Answer:
T10 = 16Step-by-step explanation:
Using the expression for calculating the sum of an AP as:
Tn = Sn - Sn-1
When n = 10
T10 = S10 - S9
Given that;
Sn = n²-3n
S10 = 10²-3(10)
S10 = 100 - 30
S10 = 70
S9 = 9² - 3(9)
S9 = 81 - 27
S9 = 54
Substitute the given values
T10 = S10 - S9
T10 = 70 - 54
T10 = 16
Hence the 10th term of the sequence is 16
A car travels 32 km due north and
then 46 km in a direction 40° west of
north. Find the magnitude of the
car's resultant vector.
[ ? ] km
Round to the nearest tenth.
9514 1404 393
Answer:
73.5 km
Step-by-step explanation:
The magnitude can be found from the law of cosines. The angle between the two vectors is 140°, so the magnitude is ...
c^2 = a^2 + b^2 -2ab·cos(C)
c^2 = 32^2 +46^2 -2·32·46·cos(140°) ≈ 5395.2348
c = √5395.2348 ≈ 73.452
The magnitude of the resultant vector is about 73.5 km.
What is the solution to the equation?
Answer:
r = 29.82
Step-by-step explanation:
r/7.1 = 4.2
r = 7.1 x 4.2
r = 29.82
Answer:
29.82
Step-by-step explanation:
First, we multiply all terms by the same number to get rid of the denominators.
71 x /71/10 = 71 x 42
Next, we cancel the multiplied terms in denominator.
10 = 71 x 4.2
Solve!
10 = 29.82
please help! I get how to do the first part I just don't get how to do the second part.
9514 1404 393
Answer:
WX = 33
(x, y) = (2, 10)
Step-by-step explanation:
The hash marks tell you WX is a midline, so has the measure of the average of the two bases.
WX = (PQ +SR)/2 = (27 +39)/2 = 66/2
WX = 33
__
The hash marks also tell you ...
PW = WS
y +4x = 18 . . . . . . substitute the given expressions
and also
QX = XR
2y +x = 22 . . . . . substitute the given expressions
__
If you solve the first equation for y, you get ...
y = 18 -4x
Substituting that into the second equation gives ...
2(18-4x) +x = 22
36 -7x = 22 . . . . . . . simplify
14 = 7x . . . . . . . . . . . add 7x-22 to both sides
2 = x . . . . . . . . . . . . divide by 7
y = 18 -4(2) = 10 . . . find y using the above relation
The values of x and y are 2 and 10, respectively.
__
My favorite "quick and dirty" way to solve a set of linear equations is using a graphing calculator. It works well for integer solutions.
Liam and Michael are going to play video games this afternoon. Together, they have 38 video games. If they decide to randomly choose two video games, what is the probability that the two they choose will consist of each of their favorite video games? Assume they have different favorites. Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
The probability that the Liam and Michael are 0.001422 as a fraction in lowest terms or a decimal rounded to the nearest millionth is 5 decimal.
Liam and Michael are going to play video games this afternoon.
Then, Liam going to play video games = 38
Michael going to play video games = 2
In 38 video games and 2 video games are exactly what Liam and Michael need.
So,
We can write,
Probability = [tex]\frac{2C_{2} }{38C_{2} }[/tex]
As only one case is possible,
That is, [tex]2C_{2}[/tex] = 1
Probability = 1/(38!/(38-2)!2!)
= 1/(38!/36!2!)
=( 2! * 36! )/38!
= (2! * 36! )/38!*37!*36!
= 2!/38!37!
= 1/19!37!
= 1/703
= 0.001422
Rounding to nearest million ( 5 decimal )
Required probability = 0.001422
Therefore,
The probability 0.001422 as a fraction in lowest terms or a decimal rounded to the nearest millionth is 5 decimal.
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PLEASE NEED HELP ASAP
Answer:
reflect over the y axis, move two units to the left and 8 units down
Which choice is equivalent to the fraction below?
5/16
O A. 5.16
O B. 5 divided 16
O C. 5-16
O D. 16 divided 5
Answer:
I think A
Step-by-step explanation:
But im not sure
A person is driving a car on a straight road. The graph shows the distance y in
miles that the individual is from home after x hours.
Find the slope-intercept form of the line.
y=x+
n
Answer:
Step-by-step explanation:
The equation of the line that passes through the points (1, 50) and
(3, 120) is y = 35x + 15.
We have,
The point-slope form of a linear equation is given by:
y - y₁ = m(x - x₁)
Where (x₁, y₁) represents the coordinates of a point on the line, and m represents the slope of the line.
The slope (m) using the given points:
m = (y₂ - y₁) / (x₂ - x₁)
Substituting the values from the given points (1, 50) and (3, 120).
m = (120 - 50) / (3 - 1)
= 70 / 2
= 35
Use (1, 50)) and substitute its coordinates into the point-slope form:
y - y₁ = m(x - x₁)
y - 50 = 35(x - 1)
Simplifying further:
y - 50 = 35x - 35
y = 35x - 35 + 50
y = 35x + 15
Therefore,
The equation of the line that passes through the points (1, 50) and
(3, 120) is y = 35x + 15.
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Solve and check please i need help
find the perimeter of the figure
Answer: [tex]9 \frac{1}{2} x+5[/tex]
Step-by-step explanation:
In order to find the Perimeter, we add all the segments up.
(2x-1)+(4x+3)+(x+2)+(2x+2)+(1/10x-1)+(2/5x)
=2x-1+4x+3+x+2+2x+2+1/10x-1+2/5x ⇔ Expand Parenthesis
=2x-1+4x+3+x+2+2x+2+1/10x-1+4/10x ⇔ Convert fractions into same
denominator
=(2x+4x+x+2x+1/0x+4/10x)+(3-1+2+2-1) ⇔ Put like terms together
=(9x+1/2x)+5 ⇔ Combine like terms
=9 1/2 x +5
Hope this helps!! :)
Please let me know if you have any questions
The choices below contain the lengths of sides of four separate triangles. Which of the choices
is NOT a right triangle?
a. 12, 16, 20
b. 15, 36, 39
C. 20, 24, 26
d. 30, 40, 50
Answer:
C
Step-by-step explanation:
Option c (20, 24, 26) doesn't follow the Pythagoras triplet, it is a not right-angle.
What is the right triangle?The right-angle triangle is a triangle in which the measure of two sides of a triangle is smaller than the longest side of the triangle.
To find the right angle triangle it should satisfy the Pythagoras theorem
a. 12, 16, 20
[tex]12^{2} +16^{2} = 144 + 256[/tex]
= 400
[tex]20^{2}[/tex] = 400
Since it follows the Pythagoras triplet, it is a right-angle triangle.
b. 15, 36, 39
[tex]15^{2} +36^{2} \\= 1521[/tex]
[tex]39^{2} =1521[/tex]
Since it follows the Pythagoras triplet, it is a right-angle triangle.
c. 20, 24, 26
[tex]20^{2} + 24^{2} \\= 976[/tex]
[tex]26^{2} = 676[/tex]
Since it does not follow the Pythagoras triplet, it is a not right-angle triangle.
d. 30, 40, 50
[tex]30^{2} +40^{2} \\= 2500\\50^{2} = 2500[/tex]
Since it follows the Pythagoras triplet, it is a right-angle triangle.
Hence, option c doesn't follow the Pythagoras triplet, it is a not right-angle.
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u - 6.46 = 4.42
u = _
Answer:
u = 10.88
Step-by-step explanation:
u - 6.46 = 4.42
u - 6.46 + 6.46 = 4.42 + 6.46
u = 10.88
How many times larger is the volume of Figure B than Figure A?
Answer:
k
Step-by-step explanation:
