Find the slope of the slope of a line passing through (-4,7)(-4,1)

Answer:

3

Step-by-step explanation:

midline is the distance or the midway between the highest point and the lowest one or between maximum and minimum,

for the given graph,

maximum point = 5

minimum point = 1

midline = 5 +1 / 2 = 6 / 2 = 3

The tax charged on Omari's monthly earning of Ksh 24,200 is Ksh 3,340.

To calculate the tax charged on Omari's monthly earning, we need to consider the tax brackets and rates applicable in the specific tax system or country. Since you haven't specified a particular tax system, I will provide a general explanation.

Assuming we have a simplified progressive tax system with three tax brackets:

For the first tax bracket, let's say income up to Ksh 10,000 is taxed at a rate of 10%.

For the second tax bracket, income between Ksh 10,001 and Ksh 20,000 is taxed at a rate of 15%.

For the third tax bracket, income above Ksh 20,000 is taxed at a rate of 20%.

To calculate the tax charged on Omari's monthly earning of Ksh 24,200, we can divide it into the respective tax brackets:

Ksh 10,000 falls in the first tax bracket. So, the tax for this portion is 10% of Ksh 10,000, which is Ksh 1,000.

Ksh 20,000 - Ksh 10,000 = Ksh 10,000 falls in the second tax bracket. The tax for this portion is 15% of Ksh 10,000, which is Ksh 1,500.

The remaining amount, Ksh 24,200 - Ksh 20,000 = Ksh 4,200, falls in the third tax bracket. The tax for this portion is 20% of Ksh 4,200, which is Ksh 840.

Now, we can sum up the taxes for each bracket:

Total Tax = Tax in the first bracket + Tax in the second bracket + Tax in the third bracket

Total Tax = Ksh 1,000 + Ksh 1,500 + Ksh 840

Total Tax = Ksh 3,340

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The degree of f(x) is 5, and the leading coefficient is negative. There are 3 distinct real zeros and 2 relative maximum values.

From the graph of a function, the zeros of the function are the x-intercepts, that is, the values of x for which the graph crosses or touches the x-axis.

The function in this problem has three distinct zeros, given as follows:

Hence the degree of the function is given as follows:

2 x 2 + 1 = 5.

The leading coefficient is negative, as the function has an odd degree, but increases to left and decreases to right.

The relative maximums of the functions are the points where the function makes a downward turn, changing from increasing to decreasing, hence there are two points.

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In a right triangle, the length of side "a" is 12.

The Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides, can be used to find the length of side "a" in a right triangle with sides of 13 and 5 units.

Let's assign "a" as the unknown side. According to the Pythagorean theorem, we have the equation: [tex]a^{2}[/tex] = [tex]13^{2}[/tex] - [tex]5^{2}[/tex].

Simplifying the equation, we get [tex]a^{2}[/tex] = 169 - 25, which becomes [tex]a^{2}[/tex] = 144.

To solve for "a," we take the square root of both sides: a = √144.

The square root of 144 is 12. Therefore, side "a" has a length of 12 units.

In summary, using the Pythagorean theorem, we determined that side "a" in the right triangle with side lengths 13 and 5 units has a length of 12 units.

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The simplified form of the expression 15x - 12 - 4x + 3x + 13 is 14x+1. Option A

To simplify the expression 15x - 12 - 4x + 3x + 13, we can combine like terms. Like terms are those that have the same variable and exponent.

First, let's combine the x terms:

15x - 4x + 3x = (15 - 4 + 3)x = 14x

Next, let's combine the constant terms:

-12 + 13 = 1

Putting it all together, the simplified form of the expression is:

14x + 1

Therefore, the correct answer is "14x + 1."

To simplify the expression, we added the coefficients of the x terms (15, -4, 3) to get 14x. Then, we added the constant terms (-12, 13) to get 1. This final expression, 14x + 1, does not have any like terms that can be combined further, so it is considered simplified.

It's important to note that when simplifying expressions, we group like terms together and perform the indicated operations, such as addition or subtraction. By doing so, we reduce the expression to its simplest form, where no further combining of like terms is possible.

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Answer:

Step-by-step explanation:

To find the maximum width of an aircraft seat that will accommodate 98% of all adult women, we need to determine the corresponding z-score for the 98th percentile of the normal distribution.

First, we find the z-score corresponding to the 98th percentile using a standard normal distribution table or calculator. The z-score for the 98th percentile is approximately 2.05.

Next, we use the z-score formula to find the corresponding value in the original distribution:

z = (x - μ) / σ

Solving for x (the maximum width of the aircraft seat):

x = z * σ + μ

Substituting the values given:

x = 2.05 * 4.36 + 37.6

x ≈ 45.98

Therefore, the maximum width of an aircraft seat that will accommodate 98% of all adult women is approximately 46 cm (rounded to one decimal place).

Answer:

Step-by-step explanation:

(x^3 - 10x + K)/(X+3) = 6 GIVEN

for different values of x there are many possible values of k some i will show

when we substitute x=1

we get k=33

at x=2

weget k=42

so many values are possible for k

because there is no intervel in question which restrics us from taking different values of x or k so you take any value of x you will get different values of k

Answer:

a)  Commutative Property of Multiplication

b)  Associative Property of Multiplication

c)  Distributive Property of Multiplication over Addition

d)  Inverse Property of Multiplication

e)  Zero Property of Multiplication

Step-by-step explanation:

The Commutative Property of Multiplication states that the order of factors in a multiplication operation can be rearranged without changing the end result.

The Associative Property of Multiplication states that the grouping of factors in a multiplication operation by parentheses in a different way does not affect their product.

The Distributive Property of Multiplication over Addition states that multiplying a number by the sum of two other numbers is equivalent to multiplying the number separately by each of the two numbers and then adding the results.

The Inverse Property of Multiplication states that if a number is multiplied by its reciprocal (multiplicative inverse), the product is always equal to 1.

The Zero Property of Multiplication states that the product of any number and zero is always zero.

Step-by-step explanation:

Perimeter =  pi * diameter

  radius = 1  1/3  yard   then diameter =  2  2/3 yd

perimter = pi *  2 2/3   yds = 8.38 yds

Step-by-step explanation:

Parallel to the x-axis means it is just a horizontal line with the value being the y-coordinate of the point:

y = -2

Answer:

y=-2

and m=0 must be your answer

Step-by-step explanation:

as line is parallel to x axis its slope will be zero as it does not have any definite x coordinate

so

equation of line is y-y'=m(x-x')

so m=0 m is slope

y'=-2 and x'=4

so by substituting the values

y+2=0

so y=-2

and m=0 is your answer

Answer:

Step-by-step explanation:

To find the value of x, we can use the Angle Bisector Theorem, which states that in a triangle, a line segment that bisects an angle divides the opposite side into segments that are proportional to the other two sides.

In this case, segment AD bisects angle A, so we can set up the following proportion:

BD/DC = AB/AC

Plugging in the given values, we have:

14/DC = 28/25

To solve for DC (segment CD), we can cross-multiply:

28 * DC = 14 * 25

Simplifying further:

DC = (14 * 25) / 28

DC ≈ 12.5

Therefore, the length of segment CD is approximately 12.5.

Answer:

Step-by-step explanation:

Step 1.   Determine the dollar amount of the markup

          175 - 79 = 96

Step 2:   Divide the markup Amount by the Cost

          96/79 = 1.215

Step 3:   Multiply by 100 and add the % sign

           1.215 x 100 = 121.5%

Answer:

Step-by-step explanation:

The quadratic formula is y=ax^2+bx+c

If we move everything to the left side of the equation,

-6x^2=-9x+7 becomes

-6x^2+9x-7=0

a=-6, b=9, c=-7, so the third answer choice

An estimate for the mean is 47.6 kg.

In Mathematics and Geometry, the mean for this set of data can be calculated by using the following formula:

Mean = [F(x)]/n

Cumulative frequency = 10 + 7 + 2 + 8 + 3

Cumulative frequency = 30

For the total number of data based on the frequency, we have;

Total weight, F(x) = 10(40) + 7(52.5) + 2(65) + 8(77.5) + 3(90)

Total weight, F(x) = 40 + 367.5 + 130 + 620 + 270

Total weight, F(x) = 1427.5

Now, we can calculate the mean weight as follows;

Mean = 1427.5/30

Mean = 47.6 kg.

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Answer:

[tex]{A = 20000(1 + \frac{0.0625}{4})^{4t}}[/tex]

Step-by-step explanation:

The question asks us to find an expression for compound interest for the given scenario.

To do this, we have to use the following formula for compound interest:

[tex]\boxed{A = P(1 + \frac{r}{n})^{nt}}[/tex]

where:

• A ⇒ final amount

• P ⇒ principal amount = $20,000

• r ⇒ interest rate (decimal) = [tex]\frac{6.25}{100}[/tex] = 0.0625

• n ⇒ number of times interest is compounded per year = 4

• t ⇒ time in years

Therefore, if we substitute the data above into the formula, we can find the required expression:

[tex]{A = 20000(1 + \frac{0.0625}{4})^{4t}}[/tex]

The answer is:

↬ f(x + 2) = 2x + 11

Work/explanation:

To evaluate the function, plug in x + 2 for x:

[tex]\boxed{\large\begin{gathered}\sf{f(x)=2x+7}\\\\\bf{distribute}\\sf{f(x+2)=2(x+2)+7}\\\\\bf{simplify}\\\sf{f(x+2)=2x+4+7}\\\\\sf{f(x+2)=2x+11}\end{gathered}}[/tex]

Starting with an initial population of 3.3 million yeast cells and a constant relative growth rate of 0.4465 per hour, the population size reaches approximately 5.892 million cells after 4 hours.

To calculate the population size after 4 hours, we can use the formula for exponential growth:

Population size = Initial population * [tex](1 + growth rate)^t^i^m^e[/tex]

Given that the initial population is 3.3 million cells and the relative growth rate is 0.4465 per hour, we can plug in these values into the formula:

Population size = 3.3 million *[tex](1 + 0.4465)^4[/tex]

Calculating the exponent first:

[tex](1 + 0.4465)^4 = 1.4465^4[/tex] ≈ 1.7879

Now, we can substitute this value back into the formula:

Population size = 3.3 million * 1.7879

Calculating the population size:

Population size = 5.892 million

Therefore, the population size after 4 hours is approximately 5.892 million cells.

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Answer:

m=

[tex] \frac{y2 - y1}{x2 - x1} [/tex]

where x1 is- -1

x2 is -6

y1 is -11

y2 is -7

m=

[tex] \frac{ - 7 - ( - 11)}{ - 6 - ( - 1)} [/tex]

[tex] \frac{ - 7 + 11}{ - 6 + 1} [/tex]

[tex] \frac{4}{ - 5} [/tex]

gradient is

[tex] gradient = \frac{4}{ - 5} [/tex]

Answer:

  (c)  y = 2b/(2a -c)x -2bc/(2a -c)

Step-by-step explanation:

Given the equation of line BD in point-slope form you want the simplified equation.

  y -0 = (2b/(2a -c))(x -c)

The equation is simplified by using the distributive property to eliminate parentheses.

  [tex]y-0=\dfrac{2b}{2a-c}(x -c)\\\\\\y=\dfrac{2b}{2a-c}x-\dfrac{2b}{2a-c}c\\\\\\\boxed{y=\dfrac{2b}{2a-c}x-\dfrac{2bc}{2a-c}}\qquad\text{matches choice C}[/tex]

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The best measure of center of the data is (a) mean; because the data are close together

From the question, we have the dataset of 10 values

In the given dataset, we can see that there are no outliers present in the dataset

By definition, outliers are extreme values.

Since there are no outliers, it means that the mean is the best measure of center

This is because the mean is affected by the presence of outliers and since no outlier is present, we use the mean

From the list of options, we have the mean value to be 42.536

Hence, the true statement is (a)

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Answer:

No

Step-by-step explanation:

To determine if the average number of miles flown per passenger increased by one-third between 1966 and 1976, we need to compare the increase in miles flown during that period.

According to the given table:

To find the increase in miles flown, subtract the 1966 value from the 1976 value:

[tex]\begin{aligned}\sf Increase\; in\; miles\; flown &= \sf 831 \;miles - 711\; miles\\&= \sf 120\; miles\end{aligned}[/tex]

Therefore, the average number of miles flown per passenger between 1966 and 1976 increased by 120 miles.

To check if the increase is one-third of the initial value, we need to calculate one-third of the 1966 value:

[tex]\begin{aligned}\sf One\;third \;of \;711 \;miles &= \sf \dfrac{1}{3} \times 711\; miles\\\\ &= \sf \dfrac{711}{3} \; miles\\\\&=\sf 237\;miles\end{aligned}[/tex]

Since the increase in miles flown (120 miles) is not equal to one-third of the initial 1966 value (237 miles), the statement that the average number of miles flown per passenger increased by one-third between 1966 and 1976 is not true.

Trent will need approximately 2.86 bottles of waterproof spray to cover his tent.

To calculate the number of bottles of waterproof spray Trent will need to cover his tent, we first need to find the surface area of the tent.

The surface area of a square-based pyramid is given by the formula:

Surface Area = Base Area + (0.5 x Perimeter of Base x Slant Height)

The base of the pyramid is a square with a side length of 14 feet, so the base area is:

Base Area = (Side Length)^2 = 14^2 = 196 square feet

To find the slant height of the pyramid, we can use the Pythagorean theorem. The slant height is the hypotenuse of a right triangle formed by one side of the base, the height of the pyramid, and the slant height. The height of the pyramid is given as 8 feet, and half the length of the base is 7 feet.

Using the Pythagorean theorem:

[tex]Slant Height^2 = (Half Base Length)^2 + Height^2[/tex]

[tex]Slant Height^2 = 7^2 + 8^2Slant Height^2 = 49 + 64Slant Height^2 = 113Slant Height ≈ √113 ≈ 10.63 feet[/tex]

Now we can calculate the surface area of the tent:

Surface Area = 196 + (0.5 x 4 x 10.63)

Surface Area = 196 + (2 x 10.63)

Surface Area = 196 + 21.26

Surface Area ≈ 217.26 square feet

Since each bottle of waterproof spray covers 76 square feet, we can divide the total surface area of the tent by the coverage of each bottle to find the number of bottles needed:

Number of Bottles = Surface Area / Coverage per Bottle

Number of Bottles = 217.26 / 76

Number of Bottles ≈ 2.86

Therefore, Trent will need approximately 2.86 bottles of waterproof spray to cover his tent. Since we can't have a fraction of a bottle, he will need to round up to the nearest whole number. Therefore, Trent will need 3 bottles of waterproof spray to fully waterproof his tent.

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Answer:

BC = 24 (D)

Step-by-step explanation:

Special Right Triangles (30-60-90 triangle)

The functions y₁(t) = e^ãt cos(μt) and y₂(t) = e^ãt sin(μt) are a fundamental set of solutions because they are linearly independent and satisfy the given homogeneous linear differential equation, allowing for the formation of the general solution.

To show that y₁(t) = e^ãt cos(μt) and y₂(t) = e^ãt sin(μt) are a fundamental set of solutions, we need to demonstrate two things: linear independence and satisfaction of the given homogeneous linear differential equation.

First, let's consider linear independence. We can prove it by showing that there is no constant c₁ and c₂, not both zero, such that c₁y₁(t) + c₂y₂(t) = 0 for all t.

Now, let's verify that y₁(t) and y₂(t) satisfy the homogeneous linear differential equation. If the given differential equation is of the form ay''(t) + by'(t) + cy(t) = 0, we can substitute y₁(t) and y₂(t) into the equation and verify that it holds true.

Once we have established linear independence and satisfaction of the differential equation, we can state that the general solution to the homogeneous linear differential equation is given by y(t) = c₁y₁(t) + c₂y₂(t), where c₁ and c₂ are arbitrary constants. This general solution represents the linear combination of the fundamental set of solutions.

In summary, y₁(t) = e^ãt cos(μt) and y₂(t) = e^ãt sin(μt) form a fundamental set of solutions for the given differential equation, and the general solution is given by y(t) = c₁y₁(t) + c₂y₂(t).

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The limit of the trigonometric expression is equal to 0.

In this problem we find the case of a trigonometric expression, whose limit must be found. This can be done by means of algebra properties, trigonometric formula and known limits. First, write the entire expression below:

[tex]\lim_{\Delta x \to 0} \frac{\cos (\pi + \Delta x) + 1}{\Delta x}[/tex]

Second, use the trigonometric formula cos (π + Δx) = - cos Δx to simplify the resulting formula:

[tex]\lim_{\Delta x \to 0} \frac{1 - \cos \Delta x}{\Delta x}[/tex]

Third, use known limits to determine the result:

0

The limit of the trigonometric function [cos (π + Δx) + 1] / Δx evaluated at Δx → 0 is equal to 0.

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The value of `a5 = λ5 = 824`.Therefore, the value of `a5` is 824.

Given the following values; `λ1 = 4` and `λn = na(n-1) + 4`.

We are required to calculate the value of `λ5` which is `a5`.

Solution We are given that;`λ1 = 4` which can also be expressed as `a1 = 4`. We are also given that `λn = na(n-1) + 4`. For `n=2`, `λ2 = 2a1 + 4 = 2(4) + 4 = 12`.

For `n=3`, `λ3 = 3a2 + 4 = 3(12) + 4 = 40`. For `n=4`, `λ4 = 4a3 + 4 = 4(40) + 4 = 164`. For `n=5`, `λ5 = 5a4 + 4 = 5(164) + 4 = 824`.

Hence, the value of `a5 = λ5 = 824`.Therefore, the value of `a5` is 824.

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Step-by-step explanation:

The coordinates and vertices

which reflected over the y- axis are

r(-2,0) , s(2,-3) , and t(2,3).

1. 1/3 of a full rotation: The coordinates of point P after rotating 1/3 of a full rotation counterclockwise are approximately (0.5, 0.866).

2. 1/2 of a full rotation: The coordinates of point P after rotating 1/2 of a full rotation counterclockwise are (-1, 0).

3. 2/3 of a full rotation: The coordinates of point P after rotating 2/3 of a full rotation counterclockwise are approximately (-0.5, -0.866).

1/3 of a full rotation:

To find the coordinates of point P after rotating 1/3 of a full rotation counter clockwise, we need to determine the angle of rotation.

A full rotation around the unit circle is 360 degrees or 2π radians.

Since 1/3 of a full rotation is (1/3) [tex]\times[/tex] 360 degrees or (1/3) [tex]\times[/tex] 2π radians, we have:

Angle of rotation = (1/3) [tex]\times[/tex] 2π radians

Now, let's use the properties of the unit circle to find the new coordinates.

At the initial position, point P is located at (1, 0).

Rotating counterclockwise by an angle of (1/3) [tex]\times[/tex] 2π radians, we move along the circumference of the unit circle.

The new coordinates of point P after the rotation will be (cos(angle), sin(angle)).

Substituting the angle of rotation into the cosine and sine functions, we get:

New coordinates of P = (cos((1/3) [tex]\times[/tex] 2π), sin((1/3) [tex]\times[/tex] 2π))

Calculating the values:

cos((1/3) [tex]\times[/tex] 2π) ≈ 0.5

sin((1/3) [tex]\times[/tex] 2π) ≈ 0.866

Therefore, the coordinates of point P after rotating 1/3 of a full rotation counterclockwise are approximately (0.5, 0.866).

1/2 of a full rotation:

Following a similar process, when rotating 1/2 of a full rotation counterclockwise, we have an angle of (1/2) [tex]\times[/tex] 2π radians.

New coordinates of P = (cos((1/2) [tex]\times[/tex] 2π), sin((1/2) [tex]\times[/tex] 2π))

Calculating the values:

cos((1/2) [tex]\times[/tex] 2π) = cos(π) = -1

sin((1/2) [tex]\times[/tex] 2π) = sin(π) = 0

Therefore, the coordinates of point P after rotating 1/2 of a full rotation counterclockwise are (-1, 0).

2/3 of a full rotation:

For a rotation of 2/3 of a full rotation counterclockwise, the angle is (2/3) [tex]\times[/tex] 2π radians.

New coordinates of P = (cos((2/3) [tex]\times[/tex] 2π), sin((2/3) [tex]\times[/tex] 2π))

Calculating the values:

cos((2/3) [tex]\times[/tex] 2π) ≈ -0.5

sin((2/3) [tex]\times[/tex] 2π) ≈ -0.866

Therefore, the coordinates of point P after rotating 2/3 of a full rotation counterclockwise are approximately (-0.5, -0.866).

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The function Sam can use to figure his total earnings for the day, based on the number of people he serves, is E(n) = 42 + 5n.

To calculate Sam's total earnings for the day, we need to consider both his hourly wages and the tips he receives based on the number of people he serves. Let's break it down step by step.

First, we know that Sam earns $7 per hour as his wage. Since he works for 6 hours, his earnings from wages alone would be $7 multiplied by 6, which equals $42.

Next, Sam also earns about $5 in tips for each person he serves. We can represent the number of people Sam serves as "n". Therefore, his total tip earnings would be $5 multiplied by "n", which gives us 5n.

To calculate Sam's total earnings for the day, we add his earnings from wages and tips together. So the function representing his total earnings, "E", can be written as:

E(n) = 7(6) + 5n

Simplifying further, we get:

E(n) = 42 + 5n

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