Answers
The equation of the circle in the standard form is (x - 2)²+(y + 2)² = 34.
What is standard form?The fundamental form of an equation is the linear equation in standard form. Below is shown the standard form of a linear equation with two variables and more than two variables.
Here, a, b, (A)1, (A)2, (A)3,........ (A)n are referred to as the coefficients, and x, y, or (x)1, (x)2, (x)3,.... represent the variables. Constants are the numbers that appear after the equals to sign.
ax + by = c
A quadratic equation's standard form is a second-degree equation with a variable, coefficients, and constant term. X is a single variable of degree 2 in this situation. A quadratic equation has the following standard form.
ax² + bx + c = 0
We have given that:
[tex]$\left(x-x_0\right)^2+\left(y-y_0\right)^2=r^2$[/tex]
Lets solve
[tex]$P_0(2,-1)$[/tex]
[tex]$d^2=10^2+6^2$[/tex]
[tex]$r=\frac{d}{2}=5.831$[/tex]
[tex]$r^2=34$[/tex]
[tex]$(x-2)^2+(y+1)^2=34$[/tex]
Thus, the equation of the circle in the standard form is (x - 2)²+(y + 2)² = 34.
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Related Questions
Find the coordinates of the vertices of the triangle if it’s rotated 270° counterclockwise.
Answers
If these coordinates are rotated 270° counterclockwise, the resulting coordinates will be;
X' = (3, -1)
Y' = (2, -2)
Z' = (-1, -3)
Rotation of coordinatesIf the coordinates (x, y) is rotated 270° counterclockwise, the resulting coordinate point will be;
(x, y) - > (y, -x)
From the given triangles, the coordinate points are expressed as
X = (1, 3)
Y = (2, 2)
Z = (3, -1)
If these coordinates are rotated 270° counterclockwise, the resulting coordinates will be;
X' = (3, -1)
Y' = (2, -2)
Z' = (-1, -3)
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Find the distance between points H(8, 2) and K(6, 10). Round your answer to the nearest tenth
Answers
Step-by-step explanation:
when you mark such points on a coordinate grid, and mark also the coordinate differences in x and y direction as soft lines, you notice that these coordinate difference lines and the direct connection between the 2 points create a right-angled triangle.
so, Pythagoras applies :
c² = a² + b²
with c being the Hypotenuse (the baseline opposite of the 90° angle, which is the direct connection between the 2 points). a and b are the legs (coordinate differences).
so,
distance² = (8 - 6)² + (2 - 10)² = 2² + (-8)² = 4 + 64 = 68
distance = sqrt(68) = 8.246211251... ≈ 8.2
To support the tree a guy wire 8.1 m long is attached to the trunk and then secured in the ground find the height of the leafty part of the tree to the nearest tenth
Answers
The height of the leafy part will be 6m.
How to calculate the height?Other part of the question:
At the same time, a vertical pole 3m high vast s shadow 4m long.
Based on the information given, the height will be:
h/8 = 3/4
h = (3 × 8)/4
h = 6
Therefore, the height is 6m.
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paulette spent 45.50 on concert tickets before fees. there was a service fee of 6% added on to her purchase.
Answers
The original price of concert tickets before the addition of service fee is 42.93
PercentageAmount spent on tickets including service fee = 45.50Percentage if service fee = 6%Original cost before service fee = x45.50 = x + (6% of x)
45.50 = x + (0.06 × x)
45.50 = x + 0.06x
45.50 = 1.06x
x = 45.50/1.06
x = 42.9245283018867
Approximately,
x = 42.93
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Nicole sold 15 tickets to the school play and Andrew sold 24 tickets. what is the ratio of the number of tickets Nicole sold to the number of tickets Andrew sold
Answers
Answer:
5:8
Step-by-step explanation:
Nichole sold 15 while Andrew sold 24, so the ratio is 15:24. Simplify the ratio by dividing both sides by 3, and we’ll get 5:8.
A restaurant hands out a scratch-off game ticket with prizes being worth
purchases at the restaurant. The back of the ticket lists the odds of winning
each dollar value: 0.4 for $10, 0.2 for $25, 0.01 for $30, and 0.004 for $75.
What are the odds that the ticket is worth at least $25?
Answers
Using the probability concept, the odds that the ticket is worth at least $25 are of 1:3.67.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
Considering the probability, the odd is given by:
o = probability:(1 - probability)
From the given table, the probability that the ticket is worth at least $25 is:
p = 0.2 + 0.01 + 0.004 = 0.214.
