[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 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]
I need so.e help with this
Answer:
(3,7) is not a solution
Step-by-step explanation:
You fill in the values x=3 and y=7 in both equations and see if you end up with something that is true.
-5·3 - 2·7 = 23 is not true, because it simplifies to -29 = 23
no need to look further, but if you would, the second equation is also false:
3 + 4·7 = -19 is also not true.
The real solution by the way is (-3, -4).
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
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
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]
Mr. Brookins asked his students to plot an integer on a number line. Which two students could have represented the same number?
Makayla
A number line going from negative 10 to 0. A point is at negative 7.
Aaron
A number line going from negative 18 to positive 6. A point is at negative 5.
Serena
A number line going from negative 20 to positive 12. A point is at negative 5.
Dontae
A number line going from negative 8 to 0. A point is at negative 6.
Serena and Dontae
Makayla and Aaron
Serena and Aaron
Makayla and Dontae
Mark this and return
Answer:
Serena and Aaron.
Step-by-step explanation:
Answer:
Serena and Aaron.
Step-by-step explanation:
Farid's friend can't eat wheat, so Farid is baking him a loaf of gluten-free raisin bread. He mixes the dough and leaves it in a bowl to rise. Then, Farid forms the dough into a loaf and puts it in a pan to rise for another 1 /2 of an hour. In all, the dough rises for 1 3 /4 hours.
PLEASE ANSWER FAST IT WILL HELP ME SO MUCH
Answer:
I believe it's enlargement
Step-by-step explanation:
because you have a positive scale factor and it goes to the right 3 and up 4
A square metallic frame has a perimeter 208cm .It is bent in the shape of a circle. Find the area of the circle.
Answer:
676 pi
Step-by-step explanation:
208 ÷ 4 =52
(each length =52cm)
diameter = 52 cm
radius = 52÷2 = 26cm
area of circle = pi × radius ^2
pi × 26^2 = 676 pi
consider the linear function f(x)=4x-5 Find the values of x for which f(x)=3,f(x)=5,f(x)=-3
Answer:
f(2) = 3
f(5/2) = 5
f(½) = -3
Step-by-step explanation:
Given the linear function f(x) = 4x - 5:
f(x) = 33 = 4x - 5
3 + 5 = 4x - 5 + 5
8 = 4x
8/4 = 4x/4
2 = x
Therefore, when f(x) = 3, x = 2.
f(x) = 55 = 4x - 5
5 + 5 = 4x - 5 + 5
10 = 4x
10/4 = 4x/4
5/2 = x
Therefore, when f(x) = 5, x = 5/2.
f(x) = -3-3 = 4x - 5
-3 + 5 = 4x - 5 + 5
2 = 4x
2/4 = 4x/4
½ = x
Therefore, when f(x) = -3, x = ½.
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
Fiona planted tomato plants in her back yard earlier this year. So far, they have produced 55 tomatoes. From past experience, she expects the tomato plants to produce an additional 14 tomatoes each week for the rest of the summer. Which of the following recursive formulas can be used to determine the total number of tomatoes produced by her plants after any given number of weeks in the summer, assuming that her expectations are correct?
Answer:
Although it is a short-lived perennial, tomato plants can bear fruit for more than one year in parts of the world that never dip below 65 degrees Fahrenheit. If you have a greenhouse and can keep it heated during the cold months, consider placing an experimental beefsteak, plum or grape tomato plant among your tropical flowers.
Step-by-step explanation:
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.
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.
What is the atomic number of an atom?
Question 3 options:
the number protons and neutrons
the number of protons
the number of electrons and neutrons
the number of neutrons
Answer:
The number of protons
Step-by-step explanation:
Its the correct answer
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]
5/6x10..........................
Answer:
Your answer is 8 1/3 or 25/3.
Step-by-step explanation:
Hope this helps!
Which rule explains why these triangles are congruent?
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
Hello wonderful people! I am having trouble with the one question and I was wondering if someone could help me? I promise brainiest for the correct answer. Thanks so much for your time!
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
[tex]5x - 3(2x - 4)[/tex]
please help me
What is the value of Y when X=-3 ?
Answer:
2
Step-by-step explanation:
the line is at 2 for Y
simplify (x+y)(x-y)(x^2+y^2)
Answer:
x⁴-y⁴
Step-by-step explanation:
=(x+y)(x-y)(x²+y²)
=(x²-y²)(x²+y²)
=x⁴-y⁴
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
The polynomial x2+ 3x - 1 is a factor of x3 + 2x2 - 5x-6 true or false
Answer:
it's false
Step-by-step explanation:
I hope it helps
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 goodtwo 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
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