In the figure, line TU is tangent to the circle at point U. Use the figure to answer both of the questions. Show all of your work.
(a) Describe the relationship among the lengths of the segments formed by the secant, RT , and the tangent segment, TU. You may use words and/or an equation to describe.
(b) Suppose RT= 9 in. and ST = 4 in. Is it possible to find the length of TU ? If so, show how to find the length. If not, explain why not.
Answers
RT×ST = TU²
b) Using the above relationship, fill in the given values and solve for TU.
(9 in)×(4 in) = TU²
TU = √(36 in²) = 6 in
Answer:
(a) The relation is RT × ST = TU²
(b) TU = 6
Step-by-step explanation:
(a) There is a secant law for circles that says the following: "if two secants are drawn to a circle from one exterior point, then the product of the external segment and the total length of each secant are equal". Applying this for the mentioned question, we have that RT × ST = TU x TU = TU² (considering that for TU case, the tangent is also a secant).
Then RT × ST = TU²
(b) Let's apply the equation in (a). RT × ST = TU² means 9 × 4 = TU²
Solving that equation, we have TU = √36 = 6
Thus TU = 6
Related Questions
Please someone HELP QUICK
ILL GIVE BRAINLIEST TO CORRECT ANSWER
HURRYYYYYY
Answers
1. f(8) = 68,594
2. f(11) = 91,299
3. f(2) = 38,720
4. f(17) = 161,743
Stephanie is 20 years old and has a base annual premium of $930 and a rating factor of $1.30. What is her total premium?
A) $1,209
B) $100.75
C) $604.50
D) $1,032.65
Answers
Hope I help
Answer:
Her total premium would be $1,209.00
Other answer is incorrect.
The management of the unico department store has decided to enclose an 833 ft2 area outside the building for displaying potted plants and flowers. one side will be formed by the external wall of the store, two sides will be constructed of pine boards, and the fourth side will be made of galvanized steel fencing. if the pine board fencing costs $6/running foot and the steel fencing costs $2/running foot, determine the dimensions of the enclosure that can be erected at minimum cost. (round your answers to one decimal place.)
Answers
To maximize area and minimize perimeter, you want a figure that is as close to equilateral as you can get. Therefore we take the square root of our area:
√833 = 28.9.
Dividing 833/28.9 we get 28.8.
We want to use the shorter side, 28.8, for the pine boards, as they cost more. 28.8*2*6 = 345.60.
The cost of the steel side is given by 28.9*2 = 57.80.
Together it costs 345.60+57.80 = 403.40.
A lawn mower uses 0.7 gallons of gas every 3 hours. the gas tank holds 2 gallons. how long can the mower run on a full tank?
Answers
[Divide by 0.7 through]
1 gallon = 4.286 hours
[Multiply by 2 through]
2 gallon = 4.286 x 2
2 gallon = 8.57 hours
The lawn mower can run for approximately 8 hours and 34 minutes on a full tank of gas.
Explanation:
To find out how long the lawn mower can run on a full tank, we can divide the total amount of gas in the tank by the amount of gas used per hour. The lawn mower uses 0.7 gallons of gas every 3 hours. So, it uses 0.7/3 = 0.2333 gallons of gas per hour. The gas tank holds 2 gallons, so the lawn mower can run for 2/0.2333 = 8.57 hours, which is approximately 8 hours and 34 minutes.
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19. How many 2-inch segments are there in 12 ft.? A. 24 B. 72 C. 10 D. 6
Answers
There are 24 2-inch segments in 12 ft.
In order to convert from radians to degrees multiply the radians by...
Answers
The polygons below are similar. Find the value of y.
12
16
Guess: 16
Answers
Answer:
4.5
Step-by-step explanation:
In similar polygons, the ratios of corresponding sides is equal.
The only two corresponding sides we have measurements for are BC, with a measure of 8, and FG, with a measure of 6. This makes their ratio 8/6.
The other half of the proportion will be comparing AB, with a measure of 6, to EF, with a measure of y:
8/6= 6/y
Cross multiply:
8(y) = 6(6)
8y = 36
Divide both sides by 8:
8y/8 = 36/8
y = 4.5
The value of y will be 4.5.
What is an expression?
Expression in math is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Given that;
The polygons are similar.
Now,
Since, The polygons are similar.
Hence, The proportional of corresponding sides are equal.
So, We can formulate;
⇒ 6 / y = 8 / 6
⇒ 6×6 / 8 = y
⇒ y = 36 / 8
⇒ y = 4.5
Thus, The value of y will be 4.5.
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Jon’s car averages 9 kilometers per liter of gas. How many kiloliters can Jon drive with 22 liters of gas in his car?
Answers
Final answer:
Jon can drive 198 kilometers with 22 liters of gas in his car since the car averages 9 kilometers per liter.
Explanation:
The student's question asks how many kiloliters Jon can drive with 22 liters of gas in his car, given that the car averages 9 kilometers per liter of gas. To solve this problem, we will convert liters to kiloliters and then calculate the total distance that Jon can drive.
Firstly, we must recognize that 1 kiloliter (kL) is equal to 1,000 liters (L). Therefore, to convert 22 liters to kiloliters, we simply divide 22 by 1,000, which gives us 0.022 kL.
Now, since Jon's car goes 9 kilometers per liter, to find out how far he can go with 22 liters, we multiply 9 kilometers/liter by 22 liters:
9 km/L × 22 L = 198 km
To express this distance in kiloliters, we once again need to note that 1 kL is the same as 1,000 L. Since the car's consumption is measured per liter, we don't actually need to convert kilometers to kiloliters - the initial conversion of liters to kiloliters was not required to answer this particular problem.
Therefore, Jon can drive a total of 198 kilometers with his 22 liters of gas.
Jon's car with fuel efficiency of 9 km/l can drive 198 kilometers with 22 liters of gas. The distance in volume terms is 0.022 kiloliters, illustrating that 22 liters of gasoline would be used on such a trip.
Explanation:The student's question is how many kiloliters Jon can drive with 22 liters of gas if his car averages 9 kilometers per liter of gas. To answer this question, we need to perform a simple multiplication. Given that Jon's car has a fuel efficiency of 9 kilometers per liter, we multiply this rate by the amount of fuel he has, which is 22 liters, to determine the distance he can drive:
9 kilometers/liter × 22 liters = 198 kilometersTo convert kilometers to kiloliters (assuming the question intends to ask for the distance in kilometers rather than 'kiloliters'), we note that kiloliters is not a unit of distance, but rather a volume. Therefore, it is likely that the question contains a typo and should ask how many kilometers can Jon drive. To find out how many kiloliters that distance amounts to, we remember that 1 kiloliter equals 1,000 liters, so:
198 kilometers × (1 liter/9 kilometers) = 22 liters22 liters / 1,000 = 0.022 kilolitersTherefore, Jon can drive 198 kilometers with 22 liters of gas, which equals 0.022 kiloliters of gasoline consumed.
In the year 1997 d takahashi and y kanada calculated pi to 51,539,600,000 decimal places. what type of computer did they use? where did they do the calculations
Answers
They used a computer called the HITACHI SR2201 which has 1024 processors. As an example most desktops in use now (by individuals such as you and I -- not by computer scientists doing research) have 1-2 processors with 2 cores each.
Help me please I’ll mark brainliest
Answers
After replacement, we now have the equation shown in A.
Hope this helps!
Movements to the left and to the right in graphs change the x-values, while movements up and down in graphs change the y-values. Further, when shifting left, you'll add to x, and when shifting right, you'll subtract from x. When shifting up, you'll add to y, and when shifting down, you'll subtract from y. (Upward and downward movements are more intuitive than movements to the left or movements to the right.)
g(x) is f(x) shifted to the left 3 units, so we'll add 3 to x in the function:
f(x) = x² + 5x - 1
g(x) = (x + 3)² + 5(x + 3) - 1
The answer is A.
What is the quotient in simplest form? State any restrictions on the variable.
(z^2 - 4)/(z - 3) divided by (z+2)/(z^2+z -12),
Answers
The first step to solve this problem is to completely factor the expressions first.
(z^2 - 4)/(z - 3) / (z+2)/(z^2+z -12)(z + 2)(z – 2)/(z – 3) / (z + 2)/(z +4)(z – 3)
When dividing two fractions, you have to reciprocate the denominator and do the multiplication:
(z + 2)(z – 2)/(z – 3) / (z +4)(z – 3)/(z + 2)
The expressions (z + 2) and (z – 3) will be cancelled. So the expression would become: (z – 2)(z + 4) = z^2 + 2z - 8
Final Answer:
The quotient in its simplest form is [tex]\(z^2 + 2z - 8\)[/tex].
The restrictions on the variable are [tex]\(z \neq -4\)[/tex] and [tex]\(z \neq 3\)[/tex].
Explanation:
To find the quotient in simplest form when dividing two rational expressions, you need to multiply the first expression by the reciprocal of the second. The given expressions are:
Expression 1: [tex]\(\frac{z^2 - 4}{z - 3}\)[/tex]
Expression 2: [tex]\(\frac{z + 2}{z^2 + z - 12}\)[/tex]
Firstly, let's take the reciprocal of Expression 2, which is:
Reciprocal of Expression 2: [tex]\(\frac{z^2 + z - 12}{z + 2}\)[/tex]
Now, to find the quotient, multiply Expression 1 by the reciprocal of Expression 2:
Quotient: [tex]\(\frac{z^2 - 4}{z - 3} \cdot \frac{z^2 + z - 12}{z + 2}\)[/tex]
Before multiplying, it's helpful to factor where possible to simplify. Let's factor both the numerator and the denominator where applicable:
For the expression [tex]\(z^2 - 4\)[/tex] (the difference of squares), it factors into:
[tex]\(z^2 - 4 = (z - 2)(z + 2)\)[/tex]
For the quadratic expression [tex]\(z^2 + z - 12\)[/tex], we look for two numbers that multiply to -12 and add to +1. These numbers are +4 and -3.
So this expression factors into:
[tex]\(z^2 + z - 12 = (z - 3)(z + 4)\)[/tex]
Now substitute in these factorizations:
[tex]\(\frac{(z - 2)(z + 2)}{z - 3} \cdot \frac{(z - 3)(z + 4)}{z + 2}\)[/tex]
Next, we cancel out the common terms in the numerator and the denominator:
The z + 2 term in the numerator of the first fraction cancels with the z + 2 term in the denominator of the second fraction.
Similarly, the z - 3 term in the denominator of the first fraction cancels with the z - 3 term in the numerator of the second fraction.
What remains is:
Quotient: (z - 2)(z + 4)
Finally, you can expand this to get the simplest form of the quotient:
[tex]\(z^2 + 4z - 2z - 8\)[/tex]
Combine like terms:
[tex]\(z^2 + 2z - 8\)[/tex]
So the simplest form of the quotient is:
[tex]\(\frac{z^2 + 2z - 8}{1}\)[/tex]
or simply:
[tex]\(z^2 + 2z - 8\)[/tex]
Now let's consider the restrictions on the variable z. Before we canceled terms, the original expression had denominators of z - 3 and [tex]\(z^2 + z - 12\)[/tex]. Division by zero is undefined, which means we have restrictions where these denominators equal zero:
For z - 3 = 0, the restriction is [tex]\(z \neq 3\)[/tex].
For [tex]\(z^2 + z - 12 = 0\)[/tex], we had already factored this into (z - 3)(z + 4). From the factored form, we can find the restrictions by setting each factor equal to zero:
z - 3 = 0 gives z = 3 (which we already noted) and z + 4 = 0 gives z = -4.
Therefore, the restrictions on the variable z are [tex]\(z \neq -4\)[/tex] and [tex]\(z \neq 3\)[/tex].
