What is the length of the radius of a circle with a center at 2 – i and a point on the circle at 8 + 7i?
Answers
Answer:
10
Step-by-step explanation:
The radius is the magnitude of the complex number that is the difference between any point on the circle and the center point. A suitable calculator can tell you that magnitude:
║(8+7i) - (2-i)║ = √((8-2)² +(7-(-1))²) = √(36+64) = √100 = 10
Answer:
10
Step-by-step explanation:
Related Questions
Given the equation −4 Square root of x minus 3= 12, solve for x and identify if it is an extraneous solution
Answers
Answer:
[tex]x=\frac{225}{16}[/tex] is an extraneous solution.
Step-by-step explanation:
Given : Equation [tex]-4\sqrt x-3=12[/tex]
To find : Solve for x and identify if it is an extraneous solution?
Solution :
Step 1 - Write the equation,
[tex]-4\sqrt x-3=12[/tex]
Step 2 - Add 3 both sides,
[tex]-4\sqrt x-3+3=12+3[/tex]
[tex]-4\sqrt x=15[/tex]
Step 3 - Squaring both sides,
[tex](-4\sqrt x)^2=(15)^2[/tex]
[tex]16x=225[/tex]
Step 4 - Divide both side by 16,
[tex]\frac{16}{16}x=\frac{225}{16}[/tex]
[tex]x=\frac{225}{16}[/tex]
For extraneous solution, Substitute the value of x back in the equation.
[tex] -4\sqrt (\frac{225}{16})-3=12[/tex]
[tex]-4\times\frac{15}{4}-3=12[/tex]
[tex]-15-3=12[/tex]
[tex]-18\neq12[/tex]
The value of x does not satisfy the equation which means the value of x is an extraneous solution.
So, [tex]x=\frac{225}{16}[/tex] is an extraneous solution.
What is a distributive property of 72 divided by 4
Answers
Answer:
[tex]\frac{72}{4}=18[/tex]
Step-by-step explanation:
To find : What is a distributive property of 72 divided by 4 ?
Solution :
The distributive property of division is given by,
[tex]\frac{a+b}{c}=\frac{a}{c}+\frac{b}{c}[/tex]
We have to divide 72 by 4,
So, Re-write 72 as 60+12.
Substitute,
[tex]\frac{72}{4}=\frac{60+12}{4}[/tex]
[tex]\frac{72}{4}=\frac{60}{4}+\frac{12}{4}[/tex]
[tex]\frac{72}{4}=15+3[/tex]
[tex]\frac{72}{4}=18[/tex]
Therefore, [tex]\frac{72}{4}=18[/tex]
While the distributive property is typically relevant for multiplication over addition or subtraction, you can apply it to division by first rewriting the division as multiplication by the reciprocal. For example, 72 divided by 4 can be rewritten as 72 times 1/4, and then distributed over a sum or difference.
Explanation:The distributive property involves multiplication and addition or subtraction, not division. However, if we interpret your question in a bit different way, we can make use of the distributive property for division. To start, dividing 72 by 4 is the same as multiplying 72 by 1/4. So, we can rewrite it as follows:
72 * 1/4
The distributive property is applied when you multiply a number by a sum or a difference. For example, in case of [tex]72*1/4 = (40+32)*1/4[/tex], it would distribute as: [tex]40*1/4 + 32*1/4[/tex]. It gives us 10 + 8 = 18 which is the correct answer. This way, the distributive property can be used in division if the division is expressed as a multiplication.
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9.17/15.00
Is this a A+ or A or B or C
Answers
That would likely earn a grade of D, unless the grading scale used is different from the usual 91-100, 81-90, 71-80, 61-70, 51-60.
P(-9,1);m=1 use slope intercept form to write an equation of a line passing through the given point and having the given slope. Express answer in Standord form
Answers
Use slope-intercept form to answer this question.
Remember, slope-intercept form is : y=mx+b, where m=slope, b=y-intercept.
Our m=1, our b=1
So, simply plug these into the equation.
y=mx+b → y = (1)x + (1)
Simplify.
y = x + 1 → Slope-intercept form.
However, we want this in standard form.
Standard form : Ax+Bx=C
In Standard Form, "x" and "y" are on the same side, so we must subtract x from both sides.
-x + y = 1 ← Standard Form
~Hope I helped!~
PLEASE HELP!
Yolanda will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of $57 and costs an additional $0.11 per mile driven. The second plan has an initial fee of $50 and costs an additional $0.13 per mile driven.
For what amount of driving do the two plans cost the same?
What is the cost when the two plans cost the same?
Answers
The function f(x) is graphed on the coordinate plane.
What is f(−2) ?
Enter your answer in the box.
f(−2) = ?
Answers
PLEASE HELP ASAP!!/BRAINLIEST/5 STARS/HEART(THX)!
Jimmy is going to pack his backpack for a trip. His backpack is 60 cubic litres. He has a pile of equipment that takes up 43 cubic litres and then he has his sleeping bag that takes up 23 cubic litres. Let r be the amount of room left in his backpack. Which equation could you use to determine if he has enough room in his backpack.
A) r = 23 + 43
B) r = 23 + 43 + 60
C) 23 + 43 + r = 60
D) 23 + r = 60 + 43
Answers
His backpack is 60 cubic L
His equipment is 43 cubic L
His sleeping back is 23 cubic L
R = amount of room left.
The best formula to use is
C) 23 + 43 + R = 60
This is because we want to be able to solve for R in order to find how how much space he has left.
23 + 43 + R = 60
66+ R = 60
66-66 + R = 60-66
R = -6
He is over his amount by 6.
ANSWER:
C) 23 + 43 + R = 60
The equation for the given situation is 23 + 43 + r = 60. Therefore, option C is the correct answer.
Given that, Jimmy backpack is 60 cubic liters. He has a pile of equipment that takes up 43 cubic liters and then he has his sleeping bag that takes up 23 cubic liters.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Let r be the amount of room left in his backpack.
Total space in backpack = A pile of equipment + Sleeping bag + Room left
So, 60 = 43+23+r
The equation for the given situation is 23 + 43 + r = 60. Therefore, option C is the correct answer.
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Peter wants to borrow $3,000. He has two payment plans to choose from. Plan A is 4% interest over 6 years. Plan B is 5% interest over 4 years. Using the formula mc024-1.jpg for payment, m, which statement best compares the plans?
Plan A has a monthly payment of about $23 less and a total interest charge of $120 less than plan B.
Plan A has a monthly payment of about $23 less and a total interest charge of $120 more than plan B.
Plan A has a monthly payment of about $23 more and a total interest charge of $120 more than plan B.
Plan A has a monthly payment of about $23 more and a total interest charge of $120 less than plan B
Answers
To determine which payment plan is better for borrowing $3,000, Plan A or Plan B, one must calculate both the monthly payments and total interest charges using the given annual interest rates and compounding periods for each plan and compare the results accordingly.
Peter wants to borrow $3,000 and is considering two different payment plans. To compare these plans, we need to calculate the monthly payment and total interest charge for each.
Plan A has an annual interest rate of 4%, compounded monthly over 6 years (or 72 months). Using the formula for monthly payment (m), we can find the monthly payment for Plan A:
m = P[r(1+r)^n] / [(1+r)^n-1]
Where:
Similarly, Plan B has an annual interest rate of 5%, compounded monthly over 4 years (or 48 months). We use the same formula to calculate the monthly payment for Plan B.
After calculating m for both plans, we can also calculate the total interest paid by multiplying the monthly payment by the number of payments and subtracting the principal amount from the result for each plan. Then, we can compare the monthly payments and total interest charges between Plan A and Plan B.
A chicken breast weighs 1.375 pounds on a digital scale. What is that same weight as a mixed number?
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write a comparison sentence to resent this equation 6 times 7 equals 42
Answers
A comparison sentence for the equation '6 times 7 equals 42' using multiplication.
Comparing the given equation '6 times 7 equals 42' using a sentence:
In comparison to the equation 6 times 7 equals 42, the sentence '7 multiplied by 6 results in 42' represents the relationship between the factors and the product.
Angelica’s bouquet of a dozen roses contains 5 white roses. The rest of the roses are pink. What fraction of the bouquet is pink roses? There are 12 roses in a dozen.
Answers
5 are white.
All you have to do is subtract 12 and 5. Once you do that you will have your answer!
Answer: 7/12 for pink roses.
Hope this helps! =)
The requried fraction of the bouquet that is pink roses is 7/12, as of the given proportion.
If Angelica's bouquet of a dozen roses contains 5 white roses, then the remaining roses must be pink. Since there are 12 roses in a dozen, the number of pink roses in the bouquet would be 12 - 5 = 7.
To find the fraction of the bouquet that is pink roses, we divide the number of pink roses by the total number of roses:
Fraction of pink roses = Number of pink roses / Total number of roses
Fraction of pink roses = 7 / 12
Therefore, the fraction of the bouquet that is pink roses is 7/12.
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Felicity is placing a rectangle in the coordinate plane. She knows that the longer side of the rectangle is 3 times its shorter side. She places the longer side on the x-axis.
What coordinates should she assign to the top-right vertex of the rectangle?
Answers
(3a , a)
Answer:
(3a,a)
Step-by-step explanation:
As you know the component on the X vertex is the first that is represented when setting point coordenates, and the second value is in the Y vertex, as you can see the value for Y is a, and in the problem says that the longer side is three times the short side, since the Y vertex is the short side, that means the X vertex will have the longer side, making it 3a. So the coordenates will be (3a,a).
What is the solution of -8/2y-8=5/y+4 - 7y+8/y^2-16
Answers
Answer:
y = 8Step-by-step explanation:
[tex]Domain:\\\\2y-8\neq0\ \wedge\ y+4\neq0\ \wedge\ y^2-16\neq0\\\\2y\neq8\ \wedge\ y\neq-4\ \wedge\ y^2\neq16\\\\y\neq4\ \wedge\ y\neq-4\ \wedge\ y\neq\pm\sqrt{16}\\\\y\neq4\ \wedge\ y\neq-4\ \wedge\ y\neq-4\ \wedge\ y\neq4\\\\\boxed{y\neq-4\ \wedge\ y\neq4}\\\\===========================[/tex]
[tex]\dfrac{-8}{2y-8}=\dfrac{5}{y+4}-\dfrac{7y+8}{y^2-16}\\\\\dfrac{-8}{2(y-4)}=\dfrac{5}{y+4}-\dfrac{7y+8}{y^2-4^2}\qquad\text{use}\ a^2-b^2=(a-b)(a+b)\\\\\dfrac{-8}{2(y-4)}=\dfrac{5}{y+4}-\dfrac{7y+8}{(y-4)(y+4)}\qquad\text{multiply both sides by (-2)}\\\\\dfrac{8}{y-4}=-\dfrac{10}{y+4}+\dfrac{14y+16}{(y-4)(y+4)}\qquad\text{add}\ \dfrac{10}{y+4}\ \text{to both sides}\\\\\dfrac{8}{y-4}+\dfrac{10}{y+4}=\dfrac{14y+16}{(y-4)(y+4)}[/tex]
[tex]\dfrac{8(y+4)}{(y-4)(y+4)}+\dfrac{10(y-4)}{(y-4)(y+4)}=\dfrac{14y+16}{(y-4)(y+4)}\\\\\dfrac{8(y+4)+10(y-4)}{(y-4)(y+4)}=\dfrac{14y+16}{(y-4)(y+4)}\qquad\text{use the distributive property}\\\\\dfrac{8y+32+10y-40}{(y-4)(y+4)}=\dfrac{14y+16}{(y-4)(y+4)}\qquad\text{combine like terms}\\\\\dfrac{(8y+10y)+(32-40)}{(y-4)(y+4)}=\dfrac{14y+16}{(y-4)(y+4)}\\\\\dfrac{18y-8}{(y-4)(y+4)}=\dfrac{14y+16}{(y-4)(y+4)}\iff18y-8=14y+16\\\\18y-8=14y+16\qquad\text{subtract 14y from both sides}[/tex]
[tex]4y-8=16\qquad\text{add 8 to both sides}\\\\4y=24\qquad\text{divide both sides by 4}\\\\y=8\in D[/tex]
Answer:
6
Step-by-step explanation:
9+(6-6)x4-(-7-(-2)) solved in order of operations
Answers
Which equation represents a line that passes through (–9, –3) and has a slope of –6?
Answers
If Sam has 6 different hats and 3 different scarves, how many different combinations could he wear
Answers
He can wear a different hat with one scarf so if that is multiplied by 6*3 you will get 18 different combinations that Sam can wear
If Sam has 6 different hats and 3 different scarves, the number of combinations he could wear is: 18 ways.
Given the following data:
Number of hats = 6 hats.Number of scarves = 3 scarves.How to determine combinations.In this exercise, the number of ways 6 different hats and 3 different scarves can be worn without any form of repetition should be calculated by using a combination.
Mathematically, combination is given by this formula:
[tex]_nC_r = \frac{n!}{r!(n-r)!}[/tex]
Where:
n is the number of items.r is the number of times of choosing items.For Sam's combination:
[tex]_hC_s = 6 \times 3[/tex]
Sam = 18 ways.
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The function g(x) = –x2 + 16x – 44 written in vertex form is g(x) = –(x – 8)2 + 20. Which is one of the transformations applied to the graph of f(x) = x2 to change it into the graph of g(x) = –x2 + 16x – 44?
Answers
Answer:
the graph of f(x) will be reflected over x axis, moved 8 units to the right and shifted 20 units up to get g(x)
Step-by-step explanation:
The function [tex]g(x) = -x^2 + 16x - 44[/tex] written in vertex form is [tex]g(x) = -(x - 8)^2 + 20[/tex]
The parent function is f(x)=x^2
Now we compare parent function f(x) and g(x)
In g(x), negative sign at first
f(x) ----> -f(x) , the graph is reflected across x axis
f(x)-----> f(x-h), the graph will be transformed h units to right
f(x)----> f(x) +k , the graph will be transformed k units up
[tex] g(x) = -(x - 8)^2 + 20[/tex], the graph of f(x) will be reflected over x axis, moved 8 units to the right and shifted 20 units up to get g(x)
Jasmine earns $36 for 4 hours of baby-sitting. She charges a constant hourly rate. Which table correctly shows the amount Jasmine earns baby-sitting for different numbers of hours?
Answers
Answer:
A
Step-by-step explanation:
Janelle has 4 hours to spend training for an upcoming race. She completes her training by running full speed the distance of the race and walking back the same distance to cool down. If she runs at a speed of 7mph and walks back at a speed of 3mph how long should she plan to spend walking back?
Answers
Final answer:
Janelle should plan to spend 3 hours walking back.
Explanation:
To find out how long Janelle should plan to spend walking back, we need to calculate the total time it takes her to run and walk. Since she runs at a speed of 7mph, she completes the distance of the race in 1 hour (4 miles / 7mph = 0.57 hours = 1 hour). Therefore, she spends 1 hour running and 3 hours left for walking. To find out the distance she walks back, we use the formula distance = speed x time. Since she walks at a speed of 3mph, the distance she walks back is 3mph x 3 hours = 9 miles.
Ben earns $1500 each summer and puts the money in a savings account with a 6% simple interest rate. If he deposits the same amount each year, how much money will he have at the end of his third summer
$4770
$3250
$3175
$2850
Answers
The amount that Ben gets by the first year:
1,500 + (1,500 x 6%) = 1590
The amount that Ben gets by the second year:
(1590+1500) + (3090 x 6%) = 3270.4
The amount that Ben gets by the third summer
(3270.4 + 1500 = $ 4770
The interest rate is not calculated because the Bens till hasn't pass the rest of the year
find the measure of <ghk <hki and <hkj show your work or wite and explanation
Answers
Over the last three evenings, Latoya received a total of 79 phone calls at the call center. The first evening, she received 6 fewer calls than the third evening. The second evening, she received 3 times as many calls as the third evening. How many phone calls did she receive each evening?
Answers
Third evening: x calls
First eve: x-6 calls
Second evening: 3x calls
Find x. Add up these three numbers x, x-6 and 3x and equate your sum to 79:
x+x-6+3x = 79. Then 5x=79+6, or 5x = 85. Thus, x = 17.
17 calls on the 3rd night,
17-6 calls on the 1st night, and
3(17) = 51 calls on the 2nd night.
Check! Add together 17, 11 and 51. Do these add up to 79? Yes.
In the circle graph above, you can see that 47% of the company's monthly income is used to pay the owner's personal salary. If the amount of the owners's personal salary was $2,176.10 this month, what was the company's total monthly income this month?
Answers
In this question, 47% of the company income is used to pay owner's personal salary, which was $2,176.10
Then, to find the company total income the calculation would look like this:
owner's personal salary= 47% * total company income
$2,176.10= 0.47 * total company income
total company income= $2,176.10/ 0.47 = $4630
Final answer:
To find the total monthly income, set up a proportion using the percentage of the owner's salary with the given amount. Solve for the total income to find the answer.
Explanation:
In the circle graph above, the owner's personal salary represents 47% of the company's monthly income. This means that $2,176.10 is 47% of the total monthly income. To find the total income, you can set up a proportion: $2,176.10 is to 47% as X is to 100%. Solving this equation gives you the company's total monthly income as $4,635.
Hannah travels 6 times as many minutes than Raoul does. Together, they travel 63 minutes. How many minutes does Hannah travel? Draw a model and wrote an equation to solve.
Answers
Then 6r + r = 63 min, so:
7r = 63 min, and r=63 min / 7 = 9 min.
Raoul travels for 9 minutes and Hannah travels for 6(9 minutes) = 54 minutes.
what is the greatest common factor of 15 and 27
Answers
Final answer:
The greatest common factor of 15 and 27 is 3, which is the largest number that divides both numbers without a remainder.
Explanation:
The greatest common factor (GCF) of two numbers is the largest number that divides both of them without leaving a remainder. To find the GCF of 15 and 27, list the factors of each number:
Factors of 15: 1, 3, 5, 15
Factors of 27: 1, 3, 9, 27
The common factors of 15 and 27 are 1 and 3. The largest of these is 3, therefore the greatest common factor of 15 and 27 is 3.
What is the unit rate of 15 degrees in 2 hours.
Answers
It says here that in 2 hours, there are 15 degrees.
So we need to find the unit rate of this given situation per hours.
There are 2 hours
so you'll divide 2 by 15 to get the unit rate of the given situation
15 divided by two is 7.5
So the unit rate would be 7.5 degrees per hour.
Estimated the difference
645,908 + 335,297
_ - _ = _
Answers
Have a great day!
Parallelogram MNPQ was dilated to create parallelogram M'N'P'Q'.
Which statements are true about the parallelograms? Check all that apply.
The length of side MN is 2 units.
The length of side M'N' is 5 units.
The image is smaller than the pre-image.
Sides MQ and M'Q' both have the same slope, 1.
The scale factor is 2/5
Answers
Answer:
Options 1,2 and 4 are correct.
Step-by-step explanation:
We have been given a parallelogram MNPQ was dilated to create parallelogram M'N'P'Q' and we asked to find out which of the given options are correct.
Let us see all the options one by one.
On using distance formula we can see that side MN is 2 units.
[tex]MN=\sqrt{(x_2-x_1)^{2} +(y_2-y_1)^{2} }[/tex]
[tex]MN=\sqrt{(4-2)^{2} +(-2-(-2))^{2} }[/tex]
[tex]MN=\sqrt{(2)^{2} } =2[/tex]
Therefore,option 1 is correct.
We can find the side M'N' by distance formula as we solved for side MN. After solving for M'N' we will get 5 units. Therefore, option 2 is also correct.
Now let us see third option. We can see that image M'N'P'Q' is bigger than pre-image MNPQ. Therefore, option 3 is false.
Now look at our option 4.
Since we know slope is rise (difference of y coordinates) over run (difference of x coordinates) . Upon looking at our image and pre-image we can see that as we increase our x coordinate by one unit our y coordinate also increase by one.
Therefore, option 4 is correct indeed.
Upon looking at our fifth option we can see that our image is bigger than our pre-image. If our image was dilated by factor of 2/5 it would have been smaller than our pre-image. We can see the scale factor is 5/2 instead of 2/5.
Therefore, our fifth option is false.
Considering the slopes and scale factor of the diagram given, the statements that are true about the parallelogram are: A, B, and D.
How to find SlopeSlope = vertical distance / horizontal distance = change in y / change in x.
How to find Scale FactorScale factor = length of image/corresponding length of pre-image.
Find the length of MN:
MN = |4 - 2| = 2 units (Option A is true).
Find M'N':
M'N' = |10 - 5| = 5 units (Option B is true).
MNPQ is the pre-image, while M'N'P'Q' is the image, therefore, the image is bigger than the pre-image. (Option C is NOT true).
Find Slope of MQ:
Slope = 1/1 = 1
Find Slope of M'Q':
Slope = 2/2 = 1 (Option D is true).
Find the scale factor:
Scale factor = dimension of image/dimension of pre-image = M'N'/MN
Scale factor = 5/2 (Option E is NOT true).
Therefore, considering the slopes and scale factor of the diagram given, the statements that are true about the parallelogram are: A, B, and D.
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Which linear system has a solution of
[tex]x = 2 \: and \: y = - 3[/tex]
Answers
now, about those two lads above, check the picture below.
notice, that, the horizontal line, by definition will never touch the x-axis, whilst the other one does, at x = 2.
The expected (mean) life of a particular type of light bulb is 1,000 hours with a standard deviation of 50 hours. the life of this bulb is normally distributed. what is the probability that a randomly selected bulb would last longer than 1150 hours?