Answer:
D.
Step-by-step explanation:
You could find the 8 terms and then add them up.
Let's do that.
Luckily we have the common ratio which is -5. Common ratio means it is telling us what we are multiplying over and over to get the next term.
The first term is -11.
The second term is -5(-11)=55.
The third term is -5(55)=-275.
The fourth term is -5(-275)=1375.
The fifth term is -5(1375)=-6875.
The sixth term is -5(-6875)=34375.
The seventh terms is -5(34375)=-171875.
The eighth term is -5(-171875)=859375.
We get add these now. (That is what sum means.)
-11+55+-275+1375+-6875+34375+-171875+859375
=716144 which is choice D.
Now there is also a formula.
If you have a geometric series, where each term of the series is in the form [tex]a_1 \cdot r^{n-1}[/tex], then you can use the following formula to compute it's sum (if it is finite):
[tex]a_1\cdot \frac{1-r^{n}}{1-r}}[/tex]
where [tex]a_1[/tex] is the first term and [tex]r[/tex] is the common ratio. n is the number of terms you are adding.
We have all of those. Let's plug them in:
[tex]a_1=-11[/tex], [tex]r=-5[/tex], and [tex]n=8[/tex]
[tex]-11 \cdot \frac{1-(-5)^{8}}{1-(-5)}[/tex]
[tex]-11\cdot \frac{1-(-5)^{8}}{6}[/tex]
[tex]-11 \cdot \frac{1-390625)}{6}[/tex]
[tex]-11 \cdot \frac{-390624}{6}[/tex]
[tex]-11 \cdot -65104[/tex]
[tex]716144[/tex]
Either way you go, you should get the same answer.
Final answer:
The sum of the 8-term geometric series with the given first term and common ratio is calculated using the geometric series sum formula, resulting in a sum of 716,144, Which is option D.
Explanation:
The sum of a geometric series is determined by the formula Sₙ = a(1 - rⁿ)/(1 - r), where Sₙ is the sum of the first N terms, a is the first term, r is the common ratio, and N is the number of terms. Since we have an 8-term geometric series with a first term of -11 and a common ratio of -5, we can calculate the last term (-11 x (-5)⁷) to ensure it is indeed 859,375, confirming the ratio and the number of terms.
The sum can then be calculated as follows: S₈ = -11 x (1 - (-5)⁸) / (1 - (-5)) = -11 x (1 - 390625) / (1 + 5) = -11 x (-390624) / 6 = -11 x -65104 = 716,144, which corresponds to option D.
Use division of numbers in scientific notation to answer the question.
(8.64 × 104)
(2.4 × 102)
What is the quotient in scientific notation?
3.6 × 102
6.24 × 102
1.104 × 107
2.0736 × 109
Answer:
[tex]3.6*10^{2}[/tex]
Step-by-step explanation:
we have
[tex]\frac{8.64*10^{4}}{2.4*10^{2}}=\frac{8.64}{2.4}*10^{4-2}\\ \\=3.6*10^{2}[/tex]
Answer:
A) 3.6 × 10^2
Step-by-step explanation:
Got it right in the instruction on Edge 2021 ;D
The times of the runners in a marathon are normally distributed, with a mean of 3 hours and 50 minutes and a standard deviation of 30 minutes. What is the probability that a randomly selected runner has a time less than or equal to 3 hours and 20 minutes? Use the portion of the standard normal table below to help answer the question.
16%
32%
34%
84%
Answer:
The answer is 16%
Step-by-step explanation:
Given a mean of 3 hours and 50 minutes and a standard deviation of 30 minutes
so a time less than or equal to 3 hours and 20 minutes is a time 1 standard deviation OUTSIDE from the mean
Use the probability table:
The probability that a randomly selected runner has a time less than or equal to 3 hours and 20 minutes
= Probability of z being outside 1 SD from mean
= 1 - Probability of z within 1 SD from mean
= 1 - 0.84
= 0.16 or 16%....
What is the equation of the line with m = 2.5 and b = 7? A. y = −2.5x − 7 B. y = 2.5x −7 C. y = −2.5x + 7 D. y = 2.5x + 7
Answer:
y=2.5x+7
Step-by-step explanation:
You are basically being asked to use slope-intercept form for linear equations. It says y=mx+b where m is the slope and b is the y-intercept.
Plug in 2.5 for m and 7 for b giving you y=2.5x+7.
The equation is: y = mx + b
y = 2.5x + 7
so it's option D.
Mustafa, Heloise, and Gia have written more than a combined total of 222222 articles for the school newspaper. Heloise has written \dfrac{1}{4}
4
1
start fraction, 1, divided by, 4, end fraction as many articles as Mustafa has. Gia has written \dfrac{3}{2}
2
3
start fraction, 3, divided by, 2, end fraction as many articles as Mustafa has.
Write an inequality to determine the number of articles, mmm, Mustafa could have written for the school newspaper.
What is the solution set of the inequality?
Answer:
m + m/4 + 3m/2 > 22m > 8 . . . . m restricted to multiples of 4, perhapsStep-by-step explanation:
Let m represent the number of articles Mustafa has written. Then the total number of articles written must satisfy the inequality ...
m +m/4 +3m/2 > 22
This has solution ...
(11/4)m > 22
m > (4/11)22
m > 8 . . . . . . . . the solution to the inequality
If all the numbers are integers, and the ratios are exact, then we must have m be a multiple of 4 (that is, 4 times the number of articles Heloise wrote).
The solution set will be ...
m ∈ {12, 16, 20, 24, ...} (multiples of 4 greater than 8)
Answer:
inequality - m+ 1/4m + 3/2m > 22
solution set - m>8
Step-by-step explanation:
i promise
In the spinner below the large wedges are twice the size of the smaller ones. What is true about the probablilty of landing on 6 and the probability of landing on 5
Answer:
we need an image of the spinner to answer the question. are we supposed to just know what it looks like?
Step-by-step explanation:
flvs she cheating
Question about Radicals.
Answer:
Conjugate
Step-by-step explanation:
Those are conjugates. In factoring polynomials, if you have one with a + sign separating the a and the square root of b, you will ALWAYS have one with a - sign. They will always come in pairs. Same with imaginary numbers.
Find the GCF of the following numbers:
n and (n-1), where n is a natural number, greater than 1.
13 POINTS! NEED ANSWER QUICK! THANKS!!
Answer:
1
Step-by-step explanation:
The numbers are mutually prime, so the GCF is 1.
Answer:
1
Step-by-step explanation:
n-1 and n are consecutive integers.
Examples of consecutive pairs:
(7,8)
(10,11)
(100,101)
and so on...
The remainder will always be 1 when doing n divided by n-1.
n=(n-1)(1)+1.
All this is here to try to convince you that n and n-1 will only have common factor of 1.
Suppose that the length of a certain rectangle is four centimeters more than three times its width. If the area of the rectangle is 95 square centimeters, find its length and width.
Answer: The length and width of the rectangle are 19 cm and 5 cm respectively.
Step-by-step explanation: Given hat the length of a rectangle is four centimeters more than three times its width and the area of the rectangle is 95 square centimeters.
We are to find the length and width of the rectangle.
Let W and L denote the width and the length respectively of the given rectangle.
Then, according to the given information, we have
[tex]L=3W+4~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
Since the area of a rectangle is the product of its length and width, so we must have
[tex]A=L\times W\\\\\Rightarrow 95=(3W+4)W\\\\\Rightarrow 3W^2+4W-95=0\\\\\Rightarrow 3W^2+19W-15W-95=0\\\\\Rightarrow W(3W+19)-5(3W+19)=0\\\\\Rightarrow (W-5)(3W+19)=0\\\\\Rightarrow W-5=0,~~~~~3W+19=0\\\\\Rightarrow W=5,~-\dfrac{19}{3}.[/tex]
Since the width of the rectangle cannot be negative, so we get
[tex]W=5~\textup{cm}.[/tex]
From equation (i), we get
[tex]L=3\times5+4=15+4=19~\textup{cm}.[/tex]
Thus, the length and width of the rectangle are 19 cm and 5 cm respectively.
The length of the rectangle is 19 and the width is 5 and it can be determined by using the formula of area of the rectangle.
Given that,The length of a certain rectangle is four centimeters more than three times its width.
If the area of the rectangle is 95 square centimeters,
We have to determine,The length and width of the rectangle.
According to the question,Let the length of the rectangle be L,
And the width of the rectangle is W.
The length of a certain rectangle is four centimeters more than three times its width.
The perimeter of a square is the sum of the length of all its four sides.The perimeter formulas of different two-dimensional shapes:
Then,
[tex]\rm L = 3W+4[/tex]
And If the area of the rectangle is 95 square centimeters,
The area of any polygon is the amount of space it occupies or encloses.It is the number of square units inside the polygon.
The area is a two-dimensional property, which means it contains both length and width
[tex]\rm Area \ of \ the \ rectangle = length \times width\\\\L\times W = 95[/tex]
Substitute the value of L from equation 1,
[tex]\rm L\times W = 95\\\\(3W+4) \times W = 95\\\\3W^2+4W=95\\\\3W^2+4W-95=0\\\\3W^2+19W-15W-95=0\\\\W(3W+19) -5(3W+19) =0\\\\(3W+19) (W-5) =0\\\\W-5=0, \ W=5\\\\3W+19=0, \ W = \dfrac{-19}{3}[/tex]
The width of the rectangle can not be negative than W = 5.
Therefore,
The length of the rectangle is,
[tex]\rm L = 3W+4\\\\L = 3(5)+4\\\\L=15+4\\\\L=19[/tex]
Hence, The length of the rectangle is 19 and the width is 5.
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Please help *image attached*
Answer:x=25
Step-by-step explanation:
One line is 180 , AB equals 180 ,angle AD is 110,180-110=70
So corner O on line DC is 70 and angle CE is 60. 60+70=130
180-130=50, 2x=50,50/2=25
The variable z is directly proportional to x, and inversely proportional to y. When x is 4 and y is 10, z has the value 0.8. What is the value of z when x= 13, and y= 18
Answer:
13/9
Step-by-step explanation:
Directly proportional means it will be multiply to our constant k.
Inversely proportional means it will divide our k.
So we are given z is directly proportional to x and inversely proportional to y.
This means:
[tex]z=k \cdot \frac{x}{y}[/tex].
We are given (x=4,y=10,z=0.8). We can use this to find k. The k we will find using the point will work for any point (x,y,z) since k is a constant. A constant means it is to remain the same no matter what.
[tex]0.8=k \cdot \frac{4}{10}[/tex]
[tex]0.8=k(.4)[/tex]
Divide both sides by .4:
[tex]\frac{0.8}{0.4}=k[/tex]
[tex]k=2[/tex]
The equation for any point (x,y,z) is therefore:
[tex]z=2 \cdot \frac{x}{y}[/tex].
We want to find z given x=13 and y=18.
[tex]z=2 \cdot \frac{13}{18}[/tex]
[tex]z=\frac{2 \cdot 13}{18}[/tex]
[tex]z=\frac{13}{9}[/tex]
Use the following net to find the surface area of the solid figure it represents.
For this case we have that by definition, the surface area of a cylinder is given by:[tex]SA = LA + 2B[/tex]
Where:
LA: It is the lateral area of the cylinder
B: It is the area of the base
We have as data that:
[tex]LA = 75.36 \ cm ^ 2\\B = 28.26 \ cm ^ 2[/tex]
Substituting:
[tex]SA = 75.36 + 2 (28.26)\\SA = 75.36 + 56.52\\SA = 131.88[/tex]
Finally, the surface area is:
[tex]131.88 \ cm ^ 2[/tex]
Answer:
Option D
Answer:
The solid formed is a cylinder
The total surface area is [tex]131.88cm^2[/tex]
Step-by-step explanation:
The given net is made up of a rectangle and two circles.
The total surface area is the area of the rectangle plus the area of the two circles.
This implies that:
[tex]S.A=75.36+2(28.26)[/tex]
[tex]\implies S.A=75.36+56.52[/tex]
[tex]\implies S.A=131.88cm^2[/tex]
The rectangular surface can be folded into the curved surface of a cylinder with the two circles becoming the lid.
I really need this answer
Answer:
D
Step-by-step explanation:
If the lines are parallel, the slope of both of them are going to be the same. So if one line is 3, the other one will be too.
The answer is:
If the red line has a slope of 3, the slope of the red line will also be 3.
So, the correct option is, D. 3
Why?We need to remember that if two or more lines are parallel, they will share the same slope, no matter where are located their x-intercepts and y-intercepts, the only condition needed for them to be parallel, is to have the same slope.
So, if two lines are parallel, and one of them (the red line) has a slope of 3, the slope of the other line (the green line) will also be 3.
Have a nice day!
Three fourths of a gasoline storage tank is emptied by filling each of five trucks with the same amount of fuel what part of the total capacity of the storage tank did each vehicle receive
Answer:
Each vehicle received [tex]\frac{3}{20}[/tex] of the total capacity of the storage tank
Step-by-step explanation:
we know that
To find out what part of the total capacity of the storage tank that each vehicle received, divide three fourths by five
so
[tex]\frac{(3/4)}{5}=\frac{3}{20}[/tex]
therefore
Each vehicle received [tex]\frac{3}{20}[/tex] of the total capacity of the storage tank
Geometry: write a two column proof
Step-by-step explanation:
[tex]\angle1\ and\ \angle 2\ \text{are complementary}\to m\angle1+m\angle2=90^o\\\\m\angle ACX=m\angle1+m\angle2=90^o\to XA^{\to}\perp XC^{\to}[/tex]
Select the correct answer.
What is the sum of
The sum of the mixed fraction numbers - 6 ⁴/₅ and 6 ⁴/₅ will be 0. Then the correct option is C.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
The expression is given below.
- 6 ⁴/₅ and 6 ⁴/₅
Convert the mixed fraction number into a fraction number. Then we have
- 6 ⁴/₅ = -34/5
6 ⁴/₅ = 34/5
Then the sum of the expressions will be given as,
⇒ - 34/5 + 34/5
⇒ 0
The sum of the mixed fraction numbers - 6 ⁴/₅ and 6 ⁴/₅ will be 0. Then the correct option is C.
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Elijah drove 45 miles to his job in an hour and ten minutes in the morning. On the way home: however, traffic was much heavier and the same trip took an hour and half. What was his average speed in miles per hour for the round trip?
Answer:
33.75
Step-by-step explanation:
You first need to determine the total distance of the round trip. This is twice the 45 mile trip in the morning, which is 90 miles. In order to determine the total amount of time spent on the round trip, convert the time travel to minutes.
1 hr + 10 mins = 70 mins
1hr + 30 = 90 mins
So his total travel time would equal to 90+70=160 minutes
his average speed is:
90mi/160min * 60min/1hr = 90*60/160
= 33.75
Elijah's average speed for the round trip is approximately 31.76 miles per hour.
To calculate the average speed for the round trip, we need to determine the total distance traveled and the total time taken.
In the morning, Elijah drove 45 miles in 1 hour and 10 minutes. To convert the minutes to hours, we divide 10 minutes by 60, which gives us 10/60 = 1/6 hours. Therefore, his morning travel time is 1 hour + 1/6 hour = 7/6 hours.
On the way home, the same trip took him 1 hour and 30 minutes. Converting the minutes to hours, we divide 30 minutes by 60, which gives us 30/60 = 1/2 hours. Therefore, his return travel time is 1 hour + 1/2 hour = 3/2 hours.
To calculate the total distance traveled, we sum the distance from the morning trip and the return trip: 45 miles + 45 miles = 90 miles.
The total time taken for the round trip is the sum of the morning travel time and the return travel time: 7/6 hours + 3/2 hours = 17/6 hours.
To calculate the average speed, we divide the total distance by the total time: 90 miles / (17/6 hours).
Dividing 90 miles by 17/6 hours is the same as multiplying 90 miles by 6/17, which gives us (90 * 6) / 17 = 540/17.
Therefore, Elijah's average speed for the round trip is approximately 31.76 miles per hour.
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The problem is in the pictures, please show step by step how to do it. Thanks! :)
Answer:
-4,-5/2
Step-by-step explanation:
2x^2+3x-20 =0
2x^2+8x-5x-20 =0
2x(x+4)-5(x+4) =0
(x+4)(2x-5) =0
Either,
x+4=0
x=-4
Or,
2x-5=0
2x=5
x=5/2
[tex]2x^2+3x-20=0\\2x^2+8x-5x-20=0\\2x(x+4)-5(x+4)=0\\(2x-5)(x+4)=0\\x=\dfrac{5}{2} \vee x=-4[/tex]
NEED HELP WITH A MATH QUESTION
Answer:
33π square units
Step-by-step explanation:
The area of a sector is given by this formula. The larger sector angle is 2π-π/6 = 11π/6 radians.
A = (1/2)r²θ = (1/2)6²(11π/6) = 33π . . . . square units
Answer:
Area of larger sector = 33π units²
Step-by-step explanation:
Points to remember
Area of circle = πr²
Where 'r' is the radius of circle
To find the area of circle
Here r = 6 units
Area = πr²
= π * 6²
= 36π units²
To find area of large sector
The central angle of larger sector = 360 - 30 = 330
Area of larger circle = (330/360) * area of circle
= (330/360) * 36π
= 33π units²
Half of the students in a freshman class are 14 years old one third are 15 and the rest are 13 . Is the mean age greater than or less than the median age
Answer:
the mean age is greater
Step-by-step explanation:
The mean age is ...
(1/2)14 + (1/3)15 + (1/6)13 = 14 1/6
The median age is 14. (half the students are 14 or younger)
The mean age is greater.
_____
1 -1/2 -1/3 = 6/6 -3/6 -2/6 = 1/6 . . . . . 1/6 of the students are 13.
Answer:
Step-by-step explanation:
Given that half of the students in a freshman class are 14 years old one third are 15 and the rest are 13
If no of students are n, then we have
n/2 have ages as 14, n/3 as 15 and remaining n/6 as 13.
Average would be total/n
= [tex]\frac{\frac{14n}{2}+\frac{15n}{3} +\frac{13n}{6} }{n} \\=7+5+\frac{13}{6} =14.67[/tex]
Median would be middle entry when arranged in ascending order hence = 14
Mean > median
This question might be confusing to me because it talks about Unknown angle problems with Algebra and I may need help on this, please.
Answer:
40 = x
Step-by-step explanation:
They reflect each other like a mirror, so set 120 equal to 3x, then simply divide by 3 to get your answer.
Identify the three similar triangles in the figure we should to name the verticals in the correct order
Answer: ΔABC ~ ΔBDC ~ ΔADB
Step-by-step explanation:
Match the degrees of each angle:
In ΔABC: ∠A = 60° , ∠B = 90° , ∠C = 30°
In ΔBDC: ∠B = 60° , ∠D = 90° , ∠C = 30°
In ΔADB: ∠A = 60° , ∠D = 90° , ∠B = 30°
Answer:
See below.
Step-by-step explanation:
Triangle ABC is similar to triangle ADB is similar to triangle BDC.
Stone Pine Corporation, a calendar year taxpayer, has ending inventory of $150,000 on December 31, 20X2. During the year 20X2, the corporation purchased additional inventory of $375,000. If cost of goods sold for 20X2 is $470,000, what was the beginning inventory at January 1, 20X2?
Answer:
beginning inventory is $245000
Step-by-step explanation:
Given data
ending inventory = $150,000
purchased additional inventory = $375,000
goods sold = $470,000
to find out
beginning inventory
solution
according to question beginning inventory is calculated by this formula i.e.
beginning inventory = ( cost of goods sold + ending inventory ) - amount of inventory purchase .....................1
now put all value cost of goods sold, ending inventory and amount of inventory purchase in equation 1 and we get beginning inventory
beginning inventory = ( cost of goods sold + ending inventory ) - amount of inventory purchase
beginning inventory = ( 470000 + 150000 ) - 375000
beginning inventory = 245000
so beginning inventory is $245000
Please help! Brainliest if correct!
Answer:
x:(x +15)
Step-by-step explanation:
The corresponding sides that are in proportion are apparently ...
PS:PQ = PT:PR
PT = x
PR = x+15
so the proportion of interest is ...
28:40 = x:(x+15)
Please help with #12
Answer:
a. 1 1/8 b. 8/9
Step-by-step explanation:
You can set this up as a proportion to solve. For part a. we know that 2/3 of the road is 3/4 mile long. 2/3 + 1/3 = the whole road, so we need how many miles of the road is 1/3 its length. Set up the proportion like this:
[tex]\frac{\frac{2}{3} }{\frac{3}{4} } =\frac{\frac{1}{3} }{x}[/tex]
Cross multiplying gives you:
[tex]\frac{2}{3}x=\frac{1}{3}*\frac{3}{4}[/tex]
The 3's on the right cancel out nicely, leaving you with
[tex]\frac{2}{3}x=\frac{1}{4}[/tex]
To solve for x, multiply both sides by 3/2:
[tex]\frac{3}{2}*\frac{2}{3}x=\frac{1}{4}*\frac{3}{2}[/tex] gives you
[tex]x=\frac{3}{8}[/tex]
That means that the road is still missing 3/8 of a mile til it's finished. The length of the road is found by adding the 3/4 to the 3/8:
[tex]\frac{3}{4}+\frac{3}{8}=\frac{6}{8}+\frac{3}{8}=\frac{9}{8}[/tex]
So the road is a total of 1 1/8 miles long.
For b. we need to find out how much of 1 1/8 is 1 mile:
1 mile = x * 9/8 and
x = 8/9. When 1 mile of the road is completed, that is 8/9 of the total length of the road completed.
A widget company produces 25 widgets a day,5 of which are defective.Find the probability of selecting 5 widgets from the 25 produced where none are defective
Answer:
1/5
Step-by-step explanation:
The probability of selecting 5 widgets from the 25 produced where none are defective is 0.2914.
To calculate the probability of selecting 5 non-defective widgets from the 25 produced.
The number of ways to choose 5 non-defective widgets:
[tex]\[ \binom{20}{5} = \frac{20!}{5!(20-5)!} \][/tex]
[tex]\[ = \frac{20 \times 19 \times 18 \times 17 \times 16}{5 \times 4 \times 3 \times 2 \times 1} \][/tex]
[tex]\[ = \frac{20 \times 19 \times 18 \times 17 \times 16}{5 \times 4 \times 3 \times 2 \times 1} \][/tex]
[tex]\[ = \frac{1860480}{120} \][/tex]
= 15504
The total number of ways to choose 5 widgets from the 25 produced:
[tex]\[ \binom{25}{5} = \frac{25!}{5!(25-5)!} \][/tex]
[tex]\[ = \frac{25 \times 24 \times 23 \times 22 \times 21}{5 \times 4 \times 3 \times 2 \times 1} \][/tex]
[tex]\[ = \frac{7893600}{120} \][/tex]
= 53130
The probability:
Probability = (Number of ways to choose 5 non-defective widgets)/(Total number of ways to choose 5 widgets)
[tex]\[ = \frac{15504}{53130} \][/tex]
[tex]\[ = 0.2914 \][/tex]
Complete question:
A widget company produces 25 widgets a day, 5 of which are defective. Find the probability of selecting 5 widgets from the 25 produced where none are defective.
You bought a guitar 6 years ago for $400. If its value decreases by
about 13% per year, how much is your guitar worth now?
$351.23
$226.55
$322
$173.45
Answer:
$173.45
Step-by-step explanation:
the beginning value is $400. if it loses 13%, that means it keeps 87% of its value. so you multiply by 0.87 6 times for each year
A bag contains 12 red marbles, 5 yellow marbles, and 15 green marbles. How many additional red marbles must be added to the 32 marbles already in the bag so that the probability of randomly drawing a red marble is ?
Answer:
18 red marbles.
Step-by-step explanation:
The complete question asks the probability of randomly drawing a red marble is 3/5?
Let x be the number of red marbles that must be added.
To find x we will do the following:
[tex]\frac{x+12}{x+32} =\frac{3}{5}[/tex]
=>[tex]5(x+12)=3(x+32)[/tex]
=> [tex]5x+60=3x+96[/tex]
=> [tex]2x=36[/tex]
This gives x = 18
Hence, 18 red marbles will be added to the bag.
Need help big time...please explain how you got the answer.
Answer:
Step-by-step explanation:
This is a right triangle with the 90 degree angle identified at D and the 60 degree angle identified at B. Because of the triangle angle sum theorem, the angles of a triangle all add up to equal 180 degrees, so angle C has to be a 30 degree angle.
There is a Pythagorean triple that goes along with a 30-60-90 triangle:
( x , x√3 , 2x )
where each value there is the side length across from the
30 , 60 , 90 degree angles.
We have the side across from the 90 degree angle, namely the hypotenuse. The value for the hypotenuse according to the Pythagorean triple is 2x. Therefore,
2x = 2√13
and we need to solve for x. Divide both sides by 2 to get that
x = √13
Now we can solve the triangle.
The side across from the 30 degree angle is x, so since we solved for x already, we know that side DB measures √13.
The side across from the 60 degree angle is x√3, so that is (√13)(√3) which is √39.
And we're done!
To find the standard equation for a circle centered at the origin, we use the distance formula, since the radius measures? A. The distance from any point in the circle to the origin.B. The circumference c. The distance from any point inside the circle to the origin.D. The distance from the x-coordinate to the origin.
Answer:
A. The distance from any point in the circle to the origin
Step-by-step explanation:
The distance formula tells you that the distance (d) is related to the coordinates of two points (x1, y1) and (x2, y2) by ...
d² = (x2 -x1)² +(y2 -y1)²
For points (x, y) on the circle and (0, 0) at the origin, this becomes ...
d² = (x -0)² +(y -0)²
If we want the distance to the point (x, y) to be equal to the radius of the circle, this becomes ...
x² +y² = r² . . . . . . the standard equation of a circle centered at the origin
Answer: The distance from any point in the circle to the origin
Step-by-step explanation:
answer key
What is the magnitude of the position vector whose terminal point is (-2, 4)?
Answer:
2√5
Step-by-step explanation:
The Pythagorean theorem tells you how to find the distance from the origin.
d = √((-2)² +4²) = √20 = 2√5
The vector's magnitude is 2√5 ≈ 4.47214.
Answer:
The magnitude of the position is [tex]|x|=\sqrt{20}[/tex]
Step-by-step explanation:
Given : Vector whose terminal point is (-2, 4).
To find : What is the magnitude of the position vector?
Solution :
We have given, terminal point (-2,4)
The magnitude of the point x(a,b) is given by,
[tex]|x|=\sqrt{a^2+b^2}[/tex]
Let point x=(-2,4)
[tex]|x|=\sqrt{(-2)^2+(4)^2}[/tex]
[tex]|x|=\sqrt{4+16}[/tex]
[tex]|x|=\sqrt{20}[/tex]
Therefore, The magnitude of the position is [tex]|x|=\sqrt{20}[/tex]