Answers
Answer:
x = 21°, y = 42°, TQ = 3.75 cm
Step-by-step explanation:
In Δ SRT
∵ m∠RST = 21°, m∠STR = 117°
∵ The sum of the measures of the interior angles of a triangle is 180°
∴ m∠RST + m∠STR + m∠SRT = 180°
∴ 21° + 117° + m∠SRT = 180°
→ Add the like angles
∴ 138° + m∠SRT = 180°
→ Subtract 138° from both sides
∴ m∠SRT = 42°
In the given circle
∵ ∠SRP and ∠SQP are inscribed angles subtended by the arc SP
→ Inscribed angles subtended by the same arc are equal in measures
∴ m∠SRP = m∠SQP ⇒ (1)
∵ m∠SRP = 42° , m∠SQP = y
∴ y = 42°
∵ ∠RSQ and ∠RPQ are inscribed angles subtended by the arc RQ
→ Inscribed angles subtended by the same arc are equal in measures
∴ m∠RSQ = m∠RPQ ⇒ (2)
∵ m∠RSQ = 21° , m∠RPQ = x
∴ x = 21°
∵ The chord SQ intersects the chord PR at the point T
∴ ∠STR and ∠PTR are vertically opposite angles
→ The vertically opposite angles are equal in measures
∴ m∠STR = m∠PTR ⇒ (3)
→ From (1), (2), and (3) the two triangles SRT and PQT are similar using
AAA postulate of similarity
∴ Δ SRT ≈ ΔPQT ⇒ AAA postulate
∴ Their sides are proportion
∴ [tex]\frac{SR}{PQ}=\frac{RT}{TQ}=\frac{ST}{PT}[/tex]
∵ SR = 8.32 cm, PQ = 9.43 cm, RT = 3.31 cm
→ Substitute them in the ratio above
∴ [tex]\frac{8.32}{9.43}=\frac{3.31}{TQ}[/tex]
→ By using cross multiplication
∴ TQ × 8.32 = 9.43 × 3.31
→ Divide both sides by 8.32 to find TQ
∴ TQ = [tex]\frac{(9.43)(3.31)}{8.32}[/tex]
∴ TQ = 3.751598558
→ Round it to 2 d.p
∴ TQ = 3.75 cm
Related Questions
PLEASE HELP!!!
Equation: 2 (1/2x + 1) = -3 (2x - 1) +4 (2x + 1)
Answer Choices:
A. 5
B. All real numbers
C. No solution
D. None of the above
I got D but I wanted some confirmation. I feel like I got it wrong... Thanks!
Answers
Answer:
Step-by-step explanation:
2(1/2x+1) = -3(2x-1)+4(2x+1)
Distributive Property 1x+2 = -6x+3+8x+4
Combine Like Terms. 1x+2 = 2x+7
Subtract 1x from both sides 2 = x+7
Subtract 7 from both sides -5 = x
Thus the solution is non of the above
the percentage of registered voters who voted in this election was 55%, up 17% from the last election. what was the percentage that voted at the last election?
Answers
Answer:
0.38 or 38%
Step-by-step explanation:
Because I subtracted 17% from 55% and got 0.38 Then, I turned the decimal 0.38 into the percentage 38%.
Mrs. Thomas has $71.00 to purchase bottles of juice for her class. If the bottles of juice cost $3.55 each, how many
bottles can she buy?
O 2 bottles
O 5 bottles
O 20 bottles
O 25 bottles
Answers
71 divided by 3.55 = 20
Examine the division problem.
StartFraction 15 over 4 EndFraction divided by (negative StartFraction 5 over 8 EndFraction
To solve the problem, you first must find the reciprocal of the second fraction. Which reciprocal fraction should you use?
Negative StartFraction 5 over 1 EndFraction
Negative one-fifth
Negative StartFraction 5 over 8 EndFraction
Negative StartFraction 8 over 5 EndFraction
Answers
Answer:d -8/5
i just toke the test and got it right
Answer:
Actually its negative 6 -6
Step-by-step explanation:
Convert the Cartesian coordinate (1,3) to polar coordinates
Answers
The polar coordinates of the Cartesian coordinate (1,3) is (√10, 74.49°).
To convert the Cartesian coordinate (1,3) to polar coordinates, follow the steps below:
Step 1: Plot the point (1,3) in the Cartesian plane. We have;Cartesian Plane
Step 2: Determine the distance (r) of the point from the origin using the distance formula;r = √(x² + y²)r = √(1² + 3²)r = √(1 + 9)r = √10
Step 3: Determine the angle (θ) between the positive x-axis and the line segment connecting the origin to the point (1,3).