Hence the odd is:
o = 0.214/(1 - 0.214) = 0.214/0.786 = 1:3.67.
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Find possible zeroes
f(x)=3x^6+4x^3-2x^2+4
Answers
The possible zeros of f(x) = 3x^6 + 4x^3 -2x^2 + 4 are [tex]\mathbf{\pm\{1,2,4,\frac 13, \frac 23,\frac{4}{3}}\}[/tex]
How to determine the possible zeros?The function is given as:
f(x) = 3x^6 + 4x^3 -2x^2 + 4
The leading coefficient of the function is:
p = 3
The constant term is
q = 4
Take the factors of the above terms
p = 1 and 3
q = 1, 2 and 4
The possible zeros are then calculated as:
[tex]\mathbf{Zeros = \pm\frac{Factors\ of\ q}{Factors\ of\ p}}[/tex]
So, we have:
[tex]\mathbf{Zeros = \pm\frac{1,2,4}{1,3}}[/tex]
Expand
[tex]\mathbf{Zeros = \pm\frac{1,2,4}{1},\pm\frac{1,2,4}{3}}[/tex]
Solve
[tex]\mathbf{Zeros = \pm\{1,2,4,\frac 13, \frac 23,\frac{4}{3}}\}[/tex]
Hence, the possible zeros of f(x) = 3x^6 + 4x^3 -2x^2 + 4 are [tex]\mathbf{\pm\{1,2,4,\frac 13, \frac 23,\frac{4}{3}}\}[/tex]
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In a class there are 15 boys and 15 girls 5/6 of the children have brown hair if someone is chosen at random what is the probability that they will not have brown hair
Answers
Probability someone chosen at random will not have brown hair = 1/6
Probability of two variablesThe number of girls = 15
The number of boys = 15
The total number of children = 15 + 15 = 30
Probability that someone chosen at random will have a brown hair, P(Brown hair) = 5/6
P(Brown hair) + P(Not Brown hair) = 1
5/6 + P(Not brown hair) = 1
P(not brown hair) = 1 - 5/6
P(not brown hair) = 1/6
Therefore, if someone is chosen at random, probability that they will not have brown hair = 1/6
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60 POINTS PLEASE HELP NOW
Answers
The pre-image of the triangle has the following vertices: A'(x, y) = (4, 4/3), B'(x, y) = (- 2, 0) and C'(x, y) = (1, 3).
How to find the pre-image of the triangle
In this problem we must use a transformation rule known as dilation, a kind of rigid transformation, to derive the preimage of the triangle, whose formula is:
P'(x, y) = O(x, y) + k · [P(x, y) - O(x, y)] (1)
Now we proceed to find the preimage of the triangle: O(x, y) = (0, 0), k = 2/3
Point A'
A'(x, y) = (0, 0) + (2/3) · [(6, 2) - (0, 0)]
A'(x, y) = (4, 4/3)
Point B'
B'(x, y) = (0, 0) + (2/3) · [(- 3, 0) - (0, 0)]
B'(x, y) = (- 2, 0)
Point C'
C'(x, y) = (0, 0) + (2/3) · [(1.5, 4.5) - (0, 0)]
C'(x, y) = (1, 3)
The pre-image of the triangle has the following vertices: A'(x, y) = (4, 4/3), B'(x, y) = (- 2, 0) and C'(x, y) = (1, 3).
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Please answer the question below . Help is greatly appreciated!
Answers
Using proportions, it is found that 40 ml of water have to be added to make the ratio of oil to water of 1:3.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The jar contains 100 ml of oil and water in the ratio 1:4, hence:
The amount of oil is: 1/5 x 100 = 20 ml.The amount of water is: 4/5 x 100 = 80 ml.Oil was added to make the ratio 1/2, hence:
[tex]\frac{20 + x}{100 + x} = \frac{1}[3}[/tex]
3(20 + x) = 100 + x
60 + 3x = 100 + x
x = 20.
Then there are 40 ml of oil and 80 ml of water, for a total of 120 ml. Now we want a ratio of 1:3, that is, 3/4 of the mixture being water, hence:
[tex]\frac{80 + x}{120 + x} = \frac{3}{4}[/tex]
4(80 + x) = 3(120 + x)
320 + 4x = 360 + 3x
x = 40
40 ml of water have to be added to make the ratio of oil to water of 1:3.
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Emma has money in two savings accounts. One rate is 6% and the other is 14%. If she has $950 more in the 14% account and the total interest is $342, how much is invested in each savings account?
Answers
$1045 was invested at the interest rate 6% whereas $1,995 was invested at 14%
How is interest computed?
Interest is determined as the amount invested multiplied by the interest rate.
Let Y be the amount invested at 6%
Interest=Y*6%
Interest=0.06Y
The amount invested at 14%, which is $950 more , is Y+950
Interest=(Y+950)*14%
Interest=0.14Y+133
Total interest =0.06Y+0.14Y+133
Note that total interest is 342
342=0.06Y+0.14Y+133
342=0.20Y+133
342-133=0.20Y
209=0.20Y
Y=209/0.20
Y=$1,045(amount invested at 6%)
Amount invested at 14%=$1,045+$950
Amount invested at 14%=$1,995
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6) Ron bought a car 8 years ago for $15,694. If the rate of depreciation is 4.75% per year, what is the value of
Ron's car now? Round answer to nearest cent.
O a.) $10,642.94
Ob.) $10,332.94
Oc.) $10,632.94
Od.) $10,662.94
Answers
find the slope of this line
Answers
Answer:
2
Step-by-step explanation:
Select two points that the red line goes through like (0,-10) and (2,-6). If I start at the bottom left of the red line, I can see that I am moving to the right and up. That means that the slope will be positive. As my x is increasing so is my y. Starting at point (0,-10) 2 space, but each space counts as 2, so I really move up 4. Then I check to see how much I moved right. It is only one space, but again, I am counting by 2s, so I really moved 2 units to the right.
The fraction would be 4/2 which just equals 2/1 or 2.
Using the drawing what is the vertex of angle 4?
Answers
Answer: A
Step-by-step explanation:
define cultural identity in your own words
Answers
Cultural identity component of an individual which makes him identifiable with a given group. For example, British Asian is a cultural identity.
What is the Meaning of Cultural Identity?Cultural identity can be described as a component of an individual which makes him identifiable with a given group that share the same characteristics.
Examples of cultural identities may include the following:
ReligionEthnic backgroundTraditionNationalityFoodI can state that I am a British Asian. British Asian is my cultural identity.
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James has $20 in his wallet and makes $10 per hour. Kelly has $50 in her wallet but only makes $8 per hour.
How many hours of work will it take for these two people to have the same amount of money?
Answers
Answer:
At 15 hours of work they will be equal.
Step-by-step explanation:
James: y = 10x + 20
Kelly: y = 8X + 50
Set them equal to each other and solve
10x + 20 = 8x + 50 Subtract 8x from both sides of the equation
2x + 20 = 50 Subtract 20 from both sides of the equation
2x = 30 Divide both sides by 2
x =15
There are some 1-dollar bills, some 5-dollar bills, and a 20-dollar bill in an envelope. The number of 1-dollar bills is five times the number of the 5-dollar bills. We randomly pull a bill from the envelope. How many 1-dollar bills are in this envelope if the expected value of the bill pulled is $2.00?
Answers
Answer:
the number of 1 dollars bills was 5 si make 1 more 5 dollars so 8n total it is 10 dollars.
where is the center of the circle and the radius is how many units?
Answers
Answer:
8,9,5
Step-by-step explanation:
Find the sum of the geometric series given a1 = 5, r = 3, n = 12.
Answers
The sum of the geometric series is 1328600
How to determine the sum?The given parameters are:
a1 = 5
r = 3
n = 12
The sum of the terms is:
[tex]S_n = \frac{a(1 - r^n)}{1 - r}[/tex]
This gives
[tex]S_n = \frac{5 * (1 - 3^{12})}{1 - 3}[/tex]
Evaluate the difference
[tex]S_n = \frac{5 * (1 - 531441)}{-2}[/tex]
This gives
[tex]S_n = \frac{5 * - 531440}{-2}[/tex]
Evaluate
[tex]S_n = 1328600[/tex]
Hence, the sum of the geometric series is 1328600
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Zaidah plans a raised flower bed 2 ft high by 15 ft wide by 24 ft long. The mulch, soll, and peat mixture used to fill the raised bed costs $12.75 per cubic yard. What is the total cost (in dollars) of the
Ingredients used to fill the raised garden?
