the weight of the substance after 28 years is 8 grams.
How to determine the amountWe have that the half life of a substance is defined as the time required for the substance to decrease by half
The formula for calculating the half - life of a material is given as;
[tex]N(t) = N0 (\frac{1}{2} )^\frac{t}{t^\frac{1}{2} }[/tex]
Where
N(t) is final amountNo is the initial amount = 128 gramst1/2 is the half life = 7 yearst is the time elapsed = 28 yearsSubstitute into the formula
N(t) = 128 × (0. 5) ^28/ 7
N (t) = 128 × ( 0. 5) ^ 4
N(t) = 128 × 0. 0625
N(t) = 8 grams
Thus, the weight of the substance after 28 years is 8 grams.
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A.22
B.183
C.246
D.213
Answer:
B. 183
Step-by-step explanation:
m<L = (1/2)[m(arc)KN - m(arc)KM)]
35 = (1/2)(177x - 107x)
70 = 70x
x = 1
m(arc)KN = 177x = 177
m(arc)NMK = 360 - m(arc)KN
m(arc)MNK = 360 - 177
m(arc)MNK = 183
A boat sails on a bearing of 63 for 124 miles and then turns and sails 201 miles on a bearing of 192. Find the distance of the boat from its starting point.
The distance of the boat from its starting point is 156.226 .
According to the question
A boat sails on a bearing of 63 degree for 124 miles
i.e
By making 63 degree covers 124 miles
therefore ,
In figure below
AC = 124 miles
Then turns and sails 201 miles on a bearing of 192 degree
therefore ,
In figure below
CD = 201 miles
Now,
According to the sum of triangle
∠ACB + ∠ABC + ∠BAC = 180°
∠ACB + 90° + 63° = 180°
∠ACB = 27°
CE = 180° (Straight line )
therefore,
∠DCE = 192° - 180°
= 12°
As ∠C = 90°
therefore
∠ACD = ∠C - ∠DCE - ∠ACB
= 90° - 12°- 27 °
= 51°
Now,
The distance of the boat from its starting point = AD
By using Law of Cosines
As
The Law of Cosines can be used to find the unknown parts of an oblique triangle(non-right triangle), such that either the lengths of two sides and the measure of the included angle is known (SAS) or the lengths of the three sides (SSS) are given.
The Law of Cosines (also called the Cosine Rule) says:
c² = a² + b² − 2ab cos(C)
As we have 2 sides and one angle available we can use Law of Cosines
Therefore,
by substituting the value
(AD)² = (AC)² + (CD)² − 2(AC)(CD) cos(∠ACD)
(AD)² = (124)² + (201)² − 2*124*201 cos(51)
AD = 156.226
Hence, the distance of the boat from its starting point is 156.226 .
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Rearrange the formula to highlight the height
Answer:
[tex]h = \frac{2A}{b+c}[/tex]
Step-by-step explanation:
Original Equation:
[tex]A = \frac{1}{2} (b+c)h[/tex]
Divide both sides by height
[tex]\frac{A}{h} = \frac{1}{2}(b+c)[/tex]
Raise both sides to the exponent -1 :
[tex](\frac{A}{h})^{-1} = (\frac{1}{2}(b+c))^{-1}[/tex]
Rewrite using the definition of a negative exponent: [tex](\frac{a}{b})^{-x} = (\frac{b}{a})^{x}[/tex]
[tex]\frac{h}{A} = \frac{1}{\frac{1}{2}(b+c)}\\[/tex]
Multiply 1/2 by (b+c)
[tex]\frac{h}{A} = \frac{1}{\frac{b+c}{2}}\\[/tex]
Keep, change, flip
[tex]\frac{h}{A} = \frac{1}{1} * \frac{2}{b+c} = \frac{2}{b+c}[/tex]
Multiply both sides by A
[tex]h = \frac{2A}{b+c}[/tex]
Also I forgot to mention but the exponent (-1) can be ignored after you flip it, since: [tex](\frac{a}{b})^x = \frac{a^x}{b^x}[/tex], but since in our case the exponent is 1, and [tex]a^1 = a[/tex], so there's really no need to write out the distribution part, since we just get the same fraction, after flipping it.
