The kinetic energy, K, of an object due to its motion is given by K = mv2, where m is the mass of the object and v is its velocity. What is the mass of the object, m, in terms of its kinetic energy and velocity?​

Answer:

4/3

I just guessed I think it's right

The equivalent expressions to \(24^{-7}\) are given as follows:

C. \(\left(\frac{1}{24^{-7}}\right)^{-1}\)

F. \((24^3 \times 24^4)^{-1}\)

Equivalent expressions are expressions that have the same value for all possible values of the variables. In other words, equivalent expressions are different ways of writing the same mathematical idea.

The exponent in the denominator can be moved to the numerator with the changed signal, hence:

\(\left(\frac{1}{24^{-7}}\right)^{-1} = (24^7)^{-1}\)

Applying the power of power rule, we multiply the powers, hence:

\((24^7)^{-1} = 24^{-7}\)

When two terms with the same base and different exponents are multiplied, we add the bases and keep the exponents, hence:

\((24^3 \times 24^4)^{-1} = (24^7)^{-1} = 24^{-7}\)

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Sorry I don't know the answer...

The definite integral for this problem has the result given as follows:

\(\int_1^5 x^2 + 2x - \tan{x} dx = 212 - \ln{|\sec{5}|} + \ln{|\sec{1}|}\)

The definite integral for this problem is defined as follows:

\(\int_1^5 x^2 + 2x - \tan{x} dx\)

We have an integral of the sum, hence we can integrate each term, and then add them.

For the first two terms, applying the power rule, the integrals are given as follows:

The integral of the tangent is given as follows:

ln|sec(x)|

Then the integral is given as follows:

I = x³/3 + x² - ln|sec(x)|, from x = 1 to x = 5.

Applying the Fundamental Theorem of Calculus, the result of the integral is obtained as follows:

I = 5³/3 + 5² - ln|sec(5)| - (1³/3 + 1² - ln|sec(1)|)

I = 625/3 - 1/3 + 5 - 1 - ln|sec(5)| + ln|sec(1)|

I = 208 + 5 - 1 - ln|sec(5)| + ln|sec(1)|

I = 212 - ln|sec(5)| + ln|sec(1)|.

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Answer:

Step-by-step explanation:

It is assumed that the points represent consecutive vertices.

These points have equal x- coordinates so the distance between them is the absolute value of difference of the y-coordinates:

Find the distance

\(\\ \tt\longmapsto \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

\(\\ \tt\longmapsto \sqrt{(-2+2)^2+(-2-4)^2}\)

\(\\ \tt\longmapsto \sqrt{(-6)^2}\)

\(\\ \tt\longmapsto \sqrt{36}\)

\(\\ \tt\longmapsto 6units\)

Step-by-step explanation:

Let x=distance traveled on 20 gal

One approach is to set up a simple ratio: 15 is to 240 as 20 is to x and this is written as follows:

15/240=20/x cross multiply (actually we are multiplying both sides by 240x)

15x=240*20=4800 divide both sides by 15

x=320 mi------------------------------------distance travelled on 20 gal

Another approach would be to determine the mileage the car gets in miles/gal:

If the car goes 240 mi on 15 gal, then it goes 240/15 or 16 mi on 1 gal.

Soooooooooo our car gets 16 mi/gal and it can go 16*20 or 320 mi on 20 gal

Answer:

i guess it is 54-11+7 , the second one

Answer:

Step-by-step explanation:

\(\sf 14=-6+2\left(2x+4\right)\)

\(\sf -6+2\left(2x+4\right)=14\)

\(\sf -6+2\left(2x+4\right)+6=14+\)

\(\sf 2\left(2x+4\right)=2\)

\(\sf \frac{2\left(2x+4\right)}{2}=\frac{20}{2}\)

\(\sf 2x+4=10\)

\(\sf 2x+4-4=10-4\)

\(\sf 2x=6\)

\(\sf \frac{2x}{2}=\frac{6}{2}\)

\(\sf x=3\)

Answer:

A = 120 C = 45

Step-by-step explanation:

180 - 15 = 165
(12x + 12) + (3x + 18) = 165
15x + 30 = 165
15x = 135
135 ÷ 15 = 9
x = 9

A = (12x + 12) = 108 + 12 = 120
C = (3x + 18) = 27 + 18 = 45

A triangle is shown with its exterior angles and the interior angles of the triangle are angles 2, 3, 5. The true statements are m∠3 + m∠4 + m∠5 = 180°, m∠5 + m∠6 = 180°, and m∠2 + m∠3 = m∠6. The correct answers are B, C, and E.

We know that the sum of the measures of the interior angles of a triangle is always 180 degrees. We can use this fact, along with the properties of exterior angles of a triangle, to determine which statements are always true regarding

m∠5 + m∠3 = m∠4 This statement is not always true. It is only true in this case because angle 4 is an exterior angle at vertex 3, which means that m∠4 = m∠3 + m∠5. Therefore, m∠5 + m∠3 = m∠3 + m∠5, which simplifies to m∠5 = m∠5. However, in general, this statement is not always true.

m∠3 + m∠4 + m∠5 = 180° This statement is always true, because the sum of the measures of the three exterior angles of a triangle is always 360 degrees. Therefore, m∠3 + m∠4 + m∠5 = 360°, which simplifies to m∠3 + m∠4 + m∠5 = 180°.

m∠5 + m∠6 = 180° This statement is always true, because the sum of an exterior angle and its adjacent interior angle is always 180 degrees. Therefore, m∠5 + m∠6 = m∠1 (because angle 1 is an exterior angle at vertex 2), and m∠1 + m∠2 + m∠3 = 180° (because the sum of the measures of the interior angles of a triangle is 180 degrees). Therefore, m∠5 + m∠6 = m∠2 + m∠3, which is equal to 180° (because m∠2 + m∠3 = m∠1, and m∠5 + m∠6 = m∠1).

m∠2 + m∠3 = m∠6 This statement is not always true. It is only true in this case because angle 6 is an exterior angle at vertex 5, which means that m∠6 = m∠5 + m∠3. Therefore, m∠2 + m∠3 = m∠2 + m∠5 + m∠3, which simplifies to m∠2 + m∠3 = m∠5 + m∠3. Then, by subtracting m∠3 from both sides, we get m∠2 = m∠5. However, in general, this statement is not always true.

m∠2 + m∠3 + m∠5 = 180°: This statement is always true, because the sum of the measures of the interior angles of a triangle is always 180 degrees. Therefore, m∠2 + m∠3 + m∠5 = 180°.

Based on the above analysis, the statements that are always true regarding the diagram are

m∠3 + m∠4 + m∠5 = 180°

m∠5 + m∠6 = 180°

m∠2 + m∠3 + m∠5 = 180°

Therefore, the correct options are B, C, and E.

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A probability mass function (pmf) for a random variable X must satisfy the following two conditions:
1. f(x) ≥ 0 for all x
2. Σf(x) = 1

(a) f(x) = x/c
To find the constant c, we can use the second condition and sum over all possible values of x:
Σf(x) = Σ(x/c) = 1/c Σx = 1
Since we don't have a specified range for x, we cannot solve for c.

(b) f(x) = cx
Again, we can use the second condition to find the constant c:
Σf(x) = Σ(cx) = cΣx = 1
Without a specified range for x, we cannot solve for c.

(c) f(x) = c(1/4)^x
Using the second condition:
Σf(x) = Σ(c(1/4)^x) = cΣ(1/4)^x = 1
We can use the formula for an infinite geometric series to find the sum:
Σ(1/4)^x = 1/(1 - 1/4) = 4/3
So, c = 3/4

(d) f(x) = c(x + 1)^2
Using the second condition:
Σf(x) = Σ(c(x + 1)^2) = cΣ(x + 1)^2 = 1
Without a specified range for x, we cannot solve for c.

(e) f(x) = x/c
This is the same as part (a), so we cannot solve for c without a specified range for x.

(f) f(x) = c/(x+1)(x+2)
Using the hint, we can rewrite f(x) as:
f(x) = c(1/(x+1) - 1/(x+2))
Using the second condition:
Σf(x) = Σ(c(1/(x+1) - 1/(x+2))) = cΣ(1/(x+1) - 1/(x+2)) = 1
We can use the formula for a telescoping series to find the sum:
Σ(1/(x+1) - 1/(x+2)) = 1 - 1/(x+2)
As x approaches infinity, the sum approaches 1.
So, c = 1

To depict each pmf as a line graph, we would plot the values of f(x) on the y-axis and the values of x on the x-axis. However, without a specified range for x, we cannot create accurate graphs for parts (a), (b), (d), and (e). For part (c), the graph would be a decreasing exponential curve, with f(x) approaching 0 as x increases. For part (f), the graph would be a decreasing curve, with f(x) approaching 0 as x increases.

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Answer:

\(\frac{9}{10}\) ÷ \(\frac{5}{10}\) = 1.8 / \(\frac{9}{5}\) (or 1 \(\frac{4}{5}\))

Step-by-step explanation:

when you convert these fractions to decimals, you get 0.9 and 0.5. then multiply them. the answer is 1.8 as a decimal, 9/5 as a fraction, or 1 4/5 as a mixed number.

Answer:

ur mom ;),its 1.8, just delete it i swear :D

R(-9, 4) and S(2, -1); Find T.

we know that

The formula to calculate the midpoint between two points is equal to

In this problem we have

(x1,y1)=R(-9,4)

(x2,y2)=S(2,-1)

substitute the given values in the formula above

therefore

point T(-3.5,1.5)

The situations that represent a proportional relationship are:

A). Natalia is selling fresh eggs at the local farmer's market. She sells 6 eggs for $3.12, a dozen eggs for $6.24, and eighteen eggs for $9.36.

C). Graph 1 provided in the pictures. This graph shows a straight line passing through the origin, which indicates a proportional relationship.

D). Graph 2 provided in the pictures. This graph also shows a straight line passing through the origin, which indicates a proportional relationship.

E). Azul bought several different packages of 8-inch by 10-inch art canvases for a craft project at her family reunion. The number of canvases in a package and the cost of the package is shown in the table.

Therefore, the situations A, C, D, and E represent proportional relationships.

A proportional relationship is a relationship between two quantities where one quantity is a constant multiple of the other quantity. In other words, if one quantity increases or decreases by a certain factor, then the other quantity will increase or decrease by the same factor. This relationship can be represented by a straight line passing through the origin on a graph.

For example, if the price of gasoline is proportional to the number of gallons purchased, then buying twice as many gallons would cost twice as much money. Similarly, if the distance traveled is proportional to the time taken, then traveling twice as long would cover twice the distance.

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Answer:19.26%

Step-by-step explanation: yeah

Answer:

19%

Step-by-step explanation:

There are only 5 steps here they are:

1. Divide 144.77 by 179.30

2. You get the answer 0.80741773...

3. You round it to 0.81.

4. You turn it into a percent by moving the dot(decimal) to the right four times.

5. And then you subtract it from 100 and you get 19% for the discount.

so therefore the answer is 19%

here some other answer that is just like this one:

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Most problems like this can be done with two tools only: partial fractions, and the result 1/(1−w)=1+w+w2+⋯ for |w|<1. So first split your function f into 1/(z−2)−1/(z−1). I will show you how to cope with one of these factors, 1/(z−2). Writing this as −1211−z/2 is tempting but no good: the "1/(1−w)" expansion will converge only for |z/2|<1, not on the regions you are supposed to care about. So you take out a factor of z−1 instead:

1/(z−2)=z−111−2/z

The final term can be expanded with the 1/(1−w) series, valid for |2/z|<1 that is |z|>2. So that does give you a Laurent series valid in the right region (once you multiply bu z−1. These methods can be used to solve all of your problems.

Partial fractions:

\(f(z) = \dfrac z{(z-1)(2-z)} = -\dfrac1{1-z} + \dfrac2{2-z}\)

For |z| < 1, we have

\(\displaystyle \frac1{1-z} = \sum_{n=0}^\infty z^n\)

and

\(\displaystyle \frac2{2-z} = \frac1{1-\frac z2} = \sum_{n=0}^\infty \left(\frac z2\right)^n\)

(The latter series is valid for |z/2| < 1 or |z| < 2, but |z| < 1 is a subset of this region.)

Then

\(\boxed{f(z) = \displaystyle \sum_{n=0}^\infty \left(\frac1{2^n} - 1\right) z^n}\)

Answer:

A

Step-by-step explanation:

For a right triangle

\(A=\frac{ab}{2} \\\frac{(10.4)(15.3)}{2} =79.56\)

This is the same as the other triangle because they are the same size because of congruency

Area of the rectangle

\(a^2+b^2=c^2\\\)

\(\sqrt{(10.4^2+15.3^2} =c\)

\(c= 18.5\)

18.5 x 7 = 129.5

Add them all up

129.5+79.56+79.56= 288.62

I assume the equation is

\(x \, dy - (y^2 - 4y) \, dx = 0\)

since separating variables leads to

\(x\,dy = y(y-4) \, dx\)

\(\dfrac{dy}{y(y-4)} = \dfrac{dx}x\)

for which the condition that \(x>0\) is actually relevant, as opposed to the simpler differential equation

\(x \, dx - (y^2-4y)\, dy = 0 \implies y(y-4) \, dy = x \, dx\)

(though it's a bit more work to solve for \(y(x)\) in this case)

That the slope \(\frac{dy}{dx}\) is non-zero tells us that

\(\dfrac{dy}{dx} = \dfrac{y(y-4)}x \neq 0 \implies y\neq0 \text{ and } y \neq 4\)

Integrate both sides.

\(\displaystyle \int \frac{dy}{y(y-4)} = \int \frac{dx}x\)

On the left, expand into partial fractions.

\(\displaystyle \frac14 \int \left(\frac1{y-4} - \frac1y\right) \, dy = \int \frac{dx}x\)

\(\dfrac14 (\ln|y-4| - \ln|y|) = \ln|x| + C\)

With the given initial value, we find

\(y(1) = 2 \implies \dfrac14 (\ln|2-4| - \ln|2|) = \ln|1| + C \implies C = 0\)

so the particular solution is

\(\dfrac14 (\ln|y-4| - \ln|y|) = \ln|x|\)

By definition of absolute value, with the initial condition of \(0 < y=2 < 4\) and the condition \(x>0\), we can remove the absolute values.

\(\dfrac14 (\ln(4-y) - \ln(y)) = \ln(x)\)

Solve for \(y\).

\(\ln\left(\dfrac{4-y}y\right) = 4 \ln(x) = \ln\left(x^4\right)\)

\(\dfrac{4-y}y = \dfrac4y - 1 = x^4\)

\(\implies y(x) = \dfrac4{1 + x^4}\)

Then

\(10y\left(\sqrt2\right) = \dfrac{40}{1 + \left(\sqrt2\right)^4} = \boxed{8}\)

On the off-chance you meant the other equation I suggested, we find

\(\displaystyle \int y(y-4) \, dy = \int x \, dx\)

\(\displaystyle \frac{y^3}3 - 2y^2 = \frac{x^2}2 + C\)

\(y(1) = 2 \implies \dfrac83 - 2\cdot4 = \dfrac12 + C \implies C = -\dfrac{35}6\)

Solving for \(y(x)\) involves picking the right branch of the cube root that agrees with \(y(1)=2\). With the cube root formula, we find

\(y(x) = 2 - \xi(1 - i\sqrt3) - \dfrac1\xi (1+i\sqrt3)\)

where

\(\xi = \dfrac{2\sqrt[3]{4}}{\sqrt[3]{3x^2 - 3 + \sqrt{9x^4 - 18x^2 - 1015}}}\)

With a calculator, we find

\(10y\left(\sqrt2\right) \approx 18.748\)

Answer:

x - 4 yards.

Step-by-step explanation:

Given:

Area of rectangle = 3x^2 - 12x square yards

Width = 3x yards

To find:

Length of rectangle

Solution:

The area of a rectangle is equal to the product of its length and width.

Area of rectangle = Length * Width

Substituting the given values, we get:

3x^2 - 12x = Length * 3x

Length =( 3x^2 - 12x )3x

Length = x-4

Therefore, the length of the rectangle is x - 4 yards.

Answer: The length of the rectangle is x - 4 yards.

Step-by-step explanation:

We can create an equation to solve this word problem, where the variable L = length.

3x  ×  L  = \(3x^2 - 12x\)

We need to solve for the variable L, to find the length of the rectangle.

First lets factor the right side of the equation to make it easier to divide with.

3x  ×  L  = \(3x^2 - 12x\)

We can factor out 3x from the right side of the equation.

3x  ×  L  = 3x(x - 4)

Now we need to get the variable L by itself (isolating the variable). In order to do that, we can divide both sides by 3x.

3x ×  L  = 3x(x - 4)

/3x           /3x

L = x - 4

The length of the rectangle is x - 4 yards.

Answer:

50 cents The red on the right end.

Step-by-step explanation:

Let the chocolate chip cookies = x

Let the jumbo popcorn = y

Julie

y + 2x = 5

Marvin

y + 4x = 6                  Subtract

-2x = - 1                     The y's disappear. You are left with 1 dollar (negative). Divide by - 2

-2x/-2 = - 1 / -2

x = 1/2

x  = 0.5 or 50c

Each cookie costs 50c

"the difference between five more than the larger number and twice the smaller number' can be written as the expression 31 -3x.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Given, the sum of two numbers is twenty-six the difference between five is more than the larger number and twice the smaller number' into a variable expression.

Since x represents the smaller of the two numbers,

Thus the larger number will be 26 - x

The expression asked above will be:

=> 5 + larger number - 2 * smaller number

=> 5 + 26 - x - 2 * x

=> 31 -3x

therefore,  "the difference between five more than the larger number and twice the smaller number' can be written as the expression 31 -3x.

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9514 1404 393

Answer:

  5/9

Step-by-step explanation:

Compare the given equation ...

  y = (5/9)x

to the equation for proportionality ...

  y = rx

where r is the constant of proportionality.

Matching the two patterns, you should be able to see that r = 5/9.

The constant of proportionality is 5/9.

The piecewise function f(x) is composed bt two lines: 3/2x + 1 and x - 5. To graph a line, we need to connect two points that lie on the line. In the case of the first line, we can use its endpoints x = -4 and x = 0.

Substituting x = -4 into the equation of the first line, we get:

Then, the point (-4, -5) lies on the first line.

Substituting x = 0 into the equation of the first line, we get:

Then, the point (0,1) lies on the first line.

In the case of the second line, the endpoints x = 1 and x = 3.

Substituting x = 1 into the equation of the second line, we get:

Then, the point (1,-4) lies on the second line.

Substituting x = 3 into the equation of the second line, we get:

Then, the point (3,-2) lies on the second line.

Connecting these points with two different lines as stated before, we get the graph of f(x) as follows:

Answer:

Step-by-step explanation:

saw it on chegg

.05x+.17y=.13

x+y=60

The two correct equations are "\(0.05 x+0.17 y=0.13\) and \(x+y=60\)". A further solution is provided below.

According to the question,

Let,

Given total acid solution,

= 60 mL

then,

→  \(x+y = 60\)...(equation 1)

We know that the concentration of mixture = 13%

hence,

→  \(5 \ percent \ of \ x + 17 \ percent \ of \ y =13 \ percent (x+y)\)

or,

→  \(0.05x+0.17y=0.13(60)\)

Thus the above answer is correct.

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Answer:

$54.00

Step-by-step explanation:

30% can be written at 0.30

0.30 x $180 = $54.00

So on solving the provided question, we can say that by equation , y = 5/8x; it makes a vertical line.

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

Let y be the number of gallons of fertilizer produced by combining x tsp of fertilizer powder.

5 litres of liquid fertilizer are created by combining 8 tsp of fertilizer powder.

Therefore, the amount of liters of liquid fertilizer produced by combining 1 tsp of fertilizer powder = 5/8

gallons of LF by mixing x tsp of powder fertiliser  = 5/8x

the required equation is => y = 5/8x

so by graph it makes a vertical line.

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Using the cross product for the proff of Pythagoras theorem, the correct step is

By the cross product property, AB² =  BC multiplied by BD

The cross product property is typically used to solve equations with two values, where the product of the extremes (the outer terms) is equal to the product of the means (the inner terms).

For the similar triangles, the ratio is as follows

BD / BA = BA / BC

BA² = BD * BC

and AB = BA, hence

BA² = BD * BC

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Answer:

\(x=\pm \frac{2}{7}i\)

Step-by-step explanation:

\(49x^2+4=0\)

\(49x^2=-4\)

\(x^2=-\frac{4}{49}\)

\(x=\pm \frac{2}{7}i\)

Answer:

,

Step-by-step explanation:

step by step solution is given