We can find θ using any of the following formulas;
θ = tan⁻¹(y/x)θ = cos⁻¹(x/r) if x is positiveθ = cos⁻¹(x/r) + π if x is negative and y is positiveθ = tan⁻¹(y/x) + π if x is negative and y is negativeθ = ½ π if x is zero and y is positiveθ = 3/2 π
if x is zero and y is negativeθ is undefined if x is zero and y is zeroθ = cos⁻¹(1/√10) if x is positiveθ = cos⁻¹(-1/√10) + π if x is negative and y is positiveθ = tan⁻¹(3/1) + π
if x is negative and y is negativeSince x = 1 and y = 3,θ = cos⁻¹(1/√10)θ ≈ 74.49°
Step 4: Write the polar coordinates as (r, θ) using the determined values;r = √10 and θ ≈ 74.49°
To learn more about : polar coordinates
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Solve the equation.
x^2 − 4x + 4 = 3
Answers
ASAP JUST ANSWER NO WORK
Answers
Answer: C
Step-by-step explanation:
When drawn on a circle, the angle 472° is drawn in the same position as
Answers
Answer:
112°
Hope it helps :)
Answer:
112 degrees
Step-by-step explanation:
since a circle is 360 degrees, we can subtract 472 and 360 to get an angle that is in the same position. the result is 112 degrees.
Solve the expression when x = 4 and y = -2 x² - 2xy + y² 36
Answers
Answer:Did u mean plus 36
Step-by-step explanation:
I've done every problem I only need with the help this problem
Answers
Answers:
[tex]\displaystyle \lim_{x \to 2^{+}} f(x) = 1\\\\\displaystyle \lim_{x \to 2^{-}} f(x) = 1\\[/tex]
Both result in the same limit value. This allows us to say [tex]\displaystyle \lim_{x \to 2} f(x) = 1[/tex] without the plus or minus over the 2.
The left and right hand limits may not always match like this.
==================================================
Explanation:
The notation [tex]\displaystyle \lim_{x \to 2^{+}} f(x)[/tex] means that we are approaching x = 2 from the right hand side. This is from the positive direction. So we start at say x = 3 and move to x = 2.5 then to x = 2.1 then to x = 2.01 and so on.
Because we started with values x > 2, we will use the third definition of the piecewise function
if x > 2, then f(x) = 3x-5
Plug in x = 2 to get
f(x) = 3x-5
f(2) = 3(2)-5
f(2) = 6-5
f(2) = 1
This shows [tex]\displaystyle \lim_{x \to 2^{+}} f(x) = 1[/tex]
-----------------------------
For the other limit, we're approaching x = 2 from the negative side. So we could start at say x = 0, then move to x = 1, then to x = 1.5 then to x = 1.9 then to x = 1.99, and so on.
We're using x values such that x < 2 now.
So we'll be using the first definition of the piecewise function
If x < 2, then f(x) = x^2 - 3
f(x) = x^2-3
f(2) = 2^2-3
f(2) = 4-3
f(2) = 1
We end up with [tex]\displaystyle \lim_{x \to 2^{-}} f(x) = 1[/tex]
---------------------------------
Both right hand limit and left hand limit result in the same value
Because [tex]\displaystyle \lim_{x \to 2^{+}} f(x) = \displaystyle \lim_{x \to 2^{-}} f(x) = 1[/tex]
We can shorten that to [tex]\displaystyle \lim_{x \to 2^{}} f(x) = 1[/tex] meaning we can approach x = 2 from either direction to arrive at the same limiting value.
A thing to notice is that f(2) is not equal to 1. Instead the second line of the piecewise function says f(2) = 3.
The fact that the limit as x approaches 2 and f(2) don't agree means this function is not continuous at x = 2.
The graph shows this. We have a removable discontinuity where we effectively picked the point off the graph and move it upward.
See the diagram below.
Yesterday, Charlie had k baseball cards. Today, he got 24 more. Using k
Answers
Identify the following errors as systematic or random.
a. A micropipet is improperly calibrated, and the balance dispensed is always smaller than expected.
b. The last digit on a pH meter fluctuates up and down as a measurement is taken.
c. A thermometer is placed such that the bulb makes poor contact with the measured substance, giving erratic temperature reading.
d. A few drops of water are on a balance pan, causing the mass output on the balance to be high each time it is used.
