Simplify:(picture)
and can you please show your work so that i can understand how to do it myself? Thank you
Answers
Because they are square roots, we look for factors for the number inside the radical that repeat twice. In this case, the number inside the radical is 32. The factors of 32 are 2 and 16. 16 can be broken down into 4*4. So our factors will be 2*4*4 inside the radical. Any number without a match stays inside.
3√32 becomes 3√(4*4*2). Notice there are two 4's so we pull those out. This number becomes (3*4)√2 which simplifies to 12√2. Now since the number in the radicals match, we add the outside numbers like normal and the number inside the radical stays the same.
12√2 + 6√2 is the same as (12 + 6)√2 which equals 18√2, the second option is your answer.
=3√4²×2=
=3√4²√2=
=3×4√2=
=12√2
12√2+6√2=
=18√2
Hope this helped!
Related Questions
a recipe for 2 1/2 dozen whole-wheat muffins require 600 g of flour. How many muffins can be made with 900 g of flour?
Answers
With 900 g of flour, you can make 45 muffins.
Explanation:To find out how many muffins can be made with 900 g of flour, we can set up a proportion:
2.5 × 12 = 600
x × 900 = 1
Cross-multiplying gives us:
2.5 × 12 × 900 = 600 × x
30 × 900 = 600 × x
27000 = 600x
x = 27000 / 600
x = 45
Therefore, with 900 g of flour, you can make 45 muffins.
Which pair of numbers is an example of opposites? 1/2 and 2 -1/2 and 2 -2 and 1/2 -2 and 2
Answers
ANSWER: -2 and 2
Hops this helps! :)
Answer is : -2 and 2
Step-by-step explanation:
Over the last 4 years, Michael has earned $240 interest on an initial investment of $2,000. What simple annual interest rate is the bank paying on this account?
Answers
Answer:
3%
Step-by-step explanation:
what is the missing constant term in the perfect square that starts with x^2 +6x
Answers
The answer is 9
x^2 + 6x + 9 is the same thing as (x+3)^2
PLZ HELP ASAP Using the frequency table below, find how many students received a score of 70 or better on a mathematics test.
A.19
B.12**
C.17
D.14
Score Interval Frequency
50 – 59 [2]
60 – 69 [5]
70 – 79 [5]
80 – 89 [7]
90 – 99 [2]
Answers
Here are the steps:
1. we know that 70 - 79 = 5 students 80 - 89 = 7 students 90 - 99 = 2 students.
2. ADD
3. 5 + 7 + 2= 14
4. ANSWER
A: D there are 14 students scored 70 and above!
Hope this helped! (tell me if i'm wrong or right please!!!)
Answer:
D.14
Step-by-step explanation:
To find out the answer, we need to add up all the student s that a 70 or above. 5 got 70-79, 7 got 80-89, and 2 got 90-99.Add these up and we get 14. The answer is D.14
The base of this regular right pyramid is a square. What is its surface area?
base edge = 8in
Height = 12in
Answers
B=8^2=64 inches2
T.S.A.=1/2(32)(12)+ 64
=192+ 64
= 256 inches2
Answer:
C
Step-by-step explanation:
The endpoints of GE are located at G(-6,-4) , and E(4,8). Using slope-intercept form, write the equation of GE.
Answers
Answer:
The line would be y = 6/5x + 26/5
Step-by-step explanation:
To find the equation, we first need to find the slope. We can do this by using the slope formula.
m(slope) = (y2 - y1)/(x2 - x1)
m = (8 - -4)/(4 - -6)
m = 12/10
m = 6/5
Now that we have the slope, we can use that and either point in point-slope form to get the equation.
y - y1 = m(x - x1)
y - 8 = 6/5(x - 4)
y - 8 = 6/5x - 24/5
y = 6/5x + 26/5
HELP PLZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ!!!
Which of the following best describes the expression 9(x + 7)?
A. The sum of constant factors 9 and x + 7
B. The product of constant factors 9 and x + 7
C. The product of a constant factor 9 and a 2-term factor x + 7
D. The sum of a constant factor 9 and a 2-term factor x + 7
Answers
Answer:
THE ANSWER IS C NOT D
Step-by-step explanation:
The answer is C i got it correct on the test DON'T LISTEN TO THE PEOPLE THAT SAY D
The center circle of a soccer field prohibits a defender from being near the ball at the start or restart of a soccer game. On a professional soccer field this circle is 20 yards in diameter. Find the area of this circle. Show work or explain how you found your answer.
