The equation for a circle with a center (-2, 8) and a radius of 9 will be (x + 2)² + (y − 8)² = 81.
What is an equation of a circle?A circle can be characterized by its center's location and its radius's length.
Let the center of the considered circle be at the (h,k) coordinate.
Let the radius of the circle be 'r' units.
Then, the equation of that circle would be:
(x - h)² + (y - k)² = r²
Write an equation for a circle with a center (-2, 8) and a radius of 9.
Then the equation will be
(x + 2)² + (y − 8)² = 9²
(x + 2)² + (y − 8)² = 81
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The zeros of a parabola are -4 and 2 and (6,10) is a point on the graph which equation can be solved to determine the value of a in the equation of the parabola
Answer:
Let consider the following linear equation systems by using the known points and second-grade polynomial:
(-1, 7)
a + b + c = 7a+b+c=7
(5, 7)
25\cdot a + 5\cdot b + c = 725⋅a+5⋅b+c=7
(6,10)
36\cdot a + 6 \cdot b + c = 1036⋅a+6⋅b+c=10
After some algebraic manipulation, the values for the polynomial coefficients are found:
a = \frac{3}{5}a= 53 , b = -\frac{18}{5}b=− 518
, c = 10c=10
The polynomial is:
y = \frac{3}{5}\cdot x^{2} - \frac{18}{5}\cdot x+10y= 53
⋅
Step-by-step explanation:
For complete solution see the above attachment!
Please help I can’t figure it out
Answer: -4
Step-by-step explanation: Notice that the increments in the graph do not go in 1's, but in 2's. Meaning the first line is 2, and second line is 4, and in the middle is 3. Be careful.
The range is where the line on the graph hits the y-axis (horizontal line, or line going up). The only possible place the line hits the y-axis is at -4. No other y-value. Thus, the range of the function is -4.
There are 12 ducks and 11 geese in a certain park. Find the ratio of geese to ducks.
find the inequality for 20 points pls
First find the Slope-intercept form of the graph:
b=1
Given the points: (0,1)&(3,0)
slope= [tex]\frac{y1-y2}{x1-x2} =\frac{1-0}{0-3} =\frac{-1}{3}[/tex]
The line is not a dashed line, so that means the values on the slope (blue) are also counted
All the y values below the slope are counted, the inequality is:
y[tex]\leq \frac{-1}{3}x +1[/tex]
Hope it helps!
#+3)(2+1) for x = 3.
c+5)(x-5)
Answer:
x=1/3
Step-by-step explanation:
first multiply both bracket to together and then you get, 9x=3
x=1/3, then sub in to other equation and get the rest answer.
hope it helpful
Triangle 304 degrees and 115 degrees work out x
a straight line make an angle of 180° ,
so 115+y=180
y=65°
for the top part of the triangle it makes an angle of 360° , so 304+y=360
y=56
sum measure of interior angles of triangle is 180° , According to this rule (n-2)180 ; where n is the no. of sides .
so
65+56+y= 180
121+y=180
y=59( the angle next to X)
X+59=180( together they make an angle of 180)
x=121°
Hope it helps
please give brainliest
Complete the tasks to subtract the polynomials vertically. (1.3t3 0.4t2 – 24t) – (0.6t2 8 – 18t) what is the additive inverse of the polynomial being subtracted?
The difference of the polynomials is [tex]1.3t^{3}-0.2t^{2}-6t-8[/tex] and the additive inverse of the polynomial being subtracted is [tex]-0.6t^{2} +8+18t[/tex].
The given polynomials are [tex](1.3t^{3}+0.4t^{2} -24t )[/tex] and [tex]0.6t^{2} +8-18t[/tex].
We need to find the additive inverse of the polynomial being subtracted.
What is additive inverse?In mathematics, the additive inverse of a number a is the number that, when added to a yields zero. This number is also known as the opposite, sign change, and negation.
Now, [tex](1.3t^{3}+0.4t^{2} -24t )-(0.6t^{2} +8-18t)[/tex]
[tex]=1.3t^{3}+0.4t^{2}-0.6t^{2}-24t+18t-8[/tex]
[tex]=1.3t^{3}-0.2t^{2}-6t-8[/tex]
The additive inverse of the polynomial being subtracted is [tex]-0.6t^{2} +8+18t[/tex].
Therefore, the difference of the polynomials is [tex]1.3t^{3}-0.2t^{2}-6t-8[/tex] and the additive inverse of the polynomial being subtracted is [tex]-0.6t^{2} +8+18t[/tex].
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please place the dot for me(20 points will give brainliest!!!)
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:\dfrac{2}{3} + \cfrac{ \sqrt{5} }{2} [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \: \cfrac{4 + \sqrt{45} }{6} [/tex]
[tex]\qquad \tt \rightarrow \: \dfrac{4}{6} + \cfrac{ \sqrt{45} }{6} [/tex]
[tex]\qquad \tt \rightarrow \: \dfrac{2}{3} + \cfrac{ \sqrt{3 \times 3 \times 5} }{6} [/tex]
[tex]\qquad \tt \rightarrow \: \dfrac{2}{3} + \cfrac{ 3\sqrt{5} }{6} [/tex]
[tex]\qquad \tt \rightarrow \: \dfrac{2}{3} + \cfrac{ \sqrt{5} }{2} [/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
If the nth term of a sequence is 18-8n what is the 8th term
Answer:
[tex]a_{n} =18-8n\\a_{8} =18-8(8)=-46[/tex]
Answer:
-46
Step-by-step explanation:
(hello, I just answered your previous question--some stuff will sound similar because we are applying the same concept :) )
We know that the nth term of the sequence is 18 - 8n
the "nth" term of a sequence means that you can plug in the term place to get the term value (ex. if the nth term is n + 2, we can plug any term in {let's say, the eighth term, 8 + 2 = 10 ; to get our term's value} )
18 - 8n is sequence
18 - 8(8) is 8th term
18 - 64 is 8th term
-46 is the 8th term
hope this helps!! :)
Help me out!!!!!!!!!!!!!
Answer:
Add all of the sides up:
x^2 + y + 6x + 2y + y^2 + 6x + 2y + y^2 + 4x^2
= 5x^2 + 12x + 2y^2 + 5y
Kit and Kat are building a kite for the big kite festival. Kit has already
cut his sticks for the diagonals. He wants to position P so that he will
have maximum kite area. He asks Kat for advice. What should Kat
tell him?
Kat should tell Kim that It's too late to change the area of this kite because the length of the diagonals of a kite determines its area.
How to calculate the area of a kite?In Mathematics, the area of a kite is equal to one-half the product of the length of its diagonals. Mathematically, the area of a kite can be calculated by using this formula:
A = ½ × d₁ × d₂
Where:
A is the area of a kite.d₁ and d₂ are the length of the diagonals of a kite.Since Kit has already cut his sticks for the diagonals, Kat should tell him that it's too late to change the area of this kite because the length of the diagonals of a kite determines its area.
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The Law of Sines is used to solve missing side lengths in oblique triangles classified as SSS and SSA
True
False
Answer:
only AAS,ASA and SSA Are classified
It's false
Step-by-step explanation:
please mark me as brainlest
False
SSS is not classifiedThe key reason is the formula 's limitations
It need angle for ØAs SSS means only three sides and no angles are given Law of sines can't be used
What is 35.43 rounded to the nearest hundredth’s
Answer:
it already is rounded up to the nearest hundredth
Step-by-step explanation:
The question is:
Jason has 20 gallons of a 12% alcohol solution. How many gallons, to the nearest tenth, must be replaced by a 36% alcohol solution to give 20% gallons of 15% alcohol solution.
I need and explanation on how to set it up and do it. I have a test today and I don’t understand it.
Answer:
2.5 gallons of the 20% solution must be replaced by the 36% solution.
Step-by-step explanation:
[tex].12(20 - x) + .36x = 20(.15)[/tex]
[tex]2.4 - .12x + .36x = 3[/tex]
[tex]2.4 - .24x = 3[/tex]
[tex] - .24x = - .6[/tex]
[tex].24x = .6[/tex]
[tex]x = 2.5[/tex]
The average of three unique number is 50.if the loweat number is 30 what is the sum of other two numbers
Answer:
The sum of the other two numbers is 120.
Step-by-step explanation:
To find an average, you add all the numbers involved and divide it by the amount of numbers involved. in this case,
(x+y+z) ÷ 3 =50
x=30
Divide both sides by three to remove the denominator.
(30+y+z)÷ 3 (*3) = 50(*3)
(30+y+z)=150
Subtract 30 from both sides.
(30+y+z)-30= 150-30
y+z=120
This is confusing please help
Step-by-step explanation:
since we are using Pythagoras
c² = a² + b²
with c being the Hypotenuse (the baseline opposite of the 90° angle),
you want to get the expression
y² = 3² + 3²
so, you pick the ² and put it next to the y left of the "=" sign.
and to the right of the "=" sign you put 3, ², +, 3, ²
write the equation of the line that contains (-4, -3) and is parallel to the line x+2y=-10
Hello! I hope you are having a nice day. My name is Galaxy and I will be helping you with this problem. We can solve this problem in 2 steps, respectively Theory and Solving.
I'll go ahead and start with the Theory.
TheoryBefore we attempt to solve the problem mathematically, we must first figure out how we're going to solve this problem.
We know that we have a line and a point, we can start by graphing the equation and point that we've received.
SolvingNow that we have our points plotted and our equations graphed, we can start to see that something odd is happening, the given point is on the line itself.
We can check this by inputting the points into our equation:
[tex](-4)+2(-3)=-10?\\(-4)+(-6)=-10?\\-10=-10[/tex]
This proves that our point is on the line that we were given.
According to the basic rules of Euclidean Geometry, we know that parallel lines can never intersect each other and due to this there cannot be any solution to this problem.
Any other line using this point would intersect the given line, and due to this, this problem has no real solutions.
* The only line that can use these points and graph is the line provided, and that cannot work due to the lines intersecting at an infinite number of points.
Cheers,
Galaxy.
The line ax − by + 3 = 0 is parallel to the line 3x + 2y − 4 = 0 and passes through the point (1, −2). Find a and b.
Answer:
a=9
b=-6
Step-by-step explanation:
HELP
Can someone help me with number 26 plss
Answer:
(-2,-9)
(-1,8)
(0,-5)
(1,0)
(2,7)
Step-by-step explanation:
Find the sum of the largest and the smallest of the following four numbers:
3.09 3.9 0.39 0.399
PLEASE HELP
Answer:
Using the concepts of Number System, we find that the sum of the largest and the smallest of the given four numbers is 4.29.
Step-by-step explanation:
The given set of numbers is 3.09, 3.9, 0.39 and 0.399.
The given numbers are related to each other as:
3.9 > 3.09 > 0.399 > 0.39
3.9 is greater than 3.09 as
3.9 > 3.09
3 + 0.9 > 3 + 0.09
0.9 > 0.09
90 > 9
0.399 is greater than 0.39 as
0.399 > 0.39
399 > 390
Now, the smallest number in the series is 0.39 and the largest number in the series is 3.9.
The sum of the largest and the smallest of the given four numbers is:
3.9 + 0.39
4.29
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There is a lighthouse that is 25 meters tall and a boat is sinking 204 meters away from the lighthouse. To the nearest whole degree, what is the angle of depression from the top of the lighthouse to the sinking boat?
The angle of depression from the top of the lighthouse to the sinking boat is 6.9°.
What is trigonometry?Trigonometry deals with the relationship between the sides and angles of a right-angle triangle.
From ΔABC it is obtained that;
Height of lighthouse, AC = 25 meters
Distance of boat from the lighthouse, BC = 204 meters
The angle of depression from the top of the lighthouse to the sinking boat is;
[tex]\rm tan \theta = \frac{P}{B} \\\\ \rm tan \theta = \frac{AC}{BC} \\\\ tan \theta = \frac{25}{204} \\\\ \theta = tan^{-1}(0.12)\\\\ \theta = 6.9 ^0[/tex]
Hence, the angle of depression from the top of the lighthouse to the sinking boat is 6.9°
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Solve equation by using the quadratic formula. 6x^2 +2x =4?
A) x= 3/2, 1 B) x= 2/3, -1 C) x=3/2, -1 D) x=3/2, 0
Answer:
Answer x=2/3, -1
Option B
Step-by-step explanation:
Answer:
B) x =( 2/3, -1)
Step-by-step explanation:
Equation:
[tex]6x {}^{2} + 2x = 4[/tex]
Solution:
We know that,
[tex] \rm \: Quadratic \: formula (x)=\cfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
According to the problem,
a = 6b = 2c = -4Plugging them on the formulae,we obtain,
[tex]x = \cfrac{ - 2 \pm \sqrt{ 2 {}^{2} - 4 \{6 \times ( - 4) \} } }{2 \times 6} [/tex][tex]x = \cfrac{ - 2 \pm \: \sqrt{4 - 4 \{ - 24 \} } }{12} [/tex][tex]x = \cfrac{ - 2 \pm \: 10 }{12} [/tex][tex]x = \cfrac{ - 1 \pm5}{6} [/tex][tex]\boxed{x = \cfrac{2}{3} \: \rm or - 1}[/tex]Choice B is accurate.
Explain how you can prove the difference of two cubes identity. a3 – b3 = (a – b)(a2 ab b2)
Answer:
Step-by-step explanation:
Expanding the right-hand side,
[tex](a-b)(a^{2}+ab+b^{2})=a^{3}+a^{2}b+ab^{2}-a^{2}b-ab^{2}-b^{3}=a^{3}-b^{3}[/tex]
Thus, the identity is true.
pleasee help me with this function asap
Answer:
b, c
Step-by-step explanation:
A function is continuous if its graph can be drawn without lifting the pencil. It is decreasing wherever its slope is negative.
__
A graph of the function is attached. It has a "jump" discontinuity at x=0, so is not a continuous function.
The value of f(0) is 2, so the y-intercept is 2.
The given function is defined for all values of x, so its domain is all real numbers.
The function is decreasing for values of x > 0, so does not approach positive infinity for large positive x.
The function has a stationary point at x=0, so is not decreasing over its entire domain.
_____
Additional comment
The function is decreasing everywhere except at x=0. The point (0, 2) is the vertex of the quadratic portion of the function, so a tangent is horizontal there. At such horizontal tangent points, a function is neither increasing nor decreasing. It is tempting to ignore this exception, because the function is decreasing everywhere else.
The table represents the function f(x).
A 2-column table with 7 rows. The first column is labeled x with entries negative 4, negative 3, negative 2, negative 1, 0, 1, 2. The second column is labeled f of x with entries negative 66, negative 29, negative 10, negative 3, negative 1, 6.
When f(x) = –3, what is x?
Answer:
-1/2
Step-by-step explanation:
Answer:x is -1
Step-by-step explanation:
Fatoumata just accepted a job at a new company where she will make an annual salary of $43000. Fatoumata was told that for each year she stays with the company, she will be given a salary raise of $5000. How much would Fatoumata make as a salary after 3 years working for the company? What would be her salary after tt years?
Fatoumata's salary after 3 years will be $58,000.
Fatoumata's salary after tt years will be $43,000 + (5,000tt).
What is Fatoumata's salary?
The linear equation that can be used to determine Fatoumata's salary after the passage of time is:
Initial salary + (yearly increase x number of years)
$43,000 + 5000t
$43,000 + 5000(3) = $58,000.
