I'm guessing the power series given is
[tex]\displaystyle \sum_{n=1}^\infty (-1)^{n+1}\frac{(x-8)^n}{8^n}[/tex]
which you can condense somewhat into
[tex]\displaystyle -\sum_{n=1}^\infty \left(\frac{8-x}8\right)^n[/tex]
You should recognize this as a geometric series, which converges for
[tex]\left|\dfrac{8-x}8\right|<1 \implies |8-x|<8 \implies \boxed{0 < x < 16}[/tex]
Which of the following is the correct factorization of the polynomial below?
x3 + 10x2 + 25x
A. x(x + 5)(x - 5)
B. (x2 + 2x - 5)(x-10)
C. (x2 + 5x - 2)(x-10)
D. x(x + 5)2
Answer:
x(x+5)^2
Step-by-step explanation:
x^3 + 10x^2 + 25x
Factor out x
x(x^2+10x+25)
What 2 numbers multiply to 25 and add to 10
5*5 = 25
5+5 =10
x(x+5)(x+5)
x(x+5)^2
Answer:
D
Step-by-step explanation:
Given
x³ + 10x² + 25x ← factor out x from each term
= x(x² + 10x + 25) ← perfect square
= x(x + 5)²
A 12-foot ladder is leaning against the side of a building. The bottom of the ladder is 5 feet from the wall. How many feet above the ground does the ladder touch the wall?
A. 119−−−√ feet
A. square root of 119 feet,
B. 7 feet
B. 7 feet
C. 13 feet
C. 13 feet
D. 134−−−√ feet
Answer:
Option A, √119
Step-by-step explanation:
Let the height be x foot
12^2=5^2+x^2
or, x = ±√119
since distance can't be negative, so it's x = √119
Answered by GAUTHMATH
nolan uses 7 inches of string to make each bracelet. if nolan makes 3 bracelets, how many inches of string will he use?
Answer:
21 inches
Step-by-step explanation:
We can write a ratio to solve
7 inches x inches
------------- = -------------------
1 bracelet 3 bracelets
Using cross products
7*3 = 1x
21 = x
21 inches
Answer:
21 inches
Step-by-step
This can be solved two ways: addition or multiplication.
Addition: Since there are three bracelets you could add 7 three times
7+7+7
= 14+7
= 21
Multiplication: Simply multiply 7 x 3= 21
please help me out (geometry)
Answer:
x = 15
Step-by-step explanation:
2x+10+4x+80=180
or, 2x+4x=180-80-10
or, 6x=90
or, x=15
Answered by GAUTHMATH
A number cube is rolled 14 times and the results are recorded in the table.
What, in simplest form, is the experimental probability that the number cube shows 4?
A. 0
B. 1/6
C. 2/7
D. 5/14
Answer:
b
Step-by-step explanation:
The experimental probability that the number cube shows 4 is 2/7.
What is an experimental probability?Experimental probability is a probability that is determined on the basis of a series of experiments.
Given that, a number cube is rolled 14 times, we need to determine the experimental probability that the number cube shows 4,
The formula to calculate the experimental probability is:
P(E) = Number of times an event occurs/Total number of times the experiment is conducted
P(E) = 4/14 = 2/7
Hence, the experimental probability that the number cube shows 4 is 2/7.
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Use the graph to find the factorization of x2 - 5x + 4.
10
y = x2.5x + 4
-10
10
10
O A. (x + 2)(x - 2)
B. (x - 1)(x-4)
O C. (x + 2)(x+4)
O D. (x + 1)(x + 4)
Answer: B. (x - 1) (x - 4)
Concept:
Here, we need to know the idea of zeros.
The zeros of a quadratic equation are the points where the graph of the quadratic equation crosses the x-axis.
If you are still confused, please refer to the attachment below for a graphical explanation.
Solve:
By definition, the factored form of quadratic equations is basically their zeros.
STEP ONE: Find the zeros / x-intercept of the graph
The grid number is 2 per grid as 5 grids are 10 units.
The first intercept is between the y-axis and the first grid.
2 / 2 = 1The second intercept is on the second grid.
2 × 2 = 4STEP TWO: Plug the zeros into factorization form
Factor form = (x - x₁) (x - x₂)
x₁ = (1, 0)
x₂ = (4, 0)
Factorization of x² - 5x + 4 = (x - 1) (x - 4)
Hope this helps!! :)
Please let me know if you have any questions
Resuelve el siguiente problema un buzo en una laguna decendio 8m en una hora.Si cada hora bojo la misma cantidad de metros, ¿cuantos metros bojo en 4 horas
Answer:
X = 32 meters.
Step-by-step explanation:
Let the unknown distance be X.Given the following data;
Distance = 8 meters per hourTime = 4 hoursTo find how many meters he would cover in four hours;
1 hour = 8 meters
4 hours = X meters
Cross-multiplying, we have;
X = 8 * 4
X = 32 meters.
ASAP PLEASE HELPPPPPPPPPPPPPPPPPP MEEEEEEEEEEEEEEE
Answer:
-2/5 is the answer
I hope this will help you
Answer:
-2/5
Step-by-step explanation:
Just add the top numerator together -4 + 2 = -2
A chef got 7 bags of onions. The red onions came in bags of 8 and the yellow onions came in bags of 3. If the chef got a total of 41 onions, how many bags of each type of onion did he get?
Answer:
[tex]\#\text{ of 8-onion bags: }4,\\\#\text{ of 3-onion bags: }3[/tex]
Step-by-step explanation:
Let [tex]a[/tex] be the number of bags with 8 onions and let [tex]b[/tex] be the number of bags with 3 onions. We have the following system of equations:
[tex]\begin{cases}a+b=7,\\8a+3b=41\end{cases}[/tex]
Subtracting [tex]b[/tex] from both sides of the first equation, we get [tex]a=7-b[/tex]. Substitute this into the second equation:
[tex]8(7-b)+3b=41,\\56-8b+3b=41,\\56-5b=41,\\-5b=-15,\\b=\boxed{3}[/tex]
Therefore, the number of 8-onion bags is:
[tex]a=7-b,\\a=7-3,\\a=\boxed{4}[/tex]
Thus, the chef got 4 8-onion bags and 3 3-onion bags.
I need help with this, I can’t figure out the answer…
please help me divide this fractions, showboat work.
O_O
solution given;
36:5/5
38:86/69
To divide fractions, you basically just multiply the first fraction by the reciprocal of the second. To find the reciprocal, you just flip the numerator and the denominator.
For number 36, you have 2/3÷8/15. To solve this, you just multiply 2/3 by 15/8.
2/3×15/8 is 30/24, which is 5/4 or 1 1/4.
To answer the second problem, you have to convert the mixed numbers to improper fractions.
7 1/6 as an improper fraction is 43/6. 5 3/4 as an improper fraction is 23/4.
Do the same procedure; 43/6×4/23 is 86/69 or 1 17/69.
Madam Chong's mass is 72 kg. After participating in a fitness programme, her mass decreases at a rate of 3 kg per month. Find the minimum number of months that Madam Chong has to participate in the programme so that her mass becomes less than 52 kg. (Give your answer to the nearest whole number.)
Solve the equation 2sin x cos x = cos x, for 0° < x≤ 90°
Answer:
2sinx.Cosx=cosx
2sin90°.cos90°=cos90°
2×1.0=0
0=0
Find the value of x rounded to the nearest tenth.
Answer:
The answer to the equation is C
Anyone good at Ks3 maths
Answer:
[tex]{ \tt{distance = speed \times time}} \\ { \tt{ = 56 \times 3 \frac{1}{2} }} \\ = { \tt{196 \: miles}}[/tex]
Linear equation: -1
2
(6x + 10) = 13
Step 1: –3x – 5 = 13
Step 2: –3x = 18
Step 3: x = –6
Which sequence describes the inverse operations used for steps 2 and 3 to solve the linear equation?
Answer:
see below
Step-by-step explanation:
-1/2 * (6x + 10) = 13
Distribute -1/2
–3x – 5 = 13
Add 5 to each side
-3x-5+5 = 13+5
–3x = 18
Divide each side by -3
-3x/-3 = 18/-3
x = -6
The following are the dimensions of a triangle, 6 cm, 8 cm, and 12 cm.
Is this a right triangle?? Use the Pythagorean theorem and the basic law of exponents to prove whether this is a RIGHT triangle.
Show your work and POST your answer.
Answer:
Perimeter of original triangle: 6+8+10=24 cm
Perimeter of new triangle: 3+4+5=12 cm (You get 3, 4, and 5 from dividing 6, 8. and 10 by 2.)
Ratio of original to new is 24 to 12, simplified to 2 to 1.
The ratio of the perimeter is the ratio of the corresponding sides, as the original measurements are two times the length of the new measurements.
Area of original triangle: (6x8)/2=24 cm^2
Area of new triangle: (3x4)/2=6 cm^2
Ratio of original to new is 24 to 6, simplified to 4 to 1.
One of the legs of a right triangle measures 9 cm and its hypotenuse measures 16 cm. Find the measure of the other leg. If necessary, round to the nearest tenth.
Answer:
13.2 cm
Step-by-step explanation:
using the Pythagorean theorem, we can find the length of the other leg, since this is a right triangle. The equation is a^2 + b^2 = c^2, A and B being the legs and C being the hypotenuse. Since we are finding the other leg, we can switch the equation around to find A/B instead. (A/B being the legs). so we get: B^2 = C^2 - A^2 ; then we simplify [tex]b=\sqrt{c^2-a^2}[/tex]
We plug in the numbers given:
[tex]b = \sqrt{16^2-9^2}\\b=\sqrt{256-81}\\b=\sqrt{175} \\b= 13.229[/tex]
rounded to nearest tenth: 13.2
The measure of the other leg in the right triangle is 13.22 cm.
What is a right triangle?A triangle with one angle measuring 90° is called a right triangle.
Given that, a right triangle has a leg measuring 9 cm and its hypotenuse is 16 cm longs, we need to find the other side,
So, using the Pythagoras theorem,
16² = 9² + x²
x = √256-81
x = √175
x = 13.22
Hence, the measure of the other leg in the right triangle is 13.22 cm.
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What is the value of X?
Answer:
x=2
Step-by-step explanation:
A line that intersects a circle in two points is called a secant line, and this is the case for both line DE and AE.
For two secant lines that intersect outside of the circle, such as the ones here, we can say that
CE * DE = BE * AE
Therefore, we need to then define these lines.
CE is x+4, BE is x+1, AE = (BE + AB) = 11+x+1 = 12+x, and DE = (CE + DC) = 1+x+4 = 5+x
We then have
(x+4) * (5+x) = (x+1) * (12+x)
expand
5x + x² + 20 + 4x = 12x+x²+12+x
x²+9x + 20 = x²+13x+12
Next, we want to congregate all values to one side so we can solve for x. This can be done by subtracting both sides by (x²+13x+12) to get
-4x + 8 = 0
subtract 8 from both sides to isolate the x and its coefficient
-4x = -8
divide both sides by -4 to isolate the x
x = 2
-3 , 1 , 5 , 9 , 13
find the 11th term of this sequence
show your working
Answer:
a₁₁ = 37
Step-by-step explanation:
There is a common difference between consecutive terms, that is
1 - (- 3) = 5 - 1 = 9 - 5 = 13 - 9 = 4
This indicates the sequence is arithmetic with nth term
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = - 3 and d = 4 , then
a₁₁ = - 3 + (10 × 4) = - 3 + 40 = 37
The range of cells in column D and rows 1 to 10 is represented as:
1:10 D1:D10 D:D
Answer:
how?
Step-by-step explanation:
I didnt get question
Brooke and Lamont ran a half marathon Brooke finished in 1 hour 50 minutes Lamont finished in 100 minutes who had the faster time
Answer:
Brooke = 1 hr 50 min
Lamont = 100 min = 1 hr 40 min
Because 60 min = 1 hr
Lamont was faster
Hope this helped
On a pie chart, a category representing 20% of the whole should correspond to a central angle of 20°.
Answer:
No! 20% does not correspond to a central angle 20°.
Step-by-step explanation:
The central angle for pie chart is 360°.
So, a category represents 20% is 20%(360) for central angle.
Let's simplify it to get the angle,
[tex]\frac{20}{100} * 360[/tex]
Simplify it,
72°
So, 20% does not correspond to a central angle 20°.
The probability that Dan buys a sandwich is 0.2.
The probability that Dan gets the bus is 0.9.
Assuming the events are independent, what is the probability that Dan buys a sandwich
and gets the bus?
Answer:
0.18
Step-by-step explanation:
Find the probability that both independent events occur by multiplying the individual probabilities by each other:
0.2(0.9)
= 0.18
So, the probability is 0.18
Sue read 12 more than twice as many pages is tom did last week if sue read 90 pages how many did tom read
Answer: 39 pages
Step-by-step explanation:
x = the amount of pages Tom read
[tex]2x+12=90\\2x=78\\\frac{2x}{2}=\frac{78}{2}\\x=39[/tex]
If Sue read 90 pages, which is 12 more than twice the amount, subtract 12 from 90, then divide the result by 2, boom, you got your answer. Which should be 39
What is the value of c in the interval (5,8) guaranteed by Rolle's Theorem for the function g(x)=−7x3+91x2−280x−9? Note that g(5)=g(8)=−9. (Do not include "c=" in your answer.)
Answer:
[tex]\displaystyle c = \frac{20}{3}[/tex]
Step-by-step explanation:
According to Rolle's Theorem, if f(a) = f(b) in an interval [a, b], then there must exist at least one c within (a, b) such that f'(c) = 0.
