Easy math problem, please help.
O is the center of the circle. Assume that lines appear to be tangent are tangent. What is the value of x?
A. 34
B. 36.5
C. 73
D. 107
Answers
Answer:
Option C. 73
Step-by-step explanation:
In the given figure Δ OPQ is the right angle triangle because radius is always perpendicular to the tangent drawn on the circle from an external point.
Here OQ is radius and PO is tangent.
So ∠OQP = 90°
Now sum of all angles of a triangle is 180°
Therefore, ∠OPQ + ∠OQP + ∠POQ = 180°
17° + 90° + x° = 180°
107 + x = 180
x = 180 - 107
x = 73°
Option C. 73
Related Questions
PLEASE HELP :( i'm stuck
What are the amplitude and midline?
Amplitude: 1; midline: y = 1
Amplitude: 0; midline: y = 0
Amplitude: 2; midline: y = 1
Amplitude: 2; midline: y = 0
Answers
Answer:
Amplitude: 1; midline: y = 1
Step-by-step explanation:
From the graph we can conclude that it is a sine or cosine function. In their standard form, these functions are given by the following equations:
[tex]y(t)=Acos(\omega t +\phi)\\\\or\\\\y(t)=Asin(\omega t+ \phi)[/tex]
Where:
[tex]A=Amplitude=\frac{|A_m_i_n-A_m_a_x|}{2}\\\omega=Angular\hspace{3}frequency\\\phi=Initial \hspace{3}phase[/tex]
And:
[tex]A_m_a_x=Maximum\hspace{3}amplitude\\A_m_i_n=Minimum\hspace{3}amplitude[/tex]
On the other hand, we can define the midline of these kind of functions as the halfway between the maximum and minimum amplitude of the function, Therefore:
[tex]Midline=M_l=\frac{A_m_a_x+A_m_i_n}{2}[/tex]
From the graph you can see that the maximum value of the function(maximum amplitude) is 2 and the minimum value of the function (minimum amplitude) is 0, thus:
[tex]A=\frac{|A_m_i_n-A_m_a_x|}{2} =\frac{|0-2|}{2} =\frac{|-2|}{2} =\frac{2}{2} =1[/tex]
And:
[tex]M_l=\frac{A_m_a_x+A_m_i_n}{2}=\frac{2+0}{2} =\frac{2}{2} =1[/tex]
what is the complete factorization of the polynomial below
x^3-4x^2+x-4?
A. (x-4)(x+i)(x-1)
B. (x+4)(x+i)(x-i)
C. (x+4)(x-i)(x-i)
D. (x-4)(x-i)(x-i)
Answers
Answer:
B. (x+4)(x+i)(x-i)
Step-by-step explanation:
Let [tex]P(x)=x^3-4x^2+x-4[/tex]
We can factor this polynomial by grouping:
[tex]P(x)=x^2(x-4)+1(x-4)[/tex]
We factor further to obtain:
[tex]P(x)=(x^2+1)(x-4)[/tex]
[tex]P(x)=(x^2-\sqrt{-1}^2)(x-4)[/tex]
We apply difference of two squares to get:
[tex]P(x)=(x-i)(x+i)(x-4)[/tex]
Answer:
(x+1)(x-1)(x+4)
Step-by-step explanation:
For a recent project, a teacher purchased 250 pieces of red construction paper and 114 pieces of blue construction paper. what is the ratio of red to blue? select one:
a. 57:125
b. 125:57
c. 125:182
d. 182:125
Answers
Which of the following has 8.012 in written form?A.eight and twelve hundredthsB.eight and twelve thousandthsC.eight and twelve thousandsD.none of the above
Answers
Determine if the graph is symmetric about the x-axis, the y-axis, or the origin.
r = 5 + 4 cos θ
Answers
Explaining how to determine the symmetry of a polar graph based on the given equation r = 5 + 4 cos θ.
To determine the symmetry of the graph r = 5 + 4 cos θ, we can substitute (-θ) for θ in the equation and check if the resulting polar equation remains the same, indicating symmetry about the origin.
If replacing (-θ) gives us the same equation, the graph is symmetric about the y-axis. If replacing (π - θ) gives the same equation, then the graph is symmetric about the x-axis.
In this case, replacing (-θ) in r = 5 + 4 cos θ gives r = 5 + 4 cos(-θ), which simplifies to r = 5 + 4 cos θ, indicating symmetry about the y-axis.
It costs $5.75 to enter an arcade and $0.50 to play an arcade game. You have $7.25. Write an equation that represents the number g of games you can play.
Answers
Hope that helps
About 11 games
Please help with geometry
Answers
[tex]\pi . {12}^{2} . \dfrac{300}{360} + {12}^{2} \dfrac{ \sqrt{3} }{4} \\ {12}^{2} ( \dfrac{5.\pi}{6} + \dfrac{ \sqrt{3} }{4} ) \\( 120\pi + 36 \sqrt{3} ) {cm}^{2} [/tex]
[tex]\dfrac{60^o}{360^o}=\dfrac{1}{6}[/tex]
The sector is 1/6 of the circle, therefore the area of the sector is 1/6 of area of the circle.
The formula of an area of the circle: [tex]A_O=\pi r^2[/tex]
The area of the sector:
[tex]A_s=\dfrac{1}{6}\cdot\pi\cdot12^2=\dfrac{1}{6}\pi\cdot144=24\pi\ m^2[/tex]
The formula of an area of the equilateral triangle: [tex]A_\Delta=\dfrac{a^2\sqrt3}{4}[/tex]
[tex]A_\Delta=\dfrac{12^2\sqrt3}{4}=\dfrac{144\sqrt3}{4}=36\sqrt3\ m^2[/tex]
The area of the segment: [tex]A_{sg}=A_s-A_\Delta\to A_{sg}=(24\pi-36\sqrt3)m^2[/tex]
The area of the shaded region:
[tex]A=A_O-A_{sg}\to A=144\pi-(24\pi-36\sqrt3)=144\pi-24\pi+36\sqrt3\\\\=\boxed{A=(120\pi+36\sqrt3)m^2}[/tex]
2,400 principal earning 2%, compounded annually, after 7 years. Find the balance in the account
Answers
P = 2400
r = .02
n = 1
t = 7
Answer: $2756.86
The balance in the account after 7 years will be approximately $2,747.70.
How did we get the value?To calculate the balance in the account after 7 years with a principal of $2,400 earning 2% interest compounded annually, you can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future balance
P = the principal amount ($2,400)
r = the annual interest rate (2% or 0.02 as a decimal)
n = the number of times the interest is compounded per year (annually, so n = 1)
t = the number of years (7 years)
Plug these values into the formula:
A = 2400(1 + 0.02/1)^(1*7)
A = 2400(1 + 0.02)⁷
A = 2400(1.02)⁷
A = 2400(1.144877)
A ≈ $2,747.70
So, the balance in the account after 7 years will be approximately $2,747.70.
learn more about interest compounded: https://brainly.com/question/3989769
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An earthquake strikes and an isolated area is without food or water. three crews arrive. one can dispense needed supplies in 4545 hours, a second in 9090 hours, and a third in 6060 hours. how long will it take all three crews working together to dispense food and water?
Answers
1 person takes 20h, the second would hake 30h, third 60h.
1/20+1/30+1/60=1/10
Can somone help me with this 1 problem? QRST is a parallelogram. Determine the measure of ∠Q
Q (4x+10) bottom left
R (9x+1) top left
S (5x-3) top right
T bottom left
Answers
In a rhombus, opposite angles are congruent based on the alternate interior angle theorem. In other words, R and T along with Q and S are both alternate interior angle pairs.
(You can actually test this by printing out a rhombus, cutting out the angles, and matching up the opposite ones.)
We know that Q is equal to 4x + 10, but we need to solve for x. Since Q and S are congruent, we can set them equal to each other:
1) 4x + 10 = 5x - 3
2) 4x + 13 = 5x
3) 5x = 4x + 13
4) x = 13
Now let's plug 13 in for Q:
5) 4(13) + 10 = 52+10 = 62
I got m<Q = 62 degrees. Hope this helps!
In the parallelogram QRST then measure of ∠Q is 62 degrees.
What is Quadrilateral?A quadrilateral is a four-sided polygon, having four edges and four corners.
Given that QRST is a parallelogram.
We have to find the measure of ∠Q.
Both pairs of opposite sides are parallel, quadrilateral QRST is a parallelogram.
∠Q= ∠S
4x+10=5x-3
We have to find the value of to find ∠Q measure.
10+3=5x-4x
13=x
Now let us plug in the value of x in ∠Q measure.
∠Q = 4x+10
Now plug in x value in ∠Q
∠Q = 4(13)+10
=52+10
=62 degrees
Hence, in the parallelogram QRST then measure of ∠Q is 62 degrees.
To learn more on Quadrilateral click:
https://brainly.com/question/29934440
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Please help!!! Mark is learning to snowboard. The club charges $10 per hour for snowboard lessons and $40 for the lift ticket and a snowboard rental. Which value represents the rate of change for this scenario?
Answers
10h + 40
(40 represents, well $40)
Use logarithms to solve each equation
2x 9/8=111
A. 18.9561
B.25.8961
C. 10.2587
D. 35.5208
Answers
[tex]2x^{\frac{9}{8}} = 111[/tex]
and we need to find the value of x.
First of all, we multiply the whole equation for 1/2, so our goal is to isolate x, therefore:
[tex]x^{\frac{9}{8}}=\frac{111}{2}[/tex]
Next step we must do is to apply logarithms:
[tex]logx^{\frac{9}{8}} = log(\frac{111}{2})[/tex]
Next, we have to apply identities and then to solve the equation:
[tex] \frac{9}{8}logx = log(\frac{111}{2})[/tex]
[tex]logx = \frac{8}{9}log(\frac{111}{2})[/tex]
[tex]logx = 1.5504[/tex]
[tex]10^{logx} = 10^{1.5504}[/tex]
Finally, we have the value of x which was our goal. This is the answer for the question above:
[tex]x= 35.5140[/tex]
The answer is D.
40 points!!!!!!!!!!!!!! *If one of the legs of a right triangle is 4 in and the hypotenuse is 8 in, find the length of the other leg (use a calculator if necessary). Can you guess the measures of the acute angles?
Answers
the ratio of the sides of the triangle = 8 : 4 :4 sqrt3 = 2:1:sqrt3 so this is a
30-60-90 degree triangle
Ginger makes pies and sells them for $14 each. Write an equation that represents the situation, if y represents the money that Ginger earns and x represents the number of pies sold.
Answers
What are the similarities and differences between these data sets in terms of their centers and their variability?
Data Set A: 14, 21, 24, 28, 28, 35
Data Set B: 18, 19, 21, 25, 29, 32
Select from the drop-down menus to correctly complete the statements.
Comparing the centers of the data sets, the median for Data Set A is (less than, greater than, equal to) the median for Data Set B. The mean for Data Set A is (less than, greater than, equal to) the mean for Data Set B.
Answers
the mean for data A is greater.
Answer:
a
Step-by-step explanation:
How many solutions does 15x+11=8x
Answers
How many solutions does 15x + 11 = 8x
Answer: 1 solution
-------------------------------------------------------------------------------------------------------
Explanation:
To solve this, we must isolate the x.
15x + 11 = 8x
We will subtract 15x from each side to isolate the x.
15x + 11 = 8x
- 15x -15x
11 = -7x
Finally, we must simplify this by dividing each side by -7
11 = -7x
--- ----
-7 -7
Our answer is: -11/7 = x
Ths means that this equation only has one solution.
I hope I helped!
Let me know if you need anything else!
~ Zoe
To get the number of solutions that the equation is giving, we are going to need to solve the equation. Here’s how to find the solution...
15x+11= 8x
If we collect it sorta like terms we are going to get:
11=8x-15x
11=-7x dividing both of the sides by -7 we get:
x=-7/11
The number of solutions you have is 1. So your answer would be one.
points J and K lie on the same line, as shown on the coordinate plane below. What is the slope of the line passing through points J and K?
Answers
The slope is given by the formula
m = (y₂-y₁)/(x₂-x₁)
Using our two points, we have
m = (5-3.5)/(6-3) = 1.5/3 = 0.5 = 1/2
Sina played basketball on a rectangular court that was 74 feet by 42 feet. after the game, she walked across the court diagonally from one corner to the opposite corner. approximately what distance did sina walk in feet?
Answers
Distance walked = 85.088 feet
The distance Sina walked would be equal to the length of the diagonal of rectangle.
As every angle in a rectangle is 90 degree. So, we can apply Pythagoras theorem in right triangle formed by sides,
Base- 74 feet, Altitude- 42 feet and Hypotenuse- Diagonal
Base^2 + Altitude ^ 2 = Hypotenuse ^2
74^2 + 42 ^ 2 = Diagonal ^2
On solving,
Diagonal = 85.088 feet
To calculate the distance Sina walked diagonally across the basketball court, we utilize the Pythagorean theorem using the court's length and width. The calculation gives us a diagonal distance of approximately 85 feet.
To calculate the distance Sina walked across the rectangular basketball court diagonally, we can use the Pythagorean theorem. This theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. Since the court is 74 feet long and 42 feet wide, these dimensions can be considered the two shorter sides of a right triangle, with the diagonal Sina walked being the hypotenuse.
The Pythagorean theorem formula is:
[tex]c^2 = a^2 + b^2[/tex]
Where c is the length of the hypotenuse, and a and b are the lengths of the other two sides. Substituting the known values:
[tex]c^2 = 742 + 422\\c^2 = 5476 + 1764\\c^2 = 7240[/tex]
To find c, we take the square root of 7240:
c ≈ 85.09 feet
Therefore, Sina walked approximately 85 feet diagonally across the basketball court.
Use the graph below to answer the question that follows:
cosine graph with points at 0, negative 1 and pi over 3, 0 and pi, 3 and 5 pi over 3, 0 and 2 pi, negative 1
What are the amplitude, period, and midline of the function?
Amplitude: 4; period: π; midline: y = 2
Amplitude: 2; period: 2π; midline: y = 1
Amplitude: 4; period: 2π; midline: y = 1
Amplitude: 2; period: π; midline: y = 2
Answers
A = (l-1l + 3) / 2
A = 4/2
A = 2
The middle line is given by:
y = 1
The period of the function is given by:
T = l x2 - x1 l
T = l 0 - 2pi l
T = l - 2pi l
T = 2pi
Answer:
Amplitude: 2; period: 2π; midline: y = 1
Answer:
For this case the amplitude is given by:
A = (l-1l + 3) / 2
A = 4/2
A = 2
The middle line is given by:
y = 1
The period of the function is given by:
T = l x2 - x1 l
T = l 0 - 2pi l
T = l - 2pi l
T = 2pi
Answer:
Amplitude: 2; period: 2π; midline: y = 1
Step-by-step explanation:
what is the fifth term of the arithmetic sequence 7,3,-1....
Answers
In ΔPQR, what is sin Q written as a decimal?
Answers
sin Q = 9/15
sin Q = 0.6
The sine of an angle is opposite over hypotenuse. Looking at angle Q, we know the opposite side is 9 and the hypotenuse is 15. These numbers give us this equation: sin Q = 9/15. Upon solving this equation, the result is approximately 56.5.
Hope this helps!! :)
If there's anything else that I can help you with, please let me know!
The mass of a grain of sand is about 10^-3 gram. About how many grains of sand are in a 10kg bag of sand?
Answers
Divide the mass of the bag by the mass of sand. First you need to convert kg to g
About how many grains of sand are in the bag of sand
Answer
10 kg* (1000 g/ 1 kg)* (1 grain of sand/ 10^(-3) g)= 10^7 grains of sand.
(Note that the units cancel out so you get the answer)
The final answer is 10^7 grains of sand.
Hope this helps~
PLEASE HELP 20 POINTS
Answers
A sample of Bromine-82 begins at 80 mL. We are given that this value will decrease by half of its current amount every 35 hours. First, we'll determine the number of times that 35 goes into 140. This will reveal the number of times we should divide the sample by 2:
140 ÷ 35 = 4
We have now proven that there are 4 periods of 35 hours in 140 hours. This means that we will divide the sample in half a total of 4 times, as follows:
1. 80 ÷ 2 = 40
2. 40 ÷ 2 = 20
3. 20 ÷ 2 = 10
4. 10 ÷ 2 = 5
We have now proven that an 80 mL sample of Bromine-82 will be reduced to only 5 mL after 140 hours. Therefore, the correct answer is 5 mL.
I hope this helps!
[tex]A = P( \frac{1}{2} )^{\frac{t}{h} } [/tex]
This is what it looks like with the values from this scenario plugged in:
[tex]A = 80( \frac{1}{2} )^{\frac{140}{35} } \\ A = 5[/tex]
There are 5 mL of the 80 mL Bromine sample left after 140 hours.
Find the number if the square root of another number that is 6 greater than this number is equal to the number itself.
Answers
Answer:
The number is 3 and the another number is 9
Step-by-step explanation:
Let
x-------> the number
y-----> another number
we know that
[tex]y=x+6[/tex] ----> equation A
[tex]\sqrt{y}=x[/tex] ----> equation B
Substitute equation A in equation B
[tex]\sqrt{x+6}=x[/tex]
squared both sides
[tex]x+6=x^{2} \\x^{2}-x-6=0[/tex]
Using a graphing tool
solve the quadratic equation
see the attached figure
The solution is x=3
Find the value of y
[tex]y=x+6[/tex] -------> [tex]y=3+6=9[/tex]
Jamal is 167 cm tall. Which expression finds Jamal’s height in dekameters? Use the metric table to help answer the question.
Answers
1 cm is equal to -----------> 0.001 dekameters
so
167 cm------------------> X
x=167*0.001------> x=0.167 dekameters
Expression to finds Jamal’s height in dekameters
[Jamal’s height in cm]*0.001 or [Jamal’s height in cm]/1000
Answer:
It is D
Step-by-step explanation:
In a factory, a parabolic mirror to be used in a searchlight was placed on the floor. It measured 40 cm tall and 90 cm wide. Find an equation of the parabola with its vertex at the origin.
Answers
point on the parabola:(45,40)
equation:
45^2=4p(40)
4p=45^2/40=40.625
thus
x^2=(50.625)y
Answer: x^2=(50.625)y
What's the probability a number is odd given that it's an integer between 0 and 11?
Answers
sample space=s={1,2,3....,10}=total 10 numbers
So,
m=total no. of odd numbers{1,3,5,7,9} in our sample space=5 numbers
probability that number is odd=p=m/s
p=5/10=0.5
What is the equivalent decimal? Drag the answer into the box to match the fraction. 5/45
Answers
what you do is divide 5 into 45 to make it a decimal
How many radii does a circle have? Explain.
Answers
as there are infinite points on a circle
therefore there are infinite number of radii and hence there is no fixed number.
Answer:
one because the distance stay the same and infinite because the are infinite positions that the radii could be in
Step-by-step explanation:
y varies directly as x and y = 18 when x= 1/2. write an equation that relates y and x