As tangents from a single point to the circle are equal in measure
AC=BCABC is isosceles
<A=60°
We know the radius hits any tangent on right angles
So
<PAC=90°<PAD=90-60=30°Now
cosØ=Base/Hypotenusecos30=6/x√3/2=6/x√3x=12x=12/√3accurate value
x=6.9Answer:
[tex]x=4\sqrt{3}[/tex]
Step-by-step explanation:
If two tangents to a circle meet at one exterior point, the tangent segments are congruent. Therefore, AC = BC
This means that ΔABC is an isosceles triangle and so
∠ABC = ∠BAC = 60°
The tangent of a circle is always perpendicular to the radius.
Therefore, ∠PAC = 90°
With this information, we can calculate ∠PAD:
⇒ ∠PAD + ∠BAC = ∠PAC
⇒ ∠PAD + 60° = 90°
⇒ ∠PAD = 90° - 60°
⇒ ∠PAD = 30°
We now have a side length and an angle of ΔPAD (shown in orange on the attached diagram). So using the cos trig ratio, we can calculate [tex]x[/tex]:
[tex]\sf \cos(\theta)=\dfrac{A}{H}[/tex]
where:
[tex]\theta[/tex] is the angleA is the side adjacent the angleH is the hypotenuse (the side opposite the right angle)Given:
[tex]\theta[/tex] = ∠PAD = 30°A = AD = 6H = AP = [tex]x[/tex][tex]\implies \cos(30^{\circ})=\dfrac{6}{x}[/tex]
[tex]\implies x=\dfrac{6}{\cos(30^{\circ})}[/tex]
[tex]\implies x=\dfrac{6}{\frac{\sqrt{3}}{2}}[/tex]
[tex]\implies x=4\sqrt{3}[/tex]
Giving Brainiest help me pleasee tyyy <3
Answer:
252 in^3
Step-by-step explanation:
Multiply all 12 x 7 x 3 = 84 x 3 = 252 in^3.
Hope this helps!
PLEASE HELP, I NEED THE ANSWER BEFORE 3 HOURS 1. In the fraction the 11 represents the? a. Dividend b. Divisor c. Denominator 2. In the decimal number 125.795 the 9 represents the d. Quotient e. Both B & C place.
Answer:
e. Both B & ChundredthsStep-by-step explanation:
Q1
In the fraction 5/11, 11 represents the divisor and the denominator.The correct option is eQ2
In the number 125.795, the 9 represents the hundredths placeAnswer:mbvcdhfguh
Step-by-step explanation:kvghjve5yr
Nick has a rope that is 3 1/4 yards long. He cuts off a piece of the rope so that it is now 5/9 as long as the original rope? What is the length of his rope now?
The length of the rope remaining after Nick cut off a piece of the rope is 1 29/36 yards
How to solve fractionsTotal length of Nick's rope = 3 1/4 yardsLength remaining = 5/9 of original length
5/9 of 3 1/4
= 5/9 × 13/4
= 65/36
= 1 29/36 yards
Therefore, the length of the rope remaining after Nick ncur off a piece of the rope is 1 29/36 yards
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Verify each trigonometric identity
Answer:
hope it helps you.......
How much is 30 pounds if the price per pound is 3.50.
B. If one of the data points at 15 were moved to 10, how could you change another data
point to keep the mean the same?
Answer:
Below.
Step-by-step explanation:
You have a data point 5 to the left.
So you would move another data point 5 units to the right - like for example 14 to 19.
I need help finding the value of x which is the base of a triangle.
Answer:
sqrt(13)
Step-by-step explanation:
The entire base is 4, so 1/2 of the base is 2
We can use the pythagorean theorem
a^2 = b^2 = c^2
2^2 + 3^2 = x^2
4+9 = x^2
13 = x^2
Taking the square root of each side
sqrt(13) = x
Check the picture below.
Watch help video
ruby was out at a restaurant for dinner when the bill came. her dinner came to $27.
after adding in a tip, before tax, she paid $34.29. find the percent tip.
