Answer: length = 12
Step-by-step explanation:
Use Pythagorean Theorem: length² + height² = hypotenuse²
length = L
height = L - 7
hypotenuse = L + 1
L² + (L - 7)² = (L + 1)²
L² + L² - 14L + 49 = L² + 2L + 1
2L² - 14L + 49 = L² + 2L + 1
L² - 14L + 49 = 2L + 1
L² - 16L + 49 = 1
L² - 16L + 48 = 0
(L - 4)(L - 12) = 0
L - 4 = 0 L - 12 = 0
L = 4 L = 12
Input L = 4 and L = 12 to find the height:
Height = L - 7 height = L - 7
= 4 - 7 = 12 - 7
= -3 = 5
↓
negative height is not valid
So, the only valid solution is L = 12
Why should you find the least common denominator when adding or subtracting rational expressions?
Answer:
It is necessary to look for the least common denominator when one is trying to add or subtract rational expressions that do not have the same denominator.
Step-by-step explanation:
for example the denominator of the two addends are not the same. One has (x+2), the other (x-2).
Determine all numbers at which are function Continuous..
f(x)={
x^2 + 5x - 36/
x^2 + 8x - 9
if x≠-9
if x= -9}
a.
continuous at every real number except x = 1 and x = -9
b. continuous at every real number except x = -9
c.continuous at every real number except x = 1
d. continuous at every real number except x = -9 and x = 4
Answer:
For this case we have this function:
[tex] f(x) =\frac{x^2 +5x-36}{x^2 +8x-9}, x=9[/tex]
We can factor the denominator and we got:
[tex] f(x) =\frac{x^2 +5x-36}{(x+9)(x-1)}, x=9[/tex]
And since we can't divide by 0 then the value of x can't be 1 or -9 so then the best answer for this case would be:
Continuous at every real number except x=1 and x=-9
Step-by-step explanation:
For this case we have this function:
[tex] f(x) =\frac{x^2 +5x-36}{x^2 +8x-9}, x=9[/tex]
We can factor the denominator and we got:
[tex] f(x) =\frac{x^2 +5x-36}{(x+9)(x-1)}, x=9[/tex]
And since we can't divide by 0 then the value of x can't be 1 or -9 so then the best answer for this case would be:
Continuous at every real number except x=1 and x=-9
Answer:
A or continuous at every real number except x=1 and x=-9
Step-by-step explanation:
Just took the test :)
if f(x) = √(x²-9) , then Domain of f = __________ (a) (-∞,-3)∪(3,∞) (b) (-∞,-3]∪ [3,∞) (c) (-∞,∞) (d) [-3,3]
Answer:
domain is:(-∞,-3]∪ [3,∞)
Step-by-step explanation:
f(x)=√(x²-9)
f(x)=√(x-3)(x+3)
domain is:(-∞,-3]∪ [3,∞)
A car with a standard engine costs $14 000 to purchase and 25€/km to drive. An electric car costs S15 000
to purchase and 20¢/km to operate. How many kilometres would you have to drive for the costs of the
cars to be the same?
Answer:
200km
Step-by-step explanation:
Car A purchase worth = $14000
Car B purchase worth = $15000
Car A drive worth= 25€ per km
Car B drive worth= 20€ per km
For the worth of the two cars to be equal let's first assume all of the currency to be in dollars$
For A
Worth= 14000+25(x)
For B
Worth= 15000+20(x)
Where x is the distance covered
For the both worth to be equal we equate.
14000+25(x)= 15000+20(x)
25x-20x= 15000-14000
5x= 1000
X= 200
The distance covered by the two cars for the worth to be equal is 200km
Can Someone plz help me with the question??
Answer:
[tex]\boxed{x^2+y^2 = 49}[/tex]
Step-by-step explanation:
First, we'll find the length of the radius using distance formula and the coordinates (0,0) and (7,0)
Distance Formula = [tex]\sqrt{(x2-x1)^2+(y2-y1)^2}[/tex]
R = [tex]\sqrt{(7-0)^2+(0-0)^2}[/tex]
R = [tex]\sqrt{7^2}[/tex]
Radius = 7 units
Now, Equation of circle:
[tex](x-a)^2+(y-b)^2 = R^2[/tex]
Where (a,b) = (0,0) So, a = 0, b = 0 and R = 7 units
=> [tex](x-0)^2+(y-0)^2 = (7)^2[/tex]
=> [tex]x^2+y^2 = 49[/tex]
This is the required equation of the circle.
Answer:
x^2 + y^2 = 49
Step-by-step explanation:
We can write the equation of a circle as
( x-h) ^2 + ( y-k) ^2 = r^2
where ( h,k) is the center and r is the radius
The radius is the distance from the center to a point on the circle
(0,0) to (7,0) is 7 units
so the the radius is 7
( x-0) ^2 + ( y-0) ^2 = 7^2
x^2 + y^2 = 49
A scale diagram of a garden shows the length as 14.5cm. If the scale is 1:150, what is the actual length? The garden is _______m in length.
Answer:
21.75m
Step-by-step explanation:
14.5×150 =2175cm
1m =100cm
to convert into m divide 2175 by 100
=21.75m
Find the area of the trapezoid in the figure below round your final answer to the nearest tenth
Answer: 60.9 u^2
Step-by-step explanation:
The area of a trapezoid can be calculated as seen in the attachment.
Thus:
[tex]A = \frac{3.7+14.2}{2} * 6.8\\A = \frac{17.9}{2} *6.8\\A = 8.95*6.8\\A = 60.86\\Round\\\left[\begin{array}{c}A=60.9\end{array}\right][/tex]
Hope it helps <3
Answer:
60.9 units^2
Step-by-step explanation:
Well the formula for the area of a trapezoid is,
[tex]\frac{b1+b2}{2} h[/tex]
So b1 and b2 are 142 and 3.7,
14.2 + 3.7 = 17.9
17.9 ÷ 2 = 8.95
8.95 × 6.8 = 60.86
60.9 units^2 rounded to the nearest tenth.
Thus,
the area of the trapezoid is 60.9 units^2.
Hope this helps :)
A jet flies 425 km from Ottawa to Québec at rate v + 60. On the return flight, the
plane encountered wind resistance and travelled at rate v - 40. What is the
difference in flight times of the initial and return flights?
Answer:
a. [tex] \frac{- 42,500}{(v + 60)(v - 40)} [/tex]
Step-by-step Explanation:
Given:
Distance Ottawa to Québec = 425 km
Initial flight rate = v + 60
Return flight rate = v - 40
[tex] t = \frac{d}{r} [/tex]
Required:
Flight times difference of the initial and return flights
Solution:
=>Flight time of the initial flight:
[tex] t = \frac{d}{r} [/tex]
[tex] t = \frac{425}{v + 60} [/tex]
=>Flight time of the return flight:
[tex] t = \frac{425}{v - 40} [/tex]
=>Difference in flight times:
[tex] \frac{425}{v + 60} - \frac{425}{v - 40} [/tex]
[tex] \frac{425(v - 40) -425(v + 60)}{(v + 60)(v - 40)} [/tex]
[tex] \frac{425(v) - 425(40) -425(v) -425(+60)}{(v + 60)(v - 40)} [/tex]
[tex] \frac{425v - 17000 -425v - 25500}{(v + 60)(v - 40)} [/tex]
[tex] \frac{425v - 425v - 17000 - 25500}{(v + 60)(v - 40)} [/tex]
[tex] \frac{- 42,500}{(v + 60)(v - 40)} [/tex]
An anchor lowered at a constant rate into the ocean takes 5 seconds to move -17.5 meters. What is the rate of the anchor in meters per second?
Answer:
-3.5 meters per second
Step-by-step explanation:
Take the distance and divide by the time
-17.5 meters/ 5 seconds
-3.5 meters per second
Answer:
-3.5 m/s
Step-by-step explanation:
Rate of the anchor = [tex]\frac{distance}{time}[/tex]
[tex]\frac{-17.5}{5}[/tex]
-3.5 meters per second.
the endpoints of GH are g(-7,3) and h(1,-2) what’s the midpoint of GH
Answer: [tex]\bigg(-3,\dfrac{1}{2}\bigg)[/tex]
Step-by-step explanation:
G = (-7, 3) H = (1, -2)
[tex]M_{GH}=\bigg(\dfrac{X_G+X_H}{2},\dfrac{Y_G+Y_H}{2}\bigg)\\\\\\.\qquad = \bigg(\dfrac{-7+1}{2},\dfrac{3+(-2)}{2}\bigg)\\\\\\.\qquad = \bigg(\dfrac{-6}{2},\dfrac{1}{2}\bigg)\\\\\\.\qquad = \large\boxed{\bigg(-3,\dfrac{1}{2}\bigg)}[/tex]
The mid point of the line GH whose end points are (-7,3) and (1,-2) is (-3,1/2).
What is the mid point of a line?The mid point is a line which divides the line into two equal parts. The formula to calculate the mid point of line whose end points are (x1,y1) and (x2,y2) is {(x1+x2)/2,(y1+y2)/2}.
How to calculate mid point of a line?To calculate the mid point of the line GH we have to put x1=-7, x2=1,y1=3 and y2=-2 so,
the mid point is {(-7+1)/2,(3-2)/2}
=(-3,1/2)
Hence the mid points of a line GH whose end points are g(-7,3) and h(1,-2) is (-3/1/2).
Learn more about mid point of a line at https://brainly.com/question/18315903
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karen wants to find the area of the isosceles triangle ABC. she knows that the base of the triangle (side CB) is equal to 8 squares. she also knows the height, or altitude, of the triangle is equal to 4.
Answer:
16 squares
Step-by-step explanation:
The area of an isosceles is [tex]\frac{bh}{2}[/tex]
[tex]8 \cdot 4 = 32\\32 \div 2 = 16[/tex]
Hope this helped!
Answer:
area = 16 unit ²
Step-by-step explanation:
given:
base = 8
height = 4
req'd : area of a triangle
area of isoceles triangle = 1/2 * b * h
= 1/2 * 8 * 4
= 16 unit²
Suppose that there are two types of tickets to a show: advance and same-day. Advance tickets cost 15 and same-day tickets cost 30 . For one performance, there were 55 tickets sold in all, and the total amount paid for them was 1125 . How many tickets of each type were sold?
Answer:
30 same day 15 advance
Step-by-step explanation:
A movie earned $438 million at the box office in
2013. That is 24% more than book of the same
name earned. Estimate how much the book
earned?
Round your answer to the nearest hundredth of
a million dollars.
Answer:
332.88 million
Step-by-step explanation:
you do the thing
assume that when adults with smartphones are randomly selected 42 use them in meetings or classes if 15 adult smartphones are randomly selected, find the probability that "fewer" than 4 of them use their smartphones
Complete Question
Assume that when adults with smartphones are randomly selected 42% use them in meetings or classes if 15 adult smartphones are randomly selected, find the probability that "fewer" than 4 of them use their smartphones
Answer:
The probability is [tex]P[X < 4]= 0.00314[/tex]
Step-by-step explanation:
From the question we are told that
The proportion of those that use smartphone in meeting and classes is p = 0.42
The sample size is [tex]n = 15[/tex]
The proportion of those that don't use smartphone in meeting and classes is
[tex]q = 1- p[/tex]
=> [tex]q = 1- 0.42[/tex]
=> [tex]q = 0.58[/tex]
Now from the question we can deduce that the usage of the smartphone is having a binomial distribution since there is only two outcome
So the probability that "fewer" than 4 of them use their smartphones is mathematically evaluated as
[tex]P[X < 4 ] = P[X = 0] + P[X = 1] +P[X = 2] +P[X = 3][/tex]=
=> [tex]P[X < 4] = [ \left 15} \atop {0}} \right. ] p^{15-0} * q^0 + [ \left 15} \atop {1}} \right. ] p^{15-1 }* q^1 + [ \left 15} \atop {2}} \right. ] p^{15-2 }* q^2 + [ \left 15} \atop {3}} \right. ] p^{15-3 }* q^3[/tex]
Where [tex][\left 15} \atop {0}} \right. ][/tex] implies 15 combination 0 which has a value of 1 this is obtained using a scientific calculator
So for the rest of the equation we will be making use of a scientific calculator to obtain the combinations
[tex]P[X < 4] = 1 * ^{15} * q^0 + 15 * p^{14 }* q^1 + 105 * p^{13 }* q^2 + 455 * p^{12 }* q^3[/tex]
substituting values
[tex]= 1 * (0.42)^{15} * (0.58)^0 + 15 * (0.42)^{14 }* (0.58)^1[/tex]
[tex]+ 105 * (0.42)^{13 }* (0.58)^2 + 455 * (0.42)^{12 }* (0.58)^3[/tex]
=> [tex]P[X < 4]= 0.00314[/tex]
Evaluate 7(-4) - |-6| + |4| a 13 b -18 c -30
Answer:
C. -30
Step-by-step explanation:
We would have to do order of operations or P.E.M.D.A.S. So fist we would do 7 times -4 which is -28 than we would do the absolute value of -6 which is 6 so we would do -28-6 which is -34 and we would do the absolute value of 4 which is 4 and we would add it to -34 which is -30 so our final answer would be C. -30
When solving the equation, which is the best first step to begin to simplify the equation? Equation: -2 (x + 3) = -10 A: (-2)(-2)(x+3)= -10(-2) B: -1/2(-2)(x+3)= -10(-1/2) C: -2/2(x+3)= -10/2 D: -2/-10(x+3)= -10/-10
Answer:
B: -1/2(-2)(x+3)= -10(-1/2)
Step-by-step explanation:
The best step to begin to simplify the equation is to try to get a coefficient for the variable x equal to 1. we can do that if we multiply in both sides of the equation by -1/2 as option B.
So, if we keep simplifying, we get:
-2 (x + 3) = -10
-1/2(-2)(x+3) = -10(-1/2)
x + 3 = 5
x + 3 - 3 = 5 - 3
x = 2
Answer:
The answer is B
Step-by-step explanation:
-1/2(2)(x+3)=-10(1/2)
Mary wants to make brownies to make brownies she needs 7/12 of a cup of flour per batch of brownies if Mary has 7 cups of flour then how many batches of brownies can mary make?
━━━━━━━☆☆━━━━━━━
▹ Answer
12
▹ Step-by-Step Explanation
[tex]7/\frac{7}{12} \\\\= 7 * \frac{12}{7} \\\\= \frac{84}{7} \\\\= 12[/tex]
Hope this helps!
CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
Suppose you deposit $600 into an account that pays 5% annual interest, compounded continuously. How much will you have in the account in 4 years? ƒ(t) = aert A) $4,433.43 B)635.62 C)$729.30 D)$732.84
Answer:
D)$732.84
Step-by-step explanation:
A=p(1+r/n)^nt
P=principal=$600
r=5%=0.05
t=4 years
n=12 months
A=p(1+r/n)^nt
=600(1+0.05/12)^12*4
=600(1+0.0041666666666 )^48
=600(1.0041666666666 )^48
=600( 1.2208953550215 )
=732.53
A=$732.53
Option D)$732.84 is the answer
Need Help finding the process for both of these ( due today)
Similar triangles have side lengths that are proportional to each other. To find each of the missing lengths, we need to set up proportions.
The proportions will look as follows:
(length or unknown of triangle 1) / (length or unknown of triangle 2) = (length of triangle 1) / (length of triangle 2)
-On both sides, remember to be consistent with which length/unknown you put on top! If a triangle 1 length is the numerator on the left, then it also needs to be the numerator on the right! And this also works vice versa with triangle 2.
In each proportion equation, we can only have one unknown. On the left side of the equation, we choose one length or unknown of triangle 1, and the corresponding side length of unknown of triangle 2 (whichever you did not choose from triangle 1). On the right side of the equation, we use a completed proportion. This is because all of the sides of one triangle are proportional to the other triangle, but we need to know that proportion/ratio in order to find other side lengths.
Let's start with problem a, to show how this works:
Triangle 1 side lengths - 16, a, 11
Triangle 2 side lengths - 8, 3, b
As you can tell, the side lengths match up (corresponding!) on each triangle, as in they are in the same position on each triangle. Now, we will set up a proportion to find the length of side a on triangle 1.
a / 3 = 16 / 8
48 = 8a
a = 6
Next, let's find the length of side b on triangle 2.
11 / b = 16 / 8
16b = 88
b = 5.5
Moving on to problem b, we'll apply the same concept and steps from problem a in order to find the missing side lengths.
Triangle 1 side lengths: 5, 5.5, d
Triangle 2 side lengths: 15, c, 18
5 / 15 = 5.5 / c
5c = 82.5
c = 16.5
5 / 15 = d / 18
15d = 90
d = 6
Hope this helps!! :)
Answer:
On a) you can see the shapes are simular. The blue line signatures that they are equal just reduced. You can see that 8 goes into 16 two times so for the orange line 3 must times 2. Which would mean a is 6. Now on the red line all you see is 11. So divide 11 by 2 and your answer should be 5.5 for b.
On b) it is the same thing but you have to find how the blue line is divisible. 5 divided by 15 is 3. So 3 is the number you will be using to divide or multiply. For the orange line you divide 18 by 3. The answer is 6 for d. For the red line 5.5 times 3 and you should get 11 for c.
Step-by-step explanation:
Hope this helped
Chloe needs to rent a car while on vacation . The rental company charges $17.95 , plus 18 cents for each mile driven. If Chloe only has $40 to spend on the car rental, what is the maximum number of miles she can drive ?
Answer:
17.95+18x <= 40
Step-by-step explanation
<= less than or equal to0
Answer:
The maximum number of miles than Chloe can drive are:
122.5
Step-by-step explanation:
$1 = 100¢
18¢ = 18/100 = $0.18
17.95 + 0.18m = 40
m = maximum number of miles than can drive
0.18m = 40 - 17.95
0.18m = 22.05
m = 22.05/0.18
m = 122.5
During the summer months Terry makes and sells necklaces on the beach. Last summer he sold the necklaces for $10 each and his sales averaged 20 per day. When he increased the price by $1, he found that the average decreased by two sales per day. If the material for each necklace costs Terry $6, what should the selling price be to maximize his profit?
Answer:
The selling price in other to maximize his profit is $13
Step-by-step explanation:
In the above question we are given the following information:
Cost of material per necklace = $6
Firstly, terry sold 20 necklaces per day
= $10 each
Later he increased he increased the prices by 1 dollar and the number of necklaces he sold reduced by 2
Mathematically
18 necklaces = $11 each
Step 1
We find the Cost function C(x)
Let's assume that x = number of necklaces sold
If each material cost $6 , then
C(x) = 6 × x = 6x
Step 2
P(Profit) = R(x) - C(x)
R(x) = Revenue
Where Revenue = x × p(x)
Since p(20) = 10 and p(18) = 11
p(x) = -1/2x + 20
P(Profit) = x ( -1/2x + 20) - C(x)
C(x) = 6x
P = x(-1/2x + 20) - 6x
P = -1/2x² + 20x - 6x
P = -1/2x² + 14x
Step 3
We maximise the profit by differentiating P
P = Profit
P = -1/2x² + 14x
We differentiate P to find x
∆P/∆x = dp/dx = -x + 14
-x + 14 = 0
-x = -14
x = 14
Hence, we substitute 14 for x in the price function
p(x) = - 1/2x + 20
since , x = 14
p(14) = - 1/2 × 14 + 20
= -7 + 20
= $13
Therefore, the selling price function to maximize his profit is $13
Above question the given data:
Cost of material per necklace = $6 Terry sold 20 necklaces per day = $10 each Price increase by 1 dollar Number of necklaces sold reduced by 2
1.Cost function C(x)
Let's assume that x = number of necklaces sold
If each material cost $6 , then
C(x) = 6 × x
C(x) = 6x
2.P(Profit) = R(x) - C(x)
R(x) = Revenue ,Where Revenue = x × p(x)
Given data:
p(20) = 10
p(18) = 11
p(x) = -1/2x + 20
P(Profit) = R(x) - C(x)
P(Profit) = x ( -1/2x + 20) - C(x)
P = x(-1/2x + 20) - 6x
P = -1/2x² + 20x - 6x
P = -1/2x² + 14x
3.Maximise Profit
P = Profit
P = -1/2x² + 14x
We differentiate P to find x
∆P/∆x = dp/dx = -x + 14
-x + 14 = 0
-x = -14
x = 14
Now, we will substitute 14 for x in the price function
Now ,p(x) = - 1/2x + 20
since , x = 14
p(14) = - 1/2 × 14 + 20
p(14)= -7 + 20
p(14)= $13
Thus, the selling price function to maximize his profit is $13.
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PLEASE HELP QUICK!!! A bowl has 85 pieces of candy. Nineteen children empty the bowl of candy. Some children take 3 pieces, some children take 5 pieces, and 1 child takes 7 pieces of candy. How many children take 3 pieces of candy?
Answer: 3 kids take 3 pieces of candy each
Step-by-step explanation:
Let the number of children that took 3 pieces is x ( total take 3*x pieces of candy)
Number of children that took 5 pieces is y ( total take 5*y pieces of candy)
1 child took 1 piece that actually means that x+y=18 and 3*x+5*y=84.
( Because total number of all kids is 19. We just deduct one kid (Let his name is John) who took only 1 candy. So we have 19-1 =18 kids without John. The similar is with the candies. Total number is 85. We deduct 1 piece which John has taken. )
So we have 2 equations or the system of 2 equations:
1). x+y=18
2). 3*x +5*y=84
Multuply both sides of equation 1) by 3
We have 3*x+3*y=18*3
Deduct 3*y from both sides of this equation
3*x+3*y-3*y=54-3*y
3*x=54-3*y
Substitute 3*x in equation 2). by 54-3*y
2) 54-3*y+5*y=84
2*y=30
y=15 ( kids take 5 pieces of candy each)
Using equation 1) find x
x+15=18
x=3 (kids take 3 pieces of candy each)
A club is holding a raffle. Ten thousand
tickets have been sold for $2 each. There
will be a 1st prize of $3000, 3 second prizes
of $1000 each, 5 third prizes of $500 each
and 20 consolation prizes of $100 each.
Find the expected winnings of a single ticket.
Answer: Other answer is incorrect. It’s asking for the expected winnings of a single ticket. The answer is -.95
Step-by-step explanation:
1/10,000
3/10,000
5/10,000
20/10,000
9971/10,000
-
2998
998
498
98
-2
-
2998+2994+2490+1960-1992 =
-9500/10000 = -.95
6th grade math help me, please :)))
Answer:
700✖️0.08=56 people is late
700✖️0.12=84 people bought the shirt.
Step-by-step explanation:
8%=0.08
12%=0.12
700✖️0.08=56 people is late
700✖️0.12=84 people bought the shirt.
HOPE THIS HELPS!
Belen wants to create a nut-mix. She can buy peanuts for $1.80 per pound and cashews for $4.50 per pound. If she wants to make a 10 pounds of nut-mix at a cost of $2.61 per pound, how many pounds of peanuts and how many pounds of cashews should she buy?
Answer:
7 and 3 respectively
Step-by-step explanation:
Peanuts (p/lb) = $1.80
Cashews (p/lb) = $4.50
Total pound = 10 pounds
Aggregate amount (at $2.61 per lb) = $26.1
Pound of peanut to buy = x
Pound of cashew to buy = y
x + y = 10..........(i)
1.8x + 4.5y = 26.1.....(ii)
Multiply equ (i) by 1.8 and equ (ii) by 1
1.8x + 1.8y = 18
1.8x + 4.5y = 26.1
Subtract (i) from (ii)
4.5y - 1.8y = 26.1 - 18
2.7y = 8.1
y = 3
Sub y = 3 into (i)
x + y = 10
x + 3 = 10
x = 10 - 3
= 7
Pounds of peanut to buy = 7 pounds
Pounds of cashew to buy = 3 pounds
Geographers use negative numbers to represent points below sea level and positive numbers to represent points above sea level. For example, the lowest point in Minnesota is at -17.3−17.3minus, 17, point, 3 meters, and the highest point is at 14.114.114, point, 1 meters.
What does 000 meters represent?
plzz hurry
Choose 1 answer:
Choose 1 answer:
(Choice A, Checked)
A
The lowest point in Apple Valley
(Choice B)
B
The lowest point in Minnesota
(Choice C)
C
Sea level
Answer:
C . Sea level
Step-by-step explanation:
If points below the sea level are represented using negative numbers; and
Points above the sea level are represented using positive numbers.
The point labeled 0 meters represents the sea level since it is the indicator of whether a point is positive or negative.
The correct option is C.
Answer:
A) Sea level
Step-by-step explanation:
Find the axis of symmetry and vertex for the parabola y=−5x2+30x+7.
Answer:
axis of symmetry x=3
vertex (3, 52)
Step-by-step explanation:
y = -5x² + 30x + 7
x = -b/2a = -30/2(-5) = -30/-10 = 3
y = -5(3)² + 30(3) + 7
y = -45 + 90 + 7
y = 52
Please answer this correctly without making mistakes
Simplify the correct answer
Answer:
7/44
Step-by-step explanation:
First find the total number of presidents.
2 + 7 + 13 + 12 + 7 + 3 = 44
There were 7 presidents that were 45-49 when elected. Divide this number by the total number of presidents to find the fraction.
7/44 ≈ 0.159
Verify by direct substitution that the given power series is a solution of the indicated differential equation. [Hint: For a power x2n + 1 let k = n + 1.] y = (-1) nx2n, (1 + x2)y' + 2xy = 0
Answer:
The given power series [tex]y =\sum^{\infty}_{n=0} {(-1)^n x^{2n}}[/tex] is a solution of the differential equation (1+x^2)y' + 2xy = 0
Step-by-step explanation:
This is a very trivial exercise, follow the steps below for the solution:
Step 1: Since n = 0, 1, 2, 3, 4, ........, Substitute the values of n into equation (1) below.
[tex]y =\sum^{\infty}_{n=0} {(-1)^n x^{2n}}[/tex].....................(1)
[tex]y = 1 - x^2 + x^4 - x^6 + x^8.........[/tex]
Step 2: Find the derivative of y, i.e. y'
[tex]y' = -2x + 4x^3 - 6x^5 + 8x^7 .............[/tex]
Step 3: Substitute y and y' into equation (2) below:
[tex](1+x^2)y' + 2xy = 0\\\\(1+x^2)(-2x + 4x^3 - 6x^5 + 8x^7......) + 2x(1 - x^2 + x^4 - x^6 + x^8.......) = 0\\\\-2x+ 4x^3 - 6x^5 + 8x^7........ - 2x^3 +4x^5 - 6x^7 + 8x^9 ......+ 2x - 2x^3 + 2x^5 - 2x^7 + 2x^9...... = 0\\\\0 = 0[/tex]
(Verified)
Since the LHS = RHS = 0, the given power series [tex]y =\sum^{\infty}_{n=0} {(-1)^n x^{2n}}[/tex] is a solution of the differential equation (1+x^2)y' + 2xy = 0
Question 13 of 20 :
Select the best answer for the question.
13. Which of the following groups of numbers are all prime numbers?
O A.2.3,5,9
O B.7.17.29.49
O C.3. 11, 23, 31
O D.2.5, 15, 19
Mark for review (Will be highlighted on the review page)
Answer: C. 3, 11, 23, 31
Step-by-step explanation:
None of these can be divided by anything except themselves and 1.