The equation of the circle in the standard form is:
(x + 13)² + (y - 13)² = 4².
What is defined as the equation of the circle?The equation for a circle with (h, k) center and radius r is as follows:(x - h)² + (y - k)² = r².This is the equation's standard form. And thereby, if we learn the coordinates of the circle's center and radius, we can quickly find its equation.For the given question;
The centre of the circle lies at (-13, 13).
Thus, (h. k) = (-13, 13).
The radius 'r' of the circle is 4 units.
Put the values in the standard form.
(x - (-13))² + (y - 13)² = 4²
(x + 13)² + (y - 13)² = 4² is the (standard form)
Therefore, the equation of the circle with radius 4 in the standard form is represented as: (x + 13)² + (y - 13)² = 4²
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the sporting goods store sold 10 balls, 3 bats, and 2 bases for $99 on Monday. They sold 4 balls, 8 bats, and 2 bases for $78 on Tuesday. On Wednesday they sold 2 balls 3 bats and 1 base for 33.60. What is the cost of each individual item?
Answer:
ball: $8.00bat: $5.40base: $1.40Step-by-step explanation:
Given three relations between the costs of balls, bats, and bases, you want to find the cost of each.
10 balls + 3 bats + 2 bases = $994 balls + 8 bats + 2 bases = $782 balls + 3 bats + 1 base = $33.60SolutionSolving three linear equations in three unknowns can be accomplished easily by any number of calculators, apps, or spreadsheets. Here, we'll use an ad hoc solution.
Subtracting twice the third equation from the second, we have ...
(4 balls + 8 bats + 2 bases) -(2(2 balls + 3 bats + 1 base) = 78 -2(33.60)
2 bats = 10.80 . . . . . . . simplify
1 bat = 5.40 . . . . . . divide by 2
Subtracting the second equation from the first, we have ...
(10 balls +3 bats +2 bases) -(4 balls +8 bats +2 bases) = (99) -(78)
6 balls -5 bats = 21 . . . . . simplify
6 balls = 21 + 5(5.40) . . . . . add 5 bats and substitute their cost
6 balls = 48 . . . . . . . . simplify
1 ball = 8.00 . . . . . . . divide by 6
Using the last equation, we can find the cost of 1 base.
1 base = 33.60 -2 balls -3 bats = 33.60 -2(8.00) -3(5.40)
1 base = 1.40
The costs are ...
1 ball: $8.00
1 bat: $5.40
1 base: $1.40
greg can eat 1/8 of a hamburger in 1/12 of an hour how many hamburgers can greag eat in one hour
Answer: 1.5 Burgers an hour
1/8 x 12 = 1.5
Multiply 1/8 by 12 to get and hour because 12/12ths = 1 hour
Can ya'll help me? This problem has stumped me for a few days.
work out the area of the shape
Answer:
88 [tex]cm^{2}[/tex]
Step-by-step explanation:
We need to find the area of the rectangle and the triangle.
Area of the rectangle:
a = length x width
a = 11 x 6 = 66
Area of the triangle:
a = [tex]\frac{ b x h}{2}[/tex] We need to find the base and height of the triangle. The base is the same length as the length of the rectangle: 11 and the height is 10 - 6 or 4
a = [tex]\frac{11 x 4}{2}[/tex]
a = [tex]\frac{44}{2}[/tex]
a = 22
Add the area of the rectangle and the triangle together. 66 + 22 = 88
Find values of m so that the function y xm is a solution of the given differential equation. x^2y''-7xy' 15y=0
If [tex]y=x^m[/tex] is a solution to the ODE
[tex]x^2 y'' - 7xy' + 15y = 0[/tex]
then substituting [tex]y[/tex] and its derivatives
[tex]y' = mx^{m-1} \text{ and } y'' = m(m-1)x^{m-2}[/tex]
gives
[tex]m(m-1)x^2x^{m-2} - 7mxx^{m-1} + 15x^m = 0[/tex]
[tex]m(m-1)x^{m} - 7mx^{m} + 15x^m = 0[/tex]
[tex](m(m-1) - 7m + 15)x^{m} = 0[/tex]
We ignore the trivial case of [tex]y=x^m=0[/tex]. Solve for [tex]m[/tex].
[tex]m(m-1) - 7m + 15 = 0[/tex]
[tex]m^2 - 8m + 15 = 0[/tex]
[tex](m - 3) (m - 5) = 0[/tex]
[tex]\implies \boxed{m=3} \text{ or } \boxed{m=5}[/tex]
If f(x) = 4x20, what is f(4)?
Answer:
320
Step-by-step explanation:
Plug the 4 into x and go from left to right:
4 times 4 is 16 times 20 is 320
Which shows ray C A?
Suppose that you are playing blackjack against a dealer. in a freshly shuffled deck, what is the probability that neither you nor the dealer is dealt a blackjack?
The probability that neither you nor the dealer is dealt a blackjack will be 1/26.
What is probability?Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.
Suppose that you are playing blackjack against a dealer. In a freshly shuffled deck.
Then the total number of the event will be
Total events = 52
Then the probability that neither you nor the dealer is dealt a blackjack will be
Favorable event = 2 {Spade of Jack and Club of Jack}
Then the probability of that events will be
P = 2 / 52
P = 1 / 26
The probability that neither you nor the dealer is dealt a blackjack will be 1/26.
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A woman went shopping and spent 2/3 of all the money she had. Then she lost 3/5 of what she had left after shopping. How much money did she have in the beginning if she now has $10.00.
The amount of money the women had in the beggining was $75.
Let the total amout of money the women had intially be x.
According to the questio.
A woman went shopping and spent 2/3 of all the money she had. Then she lost 3/5 of what she had left after shopping.
So, the amount of money she spent for shopping = (2/3)x = 2x/3
⇒ The amount of money she had after shopping
= x -2x/3
= 3x -2x/3
= x/3
Now, the amount of money she lost 3/5 × (x/3) = x/5
⇒ Amount of money she have after the lost of money
= x/3 - x/5
= 5x - 3x /15
= 2x/15
It is given that she have $10.
⇒ 2x/15 = 10
⇒ 2x = 150
⇒ x = 150/2
⇒ x = $75
Hence, the amount of money the women had in the beggining was $75.
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your friend is also saving pennies. she puts one penny into her piggy bank the first day, two pennies the second day, four the third day, and so on, each day doubling the number of pennies added. how much money would she have at the end of vacation, if she could keep saving at this rate? (this would be hard to do, even if bill gates were your dad!)
money would she have at the end of vacation = 377,789,318,629,571,617,095.67 dollars.
What does "compounding" mean?When interest is applied to a principal amount together with the interest that has already been paid, this process is known as compounding. This means that compounding, sometimes known as the "wonder of compounding," can be thought of as interest on the compound, which has the effect of increasing returns from interest over time.
What is an appropriate compounding procedure?Current good compounding practices refer to the minimal requirements for the procedures, facilities, and controls used to compound medicine to ensure that it has the identity, and strength, and satisfies the quality and purity requirements it is claimed to have.
According to the given information:She puts in one penny the first day, 2 pennies the second, 4 pennies the third...and so on.
The total sum is thus,
(1, 3, 7, 15, 31, 63, 127)
Which translate to
(2^1-1, 2^2-1, 2^3-1, 2^4-1, 2^5-1, 2^6-1, 2^7-1,..)
So at the end of the 75th day, the total amount is 2^75-1
or
37778931862957161709567 pennies
or
377,789,318,629,571,617,095.67 dollars.
money would she have at the end of vacation = 377,789,318,629,571,617,095.67 dollars.
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I understand that the question you are looking for is:
Your friend is saving pennies. She puts one penny into her piggy bank the first day, two pennies the second day, four the third day, and so on, doubling the number of pennies added. How many much money would she have at the end of vacation, if she could keep saving at this rate? Vacation lasts 75 days.
A. Independent Activity 1 Identify whether the following equations are quadratic equations or not? m( 2m + 3) =0 11t2 (t - 4 ) = 0 5h + h2 = - 7 4b (b - 2 ) = - 8 y2 + 7y - 6 = 0 please answer
1, 3, 4,5
The polynomial equations of degree two in one variable of type f(x) = ax² + bx + c = 0 and with a, b, c, and R R and a 0 are known as quadratic equations. It is a quadratic equation in its general form, where "a" stands for the leading coefficient and "c" for the absolute term of f. (x). The roots of the quadratic equation are the values of x that fulfill the equation (α, β).
It is a given that the quadratic equation has two roots. Roots might have either a real or imaginary nature.
1)m( 2m + 3) =0
2m²+3m=0
Yes it is a quadratic equation.
2) 11t² (t - 4 ) = 0
11t³-44t²=0
NO
3) 5h + h² = - 7
Yes it is a quadratic equation.
4)4b (b - 2 ) = - 8
4b²-8b +8 =0
Yes, it is a quadratic equation.
5) y² + 7y - 6 = 0
Yes it is a quadratic equation.
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if f(x) = mx +c, f(4) = 11 and f(5) = 13, find the value of f(2).
Answer:
7
Step-by-step explanation:
[tex]f(4)=4m+c=11 \\ \\ f(5)=5m+c=13[/tex]
Subtracting the equations yields that m=2, and thus c=3.
[tex]\implies f(2)=2(2)+3=7[/tex]
which expressions below equal a rational number? select all that apply.
The expressions that are equal to a rational number are [(2/3)+(4/5)], [(√3) - (√3)], and [(√49)(√1)].
A rational number is one that can be stated as the ratio of two numbers, with the denominator not equal to zero.All real numbers that are not rational numbers are referred to as irrational numbers. The ratio of two integers cannot be used to express irrational values.(a) π√4π√4 is equal to 2π, which is an irrational number.(b) (2/3)+(4/5)(2/3)+(4/5) = (22/15), which is a rational number.(c) (√36)-(√5)(√36)-(√5) = 6-√5, which is an irrational number.(d) (√3)-(√3)(√3)-(√3) = 0, which is a rational number.(e) (√49)(√1)(√49)(√1) = 7*1 = 7, which is a rational number.To learn more about real numbers, visit :
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Jackie makes $11.75 an hour and worked for 14 hours this week.
How much more money did she make?
Answer: $164.5
Step-by-step explanation:
11.75*14=$164.5
what is the domain and range of this function?
y=|5x|-8
Answer:
Domain:
$%error%$
Range:
$%error%$
Explanation:
Both
x
and
y
belong to all the real numbers since there is no restriction on either the domain or the range.
Step-by-step explanation:
Brook went bowling with her friends she bowled 3 games and her average score for those games was 121 she had 117 her first game and 108 on her second game write an equation to find g the score of her third game
Answer:
121 x 3 = 363
117 + 108 = 225
363 - 225 = 138
138 is the third game
I'm not very sure how to write an equation for this, I guess it would look something like
117 + 108 + x = 363
Step-by-step explanation:
Can I have brainliest? It would help me out, if not thanks anyways! Hope this helped and have a nice day!
Math's Question. Please answer
Answer:
i think 15.84 is right
Step-by-step explanation:
bcz Ian all there is 99 4/5 paper towels and tere were 5 rolls. so, to calculate meters of each roll of paper towels we should divide the given value by 5
99 4/5 /5
is this false, i think maybe because you cant factor the right side. am i right
Answer:
its true
Step-by-step explanation:
What’s the answer to the question attached
(a) The third term of the sequence is 19.
(b) The term-to-term rule of the new sequence is "subtract 13 and then divide by 6".
The first term is given to be -2.The term-to-term rule is to multiply by 6 and then add 13.(a) The second term is equal to (-2)*6 +13The second term equals -12 +13The second term is 1The third term equals (1)*6 +13The third term equals 6 +13The third term is 19(b) The order of the three terms of the sequence is reversed.This means the term-to-term rule will be the inverse of the current term-to-term rule.We will now first subtract 13 and then divide by 6.To learn more about sequence, visit :
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Which of the following fractions is not equivalent to
Answer:
The third option is right
Step-by-step explanation:
This is because if you have two negative it becomes a positive
The coordinate -8 has a weight of 3 and the coordinate 4 has a weight of 1. Find the weighted average
The weighted average is -5
The formula for the weighted average is
= Σwixi/Σwi (1)
Where wi = are the weights and
xi are the coordinates
We have been given that
w1 = 3 , x1 = -8 and w2 = 1 , x2 = 4
Σwixi = w1x1 + w2x2
= 3*-8 + 1*4
= -24 + 4
= -20
Σwi = w1 + w2
= 3 + 1
= 4
Now putting the required value in equation (1) we get
Weighted average = -20/4
= -5
Hence the weighted average is -5
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Which expression represents the product of n and
25?
A. 25n
C. 25 + n
B. 25-n
D. 25 ÷ n
Answer:
25n
Step-by-step explanation:
product of n and 25
Product means multiply
25n
why is this so got dam fake
Answer:
Not sure, is there a problem or only the rant? lol. I'd appreciate my first brainliest though.
Step-by-step explanation:
Adam is re tilling his rectangular bathroom floor with one-square foot tiles.the bathroom floor is 1,770 square feet and the width is.he wants to know the approximate length of the bathroom show two methods
Answer:
length = area/width
Step-by-step explanation:
The width is missing.
area = length × width
length = area/width
Divide the area by the width to find the length.
What is the value of x
Answer: 68
Step-by-step explanation: do 75+37 which equals 112 then subtract 180 by 112 which equals 68
hope this helps
Answer:
A
Step-by-step explanation:
the sum of the 3 angles in a triangle = 180° , then
x + 37° + 75° = 180° , that is
x + 112° = 180° ( subtract 112° from both sides )
x = 68°
Evaluate the function.
f(x) = x² - 4x – 12
Find f(-7)
Answer:
Your answer is 65
Step-by-step explanation:
f(x) = x² - 4x - 12
f(-7) = (-7)² - 4 x (-7) - 12
= 49 - (-28) - 12
= 49 + 28 - 12
= 77 - 12
= 65
1) 3 (x - y)² - 10 (x-y) + 8
Answer:
[tex](3x-3y-4)(x-y-2)[/tex]
Step-by-step explanation:
Given expression:
[tex]3(x-y)^2-10(x-y)+8[/tex]
Let u = (x - y):
[tex]\implies 3u^2-10u+8[/tex]
To factor a quadratic in the form [tex]ax^2+bx+c[/tex] find two numbers that multiply to [tex]ac[/tex] and sum to [tex]b[/tex]:
[tex]\implies ac=3 \cdot 8=24[/tex]
[tex]\implies b=-10[/tex]
Therefore, the numbers are: -6 and -4.
Rewrite [tex]b[/tex] as the sum of these two numbers:
[tex]\implies 3u^2-6u-4u+8[/tex]
Factor the first two terms and the last two terms separately:
[tex]\implies 3u(u-2)-4(u-2)[/tex]
Factor out the common term (u - 2):
[tex]\implies (3u-4)(u-2)[/tex]
Substitute back in u = (x - y):
[tex]\implies (3(x-y)-4)((x-y)-2)[/tex]
Simplify:
[tex]\implies (3x-3y-4)(x-y-2)[/tex]
40 35 37 40 39 41 39 39 36 38 36 39 36 39 35 39 36 37 41 37 38 36 35 40 40 41 39 38 39 35 35 40 39 39 37 38 38 39 35 35 41 37 40 39 38 37 37. Calculate the mode
The mode of the data is 39 as it's frequency is highest .
Mode is a measure of central tendency . It is the no . which has highest frequency in data .
Data - Frequency
40 - 6
35 - 7
37 - 7
39 - 12 ( max . )
36 - 5
38 - 6
41 - 4
The value of frequency corresponding to 39 is maximum .
Therefore , as 39 occurs most of the time in the data , hence it is the mode of this data .
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Find the magnitude of the net electric field at the origin (created by charges q1 and q2).
The direction of the net magnetic field is [tex]$167.36^{\circ}$[/tex]
How to find the magnitude?[tex]q_1=-4 \mathrm{nC} \text { at }(0.6,0.8)[/tex]
[tex]$q_2=6 \mathrm{nC}$[/tex] at (0.6,0)
[tex]$r_1=$[/tex]Distance of [tex]$q_1$[/tex] from origin[tex]$=\sqrt{0.6^2+0.8^2}$[/tex]
[tex]$r_2=$[/tex] Distance of [tex]$q_2$[/tex] from origin [tex]$=0.6$[/tex]
[tex]$\mathrm{k}=$[/tex] Coulomb constant[tex]$=9[/tex]times [tex]10^9 \mathrm{Nm}^2 / \mathrm{C}^2$[/tex]
Electric field is given by
[tex]&E_1=\frac{k q_1}{r_1^2} \\[/tex]
[tex]&\Rightarrow E_1=\frac{9 \times 10^9 \times 4 \times 10^{-9}}{\sqrt{0.6^2+0.8^2}} \\[/tex]
[tex]&\Rightarrow E_1=36 \mathrm{~N} / \mathrm{C}[/tex]
[tex]&\theta=\tan ^{-1} \frac{0.8}{0.6} \\[/tex]
[tex]&\Rightarrow \theta=53.13^{\circ} \\[/tex]
[tex]&E_1=36 \cos 53.13^{\circ} \hat{i}+36 \sin 53.13^{\circ} \hat{j} \\[/tex]
[tex]&\Rightarrow E_1=21.6 \hat{i}+28.8 \hat{j}[/tex]
[tex]&E_2=\frac{k q_2}{r_2^2} \\[/tex]
[tex]&\Rightarrow E_2=\frac{9 \times 10^9 \times 6 \times 10^{-9}}{0.6^2} \\[/tex]
[tex]&\Rightarrow E_2=150 \mathrm{~N} / \mathrm{C}[/tex]
The charge [tex]$q_2$[/tex] is on the [tex]$\mathrm{x}$[/tex] axis itself and it is pointing towards the origin (left side) so the sign will be negative
[tex]E_2=-150 \hat{i}[/tex]
Resultant electric field
[tex]&E=E_1+E_2 \\[/tex]
[tex]&\Rightarrow E=21.6 \hat{i}+28.8 \hat{j}+(-150 \hat{i}) \\[/tex]
[tex]&\Rightarrow E=-128.4 \hat{i}+28.8 \hat{j}[/tex]
Magnitude of electric field is given by
[tex]&|E|=\sqrt{(-128.4)^2+28.8^2} \\[/tex]
[tex]&\Rightarrow|E|=121.6 \mathrm{~N} / \mathrm{C}[/tex]
Magnitude of the net electric field is [tex]$121.6 \mathrm{~N} / \mathrm{C}$[/tex]
Direction is given by
[tex]\theta=\tan ^{-1} \frac{128.4}{28.8}=77.36^{\circ}[/tex]
From the -x axis
[tex](90+77.36)^{\circ}=167.36^{\circ}[/tex]
The direction of the net magnetic field is [tex]$167.36^{\circ}$[/tex]
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Perform the indicated operation and express the result as a simplified complex number.
6 + 7i
6-7i
The value of complex number 6 + 7i / 6-7i is -13 / 85 + 84i/85
What are complex numbers?Complex numbers are those that are represented as a+ib, where a and b are actual numbers and I is a fictitious number termed a "iota." I has the value (-1). As an illustration, the complex number 2+3i is made up of the real number 2 (Re) and the imaginary number 3i (Im).
Given the complex number is -
6 + 7i / 6-7i
⇒ 6 + 7i / 6 - 7i × 6 + 7i / 6 + 7i
⇒ (6+7i)² / 6² - 7²(i²)
Using (a+b)² = a² + b² + 2ab
⇒ 6² + (7i)² +2(6)(7i) / 36 - 49(-1)
⇒ 36 - 49 + 84i / 36 + 49
⇒ -13 + 84i / 85
⇒ -13 / 85 + 84i/85
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