Answer:
[tex]\text{C.} \ \ \ {\left(\textit{AB}\right)}^{2} \ = \ \left(\textit{AC}\right)\left(\textit{AD}\right)[/tex]
Step-by-step explanation:
This problem uses the concept of the tangent-secant theorem which describes the relationship of the segments a secant line and a tangent line with the associated circle. This theorem is found as Proposition 36 in Book 3 of Euclid's Elements.
As shown in the figure attached below, segment AB (in blue) forms a tangent with the circle BCD and segment AD (in orange) is the secant where it intersects the circle at point C.
Furthermore, let two segments (in green) be drawn one from point C and point D.
To show that [tex]\triangle ABC[/tex] is similar to [tex]\triangle ADB[/tex], notice that both triangles share a common angle [tex]\angle BAC[/tex]. Additionally, by the alternate segment theorem, [tex]\angle ABC[/tex] is equal to [tex]\angle ADB[/tex]. Therefore, [tex]\angle ACB[/tex] is also equal to [tex]\angle ABD[/tex].
Hence, [tex]\triangle ABC[/tex] is indeed similar to [tex]\triangle ADB[/tex]. This implies the ratio of the sides of both triangles is the same. Particularly,
[tex]\displaystyle{\frac{AB}{AD} \ \ = \ \ \frac{AC}{AB}}[/tex].
Then, performing cross multiplication yields
[tex]{\left(AB\right)}^{2} \ \ = \ \ \left(AC\right)\left(AD\right)[/tex].
Therefore, the product of the lengths of the secant segment and its external segment is equal to the square of the length of the tangent segment.
If the sum of a number and eight is doubled the result is five less than the number find the number
Answer: -21
Step-by-step explanation:
Let the number be x.
Then, this means 2(x+8)+5=x.
2x+16+5=x [distributive property]2x+21=x [combine like terms]x+21=0 [subtract x from both sides]x= - 21 [subtract 21 from both sides]1. Draw an appropriate Venn diagram to depict each of the following sets. U = The set of integers. A = The set of even integers. B = The set of odd integers. C = The set of multiples of 3. D= The set of prime numbers. 1. Draw an appropriate Venn diagram to depict each of the following sets . U = The set of integers . A = The set of even integers . B = The set of odd integers . C = The set of multiples of 3 . D= The set of prime numbers .
The attached diagram represents the Venn diagram of the sets
How to draw the Venn diagram?The sets are given as:
The universal set, U = The set of integers. A = The set of even integers. B = The set of odd integers. C = The set of multiples of 3. D= The set of prime numbersFrom the above representation, we have the following highlights:
Set A and set B will not intersect, because no number can be even and oddSet C and set D will intersect set A because they have common elements 6 and 2, respectivelySet C and set D will intersect set B because they have common elements 3 and 3, respectivelyUsing the above highlights, we can now draw the Venn diagram
See attachment for the Venn diagram
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For each of the following research questions, determine whether an observational study, an
experiment, or neither should be used to answer the question. Note - each term on the right may be
used more than once or not at all.
The situations described can be classified as experiment, and observational study.
What is an experiment?An experiment is a tool to test a hypothesis about the occurrence of a particular phenomenon. According to the above, it can be stated that student-centered instruction can be classified as an experiment because this method of education is used and it is verified whether it is effective or not.
What is an observational study?An observational study is a methodology to identify the occurrence of an event in a particular situation. From the foregoing, it can be inferred that the participation of women in the 2016 election is the product of an observational study because only the number of voters should be counted and the number of women who participated should be identified.
Note: This question is incomplete because there is some information missing. Here is the information missing.
OPTIONS:
Does learner-centered instruction increase students' success rates in maths?
What proportion of registered women voters voted in the 2016 U.S. presidential election?
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A rectangular floor of area 21.6 m2 is going to be tiled. Each tile is rectangular, and has an area of 288 cm2. An exact number of tiles can be put into the space. How many tiles will be needed?
Answer:
Area of Floor = 21.6.m²
Area of tile = 288 cm² = 0.0288 m²
No. of tiles = Area of floor/ area of tile
= 21.6/0.0288
= 750
750 tiles can be put into the spaceIn the year 2015, New Jersey had 1,218 people per square mile. The land area of New Jersey is 7,354 square miles. What was the approximate population of New Jersey in 2015? In the year 2015 , New Jersey had 1,218 people per square mile . The land area of New Jersey is 7,354 square miles . What was the approximate population of New Jersey in 2015 ?
Answer:
8,957,172 people
Explanation:
Population = 1,218 people per square mile
Land area of New Jersey = 7,354 square miles
Total population:
people living in per square mile × total land area
1,218 × 7,354
8,957,172
Which of the following choices name the sides of DGF?
Answer:
Second choice GD and GF with the LINE symbol over each
Step-by-step explanation:
Angle named DGF means that G ( in the middle) is the vertex so GD would be a line starting at G going out toward D and G F would be a line starting at G going out to F
Liliana decides to crop a square photo 2 inches on each side to fit it into a frame. The area of the original photo was 121 square inches. In the equation (x + 2)2 = 121, x represents the side measure of the cropped photo.
What are the dimensions of the cropped photo?
8 inches by 8 inches
9 inches by 9 inches
12 inches by 12 inches
13 inches by 13 inches
Answer:
x = 9 or B
Step-by-step explanation:
Formula
(x + 2)^2 = 121
Comment
The easiest way to do this is to take the square root immediately, which is usually possible.
Solution
√(x + 2)^2 = √121 Take the square root
x + 2 = 11 Subtract 2 from both sides
x + 2 - 2 = 11 - 2
x = 9
Answer: B) 9 inches by 9 inches
Step-by-step explanation:
Edg 2022
If it is now 1:15, what time will it be in 1 1/2 hours' time?
Answer:
2:45
Step-by-step explanation:
1 1/2 hour is 1 hour and 30 minutes.
If we add 30 minutes to 1:15, we get 1:45
if we add 1 hour to 1:45, we get 2:45, which is our answer.
Make a tree diagram to show all possible arrangements of the letters in the word MAT. If each of the letters is ordered randomly, what is the fractional probability of M being the last letter?
If each of the letters is ordered randomly, the fractional probability of M being the last letter is 1/6.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
We have to make a tree diagram to show all possible arrangements of the letters in the word MAT.
M ⇒ A ⇒ T
⇒ T ⇒ A
A ⇒ M ⇒ T
⇒ T ⇒ A
T ⇒ M ⇒ A
⇒ A ⇒ M
If each of the letters is ordered randomly, the fractional probability of M being the last letter is 1/6.
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What are the zeros of the quadratic function f(x) equals 6X squared +12 X -7
The zeroes of the function will be [tex]\rm -1 \pm \dfrac{\sqrt{78}}{6}}[/tex]
What is a Quadratic Function ?A quadratic function is given by ax² +bx+c = f(x)
The given quadratic function is
f(x) = 6x² +12x - 7
The zeroes of the function will be given by
f(0) = 0
6x² +12x - 7 = 0
The zeroes are given by
[tex]\rm \dfrac {-b \pm \sqrt{b^2 -4ac}}{2a}[/tex]
here
a = 6
b = 12
c = -7
Therefore the zeroes of the function will be
[tex]\rm \dfrac {-12 \pm \sqrt{12^2 -4*6*(-7)}}{2 *6}[/tex]
[tex]\rm \dfrac {-12 \pm \sqrt{312}}{12}[/tex]
[tex]\rm -1 \pm \dfrac{\sqrt{78}}{6}}[/tex]
Therefore these are the two zeroes of the function.
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Write the equation of the line with a slope of 3/4 and a y'-intercept of -7 in Slope-Intercept and Poin Slope Form.
Write an expression to represent:
The sum of 5 and the quotient of a
number x and 2
O 2x + 5
O 2/x - 5
O x/2 + 5
Answer:
Step-by-step explanation:
2/x-5
What is the explicit formula for this sequence?
60, 30, 15, 7.5, ...
A. an = 60.
(9)
OB. an= = (1.60
OC. an = 60.
• (+)-
OD. an=3.2(n-1)
60(n-1)
(n-1)
i beilive this is unknown
a woman at a point a on the shore of a circular lake with radius 1.2 mi wants to arrive at the point B diametrically opposite A on the other side of the lake in the shortest possible time (see the figure). she can walk at the rate of 5 mi/h from C to B and row a boat at 3.5 mi/h from A to C . setting T (x) function to the time by interlaced AC, x is interlacted AC. how to move for shortest.
The angle θ to the diameter that she should row is; θ = 56.44°
How to find the angle of an arc?It should be noted that;
a = 90° - θ. Thus;
b = 2θ
For any circle, the angle subtended (in radians) is equal to the arc length (d_w ) divided by the radius (1.2). Thus; d_w = 4θ .
The time required to walk this distance is given by;
t_w = 4θ/5 = 0.8θ
The distance rowed is given by: cos θ = d_r/2.4
d_r = 2.4cos θ while the time needed for it is;
t_r = 2.4cos θ/3.5
t_r = 0.6857θ
Thus, total time is;
T(θ) = t_r + t_w
T(θ) = 0.6857θ + 0.8θ
T(θ) = 1.4857θ
Now we need the critical numbers:
T'(θ) = 1 - 1.2 sin θ
At T'(θ) = 0, we have;
1 - 1.2 sin θ = 0
1/1.2 = sin θ
θ = sin⁻¹(1/1.2)
θ = 56.44°
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Evaluate 21 + (-3c) when c=-2
27
Solution:
Substitute c with -221 + ( -3 ) ( -2 )
Simplify21 + 6
27
Therefore, The answer is 27.
A greedy hamster hoarded 2 piles of sunflower seeds. Yesterday the ratio of the seeds in these piles 3:4; but today the greedy hamster placed another 2 pounds of seeds in the bigger pile. He also ate 1/4 pound from the smaller pile and now the quantities of seeds in those piles is in the ratio of 5:16. What was the weight of each pile yesterday
The weight of each pile yesterday will be 6 and 8 pounds.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
It is Given that Yesterday the ratio of seeds in these piles was 3:4.
Let 3x and 4x represent the seeds.
If the 2 pounds of seeds are added in the bigger pile, then
4x + 2
He also ate 1/4 pound from the smaller pile,
3x - 1/4
The quantities of seeds in those piles is in the ratio of 5:16.
So, 4x + 2 = 5x
3x - 1/4 = 16x
Solve;
So, 4x + 2 = 5x
2 = 5x - 4x
x = 2
The weight of each pie will be
3x = 6 pound
4x = 8 pound
Hence, The weight of each pile yesterday would be 6 and 8 pounds.
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There is a mound of g pounds of gravel in a quarry. Throughout the day, 200 pounds of gravel is added to the mound. Two orders of 700 pounds are sold and the gravel is removed from the mound. At the end of the day, the mound has 1,200 pounds of gravel.
Answer:
[tex]\fbox {2,400 pounds}[/tex]
Step-by-step explanation:
Information we have :
200 pounds is added2 orders of 700 pounds is removed1,200 pounds remainWhat we need to find :
Original amountSolving :
g + 200 - 2(700) = 1200g + 200 = 1200 + 1400g + 200 = 2600g = 2,400 pounds of gravelWhich expression represents a difference of squares?
A. t² +100
B. 4x² - 16x
C. 25k-64
D. 81-49y²
Answer:
D represents a difference of squares.
Answer: Choice [D] - [tex]\boldsymbol{81-49y^2}[/tex]
Step-by-step explanation:
Hii, do you need to know which expression represents a difference of squares? No problem! (:
The Difference of SquaresLet's consider it for a moment. The "difference of squares" means we subtract two numbers squared, like [tex]\boldsymbol{a^2-b^2}[/tex].
Now let's check our choices and see where we subtract two numbers squared.
The only choice like that is Choice [D] - [tex]\boldsymbol{81-49y^2}[/tex].
In choice A, we add 2 numbers; in choices B and C we don't subtract two numbers squared.
Voila! There's our solution, cheers! (:
--
Hope that this helped! Best wishes.
[tex]\it Reach\;far.\;Aim\;high.\;Dream\;big.[/tex]
--
Each point has been reflected over the x-axis or y-axis.
Select the axis over which each point has been reflected.
The reflection is
x-axisx-axisy-axisWhat is reflection over axis?A reflection of a point, a line, or a figure in the X axis involved reflecting the image over the x axis to create a mirror image. In this case, the x axis would be called the axis of reflection.
For reflecting over the X axis is to negate the value of the y-coordinate of each point, but leave the x-value the same.
and, for reflecting over the Y axis is to negate the value of the x-coordinate of each point, but leave the y value the same.
So, by considering the above value rules the reflection of the given points as follows over respective axis.
E(7, 1) ⇒ (7, -1)
Here, the reflection is over x-axis because the y value is changing
F(-3, 5) ⇒ (-3, -5)
Here, the reflection is over x-axis because the y value is changing
G(6, -2) ⇒ (-6, -2)
Here, the reflection is over y-axis because the x value is changing.
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A rectangular parking lot has a perimeter of 820 ft. The area of the parking lot measures 42,000 ft2. What is a dimension of the parking lot?
By solving a system of equations, we will see that the parking lot is 210ft by 200ft.
How to get the dimensions of the parking lot?For a rectangle of length L and width W, the perimeter is:
P = 2*(L + W)
And the area is:
A = L*W
Here we know that the perimeter is 820 ft and the area is 42,000 ft²
Then we can write the two equations (ignoring units).
820 = 2*(L + W)
42,000 = L*W
We can isolate L in the first equation to get:
820/2 = L + W
410 - W = L
Now we can replace that in the other equation:
42,000 = (410 - W)*W = 410*W - W^2
Now we want to solve the quadratic equation:
-W^2 + 410*W - 42,000 = 0
The solutions are given by:
[tex]W = \frac{-410 \pm \sqrt{410^2 - 4*(-1)*(-42000)} }{-2} \\\\W = \frac{-410 \pm 10 }{-2}[/tex]
Then the solutions are:
W = (-410 + 10)/(-2) = 200
W = (-410 - 10)/2 = 210
If we take W = 200, then:
L = 410 - W = 410 - 200 = 210
So we can conclude that the parking lot is 200ft by 210ft.
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Answer: C, 210 ft
Step-by-step explanation: edge :)
3. When using set builder notation, what does it mean to 'Define a set'?
Answer:
A set is a well-defined collection of distinct mathematical objects.
Please help me!!! I will give brainliest to the correct answer.
[tex]\mathsf {2(10 + 2) = 3(y + 3)}[/tex]
[tex]\mathsf {24 = 3y + 9}[/tex]
[tex]\mathsf {3y = 15}[/tex]
[tex]\textsf {y = 5}[/tex]
[tex]\textsf {The value of y will be 5. }[/tex]
ABCD is a parallelogram. Find the measure of angle C.
A
B
C (3x+6)
D (2x+9)
Find out the measure for angle C
Answer:
C = 105°
Step-by-step explanation:
added in the picture
What's the solution to –9x + 4 < 40? Question 4 options: A) No solutions B) All real numbers C) x > –4 D) x < –6
Hey there!
-9x + 4 < 40
SUBTRACT 4 to BOTH SIDES
-9x + 4 - 4 < 40 - 4
SIMPLIFY IT!
-9x < 40 - 4
-9x < 36
DIVIDE -9 to BOTH SIDES
-9x/-9 < 36/-9
SIMPLIFY IT!
x < 36/-9
x < -4
Therefore, the answer should be:
x < -4
(The graph is down below)
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
need help with this question please
∠ A = 132°
Step-by-step explanation:
∠ A + ∠C = 180° (Angle sum of cyclic quadrilateral)
∠ A = 180° - ∠ C = 180° - 48°
∠ A = 132°
There are 5 white balls. 8 red balls, 7 yellow balls, and 4 green balls in a container. A ball is chosen randomly. Find the probability of the following events.
1.What is the probability of choosing
green?
Answers:________ work space:______
2. What is the probability of choosing
red?
Answers:________ work space:______
3. What is the probability of choosing
neither white nor green?
Answers:________ work space:_______
4. . What is the probability of choosing
other than yellow?
Answers:________ work space:_______
5. What is the probability of choosing
purple?
Answer:_________ work space:_______
Given :
White balls = 5 Red balls = 8 Yellow balls = 7Green balls = 4Answer 1 :-
We know that,
P (E) = No. of favourable outcomes / Total number of outcomes.>> Total no. of outcomes = 5 + 8 + 7 + 4
>> Total no. of outcomes = 24
As there are 4 green balls. Therefore,
P (E) = 4 / 24P (E) = 2 / 12 P (E) = 1 / 6Answer 2 :-
We know that,
P (E) = No. of favourable outcomes / Total number of outcomes.>> Total no. of outcomes = 5 + 8 + 7 + 4
>> Total no. of outcomes = 24
As there are 8 red balls. Therefore,
P (E) = 8 / 24 P (E) = 4 / 12 P (E) = 2 / 6 P (E) = 1 / 3Answer 3 :-
We know that,
P (E) = No. of favourable outcomes / Total number of outcomes.>> Total no. of outcomes = 5 + 8 + 7 + 4
>> Total no. of outcomes = 24
As there are 15 balls that are neither green nor white. (Red balls+ yellow balls)
P (E) = 15 / 24 P (E) = 5 / 8Identify the value of the variable in the equivalent expressions.
What is the value of n in the simplified expression?
(4k7)3= 4n ·(k7) 3= 64k21
n =
What is the value of m in the simplified expression?
(Negative 3 r Superscript negative 4 Baseline) Superscript negative 4 Baseline = (negative 3) Superscript negative 4 Baseline times (r Superscript negative 4 Baseline) Superscript negative 4 Baseline = StartFraction 1 Over 81 EndFraction r Superscript m
m =
The value of expression is n=3 and r= 16
What is expression?An expression is a set of terms combined using the operations +, – , x or , /.
Given:
[tex](4k^{7})^{3} = 4^{n}* (k^{7})^{3} = 64 k^{21}[/tex]
[tex](64 k^{21}) = 4^{n}* k^{21} = 64 k^{21}[/tex]
[tex]4 ^{3} * k^{21}= 4^{n}* k^{21}[/tex]
On comparing
n=3
Now,
[tex](-3r^{-4})^{-4} = (-3)^{-4} * (r^{-4})^{-4} = 1/81* r^{m}[/tex]
[tex](-3)^{-4} * (r^{-4})^{-4} = 1/81* r^{m}\\1/ (-3)^{4} * 1/(r^{-4})^{4} = 1/81* r^{m}\\1/ (-3)^{4} * (r^{16}) = 1/81* r^{m}[/tex]
1/81 * r^16 = 1/81 * r^{m}
On compairing
r = 16.
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Answer:
answer in picture
Step-by-step explanation:
Eve has two more marbles than Solene. Solene has twice as many marbles as Steve. Steve has 7 less marbles than eve. How many marbles do they have in all?
A. 27 B. 20 C. 34 D. 13
Using a system of equations, the total number of marbles that they have is given by:
A. 27.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
The variables are given as follows:
Variable x: Eve's marbles.Variable y: Solene's marbles.Variable z: Steve's marbles.Eve has two more marbles than Solene, hence:
x = y + 2.
Solene has twice as many marbles as Steve, hence:
y = 2z -> z = y/2.x = 2z + 2.Steve has 7 less marbles than eve, hence:
z = x - 7.
Hence:
[tex]\frac{y}{2} = x - 7[/tex]
y = 2(x - 7)
y = 2(y + 2 - 7)
y = 2y - 10
y = 10.
Then:
x = y + 2 = 10 + 2 = 12.z = x - 7 = 12 - 7 = 5.Hence the total is given by:
T = 12 + 10 + 5 = 27.
Which means that option A is correct.
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50/22 as a decimal rounded to the nearest hundreth
Step-by-step explanation:
the answer is 2.27. hope this helps
[tex]\frac{5}{x+5}(2x-5(2))[/tex]
Answer: 10
Step-by-step explanation:
[tex]\frac{5}{x+5} (2x-5(2))\\\frac{5}{x+5} (2x-10)\\\frac{10x-50}{x+5}\\\frac{10(x+5)}{x+5} \\\frac{10}{1} \\10[/tex]