Answer:
Step-by-step explanation:
nth term = (n-1)th term + common difference
d = -10
a₁ = 3
a₂ = a₁ + d = 3 + (-10) = -7
a₃ = a₂ + d = -7 + (-10) = -17
a₄ = a₃ + d = -17 + (-10) = -27
a₅ =a₄ + d = -27 + (-10) = -37
a₆ = a₅ + d = -37 + (-10) = -47
First six terms: 3 , -7 , -17, -27, -37 , -47
A SQUARE CARPET IS LAID IN ONE CORNER OF A RECTANGULAR ROOM, LEAVING STRIPS OF UNCOVERED FLOOR 2M WIDE ALONG ONE SIDE AND 1M ALONG OTHER . THE AREA OF THE ROOM IS 56m SQUARED .FIND THE DIMENSIONS OF THE CARPET
Answer:
Step-by-step explanation:
A square has equal sides. Let x represent the length of each side of the square carpet. The diagram representing the room and the carpet is shown in the attached photo. Therefore, the length of the room would be (x + 2)m while the width of the room would be (x + 1)m
Since the area of the room is 56m², it means that
(x + 2)(x + 1) = 56
x² + x + 2x + 2 = 56
x² + 3x + 2 - 56 = 0
x² + 3x - 54 = 0
x² + 9x - 6x - 54 = 0
x(x + 9) - 6(x + 9) = 0
x - 6 = 0 or x + 9 = 0
x = 6 or x = - 9
Since the dimension of the carpet cannot be negative, then x = 6
The dimension of the carpet is 6m × 6m
here are the ingredients for making pineapple sorbet for 6 people. 800 g pineapple 4 egg whites 1/2 lemon 100 g caster sugar Dan makes pineapple sorbet. he uses 2 and a 1/2 lemons How many people does he make pineapple sorbet for?
Answer:
30 people
Step-by-step explanation:
If you start off with 1/2 a lemon for 6 people, then 1 whole would be 12. 1 1/2 would be 18 people and 2 whole lemons would be 24. so 2 1/2 is 30 people.
PLEASE HELP!!!
What is the third quartile for this data set?
Answer:
38
Step-by-step explanation:
Using the five number summary it is 38 since it is 75 percent of the sample
You have the correct answer. Nice work
==========================================================
Explanation:
If the values aren't sorted, then list them from smallest to largest. The values are already sorted for us, so we move onto the next step.
That next step is to find the median. The median is 29 because four values are smaller than it, and four values are larger than it. The value 29 is right in the middle. This value is in slot 5.
Next, split the data into two halves where L = {21,24,25,28} is the lower half and U = {35,37,39,42} is the upper half. As you can see, any value in set L is smaller than the median. While any value in set U is larger than the median.
The third quartile is the median of set U. We have four values in this set, so the median will be between slots 3 and 4 (between 37 and 39)
Average 37 and 39 to get (37+39)/2 = 38. We see that 38 is the midpoint of 37 and 39.
Therefore, the third quartile is 38.
3. In the polygon below, what kind of
angle is P?
A Acute
B Obtuse
C Right
D Straight
Answer:a
Step-by-step explanation:
can somebody help me plz
Answer:
126 people
Step-by-step explanation:
9/5 is the ratio tea/coffee
let x be the one who preferred coffee and x+36 preferred tea
9/5=x+36/x
9x=5x+5(36)
9x-5x=180
4x=180
x=180/4=45
x=45 coffee
x+36=45+36=81
45+81=126
check : 81/45= 9/5
Please help with this 3a² = 27. Find a
Answer:
[tex]a = 3[/tex]
Step-by-step explanation:
[tex]3 {a}^{2} = 27 \\ \frac{3 {a}^{2} }{3} = \frac{27}{3} \\ {a}^{2} = 9 \\ a = \sqrt{9} \\ a = 3[/tex]
Answer: 9
Step-by-step explanation:
First divide both sides by 3
[tex]a^2=9[/tex]
Then root both sides([tex]\sqrt{a^2}=\sqrt{9}[/tex])
a = 9
Hope it helps <3
Edit: :o this is my 250th answer
There are 6 women and 9 men eligible to be in a committee of 5. Find the expected number of women on the committee given that at least one woman must be on the committee. Round the probabilities of the distribution to four decimal places or keep them as fractions. Round the answer to two decimal places.
Answer:
P = 0.2517
Step-by-step explanation:
In this case we must calculate the probability of event, which would be the number of specific events (that is, at least one woman and the rest men, 4), then it would be to choose 1 of 6 women by 4 of 9 men divided by the number of total events, which would be to choose 5 (committee size) out of 15 (9 men + 6 women, total number of people)
P (at least one woman) = 6C1 * 9C4 / 15C5
we know that nCr = n! / (r! * (n-r)!)
replacing we have:
6C1 = 6! / (1! * (6-1)!) = 6
9C4 = 9! / (4! * (9-4)!) = 126
15C5 = 15! / (5! * (15-5)!) = 3003
Therefore it would be:
P (at least one woman) = 6 * 126/3003
P = 0.2517
That is, approximately 1 out of 4 women.
Can someone help me out with this please
Answer:
143.81
Step-by-step explanation:
Trapezoid Area
A = 2b/2 * h
A = 9 + 23/2 * 7
A = 32/2 * 7
A = 16 * 7
A = 112
Semi-circle Area
A = πr²/2
A = π4.5²/2
A = π20.25/2
A = 63.62/2
A = 38.81
Total Area
112 + 38.81
143.81
Find the value of x in the following
a) x:2 = 10:4 b) 3:x= 6:8
Answer:
a) x = 5
b) x = 4
Step-by-step explanation:
a) x:2 = 10:4
Product of extremes = Product of means
=> x*4 = 10*2
=> 4x = 20
Dividing both sides by 4
=> x = 5
b) 3:x = 6:8
Product of extremes = Product of Means
=> 3*8 = 6*x
=> 24 = 6x
Dividing both sides by 6
=> x = 4
Answer:
a. X= 5b. X= 4Solution,
[tex]a. \: \: \frac{x}{2} = \frac{10}{4} \\ \: \: or \: x \times 4 = 10 \times 2 \: ( \: cross \: multiplication) \\ \: \: or \: 4x = 20 \\ or \:x = \frac{20}{4} \\ \: \: \: x = 5[/tex]
[tex]b. \: \frac{3}{x} = \frac{6}{8} \\ or \: 6 \times x = 3 \times 8 \: ( \: cross \: multiplication) \\ or \: 6x = 24 \\ \: or \: x = \frac{24}{6} \\ x = 4[/tex]
Hope this helps...
Good luck on your assignment
Complete the table of values below: x -3 -2 -1 0 1 2 3 How the graph relates to y=2x y=2x Answer Answer Answer Answer Answer Answer Answer Not applicable y=-2x Answer Answer Answer Answer Answer Answer Answer multiplied by Answer y=(3)(2x)
Answer:
The values of x are:
x : -3, -2, -1, 0, 1, 2, 3
Let's solve each by putting each value of x into each equation:
a [tex]y = 2^x[/tex]
> x = -3
=> y = 2^(-3) = 1/8
> x = -2
=> y = 2^(-2) = 1/4
> x = -1
=> y = 2^(-1) = 1/2
> x = 0
=> y = 2^0 = 1
> x = 1
=> y = 2^1 = 2
> x = 2
=> y = 2^2 = 4
> x = 3
=> y = 2^3 = 8
b. [tex]y = -2^x[/tex]
> x = -3
=> y = -2^(-3) = -1/8
> x = -2
=> y = -2^(-2) = -1/4
> x = -1
=> y = -2^(-1) = -1/2
> x = 0
=> y = -2^0 = -1
> x = 1
=> y = -2^1 = -2
> x = 2
=> y = -2^2 = -4
> x = 3
=> y = -2^3 = -8
c. [tex]y = (3)(2^x)[/tex]
> x = -3
=> y = 3 * 2^(-3) = 3 * 1/8 = 3/8
> x = -2
=> y = 3 * 2^(-2) = 3 * 1/4 = 3/4
> x = -1
=> y = 3 * 2^(-1) = 3 * 1/2 = 3/2
> x = 0
=> y = 3 * 2^0 = 3 * 1 = 3
> x = 1
=> y = 3 * 2^1 = 3 * 2 = 6
> x = 2
=> y = 3 * 2^2 = 3 * 4 = 12
> x = 3
=> y = 3 * 2^3 = 3 * 8 = 24
Input these values into the table.
Answer:
a y = 2^x
> x = -3
=> y = 2^(-3) = 1/8
> x = -2
=> y = 2^(-2) = 1/4
> x = -1
=> y = 2^(-1) = 1/2
> x = 0
=> y = 2^0 = 1
> x = 1
=> y = 2^1 = 2
> x = 2
=> y = 2^2 = 4
> x = 3
=> y = 2^3 = 8
b. y = -2^x
> x = -3
=> y = -2^(-3) = -1/8
> x = -2
=> y = -2^(-2) = -1/4
> x = -1
=> y = -2^(-1) = -1/2
> x = 0
=> y = -2^0 = -1
> x = 1
=> y = -2^1 = -2
> x = 2
=> y = -2^2 = -4
> x = 3
=> y = -2^3 = -8
c. y = (3)(2^x)
> x = -3
=> y = 3 * 2^(-3) = 3 * 1/8 = 3/8
> x = -2
=> y = 3 * 2^(-2) = 3 * 1/4 = 3/4
> x = -1
=> y = 3 * 2^(-1) = 3 * 1/2 = 3/2
> x = 0
=> y = 3 * 2^0 = 3 * 1 = 3
> x = 1
=> y = 3 * 2^1 = 3 * 2 = 6
> x = 2
=> y = 3 * 2^2 = 3 * 4 = 12
> x = 3
=> y = 3 * 2^3 = 3 * 8 = 24
Step-by-step explanation:
If x - 10 is a factor of x2 - 8x - 20, what is the other
factor?
X +
Answer:
(x + 2)
Step-by-step explanation:
When we factor the expression x² - 8x - 20, we should get (x + 2)(x - 10).
Alternatively, we can use synthetic division or long division to get our answer.
Answer:
x + 2
Step-by-step explanation:
got it right edg '22
A rectangle has an area of 524.4m2. One of the sides is 6.9m in length. Work out the perimeter of the rectangle. PLEASE ANSWER!!! SOON ASAP
Answer:
165.8 mSolution,
Area of rectangle= 524.4 m^2
Length(L)= 6.9 m
Breadth(B)=?
Now,
[tex]area = length \times breadth \\ or \: 524.4 = 6.9 \times b \\ or \: 524.4 = 6.9b \\ or \: b = \frac{524.4}{6.9} \\ b = 76 \: m[/tex]
Again,
Perimeter of rectangle:
[tex]2(l + b) \\ = 2(6.9 + 76) \\ = 2 \times 82.9 \\ = 165.8 \: m[/tex]
Hope this helps...
Good luck on your assignment.....
Answer:
The perimeter of the rectangle is 165.8cm
Step-by-step explanation:
Area of a rectangle = length × width
Area = 524.4m²
length = 6.9m
524.4 = 6.9 × width
width = 524.4 / 6.9
width = 76m
Perimeter of a rectangle =
2(length ) + 2(width)
length = 6.9m
width = 76m
Perimeter = 2( 6.9) + 2(76)
= 13.8 + 152
The final answer is
= 165.8cm
Hope this helps you
(1) 10x’y' + 15xy? :
Answer:
factor: 5(2x'y'+3xy)
Step-by-step explanation:
thats for factoring, i didnt know what you needed
Answer:
25xy
Step-by-step explanation:
collect like terms
Grey’s Labs is testing a new growth inhibitor for a certain type of bacteria. The bacteria naturally grows exponentially at a rate of 4.7% each hour. The lab technicians know that the growth inhibitor will make the growth rate of the bacteria less than or equal to its natural growth rate. The current sample contains 90 bacteria. Once a standard tube contains more than 270 bacteria, the sample will stop growing. So, to analyze the effect of the inhibitor over longer spans of time, the lab technicians move the bacteria to larger containers, essentially increasing the container size at a constant rate. This adaptation accommodates 100 more bacteria each hour. The research team wants to track the number of bacteria over time given these two conditions. Select the two inequalities they can use to model this situation.
P ≥ 90e^(0.047t)
P ≤ 270 + 100t
P ≤ 270 – 100t
P ≤ 0.047e^(90t)
P ≤ 90e^(0.047t)
Answer:
The two inequalities are;
P ≤ 90e^(0.047t)
P ≤ 270 + 100·t
Step-by-step explanation:
The parameters given for the testing of the new growth inhibitor are;
The growth rate of the bacteria = 4.7% exponentially
The growth inhibitor lowers the growth rate
The population of bacteria after time, t = P
The increase in the number of bacteria per unit time in the 100
The maximum number of bacteria in the standard tube = 270
Therefore, the number of bacteria after the first filling of the tube is P ≤ 270 + 100·t
The equation for exponential growth is [tex]A_0 e^{kt}[/tex]
Where:
A₀ = Initial population = 90
k = Percentage growth rate as percentage
t = Time
The equation for the population of bacteria under the influence of the inhibitor is therefore;
P ≤ [tex]90 \times e^{0.047 \cdot t}[/tex] which is P ≤ 90e^(0.047t).
Answer:
P≤270+100t
P≤90e^(0.047t)
Find the difference in area between the large circle and the small circle. Click on the answer until the correct answer is showing.
A=4[tex]\pi -8[/tex]
that is your answer :-)
Answer:
[tex]A = 4\pi - 8[/tex]
Step-by-step explanation:
ody
Derive the equation of the parabola with a focus at (6, 2) and a directrix of y = 1. f(x) = −one half(x − 6)2 + three halves f(x) = one half(x − 6)2 + three halves f(x) = −one half(x + three halves)2 + 6 f(x) = one half(x + three halves)2 + 6
Answer:
Second choice.
f(x) = 1/2(x - 6)^2 + 3/2.
Step-by-step explanation:
The distance of a point (x, y) from the focus = the distance of the point from the directrix, so:
(x - 6)^2 + (y - 2)^2 = (y - 1)^2
x^2 - 12x + 36 + y^2 - 4y + 4 = y^2 - 2y + 1
x^2 -12x + 39 = 2y
y = f(x) = 1/2 (x^2 - 12x + 39)
I see you want the answer in vertex for so it is:
f(x) = 1/2 [ (x - 6)^2 - 36) + 39)
f(x) = 1/2(x - 6)^2 + 3)
f(x) = 1/2(x - 6)^2 + 3/2.
A parabola is a plane that is approximately U-shaped.
The equation of the parabola is: [tex]\mathbf{y = \frac{1}{2}(x - 6)^2 + \frac 32}[/tex]
The given parameters are:
[tex]\mathbf{Focus = (6,2)}[/tex]
[tex]\mathbf{Directrix: y = 1}[/tex]
First, equate the directrix to 0
[tex]\mathbf{y - 1 = 0}[/tex]
The equation is then calculated as:
[tex]\mathbf{(x - a)^2 + (y - b)^2 = (y- 1)^2}[/tex]
Where:
[tex]\mathbf{(a,b) = (6,2)}[/tex]
So, we have:
[tex]\mathbf{(x - 6)^2 + (y - 2)^2 = (y- 1)^2}[/tex]
Expand
[tex]\mathbf{x^2 - 12x +36 + y^2 - 4y + 4 = y^2 - 2y + 1}[/tex]
Subtract y^2 from both sides
[tex]\mathbf{x^2 - 12x +36 - 4y + 4 =- 2y + 1}[/tex]
Collect like terms
[tex]\mathbf{x^2 - 12x +36 + 4 - 1 =4y - 2y}[/tex]
[tex]\mathbf{x^2 - 12x +39 =2y}[/tex]
Divide through by 2
[tex]\mathbf{y = \frac{1}{2}(x^2 - 12x +39)}[/tex]
Express 39 as 36 + 3
[tex]\mathbf{y = \frac{1}{2}(x^2 - 12x +36 + 3)}[/tex]
Factor out 3/2
[tex]\mathbf{y = \frac{1}{2}(x^2 - 12x +36) + \frac 32}[/tex]
Expand the bracket
[tex]\mathbf{y = \frac{1}{2}(x^2 - 6x - 6x +36) + \frac 32}[/tex]
Factorize
[tex]\mathbf{y = \frac{1}{2}(x(x - 6) - 6(x -6)) + \frac 32}[/tex]
Factor out x - 6
[tex]\mathbf{y = \frac{1}{2}((x - 6) (x -6)) + \frac 32}[/tex]
Express as squares
[tex]\mathbf{y = \frac{1}{2}(x - 6)^2 + \frac 32}[/tex]
Hence, the equation of the parabola is: [tex]\mathbf{y = \frac{1}{2}(x - 6)^2 + \frac 32}[/tex]
Read more about equations of parabola at:
https://brainly.com/question/4074088
Which statement explains how the lines x+y=2 and y=x+4 are related?
(1) They are parallel.
(2) They are perpendicular.
(3) They are the same line.
4) They are not related.
Answer:
(2)They are perpendicular.
Step-by-step explanation:
PLZ HELP ME!!! I WILL NAME BRAINLIEST! (:
Answer:
Options 2, 4, and 5 are correct (from top to bottom)
Step-by-step explanation:
g(0)=0
g(1)=1
g(-1)=1
g(4)≠-2
g(4)=2
g(1)≠-1
g(1)=1
Options 2, 4, and 5 are correct (from top to bottom)
What is the volume of the cylinder to the nearest whole number? a) 942 cm3 b) 3,534 cm3 c)471 cm3 d) 9,420 cm3
Answer:
V = 3534 cm^3
Step-by-step explanation:
The volume of a cylinder is given by
V = pi r^2 h
the radius is 7.5 and the height is 20
V = pi ( 7.5)^2 * 20
V =1125 pi cm^3
Using the pi button for pi
V =3534.291735 cm^3
Rounding to the nearest whole number
V = 3534 cm^3
Answer:
b)3534 cm^3
Step-by-step explanation:
To find the area of a cylinder, you first have to find the area of the base which is in the shape of a circle. The area of a circle is given by the equation πr^2. In this case r, the radius, is 7.5 cm. So plugging in 7.5 for r you get 7.5^2 × π. Plugging in 3.1415 for π you get ~176.671. Now all you do is multiply this by the height, 20cm, and get the answer of ~3534 cm^3.
I need this ASAP! When David was asked how old he was, he said: "I'm three times younger than my dad, but twice as old as Rebecca." Then little Rebecca ran up to him and declared "I am 30 years younger than my dad." How old is David?
Answer:
David is 12 years old.
Step-by-step explanation:
Let r = Rebecca's age
Let d = David's age
let p = Dad's age
David is 3 times as younger than his dad:
d = [tex]\frac{p}{3}[/tex]
David is 2 times older than Rebecca:
d = 2r
Rebecca is 30 years younger than the dad:
r = p-30
All three equations can be solved by a system
2r = [tex]\frac{p}{3}[/tex]
r = p-30
multiplying r = p-30 by negative 2 and adding it to 2r = [tex]\frac{p}{3}[/tex]
0 = (-2p + p/3) + 60
multiplying new equation by 3
0 = (-6p + p) + 180
5p = 180
p = 36
d = 36/3 = 12
The summer has ended and it’s time to drain the swimming pool. 20 minutes after pulling the plug, there is still 45 000L of water in the pool. The pool is empty after 70 minutes.
Calculate the rate that the water is draining out of the pool. (Hint: remember this line is sloping down to the right)
Answer:
900L per minute
Step-by-step explanation:
1- 70 - 20 = 50
2- in this 50 min the 45000L has been drawned
3- 45000L / 50 = 900L
.. ..
Find the slope of the line that passes through (–7, 1) and (7, 8)
Answer:
slope= 1/2x
Step-by-step explanation:
For this line, you can count it going up 7 and to the right 14. Next, to calculate the slope, you take the change in y over the change in x, and you take those numbers (7 and 14) and divide 7 by 14 to get the slope, which simplifies to 1/2x, the slope.
Answer:
1/2
Step-by-step explanation:
The slope formula is:
[tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
where (x1,y1) and (x1, y2) are 2 points the line passes through.
We are given the points:
(-7,1) and (7,8). Match the corresponding variables with the points.
x1= -7
y1= 1
x2= 7
y2= 8
Substitute these values into the formula.
[tex]m=\frac{8-1 }{7--7 }[/tex]
Solve the numerator first. Subtract 1 from 8.
[tex]m=\frac{7 }{7--7 }[/tex]
Now solve the denominator. Subtract -7 from 7, or add 7 and 7.
[tex]m=\frac{7}{7+7}[/tex]
[tex]m=\frac{7}{14}[/tex]
This fraction can be simplified. Both 7 and 14 can be divided evenly by 7.
[tex]m= \frac{(7/7)}{(14/7)}[/tex]
[tex]m=\frac{1}{2}[/tex]
The slope of the line is 1/2.
10. 80 machines can produce 4800 identical pens in 5 hours. At this rate
a) how many pens would one machine produce in one hour?
b) how many pens would 25 machines produce in 7 hours?
Answer:
a) 12 (Simply divide 4800/5 to get 960. Then divide 960/80 to get 12)
b) 2100 (Simply multiply 12 by 25 by 7)
Hope it helps <3
A car travels the first 50 km of its journey at an average speed of 25 m/s and the next 120 km at an On his outward journey, Ali travelled at a speed of s km/h for 2.5 hours. On his return journey, he increased his speed by 4 km/h and saved 15 minutes. Find Ali's average speed for the whole journey. Speed of 80 km/h. The car completes the last part of its journey at an average speed of 90 km/h in 35 minutes. Find the average speed for its entire journey, giving your answer in km/h.
Answer:
The car's average speed for the entire journey = 84.315 km/h
Step-by-step explanation:
Correct Question
A car travels the first 50km of its journey at an average speed of 25m/s and the next 120 km at an average speed of 80km/h. the car completes the last part of its journey at an average speed of 90km/h in 35 minutes. Find the average speed for its entire journey, giving your answer in km/h.
Solution
Average speed is given as total distance travelled divided by total time taken.
So, we will compute the distance covered for each part of the journey and the corresponding time it takes to cover each of these distances.
- The car travels the 50 km first part of the journey at a speed of 25 m/s.
25 m/s = 90 km/h
We have the distance covered in the first part of the journey, now, we need the time taken to cover the distance.
Speed = (Distance/Time)
Time = (Distance/Speed)
Distance = 50 km, Speed = 90 km/h
Time = (50/90) = 0.5556 hr
- The next part, the car covers 120 km at a speed of 80 km/h
Time = (Distance/Speed) = (120/80) = 1.5 hr
- For the last part of the journey, the car travels with an average speed of 90 km/h for 35 minutes.
35 minutes = (35/60) hr = 0.5833 hr
Here, we need to calculate the distance covered for the last part.
Speed = (Distance/Time)
Distance = (Speed) × (Time) = 90 × 0.5833 = 52.5 km
Total distance covered = 50 + 120 + 52.5 = 222.5 km
Total time taken = 0.5556 + 1.5 + 0.5833 = 2.6389 hr
Average Speed = (222.5/2.6389) = 84.315 km/h
Hope this Helps!!!
is 0.14 rational and irrational
Answer:
Rational.
Step-by-step explanation:
Irrational numbers are real numbers that can't be written as fractions.
One clue is that the decimal goes on forever (doesn't terminate) without repeating. (pi)
.14 can be written as a fraction: 14/100
Answer:
It's rational
Step-by-step explanation:
Because irrational numbers cannot be written s a fraction and rational numbers can
I need help with this problem ASAP please i have until tmrw to finish my course entirely so if anyone can help it would be greatly appreciated
Answer:
Equation: f(x) = -x² + 3
Step-by-step explanation:
If we want to find the roots/solve for x, we can either graph the problem or use quadratic formula to find when f(x) = 0:
To get the equation of the graph, our parent function is: f(x) = a(x - h)² + k, or f(x) = x². Since we are reflecting over the x-axis with a vertical stretch and vertically moving up to (0, 3), we are modifying a and k only.
What is the explicit formula for this sequence?
5, 10, 20, 40, 80, 160,...
O A. an = 5 + 5(n-1)
O B. an = 2(5)(n-1)
O c. an = 5(2)"
D. an = 5(2)(n = 1)
Step-by-step explanation:
The above sequence is a geometric sequence
For an nth term in a geometric sequence
[tex] a(n) = a ({r})^{n - 1} [/tex]
where
n is the number of terms
a is the first term
r is the common ratio
From the question
a = 5
r = 10/5 = 2
Therefore the explicit formula for this sequence is
[tex]a(n) = 5( {2})^{n - 1} [/tex]
Hope this helps you
help me answer this question please with full working
Answer:
A y=1/2x(powerof)2+5
B 17.5
C x=√42 or x=−√42
Step-by-step explanation:
Answer:
a. y = x^2 + 10
b. when x=5, y = 35
c. when y = 26, x = +4 or -4
Step-by-step explanation:
Given
y = k (x^2/2 + 5), and
(2,14) is on the curve.
Solution:
Substitute x=2 and y=14 in the above equation
14 = k (2^2/2 + 5)
14 = k (2+5)
14 = 7k
k = 14/7 = 2
a. equation connecting x and y is
y = 2 (x^2/2 + 5), or
y = x^2 + 10
b. when x=5
y = 5^2 + 10 = 25 + 10 = 35
c. when y = 26
26 = x^2 + 10
x^2 = 26-10 = 16
x= sqrt(16) = +4 or -4
PLEASE HELP! ! ! PLEASEEE!!
Answer:
4^2
Step-by-step explanation:
4^4 times 4^3 is equal to 4^7 since you just add the exponents. Then, when dividing, you subtract the exponents, so 4^7/4^5 is 4^2. I hope this is helpful!
Answer:
the answer is
Step-by-step explanation:
4 to the power of 2
you add 4 and 3 which is 7
and 7 subtract 5 which is
4 to the power of 2
use the bionomial theorem to write the binomial expansion
[tex]( \frac{1}{2}x + 3y) ^{4} [/tex]
Answer:
[tex]$\left(\frac{x}{2} + 3 y\right)^{4}=\frac{x^{4}}{16} + \frac{3}{2} x^{3} y + \frac{27}{2} x^{2} y^{2} + 54 x y^{3} + 81 y^{4}$[/tex]
Step-by-step explanation:
[tex]$\left(\frac{1}{2}x+3y \right)^4=\left(\frac{x}{2}+3y \right)^4\\$[/tex]
Binomial Expansion Formula:
[tex]$(a+b)^n=\sum_{k=0}^n \binom{n}{k} a^{n-k} b^k$[/tex], also [tex]$\binom{n}{k}=\frac{n!}{(n-k)!k!}$[/tex]
We have to solve [tex]$\left(\frac{x}{2} + 3 y\right)^{4}=\sum_{k=0}^{4} \binom{4}{k} \left(3 y\right)^{4-k} \left(\frac{x}{2}\right)^k$[/tex]
Now we should calculate for [tex]k=0, k=1, k=2, k=3 \text{ and } k =4;[/tex]
First, for [tex]k=0[/tex]
[tex]$\binom{4}{0} \left(3 y\right)^{4-0} \left(\frac{x}{2}\right)^{0}=\frac{4!}{(4-0)! 0!}\left(3 y\right)^{4} \left(\frac{x}{2}\right)^{0}=\frac{4!}{4!}(81y^4)\cdot 1 =81 y^{4}$[/tex]
It is the same procedure for the other:
For [tex]k=1[/tex]
[tex]$\binom{4}{1} \left(3 y\right)^{4-1} \left(\frac{x}{2}\right)^{1}=54 x y^{3}$[/tex]
For [tex]k=2[/tex]
[tex]$\binom{4}{2} \left(3 y\right)^{4-2} \left(\frac{x}{2}\right)^{2}=\frac{27}{2} x^{2} y^{2}$[/tex]
For [tex]k=3[/tex]
[tex]$\binom{4}{3} \left(3 y\right)^{4-3} \left(\frac{x}{2}\right)^{3}=\frac{3}{2} x^{3} y$[/tex]
For [tex]k=4[/tex]
[tex]$\binom{4}{4} \left(3 y\right)^{4-4} \left(\frac{x}{2}\right)^{4}=\frac{x^{4}}{16}$[/tex]
You can perform the calculations, I will not type everything.
The answer is the sum of elements calculated.
Just organizing:
[tex]$\left(\frac{x}{2} + 3 y\right)^{4}=\frac{x^{4}}{16} + \frac{3}{2} x^{3} y + \frac{27}{2} x^{2} y^{2} + 54 x y^{3} + 81 y^{4}$[/tex]
Answer: [tex]\bold{\dfrac{1}{16}x^4 + \dfrac{3}{2}x^3y + \dfrac{27}{2}x^2y^2 +54xy^3+81y^4}[/tex]
Step-by-step explanation:
Binomial Tree
n=0 1
n=1 1 1
n=2 1 2 1
n=3 1 3 3 1
n=4 1 4 6 4 1
Using the Binomial Theorem
[tex]\bigg(\dfrac{1}{2}x+3y\bigg)^4\\\\\\=1\bigg(\dfrac{1}{2}x\bigg)^4(3y)^0\quad \rightarrow \quad \dfrac{1}{16}x^4\\\\+4\bigg(\dfrac{1}{2}x\bigg)^3(3y)^1\quad \rightarrow \quad \dfrac{3}{2}x^3y\\\\+6\bigg(\dfrac{1}{2}x\bigg)^2(3y)^2\quad \rightarrow \quad \dfrac{27}{2}x^2y^2\\\\+4\bigg(\dfrac{1}{2}x\bigg)^1(3y)^3\quad \rightarrow \quad 54xy^3\\\\+1\bigg(\dfrac{1}{2}x\bigg)^0(3y)^4\quad \rightarrow \quad 81y^4[/tex]
______________________
[tex]= \dfrac{1}{16}x^4 + \dfrac{3}{2}x^3y + \dfrac{27}{2}x^2y^2 +54xy^3+81y^4[/tex]