x²+y²-6x+14y-1=0
and please show your work so I can learn
Answers
Hello there,
I hope you and your family are staying safe and healthy during this winter season.
\(x^2 + y^2 -6x+14y-1=0\)
We need to use the Quadratic Formula*
\(x =\frac{-b+\sqrt{b^2}-4ac }{2a}\) , \(\frac{-b-\sqrt{b^2} -4ac }{2a}\)
Thus, given the problem:
\(a = 1, b=-6, c=y^2+14y-1\)
So now we just need to plug them in the Quadratic Formula*
\(x=\frac{6+2\sqrt{(-6)^2-4(y^2+14y-1)} }{2}\) , \(x=\frac{6-\sqrt{(-6)^2-4(y^2+14y-1)} }{2}\)
As you can see, it is a mess right now. Therefore, we need to simplify it
\(x=\frac{6+2\sqrt{10-y^2-14y} }{2}\), \(x = \frac{6-2\sqrt{10-y^2-14y} }{2}\)
Now that's get us to the final solution:
\(x=3+\sqrt{10-y^2-14y}\), \(x=3-\sqrt{10-y^2-14y}\)
It is my pleasure to help students like you! If you have additional questions, please let me know.
Take care!
~Garebear
Related Questions
Determine the equation of the line that passes through (-8,9) and (2,-6)
Express you answer as a fraction in lowest terms.
Answers
The equation of the line that passes through the points (-8, 9) and (2, -6) is y = (-3 / 2)x - 3.Given two points (-8, 9) and (2, -6). We are supposed to find the equation of the line that passes through these two points.
We can find the equation of a line that passes through two given points, using the slope-intercept form of the equation of a line. The slope-intercept form of the equation of a line is given by, y = mx + b,Where m is the slope of the line and b is the y-intercept.To find the slope of the line passing through the given points, we can use the slope formula: m = (y2 - y1) / (x2 - x1).Here, x1 = -8, y1 = 9, x2 = 2 and y2 = -6.
Hence, we can substitute these values to find the slope.m = (-6 - 9) / (2 - (-8))m = (-6 - 9) / (2 + 8)m = -15 / 10m = -3 / 2Hence, the slope of the line passing through the points (-8, 9) and (2, -6) is -3 / 2.
Now, using the point-slope form of the equation of a line, we can find the equation of the line that passes through the point (-8, 9) and has a slope of -3 / 2.
The point-slope form of the equation of a line is given by,y - y1 = m(x - x1)Here, x1 = -8, y1 = 9 and m = -3 / 2.
Hence, we can substitute these values to find the equation of the line.y - 9 = (-3 / 2)(x - (-8))y - 9 = (-3 / 2)(x + 8)y - 9 = (-3 / 2)x - 12y = (-3 / 2)x - 12 + 9y = (-3 / 2)x - 3.
Therefore, the equation of the line that passes through the points (-8, 9) and (2, -6) is y = (-3 / 2)x - 3. Thus, the answer is (-3/2)x - 3.
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Solve for t.
3t- 2 = -11
A. -12
B. -11
C. -9
D.-3
Answers
Answer:
T = -3
Step-by-step explanation:
No explanation needed ...
The Pythagorean Theorem, given by the formula a^2+b^2=c^2 , relates the three sides of a right triangle. Solve the formula for the positive value of a in terms of b and c.
Answers
Answer:
c=√a²b²
Step-by-step explanation:
Hope this helps!
If you buy a home with less than 20% down, you will pay an additional monthly fee, PMI (private
mortgage insurance), until you reach 20% equity. Keep track of when you reach 20% equity so you
can request to have your PMI removed. Ken Buckmiller’s home recently appraised at $290,000. His
mortgage was for $275,000 at 5% for 30 years with PMI of $229. 17 per month. What is his monthly
payment plus PMI? His mortgage balance is currently $222,990. Has he reached 20% equity? (Use
Table 15. 1. ) (Do not round intermediate calculations. Round your answer to the nearest cent. )
Monthly payment $ 1,705. 43
Has he reached 20% equity? Yes
Answers
He has exceeded the 20% equity threshold. He is exempt from paying PMI because his present equity is 38.38%.
what is PMI ?Once your property has 20% equity, you can often ask to cease paying PMI after you've purchased it. When your equity reaches 22%, PMI is frequently immediately terminated. Only conventional loans are subject to PMI. Mortgage insurance for other sorts of loans frequently comes in different forms.
calculation
calculating the equivalent monthly payments
282,000 is the principal, and 5% each year, or 0.416667% per month, or 0.00416667, is the rate of interest. There are 360 installments total (30 years X 12)
Total monthly payments equal 1513.84 for the equated monthly mortgage and 299.17 for the PMI, for a total of $1,813.01 for the equated monthly mortgage and PMI.
He must continue paying the PMI until he gets 20% equity. now calculate his equity percentage.
He has exceeded the 20% equity threshold. He is exempt from paying PMI because his present equity is 38.38%.
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ASAP PLEASE HELP!!!! WRITE AN EXPRESSION
Answers
Answer:
10c + 5b + 420 + 4c
Step-by-step explanation: 10 dollars for each child, 5 dollars per a pair of rubber boots, party room is 420 and 4 is per each child's pizza
Select the correct answer from each drop-down menu. during dna replication, the strand is synthesized in the 5′ to 3′ direction. the strand that runs away from the replication fork is synthesized because .
Answers
The Leading strand is created during DNA replication in a 5′ to 3′ orientation. Because DNA polymerase cannot generate in the 3' - 5' direction, the strand that moves away from the origin of replication is created in fragments.
Okazaki fragments are the name given to the created pieces. The ligase enzyme is subsequently used to join these pieces together. Synthesis takes place on the strand that flees the replication fork. Due to DNA polymerase's inability to synthesize in the 5' - 3' direction.
The constructed pieces are referred to as Okazaki fragments.
With the aid of the enzyme ligase, each fragment is firmly connected to the other one.
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The question is -
Select the correct answer from each drop-down menu.
During DNA replication, the ___ (Lagging, Okazaki, Leading.) strand is synthesized in the 5′ to 3′ direction. The strand that runs away from the replication fork is synthesized in ___ (In Fragments, By RNA polymerase, Continuously, Without Primers.) because ___ (DNA polymerase cannot synthesize in the 5' to 3' direction, RNA polymerase can only add primers to the lagging strand, RNA polymerase can only add primers to the leading strand, DNA polymerase cannot synthesize in the 3' to 5' direction.)
Find the volume of the figure. Use 3.14 for π. If necessary, round your answer to the nearest tenth.
Answers
Answer:
If the radius and height of the cylinder are 6 meters and 3 meters. Then the volume of the cylinder is 339.3 cubic meters.
What is a cylinder?
A cylinder is a closed solid that has two parallel circular bases connected by a curved surface.
A cylinder has a radius of 6 meters and a height of 3 meters.
Then the volume of the cylinder will be
Where r is the radius of the cylinder and h is the height of the cylinder.
Then we have
V = 3.14 × 6² × 3
V = 339.3 m³
Then the volume of the cylinder is 339.3 cubic meters.
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Step-by-step explanation:
marcos is planning to travel from phoenix to flagstaff. let t represent the number of hours since marcos left phoenix and let d represent the number of miles marcos has traveled from phoenix.
Answers
In this scenario, Marcos is planning to travel from Phoenix to Flagstaff, and we are using variables to represent different aspects of his journey.
The variable t represents the number of hours since Marcos left Phoenix, which serves as a measure of time elapsed since the start of the journey. It allows us to track the progress of Marcos over time and analyze various time-related aspects such as the duration of the journey or the rate at which he is traveling. On the other hand, the variable d represents the number of miles Marcos has traveled from Phoenix. It serves as a measure of distance covered, indicating how far Marcos has progressed on his route. By monitoring the value of d, we can determine the distance remaining to reach Flagstaff or calculate other distance-related parameters such as average speed or total distance traveled.
By using these variables, we can establish a relationship between time and distance traveled by Marcos. This relationship can be represented by a function or equation that describes Marcos' progress over time, such as a velocity equation or a distance-time equation. These variables and their relationship allow us to analyze and make predictions about Marcos' journey. We can determine when he is expected to reach certain milestones, calculate his average speed or rate of travel, and estimate the time required to complete the journey. Additionally, these variables provide a framework for solving various problems or making decisions related to Marcos' travel, such as optimizing his route or estimating fuel consumption based on distance traveled.
In summary, by using the variables t and d to represent time and distance traveled, respectively, we can effectively describe and analyze Marcos' journey from Phoenix to Flagstaff, enabling us to make informed decisions and predictions about his travel experience.
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Which outcome is most likely to occur along a transform boundary?
earthquakes
deep-sea trenches
rugged mountain ranges
hot spots
Answers
Answer:
The grinding action between the plates at a transform plate boundary results in shallow earthquakes, large lateral displacement of rock, and a broad zone of crustal deformation.
Step-by-step explanation:
It transform boundaries are where plates slide past each other causing friction, leading to earthquakes.
This is my answer absolute 100% correct
Hope it helps Favor(Brainliest)
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For each of the bookcases a woodworker is building, she
charges $65 for materials. She also charges $35 for each
hour she works to build the bookcases. How much does
the woodworker charge for working 100 hours to build 18
bookcases?
A$4,735
B$3,565
C$3,583
D $4,670
Answers
35x100 hours = $3500+$65= $3565 for 100 hours of work and materials.
answer is b
my sister just had this question
Use the drawing tools to form the correct answers on the graph.
Consider this linear function:
y=\frac{1}{2}x+1
Plot all ordered pairs for the values in the domain.
D: {-8, -4, 0, 2, 6}
Answers
Answer:
y = 1/2+1 increasing by 1/2 (-8 -4 ) (-4 0) (2 6)
Step-by-step explanation:
increasing by 1/2 (-8 -4 ) (-4 0) (2 6) see attached as -2 0 and 0 1 has a midway point -1 and 1/2
Anthony wanted to get a job after school. His
neighbor said he would pay him $8.00 an hour for 4
hours a day to mow his lawn and rake the leaves.
How much would Anthony make in one day? *
Answers
Work for 4 hours a day so
$8x 4 =32
So he make $32 a day
Anthony would make 32 dollars
If 3 pizzas cost $26.97, one pizza is $ ____
Answers
Please help 60 points for a rapid answer-In the figure below which of the following is true in circle E?
Answers
Answer:
all 3 options are true : A, B, C
Step-by-step explanation:
warning : it has come to my attention that some testing systems have an incorrect answer stored as right answer for this problem.
they say that A and C are correct.
but I am going to show you that if A and C are correct, then also B must be correct.
therefore, my given answer above is the actual correct answer (no matter what the test systems say).
originally the information about the alignment of the point F in relation to point E was missing.
therefore, I considered both options :
1. F is on the same vertical line as E.
2. F is not on the same vertical line as E.
because of optical reasons (and the - incomplete - expected correct answers of A and C confirm that) I used the 1. assumption for the provided answer :
the vertical line of EF is like a mirror between the left and the right half of the picture.
A is mirrored across the vertical line resulting in B. and vice versa.
the same for C and D.
this leads to the effect that all 3 given congruence relationships are true.
if we consider assumption 2, none of the 3 answer options could be true.
but if the assumptions are true, then all 3 options have to be true.
now, for the "why" :
remember what congruence means :
both shapes, after turning and rotating, can be laid on top of each other, and nothing "sticks out", they are covering each other perfectly.
for that to be possible, both shapes must have the same basic structure (like number of sides and vertices), both shapes must have the same side lengths and also equally sized angles.
so, when EF is a mirror, then each side is an exact copy of the other, just left/right being turned.
therefore, yes absolutely, CAD is congruent with CBD. and ACB is congruent to ADB.
but do you notice something ?
both mentioned triangles on the left side contain the side AC, and both triangles in the right side contain the side BD.
now, if the triangles are congruent, that means that each of the 3 sides must have an equally long corresponding side in the other triangle.
therefore, AC must be equal to BD.
and that means that AC is congruent to BD.
because lines have no other congruent criteria - only the lengths must be identical.
N
-5-4-3
3
17
₁
-2-
3 4 5
f(x)=x
2 3 4
8
E
9
TIME REMAINING
10
42:59
Which absolute value function, when graphed,
represents the parent function, f(x) = |x|, reflected over
the x-axis?
O f(x) = -x|
O-f(x) = |-x|
O f(x) = x + 1
O f(x) = |x-1|
2
Answers
`O-f(x) = |-x|`
This is because the absolute value function reflects all negative values across the x-axis. So, if we take the opposite of the absolute value of `x`, we get the reflection of the parent function over the x-axis.
suppose x ~ n(15, 3). between what x values does 68.27% of the data lie? the range of x values is centered at the mean of the distribution (i.e., 15).
Answers
For provide normal distribution such that
x ~ n(15, 3), 68.27% of the data lie between the values of x as x= 12 to x= 18 .The range of x-values is centered around the mean of the distribution (that is, 15).
Normal Probability:
This problem uses the Z-score formula to calculate the range such that 68.27% of the data falls within the range. Z-scores are normal scores, plotted on a normal curve with mean 0 and variance 1. The Excel function NORM.S.INV() is used to get the score value.
We have given that
Mean, μ = 15
Standard deviation, σ = 3
P( a <X<b) = 0.6827
P( (a − μ)/(σ < X − μ )/σ <(b− μ)σ) = 0.6827
P ( a- 15) /3 < Z < (b- 15)/3) = 0.6827
P( Z< (b-15)/3) - P( Z< ( a - 15)/3) = 0.6827
1 - P( Z > (b-15)/3) - P( Z< ( a - 15)/3) = 0.6827
(Symmetrical Property)
We know that,
P( Z> (b-15)/3) = P( Z< ( a - 15)/3) ( symmetric)
2 × P( Z< ( a - 15)/3) = 0.3173
P( Z< ( a - 15)/3) = 0.15865
Now,
Excel function for the value of z score:
=NORM.S.INV(0.15865)
(a − 15)/3 = -1.00
=> a-15 = -3
=> a = 12 and b = 15 + 3 = 18
Hence, the values of x are 12 and 18 where 68.27% data lie.
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6. Which equation represents a quadratic function?
a. y = 2 + (x + 1)
b. y = (x + 1) - 2
c. y = (x + 1) ^ 2 + 1
d. y = (x + 2y) - 1
Answers
Answer:
option c
Step-by-step explanation:
hope it helps you
plzzz mark as brainliest
don’t understand please help
Answers
x = 3 & y = -6
Explanation:
y = -2x
y = 5x - 21
FINDING X
Since y = -2x we can substitute the y in the second equation with -2x.
-2x = 5x - 21
There is two x’s so you have to get rid of one, in this case 5x, by subtracting it from both sides.
-2x = 5x - 21
-5x -5x
—————
-7x = -21
Then we are going to isolate the x by dividing -7 by both sides.
-7x = -21
—— —— - 7 divided by 7 is 1 so it
-7 -7 would be 1x or x
x = 3
So our x is 3. Now we move on to finding y.
FINDING Y
To do that, we are going to use the first equation.
y = -2x
We are going to plug in the x.
y = -2(3)
y = -6
So our y is -6.
CHECKING
If you want to check it to make sure you have the correct answer you can just plug all of it in to the equation.
y = 5x - 21
-6 = 5(3) - 21
-6 = 15 - 21
-6 = -6
Graph the line that has a slope of 8/5 and includes the point (5,1). can you type the points on the graph, please
Answers
Answer:
Step-by-step explanation:
Sorry, I couldn't draw the line. Hope it helps. :)
\(\sf -31 - 4x = -5 - 5(1 + 5x)\)
Answers
Answer:
x = 1
Step-by-step explanation:
Given equation,
→ -31 - 4x = -5 - 5(1 + 5x)
Now the value of x will be,
→ -31 - 4x = -5 - 5(1 + 5x)
→ -31 - 4x = -5 - 5 - 25x
→ -4x + 25x = -10 + 31
→ 21x = 21
→ x = 21/21
→ [ x = 1 ]
Hence, the value of x is 1.
The value of the variable x in the equation -31 -4x = -5- 5(1+ 5x) will be 1.
The given algebraic expression with the variable x is,
-31 - 4x = -5 -5(1+ 5x)
By further solving it, we get,
- 31 - 4x = -5 -5 -25x
To simplify the equation, we have to first separate the constants and variables,
=> 25x - 4x = -5 -5 + 31
=> 21x = 31 - 5 -5
=> 21x = 31- 10
=> 21x = 21
=> x = 21/21
=> x= 1.
Hence, the value of the variable x in the algebraic expression, -31 - 4x = -5 -5(1+ 5x), is found to be 1.
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Statistics suggest that many people with a disability are Group of answer choices c) an undereducated and underemployed minority group. d) better off than nondisabled Americans. b) well taken care of by their families. a) well taken care of by the government.
Answers
Option c) "an undereducated and underemployed minority group" is the most accurate representation based on available statistics and research.
The statement that statistics suggest that many people with a disability are "an undereducated and underemployed minority group" (option c) is generally supported by research and data. People with disabilities often face challenges in accessing education and employment opportunities compared to their nondisabled counterparts. Studies have shown that individuals with disabilities have lower educational attainment levels and higher rates of unemployment or underemployment. They may encounter barriers related to discrimination, lack of accessibility, and limited accommodations in education and employment settings. Option c) "an undereducated and underemployed minority group" is correct.
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Find all the missing elements:C = 120°b = 5C = 11A = [?]° B = [ ]º a = [
![Find all the missing elements:C = 120b = 5C = 11A = [?] B = [ ] a = [](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/xrQbCgyq4XeIHqZmc84nxWpLrbdTQfmh.jpeg)
Answers
ANSWERS
• A = 36.8°
,• B = 23.2°
,• a = 7.6
EXPLANATION
We can find B using the law of sines,
We have b = 5, c = 11 and C = 120°. Using the last two ratios,
\(\frac{b}{\sin B}=\frac{c}{\sin C}\)Rise both sides of the equation to -1 - i.e. flip both sides,
\(\frac{\sin B}{b}=\frac{\sin C}{c}\)Multiply both sides by b,
\(\sin B=\frac{b}{c}\sin C\)And take the inverse of the sine,
\(B=\sin ^{-1}\mleft(\frac{b}{c}\sin C\mright)\)Replace with the values and solve,
\(B=\sin ^{-1}\mleft(\frac{5}{11}\sin 120\degree\mright)\approx23.2\degree\)Then, knowing that the sum of the measures of all the interior angles of a triangle is 180°, we find A,
\(A+B+C=180\degree\)Solving for A,
\(A=180\degree-B-C=180\degree-23.2\degree-120\degree\approx36.8\degree\)Finally, let's find a using the law of sines with the first and last ratios,
\(\frac{a}{\sin A}=\frac{c}{\sin C}\)Solving for a,
\(a=c\cdot\frac{\sin A}{\sin C}=11\cdot\frac{\sin 36.8\degree}{\sin 120\degree}\approx7.6\)Hence, the missing elements are A = 36.8°, B = 23.2° and a = 7.6.
![Find all the missing elements:C = 120b = 5C = 11A = [?] B = [ ] a = [](https://i5t5.c14.e2-1.dev/h-images-qa/answers/attachments/Y4ZvA4a71698diSqVvrLrAnL4l5nUBOD.png)
Find the divergence of the vector field. F(x, y, z) = 5x²7 - sin(xz) (i+k)
Answers
The divergence of the vector field F(x, y, z) = (5x^2 + 7 - sin(xz))i + 0j + (5x^2 + 7 - sin(xz))k is 20x - 2zcos(xz).
To find the divergence of the vector field F(x, y, z) = (5x^2 + 7 - sin(xz))i + 0j + (5x^2 + 7 - sin(xz))k, you need to take the divergence operator (∇ · F).
The divergence of a vector field in Cartesian coordinates is given by the following formula:
∇ · F = (∂Fx/∂x) + (∂Fy/∂y) + (∂Fz/∂z),
where Fx, Fy, and Fz are the x, y, and z components of the vector field F, respectively.
In this case, we have:
Fx = (5x^2 + 7 - sin(xz)),
Fy = 0, and
Fz = (5x^2 + 7 - sin(xz)).
Taking the partial derivatives, we get:
∂Fx/∂x = 10x - zcos(xz),
∂Fy/∂y = 0, and
∂Fz/∂z = 10x - zcos(xz).
Now, substituting these derivatives into the divergence formula, we have:
∇ · F = (10x - zcos(xz)) + 0 + (10x - zcos(xz)).
Simplifying further, we get:
∇ · F = 20x - 2zcos(xz).
Therefore, the divergence of the vector field F(x, y, z) = (5x^2 + 7 - sin(xz))i + 0j + (5x^2 + 7 - sin(xz))k is 20x - 2zcos(xz).
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Work out m and c for the line: y = 1 − 8 x
Answers
Answer:
m = - 8 , c = 1
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 1 - 8x = - 8x + 1 ← is in slope- intercept form
with m = - 8 and c = 1
convert rational numbers to decimal form and round to the nearest thousand 3/8
Answers
can anybody help me with this im kinda stumped
Answers
Answer:
C is the correct function.
Can somebody do this I’ll mark brainliest pls
Answers
Answer:
both are 75 degrees
Step-by-step explanation:
the angles add up to 180, as they are also vertical angles
Answer:
b=c since they are vertical angles, b=75 and c=75
Step-by-step explanation: The angle opposite of the given is the same (105) that gives you two measure. Add 105+105 to get 210. A set of vertical angles=360 degrees, take away 210 from 360 to get the measure of b+c. Divide that by two to get the measure of either b or c.
At the end of which day does Tyler have 2750 feet left to climb?
Answers
a jersey has two digit number.in how many ways can the number be arranged if a)no double digit is allowed b)double digit are allowed
Answers
Answer:
a) 90
b) 100
Step-by-step explanation:
This is a probability problem. In order to solve it, we must multiply the number of possible numbers by eachother.
a) the first digit can be any number between 0 and 9. That's 10 options. The second digit must be different from the first one: that's 9 options. 10x9=90
b) the first digit can be any number between 0 and 9. That's 10 options. The second digit can also be any number between 0 and 9. That's also 10 options. 10x10=100
I
need the details why we choose answer c
109) Use the following random numbers to simulation crop yield for 10 years: 37, 23, 92, 01, 69, 50, 72, 12, 46, 81. What is the estimated crop yield from the simulation? A) 425 B) 442 C) 440 D) 475 A
Answers
The estimated crop yield from the simulation is 443 (option b).
To estimate the crop yield from the given random numbers, we need to assign a specific meaning to each random number. Let's assume that each random number represents the crop yield for a particular year.
Given random numbers: 37, 23, 92, 01, 69, 50, 72, 12, 46, 81
To find the estimated crop yield, we sum up all the random numbers:
37 + 23 + 92 + 01 + 69 + 50 + 72 + 12 + 46 + 81 = 443
Therefore, the estimated crop yield from the simulation is 443. The correct option is b.
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