How do you find the equation of a vector given the point and direction?

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Explanation:

Pick any two points on the line to apply the slope formula.

I'll select (-5,1) and (5,-1)

[tex](x_1,y_1) = (-5,1) \text{ and } (x_2,y_2) = (5,-1)\\\\m = \text{slope} = \frac{\text{rise}}{\text{run}} = \frac{\text{change in y}}{\text{change in x}}\\\\m = \frac{\text{y}_{2} - \text{y}_{1}}{\text{x}_{2} - \text{x}_{1}}\\\\m = \frac{-1 - 1}{5 - (-5)}\\\\m = \frac{-1 - 1}{5 + 5}\\\\m = \frac{-2}{10}\\\\m = -\frac{1}{5}\\\\[/tex]

The slope as a fraction is -1/5

A slope of -1/5 means " go down 1, then to the right 5 units".

An example of this motion is when going from (-5,1) to (0,0)

Another example would be going from (0,0) to (5,-1)

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The "down 1, right 5" motion is because

Between the 100th and 400th kilometers, the average fuel consumption rate is 5/6 liters per kilometer.

A consequence of dividing the variation in a variable's function by the variation in the variable. For example The rate at which a distance changes in relation to time is known as velocity.

Given, Devin drove her truck. The fuel remaining in the truck's tank (in liters) as a function of distance (in kilometers) is graphed.

Since in the domain [100, 400] graph shows somewhat linear properties.

from the graph Fuel consumption at 100 = 375 liters

Fuel consumption at 400 = 125 liters

rate in a linear function between two points = (y₂ - y₁)/ (x₂ - x₁)

thus rate between [100, 400] = (375-125)/400-100

rate between [100, 400]  = 250/300

rate between [100, 400] = 5/6litere per kilometer

therefore, the average fuel consumption rate, between the 100th kilometer and 400th kilometer is 5/6 liters per kilometer.

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The scale factor of the dilation is 2. An expansion happens when the scaling factor's absolute value exceeds one.

The scale factor is defined as the proportion of the new image's size to that of the previous image. A fixed location in the plane serves as the center of dilatation. The scale factor and the center of dilation are used to determine the dilation transformation. The image stretches if the scaling factor is greater than 1.

As per the rule of scale factor

Q'U'/QU = SF

SF= Scale factor

=    (5+5)/5= Scale factor

=      10/5= 2

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Answer: D

Step-by-step explanation:

In this problem, we are asked to find the domain of the function. Domain is finding the interval of the function of the x value.

Since we are finding domain, we can eliminate A and B because those are looking at y interval, or range.

This leaves us with C and D. They are almost the same except for the ≤ in C and < in D. The difference between ≤ and < is the fact that ≤ includes and touches the point, and < doesn't.

The function has open circles at x=-3 and x=3. That means they don't touch and include x=-3 and x=3. The function only get's really close to those points, but not include them. This tells us that D is the answer.

The domain of the function is {x | −3 < x < 3}. Thus, Option D holds the truth.

The domain of a function refers to the interval of the x values of the function.

In this case, we are asked to find the domain of a linear function that is shown on a graph. The graph starts at an open circle at negative 3, negative 5 and ends at an open circle at 3, 7.

To find the domain, we need to look at the x interval of the function. Options A and B refer to the y interval or range and can be eliminated.

The remaining options, C and D, are similar, except for the fact that C includes and touches the point with "≤", while D doesn't with "<". The open circles at x=-3 and x=3 indicate that the function only gets close to these points, but does not include or touch them.

Thus, the correct answer is option D, {x | −3 < x < 3}.

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The inequality is x ≤ 35, where x represents the amount of gas in gallons.

This question means by the statement that we have been given that the number of gallons cannot exceed 35 so it actually means that they are either 35 or less than 35. so will use < = sign to come up with this equation.

You can have up to 35 gallons of gas at a time at the gas station. The inequality x ≤ 35 represents the fact that x (the amount of gas in gallons) is less than or equal to 35.

This means that the equation will be x≤35

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The correct representations of the inequality expression are (a) 6x – 15 > -10 + 5x and (c) 3(2x – 5) > -5(2 – x)

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

–3(2x – 5) < 5(2 – x)

Divide bot sides of the inequality by -1

So, we have the following representation

3(2x – 5) > -5(2 – x)

Next, we open the brackets

This gives

6x – 15 > -10 + 5x

Hence, the representation is 6x – 15 > -10 + 5x

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Complete question

Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options.