Answer:
I think it's 21.26%
Step-by-step explanation:
tip: 34.29-27=7.29$
the percent tip: (7.29×100)/34.29=21.26 (approximately)
what is the height of a lamp whose two radii are 20 cm and 30 cm and slant height is 40 cm?
Answer:
38.73 cm
Step-by-step explanation:
Given:
R = 30 X = 20 S = 40Solution:
S² = (R - r)^2xh^2
(40)^2=(30-20)^2+h^2
1600=(10)^2+h^2
1600-100=h^2
h=√1500
h=10√15
h=38.73 (rounded to the nearest tenth)
f(t)=t^2-3t
g(t)=2t+1
find f(g(t))
Answer:
[tex]f (2t + 1) = 4t^{2} - 2t - 2[/tex]
can you guys please help me on this question
Answer:
2.44 units
Explanation:
[tex]\sf Arc \ Length = \dfrac{\theta}{360} * 2\pi r[/tex]
Here given:
∅ = 40°radius = 3.5Solve for AB:
[tex]\rightarrow \sf \dfrac{40}{360} *2(3.14)(3.5)[/tex]
[tex]\rightarrow \sf 2.4422...[/tex]
[tex]\rightarrow \sf 2.44 \quad (rounded \ to \ two \ decimal \ places)[/tex]
The volume of this rectangular prism is 122,264 cubic millimeters. What is the value of z? (will mark brainliest)
Answer:
z = 58 mm
Step-by-step explanation:
Volume of the rectangular prism :
Volume = length x breadth x heightSolving :
122,264 = 62 x z x 34122,264 = 2,108 x zz = 122,264/2,108z = 58 mmAnswer:
z = 58 mm
Step-by-step explanation:
Volume of a rectangular prism: length × width × height
V = L×W×H
v = 122,264 mm³l = 62 mmw = z mmh = 34 mmSubstitute the values above and solve for z:
122,264 = 62 × z × 34
122,264 = 2108z
122,264/2108 = 2108z/2108
58 = z
Final answer: 58 mm
Hope this helps!
How do I solve this!! Quick and urgent (23. Is the number for the equation)
Answer:
Independent: Time
Dependent: Views
Step-by-step explanation:
Independent variables are the things that are purposefully altered.
Dependent variables are the things that change in response to the independent variables being changed.
As the hours increase, so do the views. The views will change as time goes by. A change in the number of views does not affect the time passed. Therefore, time is the independent variable and the number of views is the dependent variable.
In a class of 25 students, 6 are female and 8 have an A in the class. There are 13
students who are male and do not have an A in the class. What is the probability that
a student chosen randomly from the class is a male who does not have an A?
The probability that a student chosen randomly from the class is a male who does not have an A is 0.52
How to determine the probability?The given parameters are:
Students = 25Female = 6Students with A = 8Male students without A = 13The probability that a student chosen randomly from the class is a male who does not have an A is calculated as:
P = 13/25
Evaluate
P = 0.52
Hence, the probability is 0.52
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an investment made in the stock market decreased at a rate of 1.2% per year for 25 years. what is the current value of the 100,000 dollar investment?
Answer:
73947.52
Step-by-step explanation:
the equation would be 100000 * (0.988)^25
since time is 25 years, and rate is 0.988, since we are decreasing by 0.012.
What is the volume, in cubic meters, of a rectangular prism with a height of 14 meters, a width of 12 meters, and a length of 2 meters?
Answer:
The volume of a rectangular prism with a height of 14 m, a width of 12 m, and a length of 2 m is equal to 336 m³.
General Formulas and Concepts:
Geometry
Volume Formula [Rectangular Prism]:
[tex]\displaystyle V = lwh[/tex]
Step-by-step explanation:
Step 1: Define
Identify given variables.
h = 14 m
w = 12 m
l = 2 m
Step 2: Find Volume
[Volume Formula - Rectangular Prism] Substitute in variables:∴ the volume of the rectangular prism with the given dimensions is equal to 336 cm³.
