Select the equation of the line that passes through the point (–2, 1) and has slope 3 in point-slope form.


(x – 2) = 3(y + 1)


(y + 1) = 3(x – 2)


(y – 1) = 3(x + 2)


(x + 2) = 3(y – 1)

Answer:

• The function f is increasing to the left of -4 (-∞ , -4]

• The function f is decreasing to the right  of -4 [-4 , +∞)

Step-by-step explanation:

f(x) = -(x+6)(x+2)

     = -(x² + 2x + 6x + 12)

     = -(x² + 8x + 12)

     = -x² - 8x - 12

The leading coefficient is -1 (the coefficient of the highest term -x² of the trinomial)

Then

The parabola opens downward.

………………………………………

[tex]-\frac{b}{2a} =-\frac{-8}{2\times \left( -1\right) } =-4[/tex]

Then

The function f is increasing to the left of -4 (-∞ , -4]

The function f is decreasing to the right  of -4 [-4 , +∞)

Since parallel lines do not meet, hence we can conclude that they have infinitely many solutions

The given graph contains 2 straight lines. passing through the y- axis.

The graphed lines has np solution since they do not have any point of intersection on the place. They are known as parallel lines.

Since parallel lines do not meet, hence we can conclude that they have infinitely many solutions

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Let be P(x, y) and Q(x, y) two distinct points on Cartesian plane, which generates a line segment. The slope represents the "inclination" of that line segment:

[tex]m = \frac{y_{Q}-y_{P}}{x_{Q}-x_{P}}[/tex]

Slope is a relationship of the change in the dependent variable (y) and the change in the independent variable (x). In this question we should present the correct definition for slope, which is described below:

Let be P(x, y) and Q(x, y) two distinct points on Cartesian plane, which generates a line segment. The slope represents the "inclination" of that line segment:

[tex]m = \frac{y_{Q}-y_{P}}{x_{Q}-x_{P}}[/tex]     (1)

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Answer:

x = 9 & y = 29

Step-by-step explanation:

Since we know that 7x is next to 117, that area will be equal to 180*,

7x + 117 = 180

7x = 180-117

7x=63

x=9

to find y, you can use the same method, just by finding the other angle inside. 53+7(9) + z = 180

53+63 = 180

116+z = 180

z = 180-116

z = 64.

Then we do

4y + 64 = 180

4y = 180-64

4y=116

y = 29

The true statement about the set include:

If set X is made up of the possible ways five students, represented by A, B, C, D, and E, can be formed into groups of three, then the set X consists of such triples {ABC, ABD, ABE, ACD, ACE, ADE, BCD, BCE, BDE, CDE}.

The set X totally contains 10 elements.

There are three ways to form a group if persons A and C must be in it. This statement is true and these groups are ABC, ACD, ACE.

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The approximate value of 63000 x 200 will be 12600000.

In mathematics, multiplication is defined as the sum of the numbers to the other number given. Like if 2 is multiplied by 3 then the multiplication will be the sum of the two-three times.

Given expression is 63000 x 200 so here we need to calculate the sum of the 63000 to 200 times.

E = 63000 x 200

E = 12600000

Therefore the approximate value of 63000 x 200 will be 12600000.

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Answer:

10.4

Step-by-step explanation:

So an exponential equation with a decay can be expressed as: [tex]f(x)=a(1-r)^t[/tex] where r is the decay rate. In this case is decreasing at 4% each year, this means that the r is equal to 0.04 (divide the percent by 100 to convert to decimal). So the equation is going to be: [tex]f(x)=a(0.96)^t[/tex]. The reason this works is because whenever you decrease by x%, the new value is (1-x)%, which is expressed in the formula. But the reason the exponent is there is because after 1 year it's going to be 0.96a, but after two years, it's going to be 0.96 the previous year which is 0.96a, so after two years it's going to be 0.96(0.96a), and then the next year it's 0.96 of the second year, which is then 0.96(0.96(0.96a))... and so on. So the amount of 0.96 increases as t increases. the a is going to be the initial amount, since then t=0, 0.96^0 will be equal to 1, which makes the expression a(1), which is just a. So this gives you the complete equation: [tex]p(x)=13000(0.96)^t[/tex]

Now to find when it's equal to 8,500 you need to start by setting it equal to 8,500 so I'll work through each step

Original Equation:

[tex]p(x)=13000(0.96)^t[/tex]

Set the equation equal to 8,500

[tex]8500=13000(0.96)^t[/tex]

Divide both sides by 13,000

[tex]0.653846\approx 0.96^t[/tex]

Rewrite in logarithmic form

[tex]log_{0.96}0.653846=t[/tex]

If you're calculator allows you to enter the base when calculating log, but this expression into your calculator to calculate the value of t, otherwise use the change of base formula

[tex]\text{change of base formula: }log_ba = \frac{log(a)}{log(b)}[/tex]

[tex]t=\frac{log0.653846}{log0.96}\\[/tex]

[tex]t\approx\frac{-0.1845}{-0.0177}[/tex]

[tex]t\approx10.4[/tex]

$85000 was paid at a short term note at 10% interest while $75000 was paid at a long term note at 7% interest.

An equation is an expression that shows the relationship between two or more variables and numbers.

Let x represent the amount of fund at 10% and y represent the amount of fund at 7% interest, hence:

x + y = 160000   (1)

Also:

0.1x + 0.07y = 13750    (2)

From both equations:

x = 85000 and y = 75000

$85000 was paid at a short term note at 10% interest while $75000 was paid at a long term note at 7% interest.

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The comparison and contrast between a square and an equilateral triangle are stated and explained below:

What is a square? A square is a plane shape with an equal length of sides. This implies that the measure of its length is the same as that of its breadth.

What is an equilateral triangle? A triangle is a plane shape with three sides, and a sum of its internal angles to equal [tex]180^{o}[/tex]. Thus an equilateral triangle is a type of triangle with equal lengths of sides, and therefore equal internal angles.

Comparison: i. The two shapes have equal lengths of sides.

ii. An equilateral triangle and a square are examples of plane shapes.

Contrast: i. An equilateral triangle has three sides, while a square has four sides.

ii. An equilateral triangle has three internal angles, while a square has four internal angles which are right angles.

iii. The sum of internal angles of an equilateral triangle is [tex]180^{o}[/tex], while that of a square is [tex]360^{o}[/tex].

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Kindly get 1-on-1 help from an expert tutor for more explanations if required.

Answer:

A square has degrees that add up to 360 but an equilateral triangle only adds up to 180

Step-by-step explanation:

The resulting function after all transformations have been carried out is; 4log7(x+5) + 2.

The transformations which ensued on the function given are as follows;

Stretched vertically by a factor of 4; Hence, we have; 4f(x) = 4log7(x).

Shifted to the left by 5 units; 4f(x) = 4log7(x +5).

Shifted down by 2 units; 4f(x) +2 = 4log7(x+5) + 2.

On this note, it follows that the resulting function upon all the Transformations is; = 4log7(x+5) + 2.

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The table which shows that y vary directly with x is the first table, second table and third table.

An equation is an expression that shows the relationship between two or more numbers and variables.

From the first table, using the points (1, 3) and (3, 9):

y = 3x

From the second table, using the points (-4, -2) and (-2, -1):

y = (1/2)x

From the third table, using the points (-2, 2) and (-1, 1):

y = -x

The table which shows that y vary directly with x is the first table, second table and third table.

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Answer:

The graph is shown above.

Answer:

[tex]\frac{2 \: + \: 3 \sqrt{5} }{3} [/tex]

Step-by-step explanation:

[tex] \frac{2}{3} + \sqrt{5} = [/tex]

[tex] = \frac{2}{3} + ( \sqrt{5} \times \frac{3}{3} )[/tex]

[tex]= \frac{2}{3} + \frac{3 \sqrt{5} }{3} [/tex]

[tex]= \frac{2 \: + \: 3 \sqrt{5} }{3} [/tex]

The addition of the total choices selected in the test based on the assumed figures is 891.

Your question is incomplete and the complete question wasn't found online. An overview will be given. The assumed figures for A choices include the numbers from 20 to 46. In this case, the total of the numbers will be:

= 20 + 21 + 22 + 23 + 24 .... 46.

= 891

In conclusion, the correct option is 891.

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The interest rate to the nearest whole percentage would you need to earn in order to turn $3,500 into $7,000 over 10 years is 10%

The formula for calculating amount is expressed as;

Amount = Principal + Simple interest

Given the following

Amount = $7000

Principal = $3500

time =10 years

Substitute

7000 = 3500 + 3500(R)(10)

3500 = 35000R
R = 3500/35000
R = 0.1

Hence the interest rate to the nearest whole percentage would you need to earn in order to turn $3,500 into $7,000 over 10 years is 10%

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9680 smart phones of total 20465 sold smart phones would be made by Apple.

Percentage is a mathematical measurement of any mathematical quantity or number or another measurement out of a total of 100.

Here given that in the US 47.3% of smart phones sold are made by Apple.

And in one day 20465 phones are sold.

So,

Out of 100 sold smartphones, 47.3 phones are made by Apple.

then out of 1 sold smartphone 47.3/100 phones are made by Apple.

Hence out of 20465 smartphones (10465*(47.3/100)) = 9679.945 phones are made by Apple.

Since number of sold smart phone cannot be in decimal number in real, it always a whole number.

Approximating to the nearest whole number we get out of 20465 sold smart phones in one day, 9679.945 = 9680 smart phones are made by Apple.

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Answer:

The answer is $0.36

Step-by-step explanation:

Based on the level of seniority of Mary Beth's unit, the correct conclusions on who will be terminated is:

Cheryl will be terminated because both Fred and Mike have seniority over them which means that they are at least third in seniority.

However, we cannot tell who will be terminated between Mike and Sue because the relationship between them is undefined. Fred is safe from termination, however.

The rest of this question is:

1. Mike will be terminated

A)True

B)False

C)Unknown

2. Sue will be terminated

A)True

B)False

C)Unknown

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The median is 5.

The median is 11.

The data set is bimodal.

Mean is the average of a set of numbers. It is determined by adding the numbers together and dividing it by the total number

Mean = sum of the numbers / total number

(13 + 13 −5 −5 + 13 + 11 −5) / 7 = 35/7 =5

Median can be described as the number that occurs in the middle of a set of numbers that are arranged either in ascending or descending order

-5, -5, -5, 11,  13,13, 13

Median = 11

A bimodal data set is a distribution with two clear most frequent values.

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The approximate direction angle of v is 326°

Definition of Direction Angle

A vector's direction angle is the angle formed by the positive x-axis and the vector v. The arctangent of the ratio between the vertical and horizontal components of the vector, v=xi+yj, can be used to determine the direction angle, θ.

What is the direction angle of v?

Let θ be the direction angle of v or the angle mad by v with the horizontal line.

It is given that,

[tex]v = < 3, -2 >[/tex]

We know that,

θ = tan⁻¹([tex]\frac{y}{x}[/tex])

Here, we have y = -2 and x = 3. Hence, we get,

∴ θ = tan⁻¹[tex](\frac{-2}{3})[/tex]

⇒θ = tan⁻¹(0.66)

Hence the direction angle of v = 360 - tan⁻¹(0.66)

≈ 326°

Thus, the approximate direction angle of v is 326°.

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Answer:

Azda has the best value: 4.56

Step-by-step explanation:

azda sells three products for 1.14, so twelve products would cost 4.56(1.14 * 4)

tisco sells four products for 1.56, so twelve products would cost 4.68(1.56*3)

azda has the best value

Answer:

They will meet at 3:04 p.m

Step-by-step explanation:

Since they are walking towards each other , that means we should add their speed together:

speed = 1.35 m/s + 1.65 m/s
           = 3 m/s

Now that we have found the speed, we can calculate the time:

time = 720 meters / 3 m/s
       = 240 seconds
       = 4 minutes ( 240 seconds is 4 minutes)

Answer:

(x/2 , 17/2)

Step-by-step explanation:

To find a midpoint, you average the x's and average the y's. Average them by adding the x-coordinates and divide by 2. Same with the y's.

The x's are x for P1 and 0 for P2.

x+0 / 2

=x/2

This will be the x-coordinate of the midpoint. Then for the y, use 8 and 9, the y's.

8+9 / 2

= 17/2

This will be the y-coordinate of the midpoint.

The midpoint is:

(x/2 , 17/2)

You could also divide 17/2 and get 8.5 then the midpoint would be:

(x/2 , 8.5)

Answer:

8x - x = 70

Step-by-step explanation:

x equals 10 because,

8 x 10 = 80

and x = 10, so 80 - 10 = 70.

The statistical test that can be used for the given statements is; the goodness-of-fit test

1) For the archeologist story, the goodness-of-fit test is the best and most relevant test that can be applied because the archaeologist wishes to determine if her prediction was correct by comparing the actual number of artefacts recovered in each grid section to the expected frequencies.

2)  The economist generates a list of expected stock market index points for the next two weeks, as well as the actual points at the end of each trading day. The economist then compares the actual and expected points to ensure that the model he constructed is accurate. As a result, economists can use the goodness-of-fit test in this study.

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Answer:

15x^2y+20xy^2+28xy-9x

Step-by-step explanation:

15x²y - 4(-2xy² - 9xy) + 12xy² - 8xy - 9x ​

First distribute the -4 to all the terms in the parentheses

15x²y +8xy² + 36xy + 12xy² - 8xy - 9x ​

Now combine like terms

15x²y       +8xy²  + 12xy²      + 36xy - 8xy     - 9x ​

15x^2y+20xy^2+28xy-9x

Answer:

C. 31.64

Step-by-step explanation:

23 = sin(36) × Hypotenuse

Hypotenuse is the baseline between the angles 36° and 54°.

Hypotenuse = 23/sin(36)

x = cos(36) × Hypotenuse

x = cos(36) × 23/sin(36) = cos(36)/sin(36) × 23 =

= 1/tan(36) × 23 = 23/tan(36) = 31.63686382... ≈

≈ 31.64

The approximate value of x in the diagram is,

⇒ x = 31.5

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

The triangle is shown in figure.

Now, We can formulate;

⇒ tan 36° = 23 / x

⇒ 0.73 = 23/x

⇒ x = 23 / 0.73

⇒ x = 31.5

Thus, The approximate value of x in the diagram is,

⇒ x = 31.5

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The equivalent expression to the given logarithm without tables is [tex]\mathbf{ =log_{10} (\dfrac{3x(x^2+4)}{2})}[/tex]. Option A is correct.

Equivalent expressions are expressions that differ in appearance but when a value is being replaced for their unknown variable, gives an equivalent result.

From the given information:

[tex]\mathbf{(log_{10}(9)+log_{10}(x) + log_{10}(x^2+4) )-log_{10} (6) }[/tex]

[tex]\mathbf{=log_{10}(9)+log_{10}(x) + log_{10}(x^2+4) -log_{10} (6) }[/tex]

[tex]\mathbf{=log_{10}(9x)+ log_{10}(x^2+4) -log_{10} (6) }[/tex]

[tex]\mathbf{=log_{10}(9x(x^2+4)) -log_{10} (6) }[/tex]

Apply log rule: [tex]\mathbf{log_a(x)-log_a(y) =log_a(\dfrac{x}{y})}[/tex]

[tex]\mathbf{=log_{10}(9x(x^2+4)) -log_{10} (6) =log_{10} (\dfrac{9x(x^2+4)}{6})}[/tex]

[tex]\mathbf{ =log_{10} (\dfrac{9x(x^2+4)}{6})}[/tex]

[tex]\mathbf{ =log_{10} (\dfrac{3x(x^2+4)}{2})}[/tex]

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Answer:

B. )The graph of g(x) is a translation of the graph of f(x) right 6 units.

Step-by-step explanation:

When a positive number is directly added to an "x" variable (usually inside of parentheses), the graph is shifted to the left that many units.

When a negative number is directly added to an "x" variable, the graph is shifted to the right that many units.

A graph shifts up or down when a positive or negative number is added to the overall function. For example, if the -6 were outside of the parentheses, the graph would be translated 6 units downwards.