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in the diagram, triangle ABC is similar to triangle EDC. a. is line AB parallel to line DE? b. show that triangle ACD is similar to triangle ECB. c. find the measure of angle CAD. d find line ED. e. find line AD explain your reasoning
The measure of the angle CAD is 40 degrees, the length of ED is 12 units, and the length of AD is 12 units.
What is the similarity law?It is defined as the law to prove that the two 2-dimensional have the same shape, but it is not compulsory to have the same size. The ratio of the corresponding sides is in the same proportions and the corresponding angles are congruent.
Triangle ABC ~ EDC
Angle ACD = Angle BCE = 90 degree (vertically opposite angle)
Angle ACB = Angle DCE = 90 degree (vertically opposite angle)
BE ║ AD
Angle EBC = Angle CDA = 40 degree (alternative angles)
Triangle ABC ~ Triangle EDC
Angle ABC = Angle CDE
Angle BAC = Angle DEC
∴ AB ║ DE
Triangle ACD ~ Triangle ECB
Angle EBC = Angle CDA and
Angle BEC = Angle CAD
∴ Triangle ACD ~ Triangle ECB
Angle A + Angle E = 180 degree
∠x + 50 + 50 + ∠x = 180
∠x = 40
Angle CAD = 40 degree
We know,
Angle A = Angle E = Angle B = Angle D = 90 degree
So ABCD is a square
AB = ED = 12
AD = AB = BE = ED = 12
Thus, the measure of the angle CAD is 40 degrees, the length of ED is 12 units, and the Length of AD is 12 units.
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Find the area of the smaller sector.
Round to the nearest tenth.
50°
7.13 ft
Area = [?]ft²
Answer:
A ≈ 22.2 ft²
Step-by-step explanation:
the area (A) of the sector is calculated as
A = area of circle × fraction of circle
= πr² × [tex]\frac{50}{360}[/tex]
= π × 7.13² × [tex]\frac{5}{36}[/tex]
= 50.8369π × [tex]\frac{5}{36}[/tex]
≈ 22.2 ft² ( to the nearest tenth )
(-4,3)
-5-4-3
24
5
432
-14
-2
-3-
A
(0,1)
1 2
(4,-1)
Which linear function is represented by the graph?
Of(x) = -2x + 1
Of(x)=x+1
O f(x) = x+1
Of(x)=2x+1
Answer: [tex]f(x)=-\frac{1}{2}x+1[/tex]
Step-by-step explanation:
The slope is [tex]\frac{-1-1}{4-0}=-\frac{1}{2}[/tex], which matches the second option.
Linear function that is represented by the graph is f(x)= -1/2 x+1.
Here, we have,
From the graph,
y - intercept of the linear function is 1 , i.e. c = 1
and there are two points on the line (-4, 3), (4, -1)
We can get the equation of line by applying slope-intercept formula,
Slope of the line,
m = y₂ -y₁ / x₂-x₁
so, we get,
m = -1 -3 / 4 + 4
= -4/8
= -1/2
Now applying slope-intercept formula,
y = mx+c
Putting the values,
=> y = -1/2 x + 1
=>f(x) = -1/2 x + 1.
Therefore, linear function that is represented by the graph is
f(x) = -1/2 x + 1.
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como identifico una X Cubica en un polinomio
la componente "cubica" será aquella que tenga un exponente igual a 3.
¿como identifico una X Cubica en un polinomio?
Un polinomio tiene la forma general:
[tex]p(x) = a_n*x^n + ... + a_1*x^1 + a_0[/tex]
Donde todos los exponentes de x son numeros naturales.
Particularmente, la componente "cubica" será aquella que tenga un exponente igual a 3.
Entonces, por ejemplo, en:
[tex]p(x) = 4*x^5 + 2*x^4 + 5*x^3[/tex]
La parte cubica será:
[tex]5*x^3[/tex]
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