___
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___
Topic: Geometry
Complete the equation describing how x
and y are related
Answer:
y = x + -5
Step-by-step explanation:
Solution
To complete the equation, let's take two different points and plug their x- and y-coordinates into the equation. Then, we can solve for the question mark and see if we get the same number. I'll take (1, -4) and (2, -3):
(1, -4):
-4 = 1 + b-4 - 1 = 1 + b - 1b = -5(2, -3):
-3 = 2 + b-3 - 2 = 2 + b - 2b = -5Thus, the equation is y = x + (-5).
Can someone give me a simple explanation on how to simplify radicals.
Answer:
Step 1: Determine the prime factors of the number under the root. Step 2: Write the prime factors in groups. Step 3: Simplify any multiplication and exponents. Step 4: Simplify the radical until no further simplification can be done.
Step-by-step Have explanation:
a great day
A 30cm ruler sometimes measures inches on the other side.
How many feet are approximately same as 30cm ?
1inch = 2.5cm
1foot = 12inches
1inch = 2.5cm
∆ 30cm
1inch x 30cm \2.5cm =?5cm =2inch
so 30cm=12inchWhich statements are true? select three options. p(f|c) = 0.75 p(c|f) = 0.25 p(c∩f) = 0.09 p(c∩f) = p(f∩c) p(c|f) = p(f|c)
The true statements are:
p(f|c) = 0.75p(c∩f) = 0.09 p(c|f) = p(f|c)What are the true statements?In sets notation, the symbol, ∩ means the intersection of two groups. Here, it represents the number of people who are football fans and fans of car racing. This number is 9%.
Here is the complete question:
A survey finds that 48% of people identify themselves as fans of professional football, 12% as fans of car racing, and 9% as fans of both professional football and car racing. Let event F be choosing a person who is a fan of professional football and let event C be choosing a person who is a fan of car racing.
Which statements are true? Select three options.
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The figure below is rotated 180° clockwise. What are the coordinates of the image of point A after this transformation?
Answer:
(-2, -1)
Step-by-step explanation:
The easiest way to approach this problem is to think of each quadrant as being 90 degrees. As you can see, each quadrant has a 90 degree angle.
If we were to move 2 quadrants (or 180 degrees) clockwise, we would end up in the third quadrant (- , -)
Because we are moving clockwise on the graph, the shape would also turn clockwise. 180 degrees is the halfway point, so the shape will appear to be upside down.
If you're a visual learner, I'd recommend finding a website with an online graph (something like desmos or geogebra) that would allow you to actually graph the points and change their position with commands.
Hope this helps :)
Find the area of the triangle. area triangle 4
Answer:
12
Step-by-step explanation:
because when u plus 4+4+4 it's 12
PLEASE HELP WILL MARK BRAINLIEST
8-10
Answer:
[8] Area is = to 1017.36 Circumference is = to 113.04
[9] Area is = 490.625 Circumference is = 78.5
[10] D = 16 R = 8
Step-by-step explanation:
[8]
Area is = to 1017.36
Circumference is = to 113.04
Formula:
Area = πr²
Circumference = 2πr
Solve:
A = πr²
A = 3.14(18) ²
A = 3.14(324)
A = 1017.36
C= 2πr
C = 2(3.14)(18)
C = 113.04
⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻
Area = 490.625
Circumference is = 78.5
Formula:
Area = πr²
Circumference = 2πr
Solve:
Area = πr²
A = 3.14(12.5)²
A = 3.14(156.25)
A = 490.625
Circumference = 2πr
C = 2(3.14)(12.5)
C = 78.5
⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻
[10]
Circle area = π * r² = π * 64 [cm²] ≈ 201.06 [cm²]
π ≈ 3.14159265 ≈ 3.14
d = r * 2 = 8 [cm] * 2 = 16 [cm]
Hence,
D = 16
R = 8
⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻
Kavinsky
Which describes the process of finding the volume of a cylinder? (Help ASAP)
Using two or more complete sentences, describe how to find the general rule for the geometric sequence with a4=3 and a6=3/16. In your final answer, include all of your calculations.
The steps for the geometry sequence with the help of two terms of the sequence, make a system of equation and solve them to find common ratio and first term.
What is geometric sequence?
Geometric sequence is the sequence in which the next term is obtained by multiplying the previous term with the same number for the whole series.
It can be given as,
[tex]a_n=a_1r^{n-1}[/tex]
Here, a₁ is the first term of the sequence and r is the common ratio.
The fourth term and sixth term given in for the geometric sequence are 3 and 3/16. For the fourth term,
[tex]a_4=a_1r^{4-1}\\3=a_1r^3[/tex] ...1
For the sixth term,
[tex]a_6=a_1r^{6-1}\\\dfrac{3}{16}=a_1r^5[/tex] ....2
On solving, we get, a₁=192 and r=1/4. Thus, the geometric sequence can be given as,
[tex]a_n=a_1r^{n-1}\\a_n=192\times\dfrac{1}{4}^{n-1}[/tex]
Hence, the steps for the geometry sequence with the help of two terms of the sequence, make a system of equation and solve them to find common ratio and first term.
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6 of 6
An equilateral triangle with side length 17 cm is shown in the
diagram, work out the area of the triangle.
Give your answer rounded to 1 DP.
The diagram is not drawn accurately.
cm²
Answer:
125.1 cm^2 to 1 D.P.
Step-by-step explanation:
We could use Heron's formula to do this
Area = √(s(s-a)(s-b)(s-c) ) where s is the semi-perimeter and a b and c are the lengths of the 3 sides
So we have:
s = (17+17+17) / 2 = 25.5
and Area = √(25.5)(25.5 - 17)^3)
= √15660.1875
= 125.14 cm^2
hello im having a hard time solving part b can anyone help me?
If you know BN and AN, then you can use the fact that ∆ AQB and ∆ ABN are similar. which gives the relation
BN/BQ = AN/AB = AB/AQ
Now
AN/AB = AB/AQ ⇒ AQ = AB²/AN = 36/AN
and
BN/BQ = AN/AB ⇒ BQ = (BN • AB)/AN = 6 • BN/AN
where AB = 6 because it's the diameter of the circle, and C(O, 3) means the circle has center O and radius 3.
help me pls!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
d. 0.771.
Step-by-step explanation:
This probability is equal to the area other than the green triangle divided by the total area of backyard.
Total area = 120^2 = 14400
Area of green triangle = 1/2 * 120 * 55 = 3300
So area of the part of yard not covered by the triangle = 14400 - 3300
and the required probability = (14400 - 3300) / 14400
= 0.771.
Answer:
d. 0.771
Step-by-step explanation:
What is probability?
Probability is the likelihood of the occurrence of something.
In simpler terms we can say probability = # of favorable outcomes / total # of outcomes.
Understanding the question
Here we have a square and a triangle inside of the square and we want to find the probability that a tennis ball thrown inside of the square will not land inside of the triangle.
So we have # of favorable outcomes as the area of the outside of the triangle but inside of the square ( so area of square - area of triangle ) and we have total # of outcomes as the total area of the square including the triangle
Finding the areas
Area of square
Area of square = (side length)²
the square shown has a given side length of 120ft
So area = 120² = 120 × 120 = 14400
Area of triangle
Area of a triangle = (base length × height) / 2
Here the base length is shared with the side length of the square menaing the base length of the triangle = 120 and the given height of the triangle is 55 feet
So area would = ( 120 × 55 ) / 2 = 3300
Finding the probability
Again we want to find the probability that a ball thrown in the square will not land in the triangle
This can be calculated using the probability formula we created earlier
probability = ( area of square - area of triangle ) / area of square
we have area of square = 14400 and area of triangle = 3300
so probability = (14400 - 3300) / 14400
==> subtract 3300 from 14400
probability = 11100 / 14400 = 0.771 ( rounded )
And we are done!
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Hi I need Help* math problem ( i will give brainlist ) Is the following graph linear, exponential or quadratic
Answer:
the answer is exponential
Step-by-step explanation:
Answer:
Hi! My guess would be exponential.
Step-by-step explanation:
stay safe, and I hope I helped I apologize if I am wrong, good luck friends
3. Juan makes $9.00 per hour and works 30 hours per week. If Juan has $70 deductions, what is his
Net income?
Answer:
$200
Step-by-step explanation: You take $9.00 and multiply it by 30 and then you take whatever that answer is and subtract 70 from it to get the net income