Simplify.
Multiply and remove all perfect squares from inside the square roots. Assume b is positive.
Answers
Answer:
216*b^2
Step-by-step explanation:
first, remember that:
a*√b = √(a^2*b)
√a*√b = √(a*b)
[tex]b^n*b^m = b^{n + m}[/tex]
[tex](b^n)^m = b^{n*m}[/tex]
Now, our expression is:
[tex]2*\sqrt{8*b^3} *9*\sqrt{18*b} = (2*9)*\sqrt{8*b^3}*\sqrt{18*b}[/tex]
Where in the right I rewrite the expression so it is easier to work.
Now we can use the second property of the above ones, to have:
[tex]18*\sqrt{8*b^3*18*b} = 18*\sqrt{(8*18)*b^{3 + 1}} = 18*\sqrt{144*b^4}[/tex]
And we know that:
[tex]\sqrt{x} = x^{1/2}[/tex]
Then:
[tex]18*\sqrt{144*b^4} = 18*(144*b^4)^{1/2} = 18*\sqrt{144}*(b^4)^{1/2}[/tex]
and 12*12 = 144, then:
[tex]18*\sqrt{144}*b^{4*1/2} = 18*12*b^2 = 216*b^2[/tex]
Related Questions
A survey was conducted to see what kinds of activities high school and college students liked best. The table shows the results of the survey.
Bowling Hiking Swimming Total
8-B
12-H
10-S
30-T
High School^
10-B
14-H
16-S
40-T
College^
18-B
26-H
26-S
70-T
Total^
Choose two correct conclusions using the results of the survey.
O A. Students in high school were more likely to prefer bowling than students in college.
B. Students in high school were more likely to prefer swimming than students in college.
C. Students who prefer bowling were more likely to be in college than students who prefer hiking.
D. Students who prefer swimming were more likely to be in high school than students who prefer hiking.
(The letters are abbreviations for the sports to help see it)
Please hurry I’ll mark it brainliest!!
Answers
Answer:
C & D
Step-by-step explanation:
Because A&B are wrong
Students who prefer bowling were more likely to be in college than students who prefer hiking. Then the correct option is C.
What is decision-making?Determining the proper option, acquiring evidence, and exploring various options are all steps in the decision-making process.
A survey was conducted to see what kinds of activities high school and college students liked best. The table shows the results of the survey.
The table is given below.
Bowling Hiking Swimming Total
High School 8 12 10 30
College 10 14 16 40
Total 18 26 26 70
Students who prefer bowling were more likely to be in college than students who prefer hiking. Then the correct option is C.
More about the decision-making link is given below.
https://brainly.com/question/3369578
#SPJ2
i need help please i’ll give u a brainliest
Answers
Answer:
3 of them. Hope this helps!
Step-by-step explanation:
Mr. Davis hired a painter. He can spend no more than $500 to have his house painted. If the painter charges $20 per hour, for how many hours can Mr. Davis hire the painter?
Variable:
inequality:
solution:
Answers
Answer:
25 Hours
Step-by-step explanation:
First find how much $20 is in hours. It equals to 1 hour. Now times it as many times as you need, to get to $500, which is 25 in total.
I am greater than 17 I am less than 50 I am a even number I am a multiple of 4
Answers
Answer:
32
Step-by-step explanation:
hope this helps
Can someone help with this
Answers
Answer:
The area of the shape shown below is 32 units
Step-by-step explanation:
I cut the shape up into 2 triangles and a square.
Square
4 x 4 = 16
Triangle #1
4 x 4 = 16/2 = 8
Triangle #2
4 x 4 = 16/2 = 8
Add them up:
16 + 8 + 8 = 32
Please answer this math question for me
Answers
Answer:
Hello!! answer: a = 45
Step-by-step explanation:
This is a complimentary angle so we will just do 90 - 45 and get 45 because 45 + 45 = 90 Hope that helps!
Answer:
a = 45
Step-by-step explanation:
The total angle of the shape is 90°
That means you should subtract 90° from 45°
90 - 45 = 45
That's your answer!
Hope this helped :)
What is the solution to the equation below?
5(6 + x) = 15
A.
3
B.
-1.33
C.
-3
D.
1.33
Answers
Answer:
- 3
option c). is correct!
Step-by-step explanation:
Given :
5 ( 6 + x ) = 15
= > 30 + 5 x = 15
= > 5 x = - 30 + 15
= > 5 x = - 15
= > x = - 15 / 3
= > x = - 3
Therefore, final answer is - 3
Answer:
C. -3
Step-By-Step Explanation:
5(6+3) = 45
5(6+-1.33) = 23.35
5(6+-3) = 15
5(6+1.33) = 36.65
if peter has 27 apples and gives Tim 7, how much does peter have?
