Answer:
90
Step-by-step explanation:
Angle Formed by Two Chords= 1/2(SUM of Intercepted Arcs)
105 = 1/2 (120+x)
210 = 120+x
Subtract 120 from each side
210-120 = x
90 =x
The value of Intercepted Arcs x will be 90. so option C is correct.
What is the relation between line perpendicular to chord from the center of circle?If the considered circle has center O and chord AB, then if there is perpendicular from O to AB at point C, then that point C is bisecting(dividing in two equal parts) the line segment AB.
Or
|AC| = |CB|
Angle Formed by Two Chords= 1/2 (Sum of Intercepted Arcs)
105 = 1/2 (120+x)
210 = 120+x
Subtract 120 from each side;
210-120 = x
90 =x
Hence, the value of Intercepted Arcs x will be 90. so option C is correct.
Learn more about chord of a circle here:
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Use the method of cylindrical shells to write out an integral formula for the volume of the solid generated by rotating the region bounded by the curve y = 2x - x^2 and the line y = x about the y-axis.
Answer:
The answer is "[tex]\frac{5\pi}{6}[/tex]"
Step-by-step explanation:
Please find the graph file.
[tex]h= y=2x-x^2\\\\r= x\\\\Area=2\pi\times r\times h\\\\= 2 \pi \times x \times (2x-x^2)\\\\= 2 \pi \times 2x^2-x^3\\\\volume \ V(x)=\int \ A(x)\ dx\\\\= \int^{x=1}_{x=0} 2\pi (2x^2-x^3)\ dx\\\\= 2\pi [(\frac{2x^3}{3}-\frac{x^4}{4})]^{1}_{0} \\\\= 2\pi [(\frac{2}{3}-\frac{1}{4})-(0-0)] \\\\= 2\pi \times \frac{5}{12}\\\\=\frac{5\pi}{6}\\\\[/tex]
How many solutions will each system of linear equation have?
Answer:
The top system of equations has one solution, the middle system has infinitely many, and the bottom system has no solution.
Step-by-step explanation:
We can immediately see the top system has one solution because the two equations have different slopes.
For the middle system, we can rearrange terms and multiply by 3 to get that the equations are the same line, so there are infinitely many solutions.
Finally, we can move the -2x to the other side in the first equation of the bottom system to get 2x+y=5. But it also equals -7 from the second equation! This is impossible, so there are no solutions to the bottom system.
Describe how to transform the graph of f(x) = x2 to obtain the graph of the related function g(x).
Then draw the graph of g(x).
1. g(x) = f(x + 1)
2. g(x) = f(x) - 2
Please help i also need to graph
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Answer:
left 1 unitdown 2 unitsStep-by-step explanation:
The transformation g(x) = f(x -h) +k is a translation of f(x) to the right by h units and up k units.
1. h = -1, so the graph of g(x) is the graph of f(x) shifted left 1 unit. (blue)
__
2. k = -2, so the graph of g(x) is the graph of f(x) shifted down 2 units. (green)
What value of x makes the equation 3x +7=22
Answer:
x = 5
Step-by-step explanation:
Your goal is to isolate x
3x + 7 = 22
Subtract 7 from both sides and you are left with
3x = 15
In order to isolate x divide both sides by 3
x = 5
if one half of a number is 5 more than 6, what is the value when the number is tripled
Answer:
66
Step-by-step explanation:
let's use x to represent the unknown number
1/2x is 5 more than 6:
↓
1/2x=5+6
solve to find x
1/2x=11
x=22
next, it asks us what is the value of the number when the number is tripled
since we already found what x is equal to, we can multiply that by 3 to figure out its value when it's tripled
3(22)=66
Using mathematical equation to model the scenario, the value of the number when tripled is 66
Let the number = n
0.5n = 5 + 6
0.5n = 11
Divide both sides by 0.5
n = 22
When n is tripled :
n = 22 × 3
n = 66
Hence, the value of the number when tripled is 66
Learn more : https://brainly.com/question/25480062
Pls if anyone knows the answer that will be greatly appreciated :)
Answer:
I think the area is 60 but i couldn't figure out the perimeter, sorry.
Step-by-step explanation:
Answer:
perimeter = 36 m
area = 60 m²
Step-by-step explanation:
there is some missing information. for example about the types of the shapes. e.g. if the triangle on the top is an isosceles triangle (2 equal sides). or if the rectangle at the bottom is actually a square with 6 m on all sides. in order to make the sloped side of the top triangle a round, whole number, i assume that the bottom part is a square.
so, the area of this combined shape is the area of the bottom square plus the area of the top triangle.
area square As = 6×6 = 36 m²
so, one side of the triangle is also 6 m, the other is 14-6 = 8 m.
the area of such a right-angled triangle is half of the full rectangle of 6×8.
area triangle At = 6×8/2 = 48/2 = 24 m²
total area = As + At = 36 + 24 = 60 m²
the perimeter of the total shape is the sum of all sides.
so, 14, 6, 6 and ... the baseline/ Hypotenuse of the top triangle.
for that r need the mentioned Pythagoras :
c² = a² + b²
where a and b are the sides, and c is the Hypotenuse (the side opposite of the 90 degree angle).
so, in our case of an isosceles triangle with a 90 degree angle :
c² = 8² + 6² = 64 + 36 = 100
c = 10 m
so, the perimeter is
14+6+6+10 = 36 m
Now suppose that not every player can play in every position. The outfielders (left field, center field, right field) can play any outfield position, the infielders (1st base, 2nd base, 3rd base, short stop) can play any infield position, the pitchers can only pitch, and the catchers can only catch. Suppose a certain team has 20 players, of whom 3 are catchers, 4 are outfielders, 6 are infielders, and 7 are pitchers.
How many ways can the team assign field positions to 9 of the 19 players, putting each of the 9 selected players in a position he can play, and ensuring that all 9 field positions are filled?
Answer:
The team can assign field positions to 9 of the 19 players in 181,440 different ways.
Step-by-step explanation:
Since the outfielders (left field, center field, right field) can play any outfield position, the infielders (1st base, 2nd base, 3rd base, short stop) can play any infield position, the pitchers can only pitch, and the catchers can only catch, supposing a certain team has 20 players, of whom 3 are catchers, 4 are outfielders, 6 are infielders, and 7 are pitchers, to determine how many ways can the team assign field positions to 9 of the 19 players, putting each of the 9 selected players in a position he can play, and ensuring that all 9 field positions are filled, the following calculation must be performed:
3 x 7 x 6 x 5 x 4 x 3 x 4 x 3 x 2 = X
21 x 30 x 12 x 24 = X
630 x 12 x 24 = X
181,440 = X
Therefore, the team can assign field positions to 9 of the 19 players in 181,440 different ways.
Find the y-intercept from the line passing through (1, 3) and having slope m=2.
Answer:
The y intercept is 1
Step-by-step explanation:
The slope intercept form of a line is
y = mx+b where m is the slope and b is the y intercept
y = 2x+b
Substitute the point into the equation and solve for y
3 = 2(1)+b
3 =2+b
1 = b
The y intercept is 1
What is the difference between the temperature - 7 Celsius and - 12 Celsius on a scatter diagram
Answer:
Sự khác biệt giữa nhiệt độ - 7 độ C và - 12 độ C trên biểu đồ phân tán là gì
Step-by-step explanation:
Can you please help me
Answer:
you will type your answers and send
Answer:
Step-by-step explanation:
⅔-2/5 = 4/15
Do 8 plz find OS thanks
Answer:
OS = 10
Step-by-step explanation:
We can use a ratio to solve
QP PR
----- = ------
QO OS
14 7
----- = -------
14+6 OS
14 7
----- = -------
20 OS
Using cross products
14 * OS = 7*20
14 OS = 140
Divide by 14
OS = 140/14
OS = 10
The length of a rectangle is 2 centimeters less than three times its width. Its area is 21 square centimeters. Find the dimensions of the rectangle. Use the formula, area=length*width.
Area = length x width
Area = 21 square cm
Width = x
Length = 3x + 2
21 = 3x+ 2 * x
21 = 3x ^2 + 2x
Subtract 21 from both sides:
3x^2 + 2x -21 = 0
Use the quadratic formula to solve for x:
-2 +/- sqrt(2^2-4*3(-21))/(2*3)
X = 7/3 and -3
A dimension can’t be a negative value so x needs to be 7/3
Width = x = 7/3 = 2 1/3 cm
Length = 3(7/3) + 2 = 9 cm
Check: 9 x 2 1/3 = 21
Dimensions: width 2 1/3 cm length 9 cm
Answer:
The dimensions of the rectangle are 7 by 3 centimeters.
Step-by-step explanation:
We are given that the length of a rectangle is two centimeters less than three times its width. In other words:
[tex]\displaystyle \ell = 3w-2[/tex]
Given that the area of the rectangle is 21 square centimeters, we want to determine the dimensions of the rectangle.
Recall that the area of a rectangle is given by:
[tex]A= w\ell[/tex]
Substitute:
[tex](21)=w(3w-2)[/tex]
Solve foro the width. Distribute:
[tex]3w^2-2w=21[/tex]
Isolate the equation:
[tex]3w^2-2w-21=0[/tex]
Factor. Find two numbers that multiply to 3(-21) = -63 and add to -2.
-9 and 7 suffice. Hence:
[tex]3w^2-9w+7w-21=0 \\ \\ 3w(w-3)+7(w-3) = 0 \\ \\ (3w+7)(w-3)=0[/tex]
Zero Product Property:
[tex]3w+7=0\text{ or } w-3=0[/tex]
Solve for each case. Hence:
[tex]\displaystyle w = -\frac{7}{3}\text{ or } w=3[/tex]
Since width cannot be negative, we can ignore the first solution.
Therefore, our width is three centimeters.
And since the length is two less than three times the width, the length is:
[tex]\ell = 3(3) - 2 = 7[/tex]
The dimensions of the rectangle are 7 by 3 centimeters.
In the figure, L1 || L2. 2x=174º. Find Za+Zb.
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Answer:
12°
Step-by-step explanation:
We assume you mean ...
∠x = 174°
Angle a is supplementary to angle x, so is ...
∠a = 180° -174° = 6°
Angle b is a vertical angle with respect to angle 'a', so is the same measure.
∠a +∠b = 6° +6° = 12°
A kite is a quadrilateral with two pairs of adjacent, congruent sides. The vertex angles are those angles in between the pairs of congruent sides. Prove the diagonal connecting these vertex angles is perpendicular to the diagonal connecting the non-vertex angles. Be sure to create and name the appropriate geometric figures. This figure does not need to be submitted.
please answer all the questions and get 15 pts
Answer:
Here you go
Ans is in pictures.
Find the value of x in each case:
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Answer:
x = 36
Step-by-step explanation:
The interior angle at E is (180-2x). The interior angle at F is (180-4x). The sum of the interior angles of the triangle is 180, so we have ...
(180 -2x) +x +(180 -4x) = 180
180 = 5x . . . . . . add 5x-180 to both sides
36 = x . . . . . . . divide by 5
__
Additional comment
This value of x makes the exterior angles at E and F be 72° and 144°, respectively. The internal angles at E, F, G are then 108°, 36°, 36°, making the triangle isosceles with EF = EG.
What is the value of the expression i 0 × i 1 × i 2 × i 3 × i 4?
1
–1
i
–i
Answer:
B. -1 should be the answer
Step-by-step explanation:
Consider the sequence {an}={3n+13n−3n3n+1}. Graph this sequence and use your graph to help you answer the following questions.
Part 1: You can simplify [tex]a_n[/tex] to
[tex]\dfrac{3n+1}{3n}-\dfrac{3n}{3n+1} = \dfrac1{3n}+\dfrac1{3n+1}[/tex]
Presumably, the sequence starts at n = 1. It's easy to see that the sequence is strictly decreasing, since larger values of n make either fraction smaller.
(a) So, the sequence is bounded above by its first value,
[tex]|a_n| \le a_1 = \dfrac13+\dfrac14 = \boxed{\dfrac7{12}}[/tex]
(b) And because both fractions in [tex]a_n[/tex] converge to 0, while remaining positive for any natural number n, the sequence is bounded below by 0,
[tex]|a_n| \ge \boxed{0}[/tex]
(c) Finally, [tex]a_n[/tex] is bounded above and below, so it is a bounded sequence.
Part 2: Yes, [tex]a_n[/tex] is monotonic and strictly decreasing.
Part 3:
(a) I assume the choices are between convergent and divergent. Any monotonic and bounded sequence is convergent.
(b) Since [tex]a_n[/tex] is decreasing and bounded below by 0, its limit as n goes to infinity is 0.
Part 4:
(a) We have
[tex]\displaystyle \lim_{n\to\infty} \frac{10n^2+1}{n^2+n} = \lim_{n\to\infty}10+\frac1{n^2}}{1+\frac1n} = 10[/tex]
and the (-1)ⁿ makes this limit alternate between -10 and 10. So the sequence is bounded but clearly not monotonic, and hence divergent.
(b) Taking the limit gives
[tex]\displaystyle\lim_{n\to\infty}\frac{10n^3+1}{n^2+n} = \lim_{n\to\infty}\frac{10+\frac1{n^3}}{\frac1n+\frac1{n^2}} = \infty[/tex]
so the sequence is unbounded and divergent. It should also be easy to see or establish that the sequence is strictly increasing and thus monotonic.
For the next three, I'm guessing the options here are something to the effect of "does", "may", or "does not".
(c) may : the sequence in (a) demonstrates that a bounded sequence need not converge
(d) does not : a monotonic sequence has to be bounded in order to converge, otherwise it grows to ± infinity.
(e) does : this is true and is known as the monotone convergence theorem.
Annie bought a 2 3/4 pound roast for the family dinner. A total of 9 people will be at dinner. How many pound of roast will each person get if the roast is divided up equally?
Answer:
11 /36 of a pound
Step-by-step explanation:
Take the pounds and divide by the number of people
2 3/4 ÷ 9
Change the mixed number to an improper fraction
(4*2+3)/4 ÷9
11/4 ÷9
Copy dot flip
11/4 * 1/9
11/36
X^2 + bx + 49 is a perfect squad trinomial what is one possible value of b?
a perfect square trinomial, (x + y)² = x² + 2xy + y²
so, if we have the x of the bx, what is left is the b
the expression would have to be (x + 7)², since we have the 49 and the x²
so, what's left: x² + 14x + 49,
b = 14
hope it helps :)
Need help! Thank you :)
Answer:
The value of [tex]x[/tex] is 10.
Step-by-step explanation:
Both angles ABC and CBD are complementary, that is, the sum of the measures of both angles equals 90°, that is:
[tex]\angle ABC + \angle CBD = 90^{\circ}[/tex] (1)
If we know that [tex]\angle ABC = 5\cdot x[/tex] and [tex]\angle CBD = 4\cdot x[/tex], then the value of [tex]x[/tex] is:
[tex]5\cdot x + 4\cdot x = 90^{\circ}[/tex]
[tex]9\cdot x = 90^{\circ}[/tex]
[tex]x = 10[/tex]
The value of [tex]x[/tex] is 10.
