Algebraically find the x-coordinates where the line y=2x+3 intersects the circle (x-3)^2 + (y+6)= 50
Answers
The x-coordinates where the line y = 2x + 3 intersects the circle is equal to -2 and -4.
What is the equation of a circle?Mathematically, the standard form of the equation of a circle is represented by this mathematical expression;
(x - h)² + (y - k)² = r²
Where:
h and k represents the coordinates at the center of a circle.r represents the radius of a circle.From the information provided, we have the following system of equations:
(x - 3)² + (y + 6)² = 50 ......equation 1.
y = 2x + 3 .............equation 2.
In order to determine the x-coordinates at the point of intersection, we would substitute the equation 2 into equation 1:
(x - 3)² + (2x + 3 + 6)² = 50
(x - 3)² + (2x + 9)² = 50
x² - 6x + 9 + 4x² + 36x + 81 - 50 = 0
5x² + 30x + 40 = 0
x² + 6x + 8 = 0
x² + 6x + 9 = 1
(x + 3)² = 1
Taking the square of both sides of the equation, we have;
x + 3 = ±1
x = ±1 - 3
x = -2 and -4
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Related Questions
The sum of two numbers is 9. If one number is subtracted from the other, the difference is −3. Find the two numbers.
Answers
Answer:
The numbers are 6 and 3
Step-by-step explanation:
Let the numbers be x and y
So their sum is x + y =9 (EQ. 1)
Their difference is x - y = -3 (EQ. 2)
Solve simultaneously using subtract method.
x-x=0, x is eliminated. y- -y = +2y since -x- is +.
so it is now 2y = 9- - 3:. 2y= 12; dividing both sides by 2. Y=6.
Substitute Y=6 in EQ 1 to find x.
So x + 6=9;. x=9-6 is achieved by collecting like terms. so x=3.
:. Y=6 and x=3. The numbers are 6 and 3
I think I was able to expantiate it well.
What is the answer to 1+1 ?
Answers
Answer:
2
Step-by-step explanation:
1+1=2
Thank you for coming to my TED Talk
Answer:
22
Step-by-step explanation:
x+12=31 solve for x i’m in a breakout room i have limited time to finish this
Answers
Answer: x=19
Step-by-step explanation:
x=31-12
x=19
pleasee help me i’ll give you brainliest
Answers
Answer:
Step-by-step explanation:
its 4
Answer:
4
Step-by-step explanation:
4 ³ = 64
4 to the negative 2 = 0.0625
so 64× that is 4
Daija wants trim 3.5centimetes from her hair how should she move the decimal point to convert this number to millimeters
Answers
9514 1404 393
Answer:
right
Step-by-step explanation:
1.0 cm = 10. mm . . . . . . the decimal point is moved to the right
3.5 cm = 35. mm . . . . . . the decimal point is moved to the right
which of the following values are solutions to the ineuality x-7<5
Answers
Answer:
x>12
Step-by-step explanation:
Isabella needs to earn at least $300 a week during her summer break to pay for college. She works two jobs, one at a office
that pays $8 an hour and the other tutoring for $16 per hour.
Let x be the number of hours she works at the office and let y be the number of hours she works tutoring. Write an
inequality that models this situation.
Answers
Answer: 8x+16y _> 300
Step-by-step explanation:
What value will make the equation true -21 - ? = 1and1/2
Answers
Answer:
the answer would be -21 - (-22 1/2)= 1 1/2
The value that will make the equation true would be -21 - (-22 1/2)= 1 1/2
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.
We are given that the equation as;
-21 - (-22 1/2)
Now the mixed fraction is 22 1/2 = 45/2
The difference of the equation is;
-21 - (-22 1/2)
-21 - (-45/2)
= 1 1/2
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Explain why the two triangles below are similar by writing the appropriate similarity theorem. Then find x. Round your answer to the nearest tenth. (example answer ---> SSS,9.2 ---> no spaces)
Answers
Answer:
SSS Theorem
[tex]x = 35.7[/tex]
Step-by-step explanation:
Given
The attached triangle
Solving (a) The similarity theorem
The given sides of the triangle are similar.
In other words, they are similar by sides.
Hence, the theorem is: SSS
Solving (b): Find x
To find x, we make use of the following equivalent ratios.
[tex]\frac{14}{25} = \frac{14+6}{x}[/tex]
This gives:
[tex]\frac{14}{25} = \frac{20}{x}[/tex]
Cross multiply
[tex]14 * x = 20 * 25[/tex]
[tex]14 * x = 500[/tex]
Solve for x
[tex]x = \frac{500}{14}[/tex]
[tex]x = 35.7[/tex] -- approximated
An aquarium is to be drained. The aquarium is shaped like a rectangular prism with length 40 in, width 22 in, and height 16 in. Suppose
water is pumped out of the aquarium at a rate of 704 in per minute. If the aquarium starts completely full, how many minutes does it take
to empty the aquarium?
Answers
9514 1404 393
Answer:
20 minutes
Step-by-step explanation:
The volume is given by ...
V = LWH
V = (40 in)(22 in)(16 in) = 14,080 in³
If water is removed at the rate of 704 in³/minute, the time to remove it all is ...
t = quantity/rate = (14,080 in³)/(704 in³/min) = 20 min
It takes 20 minutes to empty the aquarium.
HELP NEEDED ASAP! Thanks :)
Answers
Answer:
3
Step-by-step explanation:
First we must find the total boxes of pens
15 + 9 = 24
Then we can divide the total cost by the total number of boxes of pens
$72 / 24 boxes = 3
HELPPP ASAP!!
A warehouse worker is stacking boxes. The height of each box is 20 centimeters. She cannot stack the boxes higher than 5 feet.
1 inch 2.54 centimeters, 1 foot = 12 inches
What is the maximum number of boxes the warehouse worker can stack? Enter the answer in the box.
boxes
Answers
Answer:
I dont know can u explaining more its not clear too much
A company spent 32% of its annual budget
developing a new machine. What fraction of the
company's budget was spent developing a new
machine?
A. 1/32
B. 5/16
C. 8/25
D. 4/125
Answers
Answer:
C
Step-by-step explanation:
To find this answer you simply perform the division and see which one gives you 32
In this case 8/25=0.32 or 32%!
3. Determine how many real solutions the quadratic equation has. x2 + 6x + 8
A. One solution
B. Two solutions
C. No solutions
Answers
7.
A company is able to sell 600 of its product in the first year of business.
products it is able to sll decreases by 20%. If this trend continues:
Each year however, the amount of
a) How many products will it be able to sell in year 5?
b) How many products will it have sold over the course of 5 years?
Answers
9514 1404 393
Answer:
246 products in year 52017 products over 5 yearsStep-by-step explanation:
The n-th term of the geometric series is ...
an = a1(r^(n-1))
for first term a1 and common ratio r. The common ratio here is the growth factor: 1 -20% = 0.8. This means the 5th term (5th year sales) will be ...
a5 = 600(0.8^(5-1)) ≈ 246 . . . . . products sold in year 5
The sum is given by ...
sn = a1(1 -r^n)/(1 -r) = 600(1 -0.8^5)/(1-0.8) = 2017
The company will have sold about 2017 products over 5 years.
Ms. Smith allows her students to choose the mean, median, or mode of their set of test scores to be their final grade. Which measure of center should Erica use to get the highest average if her scores are 80, 90, 70, 60, 90?
Answers
Answer:
Mode
Step-by-step explanation:
because 90 is the grade that shows up the most!
I hope I helped :)
Measure of center that Erica should use is mode to get the highest average on her scores.
What is Mean, Median and Mode?For a set of data, mean is the average of all the elements in the data set.
Median is the element in the exact middle when numbers are arranged from smallest to largest or largest to smallest.
Mode is the element which is most repeated.
The given data set is,
80, 90, 70, 60, 90
Mean = (80 + 90 + 70 + 60 + 90) / 5 = 78
To find median, firstly arrange the numbers in order.
60, 70, 80, 90, 90
The middle element is the element in the third place, 80 which is the median.
90 is the only element which appears more than once. So mode is 90.
Mode gives the highest score.
Hence Erica should use mode as the measure of center to get the highest average.
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Finish the first diagram so that it represents 4 × x= 15, and the second diagram so that it represents 4+y=15
Answers
Answer:
6
Step-by-step explanation:
YALL HEEEEELLLLPPPPP
Which expression is equal to 90 + 60 factored by the greatest common factor ? O A 3(30 + 20) B. 5(18 + 12) C. 10(9 + 6) D. 30(3 + 2) O E 60(1.5 + 1)
Answers
Answer:
Step-by-step explanation:
I say D but not sure this time
Answer:The answer is d
Step-by-step explanation:
Please answer the question in the picture because it would paste correctly thanksss
Answers
Answer:
b
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
146 is equal to 12.08
12 3/4 is 12.75
12 5/8 is 12.63( I rounded it.Before it was 12.625)
Then you put it in order.
solve for Angles 1 and 2 please
Answers
Answer:
angles 1 and 2 measure 118°
Step-by-step explanation:
Help please I will give brainlist
Answers
The sale this year be $400000 .
Find the maximum power of 5 which can divide 49!
Answers
Answer:
10
Step-by-step explanation:
Find the least common multiple (LCM) for the pair of numbers 6 and 18
Answers
Answer:
the lcm is 6
Step-by-step explanation:
6 divided by 3 is 1
18 divided by 3 is 6
6 becomes 3 and 2
Answer:
18
Step-by-step explanation:
Since the question is asking for the least common multiple, you factor out the 6 in 18 and 6. This gives you 631 as the LCM because you have factored out 6 and this is the GCF because there are no more common factors between 3 and 1. Since 631 equals 18, 18 is the LCM
If the probability of a chance event is 0.96, it is less likely to happen than which of the following probabilities of another chance event ?
1. 0.95
2. 0.75
3. 0.85
4. 1
Answers
In ALMN, the measure of ZN=90°, NL = 6.8 feet, and LM = 9.4 feet. Find the
measure of ZL to the nearest tenth of a degree.
Answers
Answer:
Step-by-step explanation:
The answer is 43.7
Answer:
43.7
Step-by-step explanation:
Find the area of each figure.
Answers
1536in (for rectangle). 288in (for triangle)
Area of rectangle: 48in* 32in = 1536 in
Area of triangle: 48in*12in÷1/2= 576/2=288in
Formula of area of triangle is b*h divided by 2
Formula of area of rectangle is length*width
Hope this helps!
AB is a midsegment of trapezoid DEFG what is x?
Answers
Answer:
D. 2
Step-by-step explanation:
DEFG is a trapezoid and AB is its Midsegment.
Therefore,
[tex]AB =\frac{1}{2}(DG + EF) \\ \\ 12 = \frac{1}{2} (5x - 4 + 8x + 2) \\ \\ 12 \times 2= (13x - 2) \\ \\ 24 = 13x - 2 \\ \\ 24 + 2 = 13x \\ \\ 26 = 13x \\ \\ x = \frac{26}{13} \\ \\ x = 2[/tex]
Laura runs 6 miles in 50 minutes. At the same rate,how many miles would she run in 35 minutes?
Answers
50/6=8.3
34/8.3=4.2
a city has 5 cm of snow on the ground before snow storm bonus no sign of the amount of snow on the ground increased by 2 cm in an hour which table shows a smaller 8 or change that When one describes
Answers
Answer:
yb
Step-by-step explanation:
Mr.James bought 19 crates of fruits.There were 64 fryits in each crate.If 320 were apples,414 were pears and the rest were mangoes,how many mangoes were there ?
Answers
Answer:
482 mangoes.
Step-by-step explanation:
multiply 64 x 19 which equals to 1216
subtract 320 from 1216 getting 896
Lastly, subtract 414 from 896 getting you answer of 482 mangoes.
Please tell me if you're still having trouble,I would be happy to help :) good luck!