Answers
Answer:
systematic errors [ A, C], Random errors [B, D]
Step-by-step explanation:
Random errors are errors that cause certain fluctuations around the true values of substances that are measured, as a result of difficulties being experienced while taking measurements. Systematic errors are mostly associated with the calibration of equipment. It seen to cause consistent deviations from the true value that can be gotten during measurement.
In most cases, random errors cannot be avoided while systematic errors can.
A. Find the Mode, Median, Mean and Range. Show your work.
1. 24, 31, 12, 38, 13, 15, 46, 62.
2. 17, 66, 14, 79, 47, 95, 32, 21, 10, 58.
3. 53, 22, 76, 46, 68, 32, 15, 29.
4. 17, 24, 8, 19, 6, 34, 10, 28, 12.
5. 5, 8, 9, 10, 11, 15, 21, 32.
6. 28, 15, 15, 46, 27, 21, 24
B. Find the mode, median, and range
7) 5.2, 5.7, 5.2, 4.3, 3.6, 3.8, 2.7, 4.2, 4.3, 3.9, 4.2
8) 18.1 , 18.6, 18.2, 18.1, 18.9, 18.6, 18.7, 18.3, 18.2, 18.6, 18.6
C. Find the mode and median for each data.
9) 2/9 , 7/9, 5/9, 1/9, 3/9, 8/9
10) 1/4, 1/11, 1/6, 1/9, 1/3 , 1/10
Answers
A.
1. Mode: No mode. Median: 24. Mean: 30.875. Range: 50.
2. Mode: No mode. Median: 33.5. Mean: 43.9. Range: 85.
3. Mode: No mode. Median: 46. Mean: 43.571. Range: 61.
4. Mode: No mode. Median: 17. Mean: 18. Range: 28.
5. Mode: No mode. Median: 10.5. Mean: 13.5. Range: 27.
6. Mode: 15. Median: 22.5. Mean: 25.857. Range: 31.
B.
7. Mode: 4.3. Median: 4.2. Range: 2.1.
8. Mode: 18.6. Median: 18.6. Range: 0.8.
C.
9. Mode: No mode. Median: 4/9.
10. Mode: No mode. Median: 5/24.
Determine whether the equations are parallel or not for y= 3x-2 and y= 1/3x -11
Answers
Answer:
To know if these lines are parallel, you just have to look at the slope. In this case they are not.
Step-by-step explanation:
The slope is the number in front of your x. So for the first formula the slope is 3 and for the second one it is 1/3. The slope tells you in which direction the line goes, so if they are the same, that means that the lines are parallel. In this case the slopes are not the same, so the lines are not parallel.
Answer:
not parallel
Step-by-step explanation:
while the lines have a different y-intercept they do not have the same slope which they would need to be parallel. With two different slopes the lines will eventually cross.
Subtitute 2x+y=7 and 3x-y=8
Answers
Answer:
x = 3 , y = 1
Step-by-step explanation:
2x + y = 7
3x + y = 8
solution
2x + y = 7-----------(1)
3x - y = 8------------(2)
from equation 1
2x + y = 7
y = 7 - 2x-------------(3)
substitute equation 3 into equation 2
3x - y = 8
3x - (7 - 2x) = 8
3x - 7 + 2x = 8
3x + 2x = 8 + 7
5x = 15
divide through by the coefficient of x
5x/5 = 15/5
x = 3
to find y
substitute x into equation 1
2x + y = 7
2(3) + y = 7
6 + y = 7
y = 7 - 6
y = 1
henry and his brother each start a savings account. henry begins with $200 and deposits $25 each month. his brother begins with $150 and deposits $35 each month. after how many months will the two brothers have the same in their savings account ?
Answers
Answer:
Henry after 2 months: 250
His brother after 2 months: 220
Step-by-step explanation:
Henry started with $200 so add $25 twice (for 2 months) and get $250 dollars after 2 months.
His brother started with $150 so add $35 twice and get $220 dollars after 2 months
Josh added 18 fish to his pond over a period of 6 days. He added the same number of fish each day. What was the change in the number of fish in the pond each day?
Answers
Answer:
he put 3 fish everyday for 6 days
<1 and <2 are vertical angles. If m<4=
(6x + 11)' and m<2= (10x - 91°, find m<1.
Answers
Answer:
Something
Step-by-step explanation:
Something and something and thats it!
what is length?define
Answers
Step-by-step explanation:
the measurement or extent of something from end to end; the greater of two or the greatest of three dimensions of an object.
Answer:
the measurement or extent of something from end to end.
Omar wants to measure the width of a river. He marks off two right triangles, as shown in the figure. The base of the larger triangle has a
length of 64 m, and the base of the smaller triangle has a length of 31 m. The height of the smaller triangle is 19.8 m. How wide is the
river? Round your answer to the nearest meter. (The figure is not drawn to scale.)
19.8 m
River
A
31 m
64 m
?
A
m
X
Ś
Answers
Answer:
41 meters
Step-by-step explanation:
[tex]\frac{31}{64}[/tex] = [tex]\frac{19.8}{x}[/tex]
31x = (19.8)(64)
31x = 1267.2 Divide both sides by 31 and round
x = 41
4.
If 75 persons can perform a piece of work in 12 days of 10 hours, how many men will
perform a piece of work twice as great in tenth part of time, if they work the same
number of hours a day, supposing that two of the second set can do as much work as
three of the first set?
1
n.1.1
Answers
Answer: dont know
Step-by-step explanation:
Question 3 of 10
The circle below is centered at the point (4, 3) and has a radius of length 5.
What is its equation?
D. (x-4)2 + (y-3)2 = 52
10
OA. (x-3)2 + (y - 3)² =
52
OB. (x+4)2 + (y - 3)² =
25
O C. (x-4)2 + (y + 3)² =
52
Answers
Answer:
D.
[tex](x - 4) {}^{2} + (y - 3) {}^{2} = 5 {}^{2} [/tex]
The equation of the circle centered at point (4, 3) with a radius of length 5 is (x - 4)² + (y - 3)² = 5².
What is the equation of the circle with the given parameters?The standard form equation of a circle with center (h, k) and radius r is:
( x - h )² + ( y - k )² = r²
Given that circle has a center at point (4, 3 ).
Hence:
h = 4
and k = 3
Also given that, the radius has a length of 5
r = 5
Plug these values into the above formula and simplify the equation:
( x - h )² + ( y - k )² = r²
( x - 4 )² + ( y - 3 )² = 5²
Expanding and simplifying, we get:
(x - 4)² + (y - 3)² = 25.
Therefore, the equation of the circle is (x - 4)² + (y - 3)² = 5².
Option D) (x - 4)² + (y - 3)² = 5² is the correct answer.
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What is the difference between climate and weather?
Answers
Answer:
B
Step-by-step explanation:
Climate happens over a long period of time.
Weather varies day to day.
Ex: South Texas has a hot humid summer (climate)
Ex: It is 89 degrees in California today (weather)
Solving the equation
Answers
Answer:
-40
Step-by-step explanation:
We multiply both sides by 5:
x = -5 * 8
so x = -40
If 1 yard = 3 feet and 1 mile = 5,280 feet, how many yards are there in 4 miles?
7,040 yards
15,840 yards
21,120 yards
63,360 yards
Help me please!!
Answers
Answer:
7040
Step-by-step explanation:
You do 5280 times 4 which is 21120. Then you do 21120 divided by 3 and get 7040.
Change 0.150 to a fraction.
Answers
Step-by-step explanation:
150/1000 and then you you have to simplify it
Multiplying a number by its reciprocal always results in a product of 1. What number must be multiplied by 4 5/8 to create a product of 1?
Answers
First, turn 4 5/8 into an improper fraction.
4 = 32/8
(The fraction bar is basically division)
32/8 + 5/8 = 37/8
Now, flip it to find the answer.
6/37
That is the answer.
Hope I helped
Jerry was paid $47.00 for 4 hours of work. Leigh-Anne received $84.35 for 7 hours. Who had the greater rate of pay? By how much?
Answers
Answer:
Jerry was paid $10.75 an hour and Leigh-Anne was paid $12.05 hourly
Step-by-step explanation:
What values of B make the equation 7+4-2-B=13-9 true?
Answers
Answer:
solution:
Here,7+4-2-8=13-9
or, 9-B=4
or, -B=4-9
or-B=-5
*B= 5
what 23 div 57 times 7
Answers
Answer:
187.285714286
Step-by-step explanation:
Step-by-step explanation:
27/57= 0.40350877193
0.40350877193x7=
2.82456140351
rounded ver- 2.82