Answers
[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Let's get started ~
[tex]\qquad \sf \dashrightarrow \: volume = length \sdot width \sdot height[/tex]
[tex]\qquad \sf \dashrightarrow \: v = (24) \sdot(15) \sdot(2)[/tex]
[tex]\qquad \sf \dashrightarrow \: v = 720 \: \: ft {}^{3} [/tex]
now, we know :
[tex]\qquad \sf \dashrightarrow \: 1 \: \: yard {}^{3} = 27 \: \: ft {}^{3} [/tex]
[tex]\qquad \sf \dashrightarrow \: 1 \: \: ft {}^{3} = \cfrac{1}{27} \: \: yard {}^{3} [/tex]
[tex]\qquad \sf \dashrightarrow \: 720 \: \: ft {}^{3} = \cfrac{1}{27} \times 720 \: \: yard {}^{3} [/tex]
[tex]\qquad \sf \approx\: 26.67 \: \: yard {}^{3} [/tex]
now, total cost of ingredients used is :
[tex]\qquad \sf \dashrightarrow \: 26.67 \times 12.75[/tex]
[tex]\qquad \sf \dashrightarrow \: 340.04[/tex]
so, total cost is $ 340.04
A solid right square prism is cut into 5 equal pieces parallel to its bases. The volume of each piece is V = 1/5s2h.Solve the formula for s. help asap
Answers
The solution of the formula for s is:
[tex]s = \sqrt{\frac{5V}{h}}[/tex]
What is the symbolic equation?The equation is:
[tex]V = \frac{1}{5}s^2h[/tex]
To solve for s, we isolate it, hence:
[tex]s^2 = \frac{5V}{h}[/tex]
[tex]s = \sqrt{\frac{5V}{h}}[/tex]
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The total area of a picture and its frame can be represented by ^l + 2f h^w + 2f h, where l and w represent the length and width of the picture, respectively, and f represents the thickness of the frame.
a. Sketch a diagram to represent this scenario.
b. What binomial multiplication represents the area of an 8" # 12" picture and its frame?
c. Multiply the binomials from b., and combine like terms to simplify.
d. What is the total area of an 8" # 12" picture and its frame if the frame is 1.5" thick?
Answers
The answers to the question are
b. (l + 2f) (w + 2f)
c. f + 4, f + 6
d. 52.25
a. The diagram is an attachment.
B. How to solve for the binomial multiplicationThe equation says
(l + 2f) (w + 2f)
We have the lengths of w and l as 8 and 12 respectively. Hence we have
(8 + 2f) (12 + 2f) as the area
c. (8 + 2f) (12 + 2f)
= 96 + 16f + 24f + 4f²
= 4f² + 40 f + 96
We have to factorize this using the quadratic equation calculator
f + 4, f + 6
= f = -4 and f = -6
d. If it is 1.25 thick we would have
1.25 x 2 = 2.5
12 - 2.5 = 9.5
8 - 2.5 = 5.5
Area = l * w
= 5.5 * 9.5
= 52.25
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1376x13 please solve this equation and show work
Answers
The value of 1376 * 13 is 17888
How to solve the expression?The expression is given as:
1376 * 13
Express 1376 as 1300 + 76
(1300 + 76) * 13
Expand
1300 * 13 + 76 * 13
Evaluate the product
16900 + 988
Evaluate the sum
17888
Hence, the value of 1376 * 13 is 17888
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How many proportional relationships are shown in the coordinate plane below/
Answers
Answer:
I wish I could I didnt do good with this in math
claire and martin are trying to determine the length of a slug. Claire has a mesuring stick whose markings are 1 cm apart, and Martin has a measuring stick whose markings are 0.1cm apart.
Answers
Claire's measuring stick would make a more precise measurement
How to determine the precise measurement?The given parameters are:
Claire = 1 cm
Martin = 0.1 cm
The 0.1 cm marking would make a more accurate measurement.
This is so because the length of a slug would most likely be in decimal centimeters
However, this doesn't translate to a precise measurement.
Hence, Claire's measuring stick would make a more precise measurement
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suppose that fanf g are continuous functions,
12_(^28 f(x)dx=19, and 12 (^28 g(x)dx =35.
Find
12_ f^28 [kg(x)-2f(x)] dx, where the coefficient
k=7
those are intergral symbols with numbers on
top and bottom. please show work. thanks
Answers
The required result based on given continuous functions is: 207. See the explanation for same below.
A continuous function in mathematics is one in which a continuous variation (that is, a change without a jump) of the argument causes a continuous variation of the function's value.
Since G and F are continuous functions,
[tex]\int_{12}^{28}) \, f(x) dx[/tex] = 19
[tex]\int_{12}^{28}) \, f(x) dx[/tex] = 35
Therefore,
[tex]\int_{12}^{28}) \, [K g(x) - 2 f(x)] dx[/tex]
= K [tex]\int_{12}^{28}) \, g(x) dx -2 \int_{12}^{28}) \, f(x) dx[/tex]
So, given that K = 7, we have
7 x 35 - 2 x 19
= 245 - 38
= 207
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Find the exact solutions of x2 − 3x − 5 = 0 using the quadratic formula. Show all work! 75 points please help!!!!!
Answers
Answer:
[tex]x=\dfrac{3+ \sqrt{29}}{2}, \quad \dfrac{3- \sqrt{29}}{2}[/tex]
Step-by-step explanation:
Quadratic Formula
[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]
Given quadratic equation:
[tex]x^2-3x-5=0[/tex]
Define the variables:
[tex]\implies a=1, \quad b=-3, \quad c=-5[/tex]
Substitute the defined variables into the quadratic formula and solve for x:
[tex]\implies x=\dfrac{-(-3) \pm \sqrt{(-3)^2-4(1)(-5)}}{2(1)}[/tex]
[tex]\implies x=\dfrac{3 \pm \sqrt{9+20}}{2}[/tex]
[tex]\implies x=\dfrac{3 \pm \sqrt{29}}{2}[/tex]
Therefore, the exact solutions to the given quadratic equation are:
[tex]x=\dfrac{3+ \sqrt{29}}{2}, \quad \dfrac{3- \sqrt{29}}{2}[/tex]
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Answer:
[tex]\boxed {\frac{3+\sqrt{29}}{2}} \boxed{\frac{3-\sqrt{29}}{2}}[/tex]
Step-by-step explanation:
Quadratic Formula :
[tex]\boxed {\frac{-b \pm \sqrt{b^{2}-4ac}}{2a}}[/tex]
We are given the equation x² - 3x - 5 = 0.
Here,
a = 1b = -3c = -5Solving :
3 ± √3² - 4(1)(-5) / 2(1)3 ± √29 / 2Hence, the solutions are :
[tex]\boxed {\frac{3+\sqrt{29}}{2}} \boxed{\frac{3-\sqrt{29}}{2}}[/tex]
Four students are simplifying the expression 5x(–3 – 7x).
Which student’s work is correct?
5x(–3 – 7x)
(5x)(–3) – 7x
–15x –7x
5x(–3 – 7x)
(5x)(–3) – (5x)(7x)
–15 – 35x
5x(–3 – 7x)
–3 + 5x – 7x
–3 – 2x
5x(–3 – 7x)
(5x)(–3) + (5x)(–7x)
–15x – 35x2
Answers
Answer:
So the questions isn't clear enough, but I could tell u that the nearest answer is the last answer, but without the multiplied 2
It's _15x_35xsquared
Answer:
5x(–3 – 7x)
(5x)(–3) + (5x)(–7x)
–15x – 35x2
Step-by-step explanation:
D
How do i find the slope of these points? (−4, 3) and (2, 9)
Answers
Answer:
Divide the difference of the y-coordinates of 2 points on a line by the difference of the x-coordinates of those same 2 points.
Step-by-step explanation:
Answer:
The value of the slope b/n these two pts. will be 1.
Step-by-step explanation:
Greetings !
For finding slope from two points of a line (x₁, y₁) and (x₂, y₂), we use the formula (y₂ - y₁) / (x₂ - x₁).
Thus, m=(y₂ - y₁) / (x₂ - x₁)
m=(9-3)/(2-(-4))m=6/6m=1.What is the measure of angle A?
250
140
70
110
Answers
Using the angle of intersecting tangents theorem, the measure of angle A is: C. 70°
What is the Angle of Intersecting Tangents Theorem?Based on the angle of intersecting tangents theorem, measure of angle A = 1/2(the positive difference of the intercepted arcs).
Measure of one of the intercepted arcs = 250°
The second intercepted arc = 360 - 250 = 110°
Positive difference of the intercepted arcs = 250 - 110 = 140°
Measure of angle A = 1/2(140)
Measure of angle A = 70°
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Answer:
the answer is 70. hope this helps <3
Step-by-step explanation: