a circle has a center at point C (2,2) and a point on the circle is located at point P (5,4). What is the diameter of the circle?
The centre C of the given circlee = (2, 2) P(5, 4) is a point on the circle. Join P to C and extend it to meet the circle at the other extremity Q of the diameter. Now PQ is a diameter of the circle with C as its midpoint. The the coordinates of Q be (x, y) The coordinates of midpoint are (2, 2) = [ (x +5)/2, (y + 4)/2] =%3E (x + 5)/2 = 2; =%3E x = 4 — 5 = —1 =%3E (y + 4) = 2; =%3E y = 4 — 4 = 0 The extremities of the diameter are (—1, 0) and (5, 4). Diameter² = [5 —(—1)]² + [ 4 —0]² = 6² + 4² = 36 + 16 = 52 Diameter = 2√13 We could have easily found the radius from the centre and the given point on the circumference. The radius r² = (5 — 2)² + (4 — 2)² = 9 +4 = 13 Radius r = √13 And diameter = 2 r = 2 √13
Hope i helped
-lukelaws
The surface area of a closed box is 2842 square meters. If the length is x m, the width is 6 M less than twice. The length and the height is 4 M more than the length. Calculate, the value of x
Tickets for a play cost $3 for children and $10 for adults. A group of 25 people paid a total of $201 for tickets to the play. How many children were in a group?
Answer: There were 7 children
Step-by-step explanation:
Let's use x to represent the children and y to represent the adults.
We know they combine to make a group of 25 people so x+y=25
We also know that they paid $201 and that there is $3 per child and $10 for adults so 3x+10y=201
I will solve by substitution.
Solve for y in the first equation
[tex]x+y=25\\x-x+y=25-x\\y=25-x[/tex]
Sub in our value for y into the other equation and solve for x
[tex]3x+10y=201\\3x+10(25-x)=201[/tex]
Step 1) Simplify
[tex]3x+250-10x=201\\-7x+250=201[/tex]
Step 2) Subtract 250 from both sides
[tex]-7x+250-250=201-250\\-7x=-49[/tex]
Step 3) Divide both sides by -7
[tex]\frac{-7x}{-7} =\frac{-49}{-7}\\x=7[/tex]
Answer:
7 children.
Step-by-step explanation:
Let c = children
Let a = adults
1) We can set up two equations and solve them simultaneously using substitution or elimination method.
c + a = 25
3c + 10a = 201
2) I will use substitution. Make one of the variables the subject; then, substitute it into the other equation.
a = 25 - c
3c + 10(25 - c) = 201
3) Solve for c; then, substitute it into one of the equations.
3c + 250 - 10c = 201
-7c = 201 - 250
-7c = -49
c = -49/-7
c = 7
Let's substitute it into one of the equations.
7 + a = 25
a = 25 - 7
a = 18
Since the question only asked for the number of children, the answer is 7.
Find the 2 consecutive integers whose squares have a difference of 239
Answer:
119 and 120
Step-by-step explanation:
let the consecutive integers be n and n + 1 , then
(n + 1)² - n² = 239
n² + 2n + 1 - n² = 239
2n + 1 = 239 ( subtract 1 from both sides )
2n = 238 ( divide both sides by 2 )
n = 119
n + 1 = 119 + 1 = 120
the 2 integers are 119 and 120
as a check
120² - 119² = 14400 - 14161 = 239
There were 136 students and 34 adults at a concert in the auditorium. They filled 85% of the seats in the auditorium. How many seats are there in the auditorium?
Answer:
there are 200 seats and 170 of them were filled
136+34=170
= 170 is 85% of ?
? = 200
Mary has been put in charge of buying soft drinks and chips for a party. If the soft drinks total $25
and chips are $3.29 per bag, how many bags of chips can Mary buy if she wants to spend at most $100.
Answer:22
Step-by-step explanation: he has only $75 to spend on chips . 75/ 3.29
if you can mow 90 lawns in 45 minutes how long will it take to mow 12 lawns?
Answer:
24 minutes
Step-by-step explanation:
90/45=2 x 12 = 24
Hope It Helps
What’s the distance between 240 and 0
Answer:
The distance between 240 and 0 is 240
Step-by-step explanation:
You can find the distance between two values by getting it's absolute value.
You can setup the equation like this:
| 0-240 |
When you solve the equation you will find the absolute distance between 240 and 0.
What is the true solution to l n 20 l n 5 = 2 l n x
Since the solution cannot be negative hence the true solution to the expression is x = 10
Laws of logarithmGiven the logarithmic expression
ln 20 + ln 5 = 2lnx
In logarithmic law, the sum of log is equivalent to its product .The equation above can be written as:
ln(20*5) = 2lnx
ln100 =2lnx
ln100 = lnx^2
x^2 =100
x = 10
Since the solution cannot be negative hence the true solution to the expression is x = 10
Learn more on log functions here: https://brainly.com/question/13473114
pls help me im really stuck
Answer:
10:1:5
Step-by-step explanation:
Let's mark names as their first letter:
Amy=A
Bill=B
Cara=C
The ratio should be like this A:B:C
A=10*B
C=A/2 or A*1/2
If it is the simplest, then Bill have to score 1 point.
10*1=10 (Amy's score)
10/2=5 (Cara's score)
If it is Amy:Bill:Cara then the ratio of points score by them is 10:1:5
I hope that I helped :)
Mariya is solving the quadratic equation by completing
the square.
4x2-20x+3=0
4x2-20x=-3
A(x2-5x)=-3
what is the question, I'm confused?
Answer:
This is the best I can do because your question is un clear
Step-by-step explanation:
P (-2, 4). 4 If P = (-2, 4), then find: 3 2 Ry=1 (P) y=1 1 2 3 4 5 -4 -3 -2 -1 0 -1 ([?], []) -2 -3 -4 Enter
Answer:
(-2, -2)
Step-by-step explanation:
A line of reflection is the perpendicular bisector of a point and its image. The given point is 3 units above the horizontal line of reflection. Its image will be 3 units below that line, at y = 1 -3 = -2.
The image coordinates are P'(-2, -2).
Please help!
which of the following is equivalent to (a+b)(c+d+e)?
A) ab+ac+ad+ae
B) ac+ad+ae+bc+bd+be
C) abcde
D) ac+bd+e
A triangular prism is 13 meters long and has a triangular face with a base of 12.6 meters and a height of 16.6 meters. What is the volume of the triangular prism?
Answer:
1359.54m^3
Step-by-step explanation:
The formula for the volume of a triangular prism is:
1/2([tex]b \times l )\times h[/tex]
b= base
l = length
h= height
Step 1: Plug the numbers into the formula
1/2(12.6*13)*16.6
Step 2: Simplify
163.8*16.6
1359.54
Step 3: Add units
The units used in the question were in meters, so the answer is also in meters.
Volume is always cubed, so it would be to the third power...1359.54m^3
If this answer helped you, I would greatly appreciate if you gave me brainliest :D.
Consider the equation 3p – 7 p = 13. what is the resulting equation after the first step in the solution?
Answer:
-4p=13
Step-by-step explanation:
-3p-7p=13
-4p=13
p=-13/4
The length of Ruben's rectangular living room is 9 meters and the distance between opposite
corners is 10 meters. What is the width of Ruben's living room. Use Pythagorean theorem.
pls help me with this
Answer:
4 vertices6 edgesStep-by-step explanation:
A vertex is where three or more edges come together. All of the vertices are shown in the picture, so you can count them. There are 4 vertices.
An edge is where plane faces meet in a line. All of the edges except one are shown as solid lines in the figure. (The remaining edge is shown as a dashed line.) You can count them. There are 6 edges.
a triangle’s angle measures are in the extended ratio of 2:4:9 find the measures
of the angles.
24°, 32°, 124°
20°, 40°, 90°
20°, 40º, 100°
24°, 48°, 108°
Answer: 24°, 48°, 108°
Step-by-step explanation:
3.5 divided by 0.375 with solution.
Answer:
9 and 1/3
Step-by-step explanation:
0.375 = 3/8
You can write the question as:
3.5/(3/8)
(7/2)/(3/8)
—> times to get denominator of 16
(56/16)/(6/16)
(56/16) x (16/6)
the 16 cancels out so we are left with:
56/6,
54/6 = 9
2/6 = 1/3
Therefore the answer is 9 + 1/3 = 9 and 1/3
A box of mints contains 20 mints. Allison and her family have already
eaten 8 mints. Allison puts the remaining mints on 2 dishes to serve to
visitors. She puts the same number of mints on each dish. How many
mints does Allison put on each dish?
Answer:
6+6=12 because they were 20-8=12 left and Allison puts 6 and 6 on the single dish
Answer:
6 mints
Step-by-step explanation:
after Alison eats 8 mints there's 12 remaining mints in the box . to distribute an equal amount of mints in two dishes, the number will be 12/2 that's equal 6 mints in each dish.
Find the equation of the line parallel to y = - 1/2x -5, that passes through the point (4, -3). Write your answer in slope intercept form.
Answer:
y = -1/2x - 1
Step-by-step explanation:
Hi there!
We are given the equation y = -1/2x - 5
We want to write an equation parallel to this line, that passes through the point (4, -3)
Parallel lines have the same slope
In y=-1/2x-5, the equation is written in slope-intercept form, which is y=mx+b, where m is the slope and b is the y intercept
-1/2 is in the place of where m is, therefore it is the slope of the line
It is also the slope of the new line that we want to create.
As we already know the slope of this new line, we can substitute it into our equation (y=mx+b):
y=-1/2x+b
Now we need to solve for b
As the equation passes through the point (4, -3), we can use its values to help solve for b
Substitute 4 as x and -3 as y:
-3 = -1/2(4)+b
Multiply
-3 = -2+b
Add 2 to both sides
-1 = b
Now substitute -1 as b into the equation
y = -1/2x -1
Hope this helps!
See more on this topic here: https://brainly.com/question/25642286
write down the inequality for x that is shown on this line
Answer:
x < 5
Step-by-step explanation:
the open circle above 5 means that x cannot be equal to 5
the arrow points left indicating values of x are less than 5 , then
x < 5
The required inequality for the given line is x < 5.
Inequality shows relation between two expression which are not equal to each others.
According to the given line,
The value of x is less than 5, implies that x can be 5 to -∞
Also, at x = 5, there is an open circle, implies that,
The value of x can not be equal to 5.
So the inequality can be written as,
x<5
The inequality is x<5 for the given line.
To know more about Inequality on:
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What do the following two equations represent?
y
=
−
2
3
x
+
11
y=−
3
2
x+11y, equals, minus, start fraction, 2, divided by, 3, end fraction, x, plus, 11
y
+
7
=
3
2
(
x
−
5
)
y+7=
2
3
(x−5)
Answer:
unclear sorry try 34
Step-by-step explanation:
try 34 hm
Answer:
perpendicular
Step-by-step explanation:
I got it right on khan
Preston needs to write an equation in slope-
intercept form to represent the relationship between x
and y in the table below. What will be the value of the
y-intercept in his equation? Record your answer on
the grid.
HELPS A GIRL OUT PLSSS
The line equation in its slope-intercept form is y = 1.5 · (x - 8), the slope and the y-intercept of linear function are 1.5 (according to the information of the table) and -12, respectively.
How to determine a linear function in slope-intercept form
By analytical geometry we know that linear functions can be constructed by know the location of two distinct points on a Cartesian plane and the slope-intercept form is described below:
y - y₁ = m · (x - x₁) (1)
Where:
x - Independent variabley - Dependent variablex₁, y₁ - Coordinates of the know point.m - SlopeAccording the table, the slope of the function is 1.5, as there a change in y of 3 for a change in x of 2. Lastly, we determine the line equation in slope-intercept form: m = 1.5, x₁ = 8, y₁ = 0
y = 1.5 · (x - 8)
And the y-intercept is found for x = 0:
y = 1.5 · (0 - 8)
y = -12
The line equation in its slope-intercept form is y = 1.5 · (x - 8), the slope and the y-intercept of linear function are 1.5 (according to the information of the table) and -12, respectively. [tex]\blacksquare[/tex]
To learn more on linear functions, we kindly invite to check this verified question: https://brainly.com/question/21107621
Patios can be made by mixing cubic meters of cement, gravel, and stones in the ratio 9:4:6. How much gravel is needed to make 209 cubic meters of patio?
Answer:
44 cubic meters
Step-by-step explanation
9 + 4 + 6 = 19
9/19 of the patio will be cement
4/19 of the patio will be gravel
6/19 of the patio will be stones
Work out the amount of gravel - 4/19 * 209 = 44 cubic meters
:)
An ecologist wants to know what percent of the 10,000 fish in a lake are cod. She conducts a study in which 50 fish are randomly caught. Of those 50 fish, 15 are cod. Based on this data, using a 95% confidence interval, the researcher can determine that the percent of fish that are cod in the lake is which of the following?
(1) Between 17% and 43%
(2) Exactly 30%
(3) Between 24% and 36%
(4) Between 20% and 40%
Answer:
3
Step-by-step explanation:
Because there are about 3,000 fish in the lake, 3,000 is 30 percent of 10,000. C or (3) gives the 6 percent each way around 30.
what is the exponential equation of (0,3) and (3,100)
HELP
Answer:
[tex]y=(\frac{\sqrt[3]{900}}{3})^x[/tex]
Step-by-step explanation:
Calculate the volume of each of the following prisms.
Answer:
The Rectangular prism in the top-left corner is 11,760. The top-middle rectangular prism is 7,938. The top-right rectangular prism is 4,851. The shape that is orange and pink I don't know what it is. The triangular prism on the middle of the page is 11.781. The blue cylinder is 38,936. The green rectangular prism is 23,125. The "clear" rectangular prism on the bottom row is 31,668. The rectangular prism in the bottom right corner is 14,688. That is all, I'm almost 100 percent sure they are all right!
Bailey rolls a pair of dice 12 times, and the sum of 6 came up 5 times to calculate the experimental and theoretical probabilities of rolling a sum of six with a pair of dice
Answers:
Experimental probability = 5/12
Theoretical probability = 5/36
========================================================
Explanation:
The experimental probability, aka empirical probability, is what we observe to happen. The event of rolling a six happens 5 times out of 12 total rolls. That leads directly to the experimental probability of 5/12
----------------------------
The theoretical probability is based on predetermined odds, and can be done on paper rather than actually rolling the dice.
There are 6*6 = 36 ways to roll two dice. Of those 36 ways, we have these cases that add to 6
1+5 = 62+4 = 63+3 = 64+2 = 65+1 = 6There are five ways to add to 6, out of 36 outcomes total.
This means the theoretical probability of getting a sum of 6 is 5/36
Need help on this please
Answer:
First Question is 20. Second one is 12 and the third one is 30.
Step-by-step explanation:
Hope this helps! :)