Solve for all missing sides and angles.

Answer:

See below for answer

Step-by-step explanation:

First problem

[tex]3y'+5y=x^2,\: y(0)=2\\\\3\mathcal{L}\{y'\}+5\mathcal{L}\{y\}=\mathcal{L}\{x^2\}\\\\3[sY(s)-y(0)]+5Y(s)=\frac{2}{s^{3}}\\ \\3[sY(s)-2]+5Y(s)=\frac{2}{s^{3}}\\\\3sY(s)-6+5Y(s)=\frac{2}{s^{3}}\\\\(3s+5)Y(s)-6=\frac{2}{s^3}\\ \\(3s+5)Y(s)=\frac{2}{s^3}+6\\\\Y(s)=\frac{2}{s^3(3s+5)}+\frac{6}{3s+5}\\ \\Y(s)=\frac{2+6s^3}{s^3(3s+5)}[/tex]

Perform the partial fraction decomposition

[tex]\frac{2+6s^3}{s^3(3s+5)}=\frac{A}{s}+\frac{B}{s^2}+\frac{C}{s^3}+\frac{D}{3s+5}\\ \\2+6s^3=s^2(3s+5)A+s(3s+5)B+(3s+5)C+s^3D\\\\2+6s^3=3s^3A+5s^2A+3s^2B+5sB+3sC+5C+s^3D\\\\2+6s^3=3s^3A+s^3D+5s^2A+3s^2B+5sB+3sC+5C\\\\2+6s^3=s^3(3A+D)+s^2(5A+3B)+s(5B+3C)+5C[/tex]

Solve for each constant

[tex]\begin{cases} 3 A + D = 6\\5 A + 3 B = 0\\5 B + 3 C = 0\\5 C = 2 \end{cases}[/tex]

[tex]5C=2\\C=\frac{2}{5}[/tex]

[tex]5B+3C=0\\5B+3(\frac{2}{5})=0\\5B+\frac{6}{5}=0\\5B=-\frac{6}{5}\\B=-\frac{6}{25}[/tex]

[tex]5A+3B=0\\5A+3(-\frac{6}{25})=0\\5A-\frac{18}{25}=0\\5A=\frac{18}{25}\\A=\frac{18}{125}[/tex]

[tex]3A+D=6\\3(\frac{18}{125})+D=6\\\frac{54}{125}+D=6\\D=\frac{696}{125}[/tex]

Take the inverse transform and solve for the IVP

[tex]Y(s)=\frac{\frac{18}{125}}{s}+\frac{- \frac{6}{25}}{s^{2}}+\frac{\frac{2}{5}}{s^{3}}+\frac{\frac{696}{125}}{3 s + 5}\\\\y(x)=\frac{18}{125}-\frac{6}{25}x+\frac{1}{5}x^2+\frac{232}{125}e^{-\frac{5}{3}x}[/tex]

Answer:

False

Step-by-step explanation:

9x0=0

0^1=0

0x9=0

0=9

The numbers don't match.

Hence, the equation is false.

Answer:

False

Step-by-step explanation:

9*0=0

0^1 =0

0*9 = 0

0≠9

Answer:

C

Step-by-step explanation:

To Solve, just cube the terms on the right side to see if they go back to the number on the left.

The first part is true because multiplying 11 * 11 * 11 = 1331.

The second part is true because multiplying 5 * 5* 5 = 125.

The third part is false because multiplying 8 * 8 * 8 = 512.

The fourth part is true because multiplying 1 * 1* 1 = 1.

Answer: 9

Step-by-step explanation:

36/4 = 9

also if you want me to explain I can just ask…

but also I dunno if my answer is correct tho

Answer:

512

Step-by-step explanation:

the number of subsets of the set {1, 2, 3, ..., 9} is : 2^9 = 512

Step-by-step explanation:

please mark me as brainlist please

Answer:

x=112

Step-by-step explanation:

For the function and given domain, the range is  {-9,-1,5,7}.

A linear function can be represented by a line. The standard form for this equation is: [tex]y=ax+b[/tex], for example, y=2x+7.

The domain of a function is the set of input values for which the function is real and defined. On the other words, when you define the domain, you are indicating for which values x the function is real and defined.

While the domain is related to the values ​​of x, the range is related to the possible values ​​of y that the function can have.

The equation of this exercise, 2x+1,  is a linear equation because it presents the form: ax+b. Thus, you already know that your graph will be a line.

For this, you should replace -5,-1, 2,3 for x in the equation 2x+1.

For x=-5,  [tex]y=2*(-5)+1=-10+1=-9[/tex]

For x=-1, [tex]y=2*(-1)+1=-2+1=-1[/tex]

For x=2, [tex]y=2*(2)+1=4+1=5[/tex]

For x=3, [tex]y=2*(3)+1=6+1=7[/tex]

Therefore, the range is {-9,-1,5,7}

From the  values x of domain and the values of  y calculated previously, plot the points and draw the line. See the image attached.

Learn more about the range and the domain here:

brainly.com/question/10197594  

b. You're looking for the probability

Pr [72,972 ≤ X ≤ 90,043]

Transform X to Z ∼ Normal(0, 1) using the rule

X = µ + σ Z

with µ = 64,436 and σ = 17,071. Then the probability is

Pr [(72,972 - µ)/σ ≤ (X - µ)/σ ≤ (90,043 - µ)/σ]

≈ Pr [0.5000 ≤ Z ≤ 1.5000]

You probably have a z-score table available, so you can look up the probabilities to be about

Pr [Z ≤ 0.5000] ≈ 0.6915

Pr [Z ≤ 1.5000] ≈ 0.9332

and then

Pr [0.5000 ≤ Z ≤ 1.5000] ≈ 0.9332 - 0.6915 = 0.2417

c. The 75th percentile word count that separates the lower 75% of the distribution from the upper 25%. In other words, its the count x such that

Pr [X ≤ x] = 0.75

Transforming to Z and looking up the z-score for 0.75, we have

Pr [(X - µ)/σ ≤ (x - µ)/σ] ≈ Pr [Z ≤ 0.6745]

so that

(x - µ)/σ ≈ 0.6745

x ≈ µ + 0.6745σ

x ≈ 75,950

d. Because the normal distribution is symmetric, the middle 60% of novels have word counts between µ - k and µ + k, where k is a constant such that

Pr [µ - k ≤ X ≤ µ + k] = 0.6

Also due to symmetry, we have

Pr [µ - k ≤ X ≤ µ + k] = 2 Pr [µ ≤ X ≤ µ + k]

⇒   Pr [µ ≤ X ≤ µ + k] = 0.3

Transform X to Z :

Pr [(µ - µ)/σ ≤ (X - µ)/σ ≤ (µ + k - µ)/σ] = 0.3

⇒   Pr [0 ≤ Z ≤ k/σ] = 0.3

⇒   Pr [Z ≤ k/σ] - Pr [Z ≤ 0] = 0.3

⇒   Pr [Z ≤ k/σ] - 0.5 = 0.3

⇒   Pr [Z ≤ k/σ] = 0.8

Consult a z-score table:

Pr [Z ≤ k/σ] ≈ Pr [Z ≤ 0.8416]

⇒   k/σ ≈ 0.8416

⇒   k ≈ 14,367

Then the middle 60% of novels have between µ - k = 50,069 and µ + k = 78,803 words.

Answer:

16. L

17. I

18. H

Step-by-step explanation:

Answer:

LIH

16. L

17. I

18. H

Step-by-step explanation:

[tex]16. \sqrt{45a^{2}b } =\sqrt{(9)(5)a^{2} b} =3a\sqrt{5b}[/tex]    

[tex]17. \sqrt{54a^{2}b^{3} } =\sqrt{(9)(6)a^{2}b^{2}b } =3ab\sqrt{6b}[/tex]

[tex]18. \sqrt{45ab^{4} } =\sqrt{(9)(5)ab^{2}b^{2} } =3b^{2} \sqrt{5a}[/tex]

Hope this helps

Answer:

360 fans were sitting in that section.

Step-by-step explanation:

multiply 24 by 15

Answer:

15 : 13

Step-by-step explanation:

Girls : Boys

15 : 13

Answer:

[tex]\bold{K = 5n {}^{2} + w} [/tex]

Given ,

value of n = 4

value of w = - 6

Then ,

[tex]\bold{K = 5(4) {}^{2} + ( - 6)} \\\bold{ K = 5(16) - 6} \\\bold{ K = 80 - 6} \\ \fbox\pink{K = 74}[/tex]

hope helpful~

Answer:

Step-by-step explanation:

Here we have been provided with the values of n and w that is 4 and -6 respectively.

Equation that we have,

Substituting the values of n and w in the equation,

[tex] \implies \: \sf{k \: = \: 5(4) {}^{2} \: + \: ( - 6)}[/tex]

[tex]\implies \: \sf{k \: = \: 5(4 \times 4) \: + \: ( - 6)}[/tex]

[tex] \implies \: \sf{k \: = \: 5 \: (16) \: + \: ( - 6)}[/tex]

Multiplying 16 by 5,

[tex]\implies \: \sf{k \: = \: 5 \: \times 16 \: + \: ( - 6)}[/tex]

[tex]\implies \: \sf{k \: = \: 80 \: + \: ( - 6)}[/tex]

[tex]\implies \: \sf{k \: = \: 80 \: - \:6)}[/tex]

Subtracting 6 from 80,

[tex]\implies \: \red{\bf{k \: = \: 74}}[/tex]

Therefore, value of k is 74..!!

Answer:

3592

Step-by-step explanation:

interest

Step-by-step explanation:

I dont no because I cannot try 2 counting like that money

Answer:

Put a point on (4, -4)

Count 1 down from the purple point, then go four points to the right.

Step-by-step explanation:

y=[tex]-\frac{1}{4}[/tex]x-3

the -1/4 is what tells you how much to move the point from the given one. In this case, it is one down (-1), and four to the right (4).

Answer:

377.36(2decimal places)

Step-by-step explanation:

Solution

First write down all known info about problem

Loss(L) percent:47%

Selling price(SP):200

Cost Price is unknown but CP percent equals 100%(basic percent b'cos it represents the basic cost of the item)

When at a loss, the CP is higher than the SP so subtract the L% from the CP% to get the SP percent...

∴SP% equals CP%-L%

100%-47%:53% ∴SP%:53%

We can simply cross multiply now by saying,

If 53% equals 200

∴100% equals a variable(x)

Cross multiplying,we get:

53x equals (200×100) so dividing both sides by 53,

x equals 377.36(2 decimal places)

Therefore, the CP is 377.36

Solution:

The solution to the given system of equation is the intersection point created with the 2 lines. The solution must satisfy all equations. We can see the intersection. To identify the solution, plot the solution on the graph.

Option C is correct.

~Refer to image for plotted solution~

[tex]Answer: y =\dfrac{1}{2}(x +2)^{2}+[/tex]Answer:

Step-by-step explanation:

Vertex form of quadratic function: y =a(x -h)² + k

Where (h,k) is the vertex

vertex (-2 , 6)

y = a(x -[-2])² + 6

y = a(x + 2)² + 6

This is passing through (-4,8)

8 = a(-4 + 2)² + 6

8 = a(-2)²+ 6

8  = 4a  +6

8 - 6 = 4a

4a = 2

a = 2/4

a = 1/2

[tex]Answer: y =\dfrac{1}{2}(x +2)^{2}+6[/tex]

Answer:

(x-3)(x+3)

Step-by-step explanation:

We are given the expression [tex]\displaystyle \large{x^2-9}[/tex]:—

To factor this expression, we have a formula for it which is difference of two squares:—

[tex]\displaystyle \large{a^2-b^2=(a+b)(a-b)}[/tex]

You can also swap from [tex]\displaystyle \large{(a+b)(a-b)}[/tex] to [tex]\displaystyle \large{(a-b)(a+b)}[/tex] via multiplication property.

From the expression, factor using the formula above:—

[tex]\displaystyle \large{x^2-9=(x^2)-(3)^2}\\\displaystyle \large{x^2-9=(x-3)(x+3)}[/tex]

Therefore, the factored expression is:—

[tex]\displaystyle \large{\boxed{(x-3)(x+3)}}[/tex]

__________________________________________________________

If you have any questions regarding the problem or need clarification of my answer/explanation, do not hesitate to ask in comment!

The market equilibrium is the point where the demand and supply functions are equal

The producer's surplus at market equilibrium for a product is #105

The functions are given as:

[tex]p = 121 - x^2[/tex]

[tex]p = x^2 + 6x + 65[/tex]

Equate both functions

[tex]x^2 + 6x + 65 = 121 - x^2[/tex]

Collect like terms

[tex]x^2 + x^2 + 6x + 65 - 121 = 0[/tex]

Evaluate the like terms

[tex]2x^2 + 6x -56 = 0[/tex]

Divide through by 2

[tex]x^2 + 3x -28 = 0[/tex]

Expand

[tex]x^2 + 7x - 4x - 28 = 0[/tex]

Factorize

[tex]x(x + 7) - 4(x +7)= 0[/tex]

Factor out x + 7

[tex](x - 4)(x +7)= 0[/tex]

Solve for x

x = 4 or x = -7

The number of units cannot be negative,

So, we have:

x = 4

Substitute 4 for x in [tex]p = 121 - x^2[/tex]

[tex]p = 121 - 4^2[/tex]

p = 105

Hence, the producer's surplus at market equilibrium for a product is #105

Read more about equilibrium at:

https://brainly.com/question/110832

Answer:

actually it's 0

Step-by-step explanation:

all of them have 1-1 and that is 0 and no matter what number you divide it by you will get 0

pls give me brainlest

Answer:

Money received = $(75 + 500.t)

Answer:

It is more probable that he pick two red apples than green. Because their are more red apples thank green so the chances of him picking green apples are very slim.

Have a nice day/night!

This is an example of probability without replacement and can simply be done using the formula.

The probability that both apples he ate will be green is 1/12

This is done when we pick a value from a data set and does not replace it and hence affects the value of the original data set.

Data;

Jeremy ate two apples from the basket and the probability this is green would be

[tex]8 + 4 = 12\\[/tex]

The number of green apples are = 4

[tex]\frac{4}{12} * \frac{3}{12} = \frac{12}{144} = \frac{1}{12}[/tex]

The probability that both apples he ate will be green is 1/12

Learn more on probability without replacement here;

https://brainly.com/question/11405286

#SPJ2

Answer : 14 Meters

Explanation : 2 * 3 * 14 Is = To 84

◊ YusuCr ◊

Answer:

14 m

Step-by-step explanation:

The formula to find the volume of a rectangular prism is [tex]l * w * h = V[/tex]. We are given the volume as 84, height as 3, and width as 2.

Therefore, the length of the prism is 14 meters.

Answer:

x=1/3

Step-by-step explanation:

9x+2=3x+4

Minus 2 from both sides: 9x=3x+2

Minus 3x from both sides: 6x=2

Divide by 6: 2/6=1/3

x=1/3

Answer:

x=1/3 or x=0.3

Step-by-step explanation:

If it is a fraction it will be the first one if not I will be the second one

Answer: ↓↓↓

Step-by-step explanation: Generation time (G) is defined as the time (t) per generation (n = number of generations). Hence, G=t/n is the equation from which calculations of generation time (below) derive.

Answer:B $630 Per Month So B

Step-by-step explanation: $22,500-$10,000=$12,500-$4,400=$8,100-$1,800=$6,300/10Months=$630

Answer:

$690

Step-by-step explanation:

If the student will need to save every month in order to pay off the remaining costs in 10 months, the amount she will need to save per month is $690

Amount and interest

Given the following information from the question

The total cost of fee =  $23,500

Amount got as help;

An academic scholarship of $8,200.

Other scholarships and grants of $7.400.

Grandparents pay $1,000

Amount she had = 8200 + 7400 + 1000

Amount she had = $16600

Amount remaining = 23500 - 16600

Amount remaining = $6900

If the student will need to save every month in order to pay off the remaining costs in 10 months, the amount she will need to save per month is $690

https://brainly.com/question/22112075