Answer:
[tex]\displaystyle \frac{9}{\sqrt{7}-2}=3\sqrt{7}+6[/tex]
Step-by-step explanation:
Rationalizing the Denominator
Rationalizing the denominator means to get rid of any radicals in the denominator.
We use the conjugate of the denominator to rationalize. The conjugate of a binomial is obtained by changing the sign that is between the two terms while keeping the same order of the terms. For example, the conjugate of
[tex]\sqrt{7}-2[/tex] is [tex]\sqrt{7}+2[/tex].
We need to use the algebraic identity:
[tex](a-b)(a+b)=a^2-b^2[/tex]
Let's rationalize
[tex]\displaystyle \frac{9}{\sqrt{7}-2}[/tex]
Multiply numerator and denominator by the conjugate of the denominator:
[tex]\displaystyle \frac{9}{\sqrt{7}-2}=\frac{9}{\sqrt{7}-2}\cdot\frac{\sqrt{7}+2}{\sqrt{7}+2}[/tex]
Operate in the numerator and apply the identity in the denominator
[tex]\displaystyle \frac{9}{\sqrt{7}-2}=\frac{9(\sqrt{7}+2)}{(\sqrt{7}-2)(\sqrt{7}+2)}[/tex]
[tex]\displaystyle \frac{9}{\sqrt{7}-2}=\frac{9\sqrt{7}+18}{(\sqrt{7})^2-2^2}[/tex]
[tex]\displaystyle \frac{9}{\sqrt{7}-2}=\frac{9\sqrt{7}+18}{7-4}=\frac{9\sqrt{7}+18}{3}[/tex]
Dividing:
[tex]\boxed{\displaystyle \frac{9}{\sqrt{7}-2}=3\sqrt{7}+6}[/tex]
Write a rule for the translation of AABC to AA'B'C'
Answer:
(x-1,y-2)
Step-by-step explanation:
manteo made the model below to represent the number of miles he swims in the pool each week for exercise
Answer:
What model?
Step-by-step explanation:
Find the length of the segment with endpoints of (3,2) and (-3,-6).
(Will Mark Brainlyest!)
Answer:
i think its (x2,y2)=(19,3)
Step-by-step explanation:
sorry if its wrong
Isabella deposited $2,000 in an account that earns 5% simple annual interest. After one year, how much interest will her investment earns?
Answer:
2100
Step-by-step explanation:
5% of 2000 = 2000 x 1/20 = 100.
2000+100=2100
Also, if it said how much interest will her investment PAY, then it would be $100 because of the 5% simple interest.
у + 3x = -4 2х - Зу = -21
Help plz
Answer:
у + 3x = -4 2х - Зу = -21
Step-by-step explanation:
What is the slope and y intercept of Y= -4x + 2
Answer:
Slope=-4
Y intercept= 0,2
Step-by-step explanation:
Use the slope-intercept form to find the slope and y-intercept.
Given D'E'F'G' is a dilation of DEFG, find the scale factor of dilation.
Answer:
7.5
Step-by-step explanation:
157.5/21 = 7.5
Shasta is going to her best friend's house for dinner. Her mother says she needs to be back in 2 and a half hours. If she leaves at 5:00 pm, what time will she be back?
Answer:
she will be back at 7:30pm
Step-by-step explanation:
From the question we are given
Time that Shasta leaves for her best friend place = 5:00pm
If she is to come back after 2 and a half hour, hence we will have to add 2hr 3ominutes to the time she left to know the time she will be back as shown:
She will be back at 5:00 + 2hr 30min = 7:30pm
Hence she will be back at 7:30pm
Express the recurring decimal 0.56 as a fraction in its simplest form.
Answer:
0,13
Step-by-step explanation:
the answer of the question is 14/25
Please help-
I will try and give a lot of points
Answer:
25%, since 1/4=0.25 and 0.25*100 is 25%
Hope it helps!
Answer:
Step-by-step explanation:
Given data:
The given fraction is [tex]\frac{1}{4}[/tex]
The given fraction can be written as,
[tex]\frac{1}{4}=0.25\\=\frac{25}{100} \\=25 percentage[/tex]
Thus , the given fraction is 25%.
PLEASE MARK ME AS BRAINLIEST
Every morning runs for 30 minutes. If runs 6 miles per hour, how far does travel? Use the equation drt, where d is the distance, r is the rate, and t is time.
Answer:
3 Miles
Step-by-step explanation:
D = R*T
0.5*6 = 3
so 3
What is 9,000.000.000.000.000.000.X 12.000.000.000.000.000.000.000.000.000.000
Answer:
108000.
Step-by-step explanation:
9,000 x 12
Kristina walked 1 2/3
miles on Sunday and 2 3/4 miles on Monday. What was the total distance, in
miles, that she walked over those two days
Answer: 4 5/12 miles
Step-by-step explanation: To add or subtract two fraction, you need to find a common denominator. The easiest way to do that is to just multiply the denominators of the two fractions together. 3 x 4 = 12 so I'll use 12 as my common denominator. Now that we have that, we have to convert the numerators. We must multiply the numerators by the same number we multiplied or denominators by to get the common denominator. 3 x 4 = 12, 4 x 3 = 12, 2 x 4 = 8, 3 x 4 = 12. Now the fractions we have are 9/12 and 8/12. Since they have the same denominator now we can add them. 9/12 plus 8/12 equals 17/12 or 1 and 5/12 written as a mixed number. We also add the whole numbers. 1 plus two equals 3. 3 plus 1 and 5/12 equals 4 and 5/12.
What transformation for Rectangle A would result in Rectangle B?
A
reflection across the X-axis
B
reflection across the y-axis
c
translation, 4 units up
D
translation, 2 units down
Answer:
I think A I'm not sure tho
In the transformation of rectangle A, a reflection is across the X-axis. The correct option is A.
What is a reflection?A reflection in mathematics is a mapping from a Euclidean space to itself that is an isometry with a set of fixed points known as the hyperplane, also known as the axis or plane of reflection. The mirror image of a figure in the axis or plane of reflection is the image produced by a reflection.
Given image is having a rectangle A which is having reflection across the X-axis. The meaning of the reflection is that the figure will have an image of itself across the x-axis.
Therefore, in the transformation of rectangle A, a reflection is across the X-axis. The correct option is A.
To know more about reflection follow
https://brainly.com/question/26642069
#SPJ5
What is the mean absolute deviation of the set of numbers {3, 7, 5, 6, 4}?
Answer:
5
Step-by-step explanation:
mean = sum of all values÷number of observation
= 3+7+5+6+4 ÷ 5
= 5
Can someone help me with this geometry question.
can someone anyone please help me asap
Answer:
the answer is option : D
Step-by-step explanation:
multiply 9 with the given hrs to find the correct one
answers for the 2 boxes please
Answer:
(2, 12)
Step-by-step explanation:
x + 10 = 4x + 4
- 4 - 4
x + 6 = 4x
- x - x
6 = 3x
divide 3 on each side
2 = x
then plug 2 in either equation
ei) y = 2 + 10
y = 12
Please help me, I’m brain dead right now:)
Answer:
A 40%
Step-by-step explanation:
2/5 = 40/100 (or 40%)
So 40 blocks should be filled in :)
Hope this helps!
Answer: the answer is a
Step-by-step explanation: because the equivalent fraction is 4/10 and the graph is of 10 by 10 so from it shahid 10 from breath and 4 from length
PLEASE MAKE Me THE BRAINLYEST
What is the y intercept of this line?
Answer:
-2 i think
Step-by-step explanation:
(0,4) or 4
Solution:The y-intercept is the point where the graph intersects the y-axis.It's usually written as (0, b) where "b" stands for the y-intercept.Since the line intersects the y-axis at (0, 4) the y-intercept is (0,4) or 4.Hope it helps.
Do comment if you have any query.
Find the volume of a pyramid with a square base, where the side length of the base is
4.9 m and the height of the pyramid is 5.3 m. Round your answer to the nearest
tenth of a cubic meter.
Answer:
127.253 m^3
Step-by-step explanation:
To find the volume, we start by getting the area of the square base
Mathematically, that will be 4.9^2 m^2
To complete the volume, we multiply the area of the base by the height
= 4.9^2 * 5.3 = 127.253 m^3
Answer:
Step-by-step explanation:
42.4
6) A design for a library has a scale of
1/3inch = 1 foot. The height of the library
in the drawing is 12 inches. What is the
actual height of the library?
Answer:
36 feet
Step-by-step explanation:
There are three feet to each foot, 3 times 12 is 36.
In the ordered pair below, which number represents "x", the input? (3, 5) A B 3 5
Answer:
i believe 3 would be your answer (x,y)
Step-by-step explanation:
(2x - 9) (x + 4) = 0
What the answer
Answer:
x = 4.5 AND x = -4
Step-by-step explanation:
for the first answer
add 9 to 0 and divide by 2
for the second answer
subtract 4
Answer:
x = 9/2 and x = -4
Step-by-step explanation:
you can set each expression in the parenthesis' equal to zero. this is due to it being multiplication so if one parenthesis equals 0, the answer will be 0
2x - 9 = 0 and x + 4 = 0
starting with 2x-9=0
add 9 to both sides
2x = 9
divide by 2
x = 9/2
then do x + 4 = 0
subtract 4
x = -4
so your two answers are
x = 9/2 and x = -4
Suppose the expression was (12 - 3)². Would you still simplify 3² first? Explain.
Answer:
No because the 2 is outside of the parentheses meaning it should be 9^2
Step-by-step explanation:
Answer:
No, I will not simplify 3² first.
Rather I would simplify (12-3) first, i.e., 9.
Then simplify 9² which gives the answer 81.
Step-by-step explanation:
(12-3)²= 9²= 8133) What value for x makes this equation true? 4x + 3 = 23
Answer:
x = 5
Step-by-step explanation:
4x + 3 = 23
Subtract 3 from both sides;
4x = 20
Divide both sides by 4;
x = 5
Answer:
x=5
Step-by-step explanation:
4x+3=23
4x=23-3
4x=20
x=20/4
x=5
Please help WHAT IS THE PERCENT OF 39.8 out of 200 QUICK PLEASE
Answer:
19.9%
Step-by-step explanation:
39.8/200 = 0.199 (move decimal two times)
19.9%
or you can just see what number get 200 to 100, which is by dividing by 2. What you do to the bottom you do to the top so 39.8/200 (divide both sides by 2) = 19.9/100
which is 19.9%.
Ace Carlos
Will mark Brainliest for the correct answer. Also, it wouldn’t hurt to explain your thought process when going through these problems but is not required to get Brainliest.
Answer:
Step-by-step explanation:
2a) p * [tex](3p^{3} )^{2}[/tex]
[tex]p^{1}[/tex] * [tex]9p^{2*3}[/tex]
[tex]p^{1}[/tex] * [tex]9p^{6}[/tex]
[tex]9p^{6+1}[/tex]
[tex]9p^{7}[/tex]
2b) ( [tex](-3x)^{2}[/tex] * [tex]x^{3}[/tex] *[tex]y^{5}[/tex] ) / [tex]y^{6}[/tex]
[tex]9x^{2}[/tex] *[tex]x^{3}[/tex] / [tex]y^{1}[/tex]
[tex]9x^{2+3}[/tex] / y
[tex]9x^{5}[/tex] /y
If you want to show an increase to the original quantity, how could you change the bar diagram?
Answer:
Write a situation in which positive and negative numbers are used to describe values that have opposite meaning. What does 0 represent in this situation you created?
Step-by-step explanation:
Use the slope -intercept form to graph the equation y=5/7x-1
Answer:
I’m gonna explain this best I can
Step-by-step explanation:
okay, since I dont have graphing paper or your graph, I am going to put the points that your dots would go in, and you can put them and connect the line :)
first point: (0, -1)
second point: (7, 4)
third point: (14, 9)
then connect the line