In the circle below, QR is a diameter and QT is tangent at Q. Suppose m QRS = 212°. Find the following.
(a) m/SQT =
(b) m/RQS =
Answers
Using the tangent theorem and the inscribed angle theorem, we have:
a. m∠SQT = 74°; b. m∠RQS = 16°.
What is the Tangent Theorem?Angle formed at the point of tangency between the tangent and the radius of a circle = 90 degrees based on the tangent theorem.
What is the Inscribed Angle Theorem?The inscribed angle theorem states that, measure of inscribed angle = 1/2(measure of intercepted arc).
a. Find m(SQT):
m∠RQT = 90° [tangent theorem]
m(QR) = 180° [semicircle]
m(QRS) = 212° [given]
m(RS) = m(QRS) - m(QR) = 212 - 180 = 32°
m∠RQS = 1/2[m(RS)] [inscribed angle theorem]
m∠RQS = 1/2(32)
m∠RQS = 16°
m∠SQT = m∠RQT - m∠RQS = 90 - 16
m∠SQT = 74°
b. m∠RQS = 1/2(32)
m∠RQS = 16°
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Related Questions
What is the sum of the two
expressions?
(4/5x+13) - (5/8x − 6)
Answers
Answer: 7/40x + 19
Step-by-step explanation:
---Distribute the negative sign
4/5x + 13 - 5/8x + 6
---Get common denominators on the fractions
32/40x + 13 - 25/40x + 6
---Combine like terms
(32/40x - 25/40x) + (13 + 6)
7/40x + 19
Answer: 7/40x + 19
Hope this helps!
if you have 48 apples and you gave your friend molly 20 and you gave your brother and mom 18 each how much apples do you have now?
Answers
Answer:
10
Step-by-step explanation:
48-20=28
28-18=10
that is how I see it at least
What is the area of triangle ABC?
C
12
60°
60°
A
D
B
Answers
Answer:
Area of the triangle is 36√3
Step-by-step explanation: Hope this will help
The hypotenuse of each 30 - 60 - 90 triangle is 12
The base length is 6 + 6 = 12 because the triangle is equilateral and the
altitude of the triangle divides the base into two equal parts and the altitude (DC) is the height of the triangle.
Now you have two 30 - 60 - 90 triangles with the hypotenuse of 12, the short leg = 6 and you need to find the length of DC.
Finding DC .
a² + b² = c²
6² + b² = 12² 0r the long leg = short leg times √3
36 + b² = 144 6√3
b² = 108
b = 6√3
Area of a triangle = 1/2bh
= 1/2(12)(6√3)
= 6(6√3) = 36√3
I need some help on this question please
Answers
Answer:
D
Step-by-step explanation:
everything that should happen at x+4 happens now at x. that is what that means.
so, the graph shifts 4 units to the left.
Find the magnitude of the sum of the vectors <4,5> and <-2,2>. Round your answer to the nearest 100th.
Answers
Answer:
[tex]||v||\approx7.28[/tex]
Step-by-step explanation:
Sum of the vectors
[tex]\langle4,5\rangle+\langle-2,2\rangle=\langle4+(-2),5+2\rangle=\langle2,7\rangle[/tex]
Magnitude of the resultant vector
[tex]||v||=\sqrt{x^2+y^2}=\sqrt{2^2+7^2}=\sqrt{4+49}=\sqrt{53}\approx7.28[/tex]
HELPPPP WITH MATH HOMEWORK PLS
Answers
Answer:
The length of the wing is 480 centimeters
Step-by-step explanation:
2 cm on the drawing is 192 cm on the acutal wing
2 = 192
divide both sides by 2
1 = 96
since the drawing has a length of five cm, multiply both sides by 5
5 = 480
therefore, 5 cm on the drawing is equal to 480 cm on the actual wing
Lionel computed the average rate of change in the depth of a pool over a two-week interval to be zero. Which statement must be true?
The pool must have been empty for the entire interval.
The pool must have been the same depth at the start of the interval as it was at the end of the interval.
The pool must have been deeper at the end of the interval than it was at the start of the interval.
The pool must have been more shallow at the end of the interval than it was at the start of the interval.
Answers
The pool must have been the same depth at the start of the interval as it was at the end of the interval, option second is correct.
What is the average rate of change?Finding out how much something changes over time is what the average rate of change is all about.
