[tex]\frac{1}{1+\sqrt{2} } +\frac{1}{\sqrt{2} +\sqrt{3} } +...+\frac{1}{\sqrt{99} +\sqrt{100} }[/tex]
Answer:
9
Step-by-step explanation:
the given expression can be re-written:
[tex]\frac{\sqrt{2} -1}{(\sqrt{2}-1)(\sqrt{2}+1)} +\frac{\sqrt{3} -\sqrt{2}}{(\sqrt{3} +\sqrt{2})(\sqrt{3} -\sqrt{2})} + ...+\frac{\sqrt{100} -\sqrt{99}}{(\sqrt{100} -\sqrt{99})(\sqrt{100} +\sqrt{99})};[/tex]
then
[tex]\sqrt{2} -1+\sqrt{3} -\sqrt{2} +\sqrt{4} -\sqrt{3}+\sqrt{5} -\sqrt{4}+...+\sqrt{100}-\sqrt{99}= -1+\sqrt{100}=9.[/tex]
What is 26-(-35)? Explain your reasoning
[tex]26 - ( - 35) \\ = 26 + 35 \\ = 61[/tex]
Reasoning :-
- & - together will give you +
Hey there!
GUIDES FOR YOU TO FOLLOW FOR FUTURE PURPOSES.
Guide #1:
• Double [negatives] equals _positive_
• Double [positives] equals _positive_
• 1 [negative] & 1 [positive] equal(s) _negative_
• 1 [positive] & 1 [negative] equal(s) _negative_
Guide #2:
• Positives are on the RIGHT side of the number line
• Negatives are on the LEFT side of the number line
Guide #3:
• Negatives are BELOW 0
• Positives are ABOVE 0
Guide #4:
• When you’re only working with negatives you go down certain spaces because they are below 0
• When you’re only working with positives you too up certain spaces because they are above zero
And etc.
SOLVING FOR YOUR ANSWER
26 - (-35)
= 26 + 35
= 61
Therefore, your answer should be: 61
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
Which one of the options is the correct simplified one, please help.
I have it attached
Answer:
E see below
Step-by-step explanation:
When dividing two fractions, you flip the second fraction over then multiply.
So the equation would then be:
3xy (2 + y) ab
--------------- X --------------
2ab 3xy
The 3xy on top and bottom cancel each other out. The ab on top and bottom cancel each other out.
So you are left with:
2 + y
-------
2
Answer: Number E is correct.
Step-by-step explanation:
division becomes multiplication and turns upside down. ab cuts ab and 2 remains as denominator. 3xy cuts 3xy and 2+y remains as numerator. Therefore the answer obtained is 2+y/2.
How do you make 3x-4=y standard form
[tex]\\ \sf\longmapsto 3x-4=y[/tex]
isolate y[tex]\\ \sf\longmapsto y=3x-4[/tex]
Done !
Here
m=3b=-4Note:-
Standard form
[tex]\\ \sf\longmapsto y=mx+b[/tex]
Answer:
[tex]⟼3x−4=y \\ \\
isolate y
\begin{gathered}\\ \sf\longmapsto y=3x-4\end{gathered}⟼y=3x−4
Done !
Here
m=3
b=-4
Note:-
Standard form
\begin{gathered}\\ \sf\longmapsto y=mx+b\end{gathered}⟼y=mx+b
[/tex]
What is the slope of the line whose equation is -48 = 2x - 8y?
Enter your answer in the box.
Answer:
The slope is [tex]\frac{2}{8}[/tex]
Step-by-step explanation:
Take the general equation of a straight line [tex]y = mx+c[/tex]
Here [tex]m[/tex] is the slope of the line.
So let's get the equation of the line in the question in the same form.