(a) 6x – 15 > -10 + 5x

(b) 6x – 15 < -10 + 5x

(c) 3(2x – 5) > -5(2 – x)

(d) 3(2x – 5) < -5(2 – x)

Here acccording to the question,We are examining the conditions under which the sampling distributions of the sample proportions given.

Sampling distribution is a statistic that determines the probability of an event based on data from a small group within a large population. Its primary purpose is to establish representative results of small samples of a comparatively larger population. Since the population is too large to analyze, you can select a smaller group and repeatedly sample or analyze them. The gathered data, or statistic, is used to calculate the likely occurrence, or probability, of an event.

We are examining the conditions under which the sampling distributions of the sample proportions appear uniform, roughly normal, skewed to the left or skewed to the right.

When np10 and n(1p)10, where n is the sample size and p is the sample of proportions, are true, we know that the sampling proportions of the sample distributions will have a normal shape.

Aforementioned that our sample size is 300 people and that p = 0.45, we can use the given data to calculate

Successes anticipated: np= 300(0.45) = 135 10

Failures predicted: n(1p)=300 (10.45)=165 10

Since both of these statements are accurate, sample distribution sampling proportions will have a normal shape.

Because we anticipate each sample to have at least 10 successes and 10 failures, we have a normal sampling distribution.

As a result, the sample distribution has a roughly normal shape.

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Answer:2

Step-by-step explanation:

The volume of the cone is 50π cubic units .

A cone is a three-dimensional geometric shape that tapers smoothly from a flat base to a point called the apex or vertex. A cone is formed by a set of line segments, half-lines, or lines connecting a common point, the apex, to all of the points on a base that is in a plane that does not contain the apex.

A cone has a circular base.

A cone has no edges, one face, and one vertex.

The length of the line segment from a cone's apex to any point around the circle of the cone's base is known as the slant height of the cone.

A right circular cone is a cone with its apex perpendicular to the base of the cone and directly above it.

An oblique cone is one that doesn't have its apex precisely over the base's circle.

Radius of the cone = 5

Height of the cone is 6

Volume of the cone = [tex]\frac{1}{3}\pi r^{2} h[/tex] = [tex]\frac{1}{3}\pi *5^{2}* 6 = 50\pi[/tex] cubic units.

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Answer:

Step-by-step explanation: If the sides are a,b,c (in ascending order) and c squared = the sum of the squares of a and b, then it's a right triangle.

Answer:

No, it is not a right triangle.

Step-by-step explanation:

Right triangle fulfill the pythagorean theorem:

[tex]a^2+ b^2 = c^2[/tex]

Where, c is the hypothenuse or the longest side, and b and a are the remaining two sides.

[tex]12^{2} = 144\\16^2 = 256\\256 + 144 = 400\\\sqrt {400} = 20 \neq 18[/tex]

Answer:

slope = 2

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 1, 0) and (x₂, y₂ ) = (1, 4) ← 2 points on the line

m = [tex]\frac{4-0}{1-(-1)}[/tex] = [tex]\frac{4}{1+1}[/tex] = [tex]\frac{4}{2}[/tex] = 2

Answer: The slope is 2.

Step-by-step explanation: To find the slope of a line, we first need to pick two points on a line. To solve this, I picked points (-2, -2) and (1, 4). The slope is rise over run, so you need to find the rise and run and divide.

We need to go 6 spaces up from (-2, -2) to get to (1, 4). This is our rise. Then, we go 3 spaces to the right. That is our run. 6 / 3 is 2, so that's your slope. Notice that if you cannot divide the rise and run into a whole number, keep it as a fraction instead.

Let me know if this is right! :)

NA (There is not enough information given to determine the value of MZ)

In this question, we are given that WY is 4.6 for us to find the value of MZ We need more information to be in a position to answer this. More information includes maybe we know the value of M or at least having some relationship between WY and MZ for us to draw a conclusion and come up with the value of MZ. If at all we had a common value in WY and MZ say M then it could be easier to come to a conclusion and finally get the value of MZ.

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Answer:

Both x - 5, and 4x-5-3x are equivalent to (1/3x+2x−5/3x)−(−1/3x+5)

Step-by-step explanation:

Let's reorganize the given expression:

(1/3x+2x−5/3x)−(−1/3x+5)

1/3x+2x−5/3x + 1/3x-5       [Expand the parentheses]

2/3x+2x−5/3x -5       [Combine like terms]

-3/3x+2x -5

-x + 2x - 5

x - 5                       One of the equivalent expressions

The option 4x-5-3x also reduces to x - 5

The weight of the baby after five months is 15 Kg.

Step 1:

Given:

New-born baby weight = 5kg

Monthly average weight gained = 2kg

To find:

The weight of the baby after 5 months.

Average Weight of Baby:

Birth weight is the weight of the baby at birth. [1] The average birth weight of babies of European descent is 3.5 kilograms, with a normal range of 2.5 to 4.5 kilograms (5.5 to 9.9 pounds). On average, South Asian and Chinese babies weigh about 3.26 kg. The prevalence of low birth weight infants decreased slightly from 7.9% (1970) to 6.8% (1980), then increased slightly to 8.3% (2006) and is currently at 8.2% (2016).

Step 2:

Represent the unknown.

Let x-the number of months .

Let y-weight of the baby after 5 months.

Step 3:

Formulate the equation.

The mathematical equation is:

5+2x = y

Step 4:

Solve the equation.

5+2x = y

5+2(5) = y

5+10 = y

y = 15

Thus, the baby weight is 15kg after 5 months.

Step 5:

Using the equation 5+2x=y.

5+2x = y

5+2(5) = 15

5+10 = 15

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Answer:

(-9,0)  and (1,0)

Step-by-step explanation:

The correct answer will be:

Quantitative data, both sample sizes are greater than 30 or Both population distributions could be Normally Distributed, Random Samples or Random application of treatments

There should be just one group for each subject. The observations in each category are unrelated to one another. There were no notable outliers in any category.

The following are the presumptions for a percentage significance test: Data come from a random sample [Sample is large enough, which is presumed to be true when. It should be noted that both quantitative and categorical data can be subjected to a significance test for a proportion.

Most parametric tests begin with the underlying presumption of population distribution. The ratio scale or interval scale measurements, easy random extraction, normal distribution of the data, a sufficient sample size, and homogeneity of variance are all prerequisites for performing the t-test.

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Answer:

5 hours

Step-by-step explanation:

Olivia needs to make 700 - 15 = <<700-15=685>>685 cupcakes.

So she needs to work for 685 / 137 = <<685/137=5>>5 hours

The stem plot for the given data is 3 4 5 6.

A stem and leaf plot, also known as a stem and leaf diagram, is a technique to arrange data such that it is simple to see how frequently certain sorts of values occur. It is a graph that displays ordered numerical data. A stem and a leaf are divided into each piece of data.

Arranging the given data in ascending order,

30, 34, 34, 35, 35, 36, 39, 39, 40, 40, 41, 42, 42, 43, 43, 43, 44, 46, 46, 48, 49, 49, 50, 52, 53, 58, 59, 61, 66, 68

The stem plot = 3 4 5 6

Calculated Statistics:

Minimum:30

Maximum:68

Range:38

Count:30

Sum:1365

Mean:45.5

Median:43

Mode:43

Standard Deviation:9.616

Variance:92.47

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The degree of a polynomial is the highest power of each variable in the equation. In the polynomial 7x2y3z4, the highest power of each variable is 2 for x, 3 for y, and 4 for z. Therefore, the degree of this polynomial is 8.

1. Identify the highest power of each variable.

For 7x2y3z4, the highest power of each variable is 2 for x, 3 for y, and 4 for z.

2. Add the highest powers of each variable.

2 + 3 + 4 = 9

3. Subtract 1 from the sum.

9 - 1 = 8

4. The degree of the polynomial is the result of the subtraction.

Therefore, the degree of the polynomial 7x2y3z4 is 8.

The degree of a polynomial is the highest power of each variable in the equation. To calculate the degree of a polynomial, you must identify the highest power of each variable and add them together. Then, subtract 1 from the sum to get the degree of the polynomial. For example, in the polynomial 7x2y3z4, the highest power of each variable is 2 for x, 3 for y, and 4 for z. Adding these powers together gives us 9. Subtracting 1 from this sum gives us 8, which is the degree of the polynomial. Therefore, the degree of the polynomial 7x2y3z4 is 8.

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If Hanna is walking there is a 0.4 chance of not being late. 0.75 x 0.4 = 0.3 probability of not being late.

If Hanna cycles there is a chance of 0.8 of not being late. 0.6 x 0.8 = 0.48.

0.48 + 0.3 = 0.78.

In other words, there is a 78% probability of her not being late.

Therefore , the solution ot the given problem of trigonometry comes out to be Option (A) and (F) are the correct answers since sin = BC/AC = cos(90 - ∅), and cos = AB/AC = sin(90 - ∅).

The right triangle's angle serves as the domain input value for the six basic trigonometric operations, which produce a range of numbers as their results.Understanding the trigonometric functions of the four quadrants' graphs, domains, differentiation, and integration will be achievable.

Here,

Sinx = perp./hypo.

Cosx equals base/hypo.

So,

Sin = B/C

A= cos(90 -∅ ) = BC/AC

So,

Cos(90 -∅ ) = Sin(BC/AC)

And,

cos = AC/AB

AB/AC = sin(90 -∅ )

So,

cos AB/AC = sin (90 -∅ )

Therefore , the solution ot the given problem of trigonometry comes out to be Option (A) and (F) are the correct answers since sin = BC/AC = cos(90 -∅ ), and cos = AB/AC = sin(90 - ∅).

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The relationship between the input  and output  is that the perimeter of a square is always equal to four times the length of one of its sides.

The perimeter of a square is the total distance around the outside of the square. It is the sum of the lengths of all four sides. To find the perimeter of a square, you simply multiply the length of one side by four, since all sides of a square are equal in length. The formula is P=4S

1.The relationship established between (side length of the square) and output (perimeter of the square) represent that A square's perimeter is always equal to 4 times one of its sides.

2.Yes, the function can be represented with an equation. The equation would be:

Perimeter = 4 × Side Length.

Side Length (input) 1  2  3  4  5

Perimeter (output)  4 8 12 16 20

This equation states that the perimeter of a square is equal to four times the length of one of its sides.

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The amount of money owned by JIm is $9

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

The ratio of the amount owned by Tim tohe ratio of the amount owned by Jim is 6 : 1

This means that

Tim : Jim = 6 : 1

Also from the question, we have

Tim gets $54

This means that

Tim = 54

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

54 : Jim = 6 : 1

Multiply by 9

54 : Jim = 54 : 9

So, we have

Jim = 9

Hence, the amount is $9

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Answer:

Its 22:40

Step-by-step explanation:

Answer: 22:40
Pretty simple

Step-by-step explanation:

The equation of the perpendicular bisector of the segment with the endpoints (-8,-1) and (4,5)  is 2x+y = -2.

The line between these locations' slopes must equal the negative reciprocal of the bisector's slope. It must go through the segment midway.

The slope of the line through the given points :

m = (y2 -y1)/(x2 -x1) = (5 -(-1))/(4 -(-8)) = 6/12 = 1/2

Then, The slope of the required bisector:   m = -1/(1/2) = -2

The midpoint of the given segment:

((-8, -1) +(4, 5))/2 = (-8+4, -1+5)/2 = (-4, 4)/2 = (-2, 2)

Then the point-slope form of the equation of the bisector:

y -y1 = m(x -x1)

y -2 = -2(x -(-2))

y = -2x -4 +2

y = -2x -2 . . . . . . . slope-intercept form equation

2x +y = -2 . . . . . . .standard form equation

Thus, The equation of the perpendicular bisector of the segment with the endpoints (-8,-1) and (4,5)  is 2x+y = -2.

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Answer:

The matrix does not have an inverse (D)

Step-by-step explanation:

The matrix is singular, therefore doesn't have an inverse

Answer:

4(3p - 7)

Step-by-step explanation:

First find the factors of 12 and 28:

12: 1, 2, 3, 4, 6, 12

28: 1, 2, 4, 7, 28

Notice any common factors: 1, 2, 4

Now, out of these factors, 4 is the GCF since it is the greatest common factor, so divide 12 and 28 by 4:

12/4 = 3.  28/4 = 7.

Hence, 12p-28 = 4(3p - 7)

Answer:80

Step-by-step explanation:by5 will be this and 20 by 10 mulltiply 60 by 9

something noteworthy is that the x-coordinate is the same for each point, so Check the picture below.