A positive five-digit integer is in the form ; where , and are each distinct digits. What is the greatest possible value of that is divisible by eleven
The the biggest 5 digit number based on the computation will be 87,978.
How to compute the value?The difference between the sum of the odd-numbered digits (1st, 3rd, 5th...) and the sum of the even-numbered digits (2nd, 4th...) is divisible by 11.
An example is that 34871903 is divisible by 11
3+8+1+0=12
4+7+9+3=23
23-12=11
Here, we want (b + b) - (a + c + a) to be divisible by 11.
2b - (2a + c) to be divisible by 11
ab,cba (using 7 and 8 and 9 since they biggest)
78 987 --> 2*8 - (2*7 + 9) = 16 - (14 + 9) = 16 - 23 = -7 NO
87 978 --> 2*7 - (2*8 + 9) = 14 - (16 + 9) = 14 - 25 = -11 YES
79 897 --> 2*9 - (2*7 + 8) = 18 - (14 + 8) = 18 - 22 = -4 NO
97 879 --> 2*7 - (2*9 + 8) = 14 - (18 + 8) = 14 - 26 = -12 NO
89 798 --> 2*9 - (2*8 + 7) = 18 - (16 + 7) = 18 - 23 = -5 NO
98 789 --> 2*8 - (2*9 + 7) = 16 - (18 + 7) = 16 - 25 = -9 NO
Therefore, the biggest 5 digit number is 87,978.
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On a coordinate plane, a circle has a center at (0, 0). Point (0, negative 10) lies on the circle.
A circle centered at the origin contains the point
(0, –9). Does (8, StartRoot 17 EndRoot) also lie on the circle? Explain.
No, the distance from the center to the point
(8, StartRoot 17 EndRoot) is not the same as the radius.
No, the radius of 10 units is different from the distance from the center to the point
(8, StartRoot 17 EndRoot).
Yes, the distance from the origin to the point
(8, StartRoot 17 EndRoot) is 9 units.
Yes, the distance from the point (0, –9) to the point (8, StartRoot 17 EndRoot) is 9 units.
The distance between point [tex](8, \sqrt{17})[/tex] and the center (0,0) is of 9 units, which is less than the radius, hence the correct option is:
Yes, the distance from the origin to the point [tex](8, \sqrt{17})[/tex] is of 9 units.
What is the distance between two points?Suppose that we have two points, [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The distance between them is given by:
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
In this problem, we have a circle with center at (0,0) and radius 10. Hence, every point that is less than 10 units of distance from point (0,0) will be on the circle.
The distance of [tex](8, \sqrt{17})[/tex] is:
[tex]D = \sqrt{(8 - 0)^2+(\sqrt{17} - 0)^2}[/tex]
[tex]D = \sqrt{81}[/tex]
D = 9 units.
9 < 10, hence the correct option is:
Yes, the distance from the origin to the point [tex](8, \sqrt{17})[/tex] is of 9 units.
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HELP If there are 79 people in a hip-hip dance group and 14 are girls,
what is the probability that a person chosen at random will be a boy?
State your answer as a fraction.
Answer:
you better give me brainliest
65/79
Step-by-step explanation:
number if boys =79-14 = 65
p of selecting a boy >> 65/79
can't cancel out so leave your answer like that
Determine which of the following graphs does not represent a function
Explanation:
Assuming there are four answer choices, we can eliminate choices A through C because they are functions. This is because they pass the vertical line test.
The vertical line test is where we try to draw a single vertical line through more than one point on the curve. If such a task is possible, then it is said to "fail the vertical line test" and it's not a function.
For choice A, we cannot draw a single vertical line through more than one point on the parabola. Choice A passes the vertical line test. Hence, it is a function. The same goes for choices B and C.
Unfortunately choice D is not shown, but if it's the only thing left, then I'm assuming that it's some curve that fails the vertical line test.
A con is tossed n times. How many difference sequences of head and tails can you get?