Answers
A = (π/4)d²
You have d=20 yd, so the area of the circle is
A = (π/4)×(20 yd)² . . . . substitute the given information into the formula
A = 100π yd² . . . . . . . . do the arithmetic
A ≈ 314.16 yd²
The area of the center circle on a professional soccer field, which has a diameter of 20 yards, is calculated using the formula for the area of a circle. The calculated area is approximately 314.16 square yards.
Explanation:To find the area of the center circle on a soccer field, we use the formula for the area of a circle: A = πr^2, where A is the area and r is the radius of the circle. Given that the diameter of the circle is 20 yards, the radius (which is half of the diameter) would be 10 yards. Therefore, substituting 10 for r in the formula gives A = π(10)^2.
Performing the calculations, we find that A = π(100), which equals 314.16 square yards, using 3.1416 as the approximation for σ. Hence, the area of the center circle on a professional soccer field is approximately 314.16 square yards.
What is the probability that her keys have landed within the forest?
Answers
Answer:
0.8
Step-by-step explanation:
egde
solve the equation. choose the answer in simplest form. 4x= 8/7 (A) 1/28 (B) 1/7 (C) 2/7 (D) 7/2
Answers
x=(8/7)÷4
x=2/7
/4 /4
x = (8/7)/4 (Keep, change, flip)
x = 8/7 * 1/4
x = 8/28
x = 2/7
Tommy conducts an experiment where he rolls a number cube, with sides labeled from 1 to 6, and then flips a coin. This table shows the results from 12 trials. Results 1 H 4 T 1 H 5 T 2 H 3 T 6 T 2 H 3 T 5 T 3 H 4 T How do the experimental probability and theoretical probability of rolling an odd number and then flipping a tail in Tommy's trials compare? Drag and drop the values or phrases to correctly complete the sentence. The experimental probability is , which is the theoretical probability of .
Answers
The theoretical probability of rolling an odd and flipping a coin is 1/4.
1/2 x 1/2 = 1/4
Looking at the results, there are 4 occasions where an odd numbers was flipped then tails.
That is 4 out of 12 or 1/3 which is more than 1/4 for the theoretical.
Answer:
The experimental probability is greater than the theoretical probability.
Step-by-step explanation:
Edg : )
A computer store builds custom computers by allowing customers to choose 1 of 4 different CPUs, 1 of 8 hard drives, and 1 of 3 videos cards. How many different computers are possible?
Answers
The fundamental counting principle states that the number of total options is given by multiplying the number of possibilities for each option, or
Total choices = choices x choices x ...
4*3*8 = 96
solve the area of a triangle for b and use the resulting formula to find the base of a triangle with a height of 6 ft. and an area of 9 ft. ^2.
Answers
[tex]A_\Delta=\dfrac{bh}{2}[/tex]
b - a base
h - a height
We have:
h = 6ft.and A=9 ft.²
substitute:
[tex]\dfrac{6b}{2}=9\\\\3b=9\ \ \ |:3\\\\b=3\ ft.[/tex]
Answer: b = 3ft.
What is the angle of rotation of this regular decagon? What is the measure of an interior angle?
Answers
360 / (number of sides)
Therefore,
360 = 10 = 36.
The interior angles are determined by the following equation:
180 - (angle of rotation)
Therefore,
180 - 36 = 144
The answer is A.
150% of A is equal to $120
Answers
So, to find 150% of A, we use this equation:
1.5a = 120
We divide both sides by 1.5 to isolate a:
a = 80
150% of 80 is equal to 120
150/100A=120
Simplify
3/2A=120
A=80
Rhombus WXYZ is graphed on a coordinate plane. What is the area of the rhombus? 24 square units 28 square units 32 square units 48 square units
Rhombus WXYZ is graphed on a coordinate plane.
What is the area of the rhombus?
24 square units
28 square units
32 square units
48 square units
Answers
Answer:
24 square units
Step-by-step explanation:
mrs.beluga is driving on a snow covered road with a drag factor of 0.2. she brakes suddenly for a deer. The tires leave a yaw mark with a 52 foot chord and a middle ornate of 6 feet. What is the minimum speed she could have been going?
