Write the equation of a line given its slope,m=6 and its y-intercept, b=-5

Answer: [tex]\left(-\frac{5}{13}, \frac{1}{13}\right)[/tex]

Step-by-step explanation:

The shortest distance from a point to a line is the perpendicular distance. The origin is essentially a point with coordinates (0,0); hence, we have to find the equation of the line that's both perpendicular to [tex]y=5x+2[/tex] and crosses the origin.

We can do this by recognizing that slope of a perpendicular line is the opposite reciprocal of the slope of the original line.

Opposite Reciprocal of 5: [tex]-\frac{1}{5}[/tex]

Now that we have the slope and the point, we can use the point-slope form to get the equation of the perpendicular.

Point-Slope Form: [tex]y-y_1=m(x-x_1)[/tex] (m is slope, [tex]x_1[/tex] and [tex]y_1[/tex] are the point's coordinates)

[tex]y-0=-\frac{1}{5}(x-0)\\y=-\frac{1}{5}x[/tex]

Since we need to find a point on the original line that's closest to the origin, we need to find the intersection of the line and its perpendicular. We can do this by setting both lines equal to each other and solving for x and y.

[tex]5x+2=-\frac{1}{5}x\\25x+10=-x\\26x=-10\\x=-\frac{10}{26}\\x=-\frac{5}{13}[/tex]

Substituting x in any of the equations will give us y. Here, I will put it in the equation [tex]y=-\frac{1}{5}x[/tex]

[tex]y=-\frac{1}{5}*-\frac{5}{13}\\y=\frac{5}{65}\\y=\frac{1}{13}[/tex]

The closest point to the origin on the line [tex]y=5x+2[/tex] is [tex]\left(-\frac{5}{13}, \frac{1}{13}\right)[/tex]

The point on the line y = 5x + 2 that is closest to the origin is (-5/13, 1/13).

The point slope form is used to find the equation of the straight line which is inclined at a given angle to the x-axis and passes through a given point.

The given equation of a line is y=5x+2 ------(I)

The shortest distance from a point to a line is the perpendicular distance. The origin is essentially a point with coordinates (0,0); hence, we have to find the equation of the line that's both perpendicular to y=5x+2 and crosses the origin.

We can do this by recognizing that slope of a perpendicular line is the opposite reciprocal of the slope of the original line.

So, slope of perpendicular line is -1/5

The equation of the point slope form is: (y - y1) = m(x - x1)

Now, substitute m=-1/5 and (x, y)=(0, 0), we get

y-0=-1/5 (x-0)

y=-1/5 x -----(II)

Equate equation (I) and (II), we get

5x+2=-1/5 x

⇒ -x=25x+10

⇒ -26x=10

⇒ x= -5/13

So, y=-1/5 x =1/13

Therefore, the point on the line y = 5x + 2 that is closest to the origin is (-5/13, 1/13).

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Answer: Option (1)

Step-by-step explanation:

[tex]4x^4 -38x^3 -17x^2 -30x=0[/tex]

Dividing both sides by [tex]x-10[/tex] (10 is a root, so x-10 is a factor), yields

[tex]4x^3 +2x^2 +3x=0\\\\x(4x^2 +2x+3)=0\\\\x=0, 4x^2 +2x+3=0[/tex]

Solving the second case by the quadratic formula yields [tex]x=\frac{-1 \pm i\sqrt{11}}{4}[/tex].

So, the answer is Option (1).

Given that, the estimated population of Los Angeles in 2019 was 3,979,576 and its  area is 469 square miles, the population density of Los Angeles is  8486 people per square miles.

Population density simply the measurement of population per unit area.

It is expressed as;

Population density = Number of people / Area

Given the data in question;

We substitute the given values into the above equation.

Population density = Number of people / Area

Population density = 3,979,576 people / 469 square miles

Population density = 8485.23667 ≈ 8486 people per square miles

Given that, the estimated population of Los Angeles in 2019 was 3,979,576 and its  area is 469 square miles, the population density of Los Angeles is  8486 people per square miles.

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By applying trigonometric expression and direct comparison, we conclude that a = 2 such cos 255° - cos 195° = √a / 2

In this question we need to simplify a trigonometric expression in order to find the value of a. In this case, we need to use the following formula:

[tex]\cos \theta - \cos \xi = - 2\cdot \sin \left(\frac{\theta + \xi}{2} \right)\cdot \sin \left(\frac{\theta - \xi}{2} \right)[/tex]

Then,

cos 255° - cos 195° = - 2 · sin 225° · sin 30°

cos 255° - cos 195° = - 2 · sin (- 135°) · sin 30°

cos 255° - cos 195° = 2 · sin 135° · sin 30°

cos 255° - cos 195° = 2 · (√2 / 2) · (1/2)

cos 255° - cos 195° = √2 / 2

Then, by direct comparison we find that a = 2.

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Answer:33

Step-by-step explanation: The expressions have equivalent values when x + 6

The expressions have equivalent values for any value of x.

When x=10 , both expressions have a value of 33.

Given that the inequalities and that

x ⇒ pep club donations

y ⇒ represent donations raised by the honor society

The inequality is represented by x + y≥ 500

The solution for this is the shaded area above the solid line.

Given x ≥ 100, this is also indicated by the shaded region to the right

The point (300,100) indicates that the contributions made for the pep club were $300 and the donations raised by the honor society were $100.

The point (300,100) is NOT a feasible solution since it does not conform to the gray area of the system of inequalities solution.

To proof the above,

Let x = 300; and y = 100

Plugin in both values in the inequalities we have:

300 + 100 [tex]\ngeq[/tex] 500

400 [tex]\ngeq[/tex] 500 ; Hence it is NOT true; also

300 [tex]\ngeq[/tex] 500.

The point (500,200) indicates that the contributions raised for the pep club were $500 and the donations raised by the honor society were $200.

The point (500,200) IS A possible solution since it falls inside the darkened area of the system of inequalities solution.

To proof the above,

Let x = 500; and y = 200

Plugin in both values in the inequalities we have:

500 + 200 ≥ 500

700 ≥ 500; hence, this is true and it is safe to indicate that the ordered pair satisfies the inequality A.

Conclusion:
The point (500, 200) is a viable solution.

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Percent of the total was spent on veterinary​ care is 31.3186% .

Applying simple percentage formula,

let x be the percentage

x=[tex]\frac{17.1}{54.6} \ 100[/tex]

x=31.3186 %

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The graph is shown in the attached image.

The equation of the line is y = -3/2x + 10

The given parameters are:

Slope, m = -3/2

Point, (x, y) = (10, -5)

The line equation is represented as

y = mx + b

Substitute the given parameters in the equation

-5 = -3/2 * 10 + b

This gives

-5 = -15 + b

Add 15 to both sides

b = 10

So, we have:

y = -3/2x + 10

Hence, the equation of the line is y = -3/2x + 10

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Answer:

25/36, or .694444

Step-by-step explanation:

First, let's convert 6" to inches.

That gives us 72. After we convert 4'2" into inches, we get 50.

This means that the diagram goes from 72 inches wide to 50. Put this into a proportion to find the scale factor:

50/72 = 25/36 = .6944444

The common base that can be used to rewrite each side of the equation is 2.

The common base that can be used to rewrite each side of the equation is as follows:

2ˣ⁺³ - 3 = 5

add 3 to both sides

2ˣ⁺³ - 3 + 3 = 5 + 3

2ˣ⁺³ = 8

Hence,

2ˣ⁺³ = 2³

Therefore, the common base that can be used to rewrite each side of the equation is 2.

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Answer:

Step-by-step explanation:

(0,2)

Answer:

Step-by-step explanation

So, the graph goes through the points, (-3,0) and (2,0). 3 points on the graph can be (-3,0), (2,0), and (4,3)

Answer:

A) 6.0

Step-by-step explanation:

First, total amount of hours, since average is sum of the numbers by how many numbers there is.

Day 1=8x2 hr

Day 2=6x1 hr

Day 3=4x2 hr

which is, 16+6+8=30

then divide 30 by how many days there is, which is 5 days.

30/5=6

The correct assignment of digits is D. let 1,3,5,7, and 9 represent flipping heads with a fair coin, and 0,2,4,6, and 8 represent flipping tails with a fair coin, as the probability of heads and tails is 1/2, and that of the assigned digits is 1/2.

In the question, we are given that a researcher uses a random number generator to simulate the results of an experiment and are asked for the appropriate assignment of random digits for its experimental design.

For the assignment to be correct, the probability of the random numbers must be equal to the probability of the experiment.

We analyze each option:

Thus, the correct assignment of digits is D. let 1,3,5,7, and 9 represent flipping heads with a fair coin, and 0,2,4,6, and 8 represent flipping tails with a fair coin, as the probability of heads and tails is 1/2, and that of the assigned digits is 1/2.

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Answer:

1/2×base×height

1/2×8×8

32cm²

Answer:

slope = 11/2

Step-by-step explanation:

If you are given two points, you can find the slope using the point-slope equation. The equation looks like this:

y₁ - y₂ = m(x₁ - x₂)

In this form, "m" represents the slope, "x₁" and "y₁" represent the values from one point, and "x₂" and "y₂" represent the values from the other point. You can plug the values from the points into the equation and simplify to find the slope.

Point 1: (-4, 7)                Point 2: (-6, -4)

x₁ = -4                              x₂ = -6

y₁ = 7                               y₂ = -4

y₁ - y₂ = m(x₁ - x₂)                               <----- Point-slope form

7 - (-4) = m(-4 - (-6))                            <----- Insert values

11 = m(2)                                             <----- Simplify

11/2 = m                                             <----- Divide both sides by 2

[tex]\huge\boxed{\frac{11}{2}}[/tex]

The slope is equivalent to vertical change divided by horizontal change, otherwise known as "rise over run".

Therefore, the slope can be represented with the following equation, where [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are your points:

[tex]\dfrac{y_2-y_1}{x_2-x_1}[/tex]

Substitute the values and simplify to find the answer.

[tex]\dfrac{(-4)-7}{(-6)-(-4)}[/tex]

[tex]\dfrac{-4-7}{-6+4}[/tex]

[tex]\dfrac{-11}{-2}[/tex]

[tex]\boxed{\frac{11}{2}}[/tex]

The inequalty that represents the statement must be y < - 6 · (x + 2)² + 2. (Right choice: None)

The standard form of the equation of the parabola is defined by the following expression:

y - k = C · (x - h)²     (1)

Where:

Now we proceed to find the vertex constant: (h, k) = (- 2, 2) and (x, y) = (- 4, 14)

14 - 2 = C · [- 4 - (- 2)]²

12 = C · (-2)

C = - 6

The equation of the parabola in vertex form is

y - 2 = - 6 · (x + 2)²

y = - 6 · (x + 2)² + 2

Then, the inequalty that represents the statement must be y < - 6 · (x + 2)² + 2. (Right choice: None)

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Answer:

y < 3(x + 2)2 + 2

Step-by-step explanation:

just do it

Answer:

Step-by-step explanation:

Let the age of Abel is x and age of Asare is y.

Three times the age of Abel is four more than the age of Asare:

And

In three years, the sum of their ages will be 30 years:

We got two equations.

Simplify and solve by substitution:

Find y:

Answer:

B. The domain for f(x) is the set {-2, -1, 0, 1, 2, 3, 4, 5, 6}

D. f(-1) = 6

Step-by-step explanation:

The question gives a table marking the different coordinate pairs for a function, where f(x) is y. The top row represents the x-values and the bottom row represents the y-values.

Domain

The domain of a function is the set of x-values that the graph covers. In this case, the x-values are all integers between -2 and 6. We can see this in the top row of the table. Answer choice B best represents this domain.

Solving for F(x)

F(x) represents a specific y-value, for example, f(-1) represents the y-value when x = -1. So, to test choice D, we need to find what y-value matches -1 on the table. The table shows that when x = -1, f(x) = 6. This means that answer choice D must be correct.

The points that represent this data are shown in the image attached below.

A scatter plot is a type of graph which is used for the graphical representation of the values of two variables, with the resulting points showing any association (correlation) between the data set.

Based on the information provided in table above, the points that represent this data are shown in the image attached below.

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Answer:

please look at the picture

the person with the debt ratio that is higher than 18% can be found by dividing the person's debt by their income .

the necessary information is not given so a general explanation will be given.

the debt ratio is found by the formula:
= monthly debt payment / monthly gross income

this figure allows creditors to see if a person can affort to incur more debt based on how much of their gross monthly income is being used to service debt.

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A range of 2 reveals that the smallest and largest data values are 2 units away from each other.

Range is the difference between the highest and lowest values of a set of observations. Range is a measure of variation.

Range = highest value - lowest value

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Answer:

15m

Step-by-step explanation:

Let w be the width, l the length and p the perimeter.

We know, by definition, that p = 2w + 2l. We also know that p = 80m and l = 25m.

So we can re-write the perimeter formula as:

80 = 2w + 50

2w = 30

w = 15m

So we now know that the width is 15m.

The radius of the given cylinder with a volume of 200 mm³ and a height of 17mm is: 1.93 mm.

The formula for finding the volume of any cylinder is given as: πr²h, where r is the radius and h is the height of the cylinder.

Given the following:

Volume = 200 mm³

Height (h) = 17 mm

Radius (r) = ?

Plug the values into the formula for volume

πr²(17) = 200

r² = 200/17π

r² = 3.74

r = 1.93 mm

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The perimeter of the rectangle based on the factors given is 46.

The area of the rectangle is given as (x² + 13x - 90). This will be:

= (x² + 13x - 90)

= x² + 18x - 5x - 90

= x(x + 18) - 5(x + 18)

= (x - 5)(x + 18)

The sides of the rectangle are 5 and 18. The perimeter will be:

= 2(l + w)

= 2(5 + 18)

= 46

The area of the rectangle is given as (x² + 24x - 81.

= (x² + 24x - 81)

= x² + 27x - 3x - 81

= x(x + 27) - 3(x + 27)

= (x - 3)(x + 27)

The sides are 3 and 27. The perimeter will be:

= 2(l + w)

= 2(27 + 3)

= 60

= (x + 1)² + 3(x + 1) + 2

= (x + 1)(x + 1) + 3x + 3 + 2

= x² + x + x + 1 + 3x + 5

= x² + 5x + 6

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Answer:

a = 64°

b = 138.7°

Step-by-step explanation:

First, Let's find the measure a,

______

Now,

______

Now that we found out what x equals, let's find 'b'-

Using conditional probability, it is found that:

[tex]P(A|B^\prime) = \frac{1}{3}[/tex]

Conditional probability is the probability of one event happening, considering a previous event. The formula is:

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which:

For this problem, we are given that:

Then:

[tex]P(A|B^\prime) = \frac{P(A \cap B^\prime)}{P(B^\prime)}[/tex]

[tex]P(A|B^\prime) = \frac{\frac{2}{9}}{\frac{2}{3}}[/tex]

[tex]P(A|B^\prime) = \frac{1}{3}[/tex]

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