a) The x-coordinates of the points A and B are [tex]x_{A} = 11[/tex] and [tex]x_{B} = -7[/tex].
b) The point of intersection of the tangents to the circle at A and B is [tex](x,y) = (2, 27)[/tex].
a) In this part we simplify the equation of the circle and solve for [tex]x[/tex] to determine the coordinates associated to the required points:
The coordinates of the two points so that circle intersects the x-axis, occurs when the following condition is met:
[tex]f(x, 0) = 0[/tex] (1)
Where [tex]f(x,y)[/tex] is in implicit form.
If we know that the equation of the circle is [tex]x^{2} + y^{2} - 4\cdot x + 6\cdot y - 77 = 0[/tex] and [tex]y = 0[/tex], then the reduced equation is:
[tex]x^{2} - 4\cdot x - 77 = 0[/tex] (2)
And we obtain the x-coordinates of the points by factoring (2):
[tex](x-11) \cdot (x + 7) = 0[/tex]
The x-coordinates of the points A and B are [tex]x_{A} = 11[/tex] and [tex]x_{B} = -7[/tex].
b) Lines are defined by both slope and intercept. Slope is defined by implicit differentiation and intercept is found by equation of the line.
Given that [tex]A(x,y) = (11, 0)[/tex] and [tex]B(x,y) = (-7, 0)[/tex], we determine line equations corresponding to each tangent line:
Slope
[tex]2\cdot x + 2\cdot y \cdot \dot y - 4 + 6\cdot \dot y = 0[/tex]
[tex](2\cdot y + 6)\cdot \dot y = 4 - 2\cdot x[/tex]
[tex]\dot y = \frac{2 - x}{y + 3}[/tex]
Point A
[tex]\dot y = \frac{2-11}{0 + 3}[/tex]
[tex]\dot y = -3[/tex]
Point B
[tex]\dot y = \frac{2-(-7)}{0 + 3}[/tex]
[tex]\dot y = 3[/tex]
Intercept
Point A ([tex]A(x,y) = (11, 0)[/tex], [tex]\dot y = -3[/tex])
[tex]b = y - m\cdot x[/tex]
[tex]b = 0 - (-3)\cdot (11)[/tex]
[tex]b = 33[/tex]
Point B ([tex]B(x,y) = (-7, 0)[/tex], [tex]\dot y = 3[/tex])
[tex]b = y - m\cdot x[/tex]
[tex]b = 0 - 3\cdot (-7)[/tex]
[tex]b = 21[/tex]
The equations of the lines tangent to the circle are:
[tex]y = -3\cdot x +33[/tex] (3)
[tex]y = 3\cdot x +21[/tex] (4)
The point of intersection is the solution of this system of linear equations:
[tex](x,y) = (2, 27)[/tex]
The point of intersection of the tangents to the circle at A and B is [tex](x,y) = (2, 27)[/tex].
We kindly invite you to see this question on circles: https://brainly.com/question/23988015
A king Palm can grow about 21 feet a year . Estimate the height of the kind palm , yard ,after 15 years
Answer:
10.5 yards after 15 years
Step-by-step explanation:
2.1 feet times 15 years, which equals to 31.5 feet, convert 31.5 feet into yards, so divide it by 0.3, and that equals to approximately 10.5 yards
Solve for x. 2x^2-4x=0
A.
0, -4
B.
0, -2
C.
0, 2
D.
2, 4
If $1000 is invested for 2 years with a 3% yearly interest rate. What is the amount of simple interest
Answer:
Total: 1060 Gain: 60
Step-by-step explanation:
1000 (Current Amount) x 0.03 (3% as a decimal) x 2 (year amount) = 60 + 1000 (Original Amount Invested) = 1060
Find the nth term for the following sequences, 100,96,90,82,72.(an^2+bn+c)
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Answer:
t(n) = -n^2 -n +102
Step-by-step explanation:
We can use the first 3 terms to find a, b, c.
a(1)^2 +b(1) +c = 100
a(2)^2 +b(2) +c = 96
a(3)^2 +b(3) +c = 90
Subtract the first equation from the other two:
3a +b = -4 . . . . . . [eq4]
8a +2b = -10 . . . . [eq5]
[eq5] can be reduced to
4a +b = -5 . . . . . . [eq6]
Subtracting [eq4] from [eq6] gives ...
(4a +b) -(3a +b) = (-5) -(-4)
a = -1 . . . . . . . . simplify
Filling that into [eq4], we get
3(-1) +b = -4
b = -1 . . . . . . . add 3
Putting the values for 'a' and 'b' into the first equation gives ...
-1 +-1 +c = 100
c = 102
Then the n-th term t(n) of the sequence is ...
t(n) = -n^2 -n +102
_____
Additional comment
As you might guess, there is a generic solution for quadratic sequences. In terms of the first term (a1), first first difference (d1), and second difference (d2), the coefficients can be written as ...
a = d2/2b = d1 -3ac = a1 -d1 +d2This sequence has first differences of -4, -6, -8, -10, and second differences of -2. Putting the sequence values into the above formulas, we find ...
a = -2/2 = -1b = -4 -3(-1) = -1c = 100 -(-4) +(-2) = 102 . . . . . as abovePaul bought a student discount card for the bus. The card allows him to buy daily bus passes for $1.30. After one month, Paul bought 12 passes and spent a total of $22.60.
How much did he spend on the student discount card?
Answer:
$10.24
Step-by-step explanation:
12(1.30)=12.36
22.60-12.36=10.24
Help will give Brainly points
A contractor removed 357 cubi c ya rds of earth from a building site. If the contractor’s trucks can haul 17 cubic yards per load, how many truckloads of earth were moved?
Answer:
21 loads
Step-by-step explanation:
357/17=21
PLEASE HELP- brainliest and points will be given
Answer: Choice B
[tex]\frac{1}{\sqrt{65}}<-4, 7>[/tex]
===============================================================
Explanation:
Consider a right triangle with legs a = 4 and b = 7. Through the pythagorean theorem, the hypotenuse is
c = sqrt(a^2+b^2) = sqrt(4^2+7^2) = sqrt(65)
This represents the length of the vector <-4,7>
Dividing each component by the length will normalize the vector. This is the same as multiplying by [tex]\frac{1}{\sqrt{65}}[/tex] which is what choice B shows. The phrasing "normalize the vector" means "make the vector to be of length 1". A common application of normalizing vectors will come up in computer graphics.
The original vector and the vector mentioned in choice B point in the same direction. The only thing that has changed is the length from sqrt(65) to 1.
Can someone please help me please?
[tex] \large \mathfrak{Answer : }[/tex]
The equation of the red parabola is :
[tex]f(x) = 1 - {x}^{2} [/tex]therefore , correct option in A
Evaluate the expression.
6(3 + 5)
26.
4
HELP
Answer =1267.2
Step-by-step explanation:
6(3+5)26.4
6×8×26.4
48×26.4
1267.2 is the answer
please help me answer this question.. am giving brainliest
Step-by-step explanation:
We are going to use the following properties of logarithms to solve this problem:
[tex]\log{\dfrac{a}{b}} = \log{a} - \log{b}[/tex]
and
[tex]\log{ab} = \log{a} + \log{b}[/tex]
So we can rewrite the given equation as
[tex]\log{2x^3} - \log{x} = \log{\left(\dfrac{2x^3}{x}\right)} = \log{2x^2}[/tex]
Also,
[tex]\log{16} + \log{x} = \log{(16x)}[/tex]
So we can write
[tex]\log{2x^2} = \log{(16x)}[/tex]
or eliminating the log symbols, we get
[tex]2x^2 = 16x[/tex]
The solutions for the equation above are
[tex]x = 8\:\text{and}\: 0[/tex]
40 points please help
Answer:
[tex]\huge\boxed{-2}[/tex]
Step-by-step explanation:
Use any two points from the line.
