WILL GIVE BRAINLIEST
Rewrite (see picture) in standard form. Find the center and radius of the circle. Show all of your work for full credit.
Answers
Answer:
[tex](x - 2)^{2} + (y + \frac{5}{2} )^{2} = \frac{37}{4}[/tex]
Step-by-step explanation:
The standard form of the equation: (x-2)²+ (y + 5/2)² = 37/4 , center: (2, -5/2) and radius: (√37) / 4.
What is a circle?A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle.
We have given the equation,
2x²+2y²-8x + 10y+2 = 0
Divide by 2,
x²+y²-4x + 5y+1 = 0
Arranging the terms to make a complete square of variable x and y.
x²+y²-4x + (2/2)5y+1+ 4 + 25/4 = 4 + 25/4
(x-2)²+ (y + 5/2)² = 37/4
This is the form of a circle.
Use this form to determine the center and radius of the circle.
(x−h)²+(y−k)²=r²
Match the values in this circle to those of the standard form.
The variable r represents the radius of the circle, h represents the x-offset from the origin, and k represents the y-offset from the origin.
r=(√37) / 4, h=2, k= -5/2
The center of the circle is found at (h,k).
Center: (2, -5/2)
Therefore, center: (2, -5/2), radius: (√37) / 4
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Related Questions
Find the area of this figure
Answers
Step-by-step explanation:
well, I see one large rectangle (20×6), and 2 small triangles with their horizontal sides being (20-8-6)/2 = 3 m. and their vertical joined side being 10-6 = 4 m.
the total area is simply the sum of the rectangle and the 2 triangles.
the rectangle is
20×6 = 120 m²
each triangle is
4×3/2 = 2×3 = 6 m²
we have 2 of them, so their combined area is 2×6 = 12 m².
the total area is
120 + 12 = 132 m²
what is the translation from quadrilateral EFGH to quadrilateral E' F'G'H'
Answers
Answer:
transformation down 4, transformation right 1
Step-by-step explanation:
Answer:
Four down, 1 right so [tex](x+1,y-4)[/tex]
Step-by-step explanation:
Hope this helps! Have a good day! :)
5 Henry wants to add these numbers. 53 +81 +44 + 72 Explain how he can find the sum by breaking the numbers into tens and ones. What is the sum?
Answers
Answer:
50+3+80+1+40+4+70+2
Step-by-step explanation:
Pls thank if correct
Dont get mad if not correct.
Hope this helps <3
The table shows us how many sit ups she has done over the past few days-
At this rate how many sit-ups will she do on day 12?
Answers
Answer:
177
Step-by-step explanation:
the number of sit-ups is going up in 4s , so if i take the 33 sit ups she does on the 5th day i add 4 to that 12 times , so you just do 33+12 and multiply that by 7 since thats how many days she has until 12.
A ball was projected into the air with an initial upward velocity of 72 feet per second. The quadratic function graphed below shows the height, h, of the ball t seconds after it was projected into the air.
What is the domain of the function for this situation?
Question 20 options:
0≤t≤4.5
0
0
0≤h≤80
Answers
The domain is represented by the set of values of the time, that is, the horizontal axis, and the domain of the given function is represented by t ∈ [0, 4.5].
How to determine the domain of the function of the height of the ball in function
All functions are relations in which there is no value of the domain related to more than one value of the range, functions in explicit form related the variable of the range in terms of the variable of the domain.
Based on the information shown in the graph, the domain is represented by the set of values of the time, that is, the horizontal axis, and the range is represented by the set of values of the height, that is, the vertical axis.
Hence, the domain is represented by the set of values of the time, that is, the horizontal axis, and the domain of the given function is represented by t ∈ [0, 4.5].
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. Which is a true statement about the transformation?
Answers
Answer: The orientation of the vertices was changed.
(x, y) ---> (x + 8, y - 3)
Step-by-step explanation: The triangle translation isn't on quadrant II, it's on quadrant I, so that answer choice isn't correct. The triangle ABC translated 8 units right and 3 units down, not 8 units left and 3 units up. Whenever you dilate, translate, rotate, or reflect triangles like ABC, the next triangle becomes A'B'C because it shows you that it's a transformation of the original triangle. The orientation of the figure didn't change, because it didn't change shape, rotation, or size, so the orientation wasn't affected at all, just the vertices.
The transformation is (x, y) ---> (x + 8, y - 3), because think of it like this. I already said that the triangle translated 8 units to the right, which means that the triangle is translating 8 units in the positive direction to the right. The triangle going 3 units down is in the negative direction, and that's why it's (x, y) ---> (x + 8, y -3).