[tex]-48 = 2x-8y[/tex]
Add [tex]8y[/tex] to both sides: [tex]8y - 48 = 2x[/tex]
Add [tex]48[/tex] to both sides: [tex]8y = 2x + 48[/tex]
Divide by [tex]8[/tex] to get it into the general equation: [tex]y = \frac{2}{8} x + 6[/tex]
Now compare it to the general equation to find the value of [tex]m[/tex]. The value of [tex]m[/tex] is the coefficient of [tex]x[/tex] which we can see is [tex]\frac{2}{8}[/tex]
Drag the numbers to order them from least to greatest 2/5,4/9,5/7
Answer:
2/5,4/9,5/7
Step-by-step explanation:
2/5 = 0.4
4/9 = 0.444444444
5/7 = 0.714285
HELP PLSSS THIS IS HARD SOMEONEEE
Answer:
2 option
Step-by-step explanation:
mark me as brainliest
Answer:
Oh Im so Sorry But U Can Do It
The area of a fenced in back yard can be 144 square feet. The owners are trying to decide on the dimensions of the back yard, and have decided they want the length to be 10 feet more than its width. What will the dimensions of the back yard be?
A rectangle can be defined as a 4 sided geometric figure. One side of a rectangle is longer than the other sides. A rectangle can also be referred to as a quadrilateral.
The dimensions of the background are given as Width: 8 feet and the Length: 18 feet
The formula for the area of a rectangle is Length x Width.
The question says:
The owners want the length to be 10 feet more than its width. Hence:
L = W + 10
The area of the fenced backyard = 144 square feet.
Hence,
(W + 10) x W = 144
W² + 10W = 144
Rewriting the equation
W² + 10W - 144 = 0
We factorize the algebraic expression above
W² - 8W + 18W - 144 = 0
W(W - 8) + 18(W - 8) = 0
(W - 8) (W + 18) = 0
W - 8 = 0, W = 8
W + 18 = 0, W = -18
Since the width cannot be a negative value, the width of the backyard is 8 feet
Solving for the Length,
L = W + 10
L = 8 + 10
L = 18 feet
The length of the backyard is 18 feet.
Therefore, the dimensions of the backyard are Width: 8 feet and Length: 18 feet.
To learn more, visit the link below:
https://brainly.com/question/9720917
anthony uses 8 fluid ounces of lemon juice in one batch of lemonade. How many batches can he mane with 1 pint of lemon juice
Answer:
Therefore, he can make 2 batches of lemonade with 1pint of lemon juice
Anthony can make 2 batches of lemonade with 1 pint of lemon juice.
In this problem, we'll determine how many batches of lemonade Anthony can make using a given amount of lemon juice. We'll be using the fact that 1 pint is equivalent to 16 fluid ounces.
Step 1: Convert Pints to Fluid Ounces
Since 1 pint is equal to 16 fluid ounces, we need to convert the given 1 pint of lemon juice into fluid ounces.
1 pint = 16 fluid ounces
Step 2: Calculate Batches
Now that we know 1 pint is equal to 16 fluid ounces, we can find out how many batches of lemonade Anthony can make using 8 fluid ounces of lemon juice per batch.
Number of batches = Total fluid ounces / Fluid ounces per batch
Substitute the values:
Number of batches = 16 fluid ounces / 8 fluid ounces per batch
Number of batches = 2 batches
Therefore, Anthony can make 2 batches of lemonade using 1 pint of lemon juice, given that he uses 8 fluid ounces of lemon juice in each batch.
This calculation ensures that he has enough lemon juice for the desired number of batches without any wastage.
To know more about Batches here
https://brainly.com/question/33079787
#SPJ3
Factor the algebraic expression.
7x+637x+63
Answer: 7 ( 92 x + 9 )
You have to find the greatest common number
First add the like terms (x) 7x+637x= 644
Then you know that 7 is the greatest common faxtor for 644 and 63
So that is how you get your answer 7(92x+9)
Step-by-step explanation:
I hope this helps!
If you are having a tough time with math you can use:
khan academy
math nation
Which describes the range of the function?
What is the value of {-12}
–13
–12
12
13
Answer: B. -12
Edge 21: Since the brackets are facing down, there is no need to round the -12 because it's already an integer.
can anybody answer this? 3/5 x 25
Answer:
15
Step-by-step explanation:
Answer:
15
The answer is 15 (if 3/5 is a fraction)
ANYBODY WHO ANSWERS THIS QUESTION CORRECTLY WILL GET 40 POINTS. THE ONES IN GREY ARE THE ANSWER OPTIONS.
