Find the equation of this line in slope intercept form y-2=1/2(x+8)

Answer:

The angle between \((2,2,4)\) and \((2,-1,1)\) is 60º.

Step-by-step explanation:

From linear algebra, we can determine the angle between both vectors by definition of dot point:

\(\cos \theta = \frac{\vec u\bullet \vec v}{\|\vec u\|\cdot \| \vec v\|}\) (1)

Where:

\(\vec u\), \(\vec v\) - Vectors.

\(\|\vec u\|\), \(\|\vec v\|\) - Norms of vectors.

\(\theta\) - Angle between vectors, measured in sexagesimal degrees.

If we know that \(\vec u = (2,2,4)\) and \(\vec v = (2,-1,1)\), then angle between vectors is:

\(\|\vec u\| = \sqrt{\vec u\bullet \vec u}\) (2)

\(\|\vec u\| = \sqrt{2^{2}+2^{2}+4^{2}}\)

\(\|\vec u\| \approx 4.899\)

\(\|\vec v\| = \sqrt{\vec v\bullet \vec v}\) (3)

\(\|\vec v\| = \sqrt{2^{2}+(-1)^{2}+1^{2}}\)

\(\|\vec v\| \approx 2.450\)

\(\vec u \bullet \vec v = (2,2,4)\bullet (2,-1,1)\)

\(\vec u \bullet \vec v = 4-2+4\)

\(\vec u \bullet \vec v = 6\)

\(\cos \theta = \frac{6}{(4.899)\cdot (2.450)}\)

\(\cos \theta = 0.5\)

\(\theta = 60^{\circ}\)

The angle between \((2,2,4)\) and \((2,-1,1)\) is 60º.

So, the equation of the axis of the segment AB is (A) y = 1/2 - x/2.

What is slope?

In mathematics, slope refers to the steepness or incline of a line on a graph. It is a measure of how much the dependent variable changes for every unit change in the independent variable.

The slope of the line passing through points A and B can be calculated as follows:

slope = (change in y) / (change in x) = (1-0) / (1-0) = 1/1 = 1

The equation of a line in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.

To find the y-intercept, we can use point A (0,0) and substitute the slope value.

y = mx + b

0 = 1(0) + b

b = 0

Therefore, the equation of the line passing through points A and B is:

y = 1x + 0

Simplifying, we get:

y = x

So, the answer is (A) y = 1/2 - x/2. However, this is not one of the given answer choices. We can also write the equation in point-slope form as y - y1 = m(x - x1) using point A, which gives:

y - 0 = 1(x - 0)

y = x

This confirms our earlier answer.

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Answer:

The answer is x=8.

Step-by-step explanation:

I am sure this is correct.

The additional 60 men, the provisions will last for approximately 20 weeks.

To determine how long the provisions will last with the additional 60 men, we need to consider the total number of people and the original duration the provisions were meant to last.

Originally, the provisions were intended to sustain 400 men for 23 weeks. This means that the provisions were estimated to be sufficient for a total of 400 * 23 = 9200 person-weeks.

Now, with the additional 60 men, the total number of men becomes 400 + 60 = 460.

To calculate how long the provisions will last with the increased number of men, we divide the total person-weeks by the new number of men:

Provisions last = Total person-weeks / Number of men

= 9200 / 460

≈ 20 weeks (rounded to the nearest whole number)

The additional 60 men will extend the supply's shelf life to around 20 weeks.

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Answer:

c > 9

Step by Step explanation

x<2/3

Is the answer of x

Answer:

Isolate the variable by dividing each side by factors that don't contain the variable.

Inequality Form:

x < 2

Interval Notation:

(−∞, 2)

Step-by-step explanation:

Answer:

20 blogs

Step-by-step explanation:

Step 1:  Determine the proportion of pop culture blogs:

First, we need to determine the proportion of pop culture blogs already written.  We can do this by dividing the number of pop culture blogs already written by the total number of blogs written:

The proportion of pop culture bloggers = Number of pop culture bloggers / Total number of bloggers

Proportion =  26 / (20 + 26 + 7 + 12)

Proportion = 26 / 65

Proportion = 0.4

Step 2:  Multiply the proportion of pop culture blogs by the number of upcoming blogs:

To determine the expected number of pop culture blogs that will be written given the data, we can multiply the proportion of pop culture blogs already written by the number of upcoming blogs:

Expected number of pop culture blogs = proportion of pop culture blogs *  number of upcoming blogs

Expected number = 0.4 * 50

Expected number = 20

Thus, you should expect 20 pop culture blogs to be written given the data.