We have Lionel computed the average rate of change in the depth of a pool over a two-week interval to be zero.
As we know that the average rate of change can be calculated using:
= (Last quantity - starting quantity)/Time interval
The average rate of change, on the other hand, does not account for intermediate values, therefore you can't draw any conclusions about them.
In the given problem:
The average rate of change in depth = (Last quantity - starting quantity)/2
0= (Last quantity - starting quantity)
Final depth = Initial depth
Thus, the pool must have been the same depth at the start of the interval as it was at the end of the interval, option second is correct.
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What is the simplified value of the exponential expression 16 Superscript one-fourth?
2
4
Answers
Answer:
[tex]2[/tex]
Step-by-step explanation:
[tex] {16}^{ \frac{1}{4} } \: is \: the \: same \: as \\ \\ \sqrt[4]{16} = \sqrt[4]{ {4}^{2} } [/tex]
Note we broke down the 16 into 4 squared*. This is because 4 squared is the same as 16. The four and the two would cancel each other leaving:
[tex] \sqrt[2]{4} \;\\ or \\ \: \sqrt [2]{{2}^{2}} [/tex]
Like before the two and the two would cancel each other out leaving:
[tex]2[/tex]
Answer:
C. 2
Step-by-step explanation:
edge
Use formulas to find the lateral area and surface area of the given prism. Round your answer to
the nearest whole number. The figure is not drawn to scale. The bases are right triangles.
8.94 m
4m
8m
41 m
Answers
Answer:
The answer is option B
[tex]859[/tex] [tex]m^2[/tex] [tex],[/tex] [tex]891[/tex] [tex]m^2[/tex]
Step-by-step explanation:
Step 1
Find the lateral area
we know that
The formula to calculate the lateral area is equal to
[tex]LA=Ph[/tex]
where
P is the perimeter of the base of the prism
h is the height of the prism
In this problem we have
[tex]P=4+8+8.94=20.94[/tex] [tex]m[/tex]
[tex]h=41[/tex] [tex]m[/tex]
substitute in the formula
[tex]LA=20.94*41=858.54[/tex] [tex]m^2[/tex]
[tex]LA=859[/tex] [tex]m^2[/tex]
Step 2
Find the surface area
we know that
The formula to calculate the surface area is equal to
[tex]SA=2B+Ph[/tex]
where
B is the area of the base of the prism
P is the perimeter of the base of the prism
h is the height of the prism
In this problem we have
[tex]B=8*4/4=8[/tex] [tex]m^2[/tex]
[tex]P=4+8+8.94=20.94[/tex] [tex]m[/tex]
[tex]h=41[/tex] [tex]m[/tex]
substitute in the formula
[tex]SA=4(8)+20.94*41=890.54[/tex] [tex]m^2[/tex]
[tex]SA=891[/tex] [tex]m^2[/tex]
You are in business and have a product that sells for $10 that 1,000 people buy each month You want to make a profit and wonder whether you should raise the price in increments of a dollar For each dollar you raise the price , you lose 100 customersHow many dollars can you increase in price to maximize your profit or should you increase in price at all?
Answers
Based on the attached photo and explanation below, the price should not be increased at all.
How to know when profit is maximized?Note: See the attached photo for the calculation of Revenues at Different Number of Customers and Prices.
Every other being equal, profit is maximized when revenue is at the maximum,
From the attached photo, it can be seen that revenue is at the maximum or the highest when the price is $10 and the number of customers is 1,000.
Increasing the price in increments of a dollar results in a fall in revenue progressively until it reaches $0.
Therefore, the price should not be increased at all.
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Allison wants to ride her bicycle 60 miles this week. She has already ridden 12 miles. If she rides for 6 more days, what is the average number of miles she would have to ride each day to meet her goal?
Answers
Answer:
8 miles a day
Step-by-step explanation:
First you have to subtract the amount of miles she had already gone.
60 - 12 = 48
Next you have to divide by the remaining amount of days (6 days).
48/6 = 8
which postulate or theorem proves that these two triangles are congruent?
a. ASA Congruence Postulate
b. SAS Congruence Postulate
c. AAS Congruence Theorem
d. HL Congruence Theorem
Answers
Find the equation of a line that passes through the point (2,4) and has a gradient of 1/3 . leave your answer in the form y = m x + c
Answers
Answer:
y = mx + b
y = 1/3x + b
Use (2,4) to find b
4 = 1/3(2) + b
b = 4 - 2/3
b = 12 - 2
3
b = 10/3
The equation will be:
The equation will be: y = 1/3x + 10/3
In circle H with m/GHJ = 82 and GH = 12 units, find the length of arc GJ.
Round to the nearest hundredth.
H
Answers
The length of the arc GJ is 17.17 units if the in circle H with m/GHJ = 82 and GH = 12 units.
What is a circle?It is described as a set of points, where each point is at the same distance from a fixed point (called the centre of a circle)
We have angle GHJ = 82 units
Length of GH = 12 units
We know:
s = 2πr(θ/360)
s = (2π)12(82/360)
s = 17.17 units
Thus, the length of the arc GJ is 17.17 units if the in circle H with m/GHJ = 82 and GH = 12 units.
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Mai put $4250 in the bank at 4.4% interest compounded annually. How much was in her
account after 7 years?
Answers
Answer:
$5745.03
Step-by-step explanation:
A = 4250(1 + 0.044)7 = $5745.03
The required amount in the Mai accounts after 7 years will be $5745.03.
What is compound interest?Compound interest is the interest on deposits computed on both the initial principal and the interest earned over time.
Amount = principal[1 + r/n]ⁿᵃ
Here,
Principal = 4250, rate = 4.4%, Time = 7 ,
Amount = 4250[1 + 0.044]⁷
Amount = $5745.03
Thus, the required amount in the Mai accounts after 7 years will be $5745.03.
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7. The points (−2,−4) and (5,6) are the endpoints of the diameter of a circle. Find the length of the radius of the circle.
Answers
Answer
6.10
Use the distance formula:
[tex]\sf d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}[/tex]
where (x1, y1), (x2, y1) are points
[tex]\rightarrow \sf d =\sqrt{(5-(-2))^2 + (6-(-4))^2}[/tex]
[tex]\rightarrow \sf d =\sqrt{(7)^2 + (10)^2}[/tex]
[tex]\rightarrow \sf d =\sqrt{149}[/tex]
This is the length of diameter.
Then radius:
· diameter/2
[tex]\sf \cdot \dfrac{\sqrt{149 } }{2}[/tex]
[tex]\sf \cdot 6.103277808[/tex]
[tex]\sf \cdot 6.10 \ \ (rounded \ to \ nearest \ hundreth)[/tex]
Does anybody want to help with math?
2a(-5a^8b+a^2-12ab)
Ty :D
Answers
Answer: 18a4 - 6a3b - 5a2b4 - 45a2b2 + 36ab2 - 12ab + 3b
———————————————————————————————-
3
Step-by-step explanation:
x: y = 1:5 Which is the correct equation? A y = 5x By= C y=x-4 D y=x+4
I'm leaning towards A but don't want totake the risk with a hour detention on the line if I get it wrong
Answers
Or, use the number 5 as an example. If x = 5, and the ratio between x and y is y is 5 times greater than x, then y is 5.
And if you put that into A, y = 5x, it becomes 25 = 5(5)
Then 25 = 25, which is true!
Envision Geometry 10-1 Circles 22. page 425
Answers
The segment area of the circle that's given in the envision geometry is 2.568.
How to calculate the segment area?It should be noted that the segment area is given as:
= (a/360)π × R² - Area of triangle
= (90/360)π × 3² - (1/2 × 3²)
= 9π/4 - 9/2
= 2.568
In conclusion, the segment area of the circle that's given in the envision geometry is 2.568.
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Here are two rectangles. the area of the shaded rectangle is 1/4 the area of the large rectangle. work out the value of x
Answers
The area of the rectangle is the product of length and width. The value of the variable x is 3.6 cm
What is the area of the rectangle?Let L be the length and W be the width of the rectangle.
Then the area of the rectangle will be
Area of the rectangle = L × W square units
The diagram is given below.
Let A₁ be the area of the small rectangle and A be the area of the large rectangle.
A₁ = 1/4 A
4A₁ = A
4 × 2× (12 - x) = 12 × (x + 2)
8(12 - x ) = 12x + 24
96 - 8x = 12x + 24
72 = 20x
x = 3.6
Then the value of the variable x is 3.6 cm
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Two sets of data are each symmetrical and do not contain outliers. Which measures of center and
variability would be most effective to use when making comparisons between the two data sets?