Answer:
140 students are in the school
Step-by-step explanation:
According to the Pie Chart, 70 students are 50%. So then, you multiply 50% of the survey to get 100% (the entirety surveyed). So 70 x 2 = 140
So there were 140 students in the school.
Answer:
70*2 = 140
Step-by-step explanation:
if half is 70, then 100% is 70*2 = 140
5 hours 15 min + 3 hours 33 min
show the working as well
Answer:
8 hours 48 mins
Step-by-step explanation:
h m
5:15
+3:33
--------------
8:48
or
5 hours + 3 hours =8 hours,
15 mins + 33 mins = 48 mins
Therefore, it's 8 hours 48 mins.
Step-by-step explanation:
We calculate hours by hours and minutes by minutes :)
5 hours 15 min + 3 hours 33 min
⇒ 5 hours + 3 hours = 8 hours
⇒ 15 min + 33 min = 48 min
A 16 ounce box of a certain cereal cost $2.24 what is the cost per ounce of the cereal
Answer:
$0.14 per ounce
Step-by-step explanation:
Divide $2.24 by 16 and theres your answer
Luke made an elaborate code to remember the 10-digit combination to his bicycle lock. This is the code he came up with: F-G-E-D-A-K-B-J-C-H Each letter stands for a different digit (0-9). Study the clues below to figure out what digit is represented by each letter. When two letters are written together without an operation symbol, they represent a tens digit and a ones digit. F+F+F=D B÷ H = K J + A = CC
H+H = B. F×H= CK. D×F = KG G+B+E=D+A+C. A×H = KE J÷F=K F/J = H/B
What is the 10-digit combination to Luke's bicycle lock?
this is all the information I have.
please show work by either showing a picture of explaining it in text. Thank you
9514 1404 393
Answer:
lock code: 3709528614
Step-by-step explanation:
Given:
3F = DH×K = BJ+A = CCH×2 = BH×F = CKD×F = KGG +B +E =D +A+CH×A = KEK×F = JFind:
single digit corresponding to each letter
Solution:
CC must be 11, because the sum of any pair of single digits cannot exceed 18. (C = 1).
K must be 2, because H×K = B = H×2. (K = 2)
The only single-digit products involving 3 are 3×1 = 3, 3×2 = 6, and 3×3 = 9. We know F is not 1 or 2, so for 3F = D we must have F = 3, D = 9. (F = 3)(D = 9)
CK = 12, so H×F = 3H = 12. This means H = 4. (H = 4)
2H = B, so B = 8. (B = 8)
D×F = KG. Using the values for D, F, K, we find 9×3 = 27. (G = 7)
K×F = J = 2×3. (J = 6)
At this point, the only unassigned digits are 0 and 5.
H×A = KE. Filling in known values, this is 4A = 20 +E. (A = 5)(E = 0)
The sum E+15 = A+10 can also be used to assign values to A and E.
__
Then the letters corresponding to the digits 0-9 are ...
[tex]\texttt{01234 56789}\\\texttt{ECKFH AJGBD}[/tex]
The bicycle lock code is 3709528614.
two amounts of money are in the ratio 8:3.if the second amount is $4.05, what is the value of the first amount
Answer:
10.8$
Step-by-step explanation:
(8*4.03)/3 = 10.8
evaluate: 5/6 + 4/9 =___?
Answer:
23/18 or 1 5/18
Step-by-step explanation:
In mathematics, adding and subtracting fraction required that all fractions are in similar, in converting dissimilar fraction into set of similar fraction requires finding its Least Common Denominator (LCD) or Least Common Multiple (LCM).
Equation Given
5/6 + 4/9
Finding LCM
- List down their multiples
The multiples of 6 = 6 12 18 24
The multiples of 9 = 9 18 27 36
Thus, their Least Common Multiple (LCM) is 18
Converting Dissimilar Fraction into Similar Fraction
The LCM is already the denominator
Divide the LCM by its original denominator then multiply by numerator to get the new numerator
5/6
(18 ÷ 6) × 5 = 15/18, new fraction
4/9
(18 ÷ 9) × 4 = 8/18, new fraction
Evaluate
15/18 + 8/18
= 23/18, or
= 1 5/18
Answer:
23/18 or 1 5/18
Step-by-step explanation:
In mathematics, adding and subtracting fraction required that all fractions are in similar, in converting dissimilar fraction into set of similar fraction requires finding its Least Common Denominator (LCD) or Least Common Multiple (LCM).
