We happen to have
[tex]\dfrac17 = \dfrac18 + \dfrac1{8^2} + \dfrac1{8^3} + \cdots[/tex]
which is to say, the base-8 representation of 1/7 is
[tex]\dfrac17 \equiv 0.111\ldots_8[/tex]
This follows from the well-known result on geometric series,
[tex]\displaystyle \sum_{n=1}^\infty ar^{n-1} = \frac a{1-r}[/tex]
if [tex]|r|<1[/tex]. With [tex]a=1[/tex] and [tex]r=\frac18[/tex], we have
[tex]\displaystyle \sum_{n=1}^\infty \frac1{8^{n-1}} = 1 + \frac18 + \frac1{8^2} + \frac1{8^3} + \cdots \\\\ \implies \frac1{1-\frac18} = 1 + \frac18 + \frac1{8^2} + \frac1{8^3} + \cdots \\\\ \implies \frac87 = 1 + \frac18 + \frac1{8^2} + \frac1{8^3} + \cdots \\\\ \implies \frac17 = \frac18 + \frac1{8^2} + \frac1{8^3} + \cdots[/tex]
Uniformly multiplying each term on the right by an appropriate power of 2, we have
[tex]\dfrac17 = \dfrac2{16} + \dfrac{2^2}{16^2} + \dfrac{2^3}{16^3} + \dfrac{2^4}{16^4} + \dfrac{2^5}{16^5} + \dfrac{2^6}{16^6} + \cdots[/tex]
Now observe that for [tex]n\ge4[/tex], each numerator on the right side side will contain a factor of 16 that can be eliminated.
[tex]\dfrac{2^n}{16^n} = \dfrac{2^4\times2^{n-4}}{16^n} = \dfrac{2^{n-4}}{16^{n-1}}[/tex]
That is,
[tex]\dfrac{2^4}{16^4} = \dfrac1{16^3}[/tex]
[tex]\dfrac{2^5}{16^5} = \dfrac2{16^4}[/tex]
[tex]\dfrac{2^6}{16^6} = \dfrac4{16^5}[/tex]
etc. so that
[tex]\dfrac17 = \dfrac2{16} + \dfrac4{16^2} + \dfrac9{16^3} + \dfrac2{16^4} + \dfrac4{16^5} + \dfrac9{16^6} + \cdots[/tex]
and thus the base-16 representation of 1/7 is
[tex]\dfrac17 \equiv 0.249249249\ldots_{16}[/tex]
and the first 10 digits after the (hexa)decimal point are {2, 4, 9, 2, 4, 9, 2, 4, 9, 2}.
Quadratic Equation Question
Answer: 0.68 or 13.92
Step-by-step explanation:
If the height is 47 meters, then the height, h, is equal to 47.
[tex]47=73t-5t^2\\\\5t^2 - 73t+47=0[/tex]
Using the quadratic formula,
[tex]t=\frac{-(-73) \pm \sqrt{(-73)^{2}-4(5)(47)}}{2(5)}\\\\\\t=\frac{73 \pm \sqrt{4389}}{10}\\\\\\ t=\frac{73+\sqrt{4389}}{10}, \frac{73-\sqrt{4389}}{10}\\\\\boxed{t \approx 0.68, 13.92}[/tex]
Parallelogram ABCD has vertices: A(-3, 1), B(3, 3), C(4, 0), and D(-2, -2). In two or more complete sentences, explain how you can use the coordinates of the vertices to prove that parallelogram ABCD is a rectangle.
please help
Step-by-step explanation:
via the distance formula (based on Pythagoras) I can prove that ABC is a right-angled triangle, and that ADC is fully congruent to ABC.
so, together these 2 triangles (joined at their Hypotenuses, the diagonal AC) build a rectangle.
Can someone help me on this please
Answer:
17.7 (2 dp)
Step-by-step explanation:
[tex] \sqrt{ {16}^{2} + {7.5}^{2} }[/tex]
What term does the formula sin A/a = sin B/b represent?
Answer:
Law of sines
Explanation:
The law of sines states that the ratios of the sines of angles and their opposite sides are equal for all angles inside a triangle.
Step-by-step explanation:
hope you can understand
Please Simplify 3√7 / 5√7
Step-by-step explanation:
please mark me as brainlest
Divide : (8a^2b^4 - 20a^4b^5 + 48a^6b^6) by 4a^2b^4
Hey there ! please refer to the attachment .
I hope its help you !
What is the nth term rule of the linear sequence below?
27, 25, 23, 21, 19, ...
Answer:
Step-by-step explanation:
Comment
This is an arithmetic series. It has the following givens.
a = 27 The first term
d = - 2 The difference between one term and the one behind it.
n = quite small
Tn = a + (n - 1)*d
tn = 27 - 2n + 2
tn = 29 - 2n
Label the vertices and all the elements needed. Find x. Give reasons!
Answer:
Step-by-step explanation:
Marilyn is having shelves installed to create a corner pantry. the length of one wall is 21 inches and the length of the other wall is 25 inches. the contractor who is making the shelves, which are shaped like right triangles, needs to know the measure of the angle opposite the short side of the pantry, m∠a. what is the measure of that angle? round your answer to the nearest degree.
Answer:
He says the answer is 40°
Step-by-step explanation:
Answer is on brainly, here is the link to the answer. Hope it helps with your question!
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Hope this helps!
If not, I am sorry.
A man bought a car for Gh55,000.00 and sold it for Gh65,000.00. Find the percentage gain.
Answer:
18.18%
Step-by-step explanation:
(65000-55000)/55000×100
What is the slope of a line that is parallel to the line y = 3/4x + 2?
Answer:
in this form the first one next to the x is the slope and the added value is the y intercept
if something is parrell that means the same slop so
3/4
Hope This Helps!!!
Estimate the solution to the following system of equations by graphing.
When you eat certain foods, sugar is immediately released into your bloodstream. many doctors say kids should only take in 6 teaspoons (24 grams) of added sugar each day. jack is making lemonade for his school and wants to follow that recommendation. he wants to make 206 servings, following the recommendation, how many grams of sugar will he use?
Answer:
4,944
Step-by-step explanation:
Which inequality is shown in this graph?
OA. ys-3x+3
OB. y2-3x+3
OC. ys 3x+3
OD. y23x+3
Answer:
A
Step-by-step explanation:
The line is shaded below, so we can eliminate B and D.
Also, the line has negative slope, so this eliminates C.
The inequality of the graph is y ≤ -3x + 3.
The correct option is A.
What is inequality?In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.
The inequality graph has two points on the line (0, 2) and (2, -3).
And the shaded region of the graph is left to the line made by points (0, 2) and (2, -3).
The line passing through the points (0,2) and (2,-3) can be written in a slope-intercept form as:
y = mx + b
where m is the slope and b is the y-intercept.
The slope of the line is given by:
m = (y2 - y1) / (x2 - x1) = (-3 - 2) / (2 - 0) = -5/2
The y-intercept can be found by substituting the coordinates of either point into the equation:
y = mx + b
2 = (-5/2)(0) + b
b = 2
So the equation of the line is:
y = (-5/2)x + 2
The shaded region of the graph is to the left of this line. Since the line has a negative slope, any point below the line will satisfy the inequality y ≤ -3x + 3. Therefore, the correct answer is A.
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in the diagram, triangle ABC is similar to triangle EDC. a. is line AB parallel to line DE? b. show that triangle ACD is similar to triangle ECB. c. find the measure of angle CAD. d find line ED. e. find line AD explain your reasoning
The measure of the angle CAD is 40 degrees, the length of ED is 12 units, and the length of AD is 12 units.
What is the similarity law?It is defined as the law to prove that the two 2-dimensional have the same shape, but it is not compulsory to have the same size. The ratio of the corresponding sides is in the same proportions and the corresponding angles are congruent.
Triangle ABC ~ EDC
Angle ACD = Angle BCE = 90 degree (vertically opposite angle)
Angle ACB = Angle DCE = 90 degree (vertically opposite angle)
BE ║ AD
Angle EBC = Angle CDA = 40 degree (alternative angles)
Triangle ABC ~ Triangle EDC
Angle ABC = Angle CDE
Angle BAC = Angle DEC
∴ AB ║ DE
Triangle ACD ~ Triangle ECB
Angle EBC = Angle CDA and
Angle BEC = Angle CAD
∴ Triangle ACD ~ Triangle ECB
Angle A + Angle E = 180 degree
∠x + 50 + 50 + ∠x = 180
∠x = 40
Angle CAD = 40 degree
We know,
Angle A = Angle E = Angle B = Angle D = 90 degree
So ABCD is a square
AB = ED = 12
AD = AB = BE = ED = 12
Thus, the measure of the angle CAD is 40 degrees, the length of ED is 12 units, and the Length of AD is 12 units.
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ignore the answer i clicked on, i did not mean to click it
Answer:
20√2Step-by-step explanation:
The diagonal of a square is given as, √2 × side. Rearranging this formula to calculate the side of the square, we get, side = diagonal/√2 = (√2 × diagonal)/2 . Thus, the perimeter of the square can be calculated using the formula, P = 2√2 × diagonal.
Diagonal = 5 * 2 = 10
P = 2√2 * 10
P = 20√2
What is the sum of the polynomials?
(6x+7+x²) + (2x²-3)
-x²+6x+4
3x²+6x+4
9x + 4
9x² +4
Answer:
3x^2 + 6x + 4
Step-by-step explanation:
6x + 7 + x^2 + 2x^2 - 3 = 3x^2 + 6x + 4
Answer:
3x²+6x+4
Step-by-step explanation:
Given:
(6x+7+x²) + (2x²-3)
Aim:
To add the polynomials
Solution:
Removing brackets first:
6x+7+x²+2x² - 3Collecting like terms to each other,
6x+7-3+2x²+x²Simplifying,
6x+4+3x²Rewriting it as,
3x²+6x+4Second choice is accurate.
Identify the height of a triangle in which b=12 m and A=(18x−6) m^2. SHOW YOUR WORK!!!
Answer:
[tex]3x-1[/tex]
Step-by-step explanation:
The formula to find the area of a triangle:
[tex]A = \frac{bh}{2}[/tex]
Here, [tex]A[/tex] is the area, [tex]b[/tex] is the base and [tex]h[/tex] is the height.
However, we are looking for height, so let's rearrange the equation for [tex]h[/tex]:
[tex]A = \frac{bh}{2}\\2A = bh\\h = \frac{2A}{b}[/tex]
Now we know the formula to find the height, let's do so:
[tex]h = \frac{2(18x-6)}{12}\\\\h = \frac{36x-12}{12}\\\\h = 3x - 1[/tex]
Therefore, our final answer is [tex]3x-1[/tex].
erved,
The graph of function fis shown on the coordinate plane. Graph the line representing function g, if g is defined as shown below.
g(x) = 2f(x-1)
Using the graph attached, If g(x) = 2f(x-1), the graph of the function will be: g(x) = x - 7.
What is the function about?Using the graph, the function is:
f(x-1) =1/2 (x-1) - 3
f(x-1) = 1/2x - 1/2 - 3/1
f(x-1) = 1/2x - 7/2
So:
g(x) = 2f(x-1)
g(x) = 2 (1/2x - 7/2)
g(x) = x - 7
Therefore,:
At x = 0, y = -7
y = 0, x = -7
Thus, Using the graph attached, If g(x) = 2f(x-1), the graph of the function will be: g(x) = x - 7.
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Got it right on Plato/Edmentum UωU <3
The graph below shows the solution to which system of inequalities?
Answer:
C
Step-by-step explanation:
The horizontal line, y=2, is solid and shaded above, so it represents
[tex]y \geqslant 2[/tex]
The slanted line, y=x is dashed and shaded below, so it represents y<x.
Answer
Answer is A
Step-by-step explanation:
Construct a rectangle with sides 6cm and 4cm.
Answer:
Step-by-step explanation:
Answer:
First, draw a line segment AB = 6 cm.Draw a ray AX with pencil and compass such that ∠BAX = 90°. Draw an arc of 4 cm with point A which intersects AX at D.Similarly, draw ray BY such that ∠ABY = 90°. Draw an arc of 4 cm with point B which intersects BY at C.Join CD.Thus ABCD is the required rectangle.im always having problems with this i need someone to explain please
For every meter there are 3.281 feet. The perimeter of the yard is 188ft. Divide 188 by 3.281 and you get 57.3 (rounded to 1dp). Round that up to the nearest meter and you get 58. So, Mr Smith needs 58 meters of fencing for his yard.
Line I is a perpendicular bisector
Line I is a perpendicular bisector because it bisects another line at right angles via the point of intersection or midpoint. See the Perpendicular Bisector Theorem below.
What is the perpendicular bisector theorem?According to the theorem of perpendicular bisector, any locus on the perpendicular bisector is equidistant from the terminal points of the line segment on which it is created.
Thus, Line I is a perpendicular bisector because it bisects another line at right angles via the point of intersection or midpoint. See the attached image.
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Please help me i would really appreciate it, worth 11 points
The number of seconds it takes for the waste to hit the ground for the given function is: 5 seconds.
How to Evaluate a Function?We are given the function of height to time as, h(t) = -16t² + initial height, and we have the following:
h(t) = 0 (height of the ground is 0)t = seconds the waste takes to height the groundInitial height = 400 feetPlug in the values into the equation of the function
0 = -16t² + 400
Solve for t
0 - 400 = -16t²
-400 = -16t²
-400/-16 = t²
400/16 = t²
√(400/16) = t
20/4 = t
5 = t
t = 5
The number of seconds it takes is: 5 seconds.
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Find the equivalent exponential expression. (5^5)^4
Answer:
5^20
Step-by-step explanation:
since you have brackets around (5^5) you can multiply the exponents. if you think about it what you're essentially doing is
(5 * 5 * 5 * 5 * 5) * (5 * 5 * 5 * 5 * 5) * (5 * 5 * 5 * 5 * 5) *
(5 * 5 * 5 * 5 * 5)
which is why you can multiply the exponents to simplify
r,u,t,s are positive
RXS=15
SXT=3
TXV=7
RXV=??
Answer:
35
Step-by-step explanation:
R × S = 15 could be 5 × 3 = 15, 3 × 5 = 15
15 × 1 = 15, 1 × 15 = 15
S ×T =3 From our previous step we can see that S could be 1 or 3 or 5 or 15.
Given that S×T =3, will make sense that S is 1 or 3
If S is 1 then T is 3 and if S is 3 then T is 1, so multiplied will give 3.
T×V=7 From previous step we see that T could be 1 or 3.
Since T×V = 7 it will make sense that T is 1, and therefore V is 7.
T ×V = 7, S ×T =3, R × S = 15, R × V = ??
1 × 7 = 7, S ×1 = 3, R × 3 = 15, 5 × 7 = ??
3 ×1 = 3, 5 × 3 = 15, 5 × 7 = 35
On Friday, a local hamburger shop sold a combined total 312 of hamburgers and cheeseburgers. The number of cheeseburgers sold was two times the number of hamburgers sold. How many hamburgers were sold on Friday?
What is the answer to the question?
Answer:
See attached file for answers and explanation.
Step-by-step explanation:
See attached image.
how many didgits are in 136.08
Answer:
5
Step-by-step explanation:
Count the digits.
Suppose the u.s. government put a 'special 20 percent luxury tax' on the retail price of expensive and fancy yachts in order to collect more taxes from boat owners. assume the price elasticity for these yachts is elastic at 2.50. conclusion: we can probably expect that yacht sales will go down and the government will not collect lots of new tax revenues.
True. We can probably expect that yacht sales will go down and the government will not collect lots of new tax revenues.
It is given that the US government has put a 20% luxury tax and the price elasticity for these yachts is elastic at 2.50.
Due to the new tax on luxury goods, it can be estimated that the sales of yachts go down as the maximum retail price of the yachts will become more expensive. This can mean that fewer people than before will be able to afford the yachts. Due to fewer sales, the government will not have enough tax revenues.
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