First a few reminders:
• For a ≠ 0 and b ≥ 0, [tex]\sqrt[a]{b}=b^{\frac1a}[/tex]
• 4 = 2² and 8 = 2³
• For real numbers a, b, c, we have [tex](a^b)^c=a^{bc}[/tex]
• For any real numbers a and n (so long as both are not zero), we have [tex]\frac1{a^n}=a^{-n}[/tex]
• For any numbers a, b, c, [tex]a^b\times a^c=a^{b+c}[/tex]
So we have
[tex]\sqrt2=2^{\frac12}[/tex]
[tex]\dfrac1{\sqrt2}=2^{-\frac12}[/tex]
[tex]\dfrac1{\sqrt8}=\dfrac1{(2^3)^{\frac12}}=2^{-\frac32}[/tex]
Then the given expression can be rewritten as
[tex]2\sqrt2-\dfrac3{\sqrt2}+\dfrac4{\sqrt8}=2\times2^{\frac12}-3\times2^{-\frac12}+2^2\times2^{-\frac32}[/tex]
[tex]2\sqrt2-\dfrac3{\sqrt2}+\dfrac4{\sqrt8}=2^{1+\frac12}-3\times2^{-\frac12}+2^{2-\frac32}[/tex]
[tex]2\sqrt2-\dfrac3{\sqrt2}+\dfrac4{\sqrt8}=2^{\frac32}-3\times2^{-\frac12}+2^{\frac12}[/tex]
Pull out a factor of [tex]2^{-\frac12}[/tex]:
[tex]2\sqrt2-\dfrac3{\sqrt2}+\dfrac4{\sqrt8}=2^{-\frac12}\left(2^{\frac32+\frac12}-3+2^{\frac12+\frac12}\right)[/tex]
Simplify this:
[tex]2\sqrt2-\dfrac3{\sqrt2}+\dfrac4{\sqrt8}=2^{-\frac12}\left(2^2-3+2^1\right)=2^{-\frac12}(4-3+2)=3\times2^{-\frac12}=\dfrac3{\sqrt2}[/tex]
Rationalize this last result to get the square root out of the denominator:
[tex]2\sqrt2-\dfrac3{\sqrt2}+\dfrac4{\sqrt8}=\dfrac3{\sqrt2}\times\dfrac{\sqrt2}{\sqrt2}=\dfrac{3\sqrt2}{(\sqrt2)^2}=\boxed{\dfrac{3\sqrt2}2}[/tex]
It takes 14 hours to seal a hardwood floor with varnish. If each coat requires one whole and 3/4ths of an hour to dry, how many coats are applied?
plz help PLEASE.........
Answer:
7x² + 11x - 18
Step-by-step explanation:
13x² - 8 + 11x - 6x² - 10
13x² - 6x² + 11x - 8 - 10
7x² + 11x - 18
Mr. Charles bought dinner for his family.
The dinner cost $46.95.
He left a 15% tip.
About how much tip did Mr. Charles leave?
The Answer is $7.00 because 46.95 x 0.15 is 7.0425 which is about $7
A sphere just fits inside a cube with edges 20 in. Long. What is the volume of the sphere? What is the volume of the cube? What is the volume of the space between the cube and sphere?
Answer:
Step-by-step explanation:
Volume of a cube = (side)³
= (20)³
= 8000 cubic in.
Volume of the sphere which just fits in = [tex]\frac{4}{3}\pi r^{3}[/tex]
Here, r = Radius of the sphere
Since, sphere just fits in, radius of the sphere = half of the dimension of the cube
r = [tex]\frac{20}{2}[/tex]
r = 10 in
Therefore, volume of the sphere = [tex]\frac{4}{3}\pi (10)^3[/tex]
= 4188.79 cubic inch
Volume of the space between the cube and sphere = 8000 - 4188.79
= 3811.21 cubic inch
The ratio of boys to girls in the 10th grade is 8 to 13. If there are 91 girls in 10th grade, then how many boys are there?
Answer: There are 56 boys in the 10th grade
Step-by-step explanation:
Step 1
ratio of boys to girls in the 10th grade is 8 :13
Number of girls= 91
To find the number of boys, we first find the total number of boys and girls in the 10th grade
Step 2
Now the total ratio= 8 +13=21
Number of girls = ratio of girls/ total ratio x Total number of students
91=13/ 21 x Total number of students
Total number of students =21 x 91 / 13 =147
Step 3
Therefore Number of boys =ratio of boys/ total ratio x Total number of student
8/21 x 147=56
Find the are of the triangle below in square units
(The triangle is in the picture, please help! :,))
Answer:
252
Step-by-step explanation:
14 x 6 x 12 = 1008/2 = 504/2 = 252
Help plz, I don't understand
Alex has a pile of 2p coins. She swapped exactly half of them for the same number of 10p coins.
Now she has £4.20
How much money did alex have initially?
Answer:
£8.4
Step-by-step explanation:
Since she swapped half and now has £4.20, then multiply that by 2
4.20 × 2 = 8.4
Alex initially had £8.4
The initial amount of Alex's 2p coins is £8.40
Let the initial worth of 2p coins = y
Half of y = y/2 The value of y/2 = £4.20The amount of money Alex had initially = yWe can then solve for the worth of y, which is the titla amount Alex had initially ;
y/2 = £4.20Multiply bith sides by 2 (y/2)×2 = £4.20 × 2 y = £8.40Therefore, the amount of money Alex had initially is £8.40
Learn more : https://brainly.com/question/18109354
A wire is first bent into the shape of a rectangle with width 7in and length 9in then the wire is bent and reshaped into a square what is the length of a side of a square.
Answer:
Length of side of square = 8 inch
Step-by-step explanation:
Given:
Length of rectangular wire = 9 inch
Width of rectangular wire = 7 inch
Find:
Length of side of square
Computation:
We know that same wire is used from square
So,
Perimeter of rectangle = Perimeter of square
2[l + b] = 4 x side
2[9 + 7] = 4 x Length of side of square
2[16] = 4 x Length of side of square
32 = 4 x Length of side of square
Length of side of square = 32 / 4
Length of side of square = 8 inch
what is the radius of (x+5)^{2}+(y-4)^{2}=121?
Answer: 11
Step-by-step explanation:
Answer:
Step-by-step explanation:
The figure drawn is a circle. It's center is a (-5,4) just the opposite of what is in the brackets. I'm giving you this information just to be complete.
For a circle the radius is found using the lone number on the other side of the equal side -- in this case 121
The radius is the square root of that lone number.
radius^2 = 121
sqrt(radius^2) = sqrt(121)
radius = 11
Solve the following set of equations by Cramer's Rule
3x + 2y = 12
x + 5y = 17
Answer:
please check the pdf the solution for your answer is in it. hope it helps :)
Step-by-step explanation:
ASAPPPPP
Fill in the blank
When lit, a candle loses 5% of its original height every hour. Jennifer lit a candle with
an original height of 8 inches. Until the candle had been burning for at least _______ hours, the height of Jennifer's candle will be more than 7 inches.
Answer:
2.5 hours
Step-by-step explanation:
Find the surface area of the figure.
22 m
12 m
5 m
Answer and Step-by-step explanation:
Work is in Picture:
#teamtrees #PAW (Plant And Water)
which expression represents 12x³-6x²+2x /
2x in simplest form?
Answer:
[tex]6x^{2} -3x+1[/tex]
Step-by-step explanation:
[tex]2x(6x^{2} -3x+1)/2x\\[/tex]
cancel 2 x
[tex]6x^{2} -3x+1[/tex]
–6z^2− 8z + 8 = 0
sole using the quadratic formula
Answer:
Simplifying
6z2 + -8z + 1 = 0
Reorder the terms:
1 + -8z + 6z2 = 0
Solving
1 + -8z + 6z2 = 0
Step-by-step explanation:
true or false
when you have a common factor between the numerator and the denominator you will always have a hole
Answer:
true
Step-by-step explanation:
PLEASE HELP. Brainliest to whoever gives the best answer
real-world problems: 1 for the volume of a cone and 1 for the volume of a cylinder.
Answer:
See attached image.
Step-by-step explanation:
How about this answer to both? I've seen cylindrical-conic tanks in a local brewery. The tank is a cone with a cylinder on top. It's important to know the volumes of both the cylinder and the cone.
A magazine mailed a survey to 3,975 subscribers. Twenty-six percent of the subscribers answered the survey. About how many people answered the survey?
Jovan has a credit card with a $1,583 balance his interest rate is 8.8% if he does not pay for 3 years how much interest does
Answer:
$417.91
Step-by-step explanation:
PLEASE HELP !!!!!!!!!!! WILL MARK BRIANLIEST !!!!!!!!!!!!!
Answer:
3:2
Step-by-step explanation:
I'd say 3:2 because when you divide 45/30, you get 3/2, which is the same as 3:2. Hope this helps!
Answer: 1 boy for every 3 girls
Step-by-step explanation:
I put 30/45 into a fraction and simplified.
A rectangular prism has a volume of 819 cubic meters. It has a length of 10 meters and a width of 9 meters. What is the height of the prism?
Answer:
9.1m
Step-by-step explanation:
h = V ÷ l w = 819 ÷ (10 × 9) = 9.1m
Have a good day
help please i am stuck
Answer:
x = 25
Angle B = 65 degrees
Angle C = 50 degrees
Step-by-step explanation:
All triangles will add up to 180 degrees.
65 + 3x - 10 + 2x = 180
Combine like terms
55 + 5x = 180
Subtract both sides by 55
5x = 125
Divide both sides by 5
x = 25
Plug in the value for x in angle B:
3(25) - 10
75 - 10
65
Do the same for angle C:
2(25)
50
Check your work:
65 + 65 + 50 = 180
180 = 180
Correct
there are between 24 to 40 students in a class. the ratio of boys to girls is 4:7. how many students are in the class.
Answer:
8 students
Step-by-step explanation:
Answer:
33
Step-by-step explanation:
There are 4:7 boys to girls, so there is a multiple of 11 people, 4 + 7 = 11.
there are 4*3 boys and 7*3 girls, 12 boys and 21 girls
What is the area, in square centimeters, of the trapezoid shown below?
3 cm
9 cm
12 cm
Please help
Which expression is equivalent to 4/9 x 2
Answer:
4 × 2/9
Im sorry if I'm wrong
Answer:
4 × 2/9
Step-by-step explanation:
both equal 8/9
What are the coordinates of point P on a directed line segment from R to Q such that P is 5/6 the length of the line segment.
Answer:
[tex]P = [-3/5,2.33][/tex]
Step-by-step explanation:
Given
See attachment for line segment RQ
[tex]P = \frac{5}{6}[/tex] of RQ
Required
The coordinates of P
Using line segment ratio formula, we have:
[tex]P = [\frac{mx_2 + nx_1}{m+n},\frac{my_2 + ny_1}{m+n}][/tex]
If P is at:
[tex]P = \frac{5}{6}[/tex]
Then:
[tex]m : n = \frac{5}{6} : 1 -\frac{5}{6}[/tex]
Solve
[tex]m : n = \frac{5}{6} : \frac{6-5}{6}[/tex]
[tex]m : n = \frac{5}{6} : \frac{1}{6}[/tex]
Multiply by 6
[tex]m : n = \frac{5}{6} *6: \frac{1}{6} * 6[/tex]
[tex]m : n = 5 : 1[/tex]
By comparison
[tex]m=5\ \& n = 1[/tex]
From the attached line segment
[tex]R(x_1,y_1) = (4,-1)[/tex]
[tex]Q(x_2,y_2) = (-5,3)[/tex]
So, we have:
[tex]P = [\frac{5*-5 + 1*4}{5+1},\frac{5*3 + 1*-1}{5+1}][/tex]
[tex]P = [\frac{-25 + 4}{6},\frac{15 -1}{6}][/tex]
[tex]P = [\frac{-21}{6},\frac{14}{6}][/tex]
[tex]P = [-3/5,2.33][/tex]
How do you write an equation of a line given (1, 2) and (3, 4) in a slope -intercept form
Answer:
y = x + 1
Step-by-step explanation:
find slope first:
(4-2) / (3-1) = 2/2 or 1
now find the y-intercept, or 'b' by using one of the two given points and the slope
2 = 1(1) + b
2 = 1 + b
1 = b
equation in slope-intercept form:
y = 1x + 1 or y = x + 1
A cylinder has a diameter of 14 cm and a volume of 112 pi.
What is the height in, centimeters, of the cylinder?
(PS I am literally giving 15 points for the correct answer!!!)
HELP! :(
Each spinner shown is divided into equal
sections. Felix spins each spinner 30 times. He
records the number of times each section is
spun.
(8)
Red
(7)
Yellow
(5)
Blue
(10)
Green
(8)
E
(3)
Based on the results of the first 30 spins, what
is the probability that Felix will spin a green and
an F on the next spin?
A
1
24
B
D Not here
45
The probability that Felix will spin a green and an F on the next spin is 2/45.
What is probability?Probability is a number that expresses the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
Given, Felix spins each spinner 30 times. He
records the number of times each section is spun. Red (7), Yellow (5), Blue (10), Green (8)
Since probability distribution:
A probability distribution is a mathematical function that describes the probability of different possible values of a variable.
probability= desired outcome/ Total Outcomes
In our case,
Total outcomes = 30 *30
Desired outcome = spin a green and an F on the next spin
Since from probability distribution getting F and getting green has a likelihood of 5 and 8.
thus,
Probability = 8 * 5/ 30 *30
probability = 2/45
therefore, the probability that Felix will spin a green and an F on the next spin is 2/45.
Learn more about probability here:
https://brainly.com/question/30034780
#SPJ2
Select all of the equations where x = 3 is a solution.
3x = 1
3x = 33
7x – 2 = 19
2x = 5
5x = 15
5x + 6 = 21
Answer:
7x-2=19
5x=15
5x+6=21
................
Step-by-step explanation:
Here x = 3
3x = 1 (False)
3* 3 ≠1
3x = 33 (False)
3 *3 ≠ 33
7x - 2 =19 (True)
7 *3 - 2 = 19
21 - 2 = 19
19 = 19
2x = 5 (False)
2 *3 ≠ 5
5x = 15 (True)
5 * 3 = 15
15 = 15
5x + 6 = 21 (True)
5 * 3 + 6 = 21
15 + 6 = 21
21 = 21
Hope it will help :)❤
