Answer:
(x-2)²+(y-3)²=5².
Step-by-step explanation:
1. the equation of line through points (5;7) and (2;-2) is:
[tex]\frac{x-5}{3} =\frac{y-7}{9}; \ => \ 3x-y-8=0.[/tex]
2. to find the equation of the line, which is perpendicular to the line 3x-y-8=0:
the vector (3;-1) is perpendicular to the line 3x-y-8=0 and it is the vector-pointer for the requred line, and if |n₁|*|n₂|=0 (where n₁ is normal vector to the line 3x-y-8=0 and n₂ is normal vector to the required line), then 3*x-1*y=0 (where 'x' and 'y' any numbers). x=1; y=3, then n₂(1;3), then the required line is x+3y+C=0, where C - is unknown number.
3. to find the equation of the line, which is perpendicular to the line 3x-y-8=0 and passes through the middle point of (5;7) and (2;-2):
middle point is (7/2;5/2), then after substitution of coordinates of the middle point into the equation x+3y+C=0 it will be 3.5+3*2.5+C=0, ⇒ C= -11.
the required equation is x+3y-11=0
4. to calculate the intersection point of x+3y-11=0 and 2x-y=1:
[tex]\left \{ {{2x-y=1} \atop {x+3y=11}} \right. \ => \ (2;3)[/tex]
the point (2;3) is the centre of the required circle.
5. to calculate the radius² of the required circle:
r²=(5-2)²+(7-3)² or r²=(2-2)²+(2+3)², then r²=5².
6. if the centre of the required circle is (2;3) and its r²=25, then it is possible to make up the equiation of the circle:
(x-2)²+(y-3)²=5².
How many dominoes will it take to topple over the Empire State Building
Answer:
29
Step-by-step explanation:
A rectangular prism has a length of 112feet, a width of 212feet, and aheight of 8 inches. What is the volume of the prism in cubic inches?
pls hurry :)
Answer:
27,353,088 cubic inches
Step-by-step explanation:
How to find the volume of a rectangular prism
To find the volume of a rectangular prism, multiply its 3 dimensions: length x width x height. The volume is expressed in cubic units.
Solve
In this case, The volume of a rectangular prism with a length of 112feet,
width of 212 feet, and height of 8 inches:
But in this case, we need to convert both the length and width to inches.
If 1ft = 12in
Then, 112ft = 1344in (Multiply 112 by 12)
Also, 212ft = 2544 (Multiply 212 by 12)
So, the volume = 1344 x 2544 x 8
Calculated out this gives a volume of 27,353,088 cubic inches.
To the nearest tenth of a centimeter what is the length of side ab
The length of side AB in the given triangle is 22.6. The correct option is the first option 22.6
Calculating the side length of a triangleFrom the question, we are to determine the length of side AB in the given triangle.
Using the law of sines, we can write that
AB/sinC = BC/sinA
From the diagram,
C = 50°
BC = 19
A = 40°
Thus,
AB/sin50° = 19/sin40°
AB = (19 × sin50°) / sin40°
AB = 22.6433
AB ≈ 22.6
Hence, the length is 22.6
Learn more on Calculating the length of a side of a triangle here: https://brainly.com/question/24138896
#SPJ1
If the mangos cost $20 per 10. how much did I spend on mangos
What is the simplified form?
Answer:
A fraction is in simplest form when the top and bottom cannot be any smaller, while still being whole numbers.
Step-by-step explanation:
Write an equivalent expression for 6( 4 + 2m) ?
Answer:
QUESTION:
Write an equivalent expression for 6( 4 + 2m) ?
ANSWER:
6(4+2m) = ?
6 X 4 = 24
6 X 2m = 12m
Final answer:
12m + 24
Step-by-step explanation:
Hope that this helps you out! :)
If you have any questions please put them in the comment section below this answer.
Have a great rest of your day/night!
Please thank me on my profile if this answer has helped you.
In the figure, what is m∠ABE? What is m∠DBE? Enter your answers in the boxes.
Answer:
<DBE is 25.5
<ABE=115.5
Step-by-step explanation:
<DBE is 90-64.5 because DBC is a right angle
<DBE is 25.5
<ABE= 90+25.5 because ABD is a right Angle and DBE is 25.5
<ABE=115.5
Solve each system.
3x – y = 5
4x – 2y = 4
Answer:
x = 3
y = 4
Step-by-step explanation:
y = 3x -5
4x - 2(3x-5) = 4
4x - 6x + 10 = 4
-2x = -6
x = 3
y = 4
14. Molly puts two shapes together to make a new shape. The new shape has 6 sides and 6 vertices. Which two shapes did she use? ΔΔ OA in
She used two trapezoids.
She put one trapezoid on top and one on the bottom.
The shape she ends up making is a hexagon.
Consider a population of people who suffer occasionally from migraine headache. Suppose 62% of those people get some relief from taking ibuprofen (true proportion). To investigate the effectiveness of ibuprofen, a random sample of 100 people is obtained at random from this population. A. (4 pts.) Determine the sampling distribution of sample proportion. Also, find the mean and standard deviation of the sampling distribution.
Answer:
The sampling distribution of sample proportion is approximately normal, with mean 0.62 and standard deviation 0.0485.
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
62% of those people get some relief from taking ibuprofen (true proportion).
This means that [tex]p = 0.62[/tex]
Sample of 100
This means that [tex]n = 100[/tex]
A. (4 pts.) Determine the sampling distribution of sample proportion. Also, find the mean and standard deviation of the sampling distribution.
By the Central Limit Theorem, it is approximately normal with
Mean [tex]\mu = p = 0.62[/tex]
Standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.62*0.38}{100}} = 0.0485[/tex]
You have a jar of Marbles in front of you 2 are Cordovan, 9 are yellow, 3 are white and 7 are red. What is the probability, as a fraction of selecting a marble that is white or yellow, followed by a marble that is Cordovan?
Answer:
2/35
Step-by-step explanation:
Assuming that this is without replacement,
The total amount of marbles is 2+9+3+7, or 21.
9 are yellow, 3 are white. this makes 12.
The probability of selecting a white or yellow marble is 12/21.
Now without replacement (comment if it is with replacement.), there are 20 marbles left, and 2 are Cordovan. This means there is a 2/20 chance then of picking a Cordovan marble.
After multiplying the fractions we get
(12/21) * (2/20) = 2/35.
There is a 2/35 chance of selecting a yellow or white, then a cordovan marble.
solve for x and y and expain
Answer:
Read explanation
Step-by-step explanation:
x+4=15
-4=15-4
x=11
0.4 is the scale factor (similarity) between the two triangles, so multiply 25 x 0.4 to get y value.
Y= 10
Hope this helped! Please heart <3
Ramona wants to buy cheese pizza for her family and friends gathering. She stops buy nine wonders pizza and figures out that they have four sizes
Answer:
????
Step-by-step explanation:
We need more information to help figure out the answer! Otherwise, I do understand it so far! :)
Answer:
she should just buy the best one
Step-by-step explanation:
Solve for each variable and tell how you found the value of each.
Answer:
A:38 c:54
Step-by-step explanation:
First off, I did the easiest which was a. i found the value of A by subtracting 180 by 142. because a flat line is 180 degrees.
For C, It was more difficult. I subtracted 88 by the value of A, since the value of A is the same as the one next to 88. So I subtracted 126 (88+38) and got 54.
Fortunately, I couldn't figure out B though, but i think it is a similar answer to c.
I need step by step answer to my question
Step-by-step explanation:
what is your questions
Answer:
The answer would be 13.5 pints
Step-by-step explanation:
when you do 2 gallons - 2 pints you get 1.75 gallons
then when you do 1.75 - 1 cup you get 13.5 pints
Please help, This is due at 5 pm
Question 1(Multiple Choice Worth 4 points)
(07.01)
Which of the values in the set {2, 3, 4, 5} is a solution to the equation 2x + 4 = 10?
2
3
4
5
Question 2(Multiple Choice Worth 4 points)
(07.01)
Geoffrey is trying to earn $50 to buy a video game. He has saved $14.25. He earns $3.75 per hour cleaning windows with his uncle and he earns $6.50 per hour working at the grocery store. Can Fred buy the video game if he works with his uncle for 3 hours and at the grocery store for 4 hours? Use the inequality 3.75y + 6.50z + 14.25 ≥ 50.
Yes, because the total will be $51.50.
Yes, because the total will be $60.25.
No, because the total will be $24.50.
No, because the total will be $37.25.
Question 3 (True/False Worth 4 points)
(07.01)
True or False?
k = 3 over 4 is a solution to the inequality 12k + 2 < 12.
True
False
Question 4(Multiple Choice Worth 4 points)
(07.01)
Which of the values for x and y make the equation 3x + 4y + 6 = 26 true?
x = 4, y = 2
x = 5, y = 6
x = 4, y = 3
x = 3, y = 5
Question 5(Multiple Choice Worth 4 points)
(07.01)
Which of the following sets shows all the numbers from the set {1, 2.5, 3, 4.5, 5} that make the inequality 3a + 4 ≥ 13 true?
{2.5, 3, 4.5}
{1, 2.5}
{3, 4.5, 5}
{4.5, 5}
Answer:
Step-by-step explanation:
1) 2x+ 4 = 10
2x = 6
x = 3 (3 is the answer)
2) we have to substitute y with 3 and z with 4
3.75*3 + 6.50*4 ≥ 50
11,25 + 26 ≥ 50
37.25 ≥ 50
so the answer is no, because the total will be $37.25
3) 12k + 2 < 12
12k < 10
k < 5/6
3/4 < 5/6 so the answer is true
4) we have to try the options
a) 3*4 + 4*2 + 6 = 26
12 + 8 + 6 = 26
26 = 26 (true)
b) 3*5 + 4*6 + 6 = 26
15 + 24 + 6 = 26
45 = 26 (false)
c) 3*4 + 4*3 + 6 = 26
12 + 12 + 6 = 26
30 = 26 (false)
d) 3*3 +4*5 + 6 = 26
9 + 20 + 6 = 26
35 = 26 (false)
so the answer is x=4 , y=2
5) 3a + 4 ≥ 13
3a ≥ 9
a ≥ 3
so the answer is {3,4.5,5}
The list shows the numbers of employees in the nine departments at a company.
14, 23, 6, 54, 30, 26, 17, 3, 26
What is the range of the numbers of employees in these departments?
51
18
26
23
Answer:
51
Step-by-step explanation:
largest number - smallest number
54 - 3 = 51
Answer:
51
step by step
Explanation: The range of a data set is the difference between the largest number in the data and the smallest number in the data set which in this case is 54 - 3 of 51. So the range of this data set is 51.
find the area of a circle whose diameter is 7cm
Answer:
3.5pi
Step-by-step explanation:
just multiply together and you'll get your answer
Answer:
38.5 cm^2
Step-by-step explanation:
Diameter ( d ) = 7 cm
Radius ( r ) = 7 / 2 cm
Formula : -
Ar ( circle ) = π r^2
π r^2
= ( 22 / 7 ) x ( 7 / 2 )^2
= ( 22 / 7 ) x ( 49 / 4 )
= 38.5 cm^2
DOES ANYONE KNOW HOW TO DO THIS AND IF SO I WILL GIVE YOU THE GROWN THING AND 31 POINTS PLS HELP meee
Answer:
-4,4
Step-by-step explanation:
(c) 80 people entered the marathon. 85% of
finished in under three hours. How many
people finished in under three hours?
Answer:
68 people
Step-by-step explanation:
Find how many finished in under 3 hours by multiplying 80 by 0.85
80(0.85)
= 68
So, 68 people finished in under 3 hours
x and y are supplementary angles. y measures 97 What is the measure of x?
Answer:
83
Step-by-step explanation:
supplementary angles have sum of 180
How can a shape have perdindicular but not parallel sides?
Answer:
Step-by-step explanation:
This uh
GIVING 30 POINTS!!!!!!!
Answer:
MEAN
Step-by-step explanation:
Have a Great Day!
Answer:
Not quite sure, but I think its the mean?
A card is drawn at random from a standard deck. That card is not put back in the deck, and a second card is drawn at random from the remaining cards in the deck. Neither of the cards drawn so far are put back in the deck, and a third card is drawn at random from the remaining cards in the deck. What is the probability that the first card drawn is a spade, the second card drawn is a heart, and the third card drawn is a heart? Do not round your intermediate computations. Round your final answer to four decimal places.
Answer:
The probability of the given scenario occuring is about 0.0153.
Step-by-step explanation:
A standard deck contains 52 cards.
We want the first card to be a spade. In a standard deck, 13 out of the total 52 cards are spades.
So, the probability that the first card is a spade is 13/52 or simply 1/4.
Now, we will draw a second card without replacing the first card. Since we did not replace the first card, the total amount of cards in the deck is now 51.
This time, we want a heart. 13 cards of the remaining 51 will be hearts. So, the probability that the second card is a heart is 13/51.
Now that we've drawn two cards without replacing them, the total number of cards left is 50.
And since we've drawn (or would like to have drawn) a heart as our second card, the total number of cards that are hearts is now 12.
Then the probability of the third card being hearts will be 12/50 or 6/25.
Then the probability that our first card is a spades, second card is a heart, and the third and final card is also a heart without any replacements will be:
[tex]\displaystyle P(\text{spade, heart, heart})=\frac{1}{4}\cdot \frac{13}{51}\cdot \frac{6}{25}=\frac{13}{850}\approx0.0153[/tex]
The probability of the given scenario occuring is about 0.0153.
Can you help me with this?
Answer:
1. Obtuse
2. Right
3.Acute
4.Acute
5.Right
6.obtuse( Not sure about this one)
Find the area of the triangle
Answer:
The answer to this problem is 12.5.
Step-by-step explanation:
The formula for finding the area of a triangle is b * h * 1/2 or divide by 2 (base times height times one-half or two).
Since this is a equilateral triangle, all of the sides are equivalent to each other. Since we know one of the sides is 5, all of the sides are 5.
5 * 5 = 25
Then you need to multiply this answer by 1/2 or divide by 2, whichever is easier.
25 / 2 = 12.5
The answer is 12.5.
Also, it would be FANTABULOUSLY AMAZING if I could get brainliest!!!
Just sayin, that would be pretty great.
Kalani has these monthly liabilities: rent $879, car payment $315, credit card payment $102. She has an annual
income of $96,448. What is her debt-to-Income ratio, expressed as a percent?
Answer:
1.34%
Step-by-step explanation:
Given data
Rent =$879
Car payment =$315
Credit card payment= $102
Annual Income= $96,448
In all the debt is
=879+315+102
=$1296
Hence the debt to income ratio is
=1296/96,448
=0.0134
As percent
=0.0134*100
=1.34%
A deck of cards has 52 cards. There
are 4 suits, diamonds, hearts, clubs
and spades. Each suit has 13 cards.
What is the probability that I will
randomly pick a King?
Please hurry and help me
Answer:
The last option is your answer
Step-by-step explanation:
X
Help me please, find the length of x and y from 34. It is a 45 45 90 triangle.
Answer: X and y are about 24.04
Step-by-step explanation:
for a 45 45 90 triangle [tex]C=a\sqrt{2}[/tex]
[tex]34=a\sqrt{2}[/tex]
[tex]34^{2} =2a^{2}[/tex]
[tex]1156=2a^{2} \\578=a^{2} \\24.04=a[/tex]