Answer:
2^n
Step-by-step explanation:
So whenever you flip a coin, you can see it as 2 nodes branching off of each existing node. so for example when you flip a coin once you're going to have 2 sequences initially H and T, now when you flip a coin again for each of those 2 sequences 2 are going to branch off of that, making the total sequences 4, and the next flip 2 sequences are going to branch off each of the 4 sequences and so on. this can generally be described as: 2^n
I attached an image describing this a bit better but the bottom line is that for each 'end node'/sequence you're going to have 2 branch off of it, thus for each coin flip the number of sequences multiplies by 2
Answer:
2^n
Step-by-step explanation:
dont worry bout it ur welcome
What is the average rate of change of f over the interval -4≤x≤5
The average rate of change over the interval is 2/9
How to determine the average rate of change?The interval is given as:
-4 ≤ x ≤ 5
From the table, we have:
f(5) = 4
f(-4) = 2
The average rate of change is then calculated as:
[tex]m = \frac{f(5) - f(-4)}{5 --4}[/tex]
This gives
[tex]m = \frac{4 - 2}{5 +4}[/tex]
Evaluate
[tex]m = \frac{2}{9}[/tex]
Hence, the average rate of change over the interval is 2/9
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If y° and 48° are a pair of complementary angles then find y°
Answer:
y = 42 and/or x = 36
Step-by-step explanation:
y + 48 = 90
y = 42 (subtracted 48 from 90)
3x + 2x = 180 (angles are linear pairs)
5x = 180 (combine like terms)
x = 36 (divided by 5 on both sides)
I didn't know which question you needed help with, I hope this makes sense :)
❄ Hi there,
the sum of complementary angles is always 90°.
If we know one of these angles, we can set up an equation –
[tex]\triangleright\sf{y+48=90}[/tex]
and then solve for y...
[tex]\triangleright \ \sf{y=42}[/tex]
That's it!
❄
A retailer allowed 4% discount on his goods to make 20% profit and sold a refrigerator for Rs 10,848 with 13% VAT. By how much is the discount to be increased so that he can gain only 15%?
The discount to be increased so that he can gain only 15% is 8%.
What is a discount? Discounts are given when a reduction in the price is permitted to promote more purchases or timely payments. Discounts are divided into Trade reduction: The discount granted when substantial purchases are made is referred to as a trade discount.Discounts are given when a reduction in the price is permitted to promote more purchases or timely payments. Discounts are divided into Trade reduction: The discount granted when substantial purchases are made is referred to as a trade discount.Since sales discounts lower the cost of a product, they are not considered costs. These monetary discounts provided to consumers do, however, have an impact on a company's financial statements. Thus they must be reported as a decrease in revenue under the accounts receivable line item.How much is the discount to be increased so that he can gain only 15%:
The cost price of the goods - y.
The selling price of the goods - x.
The selling price is
1.2y (100% + 20% = 120%).
The refrigerator was sold at 13% VAT at Rs. 10848:
=> 1.2y + 13%(1.2y) = 10848
=> 1.2y + 0.156y = 10848
=> 1.356y = 10848
=> y = 8000
Thus, the cp is Rs 8000.
The selling price is:
=> 0.96x = 1.2y
=> 0.96x = 1.2(8000)
=> x = 10000
The selling price is Rs. 10000
For a profit of 15%, that is 1.15(8000) = 9200, the discount is:
(1 - discount)10000 = 9200
1 - discount = 0.92
Discount = 1 - 0.92 = 0.08 or 8%
How much is the discount to be increased so that he can gain only 15%: Discount=8%
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Annabella wants to make the most economical decision so she chose the 3-year car loan so that after the loan is paid off to be able to invest in a structured saving account if Anabella put $200 into a saving account each month with an annual interest rate of 3.2% interest compounded monthly how much money would she have in her account after 2 years
Answer:
Annabella will save $4950.11 after 2 years.
Step-by-step explanation:
GivenPeriodic payment P = $200,Period t = 2 years,Number of compounds, monthly n = 12,Interest rate, r = 3.2% = 0.032.To findFuture value of saving, FSolutionUse periodic compound formula:
[tex]F=P\cfrac{(1+r/n)^{nt}-1}{r/n}[/tex]
Substitute the values and calculate:
[tex]F=200\cfrac{(1+0.032/12)^{12*2}-1}{0.032/12} =4950.12[/tex] rounded
Step-by-step explanation:
Given P = $200, t = 2 years, n = 12,[tex] \sf \: r = 3.2\% = \frac{3.2}{100} = 0.032[/tex]To findFuture value of savingSolutionUse periodic compound formula:
[tex] \sf \: F=P\cfrac{(1+ \frac{r}{n})^{nt}-1}{\frac{r}{n}}[/tex]
Substitute the values and calculate:
[tex]\sf \: F=200\cfrac{(1+ \frac{0.032}{12})^{12 \times 2}-1}{\frac{0.032}{12}}[/tex]
[tex]\sf \: F=200\cfrac{( \frac{ 12 + 0.032}{12})^{24}-1}{\frac{0.032}{12}}[/tex]
[tex]\sf \: F=200\cfrac{( {11.002 }{})^{24}-1}{0.002} [/tex]
[tex]\sf \: F=200 \times 24.7506[/tex]
[tex]\sf \: F=4950.12rounded[/tex]
The list 76, 56, 93, 24, 45, 88, 13, 7, 37 is sorted using bucket sort with 4 buckets. which bucket will contain 45?
The bucket number 2 will contain 45 after sorting the data.
According to the statement
we have given that the a data list which is sorted into 4 buckets then we have to find he in which the umber 45 is sorted.
So, For this purpose,
The given data list is:
76, 56, 93, 24, 45, 88, 13, 7, 37
And the data is sorted into the buckets so,it is sorted in 4 buckets. and the data contain numbers from 0 to 100.
So, let the sorting.
We know that the 100 numbers are sorted in 4 buckets then it means each bucket contain 25 numbers.
So, let us consider a
BUCKET 1 : 0 to 25
it contains the data number 7, 13,24.
Now,
BUCKET 2 : 25 to 50
it contains the data number 37,45.
Now,
BUCKET 3 : 50 to 75
it contains the data number 56.
Now,
BUCKET 4 : 75 to 100
it contains the data number 76, 88, 93.
From sorting the 45 number sort in the bucket 2.
So,The bucket number 2 will contain 45 after sorting the data.
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Are the two triangles similar?
Answer:
Yes
Step-by-step explanation:
The missing angle in triangle DER is 42 (as angles in a triangle add up to 180) and the missing angle in TVA (LOKI lol ) is 110 (as angles in a triangle add up to 180) .
Since all angles are equal the triangles must be similar .
Hope this helped and have a good day
Which equation could represent a linear combination of the system?
The equation that could represent a linear combination of the system 2/3x + 5/2y = 15 and 4x + 15y = 12 is 0 = 26
What are linear equations?Linear equations are equations that have constant average rates of change, slope or gradient
How to determine the linear combination to the system?A system of linear equations is a collection of at least two linear equations.
In this case, the system of equations is given as
2/3x + 5/2y = 15
4x + 15y = 12
Multiply the first equation by 6, to eliminate the fractions.
6 * (2/3x + 5/2y = 15)
This gives
4x + 15y = 90
Subtract the equation 4x + 15y = 90 from 4x + 15y = 12
4x - 4x + 15y - 15y = 12 - 90
Evaluate the difference
0 + 0 = -78
Evaluate the sum
0 = -78
The above equation is the same equation as option (b) 0 = 26
This is so because they both represent that the system of equations have no solution
Hence, the equation that could represent a linear combination of the system is 0 = 26
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Complete question
The system of equations below has no solution.
2/3x + 5/2y = 15
4x + 15y = 12
Which equation could represent a linear combination of the system?
Simplify.
√75
OA. 3√5
OB. 15√5
OC. 25√3
OD. 5√3
Answer:
Option D
Step-by-step explanation:
Using the surd law :
[tex]\sqrt{ab} = \sqrt{a}\sqrt{b}[/tex]
We can find the largest square number that goes into 75 :
Let's write the multiples of 75 :
1 , 75
3 , 25
5 , 15
The only square number is 25
So using the law mentioned above we split √75 into :
√25√3
The square root of 25 is 5
Now we have our final answer of 5√3
Hope this helped and have a good day
The simplified form of expression √75 is 5√3.
Option D is the correct answer.
We have,
To simplify √75, we can factor it into its prime factors and then take the square root:
√75 = √(3 * 5 * 5)
= √(3 x 5²)
Take out the perfect square factor from under the square root:
= √3 x √5²
= √3 x 5
= 5√3
Thus,
The simplified form of expression √75 is 5√3 which is option D.
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Which statement describes independent events?
A. You write the numbers 1 through 10 on
index cards. You randomly draw two
cards without replacement: a 6 and an 8.
C. You randomly draw a blue marble from a
bag, return the marble, and then
randomly draw a yellow marble.
B. A President and Vice President are
randomly selected from a group of 24
students.
D. You randomly draw four cards from a
standard deck of cards without
replacement. You draw a King, then a
Queen, then a Jack, and then an Ace.
The statement that describes independent events is:
C. You randomly draw a blue marble from a bag, return the marble, and then randomly draw a yellow marble.
How to determine the statement describes independent eventsIn this case, the events of drawing a blue marble and drawing a yellow marble are independent because the first draw does not affect the probability or outcome of the second draw.
Returning the marble to the bag ensures that each draw is independent of the previous one.
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what all can you tell me about this shape?
Answer: It is an equilateral square
Step-by-step explanation: it has 4 tick marks
Id like some help!!!
Answer:
50.24 ft^2.
Step-by-step explanation:
Area = pi r^2
Here the radius r = 4
Therefore the area of the circle
= pi * 4^2
= 16 pi
= 16 *3.14
= 50.24 ft^2.
Tim has a bag containing only red, yellow and green jelly beans.
- the number of red jellybeans is 25
- the number of yellow jelly beans is a third of red jelly beans
- a half of his jelly beans are green.
How many of Tim's jellybeans are green?
Answer:
green=100 jellybeans
Step-by-step explanation:
let the bag be (B)
red jellybeans (R)
yellow jellybeans (Y)
green jellybeans (G)
R=25
Y=3R............(1)
½ of B=G ..........(2)
from equation (1)
Y=3(25)
Y=75
since 1/2 0f the bag are G that means R+Y is equal to the remaining bag
R+Y=75+25=100 which is half of the bag
G that's half of the bag =100
What is the point slope form of a line with the slope -4 that contains the point (2,-8)
Answer:
y + 8 = -4(x - 2)
Step-by-step explanation:
Point-slope form of an equation is a fill-in-the-blank, shortcut way to write an equation of a line. This is the format:
y - Y = m(x - X)
You just fill in the slope for m and fill in the point for the X,Y.
Just leave the first y; it stays a y and the first x in the parenthesis stays as an x. You just have to be careful with your minus and negative signs.
Slope is given as -4 so fill that in for m.
and put (2,-8) in place of the X and Y.
y - Y = m(x - X)
y - -8 = -4(x - 2)
y + 8 = -4(x - 2)
Done! Hope this helps!
Which of the following is NOT a monomial? -11x
x - 4
3
22xy
Answer:
x - 4
Step-by-step explanation:
monomial is one term
-11x is only one term
x-4 isn't
3 is one term
22xy is only one term
only x-4 isn't a monomial
The total cost charged for a day of fun at Aussie World consists of an entry fee of $15 and a rate of $3 per ride. Write the rule for the total cost, C, where r rides are taken.
C = 3r + 15 is the rule for the total cost, C, where r rides are taken given that the total cost charged for a day of fun at Aussie World consists of an entry fee of $15 and a rate of $3 per ride. This can be obtained by converting the statements to algebraic equation with variables and constants.
Find the rule for the total cost:Here in the question it is given that,
The total cost charged for a day of fun at Aussie World consists of
an entry fee of $15 a rate of one ride is $3We have to find a rule for the total cost, C, where r rides are taken.
For one ride the rate is 3 ⇒ therefore for r rides the rate is 3r
We can convert the statements to algebraic equation so that we get the required rule,
⇒ The total cost consists of entry fee and rate of rides
⇒ The total cost = entry fee + rate of rides
⇒ C = 15 + 3r (from the given information)
⇒ C = 3r + 15
Hence C = 3r + 15 is the rule for the total cost, C, where r rides are taken given that the total cost charged for a day of fun at Aussie World consists of an entry fee of $15 and a rate of $3 per ride.
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Need help. i dont understand this!!!
By the quadratic formula, the solution set of the quadratic equation is formed by two real roots: x₁ = 0 and x₂ = - 12.
How to find the solution of quadratic equation
Herein we have a quadratic equation of the form a · m² + b · m + c = 0, whose solution set can be determined by the quadratic formula:
x = - [b / (2 · a)] ± [1 / (2 · a)] · √(b² - 4 · a · c) (1)
If we know that a = - 1, b = 12 and c = 0, then the solution set of the quadratic equation is:
x = - [12 / [2 · (- 1)]] ± [1 / [2 · (- 1)]] · √[12² - 4 · (- 1) · 0]
x = - 6 ± (1 / 2) · 12
x = - 6 ± 6
Then, by the quadratic formula, the solution set of the quadratic equation is formed by two real roots: x₁ = 0 and x₂ = - 12.
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Write the first five terms of the sequence with the given nth term. an = cos n 2
The first five terms of the sequence with the given n-th term [tex]a_n = cos(\frac{n\pi}{2} )[/tex] are : 0, -1, 0, 1, 0
For given question,
We have been given the n-th term of the sequence [tex]a_n = cos(\frac{n\pi}{2} )[/tex]
We need to find the first five terms of the sequence.
For n = 1
[tex]\Rightarrow a_1 = cos(\frac{1\pi}{2} )\\\\\Rightarrow a_1=0[/tex]
For n = 2,
[tex]\Rightarrow a_2 = cos(\frac{2\pi}{2} )\\\\\Rightarrow a_2=cos(\pi)\\\\\Rightarrow a_2=-1[/tex]
For n = 3,
[tex]\Rightarrow a_3= cos(\frac{3\pi}{2} )\\\\\Rightarrow a_3=0[/tex]
For n = 4,
[tex]\Rightarrow a_4 = cos(\frac{4\pi}{2} )\\\\\Rightarrow a_4=cos(2\pi)\\\\\Rightarrow a_4=1[/tex]
For n = 5,
[tex]\Rightarrow a_5 = cos(\frac{5\pi}{2} )\\\\\Rightarrow a_5=0[/tex]
Therefore, the first five terms of the sequence with the given n-th term[tex]a_n = cos(\frac{n\pi}{2} )[/tex] are : 0, -1, 0, 1, 0
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A ladder resting against a wall makes an
angle of 63° with the ground. The foot of
the ladder is 4.7 m from the wall.
Calculate the height of the top of the
ladder above the ground
Answer:
9.224
Step-by-step explanation:
A scientist uses a submarine to study ocean life. She begins 88 feet below sea level. • After traveling down for 6 seconds, she's 182 feet below sea level. Find the rate of change in the submarine's elevation in feet per second. Round your answer to the nearest tenth.
Answer:
original ft below sea level =88 feet
In six seconds goes to 182 feet
Amount of feet covered in 6 seconds=182-88=94 ft
Step-by-step explanation:
rate in feet per second = 94/6=15.66
rounding to nearest tenth=15.7ft/s
Give the equation for a circle with the given center and radius. center at (-1, 3), radius = 4
Answer:
(x + 1)² + (y - 3)² = 16
Step-by-step explanation:
the equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k ) are the coordinates of the centre and r is the radius
here (h, k ) = (- 1, 3 ) and r = 4 , then
(x - (- 1) )² + (y - 3)² = 4² , that is
(x + 1)² + (y - 3)² = 16
Answer:
(x+1)^2 + (y-3)^2 = 16
Step-by-step explanation:
The standard form of an equation of a circle with center (h,k) and radius r is (x-h)^2 + (y-k)^2 = r^2. Plugging in those values, we get (x-(-1))^2 + (y-3)^2= 4^2 = (x+1)^2 + (y-3)^2 = 16.
evaluate:25 divided by 5+2 multiplied by 3
Answer:
11
Step-by-step explanation:
25 than you divided 5 + 2 than you multiply 3 and you get
Answer:
11
Step-by-step explanation:
1. If R = 32 - 11 (OC+2y). then find R when: x=2 and y=4
The correct equation says to find R = 32 - 11 (X+2y). This gives us the value of -78.
How to solve for the equation belowWe have this
R = 32 - 11 (X+2y)
we have the following values for x and y as 2 and 4 respectively.
What we have to do would be to find the value of R after we have put in these values in the equation.
To do this, we would then have:
R = 32 - 11(2 + 2*4)
R = 32 -11(2+8)
R = 32 - 11 * 10
R = 32 - 110
This would give us the value that says
R = -78
Hence the value of R is given as -78
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