Write the equation in standard form. Identity the center and radius.
x² + y2 + 8x-4y-7=0
Answers
Answer:
equation;
[tex](x + 4) {}^{2} + (y - 2) {}^{2} = 27[/tex]
Center (-4,2)
Radius is
[tex]3 \sqrt{3} [/tex]
Step-by-step explanation:
Since the x^2 and y^2 have the same coeffiecent this will be a circle in a form of
[tex](x - h) {}^{2} + (y - k) {}^{2} = {r}^{2} [/tex]
Where (h,k) is center
r is the radius
So first we group like Terms together
[tex] {x}^{2} + 8x + {y}^{2} - 4y - 7 = 0[/tex]
Add 7 to both sides
[tex] {x}^{2} + 8x + {y}^{2} - 4y = 7[/tex]
[tex]( {x}^{2} + 8x) +( {y}^{2} - 4y) = 7[/tex]
Since the orginal form of the equation of the circle has a perfect square we need to complete the square for each problem
[tex] (\frac{8}{2} ) {}^{2} = 16[/tex]
and
[tex]( - \frac{4}{2} ) {}^{2} = 4[/tex]
so we have
[tex] {x}^{2} + 8x + 16 + {y}^{2} - 4y + 4y = 7 + 16 + 4[/tex]
[tex] {x}^{2} + 8x + 16 + {y}^{2} - 4y + 4y = 27[/tex]
[tex](x + 4) {}^{2} + (y - 2) {}^{2} = 27[/tex]
To find our center, h is -4 and k is 2
so the center is (-4,2)
The radius is
[tex] \sqrt{27} = 3 \sqrt{3} [/tex]
So the radius is 3 times sqr root of 3.
Related Questions
The point V(4, –1) is rotated 90° clockwise around the origin. What are the coordinates of its image V’? V’(1, 4) V’(–1, 4) V’(–1, –4) V’(4, 1)
Answers
Answer:
V' = (-1, -4)
Step-by-step explanation:
the original point V (4, -1) is 4 units to the right and 1 unit down.
now we turn this 90° clockwise (upper right to down to upper left).
that means the right part of the x-axis turns into the bottom part of the y-axis, and the bottom part of the y-axis into the left part of the x-axis.
so, positive x turns into negative y, and the negative y turns into negative x.
therefore, (4 -1) turns into (-1, -4).
Answer:
C V'(-1,-4)
Step-by-step explanation:
Finding the Coordinate for a 90° Rotation
The point V(4, –1) is rotated 90° clockwise around the origin.
What are the coordinates of its image V’?
V’(1, 4)
V’(–1, 4)
(V’(–1, –4)) this one <-------
V’(4, 1)
I NEER HELP ON KHAN ACADEMY PLS
A board game has players roll two 6-sided dice and subtract the numbers showing on the faces. The game
only looks at nonnegative differences. For example, if a player rolls a 4 and a 6, the difference is 2.
um
Here is the sample space showing the possible (equally likely) outcomes of a single roll:
uctio
2nd die
1st die
1
2
3
4
5
6
1
0
1
2
3
4
5
2
1
1:50
0
1
2
3
4
3
2
1
0
1
2
3
4
3
2
1
0
1
2
5
4
3
2
1
0
1
6
5
4
3
2
1
0
Which graph represents the theoretical probability distribution of the differences?
Answers
It can be deduced that the sample space is the collection of the set of possible outcomes in a random experiment.
What is a sample space?Your information is incomplete as the graphs aren't provided. Therefore, an overview of the sample space will be given.
A sample space simply means the collection of the set of possible outcomes in a random experiment.
It should be noted that a sample space is usually represented by the symbol S.
Also, the theoretical probability distribution states that the probability of occurence of an event will be equal to the number of the favorable outcomes divided by the total outcomes possible.
Learn more about sample space on:
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Order the numbers from least to greatest.
53.77
54
53.61
53.6
Answers
Answer:
53.6, 53.61, 53.77, 54
Step-by-step explanation:
That's the right order
Anita can iron a dress shirt in 15 minutes, but
it takes Michelle 18 minutes to do the same.
Working together, how many minutes will it take
them to iron 11 dress shirts?
Answers
The number of minutes it will take both of them to iron 11 dress shirt is 90 minutes
Rate:
Rate is the ratio between two related quantities in different units. Therefore,
Anita iron a shirt in 15 minutes. Therefore,
rate = 1 / 15Michelle iron the same shirt for 18 minutes. Therefore,
rate = 1 / 18Let the time they use to work together = x
Therefore,
1 / x = 1 / 15 + 1 / 181 / x = 18 + 15 / 270
1 / x = 33 / 270
cross multiply
270 = 33x
x = 270 / 33
x = 90 / 11
Both of them will use 90 / 11 minutes to iron a dress shirt
Therefore, 11 dress shirt will be ?
number of minutes to iron 11 dress shirt together = 11 × 90 / 11 = 90 minutes
learn more on rate here: https://brainly.com/question/1119145
Write a function in the form y=mx+b for the line that contains the points (2, 4) and(5, 10).
Answers
Step-by-step explanation:
gradient=∆y/∆x
=(10-4)/(5-2))
=6/3
=2
(x,y) (2,4)
y-4/x-2=2
y-4=2(x-2)
y=2x-4+4
y=2x
A standard DVD has a surface area of 134 cm2 depending on formatting it holds either 4.7 or 8.5 gigabytes find the data density in both cases
Answers
Step-by-step explanation:
Data density = Data capacity / surface areaUse the formula to find the answer:
1.
4.7 /134 = 0.0351 Gb/cm²2.
8.5/134 = 0.0634 Gb/cm²Note. the numbers above are rounded
AREA OF TRIANGLE BASE=7 and 4
Answers
Answer:
area: 14
Step-by-step explanation:
what is this x + y = 7 and x − y = −3
Answers
Answer:
x = 2, y = 5
Step-by-step explanation:
Answer:
math equation
Step-by-step explanation:
Khloe made 20% of her free throws over the season. If she shot 240 free throws, how many did she make?
Answers
find yz 11x+1 and 19x-31
Answers
The length of a segment is the number of units between its endpoints
The length of YZ is 45 units
How to determine length YZThe given parameters are:
WX = 11x + 1
YZ = 19x - 31
Lengths WX and YZ are congruent.
So, we have:
[tex]19x - 31 = 11x +1[/tex]
Collect like terms
[tex]19x - 11x = 31 +1[/tex]
Evaluate the like terms
[tex]8x = 32[/tex]
Divide both sides by 32
[tex]x = 4[/tex]
Recall that:
YZ = 19x - 31
So, we have:
[tex]YZ = 19*4- 31[/tex]
[tex]YZ = 45[/tex]
Hence, the length of YZ is 45 units
Read more about line segments at:
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Nilai akar pangkat dua dari bilangan 144, 225 dan 400 adalah
Tolong dijawab ya kakk
Answers
Answer:
harap ia membantu kamu ya saya itu dari negara lain mungkin syllables nyahh lain jadi jawapan nyahh bisa lain ia kan
i try my best for sure gudluckk
Step-by-step explanation:
144
225
400
729
1296
the radius of a circle is 7 cm .the circle is divided into two equal parts .what is the perimeter of the semi circular part
Answers
Answer:
P = 35.98 cm
Step-by-step explanation:
The Perimeter of a shape is the distance around the outside of it. This semi-circle (half circle) has a straight part and the curved part. See image. The straight part is the diameter (distance through the center) it is double the radius that was given, 7 cm.
The circumference of a circle is the perimeter of the whole circle.
C = 2pi•r or pi•d
C = 2pi•7 = 14pi
But you only need half, so 14pi/2 is 7pi.
ADD the straight part and the curved part to get the whole distance around the shape
P = 14 + 7pi
P ~= 35.98 cm
See image
Please help quick !
Answers
Answer:
1. Quadrant 2
2. Quadrant 3
Step-by-step explanation:
The quadrants are ordered in a 'c' pattern. The first quadrant has coordinates (x,y). The second quadrant has coordinates (-x,y). The third quadrant has coordinates (-x,-y). The fourth quadrant has coordinates (x,-y).
Answer:
quadrent 2 for question 1 ( negative x positive y) quadrant 3 for number 2 ( negative x and y)
a path is made of red and blue tiles a fifth of the tiles are red what is the ratio in simplest forms??
Answers
Answer:
The answer is 4:1
Step-by-step explanation:
Hope this helps!
x=y-4, 2x-y=5. Please help me
Answers
By putting x = y-4 in the equation 2x-y = 5, we get;
=) 2(y-4) -y = 5
=) 2y - 8 - y = 5
=) 2y - y = 5 + 8
=) y = 13
Now, we got the value y = 13, so by putting it in the equation x = y-4, we get;
=) x = 13 - 4
=) x = 9
Therefore, x = 9 and y = 13
Answer:
the answer is (x,y) = (9,13)
Step-by-step explanation
Formula for area of a triangle
Answers
Answer: half x base x height
I hope that will help you have a great day bye and Mark brainlist if the answer is correct .......
Step-by-step explanation:
[tex]kai6417 [/tex]
#carry on learning
One angle of a parallelogram measures 162°. What are the measures of the other three angles in the parallelogram?
Answers
Answer:
The important properties of parallelograms to know are:
-Opposite sides of parallelogram are equal (AB = DC).
-Opposite angles of parallelogram are equal (D = B).
-Consecutive angles in a parallelogram are supplementary (A + D = 180°).
-If one angle is 90 degrees, then all other angles are also 90 degrees.
FROM
SURAJ SAINI
Answer:
162,162,18,18
Step-by-step explanation:
each two opposite angles are equal
since there is an angle equals 162° then the opposite angle equals 162°
since the sum of all angles equal 360°
360-(162+162)= 36
so the sum of the other two opposite angle = 36 then the measure of one angle =36/2 =18°
AB is congruent to DE because segment DE was constructed so that DE = AB. BC is congruent to EF because segment EF was constructed so that EF = BC. Since ADEF is a right triangle, DE+ EF? = DF? by the We are given that AB + BC2 = AC? Since DE = AB and EF = BC, DE2 + EF2 = AC? by the Also, DF2 = AC2 by the Taking the square root of both sides of the equation gives DF = AC. So, AC is congruent to DF by the definition of congruence. Applying the AABC - ADEF. By CPCTC, ZB _ZE. Therefore ZB is a right angle and AABC is a right triangle.
Answers
DE = AB, EF = BC and AC = DF, hence triangle ABC is congruent to triangle DEF.
Congruent shapeTwo shapes are said to be congruent if they have the same shape, all their corresponding angles and sides are congruent to one another.
Given that DE = AB and BC = EF.
In right triangle DEF, using Pythagoras:
DF² = DE² + EF²
Also, In right triangle ABC, using Pythagoras:
AC² = AB² + BC²
But DE = AB and EF = BC, hence:
AC² = DE² + EF²
AC² = DF²
Taking square root of both sides, hence:
AC = DF
Since DE = AB, EF = BC and AC = DF, hence triangle ABC is congruent to triangle DEF.
Find out more on Congruent shape at: https://brainly.com/question/11329400
pythagorean theorem, division, substatution, SAS
Step-by-step explanation:
edmentum
Rob eats a hamburger that has 415 calories for lunch. He also eats French fries that are 10 calories each. If Rob consumed 645 calories, how many French fries did he eat?
Answers
a 65 foot ladder is leaning against a wall. Its lower end is 25 feet away from the wall. How much farther away will it be if upper end is moved down 8 feet?
Answers
Answer:
14
Step-by-step explanation:
65^2=25^2 + h^2 =52
Then, 65^2 =(25 + x) ^2 +52^2=>x=14
HURRY PLS
Part 1:
Prove that the two triangles above are similar. Provide a proof using any method (two-column, flow-chart, or paragraph). For whichever method you choose, include the statements that lead you to the necessary conclusion, as well as corresponding reasons for each statement.
Part 2:
Find the measures of AC and AB all necessary calculations.
Answers
The condition of two congruent angles in each triangle, can be used to
show that the two triangles are similar.
Response:
Part 1: The two triangles are similar by AA similarity postulatePart 2: AC = 22.5 inches, AB = 30 inchesWhich condition of similarity makes the two triangles similar?Part 1:
A two column proof is presented as follows;
Statement [tex]{}[/tex] Reason
1. ∠D ≅ ∠A [tex]{}[/tex] 1. Given
2. ∠DCE ≅ ∠ACB [tex]{}[/tex] 2. Vertical angle theorem
3. ΔCDE ~ ΔCAB [tex]{}[/tex] 3. AA similarity postulate
Angle-Angle, AA, similarity postulate states that if two angles in one
triangle are congruent to two angles in a second triangles, then the two
triangles are similar.
Part 2:
From part 1, we have;
ΔCDE is similar to ΔCAB (ΔCDE ~ ΔCAB)
The ratio of corresponding sides of similar triangles are equal, which
gives;
[tex]\dfrac{\overline{CD}}{\overline{AC}} = \mathbf{\dfrac{\overline{CE}}{\overline{CB}}}[/tex]
Which gives;
[tex]\dfrac{12}{\overline{AC}} = \mathbf{\dfrac{8}{15}}[/tex]
[tex]\overline{AC}} = \dfrac{15}{8} \times 12 = \mathbf{22.5}[/tex]
AC = 22.5 inchesSimilarly, we have;
[tex]\dfrac{\overline{DE}}{\overline{AB}} = \mathbf{\dfrac{\overline{CE}}{\overline{CB}}}[/tex]
Which gives;
[tex]\dfrac{16}{\overline{AB}} = \dfrac{8}{15}[/tex]
[tex]{\overline{AB}} = \dfrac{15}{8} \times 16 = \mathbf{30}[/tex]
AB - 30 inchesLearn more about AA similarity postulate here:
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Which values are solutions to this inequality?
x>−5
Choose each correct answer.
8
5
1
−2
−6
−9
Answers
Answer:
8,5,1,-2
Step-by-step explanation:
> = Greater than or equal to -5
The following table shows the length and width of a rectangle: Length Width Rectangle A 3x 5 2x − 3 Which expression is the result of the perimeter of rectangle A and demonstrates the closure property? 10x 4; the answer is a polynomial 2x 4; the answer is a polynomial 10x 4; the answer may or may not be a polynomial 2x 4; the answer may or may not be a polynomial.
Answers
Expression giving the result of the perimeter of rectangle A and demonstrating the closure property is given by: Option A: [tex]10x + 4[/tex] ; the answer is a polynomial
What is the closure property of a polynomial for addition operation?Closure property keeps the result in the same set.
If two polynomials [tex]f(x)[/tex] and [tex]g(x)[/tex] are there.
Then, [tex]f(x) + g(x) = h(x)[/tex]
where [tex]h(x)[/tex] is also a polynomial.
The result of the addition of two polynomials is also a polynomial. This property of polynomial for addition operation is called closure property of a polynomial for addition operation
For the given case, we have:
Length of the rectangle = [tex]3x + 5[/tex]Width of the rectangle = [tex]2x -3[/tex]Perimeter of a rectangle with width W and length L = 2(L + W)
And using that formula, the perimeter of the considered rectangle is evaluated as:
[tex]P = 2(3x + 5 + 2x - 3)\\P = 2((3+2)x + 2) = 2(5x + 2)\\\\P = 10x + 4[/tex]
Thus, expression giving the result of the perimeter of rectangle A and demonstrating the closure property is given by: Option A: [tex]10x + 4[/tex] ; the answer is a polynomial
Learn more about addition of polynomials here:
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Find the missing side length 12 cm 1,200 cm 20 cm ____ cm
Answers
Answer:
Missing side length is 5 cm.Step-by-step explanation:
Multiply 20 by 12:
20 * 12 = 240.Multiply 240 by 5:
240 * 5 = 1200.Multiply the lengths:
20 * 12= 240 * 5= 1200.Answer:
The missing side is 5 cm
Step-by-step explanation:
Step 1: Determine the missing side
[tex]V=l*w*h[/tex]
[tex]1200\ cm^3 = 20\ cm * w * 12\ cm[/tex]
[tex]\frac{1200\ cm^3}{20\ cm * 12\ cm} = w[/tex]
[tex]\frac{1200\ cm^3}{240\ cm^2} = w[/tex]
[tex]5\ cm = w[/tex]
Answer: The missing side is 5 cm
Evaluate |c 2 + b 2|, given a = 5, b = -3, and c = -2.
Answers
Hey there!
|c^2 + b^2|
= -2^2 + -3^2
= -2^2 - 3^2
= -4 - 9
= -13
Therefore, your answer is: -13
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Answer:
10
Step-by-step explanation:
|-2(2)-3(2)|
|-4-6|
|-10|
=10
Solve for X round to the nearest tenth of a degree if necessary
Answers
Answer:
63.4
Step-by-step explanation:
x° is an acute angle in a right triangle with the opposite and adjacent sides given. That means the relevant trig relation is ...
Tan = Opposite/Adjacent
tan(x°) = 18/9 = 2
The value of the angle is found using the inverse tangent function:
x° = arctan(2) ≈ 63.4°
x = 63.4 . . . . . . . rounded to tenths
Please help need answer fast
Answers
[tex] \rm \: p = \frac{favourable \: outcome}{total \: outcome} [/tex]
Total outcome = 12+5+8+1+4 = 30Favourable outcome = 12[tex] \rm \: p = \frac{12}{30} [/tex]
[tex] \rm \: p = \frac{2}{5} [/tex]
[tex] \rm \: p = 0.4[/tex]
[tex] \tt \: p = \frac{0.4}{100} [/tex]
[tex] \tt \: p = 40\%[/tex]
Simplify the expressions
1. x - 2 + 3x + 8
2. 2(-1.5x + 3) + (5x - 2)
3. (x + 3) - (2x - 1)
4. (4 - x) - 2 (-5x + 3)
5. (-4x + 3) + (9x - 5)
6. 3 (-3x - 4) - (3x + 5)
7. (-8x + 4) - (7x - 7)
8. 1/2 (x - 6) + 1/4 (x + 12)
9. (-2x - 3) - (2x - 10)
10. (-4x - 2) + 1/2 (12x - 22)
11. 2 (4.4 - 2x) + 4 (-x + 3)
12. (-2x + 5) - (-3x + 11)
Answers
Answer:
1) 2(2x+3)
2) 2x+4
3) - X + 4
4) 9x - 2
5) 5x−2
6) - 12x - 17
7) - 15x + 11
8) 3x/4
9) - 4x + 7
10) 4x-26/2
11) - 8x + 20.8
12) x - 6
How do you work out 803.309-133.36?
Answers
PLS HELPP ASP
Whats the sum of
8 1/2 2 1/2
Answers
Answer:
11
Step-by-step explanation:
1/2 + 1/2 is 1
8 + 2 = 10
1 + 10 = 11