Answer:
n = 5
Step-by-step explanation:
0A = (1,3,-1) and OD=(-1,0,n)
AD = √ (-1-1)^2 + (0-3)^2 + (n-(-1))^2
7 = √ (-2)^2 + (-3)^2 + (n+1)^2
7 = √4 + 9 + (n+1)^2
Now squaring both sides we have :
7^2 = (√4 + 9 + (n+1)^2)^2
49 = 4 +9 + (n+1)^2
49 = 13 + (n+1)^2
49 -13 = (n+1)^2
36 = (n+1)^2
Taking the square root of both sides we have :
√36 = √(n+1)^2
6 = (n+1)
6 = n + 1
6 - 1 = n
5 = n
Therefore n = 5
write down in terms of n, an expression for the nth term of the following sequences 2 5 8 11 14
Answer:
[tex]a_{n}[/tex] = 3n - 1
Step-by-step explanation:
There is a common difference d between consecutive terms, that is
d = 5 - 2 = 8 - 5 = 11 - 8 = 14 - 11 = 3
This indicates the sequence is arithmetic with n th term
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = 2 and d = 3 , thus
[tex]a_{n}[/tex] = 2 + 3(n - 1) = 2 + 3n - 3 = 3n - 1
The expression for the nth term of the series is [tex]a_n = 3n-1[/tex].
Given that,
Sequence; 2, 5, 8, 11, 14.
We have to find, the expression in terms of n for the nth term of the following given sequences?
According to the question,
The nth of the arithmetic sequence is,
[tex]\rm a_n = a+ d(n-1)[/tex]
Where a is the first term of the sequence,
d is the common difference between the terms,
n is the number of terms.
Then,
The given sequence is 2, 5, 8, 11, 14.
Here, the common difference between the terms is 3.
And the first term of the sequence is 2.
Substitute all the values in the formula,
Therefore,
The nth term of the given terms is,
[tex]\rm a_n = a+ d(n-1)\\\\a_n = 2+ 3(n-1)\\\\a_n + 2+3n-1\\\\a_n = 3n-1[/tex]
Hence, The required expression for the nth term of the series is [tex]a_n = 3n-1[/tex].
For more details refer to the link given below.
https://brainly.com/question/17043393
Ghani is going to use these instructions to make a fizzy drink instruction: mix 5 parts of lime juice with 3 parts of lemonade ghani thinks thats he has 300ml of lime juice and 200ml of lemonade if he is correct what is the greatest amount of fizzy drink can he make?
Answer: 480 ml
The greatest amount of fizzy drink can he make is 480 ml
Step-by-step explanation:
Given;
Mixing ratio = 5 : 3
Volume of lime juice = 300ml
Volume of lemonade = 200ml
From the given ratio;
5 ml of lemon juice needs 3 ml of lemonade to make 8 ml of fizzy drink.
Assuming all the lemon juice were used;
For 300ml of lemon juice,
It'll require 300/5 × 3 ml of lemonade.
Volume of lemonade needed V2= 300/5 × 3 = 180 ml
Volume of fizzy drink = volume of lemon juice + volume of lemonade
Volume of fizzy drink = 300ml + 180ml = 480ml
The greatest amount of fizzy drink can he make is 480 ml
Vx
Below is a scale drawing of a stage that Syla is designing,
8 cm
5 cm
Using the scale 1 cm: 7 m, Syla calculated the width, or the shorter side of the stage, to be 35 m. She decides to change the
scale to 1 cm 10 m. What is the width of the new stage?
35 m
50 m
56 m
80 m
Save and Exit
Next
Submit
Mark this and return
PA-Common Core...
Answer:
I beleive the new stage would be 50 meters wide
Step-by-step explanation:
I took the quiz on ed
If m vb = 60 and m bs =30 then m 3 =. 30 45 15
Answer:
Option (3)
Step-by-step explanation:
PB is a tangent and PV, PU are the secants drawn to the circle.
[tex]m(\widehat {VB})[/tex] = 60° and [tex]m(\widehat{BS})[/tex] = 30°
By theorem of tangent and secants,
"When a tangent and secant are drawn from a point outside the circle, then the measure of the angle formed is one half the difference of intercepted arcs."
m∠BPV = [tex]\frac{1}{2}[m(\widehat{BV}-m(\widehat{BS})][/tex]
m∠3 = [tex]\frac{1}{2}[60-30][/tex]
m∠3 = 15°
Therefore, Option (3) will be the answer.
The domain of the function is given. Find the range.
f(x) = 2x - 1
Domain: (-2, 0, 2, 4)
Range: (5,1, -3,7)
Range: (-5, 1, -3,7)
Range: (-5, -1,3,7)
Range: [5, 1, +3, +7)
Answer:
Range={ -5,-1,3,7). [ option C]
Please see the attached picture for full solution..
Hope it helps..
Good luck on your assignment..
What is the probability that you’re on mars right now?
The probability of you being on Mars right now is very slim, because no one that we know of currently lives on Mars.
Which complex number has a distance of V17 from the origin on the complex plane?
O 2 + 151
O 17 +7
O 20 – 3i
O 4-7
Answer:
[tex]4-i[/tex]
Step-by-step explanation:
Use the formula for the distance of a complex number from the origin on the complex plane.
[tex]\sqrt{a^2+b^2}[/tex]
[tex]a+bi[/tex]
[tex]4-i[/tex]
[tex]\sqrt{4^2-i^2}[/tex]
[tex]\sqrt{4^2+(-1)^2}=\sqrt{16+1}=\sqrt{17}[/tex]
The complex number that has a distance of [tex]\sqrt{17}[/tex] is [tex]4-i[/tex].
By Pythagorean theorem the complex number 4 - i has a distance from the origin to its location of [tex]\sqrt{17}[/tex] units on the complex plane. (Correct choice: D)
How to determine the distance of a complex numberComplex numbers are a generalization from real numbers, whose expression are of the form a + i b, where a and b are the components of the real and imaginary components, respectively. The magnitude of complex numbers is determined by Pythagorean theorem, this is, the distance from the origin to the location of the number on the complex plane:
[tex]r = \sqrt{a^{2}+b^{2}}[/tex]
If we know that a = 4 and b = -1, then the magnitude of the complex number is:
[tex]r = \sqrt{4^{2}+(-1)^{2}}[/tex]
[tex]r = \sqrt{17}[/tex]
By Pythagorean theorem the complex number 4 - i has a distance from the origin to its location of [tex]\sqrt{17}[/tex] units on the complex plane. (Correct choice: D)
RemarkThe statement presents several typing mistakes, correct form is shown below:
Which complex number has a distance of [tex]\sqrt{17}[/tex] from the origin on the complex plane?
A. 2 + i 15
B. 17 + i
C. 20 - i 3
D. 4 - i
To learn more on complex numbers, we kindly invite to check this verified question: https://brainly.com/question/10251853 #SPJ5
System of Linear Equations
through Elimination
Question #1:
Solve the system of equations. Solve for 'x' and 'y' and show your work.
x- y=7
x + y = 5
Answer:
X=6
Y= - 1
Step-by-step explanation:
X-y =7
X+y =5 cross - y and y
_______
X+x =7 +5
2x= 12
X= 12/2
X= 6
Replace X in first equation:
X - y =7
6 - y =7
6 - 7 =y
y = - 1
Hope this helps you.. Good Luck!
another EASY question for y’all mathy people, easy points! Question in photo.
Answer:
the answer is c
Step-by-step explanation:
Please help! Correct answer only!
For a fundraiser, there is a raffle with 100 tickets. One ticket will win a $150 prize, and the rest will win nothing. If you have a ticket, what is the expected payoff?
$ ___
Answer:
Expected Payoff ⇒ $ 1.50 ; Type in 1.50
Step-by-step explanation:
Considering that 1 out of the 100 tickets will have a probability of winning a 150 dollar prize, take a proportionality into account;
[tex]100 - Number of Tickets,\\1 - Number of Tickets You Can Enter,\\\\1 / 100 - Probability of Winning,\\$ 150 - Money Won,\\\\Proportionality - 1 / 100 = x / 150, where x - " Expected Payoff "\\\\1 / 100 = x / 150,\\100 * x = 150,\\\\Conclusion ; x = 1.5 dollars[/tex]
Thus, Solution ; Expected Payoff ⇒ $ 1.50
Find the value of [2-3(2-3)-1]-1 .
Answer:
the answer to this is 3
Step-by-step explanation:
hope this helps
Answer:
your answer to this question is 3
Step-by-step explanation:
Shawna says her mug holds 100 milliliters. She’ll says that the mug holds 1 liter. Is Shelly correct?
Answer:
In 1 liter there are 1000 milliliters so because 100 ≠ 1000 the answer is no.
Answer:
no shes wrong it does not hold a liter
Step-by-step explanation:
Please help ! I don’t understand :(
Answer:
A. The number quadrupled each week
Step-by-step explanation:
f(x)= 3(4)^x
As per the function, each week number increases 4 times
So the answer choice is A
state with triangle congruence postulate explain that the triangles are congruent
Answer: d) Angle-Angle-Side (AAS)
Step-by-step explanation:
See image --> I labeled the angles to show ΔABC and ΔCDE
Here is the proof that shows ΔABC ≡ ΔDEC
Statement Reason
1. AB ≡ DE 1. Given
2. ∠B ≡ ∠E 2. Given
3. ∠ACB ≡ ∠DCE 3. Vertical Angles
4. ΔABC ≡ ΔDEC 4. AAS Congruency Theorem
We have 2 angles and 1 side so our only options are AAS or ASA.
We can eliminate ASA because the side is NOT between the angles.
If you follow the path of the triangles; first you have Side (AB ≡ DE), then Angle (∠B ≡ ∠E), then Angle (∠ACB ≡ ∠DCE). We don't have SAA as an option so follow it backwards and you get Angle-Angle- Side (AAS).
Simplify
8c^3d^2
4cd^2
Answer:
[tex]2c^{2}[/tex]
Step-by-step explanation:
[tex]\frac{8c^33d^2}{4cd^2}[/tex]
[tex]\frac{2c^2d^0}{1}[/tex]
Answer:
[tex]2 {c}^{2} [/tex]
Step-by-step explanation:
[tex] \frac{8 {c}^{3} {d}^{2} }{4 {c}^{1} {d}^{2} } \\ = 2 {c}^{3 - 1} {d}^{2 - 2} \\ = 2 {c}^{2} {d}^{0} [/tex]
we know that,
[tex] {d}^{0} = 1[/tex]
so,
[tex] = 2 {c}^{2} {d}^{0} \\ = 2 \times {c}^{2} \times 1 \\ = 2 {c}^{2} [/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
Which measurements could be the length of the third
side? Select all that apply.
A student is constructing a triangle with the following
dimensions:
side length of 10 inches
side length of 30 inches
19 inches
0 21 inches
D 35 inches
45 inches
in ohon
Answer:
35 and 21
Step-by-step explanation:
the sum of the two lengths of two sides must be greater than the length of the third side.
10+30=40
45 doesn't work: 40<45.
10+19=29
29<30
19 doesn't work
10+21=31
31>30
21 works
35+10=45
45>30
35 also works
Answer:
35 and 21, good luck!! sorry I'm late
There are 80 picnic tables at the park. During the first weekend of the summer, there were 40 available tables. During the second weekend of the summer, there were 20 available tables. During the third weekend of the summer, there were 10 available tables. Based on the pattern, how many picnic tables will be available during the fourth weekend of the summer?
will mark brainliest
Answer:
5
Step-by-step explanation:
We can see a pattern of 1/2 as the week progresses. 1/2 of 80 is 40, 1/2 of 40 is 20, 1/2 of 20 is 10, so for the fourth week 1/2 of 10 is 5.
Use the law of sines to find the value of y. Round to the nearest tenth.
Law of sines: StartFraction sine (uppercase A) Over a EndFraction = StartFraction sine (uppercase B) Over b EndFraction = StartFraction sine (uppercase C) Over c EndFraction
1.4 units
1.6 units
2.5 units
2.6 units
Answer:
b) 1.6 units
y = 1.586 ≅ 1.6 units
Step-by-step explanation:
Explanation:-
step(i):-
The sine rule
[tex]\frac{a}{Sin A} = \frac{b}{Sin B} = \frac{c}{Sin C} = 2 R[/tex]
Given a = 2 and b = y
∠A = 75° and ∠ B = 50°
Step(ii):-
by sine rule
[tex]\frac{a}{Sin A} = \frac{b}{Sin B}[/tex]
[tex]\frac{2}{Sin 75} = \frac{y}{Sin 50}[/tex]
Cross multiplication , we get
2 × sin 50° = y sin 75°
2 × 0.766 = y × 0.9659
[tex]y = \frac{ 2 X 0.766}{0.9659} = 1. 586[/tex]
y = 1.586 ≅ 1.6 units
Answer:
Step-by-step explanation:
Please answer correctly !!!!!! Will mark brainliest answer !!!!!!!!!
Answer:
(x+2)²+1
Step-by-step explanation:
because the graph we know that gx is (x+2)²+1
What are the solutions to the nonlinear system of equations below? Check all that apply x ^ 2 + y ^ 2 = 4 (x ^ 2)/(2 ^ 2) - (y ^ 2)/(2 ^ 2) = 1
Answer:
hey did you happen to get the answer for this?
Step-by-step explanation:
The answer is -2.0 and 2.0
Help me im just too lazy to figure it out :)
Answer:
m=-16
Step-by-step explanation:
To solve the equation, we want to find out what m is. In order to do this, we have to get m by itself. Perform the opposite of what is being done to the equation. Keep in mind, everything done to one side, has to be done to the other.
-35=m-19
19 is being subtract from m (-19). The opposite of subtraction is addition. Add 19 to both sides (+19) The -19 and +19 equal 0, and therefore cancel each other out.
-35+19=m-19+19
-35+19=m
-16=m
Let's check our solution. Plug -16 back in for m in the original equation.
-35=m-19
-35=-16-19
-35=-35
Both sides of the equation are the same, so we know that m is equal to -16.
Divide £24 in the ratio 1:3
Answer:
6, and 18
Step-by-step explanation:
A ratio of 1:3 contains 4 parts because 1+3=4.
Therefore, divide 24 by 4 to get 6.
The number is split between three parts and one part, so the parts are 3(6) and 1(6).
The parts are 6 and 18
How do I solve this problem??
Answer:
3/10 m^2
Step-by-step explanation:
To calculate area of a triangle we multiply height with base and then divide that by 2
2/5 × 3/2 ÷ 2 = 3/10
-Common Core Math I A: P CR 46.27
Using Function Noiation
Try it
The mapping diagram shows a functional relationship.
Domain
Range
Complete the statement.
f(3) is
0
0
3
3
-1
9
→ 9
What is f
Answer:
The answer to f is 9 hope this helps can you make me answer brianlest
find the second derivative of the function P(t) =(2t+4)/(t+1)
use the quotient rule then after using it the first time use it again on your resulting equation, since you are looking for the second derivative
electricity has two different rates off peak is 10pm to 6am and charged at 8p per hour. peak is 6am to 10pm and is charged at 12p per hour. alison turns uses electricity from 8pm to 11:30 pm. what is the dost of her electricity for that period
Answer:
32p
Step-by-step explanation:
the times between 8pm and 11.30pm are:
8pm,9pm,10pm,11pm,11.30pm.
so, find the cost associated with each of them:
8pm: 12p
9pm: 12p
10pm: 12p
11pm:8p
11.30pm: 4p
sum:12+12+12+8+4 = 12 x 4 = 32p
0.9a+4.96=3.6+1.4a what is the answer simplfy
Answer:
2.72
Step-by-step explanation:
the other one copied my answer from another website.
Explanation:
Move all the terms containing a to the left side of the equation
-0.5a+4.96=3.6
Subtract 4.96 from right side
-0.5a=3.6-4.96
Would be
-0.5a=-1.36
Divide each term by -0.5 and simplify
a= 2.72
Find the surface area of the triangular prism. The base of the prism is an isosceles triangle.
Answer:
[tex]A=2\times25\times 44+14\times44+2\times\frac{14\times24}{2} =3152\; cm^2[/tex]
The surface area of the triangular prism is 3152 square cm if the base of the prism is an isosceles triangle.
What is a triangular prism?When a triangle is, stretch it out to produce a stack of triangles, one on top of the other. A triangular prism is the name given to this novel 3D object.
We have a triangular prism, is showing in the picture:
Here a = 25
b = 25
c = 14
h = 44
The surface area of the triangular prism is given by:
[tex]\rm A=ah+bh+ch+\dfrac{1}{2}\sqrt{-a^4+2(ab)^2+2(ac)^2-b^4+2(bc)^2-c^4][/tex]
Plug all the values in the formula we get:
A = 3152 square cm
Thus, the surface area of the triangular prism is 3152 square cm if the base of the prism is an isosceles triangle.
Learn more about triangular prisms here:
https://brainly.com/question/16909441
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The length of a rectangle is 15 meters more than the width. The perimeter is 50 meters. The width is:
Answer:
5 meters
Step-by-step explanation:
The perimeter of a rectangle can be expressed as 2l+2w.
2l+2w=50
l=w+15
Substitute:
2(w+15)+2w=50
2w+30+2w=50
4w+30=50
4w=20
w=5
Hope this helps!
What are the answers? No hurry; I just have other things to do.
Answer:
what u need help with
Step-by-step explanation:
