Answer:
[tex]a+b+c=9+8+6=23[/tex]
Step-by-step explanation:
Let’s first simplify our expression. We have:
[tex]\displaystyle {\sqrt2+\frac{1}{\sqrt2}+\sqrt3+\frac{1}{\sqrt{3}}[/tex]
For the second term, multiply both the numerator and denominator by √2. This yields:
[tex]\displaystyle \frac{1}{\sqrt{2}}\cdot\frac{\sqrt{2}}{\sqrt{2}}=\frac{\sqrt{2}}{2}[/tex]
Similarly, for the fourth term, multiply both the numerator and denominator by √3. This yields:
[tex]\displaystyle\frac{1}{\sqrt{3}}\cdot\frac{\sqrt{3}}{\sqrt{3}}=\frac{\sqrt{3}}{3}[/tex]
Hence, our expression is now:
[tex]\displaystyle =\sqrt{2}+\frac{\sqrt{2}}{2}+\sqrt{3}+\frac{\sqrt{3}}{3}[/tex]
Let’s combine them. First, we will need common denominators.
Our denominators are 2 and 3. So, our common denominator will be its LCM.
The LCM of 2 and 3 is 6.
Hence, let’s make each term’s denominator 6.
For the first term, we can multiply both layers by 6. Hence:
[tex]\displaystyle \sqrt{2}=\frac{6\sqrt{2}}{6}[/tex]
For the second term, we can multiply both layers by 3. Hence:
[tex]\displaystyle \frac{\sqrt{2}}{2}=\frac{3\sqrt{2}}{6}[/tex]
For the third term, we can multiply both layers by 6. Hence:
[tex]\displaystyle \sqrt{3}=\frac{6\sqrt{3}}{6}[/tex]
And for the last term, we can multiply both layers by 2. Hence:
[tex]\displaystyle \frac{\sqrt{3}}{3}=\frac{2\sqrt{3}}{6}[/tex]
So, our expression is:
[tex]\displaystyle =\frac{6\sqrt{2}}{6}+\frac{3\sqrt{2}}{6}+\frac{6\sqrt{3}}{6}+\frac{2\sqrt{3}}{6}[/tex]
Add:
[tex]\displaystyle =\frac{6\sqrt{2}+3\sqrt{2}+6\sqrt{3}+2\sqrt{3}}{6}[/tex]
Combine like terms:
[tex]\displaystyle=\frac{9\sqrt{2}+8\sqrt{3}}{6}[/tex]
This cannot be simplified. So, c is as small as possible.
Hence: a=9, b=8, and c=6.
Therefore:
[tex]a+b+c=9+8+6=23[/tex]
What is the perimeter of the rectangle?
60 feet
50 feet
Answer:
220
Step-by-step explanation:
perimeter is the sum of all sides
p= 60+60+50+50
p=220
Step-by-step explanation:
Perimeter = 2(length *width)
[tex]2(50 + 60) \\ \\ = 2 \times 110 \\ \\ = 220[/tex]
3. Is the relation {(1,2), (3, 10), (2,8), (5,
10)} a function?
a) yes
b) no
a
Answer:
the answer is yes
Step-by-step explanation:
Based on the results of the simulation, if Sally's name is represented by diamonds, what is the probability that Sally will win
the free homework pass?
A.52%
B. 24%
C. 8%
D.16%
Answer:
Step-by-step explanation:
If she's represented by diamonds, then that's 2/25 which is 8%, C
Answer:
Step-by-step explanation:
8%
Simplify each expression
-3m + 16 - (-13m)
15y - 20y + 15
Answer:
10m + 16
-5y + 15
Step-by-step explanation:
-3m + 16 - (-13m) =
= -3m + 16 + 13m
= 10m + 16
15y - 20y + 15 =
= -5y + 15
Find the value of c that completes the square
x^2-16x+c
Please help me with how to do this, and show me. Thank you.
Answer:
The value that completes the square is: c=8
Step-by-step explanation:
Find the value of c that completes the square [tex]x^2-16x+c[/tex]
The formula used is: [tex]a^2-2ab+b^2=(a-b)^2[/tex]
In the question given the value c can be found by breaking the middle term. we are given -16x while the general formula is 2ab for middle term so,
2(x)(8) = 16x
so, c= 8
Solving:
[tex]x^2-16x+c\\=x^2-2(x)(8)+(8)^2-(8)^2\\=(x-8)^2-64[/tex]
So, the value that completes the square is: c=8
Please help!!! Question is a picture
Answer:
c a b hope it helps.
Step-by-step explanation:
Solve the equation
x2 + 4x - 7 = 0
by completing the square.
Give your answers correct to 2 decimal places.
Answer:
x ≈ 1.32, x ≈ - 5.32
Step-by-step explanation:
Given
x² + 4x - 7 = 0 ( add 7 to both sides )
x² + 4x = 7
To complete the square
add ( half the coefficient of the x- term )² to both sides
x² + 2(2)x + 4 = 7 + 4
(x + 2)² = 11 ( take the square root of both sides )
x + 2 = ± [tex]\sqrt11}[/tex] ( subtract 2 from both sides )
x = - 2 ± [tex]\sqrt{11}[/tex]
Thus
x = - 2 - [tex]\sqrt{11}[/tex] ≈ - 5.32 ( to 2 dec. places )
x = - 2 + [tex]\sqrt{11}[/tex] ≈ 1.32 ( to 2 dec. places )
What is the slope of the line that contains the points (-2, 2) and (3, 4)?
A.
O B. -
O c.
OD.
Answer: m = 2/5
Step-by-step explanation:
The formula for the slope is m = rise over run = y^2 - y^1 / x^2 - x^2
which makes it 4-2 over 3-(-2) which equals 2/5
Youre answer is 2/5
Answer:
The slope of the line that contains the points (-2, 2) and (3, 4) is 2/5.
Step-by-step explanation:
The slope of a line is denoted by m and is calculated using the formula:
[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]
Here
[tex](x_1,y_1)[/tex] are the coordinates of the first point on line and
[tex](x_2,y_2)[/tex] are the coordinates of the second point on line
Given two points are:
(x1,y1) = (-2, 2)
(x2,y2) =(3, 4)
Putting the values in the formula
[tex]m = \frac{4-2}{3-(-2)}\\m = \frac{2}{3+2}\\m=\frac{2}{5}[/tex]
Hence,
The slope of the line that contains the points (-2, 2) and (3, 4) is 2/5.
can someone please help me with this question and show how you figured it out please. ill give brainlyest
Answer:
all real numbers
Step-by-step explanation:
It gives me 0
Ally ran 5 miles in 36 minutes. If Ally runs at the same rate, how long would it take her to run 1 mile?
Answer:
7.2 Minutes
Step-by-step explanation:
Use Ratios
Miles : Minutes
5:36
Divide Both Sides By 5
1:7.2
It will Take Ally 7.2 Minutes To Run 1 Mile
Angle QRS has a measure of 35°. Triangle QRS is rotated 90° clockwise about point R to create angle Q'R'S. What is the measure of angle Q'R'S?
PLEASE ANSWER URGENT
Answer:
The measure of angle Q'R'S' is 35°
Step-by-step explanation:
The given parameters are;
The measure of angle QRS = 35°
The transformation applied to triangle QRS = 90° clockwise rotation
For a 90° clockwise rotation, we have;
Coordinate of the preimage (x, y), coordinate of the image after rotation (y, -x)
Given that the distance, d, between points is given by √((x₂ - x₁)² + (y₂ - y₁)²), we have that the distance between points of the image will be given as follows;
d' =√((y₂ - y₁)² + ((-x₂) - (-x₁))²) = √((y₂ - y₁)² + (x₁ - x₂)²)
Whereby we have √((y₂ - y₁)² + (x₁ - x₂)²) = √((x₂ - x₁)² + (y₂ - y₁)²)
Therefore, d = d' and the length of the sides and measures of the angles in ∠QRS and ∠Q'R'S' will be equal and ∠Q'R'S' = ∠QRS = 35°.
2x(5x3)
Answer please??
is 16 or 30 lol
Step-by-step explanation:
....................
You need to follow the order of operations, so you would solve what is in the parentheses first. (I'm assuming that is the variable x in 2x and not a multiplication symbol. If it is, then just multiply 5 by 3 to get 15, and then multiply that by 2 to get 30) This will give you 15. Then you multiply 2x by 15 to get 30x.
Tuition for one year at the University of Houston is about $12,300 Azul plans to attend this university and will save money each month for the next 4 years. His parents have saved 54,860 for his first year of
tuition. Which plan shows the amount of money Azul will need to save in order to pay for his first year at the University of Houston?
(Answer Choices)
Azul will need to save $256 25 per month for the next 4 years
Azul will need to save $1,860 per month for the next 4 years.
Azul will need to save $620 per month for the next 4 years.
Azul will need to save $155 per month for the next 4 years
(X^3-3x^2+5x-3)/ (x-1)
Answer:
x^2-2x+3
Step-by-step explanation:
factorise by grouping method
(ax + by)^2 + (bx-ay)^2
Answer:
its (b^2+a^2) (x^2+y^2)
Ill brainlist you plus give you more points if needed I have atleast 40 somthing after this
Answer:
I think its 1/6
Step-by-step explanation:
cause there are six numbers so the probility is out of six
that could be wrong not 100% sure its been a while
Answer: B
Step-by-step explanation:
A squirrel jumps along the number line. Each of its jumps is 5 units long. The squirrel sometimes jumps to the right and sometimes to the left. It starts at point 6. Can it land at this point? (The point is 101)
9514 1404 393
Answer:
yes
Step-by-step explanation:
For some integer n, the squirrel lands on numbers that are ...
5n +6
We want to see if n is an integer when ...
5n +6 = 101
5n = 95
n = 19 . . . . yes, an integral number of jumps will get the squirrel to 101
WILL GIVE BRAINLIST!!!!! Select the correct answer. Which graph represents this function? f (x) = 1/2x -5 A. B. C. D.
Answer:
B
Step-by-step explanation:
The y-int. is -5 like the equation and the slope is positive
a treat for all my hard workers!
Answer:
thx
for the points
Step-by-step explanation:
Answers: Ice cream party, What ever you want day,Part of the day Pizza
Savvas Realize
Alabama has 140 legislators, for 4 million people. If another state has 12 million people living in it, how many legislators would it have? How do you know?
Answer: 420 legislators
Step-by-step explanation:
For this problem, we would have to multiply.
If Alabama has 140 legislators for 4 million people, we know the unit rate is:
[tex]140[/tex] legislators for [tex]4[/tex] million people.
So, we have to multiply 140 by 3 because 12 is 3 times the amount of 4, and the other state has 12 million people.
140 x 3 = 420
The answer to the question would be 420.
Answer:
420
Step-by-step explanation:
I set this up as a proportion of 140/4,000,000=x/12,000,000. Then you can cross multiply, getting 1,680,000,000=4,000,000x. Divide both sides by 4,000,000 and you get x=420. Please mark brainliest if this helped!
The employee e-mail accounts in one company are using a mean of
1.07
1.071, point, 07 gigabytes of memory with a standard deviation of
0.21
0.210, point, 21 gigabytes.
What will be the mean and standard deviation of the distribution of memory usage in megabytes?
1
11 gigabyte equals
1024
10241024 megabytes.
Answer:
Mean: 1096 megabytes
Standard deviation: 215 megabytes
Find m∠E PLEASE HELP WILL AWARD BRAINLIEST!
a. 50 degrees
b. 65 degrees
c. 34 degrees
d. 40 degrees
please dont write skmssmskandm
Answer:
b (if def d)
Step-by-step explanation:
the sum of two edges that are side by side is equal to the edge that is not adjacent
25+8x=13x
25=13x-8x
25=5x
5=x
efv=13.5=65
answer b
if def,
8.5=40
answer d
(and pls look my last question pls)
ƒ2 + 8 if ƒ = 7? Please help, LOL.
Answer:
24
Step-by-step explanation:
If f is equal to 7, you'd multiply 7 by 2 (following pemdas/gemdas). When you multiply those two numbers, you get 14. If you add 8 to 14 you get 24.
Austin is planning a canoe trip with his dad and brother. They are taking a cooler and a few supplies that weigh a total of 89 pounds with them. The canoe has a maximum weight limit of 765 pounds. Which inequality can be used to find , the average allowable weight in pounds for each person in the canoe?
A. 3p - 89 > 765
B. 3p - 89 765
C. 3p + 89 > 765
D. 3p + 89 < 765
Answer:
3p + 89 < 765
Correct answer: D.
Step-by-step explanation:
Austin, his dad, and brother make a group of three people of varying weights. Assume their average weight is p and their total weight 3p.
The cooler and other supplies weigh 89 pounds in total.
The weight of the supplies and the three people in the canoe should not be equal or exceed the maximum allowable weight of the canoe of 765 pounds.
This leads to inequality:
3p + 89 < 765
Correct answer: D.
with one question helps i just don’t understand how to do it!!
Answer:
c(0)=1.5
Step-by-step explanation:
plug it in as x
c(0)=2.5(0)+1.5
c(0)=1.5
Find the measure of ∠4.
35°
55°
70°
90°
Answer:
B.) 55 degrees
Step-by-step explanation:
Angle 4 is complementary to angle 5.
The two triangles with these two angles inside are congruent.
So angle 5 is congruent to the given angle of 35 degrees.
Thus,
90 = 35 - x
X = 90 - 35
X = 55
Answer: 55
Step-by-step explanation:
WHOEVER ANSWERS CORRECTLY GETS BRAINLIEST AND EXTRA POINTS (;
Pentagon ABCDE is a regular polygon. The length of side BC is represented by 3x - 4. The length of side DE is represented by the expression 4x - 9. Find the length of side AB.
Answer:
3x_4
Step-by-step explanation:
AB is parallel to BC
YO CORRECT ANSWER FOR BRAINLIEST AND 45 POINTS
Answer: NO SOLUTION
This equation has no solution
What is it and plz plz explain i need help asap! ty<3
Answer:
r = -14
Step-by-step explanation:
22 = r/7 + 24 <-- try and isolate r
22-24 = r/7
-2 = r/7
-2(7) = r
r = -14
Answer:
-14
Step-by-step explanation:
subtract 24 on both sides
-2=r/7
-14=r
please answer this friends
Answer: 6/9
Step-by-step explanation:
1) 2/3 + 3/4=5/7
2) 1/2+5/7=6/9
3) Did this help