Let them be:
(x1,y1) = (0,-2)
(x2,y2) = (-1,0)
Now,
[tex]\displaystyle Slope = \frac{y_2-y_1}{x_2-x_1} \\\\Slope = \frac{0-(-2)}{-1-0} \\\\Slope = \frac{2}{-1} \\\\Slope = -2\\\\\rule[225]{225}{2}[/tex]
Hope this helped!
~AH1807Really need help quick
Answer:
Total Number of times Spun = 1200
Key sentence: "Pr(Red) is same as Pr(Yellow).
Pr(Green)= 0.2
0.2 = x/1200
x= 0.2 x 1200
x = 240.
It landed on green 240 times
Pr(Brown) =0.54
0.54 = y/1200
y= 1200 x 0.54
y= 648.
Now
To get the Number of times it landed on Red and Yellow
You simply subtract that of Green and Brown from 1200 and divide this result by 2(Since Red and Yellow are have equal occurrence).
1200 – (648 + 240)
= 312.
312/2 = 156.
So It landed on Red and Yellow 156 times each.
Step-by-step explanation:
Red ----- 156times
Green -----240times
Brown ----- 648times
Yellow -----156times
How do I write 680,705 in expanded form.
Answer:
600,000+80,000+700+5
Please help me and thank you!! Show the steps also please I got 198x
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Answer:
264x³-66x
Step-by-step explanation:
The order of operations requires this be evaluated as ...
11x(96x÷4x -6) . . . . given
11x(24x·x -6) . . . . . . division inside parentheses
11x(24x² -6) . . . . . . multiplication inside parentheses
264x³ -66x . . . . . multiply by outside factor (use the distributive property)
_____
Additional comment
The appearance of the expression in parentheses may induce you to evaluate it as (96x)÷(4x) = 24. The order of operations requires that you do the division before the multiplication, left to right, so this must be evaluated as ...
((96x)÷4)x = 24x²
You need to be very careful with division and with exponents to make sure to follow the Order of Operations exactly. If you have an appropriate calculator, it will do that automatically. For example, if you tell your calculator ...
(for x=2) 11×2×(96×2÷4×2-6)
it should give you the result 1980, not 396.
Answer:
= 198x
Step-by-step explanation:
11x × { 96x ÷ 4x -6}
11x × { 24x -6}
264x - 66x
= 198x
You got the correct answer
Find the distance between the pair of points A(7,8) B(-8,4)
Answer:
Formula:
[tex]length = \sqrt{ {(x _{1} -x_{2} )}^{2} + {(y_{1} -y_{2}) }^{2} } [/tex]
substitute:
[tex]l = \sqrt{ { \{7 - ( - 8) \}}^{2} + {(8 - 4)}^{2} } \\ \\ l = \sqrt{225 + 16} \\ l = \sqrt{241} \\ { \boxed{ \boxed{length = 15.5 \: units}}}[/tex]
Find A in degrees C= 120° b= 5 c= 11
Answer:
36.8
Step-by-step explanation:
I think A=36.8
Hope it will help you (:
435 divided by 15 equals what?
A triangle with a perimeter of 30 inches has sides of x+3, 2x+5, and x. find the value of x
Answer:
x = 5.5 inches.
Step-by-step explanation:
The perimeter is the sum of the 3 sides, so:-
x + x + 3 + 2x + 5 = 30
4x + 8 = 30
4x = 22
x = 5.5.
PLEASE HELP!!! How does the multiplicity of a zero affect the graph of the polynomial function?
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Answer:
2, 4, 61crossStep-by-step explanation:
Consider a zero at x=1.
If it has multiplicity 1, the corresponding factor is (x -1). Now consider the sign of that factor for x = 1.1. The value is (1.1 -1) = 0.1, a positive number.
When the value of x is 0.9, the factor is (0.9 -1) = -0.1, a negative number.
This tells you that values to the left of a zero make the factor(s) associated with that zero be negative. For x-values to the right of the zero, the factor(s) will be positive.
If the multiplicity is even, the product of those factors is positive on either side of the zero. (A negative number to an even power is a positive number.) That is, the graph will not change sign from one side of an even-multiplicity factor to the other. At an odd-multiplicity factor, the graph changes sign.
__
For the problem at hand, the only even-multiplicity factor is (x -1), so the graph will not change sign at x=1. It will touch the axis (be tangent to the x-axis), but will not cross. The other zeros have odd multiplicity (1 or 3), so the graph will change sign there.
It is worthwhile to note that the higher the multiplicity, the "flatter" the graph is at the zero. You can see this in the attachment by comparing the shape of the graph at x=6 with the shape at x=2 (also an upward zero crossing).
_____
Additional comment
You may wonder why the curve is below the x-axis at x=1 when the product of the factors in that neighborhood is always positive. The reason is that there are an odd number of zeros to the right of x=1, so the product of those factors is negative.
Match the expression to its value.
104
1
= 0.01
102
104
102
10,000
10-4. 102
1
= 0.000001
109
10-4
1
= 0.0001
10-
Answer:
Ans; 10⁴ —> 10, 000
Ans; 10-⁴ / 10² —> 1/ 10⁶ = 0. 000 001
Ans; 10-⁴ × 10² —> 1/ 10² = 0.01
Ans; 10-⁴ —> 1/ 10⁴ = 0. 000 1
I hope I helped you^_^
Answer:
A=a
B=d
C=c
D=b
Step-by-step explanation:
Solve for x: x^2+4b=0
Answer:
[tex] {x}^{2} + 4b = 0 \\ {x}^{2} = - 4b \\ x = \sqrt{ - 4b} \\ x = 2 \sqrt{b} i \\ thank \: you[/tex]
write 3.777777777 as a mixed number
Liliana has $2.10 in nickels and quarters in her backpack. She has 12 more nickels than quarters. How many coins of each type does she have?
Step-by-step explanation:
17 nickels and 5 quarters I just thought way to much for such a simple question
A cab company charges $3 per cab ride,
plus an additional $2 per mile driven. How
long is a cab ride that costs $11?
miles
Answer:
The answer is c = 2 + 3d .
Step-by-step explanation:
It is given that a cab ride cost $2 which is a fixed amount and charges additional $3 per mile. So you have to make an equation of c in terms of d :
Let c be the cost,
Let d be the distance,
c = 2 + 3d
Evaluate u + xy, if u = 18, x = 10, and y = 8
Answer:
[tex]u + xy \\ 18 + 10 \times 8 \\ 10 + 80 \\ 90[/tex]
Answer:
Solution,
here,
u=18
x =10
y= 8
=u+xy
=18+(10×8)
=18+80
=98
3) A bullet travels 2400 feet per second. Write this in miles per hour, rounded to the nearest
whole mile per hour. Reference: 1 mile = 5280 feet
Answer:
1636mi/hr
Step-by-step explanation:
2400ft/s = _______mi/hr 1 hr = 3600s 1mi = 5280ft
2400ft/s x 3600s/hr x 1mi/5280ft = 1636mi/hr
what is statistics ???
explain !!!
Answer:
what is statistics ???
explain !!!
Step-by-step explanation:
Statistics is the science concerned with developing and studying methods for collecting, analyzing, interpreting and presenting empirical data. ... Probability is a mathematical language used to discuss uncertain events and probability plays a key role in statistics.Please mark me as brainliest
inductive reason what is next number in sequence 400, 200, 300, 150, 250
Answer:
125
Step-by-step explanation:
400÷2 = 200
300÷2 = 150
so,
250÷2 = 125
A hotel has a total of 7 floors if there are 35 standard rooms on each floor how many standard rooms are there
Answer:
245
Step-by-step explanation:
multiple the amount of rooms on each floor (35) by the amount of floors (7)
35x7=245 rooms
