Answer:
a scalar between 0 and 1
Step-by-step explanation:
i just took the test on EdG. :)
To determine the vector representing the shorter ramp, we must multiply the vector representing the first ramp by a scalar between 0 and 1.
To answer the question, we need to know what scalars and vectors are
What are scalars?These are variables that have only magnitude.
What are vectors?These are variables that have both magnitude and direction.
Now since the first ramp is 50 feet long and has a 6° incline and the second ramp is 30 feet long and runs parallel to the first ramp. We see that the magnitude of the first ramp is greater than that of the second ramp.
So, to obtain a vector representing the second ramp from that of the first ramp, we multiply by a scalar which will be between 0 and 1, since, the magnitude of the first ramp vector is greater than the magnitude second ramp vector.
So, to determine the vector representing the shorter ramp, we must multiply the vector representing the first ramp by a scalar between 0 and 1.
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Solve for y -x - 2y=8
Answer:y=4
Step-by-step explanation:
can someone PLEASE help with this i don’t understand at all
Write the equation of the parabola in vertex form.
Vertex: (−3,7); Point: (−2,−5)
Answer:
y = - 12(x + 3)² + 7
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Here (h, k ) = (- 3, 7 ), thus
y = a(x - (- 3))² + 7 , that is
y = a(x + 3)² + 7
To find a substitute (- 2, - 5) into the equation
- 5 = a(- 2 + 3)² + 7 ( subtract 7 from both sides )
- 12 = a(1)² = a
y = - 12(x + 3)² + 7 ← equation in vertex form
The expression for the sum to 'n' terms of some Arithmetic Sequence are given beliw. Find the 'nth' term of each
i)n^2+2n
ii) n^2- 2n
Arithmetic Sequence
Find:'nth' term of each
i)n^2+2n
ii) n^2- 2n
Solution:1) Sum of first n terms = n² + 2n
We know that,
Sum of first n terms = n/2 * [ a + l ]
Where,
a is first term
l is nth or last term.
Substitute n = 1 to find the sum of first 1 terms i.e., first term (a) of the AP.
→ S₁ = a = (1)² + 2(1)
→ a = 1 + 2
→ a = 3
Hence,
→ n/2 * [ a + l ] = n² + 2n
→ a + l = n(n + 2) * 2/n
→ a + l = 2n + 4
→ l = 2n + 4 - a
→ l = 2n + 4 - 3
→ l = 2n + 1
Hence, the nth term is 2n + 1.
2)S(n) = n² - 2n
→ S₁ = a = (1)² - 2(1)
→ a = - 1
Hence,
→ n/2 * [ - 1 + l ] = n² - 2n
→ l - 1 = n(n - 2) * 2/n
→ l - 1 = 2n - 4
→ l = 2n - 4 + 1
→ l = 2n - 3
Hence, the nth term is 2n - 3.
I hope it will help you.
Regards.
Step-by-step explanation:
Series
The series of a sequence is the sum of the sequence to a certain number of terms. It is often written as Sn. So if the sequence is 2, 4, 6, 8, 10, ... , the sum to 3 terms = S3 = 2 + 4 + 6 = 12.
The Sigma Notation
The Greek capital sigma, written S, is usually used to represent the sum of a sequence. This is best explained using an example:
This means replace the r in the expression by 1 and write down what you get. Then replace r by 2 and write down what you get. Keep doing this until you get to 4, since this is the number above the S. Now add up all of the term that you have written down.
This sum is therefore equal to 3×1 + 3×2 + 3×3 + 3×4 = 3 + 6 + 9 + 12 = 30.
3
S 3r + 2
r = 1
This is equal to:
(3×1 + 2) + (3×2 + 2) + (3×3 + 2) = 24 .
The General Case
n
S Ur
r = 1
This is the general case. For the sequence Ur, this means the sum of the terms obtained by substituting in 1, 2, 3,... up to and including n in turn for r in Ur. In the above example, Ur = 3r + 2 and n = 3.
Arithmetic Progressions
An arithmetic progression is a sequence where each term is a certain number larger than the previous term. The terms in the sequence are said to increase by a common difference, d.
For example: 3, 5, 7, 9, 11, is an arithmetic progression where d = 2. The nth term of this sequence is 2n + 1 .
In general, the nth term of an arithmetic progression, with first term a and common difference d, is: a + (n - 1)d . So for the sequence 3, 5, 7, 9, ... Un = 3 + 2(n - 1) = 2n + 1, which we already knew.