Equation Given
5/6 + 4/9
Finding LCM
List down their multiples
The multiple of 6
6 12 18 24
The multiple of 9
9 18 27 36
Thus, their Least Common Multiple (LCM) is 18
- Converting Dissimilar Fraction into Similar Fraction
The LCM is already the denominator
Divide the LCM by its original denominator then multiply by numerator to get the new numerator
5/6
(18 ÷ 6) × 5 = 15/18, new fraction
4/9
(18 ÷ 9) × 4 = 8/18, new fraction
- Evaluate
15/18 + 8/18
= 23/18, or
= 1 5/18
find gcf
16x^2 -16+3
Answer:
13
Step-by-step explanation:
Step 1 to find gcf of 16x^2 -16+3 is factor out the equation = (4x)^2 -13 = (4x+13)(4x-13) So we factor to show one - and one + and then step 2 we then divide 4/4 -13/4 and 4/4 13/4 and cancel out 4/4 and see what we are left with = x>+ - 13/4 = 3 1/4 we can now find gcf by working out 16x^2 = 16(3 1/4)^2 = 16(10.5625) = 169 and the gcf of 169 and +- 13 = 13
solve for x
a) 30
b)45
c) 60
d) 90
5/6x10..........................
Answer:
Your answer is 8 1/3 or 25/3.
Step-by-step explanation:
Hope this helps!
What is the slope and y intercept I’m really new to this and need help
Answer:
The y intercept is -1 and the slope is 4/1
Step-by-step explanation:
When you are trying to find the y-intercept, you look at where the line crosses over the y axis. In this case it was at -1.
The slope indicates how many units it is going up/down or left/right. In this case, the distance between each point is up 4, and right 1. so the slope would be 4/1.
I hope this helps :)
evaluate the expression 1/4[x(2y+3z)] x=8 y=3z=5/3
Answer:
Step-by-step explanation:
x = 8 ; y = 5/3
[tex]3z = \dfrac{5}{3}[/tex]
[tex]\dfrac{1}{4}[x(2y+3z)] =\dfrac{1}{4}[8*(2*\dfrac{5}{3}+\dfrac{5}{3})]\\\\=\dfrac{1}{4}(8*(\dfrac{10}{3}+\dfrac{5}{3})]\\\\=\dfrac{1}{4}(8*\dfrac{15}{3})\\\\=\dfrac{1}{4}*8*5\\\\=2*5\\\\=10[/tex]
The difference between 13 and a number is 4 more than twice the number
Answer: 3
Step-by-step explanation:
Let the number be 'a'.
Since the difference between 13 and a number is 4 more than twice the number, then 13 - a = 2a + 4
⇒ 13 - a = 2a + 4
2a + a = 13 - 4
3 a = 9
a = 3
∴ the number is 3Jesse worked at the pool all summer and saved $500. Her parents want her to put the money into a bank account, where she would earn 2% simple interest monthly on her principal deposit of $500.
How much will she make in interest?
Help in this as well
Answer:
b 321 and 322
Step-by-step explanation:
because 321.5 is between 321 and 322
if m<4= 86° what are the measures of the other seven angles in the figure
Answer:
below
Step-by-step explanation:
IF l₁ and l₂ are parallel, then:
Angles 2, 4, 5, 8 all equal 86 degrees
Then angles 1, 6, 3 , 8 all equal 180 - 86 which is 94 degrees
[tex]5x - 3(2x - 4)[/tex]
please help me
if x represent a base number in the following equation what is the value of x in 3x+101x-24x=8
Answer:
x = 1/10Step-by-step explanation:
if x represent a base number in the following equation what is the value of x in 3x+101x-24x=8?
3x + 101x - 24x = 8
80x = 8
x = 1/10
-------------------------
check
3 * 1/10 + 101 * 1/10 - 24 * 1/10 = 8
8 = 8
the answer is good