Answers
where
[tex]c[/tex] is the length of the chord
[tex]m[/tex] is the middle ordinate
We know from our problem that the tires leave a yaw mark with a 52 foot chord and a middle ornate of 6 feet, so [tex]c=52[/tex] and [tex]m=6[/tex]. Lets replace those values in our formula:
[tex]r= \frac{52^2}{8(6)} + \frac{6}{2} [/tex]
[tex]r= \frac{2704}{48} +3[/tex]
[tex]r= \frac{169}{3} +3[/tex]
[tex]r= \frac{178}{3} [/tex]
Next, to find the minimum speed, we are going to use the formula: [tex]s= \sqrt{15fr} [/tex]
where
[tex]f[/tex] is drag factor
[tex]r[/tex] is the radius
We know form our problem that the drag factor is 0.2, so [tex]f=0.2[/tex]. We also know from our previous calculation that the radius is [tex] \frac{178}{3} [/tex], so [tex]r= \frac{178}{3}[/tex]. Lets replace those values in our formula:
[tex]s= \sqrt{(15)(0.2)( \frac{178}{3}) } [/tex]
[tex]s= \sqrt{178} [/tex]
[tex]s=13.34[/tex] mph
We can conclude that Mrs. Beluga's minimum speed before she applied the brakes was 13.34 miles per hour.
The minimum speed Mrs. Beluga could have been traveling when she braked suddenly on the snow-covered road is approximately 13.68 mph.
To find this, we can use the formula for determining speed from yaw marks: v = √(15 × f × R), where v is the speed in miles per hour, f is the drag factor (0.2 in this case), and R is the radius of the yaw mark.
First, we need to determine the radius of the yaw mark using the given chord length (52 feet) and middle ordinate (6 feet). The formula for R using these values is: R = (C² / 8M) + (M / 2), where C is the chord length and M is the middle ordinate.
Plugging in the values, we get:R = (52² / 8 × 6) + (6 / 2)Calculating inside the parentheses:
R = (2704 / 48) + 3This simplifies to:
R ≈ 59.42 + 3Thus, R ≈ 62.42 feet.Now, plug R and f into the speed formula:
v = √(15 × 0.2 × 62.42)Calculating inside the square root:
v = √(187.26)This yields:
v ≈ 13.68 mph.
Therefore, the minimum speed Mrs. Beluga could have been traveling was approximately 13.68 mph.
The school's basketball team lost 4 times as many games as they won. They also tied 5 fewer games than they won.
If they played 43 games, how many did they lose?
Answers
If they played 43 games, the number of games that they lost is: 32
How to save algebra word problems?
Let
x represent number of games won
Let y represent number of lost games.
Thus;
y = 4x - - - - - equation (I)
Let z denote tied games.
Thus;
z = x - 5 - - - - - equation(II)
Total games played is 43.
Thus;
x + y + z = 43 (III) equation
substitute (I) and (II) in (III)
therefore
x+(4x)+(x-5)=43
6x-5=43
x=48/6
x=8
y = 4x
= 4*8 =32
The answer is 32 lost games
Is 7/8 the right answer
Answers
LMN≅PQR
What is the value of x in degrees?
Enter your answer in the box.
x = °
Answers
Point Q has an angle of 72, which means that point M also has an angle of 72.
Now you have two angles to find x. All interior angles of a triangle add up to 180, so you can set up the following equation to find x:
72 + 36 + x = 180
Subtract 36 from both sides.
72 + x = 144
Subtract 72 from both sides.
x = 72
The angle of point L, x, is 72.
Answer:
Step-by-step explanation:
72
the product of two consecutive even integers that are negative is 224. Write an equation and find the two integers.
Answers
the first integer be x and the second one will be x+2
HELP QUICKLY
15 men and 20 women what is the experimental probability that the next person to enter the store will be a man?
Answers
15/35
which we can simplify to
3/7
The probability that the next person to enter the store will be a man is 3/7
Answer: 3/7
Women: 20
Men: 15
Total: 35
15/35 is simplified to 3/7
The height h of an arrow in feet is modeled by h(t) = -16t^2 + 63t +4, where t is the time in seconds since the arrow was shot. what is the height of the arrow after 2 seconds?
Answers
If you substitute in the formula t = 2, you will get 66.
Hope this helps you!
Why is a square a rectangle and a rhombus??
