Answers
To find this, you can make a right triangle by connecting points R and S at a common point to form a right angle. The segments made would be 5 units and 12 units long. Using the Pythagorean Theorem, the segment RS must be 13 units.
Answer: 13 units
Step-by-step explanation:
The length of line segment AB with points [tex]A(x_1,y_1)\ and\ B(x_2,y_2)[/tex] is given by distance formula as :
[tex]\text{AB}=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Now, the length of line segment RS with points [tex]R(-4,-3)\ and\ S(1,9)[/tex] is given by distance formula as :
[tex]\text{RS}=\sqrt{(1-(-4))^2+(9-(-3))^2}\\\Rightarrow\ RS=\sqrt{(5)^2+(12)^2}\\\Rightarrow\ RS=\sqrt{25+144}=\sqrt{169}\\\Rightarrow\ RS=13[/tex]
Hence, the length of segment RS= 13 units
Related Questions
Steve earned 60 dollars and spent 2/3 of it. How much did he spend?
Answers
60* 2/3 = 60/1 x 2/3 =120/3
120/3 = 40
he spent $40
which of the following are exterior angles ?
Answers
Answer:
A, C, and E
Step-by-step explanation:
The exterior angles are ∠2, ∠3, ∠4 and ∠6.
The correct options are E, F, A, and C.
Based on the information provided, we can identify the exterior angles by their positions outside the triangle. From the given options, the exterior angles are: ∠2, ∠3, ∠4 and ∠6.
Exterior angles are formed by extending one side of the triangle outward, and they lie outside the triangle itself. In this case, angles ∠1 and ∠5 are interior angles because they are inside the triangle, while angles ∠2, ∠3, ∠4 and ∠6 are exterior angles as they extend beyond the sides of the triangle.
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Given the exponential function A(x) = P(1 + r)x, what value for r will make the function a growth function?
Answers
Answer:
The function is a growth function when [tex]r>0[/tex].
Step-by-step explanation:
We are given,
The exponential function is [tex]A(x)=P(1+r)^x[/tex], where P= initial value and r= rate of change.
Now, we know,
1. The function is an exponential growth if their is positive rate of change.
2. The function is an exponential decay if their is negative rate of change.
Since, it is required to make the function a growth function.
We need the positive rate of change for the function A(x),
That is, [tex]r>0[/tex]
Hence, the function is a growth function when [tex]r>0[/tex].
order the numbers from least to greatest. 3 29\40, 3 19\20, 3 1\2
Answers
29/40= 0.725
19/20 = 0.95
1/2 = 0.50
least to greatest = 3 1/2 , 3 29/40 , 3 19/20
What is the next term in the sequence below?
-321,108,-36,12,.....
Answers
a(n)=ar^(n-1), in this case a=-324 and r=-1/3 so
a(n)=-324(-1/3)^(n-1) so the 5th term will be
a(5)=-324(-1/3)^4
a(5)=-324/81
a(5)= -4
The next term for the given series will be equal to a(5) = -4.
What is geometric progression?When there is a constant between the two successive numbers in the series then it is called a geometric series.
This is a geometric sequence with a common ratio of -1/3 and an initial term of -324. Any geometric sequence can be expressed as:
a(n) = [tex]ar^{n-1}[/tex], in this case a=-324 and r=-1/3 so
a(n) = -324(-1/3)[tex].^{n-1}[/tex] so the 5th term will be
a(5) = -324(-1/3)⁴
a(5) = -324/81
a(5) = -4
Therefore the next term for the given series will be equal to a(5) = -4.
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angelina is working with function machines. She has the two machines shown at right. She wants to put them in order so that the output of the first machine becomes the input of the second. She wants to use a beginning input of 6. In what order must she put the machines to get a final output of 5?
Answers
In = Out
Input value is 6 and output is 5 plus (the remaining value) x
6 = 5 + x
We need to determine x:
6 = 5 + x
1 = x
So there should be another output, it could be a waste stream of 1 from machine 2 to balance the system.
PRE-ALGEBRA HELP PLEASE!
Answers
PART A) the initial value of the function is 150 at 0 weeks, that means that there are still 150 songs to be downloaded at the beginning.
The rate of change is -30 songs each week, that is because the amount of songs left to be downloaded decrease by 30 each week.
PART B:
lets use 2 points of the graph p1(0, 150), p2(1, 120)
calculate the slope:
m = (y2- y1)/(x2 - x1) = (120 - 150)/(1 - 0)
m = -30
and now use line equation in form point-slope:
y - y1 = m(x - x1)
y - 150 = -30(x - 0)
y = -30x + 150
The slope is -30/1 or -30
The equation is y = -30x + 150
Ryan is looking for the sum of the cube of a number, n, and 16.
What is the sum Ryan is looking for if n = 2?
Answers
Find the height of a triangle with an area (A) of 35 square inches and base (b) of 7 inches. Use the formula for the area of a triangle, A=1/2bh
Answers
2A=bh
h=2A/b, we are given that A=35 in^2 and b=7 in
h=2(35)/7
h=10 in
Height of the triangle is 10 inches
What is Triangle ?A triangle is a polygon with three edges and three vertices.
What is Area?Area is the quantity that expresses the extent of a region on the plane or on a curved surface.
Given,
Area of the triangle = 35 square inches
Base of the triangle = 7 inches
Area of the triangle = [tex]\frac{1}{2}bh[/tex]
where,
b is the base length and h is the height
Substitute the values in the equation
[tex]35=\frac{1}{2}(7)(h)\\ 35=3.5h\\h=\frac{35}{3.5}[/tex]
Height h = 10 inches
Hence, the height of the triangle is 10 inches
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Which property is illustrated in this problem?
33 + 0 = 33
Answers
It states that the sum of any number and 0 is that number.
Find two positive fractions with a quotient of 5/6
Answers
(x/y)/(a/b)= (x/y)*(b/a). If the x is 5 and the a is 6, as well as y and b being the same therefore cancelling out, we can write it easily. For example, we can write (5/100)/(6/100) or (5/60)/(6/60)
How many times will 1/5 go into 37
Answers
1/5 will go into 37 185 times.
you need 5 1/5ths to make a whole, because in 5/5, there are 5 1/5ths. 5*37=185
Therefore, 5 goes into 37 185 times
hope this helps:))
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solve the inequality 6x<18
Answers
6x/6<18/6
x<3
Final answer: x< 3
there is two boxes to fill out
Answers
1+2=3, 3+3=6, 6+4=10, 10+5= 15
For the second pattern, you multiply by 3 each time.
1*3=3, 3*3=9, 9*3=27, 27*3= 81
Final answers: 15 for first sequence, 81 for second sequence
If sin(x)=0.3090 , what is the approximate value of csc(x)?
0.5559
1.3090
3.2362
10.4733
Answers
3.2362
ExplanationTo solve this, we are going to use the trig identity: [tex]csc(x)=\frac{1}{sin(x)}[/tex]
We know that our problem that [tex]sin(x)=0.3090[/tex], so let's replace the value in our identity:
[tex]csc(x)=\frac{1}{sin(x)}[/tex]
[tex]csc(x)=\frac{1}{0.3090}[/tex]
[tex]csc(x)=3.2362[/tex]
We can conclude that the approximate value of [tex]csc(x)[/tex] is 3.2362.
The approximate value of csc(x) is 3.2362
Trigonometric ratios:csc ∅ = 1 / sin ∅sec ∅ = 1 / cos ∅cot ∅ = 1 / tan ∅since sin x = 0.3090
Therefore,
1 / sin x = csc x
Then
csc x = 1 / 0.3090
csc x = 3.23624595469
csc x ≈ 3.2362
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What's equivalent to 3(8+7) 24+7 24+21 Please help
Answers
The distributive property dictates that a(b+c)= ab+ac
So 3(8+7)= 3(8)+3(7)
Points (−7, 5) and (7, 5) on the coordinate grid below show the positions of two players of a football team: A coordinate plane is shown. There is a point at 7, 5 labeled Player 2. There is a point at negative 7, 5 labeled Player 1.
Answers
Answer:
you just need to make your math to right a little more math
Step-by-step explanation:
The distance between the two soccer players positioned at (-7, 5) and (7, 5) in a Cartesian coordinate system is 14 units, calculated using the difference in x-coordinates.