A.
mean and MAD
B. mean and IQR
C. median and MAD
D. median and IQR
Answers
Solution:
As, two set of data are each symmetrical and do not contain outliers.
To find the center , the best way is to find Median of data set.Median of Data set is the mid value of Data that is center of Data.
As, you have to find variability , mean can't measure variability. Mean deviation would have been better option.
So, MAD=Median absolute Deviation , would be better tool to measure variability. Because it is Absolute difference between median and Each value of data set.
So, Option (C) median and MAD, would be best way to compare the two given data set.
write 8.31752 to correct 3 decimal places
Answers
Answer:
8.318
Step-by-step explanation:
writing a number in three decimal places means writing the number in a way that there will be three digits in the number after the decimal point.
to three decimal places= 8.318
2. f(x)=4x+1 and g(x)=x2−4x−5, find (g◦f)(4).
Answers
Answer:
(g · f)(4) = 45
Step-by-step explanation:
f(x)=4x+1
g(x)=x² - 4x- 5
(g · f)(x) = 4(x² - 5) + 1
(g · f)(4) = 4(4² - 5) + 1
Following pemdas
(g · f)(4) = 4(16 - 5) + 1
(g · f)(4) = 4(11) + 1
(g · f)(4) = 44 + 1
(g · f)(4) = 45
1. whats -3 x - 5 = 6
2. whats -4 ( y - 2 ) =12
show work
Answers
Answer:
x = -11/3 or 3.666y = -1Step-by-step explanation:
Given:
1) -3x -5 = 6
2)- 4 ( y - 2 ) =12
To Find:
Value of x for no. 1Value of y for no. 2Solved:
1)-3x -5 = 6
Transpose -5 from LHS to RHS
=> -3x = 6+5=> -3x = 11Transpose -3 from LHS to RHS
=> x = (11/-3)=> x = -11/3=> x = -3.6662) -4(y-2) = 12
Apply distributive property
=>(−4)(y)+(-4)(-2)=12=>-4y+8 = 12Transpose 8 to RHS
=> -4y = 12-8=> -4y =4Transpose -4 to RHS
=> y = 4/-4=> y = -1help for 10 points that is all i have
Answers
Answer:
22 in. and o.5 ft i think so
Please help me find the answer to this problem.
Answers
Answer:
numerator - is 2, 15, 18, 6
denominator - is 12, 14, 33, 8, 64
Step-by-step explanation:
2/10, 4/12, 8/14, 9/33, 1/8, 12/64, 15/55, 18/66, 6/32
Rewrite the radical expression as an exponential expression, and then simplify.
StartRoot 121 EndRoot = one-half (121) = 60.5
StartRoot 121 EndRoot = 121 squared = 14,641
StartRoot 121 EndRoot = 121 Superscript one-half Baseline = 11
StartRoot 121 EndRoot = 121 Superscript one-half Baseline = 60.5
Answers
The radical expression written as an exponent, and simplified, is given by:
[tex]\sqrt{121} = (121)^{\frac{1}{2}} = 11[/tex].
How to transform an exponent to a power?It happens according to the following rule:
[tex]a^{\frac{n}{m}} = \sqrt[m]{a^n}[/tex]
The inverse is also valid, hence, in this problem, the expression written as an exponent and simplified is given by:
[tex]\sqrt{121} = (121)^{\frac{1}{2}} = 11[/tex].
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please help i dont get it... (average rate of change)
10.
The graph shows the price, in dollars, of a new digital toy for different levels of supply.
(image provided)
What is the average rate of change?
Answers
Answer:
-3
Step-by-step explanation:
Formula for average rate of change :
A(x) = f(a) - f(b) / a - bSolving :
A(x) = 115 - 85 / 5 - 15A(x) = 30/-10A(x) = -3PLS HELP! What is the linear function rule for this table?
Answers
Answer:
f(x) = 4x + 6
Step-by-step explanation:
Using f(x) = 4x + 6
lets find some answers
lets take x as (-2)
f(-2) = 4(-2) + 6
f(-2) = -8 + 6
= -2
Also, take x as (-1)
f(-1) = 4(-1) + 6
f(-1) = -4 + 6
= 2
12 is 48 percent of what number?
Answers
Answer:
25
Step-by-step explanation:
12 x 100 = 1200
1200 / 48 = 25
