Answers
Answer:
The equation in y = mx+b form is y = (4/3)x - 20/3
The equation in Ax+By = C form is 4x - 3y = 20
There are other ways to express the second equation.
==============================================================
Explanation:
First we must complete the square for x and y.
This will get the equation into (x-h)^2+(y-k)^2 = r^2 form so we can determine the center.
x^2+y^2 - 8x-14y + 40 = 0
(x^2-8x) + (y^2-14y) + 40 = 0
(x^2-8x+16 - 16) + (y^2-14y+49-49) + 40 = 0
(x^2-8x+16) + (y^2-14y+49) + (-16-49+40) = 0
(x-4)^2 + (y-7)^2 = 25
(x-4)^2 + (y-7)^2 = 5^2
This circle is centered at (h,k) = (4,7) and it has radius r = 5.
----------------------
Next, we need to find the slope of line AB such that
A = (4,7) = center of the circle
B = (8,4) = point on the circle, which is the point of tangency
m = slope
m = (y2-y1)/(x2-x1)
m = (4-7)/(8-4)
m = -3/4
The slope of line AB is -3/4. Any perpendicular slope will have us do two things:
flip the fractionflip the signthat would get us from -3/4 to +4/3 or just 4/3.
The perpendicular slope is 4/3.
----------------------
So we must find the equation of the line with slope m = 4/3 and it goes through (x,y) = (8,4)
That means,
y = mx+b
4 = (4/3)*8 + b
4 = 32/3 + b
4 - 32/3 = b
12/3 - 32/3 = b
(12-32)/3 = b
-20/3 = b
b = -20/3
Therefore, the equation of the tangent line is y = (4/3)x - 20/3
Optionally, we can get this equation into standard form like so
y = (4/3)x - 20/3
3y = 4x - 20 ... multiply everything by 3
3y-4x = -20
-4x+3y = -20
4x - 3y = 20
The diagram is shown below.
Related Questions
Convert this rational number
to its decimal form and round
to the nearest thousandth.
1/6
Answers
Answer: 0.166
Step-by-step explanation:
Converting to a decimal:
1/6 = 0.1666 (1 divided by 6 - long division)
Rounding:
0.1666 to the nearest thousandth = 0.166
Please help me out quickly!!
Answers
Answer:
third answer! x = -2/9
Step-by-step explanation:
:)
Can you help me please??
Answers
Answer:
either a or c sry
Step-by-step explanation:
A straw is placed inside a rectangular box that is 6 inches by 8 inches by 5 inches, as shown. If the straw fits exactly into the box diagonally from the bottom left corner to the top right back corner, how long is the straw? Leave your answer in the simplest radical form.
Answers
find out the things that can be purchased between rupees 500 to rupees 100 for your house ?
Answers
We can buy small vases,Flower pots for our houses.
[tex]\sf\orange{Hope \: it \: helps \: please \: mark \: me \: as \: brainliest!}[/tex]
Assume that when adults with smartphones are randomly selected , 44% use them in meetings or classes. If 8 adult smartphone users are randomly selected , find the probability that exactly 3 of them use their smartphone in meetings or classes
Answers
Answer:
you just answered your own question
A store advertises a sale on t-shirts. The advertised price is four t-shirts for $48. Write and solve an equation to find the cost of one t-shirt.
a.) $8
b.) $12
c.) $16
d.) $48
Answers
( Divide by 4 )
1 tshirt = $12 -b.)
Pls give me a brainliest if this helped thx
please solve its due
Answers
Answer:
2118+3391+4785+6354= 16648
Step-by-step explanation:
Write a function rulle
Answers
Hey, there! Based on the table from the picture, every hour increased is $6 increased for the cost of the rental.
First hour: $10
Second hour: $16
Third hour: $22
Fourth hour: $28
So, final answer is:
+1 hour=+$6.
Anyways, I hope this helps! Enjoy your day! Take care!
[tex] {x}^{4} - 16 = [/tex]
What is the answer and steps
Answers
Answer:
[tex](x - 2) \times (x + 2) \times ( {x}^{2} + 4)[/tex]
Step-by-step explanation:
[tex] {x}^{4} - 16[/tex]
➡️ [tex] {x}^{2 \times 2} - 16[/tex]
➡️ [tex] {x}^{2 \times 2} - {4}^{2} [/tex]
➡️ [tex]( {x}^{2} {)}^{2} - {4}^{2} [/tex]
➡️ [tex]( {x}^{2} - 4) \times ( {x}^{2} + 4)[/tex]
➡️ [tex](x - 2) \times (x + 2) \times ( {x}^{2} + 4)[/tex]
Help mee plsssssssdds
Answers
Answer:
No Inez is not correct.
Step-by-step explanation:
[tex]\frac{1}{3} > \frac{1}{5}[/tex] (1/3 is greater than 1/5)
100 10 times as much as ___ of
Answers
Answer:
1 thousand
Step-by-step explanation:
1 ten = 10 x 1 one (Read, as “1 ten is 10 times as much as 1 one.”) 1 hundred = 10 x 1 ten (Say, “1 hundred is 10 times as much as 1 ten.”) 1 thousand = 10 x 1 hundred (Say, “1 thousand is 10 times as much as 1 hundred.”)i hope im right
The solution to 12x = 36 is x =___. (Only input whole number) Numerical Answers Expected! Answer for Blank 1:
Answers
Hi ;-)
12x = 36
x = 36 : 12
x = 3
Hey there! I'm happy to help!
We see that an unknown number x multiplied by 12 is equal to 36. How do we find this number? Well, you can simply go backwards and divide 36 by 12, and this will give us our answer.
36÷12=3
Another way you can think about this is dividing both sides of the equation by 12, which isolates our x.
12x=36
12x÷12=36÷12
x=3
Have a wonderful day and keep on learning! :D
compute the absolute value and the conjugate of z = (1 + i) ^ 6
Answers
Answer:
z = (1 + i)6 =³√2(cos π4+ isinπ4)´6= 8 µcos3π2+ isin3π2)¶= −8i. Hence |z| = 8 and ¯z = 8i. z = (1 + i)
I think I am not real sure
In polar form, we have
[tex]1+i = \sqrt2 e^{i\pi/4}[/tex]
Then by DeMoivre's theorem,
[tex](1+i)^6 = \left(\sqrt2\right)^6 e^{i\,6\pi/4} = 2^3 e^{i\,3\pi/2} = -8i[/tex]
Then
[tex]|z| = |-8i| = \boxed{8}[/tex]
and
[tex]\bar z = \overline{-8i} = \boxed{8i}[/tex]
4. Solve the following equations and verify your answers: (i) 3 (x + 7) = 18
Answers
Answer:
8.33333333333
Step-by-step explanation:
Solution for 3x-7=18 equation:
3x - 7 = 18
3x = 18 + 7
3x = 25 (divide both sides by 3 to get x)
3x/3 = 25/3
x = 8.33333333333
What is the LCM for 18,24
Answers
Answer:
I think the LCM is 72 for 18 and 24
Answer:
hope it helps you........
y link
MIT
MULTIPLE CHOICE QUESTION
Is the following statement, True or False?
lf this same substance were cooling, the
freezing point, or moment when the
substance begins to freeze would happen
at 25 degrees Celsius.
Answers
Answer:
False False False because freezing point is 100 degree celsius
Help thank you………………
Answers
Answer:
it is too easy I will answer it soon.
calculate the amount that would remain in an investment account after 3 years if you were to deposit 1500 every month starting today but would withdraw 750 at the end of every 12 month period. interest is 14% compounded monthly
Answers
Answer:
58995
Step-by-step explanation:
What is 48% of 159 express your answer rounded correctly to one decimal place
Answers
Answer:
.48 * 159 = 76.32
Step-by-step explanation:
48%
=0.48
Step 2: multiply to find the percent
0.48*159=76.32
So 48% of 159 is 76.32
Step 3: Round to the nearest tenth (assuming the one decimal place means tenth place)
76.32
=76.3
If 18 drinks cost £54, how much will 7 drinks cost ?
Answers
Answer:
£21
Step-by-step explanation:
Cost of 18 drinks = £54
Cost of 1 drink
= Cost of 18 drinks/18
= £54/18
= £3
Cost of 7 drinks
= Cost of 1 drink × 7
= £3 × 7
= £21
uhhhhh help lol find angle
Answers
Answer:
129°
Step-by-step explanation:
51+51 =102
360-102=258
258÷2=129
:)
54394 plus 13768
Thank you
Answers
Answer:
[tex]54394 + 13768 \\ \\ = 68162[/tex]
Answer:
68,162 is the answer
Step-by-step explanation:
54394+ 13768 = 68162
Hello I need help in my math
12: {x,y,z} ? {a,b,c} is it equal or not?
13: {0} ? { } equal or not?
Please help no spam no links I need help mark brainliest!!
Answers
12: Equal, because the cardinal number of {x,y,z} are same as {a,b,c}, that is, 3.
13: Not equal, because in set {0}, there is one element , while in set { } , there are no elements at all .
Hope it helps you. Have a nice day!
(by Benjemin)
Benchmark of 6/10, how do I get this worked out
Answers
Answer:
0.60 or 60% is the answer!
Step-by-step explanation:
Hope I helped
11. The sales tax rate for the state of Washington was 8.4%. What is the final cost of a $5,700 car in Washington,
including tax?
$
Answers
Answer:
$5853.60
Step-by-step explanation:
8.4% of $5400 = $453.60
$453.60 + $5400 = $5853.60
What is the correct clases for this drugs
Compazine
heelp me please
Answers
Answer:
It is a addiction XD
Step-by-step explanation:
Bsgsgwgwggwgwfeffefecrcr
A: What is the perimeter of HOUSE?
perimeter of HOUSE =
(round to the nearest hundredth - two decimal places)
B: What is the length of OH?
(round to the nearest thousandth - three decimal places)
C: What is the midpoint of OU?
D: Which is longer, OH or EH?
E: What is the perimeter of the triangle HOU?
perimeter of triangle HOU
(round to the nearest hundredth - two decimal points)
Answers
First calculate distances or lengths(Refer to attachment)
A:-[tex]\\ \sf\longmapsto Perimeter=Sum\:of\:sides[/tex]
[tex]\\ \sf\longmapsto 5.3+9+11+9+9.7[/tex]
[tex]\\ \sf\longmapsto 15+29[/tex]
[tex]\\ \sf\longmapsto 44[/tex]
B:-Refer to the attchment
C:-[tex]\\ \sf\longmapsto \left(\dfrac{1+4}{2},\dfrac{1+6}{2}\right)[/tex]
[tex]\\ \sf\longmapsto \left(\dfrac{5}{2},\dfrac{7}{2}\right)[/tex]
D:-EH>OH
E:-[tex]\\ \sf\longmapsto Perimeter[/tex]
[tex]\\ \sf\longmapsto 9.7+5.3+9[/tex]
[tex]\\ \sf\longmapsto 24[/tex]
Perimeter cm, area square cm
Answers
Step-by-step explanation:
[tex]perimeter = 2(l + b) = \\ 2(15 + 8) = 2(23) = 46cm \\ area = lb \\ 15 \times 8 = 120 {cm}^{2} \\ thank \: you[/tex]
What is the measure of 2x?
Answers
Answer:
130 °
....................
Hi! I'm happy to help!
To solve this, we need to first solve for x.
The total of all the interior angles in a quadrilateral (closed, not curved, shape with 4 sides) is 360°. So, we can single out the xs by subtracting the other angles.
360-89
271
271-76
195
Now that we know that, without the other two angles, the quadrilateral is worth 195. The only 2 angles left have x in them. Since there are 3 xs, we can use this to find out our x.
3x=195
Now, divide both sides by 3.
x=65
Now that we have the value of x, the measure of 2x will just be double that.
65×2
130
The measure of 2x is 130°
I hope this was helpful, keep learning! :D