Answer:
2√2 / (5√2 + 7)
Step-by-step explanation:
Given :
x = 1 + √2Expanding
(x - 1 / x)³(1 + √2 - 1)³ / (1 + √2)³(√2)³ / (1 + √2)³2√2 / 1 + 2√2 + 3(1)(√2)(1 + √2)2√2 / 1 + 2√2 + 3√2 + 62√2 / (5√2 + 7)Answer:
[tex]-14\sqrt{2}+20[/tex]
Step-by-step explanation:
[tex]\textsf{Substituting}\quad x=1+\sqrt2\quad\textsf{into}\quad\left(\dfrac{x-1}{x}\right)^3[/tex]
[tex]\implies \left(\dfrac{(1+\sqrt2)-1}{(1+\sqrt2)}\right)^3[/tex]
[tex]\implies \left(\dfrac{\sqrt2}{1+\sqrt2}\right)^3[/tex]
[tex]\textsf{Apply exponent rule}:\left(\dfrac{a}{b}\right)^n=\dfrac{a^n}{b^n}[/tex]
[tex]\implies \dfrac{(\sqrt2)^3}{(1+\sqrt2)^3}[/tex]
Expand numerator:
[tex](\sqrt{2} )^3=\sqrt{2}\sqrt{2}\sqrt{2}=2\sqrt{2}[/tex]
Expand denominator:
[tex]\begin{aligned}(1+\sqrt2)^3 & = (1+\sqrt2)(1+\sqrt2)(1+\sqrt2)\\ & =(1+\sqrt2)(1+2\sqrt{2}+2)\\ & =1+2\sqrt{2}+2+\sqrt{2}+2\sqrt{2}\sqrt{2}+2\sqrt{2}\\ & = 7+5\sqrt{2}\end{aligned}[/tex]
[tex]\implies \dfrac{(\sqrt2)^3}{7+5\sqrt2}[/tex]
Substituting expanded numerator and denominator:
[tex]\implies \dfrac{2\sqrt{2}}{7+5\sqrt2}[/tex]
[tex]\textsf{Mulitply by conjugate :}\quad\dfrac{7-5\sqrt2}{7-5\sqrt2}[/tex]
[tex]\implies \dfrac{2\sqrt{2}(7-5\sqrt2)}{(7+5\sqrt2)(7-5\sqrt2)}[/tex]
[tex]\implies \dfrac{14\sqrt{2}-20}{49-50}[/tex]
[tex]\implies \dfrac{14\sqrt{2}-20}{-1}[/tex]
[tex]\implies -14\sqrt{2}+20[/tex]
Jia is thinking of a number she gives
three clues about the number. the number is
even, the number is less than 12 and the absolute
value of the number is between 9 and is what
is Jia's number? Explain how
you know.
The flower shop makes bouquets with ten flowers in each bouquet.
The florist said she can't make any bouquets because she has 207 flowers and there is a 0 in the tens place of 207!
Do you agree or disagree with the florist? Explain why in a full sentence below.
Hello I would really appreciate if someone could help me with this math question. I’m so confused
Answer:
a. f = 17.5/c
b. 8.75 N
Step-by-step explanation:
(a)Inverse variation means one variable is proportional to the inverse of the other. The equation for that is ...
f = k(1/c) . . . . . . force (f) is proportional to the inverse of distance (c)
We find the value of k using data given for a specific instance.
3.5 N = k(1/(5 cm)) . . . . use the given values
17.5 N·cm = k . . . . . . multiply by the denominator
Then the equation of interest is ...
f = 17.5/c . . . . . . . where c is in cm, and f is in newtons
__
(b)Using the above equation, we find the force to be ...
f = 17.5/2 = 8.75 . . . . newtons
_____
Additional comment
We often look at several different kinds of proportionality:
y = kx . . . . directy = k(1/x) . . . . inversey = kx² . . . . proportional as the squarey = kx·z . . . . jointly proportional to x and zand there are combinations of these, such as ...
y = kr²h . . . . jointly proportional to h and the square of rYou may have noticed that when x and y are inversely proportional, their product is a constant. y = k/x ⇒ xy = k
__
We have left off the units of k in the problem above. Sometimes it is a good idea to retain them, or to pay close attention to what they are. This can avoid using the wrong measures for the variables.
f = (17.5 N·cm)/(2 cm) = 8.75 N . . . . . units of cm cancel
What is the lateral surface area of the triangular prism?