Let me know if this is right! :)
The $23 rd term in a certain geometric sequence is 16 and the $28th term in the sequence is 24. What is the $43 rd term?
Answers
Answer:
81
Step-by-step explanation:
Geometric sequence formula: [tex]a_n=ar^{n-1}[/tex]
Given:
[tex]a_{23}=ar^{22}=16[/tex][tex]a_{28}=ar^{27}=24[/tex]Find common ratio (r):
[tex]\begin{aligned}\implies \dfrac{a_{28}}{a_{23}} =\dfrac{ar^{27}}{ar^{22}} & =\dfrac{24}{16}\\ \implies r^5 & =\dfrac32\\ \implies r & = \sqrt[5]{\frac32} \end{aligned}[/tex]
Find initial term (a):
[tex]\implies ar^{22}=16[/tex]
[tex]\implies a(\sqrt[5]{\frac32} )^{22}=16[/tex]
[tex]\implies a(\frac32} )^{\frac{22}{5}}=16[/tex]
[tex]\implies a=\dfrac{16}{(\frac32)^{\frac{22}{5}}}[/tex]
Find the 43rd term:
[tex]\implies a_{43}=ar^{42}[/tex]
[tex]\implies a_{43}= \left(\dfrac{16}{(\frac32)^{\frac{22}{5}}}\right)(\sqrt[5]{\frac32} )^{42}[/tex]
[tex]\implies a_{43}=16 \cdot (\frac32)^{-\frac{22}{5}} \cdot (\frac32)^{\frac{42}{5}}[/tex]
[tex]\implies a_{43}=16 \cdot (\frac32)^4[/tex]
[tex]\implies a_{43}=16 \cdot \left(\dfrac{3^4}{2^4}\right)[/tex]
[tex]\implies a_{43}=16 \cdot \left(\dfrac{81}{16}\right)[/tex]
[tex]\implies a_{43}=81[/tex]
What is the circumference (rounded to the nearest meter) of a circular swimming pool that has a radius of 10 meters?
A. 120
B. 63
C. 60
D. 31
E. 30
Please help with the answer and explain it to me.
Answers
Answer:
63
Step-by-step explanation:
You get the answer by multiplying the radius by 2 to get the diameter and then multiplying the result by pi or 3.14, which gives you 62.83 and then round it up which is 63
Which statement is most likely to be true? the scores from mrs. jones’s class are the closest to the class mean. the scores from mrs. rijo’s class are the closest to the class mean. the scores from mr. phan’s class are the closest to the class mean. the scores from mrs. scott’s class are the closest to the class mean.
Answers
Answer:
The scores from Mrs. Rijo’s class are the closest to the class mean.
Step-by-step explanation:
Jus took the test
Answer:The scores from Mrs. Rijo’s class are the closest to the class mean.
Step-by-step explanation:
B
How do you find the other side lengths of a right triangle when only given the value of one of the sides?
Answers
Some1 help pzl
Find the surface area 7m 15m 6m
Answers
Answer:
474 m²
Step-by-step explanation:
Surface area of a rectangular prism:
SA = 2(lw + lh + hw)
Given:
width (w) = 6 mlength (l) = 7 mheight (h) = 15 m⇒ SA = 2(7 · 6 + 7 · 15 + 15 · 6)
= 2(42 + 105 + 90)
= 2(237)
= 474 m²
Answer:
474 Sq m
Step-by-step explanation:
You have two sides that are 7m x 6m
(7*6)*2 = 84
You have two sides that are 15m x 6m
(15*6)*2 = 180
You have two sides that are 15m x 7m
(15*7)*2 = 210
84+180+210=474
Joshua is trying to determine the equation of a quadratic function
whose vertex is (-3,5) and passes through the point (-1,2).
If he writes his final answer in the form (x)= a(x-1)2+k, what will be
the values(numbers) of a, h, and k?
And the last answer choice is
a=-3/4
h=-3
K=5
Please help
Answers
[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \stackrel{vertex}{(-3~~,~~5)}\qquad y=a[x-(-3)]^2+5\implies y=a(x+3)^2+5 \\\\\\ \textit{we also know that} \begin{cases} x=-1\\ y=2 \end{cases}\qquad 2=a(-1+3)^2+5\implies -3=a(2)^2 \\\\\\ -3=4a\implies -\cfrac{3}{4}=a~\hfill \boxed{y=-\cfrac{3}{4}(x+3)^2+5}[/tex]
What is the value of (3^0)^-3?
Answers
Answer:
1
Step-by-step explanation:
[tex](3^{0} )^{-3} =1^{-3} =\frac{1}{1^3} =1[/tex]
Anything to the power of 0 = 1
Negative exponents = inverse
Hope this helps!
A firm is considering projects s and l, whose cash flows are shown below. These projects are mutually exclusive, equally risky, and not repeatable. The ceo wants to use the irr criterion, while the cfo favors the npv method. You were hired to advise the firm on the best procedure. If the wrong decision criterion is used, how much potential value would the firm lose?.
Answers
If the wrong discion criterion is used, the potential lose in value for the firm is $209.07.
What is the correct decision criterion?
The correct decision criterion is the net present value. Net present value is the present value of after-tax cash flows from an investment less the amount invested. The internal rate of return is the discount rate that equates the after-tax cash flows from an investment to the amount invested
What is the loss in value if the wrong decision criteria is used?The net present vaue and the internal rate of return can be calculated using the financial calcuator.
Project S:
Cash flow in year 0 = $-1025Cash flow each year from year 1 to 4 = $380I = 6%
NPV = 291.74
IRR = 17.86%
Project I:
Cash flow in year 0 = $-2150
Cash flow each year from year 1 to 4 = 765
I = 6%
NPV = 500.81
IRR = 15.78%
If the wrong criteria is used, Project S would be chosen.
Loss in value = 500.81 - 291.74 = $209.07.
Here are the cash flows used:
WACC: 6.00%
Year 0 1 2 3 4
CF S -$1,025 $380 $380 $380 $380
CF I -$2,150 $765 $765 $765 $765
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i need help with this
Answers
Answer: B) x=5, x=1
Step-by-step explanation:
To start multiply everything in the expression by 2
[tex]0.5x^{2} -3x+2.5\\x^{2} -6x+5[/tex]
Now factor the trinomials for when a=1
So you must find two numbers that add to -6 and multiply to 5
In this case, the numbers are -1 and -5
[tex]x^{2} -6x+5\\(x-1)(x-5)[/tex]
Now set each of the factors equal to 0 and solve for x
[tex]x-1=0\\x-1+1=0+1\\x=1[/tex]
[tex]x-5=0\\x-5+5=0+5\\x=5[/tex]
Simplify this equation is easiest form.
Answers
Answer:
no. 4
Step-by-step explanation:
=25x - 125/x^2 - 25
=25(x-5) / x^2 - 5^2
=25(x-5) / (x-5) (x+5) <use of formula a^2 - b^2=(a-b) (a+b)>
=25/x+5 <cut (x-5) on both side>
Find the outer perimeter of this figure. Round
your answer to the nearest hundredth. Use
3.14 to approximate pi.
P = [ ? ] ft.
Answers
Answer:
61.90 ft
Step-by-step explanation:
Perimeter: the boundary that surrounds a shape
1) Find the perimeter of the semicircle using this formula: [tex]\frac{1}{2} *2\pi r[/tex], where [tex]r[/tex] is the radius, and π is 3.14 (according to the question).
1.1) We need to find the radius first.
Radius = Diameter ÷ 2
So, 10 ÷ 2 = 5
1.2) Input the values into the semicircle formula.
[tex]\frac{1}{2} *2(3.14)(5)[/tex]
1.3) solve for the perimeter of the semicircle.
[tex]\frac{1}{2} *31.4[/tex]
= 15.7
2) Find the perimeter of the triangle and the rectangle.
= [tex]6 + 12.2 + 14 + 14[/tex]
= 46.2
3) Add them.
= [tex]46.2 + 15.7[/tex]
= 61.9 ft
3) Round the answer (61.9) to the nearest hundredth (according to the question).
= 61.90 ft
As per the total length of the arc of a semicircle, the outer perimeter of this figure is 61.9 feet.
What is the total length of the arc of a semicircle?A semicircle that has a radius of 'r' units, has the total length of it's arc is
= πr units
In the given figure, the semicircle has a diameter = 10 feet.
Therefore, the radius of the semicircle
= 10/2 feet
= 5 feet
Now, the total length of it's arc is
= πr units
= 3.14 × 5 feet
= 15.7 feet
Therefore, the outer perimeter of this figure is
= (12.2 + 6 + 14 + 15.7 + 14) feet
= 61.9 feet
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4.
1 in
14 in
2.5 in
Volume of each prisms
Answers
Answer:
ength l = 1 in
width w = 14 in
height h = 2.5 in
diagonal d = 14.3 in
total surface area Stot = 103 in2
lateral surface area Slat = 75 in2
top surface area Stop = 14 in2
bottom surface area Sbot = 14 in2
volume V = 35 in3
molly is 4 years younger than Heidi. In 3 years, Heidi will be twice as old as Molly. How old are they now
Answers
Answer:
Molly would be 1 years old.
Step-by-step explanation:
"In three years..."
(m+3) will be Molly's age then.
(h+3) will be Heidi's age then.
(h+3) = 2(m+3) :: given.
.
Subsitute what we know about m, which is it equal h-4.
.
(h+3) = 2(m+3)
(h+3) = 2m + 6
substitute m=h-4
(h+3) = 2(h-4) +6
h +3 = 2(h -4) +6
h +3 = 2h -8 +6
h +3 = 2h -2
h = 2h -8 +3
-h = -5
h = 5
Heidi is 5 years old now.
.
m = h-4
m = 5-4
m = 1
Molly is 1 years old now.
WILL GIVE BRAINLIESTTTT, FIVESTARS ANDTHANKS
PLEASEHELP
Answers
Answer:
3 is the answer
Step-by-step explanation:
answer up above
Daniel owns a synall business selling used books. He knows that in the last week 60
customers paid cash, 4 customers used a debit card, and 23 customers used a credit
card.
Based on these results, express the probability that the next customer will pay with a
credit card as a fraction in simplest form.
Answers
The probability that the next customer that comes into Daniel's business will pay with a credit card is 23 / 87.
What is the probability?Probability determines how likely it is that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The probability that the next customer will pay with a credit card = number of people who paid with a credit card / total number of customers
23 / (23 + 60 + 4)
23 / 87
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Answers
Alex and Bev sat six tests, each with 50 marks.
The table shows their mean percentages after five tests.
Alex
60%
Bev
52%
After all six tests, their mean percentages were equal.
In the sixth test, Alex scored 24 out of 50
Work out Bev's score, out of 50, in the sixth test.
Answers
Answer:
44
Step-by-step explanation:
60 × 5 or 300
or
52 × 5 or 260
24
50
× 100 or 0.48 × 100
or 48
348 implies
60 × 5 +
24
50
× 100 – 52 × 5
or
300 + 48 – 260 or 88
5. Find the value of x to the nearest tenth. Volume of the prism
is 576 cm?
Volume: 576 cm3
Answers
the volume of the triangular prism will be, the area of the triangular face times its length
[tex]\stackrel{\textit{area of the triangle}}{\left[ \cfrac{1}{2}(\underset{b}{8})(\underset{h}{8}) \right]}~~ ~~\stackrel{length}{(x)}~~ = ~~\stackrel{volume}{576}\implies 32(x)=576 \\\\\\ 32x=576\implies x=\cfrac{576}{32}\implies x=18[/tex]
expand and simplify 2(5x+3)-2(2x-3)
Answers
Answer:
hopes this helps.
Step-by-step explanation:
Hey there!
2(5x + 3) - 2(2x - 3)
DISTRIBUTE
= 2(5x) + 2(3) - 2(2x) - 2(-3)
= 10x + 6 - 4x - 6
COMBINE the LIKE TERMS
= (10x - 4x) + (6 + 6)
= 10x - 4x + 6 + 6
= 6x + 12
Therefore, your answer is: 6x + 12
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
The volume of a cylinder is 66 cubic meters and the radius is 2 meters. Find the height of the cylinder. Round to the nearest tenth.
Answers
The equation is H=V/(pi•r^2)
2•2=4
4•3.14=12.56
66/12.56=5.254
Round 5.254 to 5.3
5.3=66/(3.14•4) Is true :)
Write in standard form
(4.6 x 10^6) x (5 x 10^-4)
Answers
Here is a pyramid with a base that is a pentagon with all sides the same length
Describe the cross section that will result if the pyramid is sliced:
horizontally (parallel to the base).
vertically through the top vertex (perpendicular to the base)
Answers
The shape of the cross section formed from slicing the pyramid is called; a triangle
What is the Pyramid's Cross Section?We are told that it is a pyramid with a base that is a pentagon with all sides the same length.
Now, the Pyramid's ap-ex is usually constructed by isosceles triangles. Thus, when they are sliced from its ap-ex to from the vertex, in the cross section a triangle will be formed, This triangle will be an isosceles triangle.
In conclusion, the shape of the cross section formed from slicing the pyramid is a triangle.
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A car speeds up from 0 to 15 m/s in 5 s. What is the car's acceleration?
A. 0.3 m/s/s
B. 3 m/s/s
C. 10 m/s/s
D. 20 m/s/s
Answers
Answer: B 3m/s²
Step-by-step explanation: Acceleration is difference in speed /time = 15-0/5
You’ll know actual physic’s of your going to take it
Simplify the expression 63 + 5(4-2)
Answers
Answer:
63 + 10
Step-by-step explanation:
when you do parenthesis and the number is next to another one with no symbol you multiply so 4-2 = 2 2 x 5 = 10 giving you 63 + 10