Find the slope, y intercept and x intercept of the linear equation 5x+6y=15

The solution of the given system of equation is (3, 2).

In the given question we have to find the solution to the system of equations:

y = 4x − 10 and y = 2

We can solve the system of equation using the substitution method.

In substitution method we have to put the the value of one variable from one equation to the other equation.

We have to equations:

y = 4x − 10........................(1)

y = 2...................................(2)

Now putting the value of y from the equation 2 in equation 1

2 = 4x − 10

Add 10 on both side, we get

4x = 12

Divide by 4 on both side, we get

x = 3

Now putting the value of x in equation 1

y = 4(3) − 10

y = 12 − 10

y = 2

Hence, the solution of the given system of equation is (3, 2).

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The right question is:

What is the solution to the system of equations y = 4x − 10 and y = 2?

The hydrologic cycle, also known as the water cycle, plays a crucial role in the Earth's natural processes. It involves the continuous movement of water between the Earth's surface, atmosphere, and underground reservoirs.

The importance of the hydrologic cycle can be understood by considering its various functions:

Transport: The hydrologic cycle facilitates the transport of water across the Earth's surface, including rivers, lakes, and oceans. This movement of water is vital for the distribution of nutrients, sediments, and organic matter, which are essential for the functioning of ecosystems.

Weathering and Contaminant Transport: Water plays a significant role in weathering processes, such as erosion and dissolution of rocks and minerals. It also acts as a carrier for contaminants, pollutants, and nutrients, influencing their transport through the environment.

Energy Balance: Water has a high heat capacity, which means it can absorb and store large amounts of heat energy. This property helps regulate the Earth's temperature and climate by transporting heat through evaporation, condensation, and precipitation.

Greenhouse Gas: Water vapor is a major greenhouse gas that contributes to the Earth's natural greenhouse effect. It absorbs and re-emits thermal radiation, trapping heat in the atmosphere. Approximately 80% of the atmospheric greenhouse effect is attributed to water vapor.

Life: Water is vital for supporting life on Earth. It provides a habitat for numerous organisms and serves as a medium for various biological processes. Terrestrial life forms, including plants, animals, and humans, rely on water availability for their survival, growth, and reproduction.

It is important to note that while water is critical for most terrestrial life forms, human beings have developed technologies and systems that allow them to inhabit regions with limited water availability. However, water still remains a fundamental resource for human societies, and the hydrologic cycle plays a crucial role in ensuring its availability and sustainability.

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Answer:

Step-by-step explanation:

(t-3)^5 is the same as (t + (-3))^5

First:  t starts at the highest power and goes down and (-3) starts at the lowest power and goes up

Second: from the Pascal triangles take the coefficients  1  5  10  10  5  1

\(1*t^{5} (-3)^{0} + 5*t^{4} (-3)^{1} +10*t^{3} (-3)^{2} +10*t^{2} (-3)^{3} +5*t^{1} (-3)^{4} +1*t^{0} (-3)^{5}\)

Anything to power 0 is equal to 1

Negative number to an odd power is negative, to a even power is positive

\(t^{5} -15t^{4} +90t^{3} -270t^{2} +405t -243\)

Answer:

Step-by-step explanation:

find the semiperiter (1/2 perimeter or L+W)

80 : 2 = 40

now we know that 4z + 2 + 3z + 3 = 40

we solve for z with an equation

4z + 2 + 3z + 3 = 40

7z = 40 - 2 - 3

7z = 35

z = 35 : 7

z = 5

now we find CD

3z + 3 =      (z=5)

3 * 5 + 3 =

15 + 3 =

18

-------------------------------

check (remember pemdas)

4z + 2 + 3z + 3 = 40

4*5+2+3*5+3 = 40

20+2+15+3=40

40 = 40

the answer is good

Answer:

Translation: Shift the entire triangle 6 units to the left and 5 units down.

Dilation: Enlarge the triangle by a factor of 4.

Step-by-step explanation:

To describe how triangle FGH can be transformed to triangle F'G'H' in two steps, we need to identify the specific transformations applied.

Translation:

The first step involves a translation, where the entire triangle is shifted by a certain amount horizontally and vertically. To determine the translation vector, we subtract the coordinates of corresponding vertices from F'G'H' from those of FGH.

Translation vector = (x-coordinate difference, y-coordinate difference) = ((-8) - (-2), (-4) - 1) = (-6, -5)

So, the translation vector is (-6, -5), indicating that the triangle is shifted 6 units to the left and 5 units down.

Dilation:

The second step involves a dilation, which changes the size of the triangle. To determine the dilation factor, we can compare the lengths of corresponding sides.

The length of side FG is given by the distance formula:

FG = sqrt((x2 - x1)^2 + (y2 - y1)^2) = sqrt((-3 - (-2))^2 + (3 - 1)^2) = sqrt(1^2 + 2^2) = sqrt(5)

The length of side F'G' is given by the distance formula as well:

F'G' = sqrt((x2 - x1)^2 + (y2 - y1)^2) = sqrt((-12 - (-8))^2 + (-12 - (-4))^2) = sqrt(4^2 + 8^2) = sqrt(80) = 4sqrt(5)

The dilation factor is the ratio of the corresponding side lengths:

Dilation factor = F'G' / FG = (4sqrt(5)) / sqrt(5) = 4

The dilation factor is 4, indicating that the triangle is enlarged by a factor of 4.

Answer:

66

Step-by-step explanation:

Kindly, check below

1) As we can see, this is a piecewise function. So, let's plot that accordingly to each interval.

2) So, we can represent that this way:

Note that the open dot does not include the endpoint. And closed dots include the endpoints.

Thus, this is the answer.

Answer: You would add 9/4

Step-by-step explanation: To complete the square, you first remove the constant from the left side and move it to the right, so subtract 20 on each side . Then, divide the coefficient to the second term by two and square that answer (3/2)^2. Add that new term to both sides and viola! Your square is completed.

Answer:

6n^3

Step-by-step explanation:

3/3 *9^10/453*7+sqrt175

The polynomial expression is \($B=6 n^{3}\) ; where, \(\quad n \neq 0\).

Given:

\($\frac{n^{2}+12 n+27}{3 n^{3}+9 n^{2}} \div \frac{2 n^{2}+18 n}{B}=1$\)

To find:

the value of B is a polynomial expression.

Step 1

Let, \($\frac{n^{2}+12 n+27}{3 n^{3}+9 n^{2}} \div \frac{2 n^{2}+18 n}{B}=1$\)

\($\frac{\frac{n^{2}+12 n+27}{3 n^{3}+9 n^{2}}}{\frac{2 n^{2}+18 n}{B}}=1$$\)

Simplifying the above equation as

\($\frac{\frac{n^{2}+12 n+27}{3 n^{3}+9 n^{2}}}{\frac{2 n^{2}+18 n}{B}}: \frac{B}{6 n^{3}}$\)

then, we get

\($\frac{B}{6 n^{3}}=1$$\)

Step 2

Multiply both sides by \($6 n^{3}$\), then we get

\($\frac{B}{6 n^{3}} \cdot 6 n^{3}=1 \cdot 6 n^{3} $$\) where, \(\quad n \neq 0\)

Simplifying the equation as

\($B=6 n^{3}\) ; where, \(\quad n \neq 0\)

The value of \($B=6 n^{3}\) ; where, \(\quad n \neq 0\).

Therefore, the polynomial expression is \($B=6 n^{3}\) ; where, \(\quad n \neq 0\).

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A Poisson random variable represents the number of occurrences of an event in a fixed interval of time or space. It is a discrete random variable, which means that it can only take on integer values, starting from zero. Therefore, the smallest numerical value that a Poisson random variable can be is zero.

This means that there is a possibility that the event will not occur at all during the given interval. For example, if we are counting the number of customers who visit a store in an hour, it is possible that no customers show up during that hour, resulting in a Poisson random variable of zero.

However, the probability of this occurring depends on the average rate of the event occurring, which is denoted by the parameter λ in the Poisson distribution. The larger the value of λ, the smaller the probability of a Poisson random variable being zero.

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sum_{k=2}^{26}\binom{26}{k}

To find out the value of the given expression, we will use the Vander monde's Identity which is as follows;\[\binom{m+n}{r} = \sum_{k=0}^r\binom{m}{k}\binom{n}{r-k}\]On comparing this with the given expression, we see that $m=n=26$, and $r=0, 1, 2, \cdots, 26$.Now we substitute these values in the given expression.\[\begin{aligned} 22\binom{26}{0} 21\binom{26}{1} 20\binom{26}{2} \cdots (-3)\binom{26}{25} (-4)\binom{26}{26} & = 22\binom{26}{26} - 21\binom{26}{25} + 20\binom{26}{24} - \cdots -3\binom{26}{3} + (-4)\binom{26}{2} \\ &= \binom{26}{26} - \left(\binom{26}{24} - \binom{26}{25}\right) + \left(\binom{26}{22} - \binom{26}{23}\right) - \cdots - \left(\binom{26}{4} - \binom{26}{3}\right) + \binom{26}{2} \\ &= \binom{26}{26} + \binom{26}{25} + \binom{26}{24} + \binom{26}{23} + \cdots + \binom{26}{4} + \binom{26}{3} + \binom{26}{2} \\ &= \sum_{k=2}^{26}\binom{26}{k} \end{aligned}\]Thus, we obtain $\sum_{k=2}^{26}\binom{26}{k}$ as the simplified value of the given expression.

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Answer:6

Step-by-step explanation:

Subtract the three 1 point shots

Subtract the four 3 point shots

You are left with 12, and you split that in 2 because they're 2 point shots.

The calculated length of each side of the door is 2(3y - 2)

From the question, we have the following parameters that can be used in our computation:

Door = isosceles right triangle

Area = 18y² - 24y + 8

Represent the length of each side of the door with x

So, we have

Area = 1/2x²

Substitute the known values in the above equation, so, we have the following representation

1/2x² = 18y² - 24y + 8

This gives

x² = 36y² - 48y + 16

Factorize

x² = 4(3y - 2)²

So, we have

x = 2(3y - 2)

This means that the length of each side of the door is 2(3y - 2)

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From the matrix, The value of the variable ellipse_area is 5\(\pi\) / 3.

Find a matrix such that the linear transformation defined by T(x)=Ax sends the unit circle to the ellipse E. Save the matrix as a numpy array called ellipse_matrix, and then use the matrix to compute the area of E, and save its value as a variable ellipse_area.

To solve this problem, we first need to find the matrix A that sends the unit circle to the given ellipse. We know that T(x) = Ax, and we want T(x) to send the points on the unit circle to the points on the ellipse. We can use the equations of the unit circle and the ellipse to find the matrix A.

The unit circle can be represented as

\(x^2 + y^2 = 1.\)

We can use the fact that x = cos(\(\theta\)) and y = sin(\(\theta\)) to substitute for x and y in the equation of the unit circle.

This gives us \(cos^2(\theta) + sin^2(\theta) = 1,\) which is a familiar trigonometric identity.

The given ellipse can be represented as

\((x^2 / (5/3)^2) + (y^2 / 1^2)\) = 1,

or equivalently as

\((3x^2 / 5^2) + y^2\) = 1.

Again, we can substitute for x and y using x = cos(\(\theta\)) and y = sin(\(\theta\)).

This gives us \((3/5^2)cos^2(\theta) + sin^2(\theta) = 1.\)

Comparing these two equations, we see that we can send the points on the unit circle to the points on the ellipse by scaling the x-coordinate by 3/5 and leaving the y-coordinate unchanged. Therefore, the matrix A that sends the unit circle to the given ellipse is:

[[3/5, 0],

[0, 1]]

To compute the area of the ellipse, we need to find the lengths of the semi-major and semi-minor axes, which are a = 5/3 and b = 1. Then, the area of the ellipse is given by the formula:

area = \(\pi\)* a * b

        = \(\pi\) * (5/3) * 1

        = 5\(\pi\) / 3

Therefore, the value of the variable ellipse_area is 5\(\pi\) / 3.

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Answer:

I can't understand your language

Answer:

4 quarts

Hope it helps!

Step-by-step explanation:

Answer: 5 gallons= 20 quarts

              1 gallon = 4 quarts

Answer:

x-y=4

Step-by-step explanation:

Answer:

2,736

Step-by-step explanation:

Answer:

945 cells

Step-by-step explanation:

Number of cells in container = 315

Scientist expects the number of cells to triple in one day

Hence the expected number of cells after one day will be :

3 * number of cells in container

3 * 315

= 945 cells

Answer:165degrees

Step-by-step explanation

Use formula N-2 × 180 N is the number of sides

24-2=22

22x180=3960 total

for each angle divide total by 24=165 degrees

Answer:

C=39

Step-by-step explanation:

180=sum of angles in a triangle

67+74+C=180

141+C=180

C=180-141

C=39

The ball will hit the ground after 4 seconds (x2 = 4).

Given the formula h(x) = -16x^2 + v0x + h0, we can plug in the values for the initial velocity (v0) and the initial height (h0) to find the equation that describes the ball's height as a function of time.

v0 = 64 ft/s (initial velocity)

h0 = 12 ft (initial height)

Now, we can write the function for the ball's height:

h(x) = -16x^2 + 64x + 12

To find when the ball hits the ground, we need to solve for x when h(x) = 0:

0 = -16x^2 + 64x + 12

This is a quadratic equation, and we can solve it using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

In this case, a = -16, b = 64, and c = 12.

x = (-64 ± √(64^2 - 4*(-16)12)) / 2(-16)

First, we find the discriminant (b^2 - 4ac):

64^2 - 4*(-16)*12 = 4096 + 768 = 4864

Now we can plug the discriminant back into the quadratic formula:

x = (-64 ± √4864) / (-32)

We have two possible solutions:

x1 = (-64 + √4864) / (-32)

x1 = (-64 + 64) / (-32)

x1 = 0

x2 = (-64 - √4864) / (-32)

x2 = (-64 - 64) / (-32)

x2 = 128 / 32

x2 = 4

Since x1 = 0 represents the initial time when the ball is kicked, we discard this solution.

Therefore, the ball will hit the ground after 4 seconds (x2 = 4).

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The height, in feet, after x seconds of an object launched straight up can be found by the function h(x)=−16x2+v0x+h0, where v0 is the initial velocity of the object and h0 is the initial height.

A ball is kicked straight up into the air from a height of 12 ft with an initial velocity of 64 ft/s. After how many seconds does the ball hit the ground?

The mathematical expression y(x,t) = Asin(kx)sin(wt) provides a way to describe the behavior of a standing wave in terms of its amplitude, frequency, and location along the string.

At time t=0,

the standing wave can be mathematically expressed as

y(x,0) = Asin(kx)sin(w*0) = Asin(kx)sin(0) = 0.

This means that the displacement of the string is zero at time t=0.

However, it is important to note that this does not mean that the string is not moving at all. Rather, it means that the string is in a state of equilibrium at time t=0, with the maximum transverse displacement being A.

As time progresses, the standing wave will oscillate between the maximum positive and negative transverse displacement values, creating a pattern of nodes (points of zero displacements) and antinodes (points of maximum displacement).

The wave number k and angular frequency w are both constants that are dependent on the physical properties of the string and the conditions under which the wave is being produced.

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Answer:

750 miles

Step-by-step explanation:

25+0.05x=40+0.03x

0.02x=15

x=750

Answer: v = 40mm * 25mm * 2mm = 2000 mm^3 so, the weight is 2000 mm^3 * .0005oz/1mm^3 = 1oz

Step-by-step explanation:

A 95% confidence interval for the proportion of all the registered voters who will vote for trump is  (0.25, 0.34).

What is a random sample?

A simple random sample is a subset of people chosen at random from a larger group, all of whom were chosen with the same probability. It is a method of choosing a sample at random.

Here, we have

Given, n = 400

x = 120

95% of confidence interval = z = 1.96

p = 120/400 = 0.3

Now by applying the confidence interval formula, we get

= 0.3 ± 1.96(√{0.3(1-0.3)}/400)

= 0.3 ± 0.0449

= (0.25, 0.34)

Hence,  a 95% confidence interval for the proportion of all the registered voters who will vote for trump is  (0.25, 0.34).

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Answer: B

Step-by-step explanation:

It already is in standard form.

The equation in standard form is: 5x^5 + 10x^3 + 30x + 1.

To write the equation in standard form, we need to arrange the terms in descending order of exponents and remove any fractions.

The given equation is:

x^5 + 2x^3 + 6x + 1/5

To eliminate the fraction, we can multiply the entire equation by 5:

5(x^5 + 2x^3 + 6x + 1/5)

This simplifies to:

5x^5 + 10x^3 + 30x + 1

So the equation in standard form is:

5x^5 + 10x^3 + 30x + 1.

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Answer:

A' = (-6, -2)

Step-by-step explanation:

A is at ( -3,-1)

The dilation factor is 2 so multiply by 2

A' = (-3*2, -1*2)

A' = (-6, -2)

Answer:

(- 6, - 2)

Step-by-step explanation:

A is at (- 3, - 1)

2(- 3, - 1)

(- 6, - 2)