The sum to n terms of an arithmetic progression
This is given by:
Sn = ½ n [ 2a + (n - 1)d ]
You may need to be able to prove this formula. It is derived as follows:
The sum to n terms is given by:
Sn = a + (a + d) + (a + 2d) + … + (a + (n – 1)d) (1)
If we write this out backwards, we get:
Sn = (a + (n – 1)d) + (a + (n – 2)d) + … + a (2)
Now let’s add (1) and (2):
2Sn = [2a + (n – 1)d] + [2a + (n – 1)d] + … + [2a + (n – 1)d]
So Sn = ½ n [2a + (n – 1)d]
Example
Sum the first 20 terms of the sequence: 1, 3, 5, 7, 9, ... (i.e. the first 20 odd numbers).
S20 = ½ (20) [ 2 × 1 + (20 - 1)×2 ]
= 10[ 2 + 19 × 2]
= 10[ 40 ]
= 400
Geometric Progressions
A geometric progression is a sequence where each term is r times larger than the previous term. r is known as the common ratio of the sequence. The nth term of a geometric progression, where a is the first term and r is the common ratio, is:
arn-1
For example, in the following geometric progression, the first term is 1, and the common ratio is 2:
1, 2, 4, 8, 16, ...
The nth term is therefore 2n-1
The sum of a geometric progression
The sum of the first n terms of a geometric progression is:
a(1 - rn )
1 – r
We can prove this as follows:
Sn = a + ar + ar2 + … + arn-1 (1)
Multiplying by r:
rSn = ar + ar2 + … + arn (2)
(1) – (2) gives us:
Sn(1 – r) = a – arn (since all the other terms cancel)
And so we get the formula above if we divide through by 1 – r .
Example
What is the sum of the first 5 terms of the following geometric progression: 2, 4, 8, 16, 32 ?
S5 = 2( 1 - 25)
1 - 2
= 2( 1 - 32)
-1
= 62
The sum to infinity of a geometric progression
In geometric progressions where |r| < 1 (in other words where r is less than 1 and greater than –1), the sum of the sequence as n tends to infinity approaches a value. In other words, if you keep adding together the terms of the sequence forever, you will get a finite value. This value is equal to:
a
1 – r
Example
Find the sum to infinity of the following sequence:
1 , 1 , 1 ,
1
,
1
,
1
, ...
2 4 8 16 32 64
Here, a = 1/2 and r = 1/2
Therefore, the sum to infinity is 0.5/0.5 = 1 .
So every time you add another term to the above sequence, the result gets closer and closer to 1.
Harder Example
The first, second and fifth terms of an arithmetic progression are the first three terms of a geometric progression. The third term of the arithmetic progression is 5. Find the 2 possible values for the fourth term of the geometric progression.
The first term of the arithmetic progression is: a
The second term is: a + d
The fifth term is: a + 4d
So the first three terms of the geometric progression are a, a + d and a + 4d .
In a geometric progression, there is a common ratio. So the ratio of the second term to the first term is equal to the ratio of the third term to the second term. So:
a + d = a + 4d
a a + d
(a + d)(a + d) = a(a + 4d)
a² + 2ad + d² = a² + 4ad
d² - 2ad = 0
d(d - 2a) = 0
therefore d = 0 or d = 2a
The common ratio of the geometric progression, r, is equal to (a + d)/a
Therefore, if d = 0, r = 1
If d = 2a, r = 3a/a = 3
So the common ratio of the geometric progression is either 1 or 3 .
Find the minimum value of
C=x+3y
Answer:
DNE
Step-by-step explanation:
If x and y may be any real number, there is no minimum value for C. It can approach negative infinity.
If C is a constant, and the domain of x is all real numbers, there is no minimum for y. It can approach negative infinity.
We're not sure what you want or what restrictions may exist. The given relation does not suggest any minimum. We'd have to say it Does Not Exist
Hello there,
Use the first constraint to isolate y :
[tex]9x+2y\geq 35[/tex]
[tex]y \geq \frac{35-9x}{2}[/tex]
Now use the second one to isolate x :
[tex]x+3y\geq 14[/tex]
[tex]x\geq 14-3y[/tex]
You know that [tex]x\geq 0[/tex] and [tex]y\geq 0[/tex]
So what's the minimum value of x it's 0 ! Same for y !
