Answers
AO = AB + OB
AB = 8
OB = Radius of circle = 5
So,
AO = 8 +5 = 13
The tangent of the circle is at 90 degrees to its radius. So we can say that triangle ACO is a right angled triangle, with side AO the hypotenuse.
Using the Pythagorean theorem we can find the length of tangent AC.
13² = AC² + 5²
AC² = 169 - 25 = 144
AC = 12
So, the length of side AC is 12
Related Questions
What is the sum of the first 51 consecutive odd positive integers?
Answers
[tex] a_{n} [/tex] as the set of the first 51 consecutive odd positive integers, so:
[tex]a_{n} = \{1, 3, 5, 7, 9...\} [/tex]
Where:
[tex]a_{1} = 1[/tex]
[tex]a_{2} = 3 [/tex]
[tex]a_{3} = 5 [/tex]
[tex]a_{4} = 7 [/tex]
[tex]a_{5} = 9 [/tex]
and so on.
In mathematics, a sequence of numbers, such that the difference between two consecutive terms is constant, is called Arithmetic Progression, so:
3-1 = 2
5-3 = 2
7-5 = 2
9-7 = 2 and so on.
Then, the common difference is 2, thus:
[tex]a_{n} = \{ a_{1} , a_{1} + d, a_{1} + d + d,..., a_{1} + (n-2)d+d\} [/tex]
Then:
[tex]a_{n} = a_{1} + (n-1)d[/tex]
So, we need to find the sum of the members of the finite series, which is called arithmetic series:
There is a formula for arithmetic series, namely:
[tex] S_{k} = ( \frac{a_{1} + a_{k}}{2} ).k[/tex]
Therefore, we need to find:
[tex] a_{k} = a_{51} [/tex]
Given that [tex]a_{1} = 1[/tex], then:
[tex]a_{n} = a_{1} + (n-1)d = 1 + (n-1)(2) = 2n-1 [/tex]
Thus:
[tex]a_{k} = a_{51} = 2(51)-1 = 101[/tex]
Lastly:
[tex] S_{51} = ( \frac{1 + 101}{2} ).51 = 2601[/tex]
On a blueprint with a scale of 1cm = 2ft, the length of a wall is 12cm. If the scale of the blueprint were 1cm = 3ft, what will be the length of the wall?
(Please show work, I will mark brainliest)
Answers
The actual length of the wall is
12 cm * (2 ft / 1 cm) = 24 ft
On the new blueprint of 1 cm = 3 ft, the length on blueprint becomes
24 ft * (1 cm / 3 ft) = 8 cm
The length of the wall on the new blueprint is 8 cm.
The scores on an exam are normally distributed with a mean of 74 and a standard deviation of 7. What percent of the scores are greater than 81?
A. 50%
B. 13.5%
C. 84%
D. 16%
Answers
81 - 74 = 7
This is exactly the value of the standard deviation. You know that the "empirical rule" tells you 68% of all scores lie within 1 standard deviation of the mean. That tells you 32% of all scores lie beyond 1 standard deviation from the mean.
The normal distribution is symmetrical, so half of those (16%) lie above 1 standard deviation above the mean; the other half (16%) lie below 1 standard deviation below the mean. We're only concerned with the first group—those scores above 1 standard deviation above the mean.
The appropriate choice is
D. 16%
what is the difference? (x+5)/(x+2)-(x+1)/(X^2+2x)
Answers
Answer:
[tex]\text{The difference is }\frac{x^2+4x-1}{x(x+2)}[/tex]
Step-by-step explanation:
Given two expression, we have to find the difference of these two.
[tex]\frac{x+5}{x+2}-\frac{x+1}{x^2+2x}[/tex]
[tex]=\frac{x+5}{x+2}-\frac{x+1}{x(x+2)}[/tex]
[tex]\text{Taking (x+2) common from the denominator }[/tex]
[tex]=\frac{1}{x+2}((x+5)-\frac{x+1}{x}[/tex]
[tex]=\frac{1}{x+2}(\frac{x(x+5)-(x+1)}{x})[/tex]
[tex]=\frac{1}{x+2}(\frac{x^2+5x-x-1}{x}[/tex]
[tex]=\frac{1}{x+2}(\frac{x^2+4x-1}{x})[/tex]
[tex]=\frac{x^2+4x-1}{x(x+2)}[/tex]
which is required difference.
10q-3r=14 write a formula for g (r) in terms of r
Answers
Answer:
3/10r +7/5
Step-by-step explanation:
10q−3r=14
10q=3r-14
10q=3r/10 +14/10
q=3/10r+7/5
To find g(r) in terms of r, the equation 10q-3r=14 is manipulated algebraically to isolate q as g(r)=(14+3r)/10.
Explanation:The student's question involves solving a linear equation for a variable. This is a standard algebraic task often encountered in high school mathematics. The student is given the equation 10q-3r=14 and is asked to write a formula for g(r) in terms of r, implying a need to solve for q as a function of r, which can be named g(r).
To isolate q, we perform algebraic manipulations:
First, add 3r to both sides of the equation to get 10q = 14 + 3r.Next, divide both sides of the equation by 10 to solve for q, which gives us q = (14 + 3r) / 10.Last, we rename q as g(r) which results in the final function: g(r) = (14 + 3r) / 10.This function represents q in terms of r, and g(r) is thereby defined.
A ________ is a numerical quantity computed from the data of a sample and is used in reaching a decision on whether or not to reject the null hypothesis.
a. significance level
b. critical value
c. test statistic
d. parameter
Answers
b. critical value.
Therefore, you have that the text is: "A critical value is a numerical quantity computed from the data of a sample..."
This numeral quantity is used in statitics. Then, if the absolute value is greater that the quantity defined before, the null hypothesis must be rejected.
How to find the answers to nine and ten? Please show your work.
Answers
Comment
The figure consists of 2 figures, a rectangle and a trapezoid. You should break them up and find the area of each separately and add to get the total.
Rectangle.
Area = L * W
L = 40 yd
W = 25 yd.
Area = 40 * 25 = 1000 square yards.
Trapezoid
B1 = 40 yards
B2 = 65 yards
H = 55 - 25 yards
H = 30 yards
Area = (B1 + B2)* H / 2
Area = (40 + 65)*30 / 2 Add the 2 bases together.
Area = ( 105) * 30 / 2 You can divide either the 30 or the 105 by 2. Do the 30
Area = (105) *15
Area = 1575 square yards.
Find the total Area
Total Area = rectangle + trapezoid
Total Area = 1000 + 1575
Total Area = 2575 <<<<< Answer
Ten
Comment
Assume the other side has no windows or doors. Both sides consist of 1 triangle and 1 rectangle.
Problem A
Rectangle
Area = l * w
L = 28 feet
W = 8.5 feet
Area = 28 * 8.5
Area = 238 square feet.
Triangle
Area = 1/2 Base * Height
Base = 28 feet
Height = 12.5 - 8.5
Height = 4
Area = 1/2 * 28 * 4
Area = 56 square feet.
Total Area (1 Side)
Total Area (1 Side) = 56 + 238
Total Area (1 side) = 394
Total Area (Both sides)
Total Area (both sides) = 2 * 294
Total Area (both sides) = 588 square feet.
Problem B
Comment
You have 588 square feet. First figure out the number of bundles and then calculate the cost.
Bundles
Bundles = Total Square Feet (Rounded up) / 100
Bundles = 588 / 100 = 5.88 bundles.
But you cannot buy 0.88 bundles So you have to round up, otherwise you'll have a bit of the building uncovered.
You may not care in reality, but the question does. So your answer is that you have 6 bundles.
Cost
1 bundle costs 75 dollars.
6 bundles cost x
1/6 = 75 / x
x = 6 * 75
x = 450 dollars <<<<< Answer 10B
what if the value of x? show all work
Answers
We have then:
(root (117)) ^ 2 = x ^ 2 + 6 ^ 2
Clearing x we have:
x ^ 2 = (root (117)) ^ 2 - 6 ^ 2
Rewriting:
x = root (117-36)
x = root (81)
x = 9
Answer:
The value of x is given by:
x = 9 cm
The length of the shorter base in an isosceles trapezoid is 4 in, its altitude is 5 in, and the measure of one of its obtuse angles is 135°. Find the area of the trapezoid.
Answers
Ask me if you still don't understand it because I didn't write any explanation.
Answer:
45
Step-by-step explanation:
PLZ HELP ASAP FEATURES OF A CIRCLE FROM ITS EXPANDED EQUATION LAST ONE
Answers
x2 + y2 + 6y - 72 = 0
Rewriting we have:
x2 + y2 + 6y = 72
Complete squares we have:
x2 + y2 + 6y + (6/2) ^ 2 = 72 + (6/2) ^ 2
x2 + y2 + 6y + (3) ^ 2 = 72 + (3) ^ 2
x2 + y2 + 6y + 9 = 72 + 9
x2 + (y + 3) 2 = 81
So, the center is:
(0, -3)
The radio is:
r = 9
Answer:
(0, -3)
r = 9
WILL MARK BRAINLEST * PLEASE HELP AND FAST :)
Answers
The range of a data set is the largest value minus the smallest value; the range for this data set would be 96-54, or 42.
The range of this stem and leaf plot is 42.
Find the value of x. If necessary, found your answer to the nearest tenth. The figure is not drawn to scale
Answers
Consider a box with a square base that has a volume of 64 cubic inches and a height of 4 inches. What is the volume of a similar box whose square base has an area of 4 square inches?
Answers
That being said, the first box had dimensions of 4x4x4 - and this is confirmed by the volume being 64 sq. in. and the height being told to us as 4 in. as well as the square base having to have equal sides.
Because of this, since the question states "similar," all of the dimensions have to be reduced by the same factor. Since the square base was reduced by 1/2, we can assume the height is also reduced by 1/2, thus giving us a height of the new box as 2 in.
So, the volume of the new box is 2x2x2, which equals 8 sq. in.
hey can you please help me posted picture of question
Answers
Thus, both horizontal and vertical translations are involved. Horizontal translation of 3 units to left can be obtained by adding 3 to x in the equation and vertical translation of 1 can be obtained by adding 1 to the entire function.
So,
G(x) = F(x+3) + 1
G(x) = (x+3)² + 1
Thus the correct answer is option C
Find the general form of the complete partial fraction decomposition of the integrand. use it to determine whether or not a term of each type listed below occurs in the complete partial fraction decomposition. select true if it does occur and false if it does not.
Answers
Q # 9 Find the circumference
Answers
Pi=3.14
Radius of the circumference: r=3 m
C=2*3.14*(3 m)
C=18.84 m
Answer: First option 18.84 m
Experts/ace/geniuses helppp asapp
Answers
therefore if you round the 3.1622... it would be closer to 3.2 so point F is actually correct
Evaluate the expression
4^2+6⋅5^2−3^3÷3^2.
Answers
Evaluate exponents:
[tex]=16 + 6 \times 25- 27 \div 9[/tex]
Evaluate multiplication and division:
[tex]= 16 + 150- 3[/tex]
Evaluate addition and subtraction:
[tex]= 163[/tex]
A statistician observes the number of heads that occur when a coin is tossed 1000 times
Answers
Amy had $26 dollars to spend on school supplies. After buying 10 pens, she had $14.30 left. How much did each pen cost including tax?
Answers
Here, we need to find the cost of each pen, including tax. Since, information about tax was not given, so we will not consider this.
Total money Amy had = $ 26.
She is left with $ 14.30. The money she spent will be -
Total money - Money left = Money spent
$ 26 - $ 14.30 = $ 11.70
Total money she spent on 10 pens = $ 11.70
So, money spent on = $ 11.70 ÷ 10 = $ 1.17
So, the cost of each pen will be = $ 1.17
Identify the problem with the following study.
It was found that a third of all people in the United States live in urban centers. This finding is based on a study involving 3 randomly selected individuals.
reported results
small sample
missing data
loaded question
Answers
We know nothing about what was asked. (How could it be much more than "Where do you live?" The last one is wrong.
Is there missing data? We don't know. So the second last one is not the best answer.
The sample is too small. So far that's your best answer.
The results cannot be at fault. How can saying 2/3 of the people answered that they lived in the country.
B <<<<<< second one down <<<<< Answer
The number pi goes on forever with no repeating pattern; therefore, it is rational. A) True or B) False
Answers
False, Because it is an Irrational number.
What is Rational number?A number which can be written in the form of fraction p / q , where q is non zero, are called Rational numbers.
We have to given that;
The number π goes on forever with no repeating pattern.
Therefore, it is rational.
Since, We know that;
Number π cannot be expressed as the ratio of one number to another
Hence, in other words, Number π is an 'irrational' number that goes on forever, never repeating itself.
Hence, Statements in false, Because it is an Irrational number.
Learn more about the rational numbers visit:
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if a certain type of bacteria quadruples every 15 minutes, how many bacteria will be presents after 90 minutes if the initial population was 5 bacteria?
HELP ME FOR 97 POINTS !!!!
Answers
y = A (b) ^ (t / n)
Where,
A: initial amount
b: growth rate
t: time
n: number of time periods
Substituting values we have:
y = 5 * (4) ^ (90/15)
y = 20480
Answer:
will be presents after 90 minutes about:
y = 20480 bacteria
HOW CAN YOU WRITE THE EQUATION OF A LINE THAT IS PARALLEL AND/OR PERPENDICULAR TO ANOTHER LINE USING A POINT ON THAT LINE.?
Answers
y -k = m(x -h)
for a line of slope m through the point (h, k).
You can add k to this equation to put it in a form more like slope-intercept form:
y = m(x -h) +k
Either of these can be used to write the equation of a parallel or perpendicular line through the point (h, k). The slope "m" of a parallel line will match that of the given line.
The slope "m" of a perpendicular line will be the negative reciprocal of the slope of the given line. That is, if you are given a line with slope "s", the slope of the perpendicular line will be m = -1/s.
(-2q^4)(-8q^3b^6)
help I need to simplify this problem
Answers
[tex](-2q^{4})(-8q^{3}b^{6}) = ((-2)(-8))q^{(4+3)}b^{6}\\\\=16q^{7}b^6}[/tex]
What are the relationships among radii, chords, tangents, and inscribed angles?
Answers
The plural of radius is what we call radii. For any line that joins the center or is joining the center to any point in the circumference of a circle is what we call radii.
Note:
If there is an infinite line from the center to circumference then is it called infinite radii.
For any line that joins or is joining two points on the circumference of a circle is known as chord and any line touching the circle is what we call as tangent to the circle.
Lastly, the intersection of bisector angles is known as in-center or inscribed.
Below are attached pictures of figures
PLEASE HELP ME OUT ON THIS CRITICAL HARD QUESTION!!!!!!!! NEEDS THINKING!!!! MARK THE BRAINIEST
Answers
The first thing you have to do is make sure that the sales reps face the same conditions. Geography is going to matter. Start with the simple stuff. Does it matter whether or not the sales representatives were in the city of the country? If in the country, do the people have money enough to buy what is being sold? If in the city, what is the employment situation like? Make sure that you are comparing Apples and Apples.
What about crops? Do they matter? What about livestock does it matter? What do these rural areas need? Is he selling what they need? It's going to be harder to sell something in Detroit or Flint than it is San Francisco?
Did people experience a devastating winter? Especially in the Northeast? If they did, their heating bills are going through the roof. Literally. More money on heating less on whatever he's selling.
In short he has to consider conditions. Perhaps training will make no difference. There's other things that people have to live through. Maybe this was just a bad year. (It certainly was where I live. We got nothing but snow into mid April and East winds which are strong, cold, miserable and very nasty.)
Credit scores. I'd be well aware of any credit stats that I can obtain. What are people doing with their credit cards. You may be able to sell the stuff on credit, but will you ever receive payment that you can rely on or are these people one step away from bankruptcy? Is it different in the rural areas than in the cities? I can tell you I would hate to have it known that I disregard my credit cards in the town I live in (700 people). It would be cash only for everything.
Single or married? What's the demographics of the areas he's trying to sell in. We're retired. We don't take well to door to door sales people. Retired people have very little money to throw away on things we don't need. People on 3000 a month live very differently from those on 10000 a month.
Finally what's the competition like? Sears going under is a huge warning. Where do people get the products you are selling? This is especially important in rural areas. We have made over 170 mail purchases (we won't do that any more -- postage rates are just prohibitive).
If he has a sales force of 1000 people in 2 regions, he should think about moving some of them to other regions. Don't use this point.
Many of the things I've pointed out require a study before the the training is administered. You have to separate out what mitigates the efforts of the sales force and what they have little or no control over.
a soccer ball has the same diameter as a lenght of a cube shaped box. if the diameter of the soccer ball is 12 inches what volume inside that is not filled by a soccer ball
Answers
volume of ball is (4/3) x pi x radius cubed =288 pi
then answer is 1728 - 288 pi
Please rate me don't just say thanks
The volume of box which is not used is (1728 - 288π) inch³.
What is Volume?Volume is a three-dimensional quantity used to calculate a solid shape's capacity. That means that the volume of a closed form determines how much three-dimensional space it can fill.
If the diameter of the soccer ball is 12 inches.
So, Volume of box
= length x width x height
= 12 x 12 x 12
= 1728 inch³
and, Volume of ball
= 4/3 πr³
= 4/3π (6)³
= 864/3 π
= 288 π inch³
So, the volume of box which is not used
= 1728 - 288π
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Mission Control sends a signal to a Mars robot to travel to a mysterious rock 52.8 meters away. A return signal 59.0 minutes later tells scientists that the robot is at the rock. It took the signal 9.5 minutes to get from Earth to Mars, and the same time to get back. What was the robot’s average speed in meters per minute?
Answers
59 min = 2*(9.5 min) +travel time
59 min -2*(9.5 min) = travel time = 40 min
The speed is distance / travel time
speed = (52.8 m)/(40 min) = 1.32 m/min
The robot's average speed was 1.32 meters per minute.
There are five green marbles numbered 1-5 and there are 4 yellow marbles numbered 1-4. what is the probability of picking a green or odd numbered marble
Answers
5+4=9
P(odd/green)=3/9 = 1/3 = .33 or 33% approximately