Round to the hundredths place.
Answer:
A triangular prism is a three-dimensional shape having two triangular bases and three rectangular sides.
PLEASE HURRY 30 POINTS
A number cube is rolled and a coin is tossed. The number cube and the coin are fair. What is the probability that the number rolled is greater than 2 and the coln
toss is heads?
Write your answer as a fraction in simplest form.
hope it helps...!!!!
The probability that the number rolled is greater than 2 and the coin toss is heads is,
⇒ 1/ 3
What is mean by Probability?The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one
Now, In probability theory, "AND" means multiplication and "OR" means "addition".
Hence, We can find the 2 probabilities separately and multiply them (as there is "AND")
So, Probability for number rolled greater than 2 = number of numbers that are greater than 2/total number of numbers
Since, There are 4 numbers greater than 2 in a die (3, 4, 5, 6) and total 6 numbers, so
P(number greater than 2) = 4/6 = 2/3
Now, Probability that heads come up in coin toss = 1/2 (there are 1 tail and 1 head in a coin)
Hence,
P(number greater than 2 and heads in coin) = 2/3 × 1/2 = 1/3
Thus, the probability that the number rolled is greater than 2 and the coin toss is heads is,
⇒ 1/ 3
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PLEASE HELP ASAP!!! WITH EXPLANATION IF POSSIBLE!!!!!!!!!
Two chords PQ and ST of length 6cm and 10cm respectively of a circle are parallel to each other and are on opposite side of its center. If the distance between PQ and ST is 5cm. Find the radius of the circle
Answer:
Draw two parallel chords AB and CD of lengths 5 cm and 11 cm. Let the center of the circle be O. Join one end of each chord to the center.
Draw two perpendiculars OM and ON to AB and CD, respectively, which bisects the chords.
Two chords AB and CD of lengths 5 cm and 11 cm respectively of a circle are parallel to each other and are on opposite sides of its center. If the distance between AB and CD is 6 cm, find the radius of the circle.
Thus, MB = 2.5 cm and ND = 5.5 cm [The perpendicular drawn from the center of the circle to the chords bisects it.]
Let OM = x and ON = 6 - x
Consider ΔOMB
By Pythagoras theorem,
OM2 + MB2 = OB2
x2 + 2.52 = OB2
x2 + 6.25 = OB2..................(1)
Consider ΔOND
By Pythagoras theorem,
ON2 + ND2 = OD2
(6 - x)² + 5.52 = OD2
36 + x2 - 12x + 30.25 = OD2
x2 - 12x + 66.25 = OD2............... (2)
OB and OD are the radii of the circle. Therefore OB = OD.
Thus, OB2 = OD2
Equating (1) and (2) we get,
x2 + 6.25 = x2 - 12x + 66.25
12x = 60
x = 5
Substituting the value of x in (1),
OB2 = x2 + 6.25
OB2 = 52 + 6.25
OB2 = 31.25
OB = 5.59 (approx.)
Thus, we get the radius of the circle = 5.59 cm.
Solve the absolute value inequality 3x-1<8
Answer:
3
Step-by-step explanation:
3x - 1 < 8
Solve this inequality like a two-step equation.
Add 1 to both sides to cancel the -1.
3x - 1 < 8
3x < 9 Divide both sides by 3 to cancel the 3 in 3x.
x < 3
Find the absolute value (distance the number is from 0).
Absolute value = 3
I hope this helps and please mark me as brainliest!
absolute value of 19/24
Answer:
-19/-24 ?
Step-by-step explanation:
The absolute value is the distance between a number and zero. The distance between −19 and 0 is 19 .
-24 has an absolute value of 24
Answer:
0.791666667 I hope this helped
Step-by-step explanation:
Mark bought two candy bars and a soda for $3.96. If each candy bar cost $1.10 how much did the soda cost?
Answer:
$1.76
Step-by-step explanation:
$1.10+$1.10 = $2.2
$3.96 - $2.2 = $1.76
PLEASE HELP: PICTURE ATTACHED
Multiply 80 by number of copies sold and add to her salary:
P = 80N + 1700
Now replace N with 26:
P = 80(26) + 1700
P = 3,780
Answer:
P=1,700+80n
Total Pay if Yoko sells 26 Copies; 3,780
Hope This Helps! :) Please Mark Brainliest!
PLEASE HURRY What is the surface area of this right rectangular prism?
Enter your answer as a mixed number in simplest form
first off, let's change all the mixed fractions to improper fractions.
Check the picture below.
[tex]\stackrel{\textit{\Large Areas}}{\stackrel{\textit{left and right}}{2\left( \frac{4}{3}\cdot \frac{5}{2} \right)}~~ + ~~\stackrel{\textit{front and back}}{2\left( 3\cdot \frac{4}{3} \right)}~~ + ~~\stackrel{\textit{top and bottom}}{2\left( 3\cdot \frac{5}{2} \right)}} \\\\\\ \cfrac{20}{3}+8+15\implies \cfrac{89}{3}\implies 29\frac{2}{3}[/tex]
If z = 3cis30°, z3 in rectangular form is:
[tex]\qquad \textit{power of two complex numbers} \\\\\ [\quad r[cos(\theta)+isin(\theta)]\quad ]^n\implies r^n[cos(n\cdot \theta)+isin(n\cdot \theta)] \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ z=3[\cos(30^o)+i\sin(30^o)] \\\\\\ z^3=3^3[\cos(3[30^o])+i\sin(3[30^o])]\implies z^3=27[\cos(90^o)+i\sin(90^o)] \\\\\\ z^3=27(0~~ + ~~i1)\implies z^3=0+27i[/tex]
so that gives us the point (0 , 27) on the imaginary plane, and we also know the line goes through the origin, since it'd be a line in component form, and to get the equation of a line we only need two points off of it, let's use those two.
[tex]\stackrel{origin}{(\stackrel{x_1}{0}~,~\stackrel{y_1}{0})}\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{27}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{27}-\stackrel{y1}{0}}}{\underset{run} {\underset{x_2}{0}-\underset{x_1}{0}}}\implies \cfrac{27}{0}\implies und efined[/tex]
a line with an undefined slope is a vertical line, namely in this case x = 27.
Question 1.
Let P = {3, 5, 7, 9, 11} Q = {9, 11, 13} R = {3, 5, 9} S = {13, 11}
Write the elements for the following: [4 marks]
(a) R ⊂ P
(b) Q ⊂ P
(c) R ⊂ S
(d) S ⊂ Q
(e) S ⊂ P
(f) P ⊄ Q
(g) Q ⊄ R
(h) S ⊄ Q
Question 2.
i) Write down all the possible proper subsets for each of the following:
[3marks]
(a) {a, b, c, d}
(b) {1, 2, 3}
(c) {p, q, r}
(d) {5, 10}
(e) {x}
(f) ∅
ii) Which of the following sets is a universal set for the other four sets?
(Select your answer) [1mark]
(a) The set of even natural numbers
(b) The set of odd natural numbers
(c) The set of natural numbers
Answer:
Question 1
a) { 3, 5, 9 }
b) { 9, 11 }
c) { }
d) { 11, 13 }
e) {11}
f) {3, 5, 7}
g) {11, 13}
h) {9}
Question 2 ( i )
a) { a,b,c,d }
{a}
{b}
{c}
{d}
{a,b,c}
{a,b}
{a,c}
{a,d}
{b,c}
{b,d}
{c,d}
{a,b,d}
{b,c,d}
{a,c,d}
{ }
b) {1,2,3}
{1,2}
{1,3}
{1}
{2}
{3}
{2,3}
{ }
c) {p, q ,r}
{ p,q}
{ p,r}
{ q,r}
{p}
{q}
{r}
{ }
d) { 5,10}
{ 5}
{10}
{ }
e) {x}
{ }
f) { ○ }
{ }
Question 2 ( ii )
(c) The set of natural numbers
11. Reduce 48/72 to its lowest terms.
A. 6/9
B.2/3
c. 24/36
D. 30/54
Answer:
its A my friend because: 48/2=24. 72/2=36
24/2=12. 36/2=18
12/2=6. 18/2=9
Express (x+9)^2 as a trinomial in standard form.
Answer:
x^2 + 18x + 81
Step-by-step explanation:
(x+9) (x+9)
then distributive property
[tex](x+9)^2\\\\=x^2 + 2\cdot 9 \cdot x + 9^2\\\\=x^2 +18x+81[/tex]
If the total profit per month is Rs 200,000 and the revenue per month can be obtained as twice
the cost per month minus 50,000, find the revenue and cost per month.
Answer:
200000×2
=R400 000 and minus 50000
=300000
what is the volume of this now I don't really get it
Answer:
12
Step-by-step explanation:
Answer:
24 cubic units
Step-by-step explanation:
Count the front layer by fours because there are 3 rows of 4 and 3 rows of 4 on the other side.So count by 4's on the front layer then the back layer.
On the 11th of March, 2011, an earthquake along the eastern shore of Japan caused a tsunami, which
then damaged a nuclear power plant. Several radioactive elements were released into the air and ocean.
Use an exponential decay formula to model how long some of these elements can be expected to persist
in the environment.
4. Cesium-137 has a decay constant of
0.0231 (a 30 year half-life). If 20
pounds of cesium-137 were released
into the Pacific Ocean by the tsunami,
how much will still be there ten years
later?
5. Strontium-90 has a decay constant of
0.0248 (a 28 year half-life). If 80
pounds of strontium-90 were
released into the Pacific Ocean by the
tsunami, how much will be left in 75
years?
6. When strontium-90 decays, it transforms into yttrium-90, which has a half-life of
only 64 hours, (0.007302 years). If the decay constant of yttrium-90 is -94.93,
what percentage of a one-pound sample will be left after one month ( of a
year)?
The radioactive sponteanous decay of the parent nucleus gives rise to the daughter nucleus.
What is radioactivity?Radioactivity refers to the sponteanous decay of a substance. We have the formula;
N(t) = Noe^-kt
Where;
N(t) = amount of radioactive material left after time t
No = amount of radioactive material initially present
k = decay constant
t = time taken
Let us now solve the questions individually;
a)
No = 20 pounds
N(t) = ?
k = 0.0231
t = 10 years
N(t) = 20e^-(0.0231 * 10)
N(t) = 16 pounds
b)
No = 80 pounds
N(t) = ?
k = 0.0248
t = 75 years
N(t) =80e^-(0.0248 * 75)
N(t) = 12.45 pounds
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2 (b) The area of a rectangular window is 6272 cm cm? If the length of the window is 98 cm, what is its width?
Answer:
The width would be 64 cm
Step-by-step explanation:
Because the equation to find area is length times height
Since you have the area and the length, divide the area by the length to find the width
I hope this helps!
Let f(x) =5x-1, h(x)= -x+5.
Find (h of)(3).
(hof)(3)
(h ◦ f)(x) is the composition of h(x) with f(x),
(h ◦ f)(x) = h(f(x))
which we can compute by simplying replacing in h(x) every instance of x with f(x) itself:
(h ◦ f)(x) = h(f(x))
(h ◦ f)(x) = h(5x - 1)
(h ◦ f)(x) = -(5x - 1) + 5
(h ◦ f)(x) = -5x + 1 + 5
(h ◦ f)(x) = -5x + 6
Then
(h ◦ f)(3) = -5 • 3 + 6
(h ◦ f)(3) = -15 + 6
(h ◦ f)(3) = -9
Solve one half ÷ 8 = ___.
one seventh
one sixteenth
one twenthieth
one thirtieth
Answer:
one sixteenth
Step-by-step explanation:
I hope this helps! Have a lovely day!! :)
simplify the expression m^-6n^-3/m^-13n^-1
A)m^7n^2
B)n^-9/n^-14
C)m^3n^12
D)m^7/n^2
[tex]\dfrac{m^{-6} \cdot n^{-3}}{m^{-13} \cdot n^{-1}}\\\\=m^{-6-(-13)} \cdot n^{-3-(-1)}\\\\=m^{-6+13} \cdot n^{-3+1}\\\\=m^7 \cdot n^{-2}\\\\=\dfrac{m^7}{n^2}[/tex]
Find the chance of having a face card if a card is drawn randomly from a deck of cards.
Answer:
3/13
Step-by-step explanation:
P(Choosing a Face card) =
12/52= 3/13
pls mark as brainliest
Donna received a $90 gift card for a coffee store. She used it in buying some coffee that cost $7.59 per pound. After buying the coffee, she had $59.64 left on her card. How many pounds of coffee did she buy?
Answer: 4 pounds
Step-by-step explanation:
First, we will see how much the coffee cost by subtracting what was left by the total gift card.
$90 - $59.64 = $30.36
Now, we will divide how much the coffee cost by how much one pound costs. This will give us how many pounds she bought, and the answer to your problem
$30.36 / $7.59 = 4
She bought four pounds of coffee.
If someone can help me step by step exactly
The value of z using the information and the formula provided in the question is -5.292.
What is the value of z?
Subsituting for the missing values in the formula, the formula becomes: [tex]\frac{130 - 135}{\frac{5}{\sqrt{28} } }[/tex]
Solving for the numerator, the number becomes -5. Solving for the denominator, the number becomes 0.94491
z = -5/0.94491
z = -5.292
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help please!!!!!!!! please be correct
Answer:
Step-by-step explanation:
the answer is 66. To find the third angle subtract 80 and 34 by 180.
Order the numbers from least to greatest.
13/50
22%
0.28
1/5
0.41
1/5, 13/50, 0.28, 0.41, 22%
Step-by-step explanation:
hopes this helps
I can't manage. Can you help? Ty :)
first question is true and second question is 6cm
Kala and david each opened a savings account today, kala opened her account with a starting amount of $180, and she is going to put in $70 per month. David opened his account with no starting amount, and he is going to put in $100 per month
let x be the number of months after today
(a) for each account, write an expression for the amount of money in the account after x months
(b) write an equation to show when the two accounts have the same amount of money
[tex]Elsa:y_1=70x+180[/tex]
[tex]brian,y_2=100x[/tex]
Step-by-step explanation:[tex]Rnown\ by\ the\ topic,[/tex]
[tex]Assuming\ that\ the\ Elsa\ amount\ of\ money\ is\ y_1,[/tex]
[tex]Brian's\ amount\ of\ money\ is\ y_2[/tex]
[tex]so,y_1=70x+180[/tex]
[tex]\{put\ in\ \$70\ per\ month,\ storting\ amount\ of[/tex]
[tex]y_2=100x[/tex]
[tex]\{\ put\ in\ \&\ 100\ per\ month,\ no\ starting\ emount[/tex]
[tex]\{\$70,\ \$100\ are\ monthly\ voriation,[/tex]
[tex]\$180\ is\ fixed\ value?[/tex]
I hope this helps you
:)
Lines a, b, c, and d Intersect as shown.
124
95
42°
53
39°
95°
What is x ?
Answer:
95 is the answer I took the test