5x + 2y + 19 = 0 3x + 4y + 17 = 0​

9514 1404 393

Answer:

  10 and 24

Step-by-step explanation:

We know that some of the Pythagorean triples that appear in math problems are (3, 4, 5), (5, 12, 13), (7, 24, 25), (8, 15, 17).

These have (perimeter, area) values of (12, 6), (30, 30), (56, 84), (40, 60).

For some scale factor n, we want (p·n, a·n²) = (60, 120). Of the triangles listed, we see that the (5, 12, 13) triangle scaled by n=2 will satisfy the problem requirements. (30·2, 30·2²) = (60, 120)

The side lengths are 10 and 24.

__

Check

For the side lengths we found, the perimeter is 10+24+26 = 60; the area is 1/2(10)(24) = 120. The hypotenuse is 2×13 = 26 = 24+2.

__

In the attached, one side is x, the other is y. The hypotenuse is (x+2). The square root equation comes from ...

  x² +y² = (x+2)²   ⇒   y² = (x² +4x +4) -x²   ⇒   y² = 4x +4 = 4(x +1)

_____

Additional comment

The graph shows the solution of the various constraints. At least, the combination of constraints will give a quadratic equation in x. They can be combined in a way that gives a cubic equation in x. Either way, we prefer the graphical or "guess and check" approach (above) as being easier to do.

Using the third equation in the attachment to write an expression for y, we have ...

  y = 58 -2x

Substituting that into the second equation gives ...

  (x(58 -2x)/2 = 120

  29x -x² = 120

  x² -29x +120 = 0

  (x -5)(x -24) = 0 . . . . x = 5 or 24.

The root x=5 is a legitimate solution to the pair of equations we chose to solve. The line y=58-2x intersects the hyperbola xy/2 = 120 in two places. However, (x, y) = (5, 48) does not satisfy the hypotenuse requirement that x+2 > y.

9514 1404 393

Answer:

  A. 7√6/2

Step-by-step explanation:

The side ratios of the 30-60-90 triangle are 1 : √3 : 2. This means the horizontal line segment is 7√3.

The side ratios of the 45-45-90 triangle are 1 : 1 : √2. This means ...

  x = (horizontal segment)/√2 = (√2)/2 × 7√3 = (7/2)√(2·3)

  x = 7√6/2

(1) D

[tex]L_s\left\{t\right\} = \displaystyle\int_0^\infty te^{-st}\,\mathrm dt[/tex]

Integrate by parts, taking

[tex]u = t \implies \mathrm du=\mathrm dt[/tex]

[tex]\mathrm dv = e^{-st}\,\mathrm dt \implies v=-\dfrac1se^{-st}[/tex]

Then

[tex]L_s\left\{t\right\} = \displaystyle \left[-\frac1ste^{-st}\right]\bigg|_{t=0}^{t\to\infty}+\frac1s\int_0^\infty e^{-st}\,\mathrm dt[/tex]

[tex]L_s\left\{t\right\} = \displaystyle \frac1s\int_0^\infty e^{-st}\,\mathrm dt[/tex]

[tex]L_s\left\{t\right\} = \displaystyle -\frac1{s^2}e^{-st}\bigg|_{t=0}^{t\to\infty}[/tex]

[tex]L_s\left\{t\right\} = \displaystyle \boxed{\frac1{s^2}}[/tex]

(2) A

[tex]L_s\left\{1\right\} = \displaystyle\int_0^\infty e^{-st}\,\mathrm dt[/tex]

[tex]L_s\left\{1\right\} = \displaystyle\left[-\frac1se^{-st}\right]\bigg|_{t=0}^{t\to\infty}[/tex]

[tex]L_s\left\{1\right\} = \displaystyle\boxed{\frac1s}[/tex]

Answer:

set notation _ A set is denoted or represented by a capital letter and enclosed in a curly bracket For example {A,B,P,Q}.

Answer:

540 miles/hr and 50 miles/hr respectively

Step-by-step explanation:

Let the speed of plane in still air be x and the speed of wind be y.

ATQ, (x+y)*7.5=4425 and (x-y)*7.5=3675. Solving it, we get x=540 and y=50

Answer:

False

Step-by-step explanation:

When the Ftest is used to test the overall significance of a multiple regression model, it evaluates the significance of independent variables to the outcome of the regression model. The null hypothesis of an Ftest when used for multiple regression is that, the independent variables aren't significant in the outcome of the regression model while the alternative Hypothesis claims that the independent variables are significant .

For the overall significance evaluation, once one of the independent variables proves significant, then the overall Ftest is significant, that is it does not require that all individual independent variables are significant. The null only stands when all the independent variables are insignificant.

Therefore, the overall Ftest for significance isn't enough to prove that all individual. Independent variables are significant when the null is rejected.

[tex]Hello[/tex] [tex]There[/tex]

The answer is...

[tex]5.[/tex]

[tex]HopeThisHelps!![/tex]

[tex]AnimeVines[/tex]

Answer:

x = 38.4

Step-by-step explanation:

tan(38) = 30/x

x = 30/tan(38)

x = 38.4

Answered by GAUTHMATH

Answer:

4^15

Step-by-step explanation:

We know a^b^c = a^(b*c)

4^3^5

4^(3*5)

4^15

Answer:

was assigned with this problem (the reference text is attached):

Which of the following, if included in a student's paper, would NOT be an example of plagiarism?

1. In the game of baseball, which is rather boring, the batter stands on home base (Hughes 1).

2. Baseball is rather surprisingly known as "America's Favorite Pastime."

3. Baseball is "a rather boring sport played between two teams of nine players" (Hughes 1).

4. All of these are plagiarism.

The answer tells that only the third choice is NOT a plagiarism. My question is, why is the first choice a plagiarismwas assigned with this problem (the reference text is attached):

Which of the following, if included in a student's paper, would NOT be an example of plagiarism?

1. In the game of baseball, which is rather boring, the batter stands on home base (Hughes 1).

2. Baseball is rather surprisingly known as "America's Favorite Pastime."

3. Baseball is "a rather boring sport played between two teams of nine players" (Hughes 1).

4. All of these are plagiarism.

The answer tells that only the third choice is NOT a plagiarism. My question is, why is the first choice a plagiarism

Step-by-step explanation:

was assigned with this problem (the reference text is attached):

Which of the following, if included in a student's paper, would NOT be an example of plagiarism?

1. In the game of baseball, which is rather boring, the batter stands on home base (Hughes 1).

2. Baseball is rather surprisingly known as "America's Favorite Pastime."

3. Baseball is "a rather boring sport played between two teams of nine players" (Hughes 1).

4. All of these are plagiarism.

The answer tells that only the third choice is NOT a plagiarism. My question is, why is the first choice a plagiarism

Answer:

On the way out the train traveled at about 40 mph, while on the return it did so at 20 mph.

Step-by-step explanation:

Since an empty freight train traveled 60 miles from an auto assembly plant to an oil refinery, and there, its tank cars were filled with petroleum products, and it returned on the same route to the plant, and the total travel time for the train was 4.5 hours, if the train traveled 20 mph slower with the tank cars full, to determine how fast did the train travel in each direction the following calculation must be performed:

60/20 = 3

60/40 = 1.5

60/20 = 3

3 + 1.5 = 4.5

Therefore, on the way out the train traveled at about 40 mph, while on the return it did so at 20 mph.

Answer:

the first option because I took the test

Step-by-step explanation:

X= - 1

X=0

X=4/3

X=3

We solve for x by simplifying both sides of the equation, then isolate the variable.

Answer :

C (x=4/3)

[tex]\boxed{ \sf{Answer}} [/tex]

[tex] \sf \: 3(3x - 4) - 5(x + 3) \\ \sf =( 3 \times 3x) - (3 \times 4) + ( - 5 \times x) +( - 5 \times 3 ) \\ \sf = 9x - 12 - 5x - 15 \\ \sf = 9x - 5x - 12 - 15 \\ = \underline{ \bf 4x - 27}[/tex]

ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ

꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐

[tex]\\ \sf\longmapsto 3(3x-4)-5(x+3)[/tex]

[tex]\\ \sf\longmapsto 9x-12-5x-15[/tex]

[tex]\\ \sf\longmapsto 9x-5x-15-12[/tex]

[tex]\\ \sf\longmapsto (9-5)x-27[/tex]

[tex]\\ \sf\longmapsto 4x-27[/tex]

√50x³y

= √5²×2×x²×x×y

= 5x√2xy

d is the correct answer

Answer:

here

Step-by-step explanation:

Answer:

4y-3=0

4y = 3

y = 3/4

Step-by-step explanation:

1. equal to zero so you can start moving to the other side

2. bring three over becomes positive.

3. divide by 4 to let y stand alone, remember you are solving for the y.

that's all!

Answer:

x = 8/3

Step-by-step explanation:

Log₂(9x) – Log₂3 = 3

The value of x can be obtained as follow:

Log₂(9x) – Log₂3 = 3

Recall

Log M – Log N = Log (M/N)

Thus,

Log₂(9x) – Log₂3 = 3

Log₂(9x/3) = 3

Log₂3x = 3

3x = 2³

3x = 8

Divide both side by 3

x = 8/3

Answer:

[tex](a)\ f(4) = v[/tex]

(b) There are 7 gallons left in the tank after 4 minuted

Step-by-step explanation:

Given

[tex]f(t) = v[/tex]

[tex]t \to[/tex] time since water began draining

[tex]v \to[/tex] gallons in the tank

Solving (a): Notation for gallons remaining at 4 minutes

This means that [tex]t=4[/tex]

[tex]f(t) = v[/tex] becomes

[tex]f(4) = v[/tex]

Solving (b): Interpret f(4) = 7

We have:

[tex]f(t) = v[/tex]

[tex]t \to[/tex] time since water began draining

[tex]v \to[/tex] gallons in the tank

This means that:

[tex]t =4[/tex]

[tex]v =7[/tex]

It can be interpreted as:

There are 7 gallons left in the tank after 4 minuted

Answer:

the write answer to your question is tan 25 degree

9514 1404 393

Answer:

Step-by-step explanation:

Let s represent the number of orders Scott served. Then we have Joe served 3s, and Laura served (s+9). The total of orders served is ...

  3s +s +(s +9) = 104

  5s = 95 . . . . . . . . . . . subtract 9 and collect terms

  s = 19 . . . . . . . . . divide by 5

  3s = 3×19 = 57

  s+9 = 19+9 = 28

Joe served 57 orders, Scott served 19, and Laura served 28 orders.

Answer:

a) 0.2

b) 0.0009

c) 0.0298

d) 0.0465 = 4.65% probability that the sample proportion is less than 0.15.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

20% of customers entering her store make a purchase.

This means that [tex]p = 0.2[/tex]

180 people

This means that [tex]n = 180[/tex]

a. What is the mean of the distribution of the sample proportion of customers making a purchase?

By the Central Limit Theorem, [tex]\mu = p = 0.2[/tex].

b) What is the variance of the sample proportion?

The standard deviation is:

[tex]s = \sqrt{\frac{0.2*0.8}{180}} = 0.0298[/tex]

Variance is the square of the standard deviation, so:

[tex]s^2 = (0.0298)^2 = 0.0009[/tex]

c) What is the standard error of the sample proportion?

As found in the previous item, 0.0298.

d) What is the probability that the sample proportion is less than 0.15?

This is the p-value of Z when X = 0.15. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.15 - 0.20}{0.0298}[/tex]

[tex]Z = -1.68[/tex]

[tex]Z = -1.68[/tex] has a p-value of 0.0465.

0.0465 = 4.65% probability that the sample proportion is less than 0.15.

It looks like the integral in polar coordinates is given to be

[tex]\displaystyle\int_{\pi/2}^\pi \int_0^2 r^3\sin(\theta)\cos(\theta)\,\mathrm dr\,\mathrm d\theta[/tex]

Converting back to Cartesian, we take

x = r cos(θ)

y = r sin(θ)

dx dy = r dr dθ

so we can easily recover the integrand in Cartesian:

[tex]r^3\sin(\theta)\cos(\theta)\,\mathrm dr\,\mathrm d\theta = (r\sin(\theta))(r\cos(\theta))(r\,\mathrm dr\,\mathrm d\theta) = xy\,\mathrm dx\,\mathrm dy[/tex]

This leaves us with the limits:

• π/2 ≤ θ ≤ π corresponds to the second quadrant of the (x, y)-plane (that is, where x < 0 and y > 0)

• 0 ≤ r ≤ 2 correspond to the disk of radius 2 centered at the origin

Taken together, we see the region of integration is a quarter-disk of radius 2 in the second quadrant, which we can capture by the set

{(x, y) : -√2 ≤ x ≤ 0 and 0 ≤ y ≤ √(2 - x ²)}

So, in Cartesian coordinates, the integral would be

[tex]\displaystyle \boxed{\int_{-\sqrt2}^0 \int_0^{\sqrt{2-x^2}} xy\,\mathrm dy\,\mathrm dx}[/tex]

Answer:

(a)The probability that both marbles are blue=5/18

The probability that both marbles are yellow=1/6

(b)The probability that exactly one marble is blue​=5/9

Step-by-step explanation:

Blue marbles=5

Yellow marbles=4

Total marbles=5+4=9

(a)

Probability of drawing first  blue marble=5/9

Probability of drawing second blue marble without replacement=4/8

The probability that both marbles are blue

[tex]=\frac{5}{9}\times \frac{4}{8}=\frac{5}{18}[/tex]

Probability of drawing first  yellow marble=4/9

Probability of drawing second yellow marble without replacement=3/8

The probability that both marbles are yellow

[tex]=\frac{4}{9}\times \frac{3}{8}=\frac{1}{6}[/tex]

(b)

The probability that exactly one marble is blue​

=Probability of first blue marble (Probability of second yellow marble)+Probability of first yellow marble (Probability of second blue marble)

The probability that exactly one marble is blue​

=[tex]\frac{5}{9}\times \frac{4}{8}+\frac{4}{9}\times \frac{5}{8}[/tex]

=[tex]\frac{5}{18}+\frac{5}{18}[/tex]

=[tex]\frac{10}{18}=\frac{5}{9}[/tex]

With some rewriting, you get

[tex]\displaystyle \sum_{k=0}^\infty (-1)^k\frac{x^{k+2}}{4^k} = x^2 \sum_{k=0}^\infty \left(-\frac x4\right)^k[/tex]

Recall that for |x| < 1, you have

[tex]\displaystyle \frac1{1-x} = \sum_{k=0}^\infty x^k[/tex]

So as long as |-x/4| = |x/4| < 1, or |x| < 4, your series converges to

[tex]\displaystyle x^2 \sum_{k=0}^\infty \left(-\frac x4\right)^k = \frac{x^2}{1-\left(-\frac x4\right)} = \frac{x^2}{1+\frac x4} = \boxed{\frac{4x^2}{4+x}}[/tex]

Based on known expressions from Taylor series, the power series [tex]\sum \limits_{k = 0}^{\infty} (-1)^{k}\cdot \frac{x^{k+2}}{4^{k}}[/tex]Taylor series-derived formula of the rational function [tex]\frac{4\cdot x^{2}}{4+x}[/tex].

Taylor series are polynomic approximations used to estimate values both from trascendental and non-trascendental functions. It is commonly used in trigonometric, potential, logarithmic and even rational functions.

In this question we must use series properties and common Taylor series-derived formulas to infer the expression behind the given series. Now we proceed to find the expression:

[tex]\sum \limits_{k = 0}^{\infty} (-1)^{k}\cdot \frac{x^{k+2}}{4^{k}}[/tex]

[tex]x^{2}\cdot \sum\limits_{k = 0}^{\infty} \left(-\frac{x}{4} \right)^{k}[/tex]

[tex]x^{2}\cdot \left(\frac{1}{1+\frac{x}{4} } \right)[/tex]

[tex]\frac{4\cdot x^{2}}{4+x}[/tex]

Based on power and series properties and most common Taylor series- derived formulas, the power series [tex]\sum \limits_{k = 0}^{\infty} (-1)^{k}\cdot \frac{x^{k+2}}{4^{k}}[/tex] represents a Taylor series-derived formula of the rational function [tex]\frac{4\cdot x^{2}}{4+x}[/tex]. [tex]\blacksquare[/tex]

To learn more on Taylor series, we kindly invite to check this verified question: https://brainly.com/question/12800011

Answer:

24

Step-by-step explanation:

(4+8)×4/2

= 12×4/2

= 24

Answered by GAUTHMATH

Answer:

V = 32/3 pi cm^3

Step-by-step explanation:

The volume of a sphere is given by

V = 4/3 pi r^3

The diameter is 4 so the radius is d/2 = 4/2 = 2

V = 4/3  pi (2)^3

V = 32/3 pi cm^3

Answer for this prob

Answer:

s = 17

Step-by-step explanation:

Using the tangent ratio in the right triangle and the exact value

tan60° = [tex]\sqrt{3}[/tex] , then

tan60° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{17\sqrt{3} }{s}[/tex] = [tex]\sqrt{3}[/tex] ( multiply both sides by s )

s × [tex]\sqrt{3}[/tex] = 17[tex]\sqrt{3}[/tex] ( divide both sides by [tex]\sqrt{3}[/tex] )

s = 17