Step-by-step explanation:

The total price of sneakers including tax will be equal to $20.75.

The Latin phrase "per centum," which means "by the hundred," is where the English word "percentage" comes from. Percentage segments are those with a numerator of 100. In other words, it is a connection where the whole is always deemed to be valued 100.

As per the given information in the question,

Price of sneakers = $20

Tax on sneakers = 3.75%

Then, the amount of tax will be,

(20 × 3.75)/100

= 75/100

= $0.75

Then, the total price of the sneakers will be,

$20 + $0.75

= $20.75

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The slope and the y-intercept of the line y = 4x + 5 are given as follows:

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

The coefficients m and b represent the slope and the intercept, respectively, and are explained as follows:

The function for this problem is given as follows:

y = 4x + 5.

Hence the slope and the intercept are given as follows:

The problem asks for the slope and the intercept of y = 4x + 5.

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Answer:

The slope of the line for Restaurant B is 2 times greater than the slope of the line for Restaurant A.

Step-by-step explanation:

Answer:

distance = 245 in

Step-by-step explanation:

1 in = 50

distance = 4.9 in x 50

distance = 245 in

Answer: 245 miles

Step-by-step explanation:

fg

Answer:

y = - 3x + 7

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (0, 7) and (x₂, y₂ ) = (2, 1) ← 2 points on the line

m = \(\frac{1-7}{2-0}\) = \(\frac{-6}{2}\) = - 3

the line crosses the y- axis at (0, 7 ) ⇒ c = 7

y = - 3x + 7 ← equation of line

The equation of the line in fully simplified slope-intercept form is y = -2.8x + 7

The linear graph represents the given parameter

For the graph, we have the points

(0, 7) and (25, 0)

A linear equation is represented as

y = mx + c

Where

c = y when x = 0

So, we have

y = mx + 7

Using the point (2.5, 0) on y = mx + 7, we have

m(2.5) + 7 = 0

2.5m + 7 = 0

Evaluate

m = -2.8

So, we have

y = -2.8x + 7

Hence, the equation of the line in fully simplified slope-intercept form is y = -2.8x + 7

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This is an arithmetic sequence with a first term of 1, a common difference of 1, and a last term of 499. We can use the formula for the sum of an arithmetic series to find the sum of the numbers:

S = (n/2)(a1 + an)

where:

S = sum of the series

n = number of terms

a1 = first term

an = last term

Substituting the given values, we get:

S = (499/2)(1 + 499)

S = (249.5)(500)

S = 124,750

So the sum of the series 1 + 2 + 3 + 4 + ... + 498 + 499 is 124,750.

Answer:

23 is the right answer hope it's helps you

The value of x from the given congruent triangles is 23 units.

In the figure ΔABC and ΔDEF are given.

Triangle congruence theorem or triangle congruence criteria help in proving if a triangle is congruent or not. The word congruent means exactly equal in shape and size no matter if we turn it, flip it or rotate it.

Consider, ΔABC and ΔDEF, we have

AB=DE (Given)

∠BAC=∠EDF (Given)

AC=DF (Given)

So, ΔABC ≅ ΔDEF

We know that, by CPCT

BC=FE

⇒ x-4=19

⇒ x=23 units

Therefore, the value of x from the given congruent triangles is 23 units.

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Answer:

$312

Step-by-step explanation:

10% of $600 is $60

So $60*4=$240

$600-$240=$360

1%=$6

So $6*8=$48

$360-$48=$312

Answer:

[9/5,∞)

Step-by-step explanation:

Rearrange variables to the left side of the equation: c ≥ 11/5-2/5

Calculate: c ≥ 9/5

Express solution set in interval notation: [9/5,∞)

Answer:

The probability that the box will contain less than the advertised weight of 453 g is 0.00034.

Step-by-step explanation:

Let X represent the weight (in grams) of cereal in a box of Lucky Charms.

It is provided that X follows a Normal distribution with parameters, μ = 470 and σ = 5.

Compute the probability that the box will contain less than the advertised weight of 453 g as follows:

\(P(X<453)=P(\frac{X-\mu}{\sigma}<\frac{453-470}{5})\)

                  \(=P(Z<-3.4)\\=0.00034\)

*Use the z-table.

Thus, the probability that the box will contain less than the advertised weight of 453 g is 0.00034.

The solution to the system of equations is (x, y) = (-261/47, 44/47) as an ordered pair.

To solve the given system of equations:

Equation 1: 8x + 9y = -36

Equation 2: x + 7y = 1

We can use the method of substitution or elimination to find the values of x and y. Let's use the method of substitution:

From Equation 2, we can solve for x:

x = 1 - 7y

Substituting this value of x into Equation 1:

8(1 - 7y) + 9y = -36

8 - 56y + 9y = -36

-47y = -44

y = 44/47

Substituting the value of y back into Equation 2 to find x:

x + 7(44/47) = 1

x + 308/47 = 1

x = 1 - 308/47

x = (47 - 308)/47

x = -261/47

Therefore, as an ordered pair, the solution to the system of equations is (x, y) = (-261/47, 44/47).

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Answer:

130° and 310°

Step-by-step explanation:

the bearing of A from B is the measure of the clockwise angle from a north line at B to A

the angle at B and A are same- side interior angles and sum to 180°

angle at B = 180° - 50° = 130°

the bearing of A from B is then 130°

the bearing of B from A is the measure of the clockwise angle from the north line at A to B

the complete angle about A = 360° then clockwise angle from north line at A to B is

360° - 50° = 310°

the bearing of B from A is 310°

Answer:

Step-by-step explanation:

To find the new coordinate of a point after it has been scaled by a factor of 1/2, you can multiply the x- and y-coordinates of the point by 1/2.

For example, to find the new coordinate of point K', you can multiply the x-coordinate of K' (-8) by 1/2 to get the new x-coordinate, and multiply the y-coordinate of K' (8) by 1/2 to get the new y-coordinate. This gives you the new coordinate of K' as (-4,4).

You can use the same method to find the new coordinates of points L' and M'. The new coordinate of L' is (4,4) and the new coordinate of M' is (-2,4).

I hope this helps! Let me know if you have any questions.

Answer:

81/4

Step-by-step explanation:

From the given information; we are to use Lagrange multipliers to find the volume of the largest rectangular box

The coordinate planes and the vertex given in the plane is x + 9y + 4z = 27.

By applying Lagrange multipliers, we have;

\(fx = \lambda gx\)

where;

\(f: V = xyz\)

\(g : x + 9y + 4z = 27\)

From; \(fx = \lambda gx\)

\(yz = \lambda\)    --------- equation (1)

From; \(fy = \lambda gy\)

\(xz = 9 \lambda\)  --------- equation (2)

From; \(fz = \lambda gz\)

\(xy = 4 \lambda\) --------- equation (3)

Comparing and solving equation (1),(2) and (3);

\(\lambda x = 9 \lambda y = 4 \lambda z\)

divide through by \(\lambda\)

x = 9 y = 4z

3x = 27

x = 27/3

x = 9

From x = 9y

9 = 9 y

y = 9/9

y = 1

From

x = 4z

9 = 4 z

z = 9/4

Thus; the Volume of the largest rectangular box = 9 × 1  × 9/4

= 81/4

Answer:

  \(5\dfrac{7}{8} c +7\)

Step-by-step explanation:

The like terms are the ones containing the variable 'c'. They are combined by adding their coefficients.

Working just with the coefficients of c, we have ...

  \(2\dfrac{3}{4} +3\dfrac{1}{8}=(2+3)+\left(\dfrac{6}{8}+\dfrac{1}{8}\right)=5\dfrac{7}{8}\)

Then the simplified expression is ...

  (2 3/4)c +(3 1/8)c +7

  = (5 7/8)c +7

(a) When measuring angle 9 and the lengths of AB and BC, one observation is required.

(b) The line drawn from the center of a circle to the midpoint of a chord is perpendicular to the chord, while the line drawn from the center of a circle to an endpoint of a chord bisects the chord.

a) In the given diagram, we have angle AOB (angle 9) and line segments AB and BC.

