Answers
Applying the circle theorems, we have:
4. y = 120°
x = 45°
5. x = 90°
y = 32°
6. x = 40°
y = 20°
7. x = 116°
y = 98°
8. x = 100°
y = 60°
9. x = 54°
y = 75°
What is the Angle of Intersecting Secants Theorem?The angle formed outside a circle by the intersection of two secants equals half the positive difference of the measures of the intercepted arcs, based on the angle of intersecting secants theorem.
What is the Angle of Intersecting Chords Theorem?The angle formed when two chords of a circle intersect, equals the half the sum of the measures of the intercepted arcs, based on the angle of intersecting chords theorem.
4. y = 360 - 95 - 30 - 115 = 120°
x = 1/2(120 - 30) [angle of intersecting secants theorem]
x = 45°
5. x = 90° [based on the tangent theorem]
y = 180 - 90 - 58 [triangle sum theorem]
y = 32°
6. x = 360 - 160 - 160 [central angle theorem]
x = 40°
y = 1/2(40) [inscribed angle theorem]
y = 20°
7. x = 180 - 2(32)
x = 116°
y = 1/2[132 + 2(32)] [angle of intersecting chords theorem]
y = 98°
8. x = 180 - 80 [opposite angles of an inscribed quadrilateral are supplementary]
x = 100°
y = 1/2[(2(80) - 90) + 50] [inscribed angle theorem]
y = 1/2[70 + 50]
y = 60°
9. 40 = 1/2(134 - x) [angle of intersecting secants theorem]
2(40) = 134 - x
80 = 134 - x
80 - 134 = - x
-54 = -x
x = 54°
y = 360 - 134 - 54 - 97
y = 75°
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Related Questions
(Computer science)
The CPU fan rotation rate (R) was directly proportional to the ambient temperature (T). At a temperature of 25 degrees C, the CPU fan was rotating at 1150rpm. What would the rotation rate be for an ambient temperature of 30 degrees C?
Answers
Answer:1380
Step-by-step explanation: proportionality constant equals 1150/25=46. 46x30=1380
If a rectangle’s perimeter is 86 units and the width is 15 units, what is the length in units?
Answers
Answer:
I think the answer would be 28
The center circle on a playing field has a radius of 7.5m find its circumference
Answers
The circumference of the circular playing field.
Solution:[tex]\huge\boxed{Formula:C= 2\pi{r}}[/tex]
We'll have to multiply 2, π and radius.
Substitute the values according to the formula.
[tex]C= 2× \pi ×7.5[/tex]
[tex]C= 47.12389 [/tex]
[tex]\large\boxed{C= 47.12 \: m}[/tex]
Therefore, the circumference of the circular playing field is 47.12 feets.
A material has a density of 4.5 g/ml and a mass of 2.6 grams, what is the volume?
Answers
Answer:
The volume is 11.7
Step-by-step explanation:
[tex]\frac{m}{v}[/tex] = d
[tex]\frac{2.6}{v}[/tex] = 4.5
4.5 × 2.6 = 11.7
v = 11.7
HELP ME PLEASE I WILL MARK BRAINLIEST
Answers
Answer:
A) -4, -2
Step-by-step explanation:
The translation vector is the distance
point A: (3, 1)
point A': (-7, -3)
3 + (-7) = -4
1 + (-3) = -2
What’s the difference in these two questions and why did we divide in one and multiple in one ( also why did we divide by8 in question 2)
Answers
Answer:
times and divide
they are both diffrent equations
A father is 30 years older than his son.Three years ago he was 3 times as old as his son.How old are both of them
Answers
Answer:


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Question

A father is 30years older than his son. In 12years, the man will be three times as old as his son. Find their present ages.
Medium
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Solution

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Let the present age of the son be x years
Then father's age will be (x+30) years
Given after 12 years father will be three times as old as his son
Therefore,
(x+12)3=x+30+12
3x+36=x+42
3x−x=42−36
2x=6
x=3
x+30=3+30=33
So, the present age of son is 3 years and present age of the father is 33 years
3^x+3^x =54 what's the value of x ?
Answers
Answer:
x = 3
Step-by-step explanation:
if you need an explanation let me know
Answer:
x = 3
Step-by-step explanation:
Given:
[tex] \implies \rm 3 {}^{x} + {3}^{x} = 54[/tex]
To Find:
Value of xSolution:
We could re-write 3^x+3^x as:
[We factored here][tex] \implies \: 2(3 {}^{x} ) = 54[/tex]
Divide both sides by 2
[tex] \implies \cfrac{2(3 {}^{x}) }{2} = \cfrac{54}{2} [/tex]
[tex] \implies \: 3 {}^{x} = 27[/tex]
Take logarithm on both sides
[tex] \implies \: \log(3 {}^{x} ) = \log(27)[/tex]
[tex] \implies \: x \times \log(3) = \rm \: log \: (27)[/tex]
[tex] \implies \: x = \cfrac{ \log(27)}{ \log \:(3)} [/tex]
[tex] \implies \boxed{x = 3}[/tex]
Hence, x = 3 .
A right cone has a slant height of 6 and a radius of 4. What is its surface
area?
Answers
The surface area of the cone is 40π
What is a cone?A cone is a solid shape with a circular base and a tapered side.
Analysis:
surface area of a cone = πrl + π[tex]r^{2}[/tex] = π( 6x4) + π(4 x 4) = 40π
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What is the measure of angleq to the nearest whole degree? 43° 49° 53° 58°
Answers
Based on the calculations, the measure of angle Q to the nearest whole degree is equal to 53°. The correct answer is option C.
The complete question is attached with the answer below.
How to calculate the measure of angle Q?The angle is defined as the span between two intersecting lines or surfaces at or close to the point where they meet.
Based on the triangle attached in the image above, we can deduce the following parameters:
Side QM = 18 units.
Side MN = 17 units.
Side QN = 20 units.
In this scenario, we would apply the cosine trigonometry function to determine the measure of angle Q:
MN² = QM² + QN² - 2(QM)(QN)cosθ
17² = 18² + 20² - 2(18)(20)cosθ
289 = 324 + 400 - 720cosθ
720cosθ = 724 - 289
720cosθ = 435
θ = cos⁻¹(435/720)
θ = cos⁻¹0.6042
θ = 52.8 ≈ 53°.
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Find and label the measures of each of the three missing angles, A, B and C, below.
Lines I and M are parallel.
Answers
Hello, the detailed solution is given below.
Lines L and M are parallel. That's why [tex]B[/tex] angle and [tex]50^{o}[/tex] are equal.
What's the Co-Interior Rule? (Known as U Rule)Co-interior angles lie between two lines and on the same side of a transversal. If the two lines are parallel, then co-interior angles add to give [tex]180^{o}[/tex] and so are supplementary.
After that, [tex]C[/tex] angle found as [tex]85^o[/tex].
As [tex]A[/tex] angle and [tex]C[/tex] angle must be equal due to the parallel, the missing angles as;
[tex]A=85\\B=50\\C=85[/tex]
Good luck! If you have any questions, then feel free to ask in comments!
In a diving contest five judges score each dive. the highest and lowest scores are discarded and then the arithmetic average of the remaining scores is taken as the diver's score. if the five judges score a dive as 6.0, 6.3, 6.2, 6.8, and 6.1, then the diver's score is?
Answers
Using the given information, the diver's score is 6.2
Calculating average scoreFrom the question, we are to calculate the diver's score
From the given information,
The five judges score a dive as 6.0, 6.3, 6.2, 6.8, and 6.1.
Since the highest and lowest scores are discarded
Then, we will discard 6.8 and 6.0
The remaining scores are 6.1, 6.2, and 6.3
Now, the diver's score will be the average of the remaining scores
∴ The diver's score = (6.1 + 6.2 + 6.3) /3
The diver's score = 18.6 / 3
The diver's score = 6.2
Hence, the diver's score is 6.2
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Northlake High School has two lunch periods. Students can eat their lunch in
the cafeteria or on an outside patio. About 35% of students who have first
lunch eat outside. Compare this with the percentage of second-lunch
students who eat outside.
Answers
Answer:
Based on the data given on Northlake High School, we can infer that B. A greater percentage of second-lunch students (39%) eat outside.
What does the data on the First and Second lunches show?
The percentage of second-lunch students who eat outside is:
= Second lunch students who eat outside / Second lunch students
Solving gives:
= 0.18 / 0.46 x 100%
= 0.3913 x 100%
= 39%
This shows that the percentage of students eating their second lunch outside is 39%.
so the answer is B
Step-by-step explanation:
Think about the function f(x) = 3 - 2x.
What does the notation f(0) mean?
Answers
3 - (2*0) => 3-0 = 3
so the answer is 3
Answer:
the answer is 3
given m
m FS =
pls help me this is due tomorrow
Answers
Answer:
arc FS = 84°
Step-by-step explanation:
the inscribed angle QRF is half the measure of its intercepted arc QF , then
arc QF = 2 × 48° = 96°
the sum of the arcs on a semicircle = 180° , that is
QF + FS = 180°
96° + FS = 180° ( subtract 96° from both sides )
FS = 84°
To remain healthy, a person needs at least 8 hours of sleep. A company wants to know if their employees get enough sleep. A random sample of 24 employees revealed that the average number of hours of sleep an employee gets is 6.7 with standard deviation of 2.3. What should be the test statistic?
Answers
Answer:
how many hours a week the employees are working?
Step-by-step explanation:
I could be wrong but that's my fault if it's wrong sorry
help pls im being timed i cant do mathhh
Answers
Combine the like terms to create an equivalent expression:−3z−z
Answers
Answer:
-4z
Step-by-step explanation:
Hi student! Let me help you out.
_____________________
Note that, -3z and -z are like terms. This means we can combine them right off the bat, which gives us [tex]\mathrm{-4z}[/tex].
[tex]\mathrm{-3z-z=-4z}[/tex]. -4z is our final answer.
Hope that this helped you! have a good day ahead.
Best Wishes!
[tex]\star\bigstar\underline{\underline{\overline{\overline{\textsf{Reach far. AIm high. Dream big.}}}}}\bigstar\star[/tex]
◈◈-Greetings!-◆◆
___________________
Answer:
-4z
Step-by-step explanation:
-3z-z
On combining like terms,
= -4z
Here,the terms are -3z and -z, where - and - combines and + is the result,so we need to add the expression.Lindsay sketches a right triangle with lengths f, g, and h as shown. She uses the Pythagorean Theorem to write the equation f2 + g2 = h2 to represent the triangle. How can Lindsay correct her error? Explain your reasoning.
Answers
Answer:
hope you can understand
A basket contains six apples, three oranges, ten corn, four pears and six peaches, You randomly select a fruit. What is the conditional probability of selecting a fruit that it is a orange?
Select one:
a.
15.8%
b.
15%
c.
17.5%
d.
10.3%
Answers
Answer:
b. 15%
Step-by-step explanation:
because it is 3 oranges and 3 is equal to 15%
y=x^2+5x-8 to factored form
Answers
Answer:
Factor and set each factor equal to zero. Y=x2+5x−8
Step-by-step explanation:
Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options.
Answers
Answer:
Step-by-step explanation:
If investments double every 9 years and you start with a $600 investment, how much money would you have after 27 years? First, complete the equation: Future Amount = 600 (1 + [?]) ↑ ↑ initial amount growth rate Hint: Doubling means a 100% growth rate. time periods Enter
Answers
Answer:
600(1+1)^3 with future amount being 4800
Step-by-step explanation:
The amount of the money after 27 years will be $4800.
What is the amount?The quantity of money anyone has is termed as the amount. The solution to the question is given as follows:-
Given that investments double every 9 years and you start with a $600 investment. how much money would you have after 27 years?
We know that the amount is getting double in every 9 years so the number of times the amount will get doubled will be = 27 / 9 = 3
Future amount = 600(1+1)³
Future amount = 600 ( 2 )³
Future amount = 600 ( 8 ) = $4800
Therefore the amount of the money after 27 years will be $4800.
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Odette made this jewelry box by combining two rectangular boxes.
What is the total surface area of this jewelry box?
PLS HURRY WILL GIVE BRAINLIEST
Answers
Adding the sides up we get, 36+36+72+24+24+24+32+48+48+48
some one please help me slove this I can't figure it out I will give Brainliest answer to who ever answer frist...
Answers
keeping in mind that twin sides stemming from a common vertex make twin angles at the "base", Check the picture below.
Find Measure of angle B (m
18. a = 7 m, b = 5 m, m∠A = 45°
Answers
The value of the variable a is 19.66 and the value of the valriable b is 20.21.
What is the law of sines?For any triangle ABC, with side measures |BC| = a. |AC| = b. |AB| = c,
we have, by the law of sines,
[tex]\rm \dfrac{sin\angle A}{a} = \dfrac{sin\angle B}{b} = \dfrac{sin\angle C}{c}[/tex]
Remember that we took
The sine angle is the length of the side opposite to that angle.
Then the third angle of the triangle will be
x + 75 + 35 = 180
x = 70
[tex]\rm \dfrac{\sin 75^o}{b} = \dfrac{\sin 35^o}{12} = \dfrac{\sin 70^o}{a}[/tex]
From the first two-term, we have
sin 75 / b = sin 35 / 12
b = 20.21
From the last two-term, we have
sin 70 / a = sin 35 / 12
a = 19.66
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Which of the following could be the equation of a line perpendicular to the line 2x−5y=7?
Answers
Answer:
B.
Step-by-step explanation:
First convert the equation to slope-intercept form:
2x - 5y = 7
-5y = -2x + 7
y = 2/5 x - 7/5
So the slope of the given line is 2/5.
So the slope of a perpendicular line will be -1/ 2/5 = -5/2.
Take B:
5x + 2y = 3
2y = -5x + 3
y = -5/2.
So its B.
Mrs. Rykus does a survey of her 85 students.
20 say math is awesome
35 say math is the best
30 say math is fun
Based on these results, if Mrs. Rykus asks the whole student population 900 students what they think of math, what is the best approximation for how many students will say math is awesome?
A 400
B 212
C 200
D 315
Answers
Answer:
212
Step-by-step explanation:
85 here is 100%
And 900 is also 100%
That's for the different comparisons. So now, what we do is, we should divide 85 by 900, and then, whatever is our answer, multiply that by 20.
That is surely going to equal how many students are going to say that Math is Awesome for 900 student survey.
Step 1
85/900=10.5882352941
Let's round that to make it
10.5
Step 2
10.5x20=210
That means, if we go exactly, like multiplying all of those numbers, then our answer should be 212 or 200.
Just to be sure that our answer is correct, we will do it with 10.58 now.
Step 3
10.58x20=211.6
So now it looks like it's most probably going to be 212
But still, let's do 10.588 now.
Step 4
10.588x20=211.76
Okay, let's do it again, with 10.5882
Step 5
10.5882x20=211.764
Okay, so I just multiplied the whole number this time, and I still got a decimal, so that means that your answer is 212 basically.
Determine the period, amplitude, and phase shift of[tex]f(x)=3cos2\left \{ x-\frac{\pi }{4}]+1[/tex]
b) List the five critical points for the first cycle. (3 marks)
Use this information to sketch the graph off(x) for two
complete cycles. Determine [tex]\frac{1}{4}[/tex] wave and starting point.
Clearly label the scale on both axes. (3 marks)
Answers
->period = [tex]\frac{2\pi }{2} =\pi[/tex]
->a=3, shift [tex]\frac{\pi }{4}[/tex]
->right 1 unit up
Rest are shown in graph
Dan has a list of the scores of all his
math tests and quizzes during the
year. What are the mode and median
of the data set?
88, 79, 71, 75, 53, 88
a. mode = 88, median = 88
b. mode = 88, median = 77
C. mode = 77, median = 77
d. mode = 77, median = 88
Answers
Answer:
b. mode = 88, median = 77
Step-by-step explanation:
First, arrange all the numbers least to greatest.
53, 71, 75, 79, 88, 88
The mode is the number that occurs the most.
mode = 88
The median is the middle number. Since there is an even number of numbers, look at the two middle numbers 75 and 79. Add them together and divide by two (finding the average or mean of the numbers).
75 + 79 = 154
154/2 = 77
median = 77