To summarize:
The quotient in its simplest form is [tex]\(z^2 + 2z - 8\)[/tex].
The restrictions on the variable are [tex]\(z \neq -4\)[/tex] and [tex]\(z \neq 3\)[/tex].
What is 65% written as a fraction in its simplest form?
Answers
(divide by 5 on both sides)
Hope this helped!
A grocer wants to make a 10-pound mixture of peanuts and cashews that he can sell for $4.75 per pound. If peanuts cost $4.00 per pound and cashews cost $6.50 per pound, how many pounds of each should he use? Let p = pounds of peanuts and let c = pounds of cashews. Write a system of equations that could be used to solve the problem.
Answers
p - pounds of peanuts
c - pounds of cashews
therefore the total pounds should be equal to 10 pounds
p + c = 10 -----> 1)
the cost for ;
peanuts - 4.00 per pound * p pounds = 4p
cashews - 6.50 per pound * c pounds = 6.5c
the price of 10 pounds mixture = 4.75 per pound * 10 pounds = 47.5
4p+6.5c = 47.5 ---> 2)
to solve for p and c lets use simultaneous equations
p + c = 10 -----> 1)
4p+6.5c = 47.5 ---> 2)
multiply 1st equation by 4
4p + 4c = 40 ---> 3)
subtract 3rd equation from the 2nd
2.5c = 7.5
c = 3
substituting c= 3 in 1st equation
p+c = 10
p+3 = 10
p = 7
therefore 3 pounds of cashews and 7 pounds of peanuts are needed to make the mixture
The U.S. government borrows money by _____.
A. asking banks or foreign investors
B. printing money
C. issuing stocks
D. issuing Treasury bonds and other government-backed securities
Answers
-Hope this helps :)
Answer:
D. issuing Treasury bonds and other government-backed securities
Step-by-step explanation:
Governments create debt by issuing government bonds and bills. Less creditworthy countries sometimes borrow directly from a supranational organization (e.g. the World Bank) or international financial institutions.
Treasury bonds are how the US - and all governments for that matter - borrow hard cash: they issue government securities, which other countries and institutions buy. So, the US national debt is owned mostly in the US - but the $5.4tn foreign-owned debt is owned predominantly by Asian economies.
What is the value of X?
Answers
Answer D x=40
since x+(4x-20)=180
==>5x=200
==>x=40
What is the simplest form of ^4 sqrt 81x^8y^5
Answers
ANSWER
[tex]3 {x}^{2} y \sqrt[4]{y} [/tex]
EXPLANATION
We want to simplify:
[tex] \sqrt[4]{81 {x}^{8} {y}^{5} } [/tex]
We can split the radical sign to obtain:
[tex] \sqrt[4]{81} \times \sqrt[4]{ {x}^{8} } \times \sqrt[4]{ {y}^{5} } [/tex]
Or
[tex] \sqrt[4]{81} \times \sqrt[4]{ {x}^{8} } \times \sqrt[4]{ {y}^{4} \times y} [/tex]
[tex] \sqrt[4]{81} \times \sqrt[4]{ {x}^{8} } \times \sqrt[4]{ {y}^{4}} \times \sqrt[4]{y} [/tex]
[tex]\sqrt[4]{ {3}^{4} } \times \sqrt[4]{ {x}^{8} } \times \sqrt[4]{ {y}^{4}} \times \sqrt[4]{y} [/tex]
Recall that:
[tex] \sqrt[n]{ {a}^{m} } = {a}^{ \frac{m}{n} } [/tex]
[tex]{3}^{4 \times \frac{1}{4} } \times {x}^{8 \times \frac{1}{4} } \times {y}^{4 \times \frac{1}{4} }\times \sqrt[4]{y} [/tex]
[tex]3 {x}^{2} y \sqrt[4]{y} [/tex]
Answer:
B!!!!!!!!!
Step-by-step explanation:
Select the locations on the number line to plot the points 9/2 and −7/2 .
Answers
Now take each number and convert the improper fraction into a mixed number. 9/2 = 4 1/2 and -7/2 = -3 1/2.
4 1/2 would plotted on the line exactly in between the 4 and 5.
-3 1/2 would be plotted on the line exactly halfway between -3 and -4.
You will draw a dot to show each of these positions on a number line.
The locations of the given numbers on the number line are needed.
The locations have been shown in the figure attached.
The numbers are [tex]\dfrac{9}{2}[/tex] and [tex]-\dfrac{7}{2}[/tex]
The numbers can be written as
[tex]\dfrac{9}{2}=4.5[/tex]
[tex]-\dfrac{7}{2}=-3.5[/tex]
In the given number line it can be seen that the longer vertical lines are whole numbers which are positive and negative.
The smaller vertical lines are an increment of [tex]0.5[/tex].
As the extreme ends are [tex]+5[/tex] and [tex]-5[/tex] the center longer vertical line will be [tex]0[/tex].
So, [tex]4.5[/tex] will be the smaller vertical line to the left of [tex]+5[/tex].
[tex]-3.5[/tex] will be the smaller vertical line to the right of [tex]-4[/tex].
The locations have been shown in the figure attached.
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What is the specific name for a regular quadrilateral?
Answers
The specific name for a regular quadrilateral is a polygon
~cutie
The sum of two numbers is 50 and the difference is 22 . what are the numbers?
Answers
substitute the first x into the second equation (22-y)-y=10 22-2y=10 22-10=2y 12=2y y=6
now plug in the known y into the first equation x+6=22 x=22-6 x=16
now, let's check this sum is 22=16+6 checks difference is 10=16-6 checks
16 is the larger number
6 is the smaller number.
hope this helps.
What are the coordinates of the point? A coordinate grid with a dot placed in the second quadrant. The dot is to the left of positive 4 on the y axis and above negative 2 on the x axis
Answers
The y-coordinate is essentially given, and is y=4.
Imagine drawing a vertical line thru x=-2. This line will intersect y=4 at (-2,4).
The coordinates of the point are (-2, -4).
Mike has $25.00 to rent paddleboards for himself and a friend for 3 hours. Each paddleboard rental costs $3.75 per hour
Answers
The number of adults who attend a county fair (measured in hundreds of people) is represented by the function a(d)=−0.3d2+4d+9 , where d is the number of days since the fair opened. The number of children who attend the same county fair (measured in hundreds of people) is represented by the function c(d)=−0.2d2+5d+11 , where d is the number of days since the fair opened. What function, f(d) , can be used to determine how many more children than adults attend the fair on any day?
Answers
Given is the function for number of adults who visit fair at day 'd' after its opening, a(d) = −0.3d² + 4d + 9.
Given is the function for number of children who visit fair at day 'd' after its opening, c(d) = −0.2d² + 5d + 11.
Any function f(d) to find excess of children more than adults can be written as follows :-
f(d) = c(d) - a(d).
⇒ f(d) = (−0.2d² + 5d + 11) - (−0.3d² + 4d + 9)
⇒ f(d) = -0.2d² + 0.3d² + 5d - 4d + 11 - 9
⇒ f(d) = 0.1d² + d + 2
You are knitting a blanket. You want the area of the planet to be 24ft^2. You want the length of the blanket to be 2ft longer than it's worth. What should the dimensions of the blanket be?
Answers
length being longer than the width means that blanket is a rectangle
width of the blanket = x
length of blanket = x +2
area = length * width
area = x * (x+2)
= x² + 2x
since area = 24
x² + 2x = 24
x² + 2x - 24 = 0
we have a quadratic equation and we need to now solve for x
x² + 6x - 4x - 24 = 0
x (x + 6) - 4(x + 6) = 0
(x-4) (x+6) = 0
x-4 = 0 or x + 6 = 0
x = 4 or x = -6
x could be either 4 or -6. since dimensions cannot have negative values,
x ≠ -6
therefore x = 4
width = 4 ft
length = 6 ft
Rewrite the slope intercept equation of the line y=1/3x-2 in standard form
Answers
3y = x - 6
x - 3y = 6 ...this is standard form
The standard form of the given equation is x - 3y = 6.