Answers
A square is a rhombus because it has 4 equal sides.
Jonathan bought 10lb of flour at 7.50 he had a store cupon for 0.79 what was the final price for flour
Answers
i need your help please!!!
Answers
Area of Semicircle = ([tex] \pi 6^{2} [/tex]/2)
Area of Semicircle = (3.14 x 36/2)
Area of Semicircle = (3.14 x 18)
Area of Semicircle = 56.52[tex] in.^{2} [/tex]
Hope this helps!
[pi]r^2
So substituting...
The diameter is 12 in. And radius is half of the diameter.
12/2=6. The radius is 6 in.
To finish this, we do the r^2, which is 6^2, which is 36.
Finally, we multiply pi by 36, in this question we found pi to 3.14.
The area of the circle is 113.04 in. BUT, Half of the circle, that is being shaded, would subtract half of the circle away from the total area.
So we do 113.04/2=
56.52.
The answer is that the shaded/not shaded side of the circle is equal to 56.52 in.
120e^(2x)=75e^(3x)
Please solve with steps
Answers
[tex]120e^{2x}=75e^{3x}[/tex]
[tex]ln(120e^{2x})=ln(75e^{3x})[/tex]
Step 2. Apply product rule of logarithms [tex]ln(ab)=ln(a)+ln(b)[/tex]:
[tex]ln(120)+ln(e^{2x})=ln(75)+ln(e^{3x})[/tex]
Step 3. Apply the rule [tex]ln(e^x)=x[/tex]:
[tex]ln(120)+2x=ln(75)+3x[/tex]
Step 4. Solve for [tex]x[/tex]:
[tex]ln(120)+2x=ln(75)+3x[/tex]
[tex]ln(120)-ln(75)=3x-2x[/tex]
[tex]x=ln(120)-ln(75)[/tex]
Apply the quotient rule of logarithms [tex]ln(a)-ln(b)= ln(\frac{a}{b} )[/tex]:
[tex]x=ln( \frac{120}{75} )[/tex]
[tex]x=ln( \frac{8}{5} )[/tex]
We can conclude that the solution of our equation is [tex]x=ln( \frac{8}{5} )[/tex], which is approximately [tex]x=0.47[/tex].
solve using quadratic equations
Answers
4x² - 4x - 5x + 5 = 0
4x(x - 1) - 5(x - 1) = 0
(4x - 5)(x - 1) = 0
Set each binomial equal to zero.
4x - 5 = 0
4x = 0 + 5
4x = 5
x = 5/4
x - 1 = 0
x = 0 + 1
x = 1
Your solutions are x = 1, 5/4
I WILL MARK THE BRAINLIEST! PLZ HELP!
The track-and-field coach wants to know whether the students in the entire school prefer track races or field events. The coach draws a random sample from the following groups:
All students in each grade
All teachers in the school
All boys in each grade in the school
All students on the track-and-field team
Which group best represents the population she should take a random sample from to get the best results for her survey? (5 points)
{A} All students in each grade
{B} All teachers in the school
{C} All boys in each grade in the school
{D} All students on the track-and-field team
Answers
The track-and-field coach should select the group which contains all students in each grade to take a random sample to get the best results for her survey.
We have a situation in which track-and-field coach wants to know whether the students in the entire school prefer track races or field events. In order to do so she draws a random sample from the following groups:
• All teachers in the school
• All boys in each grade
• All students in the track-and-field team
• All students in each grade
We have to find the best group from which she should take a random sample of the above mentioned to get the best results for her survey.
What is the condition for Set A to be a Superset of Set B?Set A is superset of Set B if Set A contains all the elements of Set B.
In our question, we have four groups in the form of four sets as -
• Set of all teachers in school (say Set T)
• Set of all boys in each grade (say Set B)
• Set of All students in track-and-field team (Say Set C)
• Set of all students in each grade (Say Set S)
Since the art teacher wants to know the opinion of students, therefore Set T is not correct. Set B contains all boys in each grade, but it would exclude the girls in each grade, therefore it is also not correct. Set C consists of all students in track-and-field team, but it would exclude students who are not in track and field team, therefore incorrect. Set S consist of all Students in each grade, this means that Set S is the superset of Set B and Set C and contains all the students of the school.
Hence, the group that contains all students in each grade should be selected to take a random sample to get the best results for her survey.
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