Michelin Tires would like to estimate the average tire life of its Latitude Tour tire in terms of howmany miles it lasts. Assume the standard deviation for the tire life of this particular brand is 6000miles. Determine the sample size needed to construct a 95% confidence interval with a margin oferror within 2000 miles.ShowWork:
Answer:
6 samples
Step-by-step explanation:
Given :
Sample size, = n
Standard deviation, = 6000
Margin of Error = 2000
Confidence interval, α = 95%
Zcritical at 95% = 1.96
n = (Zcritical * σ) / margin of error
n = (1.96 * 6000) /2000
n = 11760 / 2000
n = 5.88
n = 6 samples
a family has two children. what is the probability that both are girls, given that at least one is a boy
Answer: The probability would be zero
Step-by-step explanation:
There are two children and one is a boy, so the probability of both being girls is a zero
The pie chart shows student participation in fundraisers
at Mountain View Middle School.
Mountain View Middle School
Fundraisers
Which describes a bar diagram showing the percent of
students who participated in dances?
1 shaded square out of 10 squares
2 shaded squares out of 10 squares
3 shaded squares out of 10 squares
4 shaded squares out of 10 squares
20
Carnival
Car Wash
Bake Sale
Talent Show
10
50
5
15
Dances
Answer:
Step-by-step explanation:
If you add all of the numbers up, you get 100. Dances are colored purple, and that is 20. 20/100 simplified is 1/5. 1/5 is equivalent to 2/10. Therefore, the answer is 2 shaded squares out of 10 squares.
I’m so confused. Need the help
1.621 kN
Step-by-step explanation:
Let the centerline of the canal be the x-axis. Because the forces exerted by the horses are symmetric to the centerline, only the x-components of these forces contribute to the resultant force on the barge, i.e., the y-components cancel out. Each x-component is equal to [tex]F_x = 839\cos 15[/tex] = 810.4 N. Therefore, the resultant force on the barge is twice this:
[tex]F_{net} = 2(839\:\text{N})\cos 15 = 1620.8\:\text{N}[/tex]
[tex]= 1.621\:\text{kN}[/tex]
Given the coordinates of two points on a line, explain two methods to determine the slope of the line.
Answer:
Step-by-step explanation:
1. Use the slope formula (y2 - y1 / x2 - x1)
2. Use the graph. Take two points and count the rise over the run.
I really need help
Dz,2 of X is
(0-4)
(2,-2)
(6,2)
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Answer:
(6,2)
Step-by-step explanation:
As is often the case with multiple-choice problems, you don't actually need to know the detailed working. You just need to know what the answer looks like.
When point X is dilated by a factor of 2 with point Z as the center of dilation, it will move to a location twice as far from Z. You can tell by looking at the graph that X' will be in the first quadrant, above and to the right of the location of X. The only sensible answer choice is ...
X' = (6, 2)
_____
Additional comment
X is a distance of X-Z = (4, 0) -(2, -2) = (2, 2) from Z Doubling that will put the image point a distance of 2(2, 2) = (4, 4) from Z. When this is added to Z, we find ...
X' = Z + (4, 4) = (2+4, -2+4) = (6, 2)
Diane bought new headphones originally listed for $70.99. They are 25% off. Which equation can be used to find the amount Diane will save?
Step-by-step explanation:
100% = $70.99
there is a discount of 25%.
that means 75% (100 - 25) of the original price remains.
the equation to get any x% amount of a 100% total is simply
x% amount = 100% total amount × x/100
25% = 70.99 × 25/100 = $17.75
What is the maximum amount of a loan you can get if you pay $700 each month at a yearly rate of 0.89% for 10 years?
Answer:
$785.17
Step-by-step explanation:
Given data
PV is the loan amount
PMT is the monthly payment
i is the interest rate per month in decimal form (interest rate percentage divided by 12)
n is the number of months (term of the loan in months)
PMT =$700
n = 10 years
i = 0.89%
The formula for the loan amount is
Write expression with two terms that is equivalent to the expression shown. 4(2x + 11 - x)