Answer:
[tex]\frac{2\sqrt{2}}{\sqrt{3}-\sqrt{2}}=2\sqrt{6}+4[/tex]
Step-by-step explanation:
We have the expression:
[tex]\frac{2\sqrt{2}}{\sqrt{3}-\sqrt{2}}[/tex]
To simplify the expression multiply by the conjugate of the denominator.
The denominator is
[tex]\sqrt{3}-\sqrt{2}[/tex]
Then its conjugate is:
[tex]\sqrt{3}+\sqrt{2}[/tex]
Then:
[tex]\frac{2\sqrt{2}}{\sqrt{3}-\sqrt{2}}*\frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}+\sqrt{2}}\\\\=\frac{2\sqrt{2}\sqrt{3}+2\sqrt{2}\sqrt{2}}{(\sqrt{3})^2-(\sqrt{2})^2}\\\\\frac{2\sqrt{6}+4}{3-2}}\\\\= \frac{2\sqrt{6}+4}{1}}=2\sqrt{6}+4[/tex]
Answer:
[tex]4+2\sqrt{6}[/tex]
Step-by-step explanation:
Given expression is [tex]\frac{2\sqrt{2}}{\sqrt{3}-\sqrt{2}}[/tex].
Now we need to simplify this. So multiply and divide by conjugate of denominator.
[tex]\frac{2\sqrt{2}}{\sqrt{3}-\sqrt{2}}[/tex]
[tex]=\frac{2\sqrt{2}}{\left(\sqrt{3}-\sqrt{2}\right)}[/tex]
[tex]=\frac{2\sqrt{2}}{\left(\sqrt{3}-\sqrt{2}\right)}\cdot\frac{\left(\sqrt{3}+\sqrt{2}\right)}{\left(\sqrt{3}+\sqrt{2}\right)}[/tex]
[tex]=\frac{2\sqrt{6}+2\sqrt{4}}{\left(\sqrt{3}\right)^2-\left(\sqrt{2}\right)^2}[/tex]
[tex]=\frac{2\sqrt{6}+2\cdot2}{3-2}[/tex]
[tex]=\frac{2\sqrt{6}+4}{1}[/tex]
[tex]=2\sqrt{6}+4[/tex]
[tex]=4+2\sqrt{6}[/tex]
Hence final answer is [tex]4+2\sqrt{6}[/tex].
Please Help , Is it ABC or D
Answer:
A
Step-by-step explanation:
To determine the scale factor compare the quotient of the coordinates of the image with the original coordinates
A
[tex]\frac{2}{1}[/tex] = [tex]\frac{4}{2}[/tex] = 2
B
[tex]\frac{4}{2}[/tex] = [tex]\frac{8}{4}[/tex] = 2
C
[tex]\frac{8}{4}[/tex] = [tex]\frac{16}{8}[/tex] = 2
Hence the scale factor is 2
Tools
Question 12
The bottom of a garage door is 2.8 meters above the ground. When a button is pushed, the door moves down at a rate of 0.6 meter per second. W
A 0.6 + 2.8t = 0
B 0.6 – 2.8t = 0
C 2.8 + 0.6t = 0
D 2.8 – 0.6t = 0
Answer: D. 2.8 - 0.6t
Step-by-step explanation:
The t represents how much time it takes. So, it goes down by 0.6 per second until it gets to 0.
A garage door's bottom is 2.8 meters above the ground. The door descends at a pace of 0.6 meters per second when a button is pressed. The equation for the above situation is 2.8 + 0.6t = 0. Option C is correct.
What is an equation?Equations are statements that affirm the equivalence of two expressions that are joined by the equals symbol "=". An equal sign ("=") links two expressions together to form an equation.
It is given that, the bottom of a garage door is 2.8 meters above the ground. When a button is pushed, the door moves down at a rate of 0.6 meters per second.
The two expressions on each side of the equals sign are referred to as the "left-hand side" and "right-hand side" of the equation. The right side of an equation is typically assumed to be zero.
Suppose t represents the number of seconds, The equation for the given condition is,
2.8 + 0.6t = 0.
Thus, a garage door's bottom is 2.8 meters above the ground. The door descends at a pace of 0.6 meters per second when a button is pressed. The equation for the above situation is 2.8 + 0.6t = 0. Option C is correct.
Learn more about the equation here,
https://brainly.com/question/10413253
#SPJ2
Heston wagons reported in June that 20 out of 500 wagons failed inspection. In July they reported that 25 out of 625 wagons failed inspection.which proportion can be used to represent the wagon failures?
Answer:
The proportion is [tex]\frac{y}{x} =\frac{1}{25}[/tex]
Step-by-step explanation:
We have to:
In June 20 of 500 wagons failed
On July 25 of 625 wagons failed
If we call x the number of wagons and and the number of wagons that had failures then we have to for June:
[tex]\frac{y}{x} = \frac{20}{500}\\\\\frac{y}{x} = \frac{1}{25}[/tex]
For July we have
[tex]\frac{y}{x} = \frac{25}{625}\\\\\frac{y}{x} = \frac{1}{25}[/tex]
The proportions are the same for both months
[tex]\frac{20}{500} = \frac{25}{625}[/tex]
The proportion is [tex]\frac{y}{x} =\frac{1}{25}[/tex]
This means that of every 25 wagons, one has faults
Answer:
its D
Step-by-step explanation:
hope it helps!
took a test!
The fence is 68 feet long and 1/2 feet thick. 7 feet of space is between each post. How many posts are used for the fence. I think it’s basic division but I’m not sure what to divide by lol.
Answer:
We could say 10
Step-by-step explanation:
1) Remove unneeded info
2) Divide the length by the distance between posts
68/7
3) Will give you a decimal but ro7nd up to 10
The sum of three consecutive numbers is 72. What is the middle number?
Answer:
48
Step-by-step explanation:
Assuming that the numbers went in a pattern instead of a random order it would be 48 because 48 divided by 3 would be 24. 24 would be the first number though, so it would be 48 because 24 plus 24 is 48.
Hope this helps, have a great day!
Thhe answer is 48 :]
help me with #3 please please and explain
all you have to do is 524 times 2 and then add m3
there is a formula for the volume of a cylinder. use the given info to plug into formula
Suppose that you ask three friends to go to the mall. Each one has a 0.70 chance of saying yes. What is the probability that all three friends will say they can go to the mall with you? a. 0.027 c. 0.343 b. 0.21 d. 0.657
____________________________________________________
Answer:
Your answer would be 0.343.
____________________________________________________
Step-by-step explanation:
In the probability questions like this one, in order to get the answer,we would use the multiplication rule.
In your questions, we are trying to find the probability of ALL of your friends going to the mall with you.
Lets make it easier for you.
Whenever in probability you can say and, you multiply.
This means that you would try to find if friend 1 and friend 2 and friend 3 will say yes.
That's the same as saying friend 1's probability × friend 2's probability × friend 3's probability
We know that each friend has a 0.70 chance of saying yes.
Using the multiplication rule, we would just multiply 0.7 three times.
[tex]0.7 *0.7*0.7=0.343[/tex]
When you multiply, you should get 0.343.
There is a 0.343 chance of ALL your friends saying yes to go to the mall with you.
0.343 would be your FINAL answer.
____________________________________________________
To solve this problem, you need to consider the probability of each friend agreeing to go to the mall individually, then multiply these probabilities together to find the probability that all three will say yes.
Since each friend has a 0.70 chance of saying yes, we can calculate the combined probability as follows:
For the first friend, the probability is 0.70.
For the second friend, the probability is also 0.70.
For the third friend, the probability remains 0.70.
To find the combined probability that all three friends will say yes, we multiply the individual probabilities together:
\( Probability (All Say Yes) = Probability (Friend1 says Yes) \times Probability (Friend2 says Yes) \times Probability (Friend3 says Yes) \)
\( Probability (All Say Yes) = 0.70 \times 0.70 \times 0.70 \)
When you calculate this, you get:
\( Probability (All Say Yes) = 0.343 \)
So the answer is c. 0.343.
Jonathon deposits $11,000 in an account paying 6% compounded semiannually. Find the interest earned on the investment after 10 years.
$19,867.22
$8,954.20
$8,867.22
$19,954.20
Answer:
Total = Principal * (1 + 6%/2)^2*years
Total = 11,000 * (1.03)^2*10
Total = 11,000 * (1.03)^20
Total = 11,000 * 1.8061112347
Total = 19,867.22
Step-by-step explanation:
given x-5>-2 choose the solution set
x -5 > -2
Add 5 to both sides:
x > 3
The answer is the 3rd choice.