What is equation?An equation is a mathematical statement that shows that two mathematical expressions are equal.
Given is an equation, y = 1/3 x - 2
The given equation is in slope intercept form, i.e. y = mx+ c, where m is slope and c is constant,
Here, slope (m) = 1/3 and constant (c) = -2
Converting the equation in standard form,
y = 1/3 x - 2
3y = x - 6
x - 3y = 6
Hence, the standard form of the equation is x - 3y = 6
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What is the value of h in the figure below? In this diagram, ΔNMP ~ ΔONP.
Answers
The value of h in the triangle is 6 units.
What is similar triangle?Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles. Similar triangles are the triangles that are the same in shape, but may not be equal in size.
For the given situation,
The triangles ΔNMP ~ ΔONP.
If two triangles are similar then the ratio of their sides are same.
⇒ [tex]\frac{NP}{MP} =\frac{OP}{NP}[/tex]
⇒ [tex]\frac{h}{12} =\frac{3}{h}[/tex]
⇒ [tex](h)(h)=(3)(12)[/tex]
⇒ [tex]h^{2} =36[/tex]
⇒ [tex]h=\sqrt{36}[/tex]
⇒ [tex]h=6[/tex]
Hence we can conclude that the value of h in the triangle is 6 units.
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What is the solution to the system of equations?
{x + 3y + 2z = 8
{3x + y + 3z = -10
{-2x -2y - z = 10
A: (-10, -2, 6)
B: (10, 2, 6)
C: (-10, 2, 6)
D: (-10, 2, -6)
Answers
One of the sides of a parallelogram has the length of 5 in. can the lengths of the diagonals be: c 6 in and 7 in?
Answers
In a parallelogram, only the opposite sides of the parallelogram are congruent. All the sides don't have to be congruent. Therefore we can have different measurement for the diagonals.
In a square, all of the diagonals would have to be the same.
The dimensions of 5 inches for a side and diagonals of 6 inches and 7 inches for a parallelogram violate the Pythagorean theorem and therefore are not possible for any right-angled triangle, suggesting an error if considered for a parallelogram.
Explanation:The question is whether parallelogram sides can correspond to the dimensions given, with one side being 5 inches and the possible diagonals being 6 inches and 7 inches respectively. By applying the Pythagorean theorem, we can deduce that a parallelogram with such dimensions may not be possible due to the constraints of the theorem.
Given the Pythagorean theorem, expressed as a² + b² = c², the sum of the squares of the sides of a right triangle is equal to the square of the hypotenuse. If we consider the diagonals and the side as parts of a right triangle, then 6² + 5² does not equal 7² (36 + 25 = 61, which is not equal to 49).
Therefore, it is not possible for a parallelogram to have side lengths and diagonal lengths as described in the question because the mathematically described conditions violate the rules of the Pythagorean theorem.
my final balance afrer 48 months was $896.00 if i originally put $800.00 into the bank what was the interset rate
Answers
The formula in computing the maturity value of a savings with a simple interest rate is:
MV = P (1 + rt)
Where: MV = maturity value after certain years
P = principal amount
r = interest rate
t = time in years
If you would manipulate the formula to solve for r in terms of the other variables, you will get this formula:
1 + rt = MV/P
rt = MV/P – 1
r = (MV/P – 1)/t
Substituting the given amounts to the formula:
r = ($896/$800 – 1)/4
r = (1.12 – 1)/4
r = 0.12/4
r = .03 or 3%
Note: The 48 months is equivalent to 4 years (48/12 = 4)
what is the image of g for a 240° counterclockwise rotation about the center of the regular hexagon
A. A
B. N
C. H
D. X
Answers
This would move G to the point H
C. H
What is the measure of angle A?
Answers
180 - 43 = 137
So angle A is 137 degrees