So substitute x by 0 and y by 0
[tex]y\geq \frac{35}{2} =17.5[/tex]
[tex]x\geq 14[/tex]
So the minimum value of C is :
[tex]C=14+3*17.5[/tex]
[tex]\boxed{C=66.5}[/tex]
Hope it helps !
Photon
what is the explicit formula for this sequence? -8, -3, 2, 7
Answer:
an+9n-11
Step-by-step explanation:
ILL BRAINLIST 5 times do this for me pllsss I'll make u expert I'm rlly confused on this don't get it
Answer:
a) Maria has d+f
b) Ivan has 3d+ (f-7)
c) 5d+20f
Step-by-step explanation:
12. Bob thought of a number, added 5, multiplied
by 3 and took away 5 to give an answer of 10.
What was the starting number?
Answer:
0
Step-by-step explanation:
Say the number was x.
3(x+5)-5=10
3(x+5)=15
x+5=5
x=0
PLEAAAAASEEE HEEEELPPPPP!!!! ILL GIVE BRAINLIEST!!!!
Answer:
See below
Step-by-step explanation:
[tex] \huge {4}^{3}. (3 \sqrt{16} )^{ - 2} \\ \\ = \huge 64. (3 .4 )^{ - 2}\\ \\ = \huge 64. (12)^{ - 2} \\ \\ = \huge \frac{64}{(12)^{ 2}} \\ \\ = \huge \frac{64}{144} \\ \\\huge = \frac{4}{9} \\ \\ \\ \huge( {a}^{5} . {a}^{ - 2} )^{3} \\ \\ = \huge( {a}^{5 - 2} )^{3} \\ \\ = \huge( {a}^{3} )^{3} \\ \\ = \huge{a}^{3 \times 3} \\ \\ = \huge{a}^{9} [/tex]
Suppose on a particular day, the probability (among the entire population) of getting into a car accident is 0.04, the probability of being a texter-and-driver is 0.14, and p(car accident or being a texter-and-driver)=0.15. Find the probability a person was in a car accident given that they are a texter-and-driver. Is this higher or lower than the probability among the general population and why?
Answer:
0.2143
Step-by-step explanation:
Let A be the event denote that getting into a car accident and B be the event denote being a texter-and-driver.
Thus, P(A)=0.04, P(B)=0.14.
P(A or B)=0.15.
We have to find P(A/B).
P(A/B)=P(A and B)/P(B)
P(A and B)= P(A)+P(B)-P(A or B)
P(A and B)=0.04+0.14-0.15
P(A and B)=0.03.
Thus, P(A/B)=0.03/0.14
P(A/B)=0.2143 (rounded to four decimal places)
Thus, the probability a person was in a car accident given that they are a texter-and-driver is 0.2143. This probability is higher than the probability among the general population because texting while driving is fatal.
I need helpppp?!!!
What is the slope of the line??
Please give right answer
Answer: -1/2
Step-by-step explanation:
Slope=rise/run
Up 1 and to the left 2 which makes it a negative
A lake in East Texas was stocked with 3,000 trout in the year 2000. The number of fish in the lake is modeled by f(x) = 3000 + 100x, where x represents the number of years after 2000 until 2016. Which of the following is the most reasonable domain for the function?
Answer:
x_>0,_>3000
Step-by-step explanation:
I saw the answer key :)
The domain of a function is the set of input values the function can take.
The reasonable domain of the function is [0,16]
From the question, we understand that x represents the number of years after 2000 until 2016.
In 2000, the value of x is 0In 2016, the value of x is 16Hence, the reasonable domain of the function is [0,16]
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1st shape has a 4 2nd shape has a 6 pls help-T T
I don’t know how to do this-
Answer:
2.5
Step-by-step explanation:
because you can tell by the numbers and how close they are then u have to divide
Given the formula below, solve for x
Answer:
Step-by-step explanation:
Sorry but please give detailed question
Choose the best units (liters - l) or (milliliters - ml) to measure each of the following liquids.
The amount of water needed to fill an above-ground swimming pool
The amount of medicine that would fill half a teaspoon
The amount of water that would fill a large cooking pot
Answer:
first one: liters seconds one: milliliters third one: liters
Liters
Milliliters
Liters
Liters are larger are milliliters
1. If f(x)=10- xạ, then which of the following is the value of f (-2)?
PLEASE HELP!! 20 POINTS!
Answer:
it attached in low quality im sorry :((
what is the equation for the line perpendicular to the line represented by the equation y=1/3x-2 that passes through the point (4,-7).