Answer:
x>3
Step-by-step explanation:
just add 5 to both sides :p
Find the vertical, horizontal, and slant asymptotes, if any, for f(x)=5x^3-51x^2+77x+100/x^2-11x+24
Answer:
Step-by-step explanation:
Given: f(x)=5x^3-51x^2+77x+100/x^2-11x+24
Please use parentheses to eliminate any ambiguity:
f(x) = (5x^3-51x^2+77x+100) / (x^2 - 11x + 24)
or (better yet):
5x^3-51x^2+77x+100
f(x) = ---------------------------------
x^2 - 11x + 24
The vertical asymptotes here are at the zeros of the denominator:
x^2 - 11x + 24 = 0, This quadratic equation has coefficients a = 1, b = -11 and c = 24. Thus, its roots (zeros) are:
-(-11) ± √( 121 - 4(1)(24) )
x = -------------------------------------
2(1)
or:
11 ± √( 25 )
x = --------------------
2
or: x = 8 and x = 3
The vertical asymptotes are x = 8 and x = 3.
If we attempt to divide x^2 - 11x + 24 into 5x^3 - 51x^2 + 77x + 100, we see that the first term of the quotient is 5x. As x increases or decreases without bound, 5x goes to either ∞ or -∞, so we conclude that there is no horiz. asymptote. Continuing this division results in:
5x + 4 + a fraction
This represents the slant asymptote, y = 5x + 4
Answer:
5x+4
Step-by-step explanation:
edge 2020 2021
The total distance around a running track is 1 5/8 miles. Wayne ran 1/4 of the track. What equation can be used to find d, the distance in miles that Wayne ran?
Answer:
1 5/8 * 1/4 = d
Step-by-step explanation:
Is .9 greater or less than 95%?
Less than 95%
Why because if you change .9 into a percentage, it turns into 90%
I hope that was correct
[tex]\text{Hey there!}[/tex]
[tex]\text{Is .9 greater or less than 95\%?}[/tex]
[tex]\bf{.9\rightarrow0.9\rightarrow\frac{18}{20}}[/tex]
[tex]\bf{95\%\rightarrow0.95\rightarrow\frac{19}{20}}[/tex]
[tex]\bf{You\ could\ reask\ yourself\ is\frac{18}{20}\ greater\ or\ less\ than\frac{19}{20}}?[/tex]
[tex]\text{Note: Solve the fractions/ decimals/ percentages to where you can}[/tex] [tex]\text{understand it better}[/tex]
[tex]\text{After that you'd find your result to your question}[/tex]
[tex]\boxed{\boxed{\text{Thus your answer will be: .9 is LESS THAN 95\%}}}[/tex] [tex]\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
How to get 354 by regrouping
Answer: 627-273
Step-by-step explanation:
Simplify 12√18-6√20-3√50-8√45
12√18-6√20-3√50-8√45
*Break each radical up into the product of a radical of a perfect square and a second radical*
12(√9*√2)-6(√4*√5)-3(√25*√2)-8(√9*√5)
*Simplify the radicals*
12(3√2)-6(2√5)-3(5√2)-8(3√5)
*Distribute*
36√2-12√5-15√2-24√5
*Combine like terms*
21√2-36√5
Hope this helps!!
The simplified form of the expression is 21√2-36√5.
Given,
12√18-6√20-3√50-8√45
Here,
12√18-6√20-3√50-8√45
⇒ Break each radical up into the product of a radical of a perfect square and a second radical.
Rewriting the expression,
12(√9*√2)-6(√4*√5)-3(√25*√2)-8(√9*√5)
⇒ Simplify the radicals
12(3√2)-6(2√5)-3(5√2)-8(3√5)
⇒ Distributive property
36√2-12√5-15√2-24√5
⇒ Combine like terms
21√2-36√5
Thus the simplified expression is 21√2-36√5.
Know more about radicals,
https://brainly.com/question/14923091
#SPJ4
Write the given equation in slope-intercept form, y=mx+b by solving for y. 4x - 2y =10
y = 2x - 5
Here’s a photo of the math
The equation will be y = 2x - 5
Given Equation: 4x - 2y = 10
Step 1: Move 4x to the other side to isolate -2y: -2y = -4x + 10
Step 2: Divide by -2 to solve for y: y = 2x - 5
how do i graph the lines when the equations aren’t in slope intercept form????
Slope-Intercept Form: y=mx+b
Standard Form: ax+by=c
Point- Slope: (y-y1)= m(x-x1)
There are multiple answers to your question-
If you are only missing b(the y-intercept) but are given a set of points, plug the points into x and y and solve for b.If you are only missing the slope(m) but are given a set of points, plug the points into x and y and solve for m.If you are given the standard form/point-slope form, change the equation to slope intercept form. If you are given an complete form(there is an x and y; no missing variables), but are not sure what it is, plug in some numbers in x to find y, then graph.Use the counting principle to determine the number of possible outfits that can be created using one item from each category.
7 shirts
6 pairs of pants
6 pairs of socks
4 hats
Answer:
1008
Step-by-step explanation:
To find the total outfits that can be created, we multiply the different number of stuff together. So the answer is 7*6*6*4 = 1008 outfits.
Answer:
I think it would be 1008.
Step-by-step explanation:
Hope this helps!!
what is the volume of the cone with radius 6 inches and height 10 inches express the answer in terms of pi
Answer:
V = (1/3)(π)(6 in)²(10 in) = 120π in³
Step-by-step explanation:
The volume of a cone of radius r and height h is V = (1/3)πr²h.
Here, that volume is V = (1/3)(π)(6 in)²(10 in) = 120π in³
Answer:
120pi
Step-by-step explanation:
What is the slope of the function?
-10, -5, 5, 10
It is -10
Because when you take two points from the table and put it into the equation y=my+b...
So for example, take (-4,-16) from the table and substitute into x and y...
-16=m(-4) + b
And then substitute all the options given in the question, so I tried -10 first and put it in the place of m( in the equation) because m is the slope.
Then the equation would look like this:
-16= -10(-4) +b
Now solve for b
B= 24
And then check your answer by the RHS and LHS Method..
-16=-40 +24
Which is equal to:
-16=-16
There fore the the slope of this equation is 10
Answer: 5
Step-by-step explanation:
The formula to find slope is given by :-
[tex]\text{Slope}=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
From the given table in picture,
Take [tex]x_1=0\ ;\ y_1=4\\\\x_2=2\ ;\ y_2=14[/tex]
Then, slope of the given function will be given by :-
[tex]\text{Slope}=\dfrac{14-4}{2-0}\\\\\Rightarrow\text{Slope}=\dfrac{10}{2}=5[/tex]
Hence, the slope of the given function = 5
Colin invests £1200 into his bank account. He receives 3% per year simple interest. How much will Colin have after 4 years? Give your answer to the nearest penny where appropriate.
Colin will have £1344 in his bank account after 4 years. This is calculated using the simple interest formula I = PRT (Interest = Principal x Rate x Time) yielding an interest earned of £144 over four years, which was then added to the initial investment.
Explanation:First, understand that simple interest is calculated as (principal amount × interest rate × time in years). The principal amount here is £1200, the interest rate is 3%, and the time period is 4 years.
Before doing the calculation, convert the 3% interest rate into decimal form by dividing by 100, yielding 0.03.
War is represented by the formula I = PRT, which means Interest = Principal x Rate x Time. So, use these values in the formula: £1200 * 0.03 * 4. This gives you £144, which is the interest earned after 4 years.
To find the total amount in Colin's account after 4 years, you need to add the interest earned to the principal amount. Therefore, £1200 (original amount) + £144 (interest) = £1344.
So, after 4 years, Colin will have £1344 in his bank account.
Learn more about Simple Interest here:https://brainly.com/question/40405117
#SPJ12
Consider the following equations: −x − y = 1 y = x + 3 If the two equations are graphed, at what point do the lines representing the two equations intersect? (4 points) (−1, 2) (−2, 1) (1, −2) (2, −1)
Equation 1: -x-y = 1y, -x = 2y
Equation 2: 1y = x+3 , y = x+3
Substitute equation 2 into equation 1
-x = 2y
-x = 2(x+3)
-x = 2x + 6
-3x = 6
x = -2
Substitute x=-2 into equation 2
y = x+3
y = -2+3
y = 1
So, (x,y) = (-2,1)
What is the value of x?enter your answer in the box.
Answer:
Hence final answer is x=46
Step-by-step explanation:
We need to find the value of x using given triangle.
Given that ED is angle bisector of angle E.
Then we can apply this formula
[tex]\frac{EG}{EH}=\frac{DG}{DH}[/tex]
[tex]\frac{63.8}{55}=\frac{58}{x+4}[/tex]
[tex]\frac{63.8}{55}=\frac{58}{x+4}[/tex]
Cross multiply
63.8(x+4)=55(58)
63.8(x+4)=3190[tex]x+4=\frac{3190}{63.8}[/tex]
x+4=50
x=50-4
x=46
Hence final answer is x=46
What is the initial value of the function represented by this table?
x y
0 5
1 9
2 13
A) 0
B) 3
C) 4
D) 5
Answer:
Option D. 5
Step-by-step explanation:
we know that
The initial value of the function is the y-intercept, so is the value of the function when the value of x is equal to zero
In this problem observing the table
For x=0
The value of y is equal to y=5
therefore
The initial value is 5
Answer:
It is 5!
Step-by-step explanation:
I just did the test and got it correct.
I think of a number, multiply it by three, and add four. I get twenty two.
Using the statement above, form an equation. Use the letter x for the unknown number.
Answer:
3x+4=22
Step-by-step explanation
So, if you minus 4 from 22 and divided by 3, there will be the answer for x. Which is 6.
The equation that could be formed using the letter x to be represent the unknown number is 3x + 4 = 22
let
x = the unknown number
multiply it by three
= x × 3
= 3x
add four
3x + 4
I get twenty two
3x + 4 = 22
solve for x
3x = 22 - 4
3x = 18
x = 18/3
x = 6
Therefore, the unknown number in the equation 3x + 4 = 22 is 6
check:
3x + 4 = 22
3(6) + 4 = 22
18 + 4 = 22
Read more:
https://brainly.com/question/19952256
PLEASE HELP 13 POINTS
Answer: 6/15-5/15=1/5
Answer:
Step-by-step explanation:
To find the common denominator, you must multiply 5 times three to get fifteen. Then you must multiply two times three and then one times three. Your two fractions with the same denominator would be 6/15 minus 5/15 your answer would be 1/15
round 26.86 to the nearest tenth
Answer:
26.9
Step-by-step explanation:
Right now we have '8' in the tenths place. That '6' following the '8' requires us to round up. Thus, 26.86 to the nearest tenth is 26.9.
A recipe for cookies requires 2/3 cup of butter. Anna wants to make 1/4 of the recipe. How many cups of butter should Anna use to make the cookies? You must
Answer:5/12
Step-by-step explanation:2/3-1/4=5/12
For this case we must raise a rule three:
1 recipe ----------------------->[tex]\frac {2} {3}[/tex] butter
[tex]\frac {1} {4}[/tex]recipe -------> x
Where the variable "x" represents the amount of butter that requires a quarter of the cookie recipe.
[tex]x = \frac {\frac {1} {4} * \frac {2} {3}} {1}\\x = \frac {2} {12} = \frac {1} {6}[/tex]
So, Anna requires[tex]\frac {1} {6}[/tex] cup of butter
ANswer:
[tex]\frac {1} {6}[/tex]
The longest chord of a circle is?
Answer:
diameter
Step-by-step explanation:
A chord is a line segment connecting any 2 points on the circumference of the circle.
The diameter connects 2 points and also passes through the centre of the circle, making it the longest chord.
explain why it is useful to write linear equations in equivalent form. what does each form reveal?
However, point slope equations can be awkward to use in some algebraic operations. In such cases, it may be helpful to convert the equation into a different form, the standard form. The standard form of an equation is Ax + By = C. In this kind of equation, x and y are variables and A, B, and C are integers.
Solve m + 2/3 = 1/2
1 1/6
1/6
-1
- 1/8
Answer:
m = - 1/6
Step-by-step explanation:
Since 2/3 is larger than 1/2, m is going to be less than 0 because you have to subtract 2/3 to get to the right. That makes a and b incorrect. I can tell you that the answer doesn't appear to be there.
m + 2/3 = 1/2 Subtract 2/3
m = 1/2 - 2/3 The common denominator is 6
m = 3/6 - 4/6 Do the subtraction
m = - 1/6
You might want to check out the - 1/8.
The Answer: m = - 1/6