Which line has a slope of 3 anday-intercept of 4?

9514 1404 393

Answer:

  y = -9x +49

Step-by-step explanation:

The slope of line b is the same as the slope of line a. That can be found using the slope formula:

  m = (y2 -y1)/(x2 -x1)

  m = (-1 -8)/(2 -1) = -9

The y-intercept can be found from the given point using the formula ...

  b = y - mx

  b = 13 -(-9)(4) = 13 +36 = 49

Then the slope-intercept equation of line b is ...

  y = -9x +49

Using implicit differentiation dy/dx = -(2x + y)/(x + 2y) and d2y/dx² = -2(x² - 3xy - y²)/(x + 2y)³.

Implicit differentiation is the process of differentiating an equation in which it is not easy or possible to express y explicitly in terms of x.

Given the equation x² + xy + y² = 5,

we can differentiate both sides with respect to x using the chain rule as follows:

2x + (x(dy/dx) + y) + 2y(dy/dx) = 0

Simplifying this equation yields:

(x + 2y)dy/dx = -(2x + y)

Hence, dy/dx = -(2x + y)/(x + 2y)

Next, we need to find d^2y/dx^2 by differentiating the expression for dy/dx obtained above with respect to x, using the quotient rule.

That is:

d/dx(dy/dx) = d/dx[-(2x + y)/(x + 2y)](x + 2y)d^2y/dx² - (2x + y)(d/dx(x + 2y))

= -(2x + y)(d/dx(x + 2y)) + (x + 2y)(d/dx(2x + y))

Simplifying this equation yields:

d2y/dx² = -2(x² - 3xy - y²)/(x + 2y)³

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The domain of the relation S is the set of all x-values from the ordered pairs in the relation. In this case, the given ordered pairs are (3, p), (3, 0), (4, g), and (1, 4).

To find the domain, we collect all the unique x-values from these ordered pairs.

From the given pairs, we have x = 3, x = 4, and x = 1. However, note that (3, p) and (3, 0) have the same x-value of 3. When considering the domain, we only need to list unique x-values.

Therefore, the domain of the relation S can be expressed as:

domain = {1, 3, 4}

Moving on to the range of the relation S, it refers to the set of all y-values from the ordered pairs.

From the given pairs, we have y = p, y = 0, y = g, and y = 4. Similarly, we need to consider only unique y-values when determining the range.

Thus, the range of the relation S can be expressed as:

range = {0, 4, g, p}

It's important to note that the specific values of g and p are not given in the question. So, in the range, g and p are considered as distinct symbols representing unknown values.

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Answer:

y = 6.3x + 5

Step-by-step explanation:

The balloon starts at a position of 5ft


The balloon then increases in height by 6.3 feet per second, so simply multipling x(amount of seconds) by 6.3 will give you your height after x seconds.

Answer:

46.8 cm

Step-by-step explanation:

A hexagon has six sides. If it is a regular hexagon, then it is equilateral, meaning that each side is the same length. If one side is 7.8cm, then all sides will be 7.8cm. You can find the perimeter by adding 7.8 six times, or multiplying 7.8 by six.

7.8 · 6 = 46.8

hope this helps!

Answer:

1. 30 in

2. 273 mi

3. 248 m

Step-by-step explanation:

For the first circle, you are given the radius. Multiply that by 2 in order to get 30.

For the second circle, you are given the diameter. Divide that by 2 to get 273.

For the third circle, you are given the radius. Multiply that by 2 in order to get 248.

Answer:

(x - 5)² + (y + 6)² = 16

Step-by-step explanation:

assuming you require the equation of the circle

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r is the radius

here (h, k ) = (5, - 6 ) and r = 4 , then

(x - 5)² + (y - (- 6) )² = 4² , that is

(x - 5)² + (y + 6)² = 16

Answer:

0.9851 = 98.51% probability that the person is actually infected.

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

\(P(B|A) = \frac{P(A \cap B)}{P(A)}\)

In which

P(B|A) is the probability of event B happening, given that A happened.

\(P(A \cap B)\) is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Positive test

Event B: Infected

Probability of a positive test:

99% of 25%(People have the disease).

0.5% of 100 - 25 = 75%(People do not have the disease). So

\(P(A) = 0.99*0.25 + 0.005*0.75 = 0.25125\)

Probability of a positive test and being infected:

99% of 25%, so:

\(P(A \cap B) = 0.99*0.25 = 0.2475\)

What is the probability that the person is actually infected?

\(P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.2475}{0.25125} = 0.9851\)

0.9851 = 98.51% probability that the person is actually infected.

The answer would be

50-22.50=d

Answer:

F(-5)=25

Step-by-step explanation:

Hi there!

We are given the function:

F(x)=-x²-10x

And we want to find F(-5)

If we want to find f(number), then we will be substituting that number as x into the other side of the function.

In other words, if the function is F(-3), then we would substitute -3 as x in the function, giving us -(-3)²-10(-3)

So for this, we'll substitute -5 as x in the function.

Therefore:

F(-5)=-(-5)²-10(-5)

Going with the order of operations, raise (-5) to the second power

F(-5)=-(25)-10(-5)

Now multiply 25 by -1 (the minus in front of the 25 means -1 * 25)

F(-5)=-25-10(-5)

Multiply -10 by -5

F(-5)=-25 + 50

Add the numbers together

F(-5)=25

Hope this helps!

Value of base and hypotenuse of triangle are 9√3 and 18 respectively.

A right triangle is a triangle with one interior angle measuring 90 degrees, known as a right angle. The side opposite to the right angle is called the hypotenuse, and the other two sides are known as the legs of the right triangle. The length of the hypotenuse can be found using the Pythagorean theorem,  that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs.

Height of triangle=9

Base of triangle=y

Hypotenuse of triangle=x

Using trigonometric ratio

Sin30°=Height/Hypotenuse

½=9/x

x=18

Cos30°=Base/hypotenuse

√3/2=y/18

y=9√3

Hence, value of base and hypotenuse of triangle are 9√3 and 18 respectively.

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Answer:

20 units

Step-by-step explanation:

Because it is 25 per unit, and 500, you can do 500/25=20

Answer:

Option (3)

Step-by-step explanation:

Given function is,

f(x) = 3x² - 2x

     = \(3(x^{2} -\frac{2}{3}x)\)

     = \(3(x^{2} -\frac{2}{3}x+\frac{1}{9}-\frac{1}{9})\)

     = \(3(x^{2}-\frac{2}{3}x+\frac{1}{9})-\frac{1}{3}\)

     = \(3(x-\frac{1}{3})^2-\frac{1}{3}\)

Vertex of the parabola → \((\frac{1}{3},-\frac{1}{3})\)

Here, leading coefficient is positive (+3),

Therefore, parabola will open upwards.

In a parabola opening upwards function decreases from negative infinity to the x value of the vertex.

Function will decrease in the interval (-∞, \(\frac{1}{3}\)).

Option (3) will be the answer.

Answer:

x > 1

Step-by-step explanation:

6x + 14 > 20

      -14    -14

6x > 6

/6    /6

x>1

Answer:

Matched samples

Step-by-step explanation:

A matched sample is obtained when pairing of treatment values for each subject or observation is performed. This sample obtained from a matched pair is usually called dependent sample and is usually done when each subject in an experiment is subjected to two different treatments usually at different time or stage. Hence, matched samples are used in matching observations to tie different groups.

Answer:

32

Step-by-step explanation:

A=wl=4·8=32

Answer:

47° c

Step-by-step explanation:

using the absolute value function to find the difference, that is

difference = | 42 - (- 5) | = | 42 + 5 | = | 47 | = 47

or

difference = | - 5 - 42 | = | - 47 | = 47

Answer:

D.

Hope this helps!

Step-by-step explanation:

A and C are both squares and B is a rectangle but is different because the values are in different spots than the on the solid figure shown.

The best-predicted height for someone with a foot length of 20.4 cm is approximately 65.83 cm.

To find the best-predicted height for someone with a foot length of 20.4 cm, we need to use the linear regression equation that relates foot length and height. The linear regression equation is of the form:

y = a + bx

where y is the predicted height, x is the foot length, a is the y-intercept, and b is the slope of the regression line.

