Answers
Answer:
[tex]xy+4y-6x-24[/tex]
Step-by-step explanation:
[tex]y(x+4) = xy+4y[/tex]
[tex]6(x+4) = 6x+24[/tex]
[tex]xy+4y - (6x+24) =xy+4y-6x-24[/tex]
Use number properties to simplify the following expression.
-5 + (5 + 3)
In the box below, show each step in simplifying the expression and explain which property you used in each step.
Answers
Answer:
-5 + (5 + 3) =(-5 + 5) + 3 = 0 + 3 = 3[tex]\\ \sf\longmapsto -5+(5+3)[/tex].
Remove brackets[tex]\\ \sf\longmapsto -5+5+3[/tex]
[tex]\\ \sf\longmapsto (-5+5)+3[/tex]
[tex]\\ \sf\longmapsto 0+3[/tex]
[tex]\\ \sf\longmapsto 3[/tex]
Factor Z squared minus 3Z -18
Answers
Answer:
z^2-3z-18
=(z^2+3z)+(-6z-18)
=z(z+3)-6(z+3)
=(z+3)(z-6)
Which value of x satisfies the equation
Answers
Answer:
Does the answer help you?
Guys pleaseee help!!
Calculating a Rate of Change
Try
What is the vertical change from Point A to Point B?
10
y
9
What is the horizontal change from Point A to Point B?
8
7
6
What is the rate of change shown on the graph? Give
the answer as a decimal rounded to the nearest tenth.
if necessary
5
4
3
B
2
A
1
10
8
9
1
2
4
5
3
Done
Answers
Answer:
What is the vertical change from Point A to Point B? 1
What is the horizontal change from Point A to Point B? 2
What is the rate of change shown on the graph? Give
the answer as a decimal rounded to the nearest tenth.
if necessary: 0.5
Step-by-step explanation:
The rate of change, as the own name suggest, is the rate at which the function change its value. The function, in this case is changing with a rate of 0.5 because to each unit that x grows, y grows the half part of it.
explanation would be appreciated. i don’t understand
Answers
Answer:
[tex]28\sqrt{3}[/tex]
Step-by-step explanation:
The area of the big triangle is 1/2 b h = 1/2*6*(12^2 = 6^2 + x^2)
that ends up being [tex]\sqrt{108} = 36\sqrt{3}[/tex]
the small triangle are needs to be subtracted....
[tex]\frac{\left(4\cdot \:sin\left(90\right)\right)}{sin\left(30\right)}[/tex] that is the length of the unknown side...
1/2 B * h of that triangle get you to [tex]8\sqrt{3}[/tex]
just subtract the two areas
Answer:
(B) 28√3
Step-by-step explanation:
The area of quadrilateral ABED is equal to the area of triangle CDE subtracted from the area of triangle ABC.
Area of triangle CDE:
Triangle ABC is equilateral. All sides have length 12.
AB = BC = AC = 12
BE = 8
BE + EC = BC
8 + EC = 12
EC = 4
In an equilateral triangle, all angles measure 60°.
m<C = 60°
m<CDE = 30°
Triangle CDE is a 30-60-90 triangle.
DE = EC√3
DE = 4√3
area of triangle CDE = bh/2
area of triangle CDE = (EC)(DE)/2
area of triangle CDE = (4)(4√3)/2
area of triangle CDE = 8√3
Area of triangle ABC:
Side AC is a base of triangle ABC.
AC = 12
(1/2)AC = 6
The altitude of triangle ABC from side AC to vertex B measures
h = 6√3
area of triangle ABC = bh/2
area of triangle ABC = (AC)(h)/2
area of triangle ABC = (12)(6√3)/2
area of triangle ABC = 36√3
area of quadrilateral ABED = area of triangle ABC - area of triangle CDE
area of quadrilateral ABED = 36√3 - 8√3
area of quadrilateral ABED = 28√3
Chocolate bars come in packs of 8 and graham crackers come in packs of 12. What is the smallest number of chocolate bars and graham crackers we would need to buy so we don't have any left over?
Answers
Answer:
3 chocolate bars, and 2 graham crackers
Someone forgot the marshmallows...... :P
Step-by-step explanation:
Chocolate bars = 8 pack
Graham Crackers = 12pack
To have no crackers or chocolate left over, we need to find LCM
Factors of 8:
8, 16, 24, 32, 40, 48, 56, 72....
Factors of 12:
12, 24, 36, 48, 60, 72
The smallest LCM is 24
Chocolate bars:
24/8 = 3
Graham Crackers:
24/12 = 2
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Answer:
3 packs of chocolate and 2 packs of crackers
Step-by-step explanation:
the lowest common multiple of 8 and 12 is 24. We can determine this by prime factorization:
Prime factors of 8: 2 x 2 x 2
Prime factors of 12: 2 x 2 x 3
multipyling the bottom rungs of our factor tree we get: 2 x 2 x 2 x 3 = 24.
If you need me to draw the factor tree, just ask.
for a mathematical statement to be an equation, the quantities on each side of an equal sign must be?
Answers
Answer:
equal or balanced
Step-by-step explanation
the = demonstrates the amounts need to be the same
Answer: Balanced.
Step-by-step explanation:
For an equation each side shall be equal (balanced) or else it's NOT an equation.
Trigonometric ratios
class 9
please answer my questions
Answers
Step-by-step explanation:
Hi there!
Please see the answer in the picture.
Hope it helps!
1. Approach
One is given a trigonometric equation with and one is asked to prove that it is true. Using the attached image, combined with the knowledge of trigonometry, one can evaluate each trigonometric function. Then one can simplify each ratio to solve. To yield the most accurate result, one has to each of the ratios in a fractional form, rather than simplifying it into a decimal form. Remember the right angle trigonometric ratios, these ratios describe the relationship between the sides and angles in a right triangle. Such ratios are as follows,
[tex]sin(\theta)=\frac{opposite}{hypotenuse}\\\\cos(\theta)=\frac{adjacent}{hypotenuse}\\\\tan(\theta)=\frac{opposite}{adjacent}\\\\csc(\theta)=\frac{hypotenuse}{opposite}\\\\sec(\theta)=\frac{hypotenuse}{adjacent}\\\\cot(\theta)=\frac{adjacent}{opposite}[/tex]
Please note that the terms (opposite) and (adjacent) are relative to the angle uses in the ratio, however the term (hypotenuse) refers to the side opposite the right angle, this side never changes its name. Use these ratios to evaluate the trigonometric functions. Then simplify to prove the identity.
2. Problem (9)
[tex]\frac{sin(60)+cos(30)}{1+sin(30)+cos(60)}=sin(60)[/tex]
As per the attached image, the following statements regarding the value of each ratio can be made:
[tex]sin(60)=\frac{\sqrt{3}}{2}\\\\cos(30)=\frac{\sqrt{3}}{2}\\\\sin(30)=\frac{1}{2}\\\\cos(60)=\frac{1}{2}[/tex]
Substitute,
[tex]\frac{sin(60)+cos(30)}{1+sin(30)+cos(60)}=sin(60)[/tex]
[tex]\frac{\frac{\sqrt{3}}{2}+\frac{\sqrt{3}}{2}}{1+\frac{1}{2}+\frac{1}{2}}=\frac{\sqrt{3}}{2}[/tex]
Simplify,
[tex]\frac{\frac{\sqrt{3}}{2}+\frac{\sqrt{3}}{2}}{1+\frac{1}{2}+\frac{1}{2}}=\frac{\sqrt{3}}{2}[/tex]
[tex]\frac{\frac{2\sqrt{3}}{2}}{1+\frac{1}{2}+\frac{1}{2}}=\frac{\sqrt{3}}{2}[/tex]
[tex]\frac{\frac{2\sqrt{3}}{2}}{1+1}=\frac{\sqrt{3}}{2}[/tex]
[tex]\frac{\sqrt{3}}{1+1}=\frac{\sqrt{3}}{2}[/tex]
[tex]\frac{\sqrt{3}}{2}=\frac{\sqrt{3}}{2}[/tex]
Thus, this equation is true.
2. Problem (10)
Use a similar strategy to evaluate this equation,
[tex]\frac{1-cos(30)}{sin(30)}=\frac{1-cot(60)}{1+cot(60)}[/tex]
Use the attached image to evaluate the ratios.
[tex]cos(30)=\frac{\sqrt{3}}{2}\\\\sin(30)=\frac{1}{2}\\\\cot(60)=\frac{1}{\sqrt{3}}[/tex]
Substitute,
[tex]\frac{1-cos(30)}{sin(30)}=\frac{1-cot(60)}{1+cot(60)}[/tex]
[tex]\frac{1-\frac{\sqrt{3}}{2}}{\frac{1}{2}}=\frac{1-\frac{1}{\sqrt{3}}}{1+\frac{1}{\sqrt{3}}}[/tex]
Simplify,
[tex]\frac{1-\frac{\sqrt{3}}{2}}{\frac{1}{2}}=\frac{1-\frac{1}{\sqrt{3}}}{1+\frac{1}{\sqrt{3}}}[/tex]
[tex]\frac{\frac{2-\sqrt{3}}{2}}{\frac{1}{2}}=\frac{1-\frac{1}{\sqrt{3}}}{1+\frac{1}{\sqrt{3}}}[/tex]
[tex]\frac{\frac{2-\sqrt{3}}{2}}{\frac{1}{2}}=\frac{\frac{\sqrt{3}-1}{\sqrt{3}}}{1+\frac{1}{\sqrt{3}}}[/tex]
[tex]\frac{\frac{2-\sqrt{3}}{2}}{\frac{1}{2}}=\frac{\frac{\sqrt{3}-1}{\sqrt{3}}}{\frac{\sqrt{3}+1}{\sqrt{3}}}[/tex]
[tex]2-\sqrt{3}=\frac{\frac{\sqrt{3}-1}{\sqrt{3}}}{\frac{\sqrt{3}+1}{\sqrt{3}}}[/tex]
[tex]2-\sqrt{3}=\frac{\sqrt{3}-1}{\sqrt{3}}*\frac{\sqrt{3}}{\sqrt{3}+1}}[/tex]
[tex]2-\sqrt{3}=\frac{\sqrt{3}-1}{\sqrt{3}+1}[/tex]
Rationalize the denominator,
[tex]2-\sqrt{3}=\frac{\sqrt{3}-1}{\sqrt{3}+1}[/tex]
[tex]2-\sqrt{3}=\frac{\sqrt{3}-1}{\sqrt{3}+1}*\frac{\sqrt{3}-1}{\sqrt{3}-1}[/tex]
[tex]2-\sqrt{3}=\frac{(\sqrt{3}-1)^2}{3-1}[/tex]
[tex]2-\sqrt{3}=\frac{3-2\sqrt{3}+1}{2}[/tex]
[tex]2-\sqrt{3}=\frac{4-2\sqrt{3}}{2}[/tex]
[tex]2-\sqrt{3}=2-\sqrt{3}[/tex]
Therefore, this equation is also true.
A hardware store ordered 13 packs of
nails from a supplier. Each pack contains
155 nails. How many nails did the store
order?
Answer =530
Answers
EXPLANATION:
If you multiply 155 which is the amount have nails each pack has and they orders 13 packs that gets you 2015 nails all together
14.
Which is the most reasonable measure for the length of
a bicycle?
C. 2 cm
B. 2 m
A. 2 mm
D. 2 km
Answers
Answer:
B 2 m
Step-by-step explanation:
2 cm and 2 mm are way to small they are less than the size of a cell phone
2 km is way to large it is larger than a car
y is inversely proportional to the square root of x. When y=7, x= 2.25. Write y in terms of x.
Answers
Answer:
y(x)=10.5/sqrt(x)
Step-by-step explanation:
Since y is inversely proportional to the square root of x, it can be written as y=a/sqrt(x). To compute a, we will use the point given in the question (2.25,7). 7=a/sqrt(2.25), a=10.5. The function is y(x)=10.5/sqrt(x)
Pls help I tried basic answers like 50+50+80 =180 but it’s wrong so pls help
Answers
Answer:
x = 65 degrees
Step-by-step explanation:
x° + x° + 50° = 180°
2x + 50° = 180°
2x = 180° - 50°
2x = 130°
x = 130°/2
x = 65°
Using 20 boxes of nails a carpenter was able to finish 40 bird houses. Write an
equation that can be used to express the relationship between the total number of
birdhouses completed(t)and the boxes of nails(b) used.
Help ASAP!
Answers
Answer: 20 times 2 equal 40/ 40 divided by 2 is 20
Step-by-step explanation: Both of them should help you find the answer
3x^3(4x^4)=?
i need this plz
Answers
Answer:
12x^7.
Step-by-step explanation:
3x^3(4x^4)=
3*4 * x^(3+4)
= 12x^7.
Geometry I need help someone help me
Answers
Answer:
fohohcoufohohcouvhop
Step-by-step explanation:
typing mistake sorry
[tex]\\ \sf\longmapsto x+73=90[/tex]
[tex]\\ \sf\longmapsto x=90-73[/tex]
[tex]\\ \sf\longmapsto x=17[/tex]
Why?
Sum of two complementary angles is 90°
Can anyone please help me with this thank you
Answers
Answer:
x= 0, and x=4
Step-by-step explanation:
x² -x = 3x, we can subtract 3x from both sides
x² -x -3x = 0, combine like terms
x² -4x = 0 , factor x
x *( x-4) = 0, if the product of 2 numbers equals 0 at least one is 0
x=0 and
x-4 = 0, add 4 to both sides
x= 4
Answer:
x=4 simple thing with all problems like this, is if it has a exponent, then half the exponent and add it to the numerical digit on the right of the equals sign, and you have you answer
Step-by-step explanation:
I WILL GIVE BRAINLIEST!! NO LINKS PLZ
4) Simplify.
Answers
Answer: [tex]\frac{\sqrt{5}}{6}[/tex]
==================================================
Work Shown:
[tex]\frac{\sqrt{10}}{3\sqrt{8}}\\\\\frac{\sqrt{10}*\sqrt{8}}{3\sqrt{8}*\sqrt{8}}\\\\\frac{\sqrt{10*8}}{3\sqrt{8*8}}\\\\\frac{\sqrt{80}}{3\sqrt{64}}\\\\\frac{\sqrt{80}}{3*8}\\\\\frac{\sqrt{16*5}}{24}\\\\\frac{\sqrt{16}*\sqrt{5}}{24}\\\\\frac{4*\sqrt{5}}{24}\\\\\frac{\sqrt{5}}{6}\\\\[/tex]
Note: In the second step, I multiplied top and bottom by [tex]\sqrt{8}[/tex] to rationalize the denominator.
Answer:
square root of 5 over 6 or 0.37267799…
Step-by-step explanation:
Multiply the numerator and denominator by the conjugate.
which answer is right?
Answers
Answer:
i think A
Step-by-step explanation:
i believe
Suppose the following equation is true:
3^x=81^y
What is the connection between x and y?
Answers
Answer:
x=4y
Step-by-step explanation:
3^x=3^4y
x=4y
am I correct?
Select the type of equations.
consistent
equivalent
Inconsistent
Answers
Answer:
Step-by-step explanation:
This is a consistent dependent system. This means that the lines will eventually intersect in one place.
Inconsistent systems are parallel lines and equivalent systems represent a line completely overlapped by another line because they have the same equation.
the ratio of thomson's age to racheal's age is 2:3.racheal is 24 years old. how old is thomson?
Answers
2:3
Given Racheal = 24 years
Thomson = 2/3×24
= 2×8
= 16 years
Must click thanks and mark brainliest
Ben wants to get a 94 in math class. His grade will be the average of two test scores. He scored an 89 on the first test. What grade does Ben need to get on his second test to meet his goal?
Answers
Answer:
Ben needs to get a 99% on his second test
Step-by-step explanation:
The average is the sum of both test scores, divided by the total number of test scores (2).
Let x by the grade Ben must receive on his second test.
(89 + x)/2 = 94
Multiply by 2 on both sides
89 + x = 188
Subtract 89 on both sides
x = 99
Check work:
(89 + 99)/2 = 188/2 = 99
Answer: 99
Concept:
Here, we need to know the idea of the average value.
In mathematics, average refers to the sum of a group of values divided by n, where n is the number of values in the group.
Average = Sum of value / number of values
Solve:
Given information
Scoring on first test = 89
Scoring on second test = x
Number of tests = 2
Average = 94
Given expression
Average = Sum of value / number of values
Substitute values into the expression
94 = (89 + x) / 2
Multiply 2 on both sides
94 × 2 = (89 + x) / 2 × 2
188 = 89 + x
Subtract 89 on both sides
188 - 89 = 89 + x - 89
[tex]\boxed{x=99}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Which equation represents a line which is parallel to the line y=7/6x−6?
7y-6x= -14
6x + 7y = 56
7x + 6y = 18
7x - 6y = -48
Answers
Answer:
6x+7y=56
Step-by-step explanation:
In order to have an equation that is parallel to another the slopes multiplied by one another must equal -1. In this case, the first slope is [tex]\frac{7}{6}[/tex] . So [tex]\frac{7}{6}[/tex]×what = -1
Normally you can just flip the numerator and denominator and add the opposite sign. So we can do that here. [tex]-\frac{6}{7} *\frac{7}{6} =-1[/tex]. So the equation should have [tex]-\frac{6}{7}[/tex].
But none of the answers obviously have that slope. If you try the second one, which looks different from the rest and will give you a negative x when you subtract it from both sides. Then you can divide by 7, you get [tex]y=-\frac{6}{7}x +8[/tex].
15. What is the length of segment FG
Answers
Answer:
10.49
Step-by-step explanation:
FG= squareroot(10)(11) =10.49 took quiz too
Solve: MXC multiplied by IV. Show your answer in standard form. Standard Roman Number Numeral 1 1 5 V 10 50 L 100 C 500 D 1,000 M X-003 O A) 4,060 OB) 4,360 OC) 4,440
Answers
Answer:
4360
Step-by-step explanation:
MXC is 1090 and a IV is 4 so 1090 x 4 is 4360
