In the circle shown, secants PE and PF have been drawn such that arc CE = 82, arc DF=98 and the ratio of arc CD to arc EF is 2:7. Determine the measure of angle P. Show how you arrived at your answer.
Answers
Answer:
m<P = 50°
Step-by-step explanation:
Given:
Arc CE = 82°
Arc DF = 98°
Ratio of arc CD to Arc EF = 2:7
Thus, let,
Arc CD = 2x
Arc EF = 7x
A full circle = 360°
Therefore,
Arc CE + Arc DF + Arc CD + Arc EF = 360°
Substitute
82° + 98° + 2x + 7x = 360°
Add like terms
180° + 9x = 360°
Subtract 180° from both sides
180° + 9x - 180° = 360° - 180°
9x = 180°
Divide both sides by 9
9x/9 = 180/9
x = 20
✔️Arc CD = 2x
Plug in the value of x
Arc CD = 2(20) = 40°
Arc EF = 7x = 7(20) = 140°
✔️Find m<P:
Recall: the measure of the external angle created when two secants intersect = half the difference of the major and minor arcs that are intercepted
Thus:
m<P = ½(arc EF - arc CD)
Substitute
m<P = ½(140° - 40°)
m<P = ½(100°)
m<P = 50°
Related Questions
write the equation for the circle graphed below.
Answers
Answer:
[tex](x -1)^2 + (y+1)^2 = 0.25[/tex]
Step-by-step explanation:
Given
The attached graph
Required
The equation of the circle
The equation of a circle is:
[tex](x - h)^2 + (y - k)^2 = r^2[/tex]
Where
[tex](h,k) \to center[/tex]
[tex]r \to radius[/tex]
From the attached graph,
[tex](h,k) = (1,-1)[/tex]
[tex]r = 0.5[/tex]
So, we have:
[tex](x - h)^2 + (y - k)^2 = r^2[/tex]
[tex](x -1)^2 + (y--1)^2 = 0.5^2[/tex]
[tex](x -1)^2 + (y+1)^2 = 0.5^2[/tex]
[tex](x -1)^2 + (y+1)^2 = 0.25[/tex]
PLEASE HELP ME !
Lance baked brownies for a school bake sale. The shaded figures stand for the brownies sold.
Part A What mixed number do the shaded portions stand for? Use what you know
about mixed numbers to explain why your answer is correct.
Answers
what is the answer to this question. i made it 20 pts
Answers
Answer:
the second choice
Ferris wheel has a 108-foot diameter and the center of the Ferris wheel is 58 feet above the ground. The Ferris wheel rotates in the CCW direction at a constant angular speed of 6 radians per minute. Chance boards the Ferris wheel at the 3-o'clock position and rides the Ferris wheel for many rotations. Let t represent the number of minutes since the ride started.
Required:
a. Write an expression (in terms of t) to represent the number of radians Justin has swept out from the 3-0'clock position since the ride started.
b. How long does it take for Justin to complete one full revolution (rotation)?
c. c. Write an expression (in terms of t) to represent Justin's height above the center of the Ferris wheel (in feet)
Answers
Answer:
a. θ = 6t
b. 1.048 minutes
c. y = 54sin(6t)
Step-by-step explanation:
diameter d = 108 foot
distance above the ground = 58 feet
a.) expression to represent number of radians
radian = 6 rad/min
θ = wt
w = 6
θ = 6t
t is in minutes
b.) we are to find the time period for one full revolution
time period = 2π/6
π = 22/7
[tex]T=\frac{2(22/7)}{6}[/tex]
= 1.048 minutes
c. Expression showing Justins height above the ground
y = rsinθ -----(1)
θ = wt = 6t
we find the radius r
diameter = 2 * radius
108 = 2r
r = 108/2
= 54 foot
we put these values in the equation 1 above
y = 54sin(6t)
I need this answer quick and try get it correct
Calculate 38% of 40
Answers
Answer:
15.2
Step-by-step explanation:
Answer:
the answer is 15.2
Step-by-step explanation:
you j multiple them
Which pair of expressions below are equivalent (the same)?
a) 4(3b) and 7b
b) 4b + 5b and 20b
c)-5(2b + 2) and 20b
d) 3b + b + 2b and 6b
Please help it’s really important
Answers
What is the slope of the line in the graph?
Options:
-4/3
-3/4
3/4
4/3
Answers
Answer:
Option 2: -¾
Step-by-step explanation:
First identify 2 points on the line.
(0, 1), (4, -2)
Substitute the coordinates into the gradient formula below:
[tex]\boxed{gradient = \frac{y1 - y2}{x1 - x2} }[/tex]
☆ (x₁, y₁) is the 1st coordinate and (x₂, y₂) is the 2nd coordinate.
Slope of the line
[tex] = \frac{1 - ( - 2)}{0 - 4} [/tex]
[tex] = \frac{1 + 2}{ - 4} [/tex]
[tex] = - \frac{3}{4} [/tex]
☆ Since the line is sloping downwards looking from the left to right, the line must have a negative slope.
If John starts with $85 and is spending $5 per week and Ashley has $35 and is saving $7 per week when will Ashley have more than John
Answers
Answer:
85-5=80 week 1
75= week 2
70=week 3
65=week 4
60=week 5
and so on.
Then Ashley
35+7=42 week 1
49=week 2
56=week 3
63= week 4
70=week 5
Step-by-step explanation:
The mean of five numbers in a set is 12. If the set contains a total of six numbers and the mean of all six is
14, which of the following is the sixth number?
(1) 24
(3) 32
(2) 13
(4) 18
Answers
=========================================================
Explanation:
The process of finding the arithmetic mean involves two steps
add up all the numbersdivide by n, which is the number of values in the setThe first bit of info your teacher gave you is "the mean of five numbers in a set is 12". While we don't know the actual individual values themselves, we know that they must add to some variable y. Dividing y over n gets us the mean
y/n = mean
y/5 = 12
y = 5*12
y = 60
The five values add to 60.
----------
The next bit of info is that "the mean of all six is 14". That allows us to say:
(sum of all 6 values)/6 = mean
(sum of all 6 values)/6 = 14
( (sum of 5 values) + (6th value) )/6 = 14
(y + x)/6 = 14
(60 + x)/6 = 14
where x is the 6th number we want to find.
-----------
Solve for x
(60 + x)/6 = 14
60+x = 6*14
60+x = 84
x = 84-60
x = 24 so choice (1) is the answer
Pls help!!! Will name Brainliest
Solve for x:
Answers
Answer:
I think it’s 10
One angle in an isosceles triangle measures 50°. Which of these cannot be the measure of an angle in this triangle? A 50 C 80% D130
Answers
Answer:
In an isosceles triangle, 2 of the angles are identical
Sum of the 3 angles of a triangle is always 180
Possibility 1 - 50 is one of the 2 identical angles
The 3 angles will be 50, 50, (180-50-50)
Possibility 2 - 50 is not one of the 2 identical angles
The 3 angles will be 50, (180-50)/2, (180-50)/2
You can work out the above and see which answer is not the possible angle
Please let me know if you have further questions.
Answer:
D
Step-by-step explanation:
In an isosceles triangle two angles are equal to each other, single two sides are congruent. Since the sides of a triangle add up to 180, we can figure out possible answers. This means it could either be
50, 50 and 80
Or 50, 65, 65
Which means the impossible measure would be D 130.
I need this quick, please!
What does x equal?
-x / 3 + 4 = 20
Answers
Answer:
x= -48
Step-by-step explanation:
-x is being divided by 3, so you want to muiltiple both sides of the equation by 3, move the constant to the right, find your answer and then change the signs! Don't forget about the negative sign.
Answer: x = -48
Just like what the first person said have a great day.
PLEASEEEEEE HELLPPPPP MEEEEE
Answers
Answer:
It's A
Step-by-step explanation:
The r coordinate of x is positive 4 which would be the frist number.
The r coordinate of y is positive 1 which would be the second number.
Please help! This is due today!
Answers
Use the equation for the area of a triangle 1/2(bxh)
Then multiply that number by 2 to get the area of the complete shape.
Can someone help me please
Answers
Length is 5 units and width is 8 units . What is the perimeter
Answers
Answer:
26 units all around
Step-by-step explanation:
when finding the perimeter use the formula
2(length) + 2(width)
in this case
length is 8
width is 5
5(2) = 10
8(2) = 16
10 + 16 = 26
One centimeter on the map represents 10 meters on the ground?
Answers
Solve for x. 4/x + 3/x =14 answer choices is 2,-2,1/2,3/7,1/4
Answers
Answer:
=1/2
Step-by-step explanation:
i hope i'm right
Someone, please help I will crown brainliest
Answers
Answer:
6
Step-by-step explanation:
Y=-x+7
Y=-1+7
Y=6
A triangle on the coordinate plane has vertices (-8,3), (3,9), and (9,3). What is the area, in square units, of the
triangle?
Please help
Answers
Answer:
51 sq units
Step-by-step explanation:
after plotting the vertices, the height of the triangle is 6 and the base is 17
A = 1/2(6)(17)
A = 51 sq units
change this in 12 hour clock. 19 15
Answers
Answer:
th answer is 7:15 pm
Step-by-step explanation:
basically just count with your hands if you want, start with one finger and say 13 and go up from there, 7th finger is the 19th. Thats my easiest way of doing it. Or you can subtract 24-19 and subtract 12 from the remaining sum
Chapter 12
ees
An isosceles triangular prism has a triangular end with a base of 14 inches, an altitude of 24 inches, and a side length 25 inches The height of the prism is
10 inches Calculate the Lateral and Total Surface areas of the prism?
Answers
Answer: 11176ft.
Step-by-step explanation:
Add. (−5x4+6x2−43)+(6x4−x2+12x+12) Express the answer in standard form. Enter your answer in the box.
Answers
Answer:
x^2+12x-15
Step-by-step explanation:
Answer:
Step-by-step explanation:
(-5x4+6x2-43)+(6x4-x2+12x+12)
(x4+5x2+12x-31)
Find the lateral area for the cylinder with the given measurement.
r= 4, h=5
20 pi square units
40 pi square units
80 pi square units
Answers
Answer:
Lateral area of a cylinder =2πrh
=2π x 4x 5
=40π square units
OPTION B
If 4% of a number is 8, find 1% of that number.
Answers
Answer:
8 is 4% of 200, 1% of 200 is 2
The school band is ordering customized stickers to support the band. The cost for 100 stickers is $110.00 and the cost for 200 stickers is $185.00 Write an equation to show the total cost of the stickers as a function of the number of stickers ordered.
Answers
Answer:
y = 0.75x + 35
Step-by-step explanation:
y = 0.75x + 35
where: y for cost in $, x for number of stickers ordered
A napkin is 18 inches long. A tablecloth is 6 times as long as the napkin.
How much longer, in inches, is the tablecloth than the napkin?
If d is the difference in the length of the tablecloth and the napkin,
which pairs of equations can be used to solve the problem? Select all that apply.
A. 6 × 18 = 108 and d – 18 = 108
B. 6 × 18 = 108 and 108 – 18 = d
C. 6 × 18 = 108 and d + 18 = 108
D. 6 × 18 = 108 and d + 108 = 18
E. 6 × 18 = 108 and 18 × 108 = d
Answers
Answer:
The answer is B. 6×18= 108 and 108-18= d
(D = 90) the difference between the length of the tablecloth and napkin.
2(x + _) = 2x + 10 Using the distributive property, what number would go in the blank in order for the given statement to be correct?
Answers
Answer:
10
Step-by-step explanation:
2
Answer:
2(x + 5) = 2x + 10
Step-by-step explanation:
2(x + A) = 2x + 10
2x + 2A = 2x + 10
Equating constant terms on both sides :
2A = 10
A = 5
Therefore , 2(x + 5) = 2x + 10
A manufacturer of liquid laundry detergent has a .02 probability that the detergent bottles will be improperly filled. (Either too much or too little detergent.) There is a .03 probability that the label on the bottle will not be affixed properly. If the events of bottle fill and affixing the label are independent, then the probability of a bottle being filled improperly and having an improperly affixed label is
Answers
Answer:
0.0006
Step-by-step explanation:
The probability is
Given that
A denotes the bottle being filled improperly
And,
B denotes the label on the bottle will not be affixed properly
So,
P(A) = 0.02 ,
ANd, P(B) = 0.03
Also that A and B are independent events.
So, by property of independence is
P(A \cap B) = P(A and B) = P(A) P(B)
= P(A and B) =P(A)P(B)
= 0.02 × 0.03
= 0.0006
What is the MAD? 4, 32, 33, 45, 67
Answers
Answer:
No solution can be determined from the information provided.
Step-by-step explanation: