The figure shows secant GC and tangent GB intersecting to form an angle. Find x and y If necessary, round to the tenths place.
Answers
Let`s look at the triangle: Δ GBC. GB is a tangent.
29° + 90° + y = 180°
y = 180° - 90° - 29° = 61°
Then ∠ B = 30° : 2 = 15°
In a triangle ΔADC : ∠ A = 180° - ( 29° + 15° ) = 180° - 44° = 136°
x = 180° - 136° = 44°
Answer: x = 44°, y = 61°
The value of y, calculated using the difference between the intercepted arcs, is 69.5° when rounded to the tenths place.
The figure provided depicts a circle with a secant (line GC) and a tangent (line GB) intersecting at point G, forming an angle. There are several angle measures given in the figure: angle ECA is 30°, angle ADB is 58°, and angle EAB is 161°. The angles x° and y° are what we need to find.
Here's how to find x and y:
1. To find x:
- The angle formed by a tangent and a chord (GB and BA in this case) is equal to the angle in the alternate segment of the circle. Therefore, x is equal to the angle in the alternate segment, which is angle ADB (58°). So, x = 58°.
2. To find y:
- The angle formed by a tangent and a secant (GB and GC in this case) from the external point G is equal to the difference between the measure of the intercepted arc (the large arc EAC) and the measure of the adjacent arc (the small arc EC). This can be calculated by the formula [tex]\( y = \frac{1}{2}(\text{large arc} - \text{small arc}) \).[/tex]
- The large arc EAC is the full circle (360°) minus the small arc EBC (161°), so the measure of arc EAC is 360° - 161° = 199°.
- The small arc EC is twice the angle ECA (which is an inscribed angle) because the measure of an arc is twice the measure of an inscribed angle that subtends it. So, the measure of arc EC is 2 * 30° = 60°.
- Now we can calculate y using the formula: [tex]\( y = \frac{1}{2}(199 - 60) \).[/tex]
Let's calculate the exact values for x and y.
The value of x is equal to the angle ADB, which is 58°.
The value of y, calculated using the difference between the intercepted arcs, is 69.5° when rounded to the tenths place.
Therefore, [tex]\( x = 58 \) and \( y = 69.5 \).[/tex]
Related Questions
Type the correct answer in the box. Spell all words correctly, and use numerals instead of words for numbers. If necessary, use / for the fraction bar. Simplify the expression. tan(-x) cos(-x) =
Answers
Answer:
The correct simplification of the given expression [tex]tan(-x){\times}cos(-x)[/tex] is [tex]-sinx[/tex].
Step-by-step explanation:
The given expression is:
[tex]tan(-x){\times}cos(-x)[/tex]
Now, simplifying the above given expression, we get
=[tex]\frac{sin(-x)}{cos(-x)}{\times}cos(-x)[/tex] (because [tex]tanx=\frac{sinx}{cosx}}[/tex])
=[tex]sin(-x)[/tex]
Also, we know that [tex]sin({-\theta})=-sin{\theta}[/tex], tehrefore teh expression becomes
=[tex]-sinx[/tex]
Hence, the correct simplification of the given expression [tex]tan(-x){\times}cos(-x)[/tex] is [tex]-sinx[/tex].
Which ordered pairs make both inequalities true? Check all that apply.
(–2, 2)
(0, 0)
(1,1)
(1, 3)
(2, 2)
Answers
Answer:
the answers are c and e 1,1 and 2,2
Step-by-step explanation:
Answer:
(1,1) (2,2)
Step-by-step explanation:
Find the first five terms of the sequence described by the following recursive formula: an = an – 1 + an – 2 where a1 = 1.2 and a2 = 2.3
1.2, , , ,
Find the first six terms of the sequence described by the following recursive formula:
an = an – 1 + an – 2
where a3 = -5 and a4 = 3
,
,
,
,
,
Answers
If a1=1.2 and a2=2.3 and a(n)=a(n-1)+a(n-2)
a3=3.5, a4=5.8, a5=9.3
So the first five terms are: 1.2, 2.3, 3.5, 5.8, 9.3
The second is another modified Fibonacci sequence...
If a3=-5 and a4=3 then:
3=-5+a2, a2=8
-5=8+a1, a1=-13
a5=-5+3=-2
a6=-2+3=1
So the first six terms are -13, 8, -5, 3, -2, 1
The recursive formula an = an – 1 + an – 2 describes a sequence where each term is the sum of the two previous terms. To find the first five or six terms, we substitute the given initial conditions into the formula and repeatedly apply it to find subsequent terms.
Explanation:The recursive formula an = an – 1 + an – 2 describes a sequence where each term is the sum of the two previous terms. To find the first five terms, we begin with a1 = 1.2 and a2 = 2.3. Then we use the formula to find the next terms:
a3 = a2 + a1 = 2.3 + 1.2 = 3.5a4 = a3 + a2 = 3.5 + 2.3 = 5.8a5 = a4 + a3 = 5.8 + 3.5 = 9.3So the first five terms of the sequence are 1.2, 2.3, 3.5, 5.8, and 9.3.
Similarly, to find the first six terms of the sequence with a3 = -5 and a4 = 3, we use the formula:
a5 = a4 + a3 = 3 + (-5) = -2a6 = a5 + a4 = -2 + 3 = 1So the first six terms of this sequence are -5, 3, -2, 1, -1, and 0.
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The longest side of an acute triangle measures 30 inches. The two remaining sides are congruent, but their length is unknown.What is the smallest possible perimeter of the triangle, rounded to the nearest hundredth?
Answers
If the triangle is аcute then:
y² + y² > x²
2y² > 30²
2y² > 900
y² > 450
y > √450
y > 21.21 ← to the nearest hundredth
This means the length of each of the remaining sides is not less than 21.22 in (to the nearest hundredth), so the smallest possible perimeter of the triangle =
30 + 21.22 + 21.22 = 72.44 in.
You buy a commemorative coin for $110. Each year, t, the value V of the coin increases by 4%
Part a: Write a function that can be used to find the coin’s value after t years.
Part b: If the coin’s value continues to grow 4% per year, what will the approximate value be in 8 years? Round to two decimal places.
Answers
Exponential functions follow the form of y=ab^x, where a is the principal amount, b is the rate of growth or decay (1+0.04), and x is the time.
b. f(8)= 100*1.04^8
100*1.368569...
136.856
Final answer: $136.86
Answer:
$136.86
Step-by-step explanation:
A principal of $4700 is invested at 6% interest compounded annually. How much will the investment be worth after 12 years Use the calculator provided and round your answer to the nearest dollar.
Answers
What can you conclude about the slope of the values in the table? Check all that apply.
The slope is 3.
The slope is 0.
The slope is undefined.
The graph will be a horizontal line.
The graph will be a vertical line.
The graph will have a line with a positive slope.
Answers
The conclusion that can be drawn from the slope of the values given in the table is:
3. Slope is undefined.
5. Graph is a vertical line.
First, let's determine the value of the slope by applying the slope formula using two points given from the table, say, (1000, 20) and (1000, 23):Slope formula = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]
Let,[tex](1000, 20) = (x_1, y_1)\\\\(1000, 23) = (x_2, y_2)[/tex]
Substitute:[tex]slope(m)=\frac{23 - 20}{1,000 - 1,000}\\\\slope (m) =\frac{3}{0}[/tex] (undefined)
Zero cannot divide 3 hence, the slope is undefined.Slope that are vertical have rise but no run, thus, their slope is undefined.(see attachment for image showing an example of how an undefined slope looks like on a graph.)
Therefore, the conclusion that can be drawn from the slope of values given in the table is:
3. Slope is undefined.
5. Graph is a vertical line.
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What is the value of the 11th term of the sequence 1, -2, 4, -8, ...?
4,096
1,024
-2,048
-1,024
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1
-2
4
-8
16
-32
64
-128
256
-512
1024
The answer is 1024
If 3 times a certain number is increased by 4 the result is 28. What is the number?
If x is "the number," which of the following equations could be used to solve for the number?
c.3x + 4 = 28
b.3(x + 4) = 28
a.3x = 4 + 28
Answers
x = number
the equation to use is: 3x+4=28
3x+4=28
3x=24
x-24/3 =8
x=8
what divides an angle into two congruent angles
Answers
the question isssssssss
Answers
.5[tex] r^{2} [/tex] Θ = area of a sector
theta must be in radians not degrees though
Solve the equation by completing the square. Round to the nearest hundredth if necessary x^2+3x=25
Answers
Answer:
The solutions are: [tex]x= 3.72, -6.72[/tex]
Step-by-step explanation:
[tex]x^2+ 3x = 25\\ \\ x^2+3x+(\frac{3}{2})^2 = 25 +(\frac{3}{2})^2\\ \\ (x+\frac{3}{2})^2 = 25+\frac{9}{4}\\ \\ (x+\frac{3}{2})^2 =27.25\\ \\ \sqrt{(x+\frac{3}{2})^2} =\pm \sqrt{27.25} \\ \\ x+1.5= \pm \sqrt{27.25} \\ \\ x= -1.5 \pm \sqrt{27.25}\\ \\ x=-1.5+ \sqrt{27.25}=3.72015... \approx 3.72\\ \\ or\\ \\ x=-1.5-\sqrt{27.25} =-6.72015...\approx -6.72[/tex]
So, the solutions are: [tex]x= 3.72, -6.72[/tex]
Issac is standing 174 feet from the base of the South Carolina State House in Columbia. The angle formed by the ground and the line segment from his position to the top of the building is 46°. How tall is the SC State House? Round to the nearest foot.
Answers
Using the tangent function of trigonometry, the height of the South Carolina State House is calculated to be approximately 180.2 feet. When rounded, the building stands at an estimated 180 feet tall.
To calculate the height of the South Carolina State House, we can use trigonometry. Given that Issac is standing 174 feet from the base and the angle of elevation to the top of the building is 46°, we can use the tangent function to determine the height of the building. The tangent of an angle in a right triangle is the ratio of the opposite side (the height of the building in this case) to the adjacent side (the distance from Issac to the building).
Using the formula:
tangent (angle) = opposite/adjacent
The equation would be:
tangent (46°) = height of building / 174 feet
Solving for the height of the building:
height of building = 174 feet * tangent (46°)
Using a calculator with the tangent function:
height of building = 174 * 1.035530 (approx value of tangent (46°))
So:
height of building ≈ 180.2 feet
Rounded to the nearest foot, the height of the South Carolina State House is approximately 180 feet.
The length of a rectangle is 4 cm greater than its width. the perimeter is 32 cm. find the length of the rectangle. 12 cm 18 cm 10 cm 6 cm
Answers
Subtract 8 from both sides and you're left with 4x = 24.
Divide both sides by 4 to get the value of x which is 6.
6 + 4 = 10.
Convert 28.7251° to degrees, minutes, and seconds. Round to the nearest second.
Answers
28.7251 =
28 degrees
then take the decimal and multiply by 60 to get the minutes
so 0.7251 *60 = 43.506, use the whole number (43)
so now you have 28 degrees, 43 minutes
now take the remaining decimal ( 0.506) and multiply by 60
0.506*60= 30.36
when you have a decimal left over for the seconds, keep that as is.
so you now have 28 degrees, 43 minutes and 30.36 seconds
use ' for minutes and " for seconds
28 degrees 43' 30.36"
rounded to the nearest second would be 28 degrees 43 minutes and 30 seconds
help me please!! Find the measure of angle 2. Image attached
Answers
opposite angles = 180
180-49 = 131
angle 2 = 131 degrees
Graph y = log8^x and its inverse
Answers
Answer:
Third one will be correct.
Step-by-step explanation:
Given : y =[tex]log_{8}(x)[/tex].
To find : Graph and its inverse.
Solution : We have given that
y =[tex]log_{8}(x)[/tex].
For x - intercept , y =0.
y = 0
0 =[tex]log_{8}(x)[/tex].
x = 1
(1,0)
Inverse of y =[tex]log_{8}(x)[/tex].
Interchange the x and y.
x = [tex]log_{8}(y)[/tex].
Solving for y
y = [tex]8^{x}[/tex].
Then For x = 0
y = [tex]8^{0}[/tex].
y = 1
For inverse ( 0 ,1)
Then we can see from given graphs Third one will be correct.
Therefore, Third one will be correct.
The formula is used to find the area of a parallelogram. if the base of a parallelogram is doubled and its height is doubled, how does this affect the area?
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A equals two b × two h
A equals four bh
The area of a parallelogram would be quadrupled if the height and weight of it were doubled
(I had to write out certain words because my keyboard is not fully working)
Write the equation of a hyperbola with vertices (3, -1) and (3, -9) and co-vertices (-6. -5) and (12, -5).
Answers
the main formula of hyperbola is
(x-h)² / a² - (y-k)² / b² = 1, where the center is C (h,k)
and the vertex formmula is
(h+-a, k) and the covertex is (h, k+-b)
in our case vertices are already given:
(3, -1) and (3, -9) so h+a =3 or h - a =3 and k= -1, or k= -9
and co-vertices (-6. -5) and (12, -5)
h= -6 or h= 12, and k+ b=-5, or k- b = -5
for example h= -6, h+a =3, a=3+6=9, k= -1, k+ b=-5 , we can get b= - 5 + 1 = - 4, so a=9, b=-4, h=-6, k= -1
the equation is
(x+6)² / 81 - (y+1)² / 16 = 1, if the center is C(-6, -1)
the same method can be applied with the other choices of h and k.
How is the graph of y = 8x^2 − 1 different from the graph of y = 8x^2?
Answers
Answer:
1 up⊕⊕⊕⊕⊕⊕⊕⊕
Step-by-step explanation:
Which one of the binomials is a factor of this trinomial?
x^2-13x+40
A. x-8
B. x+8
C. x-4
D. x+4
Answers
(x-8)(x-5)
Proof:
-8-5=-13
-8*-5=40
Final answer: A
How many zeros are there at the end of 100!?
Answers
Final answer:
The number of zeros at the end of 100! is determined by counting the multiples of 5 in the factorization, including higher powers like 25. The result is a total of 24 zeros at the end of 100!.
Explanation:
To determine how many zeros are at the end of the factorial of 100 (100!), we need to know how many times the number 10 can be factored within that number. Since 10 is the product of 2 and 5, we should count the number of 2s and 5s in the prime factorization of 100!. The number of zeros at the end of 100! will equal the smaller of these two counts. However, because there are more 2s than 5s in the prime factorization, we only need to count the number of 5s as every 5 will have a corresponding 2 to form a 10.
For 100!, we count how many multiples of 5 there are within that range, including the multiples of 25 (since 25 includes an extra 5), and possibly higher powers of 5 if applicable. For example, 5 is counted once, 25 is counted twice (as 25 = 5×5), and so on.
Therefore, the number of zeros at the end of 100! equals the sum of the integer division of 100 by 5, plus the integer division of 100 by 25, and so on for any higher powers of 5. However, since 100 < 125, we do not need to consider any higher powers than 25.
We calculate:
100 ÷ 5 = 20,
100 ÷ 25 = 4.
Adding these together (20 + 4), we find that there are 24 zeros at the end of 100!.
The frequency table shows the results of a survey comparing weekly gasoline costs to the average number of miles a car can drive on a gallon of gasoline. Marcel converts the frequency table to a conditional relative frequency table by row. Which value should he use for Y? Round to the nearest hundredth. 0.19 0.45 0.82 0.90
Answers
In this case if you divide 27 by 30 you will get 0.9. Round that and you will get 0.90
Answer:
Its D on Ed2022
Step-by-step explanation:
A certain forest covers an area of 1800 km2. Suppose that each year this area decreases by 8.5%. What will the area be after 14 years? Use the calculator provided and round your answer to the nearest square kilometer.
Answers
[tex]519km^{2}[/tex] will be the area after [tex]14[/tex] years.
What is area?
Area is the quantity that expresses the extent of a region on the plane or on a curved surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object.
According to questions, a certain forest covers an area of [tex]1800[/tex] [tex]km^{2}[/tex]. Each year this area decreases by [tex]8.5[/tex]%.
We have to find the area after 14 years.
Area after 14 years can be found using the below formula
[tex]A=I(1-r)^{t}[/tex]
[tex]=1800(1-0.085)^{14}[/tex]
[tex]=1800[/tex]×[tex]0.288[/tex]
[tex]=519km^{2}[/tex]
Hence, [tex]519km^{2}[/tex] will be the area after [tex]14[/tex] years.
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The value of a camcorder bought new for $2000 decreases 20% each year. Identify the function for the value of the camcorder. Does the function represent growth or decay?
A) V(t) = 2000(0.8)t; growth
B) V(t) = 2000(0.8)t; decay
C) V(t) = 2000(1.2)t; decay
D) V(t) = 2000(1.2)t; growth
Answers
20% decrease = (0.8)t
Answer: V(t) = 2000(0.8)t; decay
Step-by-step explanation:
HELP ROUND 87671.5613658 TO THE NEAREST THOUSAND
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What is best definition of combining like terms
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a restaurant offers 3 kinds of bread 4 kinds of meat and 3 kinds of cheese
Answers
Answer:
36 combos
Step-by-step explanation:
Plz vote me for Brainilest
Use the graph below to fill in the blank with the correct number:
f(−2) = _______
Numerical Answers Expected!
Answer for Blank 1:
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Triangle PIG was rotated to create triangle P'I'G'. Describe the transformation using details and degrees.
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I hope this helped. Let me know if I was correct please.