A. Y= -3x-2
B. Y= -3x-5
C. Y= 3x+2
D. Y= -3x+5
Answer:
y=-3x+5
bring (4,-7) in other three lines
you will know that it is unreasonable that
-7=-14
-7=-17
-7=14
The equation for the line perpendicular to the line represented by the equation [tex]y= \ \frac{1}{3} x-2[/tex] that passes through the point [tex](4,-7)[/tex] will be [tex]y=-3x+5[/tex].
What is equation for the perpendicular line ?Equation for the perpendicular line, the perpendicular lines have opposite-reciprocal slopes.
Now,
The equation of a perpendicular line must have a slope that is the negative reciprocal of the original slope.
Equation of a perpendicular line [tex]y=mx-b[/tex]
Here, [tex]m=[/tex] slope
So,
We have
[tex]y= \ \frac{1}{3} x-2[/tex]
Here,
[tex]m = \frac{1}{3}[/tex]
As mentioned above, we have to find the slope of perpendicular,
i.e.
(slope of perpendicular) [tex]m[/tex] [tex]=-3[/tex]
So,
[tex]y=mx-2[/tex]
[tex]y=(-3)x-b[/tex]
We have
Point [tex](4,-7)[/tex] through which line passes. i.e.
[tex]x=4[/tex]
[tex]y=(-7)[/tex]
Therefore,
[tex]-7=(-3)*4-b[/tex]
⇒ [tex]b=7-12[/tex]
[tex]b=(-5)[/tex]
So, Equation of a perpendicular line,
[tex]y=-3x+5[/tex]
So, Equation of a perpendicular line, [tex]y=-3x+5[/tex] which is derived from [tex]y=mx-b[/tex] .
Hence, we can say that the equation for the line perpendicular to the line represented by the equation [tex]y= \ \frac{1}{3} x-2[/tex] that passes through the point [tex](4,-7)[/tex] will be [tex]y=-3x+5[/tex].
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Fun fact : bannanas are curved because they are growed toward the sun
Answer:
That is Cool
Step-by-step explanation:
Because it just is.
A store sells 2 printers for every 5 computers the store sells 40 computers how many printers dose the store sell
Select all sets to which the value belongs
√2- √2
Real Numbers/Irrational numbers/ Rational numbers/ Integers/Whole numbers/ Natural numbers.
Answer:
[tex] \sqrt{2} - \sqrt{2} = 0[/tex]
0 is real number, rational number, integers, whole numbers,
Solve absolute value of x-2=4
Answer:
6
Step-by-step explanation:
2+4=6
you need to do the oppsite opporation and that the answer for example x-2=4 just add 2 and 4 and thats the answer that is aslo the same rule as divsion and multiplecation sorry for spelleng mistakes hope this helps!!!!!!
The perimeter of a rectangle is 22cm. The area is 28cm squared, what are the length of the sides?
I just need to fill 20 characters, the answer is right there on the sheet
What is the solution to 4x3 - 3x2 - 7x<0?
Answer:
[tex](-∞,1) , (0,\frac{7}{4})[/tex]
Step-by-step explanation:
Factor:
x(4x³-3x-7)<0
Pls help ASAP for BRAINLIEST
Answer:
-5
Step-by-step explanation:
h(-2)=3(-2)+1
= -6+1
= -5
hope this help you!! :))))))
2 (x-1 ) = x + 4 find x
Answer:
the answer it's x=6 i think
How do I solve both of the scenarios
Answer:
Scenario 1/129 veggie rolls/Scenario 2/59 Shrimpy BOis
Step-by-step explanation:
1/
129x .75 = 96.75=97
.95 x 56 = 53.2=53
2/
59 x .95 = 56.05=56
.75 x 38 = 28.5=28
i need help it’s algebra 2
Answer:
I sorry can't help I'm doing Geometry
How many lines of symmetry, does this quadrilateral have
Answer:
im going to say 4 hope it helps
Step-by-step explanation:
Givenl ||
т
Il n, find the value of x.
7
m
(3x-4)
n
(6x+13)°
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[tex](6x + 13) + (3x - 4) = 180[/tex]
[tex]9x + 9 = 180[/tex]
Subtract sides 9
[tex]9x + 9 - 9 = 180 - 9[/tex]
[tex]9x = 171[/tex]
Divide sides by 9
[tex] \frac{9}{9} x = \frac{171}{9} \\ [/tex]
[tex]x = 19[/tex]
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