Answers
Answer: 20
Step-by-step explanation:
27 apples - 7 apples = 20 apples
Answer:
Peter has 20 apples
Step-by-step explanation:
27 - 7 = 20
What is the area of the triangle?
Answers
Answer:
126.5 cm²
Step-by-step explanation:
(23×11)×1/2=Area
(253) × 1/2
=126.5
hope this helped
In a group of 200 students, 75 are taking Geometry, 135 are taking IPC and 35 are taking both Geometry and IPC. If a student, chosen at random, is taking Geometry, what is the probability that he or she is taking IPC?
a) 0.175
b) 0.167
c) 0.259
d) 0.467
Answers
What is a equal ratio to 4/10
Answers
Answer:
2/5
Step-by-step explanation:
How many gallons of paint is needed for a 8x9 bedroom with 8 foot ceilings?
Answers
Answer:
Wish i could help i need the answer as well
Step-by-step explanation:
A jar contains 15 quarters, 9 dimes, 10 nickels and 6 pennies. A coin is selected at random, not replaced, then another coin is selected. Find the probability of the event. P(quarter, then penny)
Answers
Answer: 0.058
Step-by-step explanation:
Number of quarters = 15
Number of dimes = 9
Number of nickels = 10
Number of pennies = 6
Total number of coins = 40
The probability of selecting a quarter first will be 15/40 = 3/8
Since it's not replaced, there'll be 39 coins left and the probability of choosing a penny is 6/39 = 2/13
Therefore, P(quarter, then penny) will be:
= 3/8 × 2/13
= 6/104
= 0.058
Glenn has a garden that is shaped like a rectangle.
The perimeter of his garden is 70 1/2 feet.
The length of the garden is 24 3/4 feet.
What is the width of the garden?
21 ft o 11ft o 10 ½ ft o 45 ¾ ft
Answers
Answer:
Solution given:
The length of the garden[l] = 24 3/4 =99/4feet.
breadth or width [b]=b
perimeter of his garden = 70 1/2=141/2 feet.
2[l+b]=141/2ft
99/4+b=141/4
b=141/4-99/4
b=21/2
b=10 ½ft
So the width of the garden is 10 ½ft.
Determine the intercepts of the line.
Answers
9514 1404 393
Answer:
y-intercept (0, -6)
x-intercept (-8, 0)
Step-by-step explanation:
You're writing the coordinates of the points where the line crosses the axes.
The y-intercept is where the line crosses the y-axis. The y-coordinate there is -6. Because it is the y-axis, the x-coordinate is 0. Written as an ordered pair, the y-intercept is (0, -6).
The x-intercept is where the line crosses the x-axis. The x-coordinate there is -8. Because it is the x-axis, the y-coordinate is 0. Written as an ordered pair, the x-intercept is (-8, 0).
Help pleaseeeeeeeeee
Answers
9514 1404 393
Answer:
47 -6√10
Step-by-step explanation:
As you know, the area of a square is the square of the side length. It can be helpful here to make use of the form for the square of a binomial.
(a -b)² = a² - 2ab + b²
(√2 -3√5)² = (√2)² - 2(√2)(3√5) + (3√5)²
= 2 - 6√10 + 3²(5)
= 47 -6√10
__
Check
√2-3√5 ≈ -5.29399 . . . . . . . . note that a negative value for side length makes no sense, so this isn't about geometry, it's about binomials and radicals
(√2-3√5)² ≈ 28.02633
47 -6√10 ≈ 28.02633
Marking brainliest
Please help
Answers
Answer:
Left:
hyp = 13
opp = 12
adj = 5
Right:
hyp = h
opp = s
adj = w
(b) Without using a calculator, the square root of 18 will be between what two values (remember to look for perfect squares/perfect square roots)? Show your reasoning. You do not need to find the decimal equivalent of the root.
Answers
Answer:
√18 = 3√2
Step-by-step explanation:
the square root of 18 = √18
18;
1 × 18 = 18
2 × 9 = 18
3 × 6 = 18
6 × 3 = 18
9 × 2 = 18
18 × 1 = 18
9 has a perfect square
So,
√18 = √(2*9)
= √2 * √9
= 3√2
√18 = 3√2
Perfect square
1 × 1 = 1
2 × 2 = 4
3 × 3 = 9
4 × 4 = 16
5 × 5 = 25
Therefore,
√18 is between 4 and 5
x+4/9=3/4 what is x?
Answers
Answer:
11/36
Step-by-step explanation:
To answer this, you must first convert your fractions to have the same denominators (so you can add and subtract them). I switched it to 36ths. So, the equation would be x+16/36=27/36. When you subtract 16/36 from 27/36 you get 11/36. This cannot be simplified, so 11/36 is the answer. I hope it helps.
How many vertices does this shape have?
A shape with 3 rectangular sides and 2 triangular sides.
Answers
Answer:
A triangular prism has 5 faces (3 rectangular and 2 triangular), 9 vertices and 6 edges.
Answer:
5
Step-by-step explanation:
- 7th Grade Work -
Please do the answer's like this:
1.
2.
3.
Thanks
Answers
Answer:
Shown Below
Step-by-step explanation:
1.You have 3 pencils and 33 cents and there is 25 cents of tax on each pencil how much does each pencil cost?
2.First you would distribute the 3 so you have 3p-75=33 then you would add 75 to each side to cancel out the 75 on the left side then get 108 on the right so you have 3p=108 and then you would divide by 3 on each side to get p=36
3.As explained above p=36
O is the center of the circle. Assume that lines that appear to be tangent are tangent. What is the value of x?
Answers
Answer:
x=48
Step-by-step explanation:
Mrs. Alberts has two seventh grade math classes this year. They took their final exam, and Mrs. Alberts just finished grading them. She made a box-and-whisker plot for each class in order to compare their results.
Analyze the box-and-whisker plots from above and then select the following comparative inferences that are true. Select all that apply.
1. The interquartile range of Class A is about twice as large as the interquartile range of Class B.
2. There is very little overlap in the two data sets.
3. The median of Class A is about 5 points higher than the median of Class B.
4. The range of Class B is about 12 points less than the range of Class A.
5. A student in Class B had the highest score of both classes.
6. In general, the students from Class B scored better than the students from Class A.
Answers
Answer:
these are true = 1, 3, 5
Step-by-step explanation:
overall class a scored better than class b
they're more students in class a compared to class b
Find the surface area of the composite figure
Answers
solution given:
For Cuboid
length[l]=11mm
breadth [b]=9mm
height[h]=6mm
For semi cylinder
height[H]=11mm
radius[r]=[tex] \frac{9}{2}=4.5mm[/tex]
Now
Totalsurface area=2(lb+bh+lh)+½(2πr(r+H))-l*b[/tex]
:2(11*9+9*6+11*6)+22/7*4.5(4.5+11)-11*9
:438+219.2-99
:558.2mm²
Here area of base is subtracted as it is not included.
Total surface area of composite figure is :558.2mm².
Answer:
[tex]\displaystyle SA_{Total} = \frac{279 \pi}{4} + 339 \ mm^2[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightAlgebra I
FactoringGeometry
Shapes
Congruency
Congruent sides and lengthsRadius Formula: [tex]\displaystyle r = \frac{d}{2}[/tex]
d is diameterSurface Area of a Rectangular Prism Formula: SA = 2(wl + hl + hw)
w is widthl is lengthh is heightSurface Area of a Cylinder Formula: SA = 2πrh + 2πr²
r is radiush is heightStep-by-step explanation:
Step 1: Define
Identify
[Rectangular Prism] w = 9 mm
[Rectangular Prism] l = 11 mm
[Rectangular Prism] h = 6 mm
[Cylinder] d = 9 mm
[Cylinder] h = 11 mm
Step 2: Derive
Modify Surface Area equations and combine
[Surface Area of a Cylinder Formula] Factor: [tex]\displaystyle SA = 2(\pi rh + \pi r^2)[/tex][Surface Area of a Cylinder Formula] Divide by 2 [Semi-Cylinder]: [tex]\displaystyle SA = \pi rh + \pi r^2[/tex][Surface Area of a Semi-Cylinder] Substitute in r [Radius Formula]: [tex]\displaystyle SA = \pi (\frac{d}{2})h + \pi (\frac{d}{2})^2[/tex][Surface Area of a Semi-Cylinder] Evaluate exponents: [tex]\displaystyle SA = \pi (\frac{d}{2})h + \pi (\frac{d^2}{4})[/tex][Surface Area of a Semi-Cylinder] Multiply: [tex]\displaystyle SA = \frac{\pi dh}{2} + \frac{\pi d^2}{4}[/tex][Surface Area of a Rectangular Prism] Remove top: [tex]\displaystyle SA = 2(wh + lh) + lw[/tex]Combine Surface Area equations: [tex]\displaystyle SA_{Total} = \frac{\pi dh}{2} + \frac{\pi d^2}{4} + 2(wh + lh) + lw[/tex]Step 3: Find Surface Area
Substitute in variables [Combined Surface Area equation]: [tex]\displaystyle SA_{Total} = \frac{\pi (9 \ mm)(11 \ mm)}{2} + \frac{\pi (9 \ mm)^2}{4} + 2[(9 \ mm)(6 \ mm) + (11 \ mm)(6 \ mm)] + (11 \ mm)(9 \ mm)[/tex]Evaluate exponents: [tex]\displaystyle SA_{Total} = \frac{\pi (9 \ mm)(11 \ mm)}{2} + \frac{\pi (81 \ mm^2)}{4} + 2[(9 \ mm)(6 \ mm) + (11 \ mm)(6 \ mm)] + (11 \ mm)(9 \ mm)[/tex]Multiply: [tex]\displaystyle SA_{Total} = \frac{99\pi \ mm^2}{2} + \frac{81\pi \ mm^2}{4} + 2[54 \ mm^2 + 66 \ mm^2] + 99 \ mm^2[/tex][Brackets] Add: [tex]\displaystyle SA_{Total} = \frac{99\pi \ mm^2}{2} + \frac{81\pi \ mm^2}{4} + 2[120 \ mm^2] + 99 \ mm^2[/tex]Multiply: [tex]\displaystyle SA_{Total} = \frac{99\pi \ mm^2}{2} + \frac{81\pi \ mm^2}{4} + 240 \ mm^2 + 99 \ mm^2[/tex]Add: [tex]\displaystyle SA_{Total} = \frac{279 \pi}{4} + 339 \ mm^2[/tex]Solve (4x – 3) > 5 for x.
Answers
Answer:
x>2
Step-by-step explanation:
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{(4x - 3) > 5}[/tex]
[tex]\mathsf{4x - 3 > 5}[/tex]
[tex]\large\text{ADD 3 to BOTH SIDES}[/tex]
[tex]\mathsf{4x - 3 + 3 > 5 + 3}[/tex]
[tex]\large\text{CANCEL out: -3 + 3 because that gives you 0}[/tex]
[tex]\large\text{KEEP: 5 + 3 because it helps solve for x}[/tex]
[tex]\mathsf{5 + 3 = \bf 8}[/tex]
[tex]\large\text{New EQUATION: }\mathsf{4x > 8}[/tex]
[tex]\large\text{DIVIDE 4 to BOTH SIDES}[/tex]
[tex]\mathsf{\dfrac{4x}{4}>\dfrac{8}{4}}[/tex]
[tex]\large\text{CANCEL out: } \mathsf{\dfrac{4}{4}}\large\text{ because that gives you 1}[/tex]
[tex]\large\text{KEEP: }\mathsf{\dfrac{8}{4}}\large\text{ because it helps you compares to x}[/tex]
[tex]\mathsf{\dfrac{8}{4}=\bf 2}[/tex]
[tex]\boxed{\boxed{\large\textsf{Therefore your ANSWER: \boxed{\mathsf{\bf x > 2}}}}}\huge\checkmark[/tex]
[tex]\large\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
In triangle $DEF,$ $\angle D = 30^\circ,$ $\angle F = 60^\circ,$ and $EF = 6.$ Find $DE + DF.$
Answers
Answer:
22.39
Step-by-step explanation:
angle D + angle F + angle E = 180 (angle of triangle)
30 +60 + E = 180
E = 180 - 90
E = 90
so triangle DEF is right angled triangle
we know that,
sin 30 = EF /DF
OR, 1/2 = 6/ DF
OR, DF= 12
again,
cos 30 = De/DF
root3 /2 = DE /12
DE= 10.39
hence DF +DE
= 12 + 10.39
= 22. 39
The students of a school fill 5 buses for a field trip. Each class fills bus. How many classes are riding on the buses?
Answers
Answer:
The answer is 5
Step-by-step explanation:
Because each bus is assigned 1 class and there is only five buses so there are 5 classes
Please find the missing side of this triangle
Answers
Answer:
The answer is 8.30
Step-by-step explanation:
Using cos 41 = x/11
x = cos 41 × 11
x = 8.30
can these three angles 47, 84, and 56 create a triangle
Answers
Answer:
No. The sum of the 3 angles of a triangle = 180 degrees. In this case the 3 angles, 47 + 84 + 56 = 187 degrees, not 180 degrees.
At the ice cream store, you can pick from two cones, five flavors of ice cream, and three types of
toppings. You pick from one of each type of cone, ice cream flavor, and topping. How many total
types of ice cream cone combinations can you make?
Answers
Answer: 30
Step-by-step explanation: you start with the base and go up, you have to options for cones each option has five options to go on top so two times five is ten, the next item is toppings which you have three options, three times ten is 30
Answer:
I believe the answer is 30
Step-by-step explanation:
You have
2 different types of cones V and U
5 flavors A B C D E
3 toppings 1 2 3
so you would have
VA1
VA2
VA3
VB1
VB2
VB3
VC1
VC2
VC3
VD1
VD2
VD3
VE1
VE2
VE3
and
UA1
UA2
UA3
UB1
UB2
UB3
UC1
UC2
UC3
UD1
UD2
UD3
UE1
UE2
UE3
if I'm wrong I'm sorry