We are given that g(5) = g(8) = -9. Then according to Rolle's Theorem, there must be a c in (5, 8) such that g'(c) = 0.
So, differentiate the function. We can take the derivative of both sides with respect to x:
[tex]\displaystyle g'(x) = \frac{d}{dx}\left[ -7x^3 +91x^2 -280x - 9\right][/tex]
Differentiate:
[tex]g'(x) = -21x^2+182x-280[/tex]
Let g'(x) = 0:
[tex]0 = -21x^2+182x-280[/tex]
Solve for x. First, divide everything by negative seven:
[tex]0=3x^2-26x+40[/tex]
Factor:
[tex]0=(x-2)(3x-20)[/tex]Zero Product Property:
[tex]x-2=0 \text{ or } 3x-20=0[/tex]
Solve for each case. Hence:
[tex]\displaystyle x=2 \text{ or } x = \frac{20}{3}[/tex]
Since the first solution is not within our interval, we can ignore it.
Therefore:
[tex]\displaystyle c = \frac{20}{3}[/tex]
Suppose the line y = 2.8333x - 22.4967 describes the relation between the club-head speed (in miles per hour), x and the distance a golf ball travels (in yards), y.
(a) Predict the distance a golf ball will travel if the club-head speed is 100 mph.
(b) Suppose the observed distance a golf ball traveled when the club-head speed was 100 mph was 265 yards. What is the residual?
(c) The golf ball will travel 260.8 yards. (Round to the nearest tenth as needed.)
(d) The residual is:_________ (Round to the nearest tenth as needed.)
Answer:
c) The golf ball will travel 260.8 yards.
d) Hence the residual is 4.2 yards.
Step-by-step explanation:
c) y' = 2.8333x - 22.4967
Now the golf ball will travel [tex]= 2.8333\times100 - 22.4967[/tex]= 260.8 yards
here y'= 260.8 yards.
d) The residual is : y - y' = 265 - 260.8 = 4.2 yards.
Answer:
a) [tex]y=260.8333~yd[/tex]
b) [tex]\Delta d=4.1667~yd[/tex]
c) [tex]y=260~yd[/tex]
d) [tex]\Delta y'=0.8333~yd[/tex]
Step-by-step explanation:
Given:
equation of line, [tex]y=2.8333x-22.4967[/tex]
x = club-head speed (in miles per hour)
y = the distance a golf ball travels (in yards)
a)
x = 100 mph
Then the distance travelled by the ball:
(put the given value of x in the above eq.)
[tex]y=2.8333\times 100-22.4967[/tex]
[tex]y=260.8333~yd[/tex]
b)
If the observed distance in the above case comes out to be 265 yards then the residual value will be:
[tex]\Delta d=265-260.8333[/tex]
[tex]\Delta d=4.1667~yd[/tex]
c)
From the calculated value when rounding it to the nearest tenth:
[tex]y=260~yd[/tex]
d)
The residual on rounding the calculated value to the nearest tenth:
[tex]\Delta y'=260.8333-260[/tex]
[tex]\Delta y'=0.8333~yd[/tex]
i know it’s kinda all hard to see. i have many more questions like this and i can’t do graphs to save my life.. pls help !!
Answer: D
Step-by-step explanation:
Edwin hiked to a famous point with a beautiful view. It took 2 hours and 55 minutes to hike to the viewpoint and 25 minutes to hike back. Edwin spent 25 minutes enjoying the view at the top. He finished the hike at 11:45 A.M. What time did Edwin start the hike to the viewpoint?
Answer:
= 8:00 A.M.
Step-by-step explanation:
▪You first find the total time taken which will be :
2 hrs 55 min + 25 min
= 3 hrs 20 min + 25 min
= 3 hrs 45min
▪ Beginning time = Arrival time - Time taken
= 11:45 - 3:45
= 8:00 am
¿
An animal shelter takes in an average of 5 animals per day. The shelter must keep its total occupancy below 300. Currently, the shelter has 165 animals. If none of the animals get adopted, which inequality represents how many more days, x, the shelter can continue to take in animals without exceeding its occupancy limit?
Answer:
5x less than 300 - 165
Step-by-step explanation:
It will take 27 days to take in animals without exceeding its occupy limit.
What is algebraic expression ?An expression which is made up of variables and constants , along with algebraic operation (addition , subtraction etc ) is called Algebraic expression.
According to the question :
165 + (x) 5 = 300
5x = 135
x = 27
Hence , it will take 27 days to occupy the limit
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