From the given information, we know that the technology found a linear correlation between height and foot length. This means that we can use the paired data to calculate the values of a and b in the regression equation.

Using the paired data and technology, we can obtain the following regression equation:

height = 34.774 + 1.4966 (foot length)

Now we can substitute the given foot length of 20.4 cm into the equation to obtain the predicted height:

height = 34.774 + 1.4966 (20.4)

height = 65.83 cm

Therefore, the best-predicted height for someone with a foot length of 20.4 cm is approximately 65.83 cm.

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In light of this, 1,0,8 is the value of the function h(x) = (x+1)2 where h is defined for all real integers.

The subject of mathematics includes quantities and their variations, equations and related structures, forms and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A relationship between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, within functions, and on functions.

given

h(x) = (x+1)²

h(-2) = 1

h(-1) = 0

h(3) = 8

In light of this, 1,0,8 is the value of the function h(x) = (x+1)2 where h is defined for all real integers.

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Regression equation correctly models the data is: y = -43.98x + 1,279.93

To determine the regression equation that correctly models the data, we can use the method of linear regression. The regression equation for a straight line is generally expressed as y = mx + b, where m is the slope and b is the y-intercept.

Using the given table, we can calculate the necessary values to determine the regression equation. Let's denote the sigma notation as Σ.

The slope (m) can be calculated using the formula:

\(m = (Σxy - (Σx)(Σy) / n(Σx^2) - (Σx)^2)\)

Plugging in the values from the table:

m =\((776,600 - (299)(12,400) / 6(18,109) - (299)^2)\)

m = (776,600 - 3,708,800 / 6(18,109) - 89,401)

m = (-2,932,200 / 66,654)

m ≈ -43.98

The y-intercept (b) can be calculated using the formula:

b = (Σy - m(Σx)) / n

Plugging in the values from the table:

b = (12,400 - (-43.98)(299)) / 6

b ≈ 1,279.93

The correct regression equation that models the data is:

y = -43.98x + 1,279.93

Out of the given options, the correct regression equation is:

y = -43.98x + 1,279.93

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Answer:

Step-by-step explanation:

To check whether the given credit card number is valid or not, we need to apply the Luhn algorithm or the mod-10 algorithm. The Luhn algorithm works by adding up all the digits in the credit card number and checking if the sum is divisible by 10 or not. If it is, then the credit card number is considered valid, otherwise, it is invalid.

Let's apply the Luhn algorithm to the given credit card number:

Step 1: Starting from the rightmost digit, double every second digit

| 5 | 4 | 2 | 4 | 9 | 8 | 1 | 3 | 2 | 7 | 2 | 0 | 0 | 0 | 8 | 5 |

|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

| | 8 | | 8 | | 16| | 6 | | 14| | 0 | | 0 | | 10|

Step 2: If the doubled value is greater than 9, add the digits of the result

| 5 | 4 | 2 | 4 | 9 | 8 | 1 | 3 | 2 | 7 | 2 | 0 | 0 | 0 | 8 | 5 |

|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

| | 8 | | 8 | | 7 | | 6 | | 5 | | 0 | | 0 | | 1 |

Step 3: Add up all the digits in the credit card number, including the check digit

5 + 4 + 2 + 4 + 9 + 8 + 1 + 3 + 2 + 7 + 2 + 0 + 0 + 0 + 8 + 5 + 1 = 61

Step 4: If the sum is divisible by 10, then the credit card number is valid, otherwise, it is invalid.

61 is not divisible by 10, therefore the given credit card number is invalid.

Hence, it can be concluded that 5424 9813 2720 0085 is an invalid MASTERCARD credit card number.

Answer: I think that the answer is 3/4 miles

Step-by-step explanation:

Answer:

what does this mean??

Step-by-step explanation:

Answer:

45 × 1/3 = 15

Step-by-step explanation:

15 / (1/3) = (3×15)/1 = 45

so, from 15 / (1/3) = 45

we can then adapt the equation by multiplying both sides by 1/3

15 = 45 × (1/3)

Answer: the last option is correct

Step-by-step explanation:Using the formulas for converting Cartesian coordinates to polar coordinates:

r = √(x^2 + y^2)

θ = atan2(y, x)

where x and y are the Cartesian coordinates, r is the distance from the origin to the point, and θ is the angle between the positive x-axis and the line connecting the origin to the point.

Given the Cartesian coordinates (x, y) = (-7√3/2, 7/2), we can substitute these values into the formulas:

r = √((-7√3/2)^2 + (7/2)^2)

θ = atan2(7/2, -7√3/2)

Simplifying the expressions:

r = √(147/4 + 49/4) = √(196/4) = √49 = 7

θ = atan2(7/2, -7√3/2)

Using a calculator or reference table to find the arctangent of 7/2 divided by -7√3/2, we get:

θ ≈ 5π/6

So the correct answer is: (7, 5π/6), which is option (6).

Answer:

0.53 x 10^ -8

Step-by-step explanation:

Just move the decimal over to the right and add 1 to the exponent.

The probability of their first child having green eyes is 0.125, and the probability of their second child not having them is 0.875.

Probability is an estimate of how likely an occurrence is to occur. It's a figure between 0 and 1, where 0 means the event is unlikely and 1 means the event is certain. A likelihood of 0.5 (or 50%) indicates that the occurrence has an equal chance of occurring or not occurring.

In the given question,

a) The probability of their first child having green eyes is 0.125. The probability of their second child not having green eyes is 1 - 0.125 = 0.875. Therefore, the probability that their first child will have green eyes and the second will not is 0.125 x 0.875 = 0.1094.

b) The probability of exactly one of their two children having green eyes can be calculated in two ways: either the first child has green eyes and the second doesn't, or the first child doesn't have green eyes and the second does. The probability of the first scenario was calculated in part (a) to be 0.1094, and the probability of the second scenario is the same, so the total probability is 2 x 0.1094 = 0.2188.

c) The probability of exactly two out of six children having green eyes can be calculated using the binomial distribution with n = 6, p = 0.125, and k = 2. The formula for this probability is:

P(k=2) = (6 choose 2) x \(0.125^2 x (1 - 0.125)^4\) = 0.1936

where (6 choose 2) = 6!/(2!4!) = 15 is the number of ways to choose 2 children out of 6.

d) The probability of at least one of their six children having green eyes is the complement of the probability that none of them do. The probability that any one child doesn't have green eyes is 1 - 0.125 = 0.875, so the probability that none of the six children have green eyes is \(0.875^6\) = 0.1779. Therefore, the probability that at least one of their six children has green eyes is 1 - 0.1779 = 0.8221.

e) The probability that the first green-eyed child will be the fourth child is the probability that the first three children do not have green eyes, multiplied by the probability that the fourth child has green eyes, multiplied by the probability that the fifth and sixth children do not have green eyes. The first three children have a probability of \((1-0.125)^3\) = 0.578 to not have green eyes. The fourth child has a probability of 0.125 to have green eyes. The probability that the fifth and sixth children do not have green eyes is \((1-0.125)^2\) = 0.765625. Therefore, the probability that the first green-eyed child will be the fourth child is 0.578 x 0.125 x 0.765625 = 0.0557.

f) It would depend on the context and the specific definition of "unusual." If the expected number of brown-eyed children is 0.75 x 6 = 4.5, then having only 2 out of 6 children with brown eyes is below average. However, the probability of this exact outcome can be calculated using the binomial distribution with n = 6 and p = 0.75:

P(k=2) = (6 choose 2) x \(0.75^2 x (1 - 0.75)^4\) = 0.0986

where (6 choose 2) = 6!/(2!4!) = 15 is the number of ways to choose 2 children out of 6. This probability is not very low (less than 10%), so it might not be considered unusual in a statistical sense.

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Answer:

y=.60x

Step-by-step explanation:

where y is the amount of money Julie can expect to pay

where x is the amount of tomatoes she is buying

i dont understand what the key means, but this would be the appropriate model for this problem

Can i get brainliest please?