The question is focused on understanding the Cartesian coordinate system and calculating distances between points on this grid. To determine the distance between two points on a soccer field, one can apply the distance formula derived from the Pythagorean theorem. If the positions of the two players are (-7, 5) and (7, 5), the players are aligned horizontally and share the same y-coordinate. Therefore, their distance apart is simply the difference in their x-coordinates, which can be calculated by subtracting the x-coordinate of player 1 from that of player 2 or vice versa. The result is the absolute value of the difference, |7 - (-7)| = 14 units, which is their horizontal separation on the field.
There are four muffins on each plate there are zero plates of lemon muffins how many lemon muffins are there
Answers
classify the following triangle check all that apply ?APEX
Answers
Because there is 3 acute angles, and equal angles/sides.
Three equal sides ⇒ Equilateral
The table shows the number of students in a school who like tacos and/or pizza: Like Tacos Do Not Like Tacos Total Like Pizza 57 13 70 Do Not Like Pizza 12 15 27 Total 69 28 97 What is the relative frequency, by row, of students who like both tacos and pizza? 0.18 0.46 0.81 0.83
Answers
The relative frequency of students who like both tacos and pizza is [tex] \frac{57}{70} [/tex] which as decimal is 0.81
What is X/60=700 ?
Plz help it's due tomorrow
Answers
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Which of the following sets shows all the numbers from the set {3, 4, 5, 6} that are part of the solution to the equation 5x + 4 < 29?
Answers
5x + 4 < 29 now becomes :
5(3) + 4 < 29.
Simplify.
15 + 4 < 29
Simplify again.
19 < 29
This statement is true, so 3 works.
Now try 4.
5(4) + 4 < 29
Simplify
20 + 4 < 29
Simplify again
24 < 29
This statement is true, so 4 works.
Now try 5.
5(5) + 4 < 29
Simplify
25 + 4 < 29
Simplify again
29 < 29
This is not true, so 5 doesn't work. This means 6 also doesn't work.
*** So your answers are 3 and 4 ***
During an epidemic, the number of people who have never had the disease and who are not immune (they are susceptible) decreases exponentially according to the function f(x) = 15000e-^(0.05t) , where t is time in days. Find the number of susceptible people at each time below.
At the beginning of the epidemic
After 14 days
After 21 days
After 5 weeks
Answers
Solving this problem is just pretty straight forward. All we simply have to do is to plug in the value of t (in days) in the function, solve then we get the number of susceptible people.
A. At the beginning of the epidemic
t = 0
f(x) = 15000 e-^(0.05 * 0)
f(x) = 15000
B. After 14 days
t= 14
f(x) = 15000 e-^(0.05 * 14)
f(x) = 7,448.78 = 7,449
C. After 21 days
t = 21
f(x) = 15000 e-^(0.05 * 21)
f(x) = 5,249
D. After 5 weeks
t = 5 * 7 = 35
f(x) = 15000 e-^(0.05 * 35)
f(x) = 2,606.61 = 2607
To find the number of susceptible people during an epidemic at various time intervals, we apply the given exponential function for t=0, 14, 21, and 35 days. This yields 15,000 susceptible individuals at the start, approximately 7439 after 14 days, about 5141 after 21 days, and around 2430 after 5 weeks.
The student asks about the number of susceptible people during an epidemic at various points in time, given by the function f(t) = 15000e-0.05t, where t is time in days. To find the number of susceptible people, we substitute the given times into the function:
At the beginning of the epidemic (t=0): f(0) = 15000e0 = 15000.After 14 days (t=14): f(14) = 15000e-0.05*14 = 15000e-0.7 extapprox 7439.After 21 days (t=21): f(21) = 15000e-0.05*21 = 15000e-1.05 extapprox 5141.After 5 weeks (35 days, t=35): f(35) = 15000e-0.05*35 = 15000e-1.75 extapprox 2430.This exponential function represents the number of people who remain susceptible as the epidemic progresses, assuming no one gains immunity other than through infection (no vaccination, and disease-induced immunity only).
William has 8 1/4 cups of fruit juice. If he divides the juice into 3/4 cup servings, how many servings will he have?
Answers
8 1/4 = 33/4
33/4 / 3/4 =
33/4 * 4/3 = 132/12
132/12 = 11
he will have 11 servings
Answer: 11 servings
Step-by-step explanation:
To get the number of servings, all we need to do is divide 8 1/4 by 3/4
converting 8 1/4 to improper fraction will yield 33/4
8 1/4 ÷ 3/4
=33/4 ÷ 3/4
= 33/4 ÷ 4/3
The 4 at the numerator will cancel the 4 at the denominator. we will be left with;
=33/3 =11
Therefore, there will be 11 servings.
if angle ABC measured 90, what is the measure of arc AC
Answers
hope this helps:)
please mark thanks and brainliest:)
The measure of arc arc [tex]AC[/tex] will be [tex]90^0[/tex] .
What is arc ?Arc is the part or segment of the circumference of a circle which is drawn between two points and an angle. And length of arc is known as arc length.
i.e. Arc length [tex](L)=\frac{\theta}{r}[/tex]
And "The measure of an arc is equal to the measure of the central angle that intercepts it".
We have,
[tex]\theta = 90^0[/tex]
So,
From the above mentioned statement i.e.,
"The measure of an arc is equal to the measure of the central angle that intercepts it".
We can say that,
The measure of arc [tex]AC=90^0[/tex]
Hence, we can say that the measure of arc arc [tex]AC[/tex] is [tex]90^0[/tex].
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What is the surface area of the right cone with a radius of 8 and height of 15?
A. 184 pi units^2
B. 304 pi units^2
C. 248 pi units^2
D. 496 pi units^2
Answers
The surface area of the right cone with a radius of 8 and slant height of 15 is,
SA = 184π units³
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
Radius of cone = 8
Slant height = 15
Since, The surface area of the right cone is,
SA = πr (r + l)
where,
r is the radius of the cone
l is the slant height of the cone.
Hence, We get;
SA = π × 8 (8 + 15)
SA = π × 184
SA = 184π units³
Thus, The surface area of the right cone with a radius of 8 and slant height of 15 is,
SA = 184π units³
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x varies directly as y, and x = 153 when y = 9. Find x when y = 13.
Answers
153/9 = x/13
153 x 13 = 1989
1989/9=221
x = 221
9 = 153k
k = 9/153
k = 3/51
so if y = 13 then
13 = 3/51 x
x = 13 (51/3)
x = 221
answer
x = 221 when y = 13.
When is factoring by grouping easier to use. How many terms must you have to have ?
Does anybody know??? :/ ;c
Answers
For example...
x^2 + 10x + 2x + 20
(x^2 + 10x) + (2x + 20)
x(x+10) + 2(x+10)
(x+2)(x+10)
The first line, the expression x^2+10x+2x+20, has four terms.
Note: Just because you have four terms doesn't automatically guarantee you can factor
Factors of 3a^2+13a-10
Answers
3a² + 13a - 10
(3a - 2)(a+5)
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I hope that helps!
Which of the following volumes represent a perfect cube? CHECK ALL THAT APPLY.
A. 1 in.3
B. 4 in.3
C. 8 in.3
D. 12 in.3
E. 25 in.3
F. 27 in.3
G. 64 in.3
Answers
Answer: A C F G
Step-by-step explanation:
The volumes that represent perfect cubes are A ) 1 inch³, C) 8 inch³, F) 27 inch³ and G) 64 inch³.
What is meant by Perfect Cubes?Perfect cubes are defined as the number which is the result of the multiplication of another number, likely integers, to itself three times.
For example, 8 = 2 × 2 × 2
So 8 is a perfect cube of 2.
Given are a set of volumes in cubes.
A ) 1 inch³ can be written as 1 inch × 1 inch × 1 inch
So it is a perfect cube.
B) 4 inch³ cannot be written as the product of a number thrice.
So not a perfect cube.
C) 8 inch³ = 2 inch × 2 inch × 2 inch
Perfect cube
D) 12 inch³ not a perfect cube.
E) 25 inch³ not a perfect cube
F) 27 inch³ = 3 inch × 3 inch × 3 inch
Perfect cube
G) 64 inch³ = 4 inch × 4 inch × 4 inch
Perfect cube
Hence the perfect cubes are found.
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