To measure angle 9, we use a protractor. We align the baseline of the protractor with the line segment OA, ensuring that the center point of the protractor coincides with the vertex O. Then, we read the degree measurement where the line segment OB intersects the protractor. Let's assume the measurement of angle 9 is x degrees.

To measure the length of line segments AB and BC, we use a ruler. We align the ruler with the line segments and read the length in units (e.g., centimeters or inches).

b) The statements to complete are:

(i) The line drawn from the center of a circle to the midpoint of a chord will be perpendicular to the chord.

(ii) The line drawn from the center of a circle to the endpoint of a chord will bisect the chord.

In a circle, the center of the circle lies on the perpendicular bisector of any chord. This means that if we draw a line from the center of the circle to the midpoint of a chord, it will be perpendicular to the chord (statement i). Similarly, if we draw a line from the center of the circle to one of the endpoints of the chord, it will bisect the chord into two equal parts (statement ii).

These properties hold true for any chord in a circle, and they are based on the geometric properties of circles and perpendicular bisectors.

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Answer:

20

Step-by-step explanation:

percentage error = predictions - actual ÷actual × 100

error

\( \frac{82 - 52 \\ }{52} \times 100\)

=

20

Answer:  

She should divide both sides by -5 while she multiplied by -5 on other side

and she also did not change the > symbol to a < symbol

Step-by-step explanation:

We are given

 -5x - 3.5 > 6.5

Since, we have to solve for x

so, we will isolate x on anyone side

step-1:

Add both sides by 3.5

-5x - 3.5 + 3.5 > 6.5 + 3.5

-5x + 10

step-2:

Divide both sides by -5

we know that whenever we divide both sides by negative sign , it's inequality gets revered

so, we get

-5x/-5 < -50/-5

we get

x < 10

so,

She should divide both sides by -5 while she multiplied by -5 on other side  and she also did not change the > symbol to a < symbol

Answer:

3, 4, 5

Step-by-step explanation:

Answer:

Step-by-step explanation:

Two events A and B are said to be independent if the occurrence of one of the events does not affect the other occurring. For example, the event of tossing two coins is an independent event since they occur simultaneously. Two events are therefore independent if the following are true.

P(A|B) = P(A)

P(B|A) = P(B)

P(A and B) = P(A)P(B)

If A and B are independent events with P( A) = 0.35 and P( B) = 0.55,

then P( A| B) is a probability of A occurring provided that B has occurred. This is known as conditional probability for an independent event.

From the condition above for independent events, P(A|B) = P(A) and since P(A) =  0.35, hence P(A|B) =0.35

(Option a) Gonzalez and Bros . Inc has the absolute advantage when it comes to producing phones.

Absolute advantage theory

Adam Smith, an economist from the 18th century, introduced the idea of absolute advantage in his book The Wealth of Nations to explain how nations might profit from trade by specializing in producing and exporting the things that they can manufacture more successfully than other nations.

On the other hand, low-cost manufactured items are produced and exported by China, Thailand, and Vietnam. These three nations enjoy a distinct advantage as a result of their significantly reduced unit labor costs.

Here, option a Gonzales and Bros. Inc has the absolute advantage when it comes to producing phones.

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The algebraic rule for translating the figure 3 units left and 2 units up is (x-3, y+2).  Option B.

To translate a figure 3 units to the left and 2 units up, we need to adjust the coordinates of the figure accordingly. The algebraic rule that represents this translation can be determined by examining the changes in the x and y coordinates.

When we move a figure to the left, we subtract a certain value from the x coordinates. In this case, we want to move the figure 3 units to the left, so we subtract 3 from the x coordinates.

Similarly, when we move a figure up, we add a certain value to the y coordinates. In this case, we want to move the figure 2 units up, so we add 2 to the y coordinates.

Taking these changes into account, we can conclude that the algebraic rule for translating the figure 3 units left and 2 units up is (x-3, y+2). The x coordinates are shifted by subtracting 3, and the y coordinates are shifted by adding 2. SO Option B is correct.

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Answer:

If the tax rate = 3.9% and the product u are buying is priced at $42 Then, the amount you will pay for the object will be, $42 + 3.9/100 * 42

Step-by-step explanation:

I hope this help