a map has a scale of 2in: 6mi. if a two twons on a map is 10 in apart then how far apart are the real twons

In accordance with the function velocity, the car will have a complete stop after 6 seconds.

Herein we have a function of the velocity of a car (v), in feet per second, in terms of time (t), in seconds. The car stops for t > 0 and v = 0, then we have the following expression:

0.5 · t² - 10.5 · t + 45 = 0

t² - 21 · t + 90 = 0

By the quadratic formula we get the following two roots: t₁ = 15, t₂ = 6. The stopping time is the least root of the quadratic equation, that is, the car will have a complete stop after 6 seconds.

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Answer:

  HM = 3   or   HM = 15

Step-by-step explanation:

The product of segment lengths is the same for both chords.

  FM·EM = GM·HM

  GM +HM = 18

Substituting for GM, we have ...

  FM·EM = (18 -HM)·HM

  5·9 = (18 -HM)·HM

Effectively, we want two factors of 45 that have a total of 18. Looking at the factors of 45, we have ...

  45 = 1·45 = 3·15 = 5·9

The totals of these pairs are 46, 18, 14. The factor pair we're looking for is 3·15.

Either of these factors could be HM. The other will be GM.

There is nothing in the problem description that suggests the length of HM relative to other lengths on the diagram. (We know the diagram is not to scale.) So, there are two possible solutions:

  HM = 3   or   HM = 15

Answer:

25x-4

Step-by-step explanation:

3x+10x

+ 2x. -4

=5x+10x-4

=15x-4

Children learning to duplicate patterns when they can identify the rule, that is, when the unit repeats and the pattern becomes predictable is a true statement.

This involves the regularity or repeated way in which something is done or arranged.

Children are very inquisitive and tend to make logical connections when dealing with patterns due to their reasoning skills thereby aiding their learning process.

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Based on the information, it can be inferred that payment option A means a payment of $450, while option B means a payment of $300.

The payment options contemplated by the employer are distributed as follows:

Option A

Option B

Note: This question is incomplete because there is some information missing. Here is the missing information:

Complete the tables to show how much money would be received for both payment options, each week, for 6 weeks.

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I don’t have an answer but by any chance did you complete the assignment?

By subtracting decimals, how much farther she ran on Saturday than on Sunday is determined as: 1.078 kilometers.

When subtracting decimals, the number value is taken into consideration.

Distance ran by Keisha on Saturday = 3.218 kilometers.

Distance ran by Keisha on Sunday = 2.41 kilometers.

Subtract both decimals to determine how much farther she run on Saturday than on Sunday.

3.218 - 2.14 = 1.078 kilometers.

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Answer:

67

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

So this problem is asking whether Parametric because have an orientation and the short answer to that is that this is true. Parametric curves do have an orientation and we'll just do a little demonstration to share. Why? So let's take these very standard privatization of the unit circle where X is he going to cause of tea and why is equal to sign of tea now? The final part of defining the characterization is defining that the main range of tea on will take t to go from zero to two pi Andi, In this case, this is the this parts of circle going in this direction in the counter clockwise direction. And this is because as X as he goes from zero to play over two x decreases and signed increases on it sets us off on this direction as if that's one orientation off this curve of the circle. But we can alter this curve to get a different orientation. So if we were to take the Parametric equation given by X is equal to the co sign a minus T and why is equal to the sign of minus T in this case? Well again, take the domain to be from 0 to 2 pi. But because of the mind, the sign when it the mind sign doesn't actually affect X, it doesn't effect for co sign Well, it does affect the sign of minus T. So as T increases, the X value still decreases. But the Y value initially decreases as well, so this sets the arrows off on the clockwise direction. So this is another orientation off the same curve. So we've got two very different characterizations that describe the same physical curve. But because of the differences, the curve is constructed in opposite direction, and that is what the orientation defines. So it's very important to make sure that when you're drawing and describing the curve, you're parametric equations are in the correct orientation because otherwise you may encounter some difficulties later on. Because you'll be working with equation start that are, in fact, wrong

Thank you,

Eddie.

Answer:

[tex]\dfrac{3^{13}}{2}[/tex]

Step-by-step explanation:

Given expression:

[tex]\dfrac{3^5 \cdot 2^4 \cdot 2^1 \cdot 3^6 \cdot (3^2)^4}{(2^3)^2 \cdot 3^6}[/tex]

[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]

[tex]\implies \dfrac{3^5 \cdot 2^4 \cdot 2^1 \cdot 3^6 \cdot 3^8}{2^6 \cdot 3^6}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]

[tex]\implies \dfrac{3^{(5+6+8)} \cdot 2^{(4+1)}}{2^6 \cdot 3^6}[/tex]

[tex]\implies \dfrac{3^{19} \cdot 2^{5}}{2^6 \cdot 3^6}[/tex]

[tex]\implies \dfrac{3^{19} \cdot 2^{5}}{3^6 \cdot 2^6}[/tex]

[tex]\textsf{Apply exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:[/tex]

[tex]\implies 3^{(19-6)} \cdot 2^{(5-6)}[/tex]

[tex]\implies 3^{13} \cdot 2^{-1}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{-n}=\dfrac{1}{a^n}:[/tex]

[tex]\implies \dfrac{3^{13}}{2^1}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^1=a:[/tex]

[tex]\implies \dfrac{3^{13}}{2}[/tex]

Answer:

The result is 3¹³ /2

Step-by-step explanation:

Greetings

Using it's concept, there is a 0.625 = 62.5% probability that he or she has a bachelor's or a master's degree.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

The company has 6 + 2 + 8 = 16 employees, out of which 2 + 8 = 10 have a bachelor's or a master's degree, hence the probability is:

p = 10/16 = 0.625.

0.625 = 62.5% probability that he or she has a bachelor's or a master's degree.

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Answer:

a = 4 first term, r = ?, T10 = 100.Tn = ar^n - 1 formula for g.pT10 = 4r^ 10 - 1100 = 4r^9Divide both side by 4100/4 = 4/4r^925 = r^9 take the 9th root of both side 9√25 = 9√r^9r = 9√25To find the nth term Since Tn = ar^n - 1

The pre-image of the triangle has the following vertices: A'(x, y) = (4, 4/3), B'(x, y) = (- 2, 0) and C'(x, y) = (1, 3).

In this problem we must use a transformation rule known as dilation, a kind of rigid transformation, to derive the preimage of the triangle, whose formula is:

P'(x, y) = O(x, y) + k · [P(x, y) - O(x, y)]     (1)

Now we proceed to find the preimage of the triangle: O(x, y) = (0, 0), k = 2/3

Point A'

A'(x, y) = (0, 0) + (2/3) · [(6, 2) - (0, 0)]

A'(x, y) = (4, 4/3)

Point B'

B'(x, y) = (0, 0) + (2/3) · [(- 3, 0) - (0, 0)]

B'(x, y) = (- 2, 0)

Point C'

C'(x, y) = (0, 0) + (2/3) · [(1.5, 4.5) - (0, 0)]

C'(x, y) = (1, 3)

The pre-image of the triangle has the following vertices: A'(x, y) = (4, 4/3), B'(x, y) = (- 2, 0) and C'(x, y) = (1, 3).

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The area of a rectangle is given by its length multiplied by its width. So that the expression that represents the area of the rectangle in the given question is  [tex]\frac{3}{2}[/tex] [tex]x^{2}[/tex] squared unit.

A rectangle is a figure that has four straight sides, in which opposite sides are equal.

The area of a rectangle can be determined by the expression;

Area = length x width

Thus considering the given question, the length of the rectangle is tribble to that of the square. And the width of the rectangle is half of that of the square.

So that;

length = 3x

width = [tex]\frac{x}{2}[/tex]

Thus,

Area = length x width

        = 3x ([tex]\frac{x}{2}[/tex])

        = [tex]\frac{3}{2}[/tex] [tex]x^{2}[/tex]

Therefore, the area of the rectangle is  [tex]\frac{3}{2}[/tex] [tex]x^{2}[/tex] squared unit.

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It would take 14 hours for all of them to paint the three houses.

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

Let t represent the time it would take them working together, hence:

(1/24 + 1/26 + 1/20 + 1/21 + 1/27)t = 3

t = 14 hours

It would take 14 hours for all of them to paint the three houses.

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Step-by-step explanation:

38<4x+3+7-3x

4x+3+7>38

4x+3+7<3x

X>7

X<-10

= Ø

Answer: D

Step-by-step explanation:

The graph is narrower, so the coefficient of [tex]x^2[/tex] has an absolute value more than 1.

Also, because g(x) opens down, the coefficient of [tex]x^2[/tex] is negative.

This leaves D as the answer.

Answer:

x=75 degrees

Step-by-step explanation:

since the shape is quadrilateral, all the angles added together should equal 360 degrees so you use 360 to subtract all the given angles on the shape and you can find X

360-131-107-47=75

Answer:

the rectangles area is 24 meters

Step-by-step explanation:

area = length x width

length is 6 using the words long and width is 4

Answer:

area = 24 cm²

Step-by-step explanation:

The area of a rectangle can be found using the formula:

[tex]\boxed {area = length \times width}[/tex].

Substituting the values into the equation:

[tex]area = 6 \space\ cm\times 4 \space\ cm[/tex]

       ⇒ [tex]\bf 24 \space\ cm^2[/tex]

Answer:

3:12:39

Step-by-step explanation:

The ratio of amount for 1 day, number of employee and total number of days is 1 : 4 : 13.

Ratio basically compares quantities, that means it show value of one quantity with respect to other quantity.

If a and b are two values, their ratio will be a:b,

Given information are,

Amount for 1 day = $3,

Number of employee = 12,

Total number of days = 39.

The ratio of amount for 1 day, number of employee and total number of days

= 3 : 12 : 39

Simplify the ratio by dividing it to 3,

= 1 : 4 : 13

The required ratio is 1:4:13.

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The slope of a line parallel to this line is -5 and the slope of a line perpendicular to this line is 1/5

The slope is given as:

m = -5

Parallel line have the same slope.

So, the slope of a line parallel to this line is -5

However, perpendicular lines have their slopes to be opposite reciprocal

This means that:

The slope of a line perpendicular to this line is 1/5

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When the number of hours decreases, the number of miles increases.

Average speed is the total distance travelled per time.

Average speed = total distance / total time

There is an inverse relationship between the distance travelled and the time travelled. If time increases, the distance travelled decreases.

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The value of the car after 5 years is 8527.02 dollars

Depreciation is the reduction in the value of an asset over time due to elements such as wear and tear. For example a car is said to "depreciate" in value after a discovery of a faulty transmission.

The value after 5 years can be found as follows:

Rate = 18% = 18 / 100 = 0.18

Initial Value  = $23,000

time = 5 years

Therefore,

y = 23000(1 + 18%)⁵

y = 23000(1 - 0.18)⁵

y = 23000(0.82)⁵

y = 23000 × 0.3707398432

y = 8527.0163936

y = 8527.02 dollars

Therefore, the value of the car after 5 years is 8527.02 dollars

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Using an exponential function, it is found that the value of the car after 5 years will be of $8,527.

A decaying exponential function is modeled by:

[tex]A(t) = A(0)(1 - r)^t[/tex]

In which:

For this problem, the initial cost and the decay rate are given as follows:

A(0) = 23000, r = 0.18.

Hence the value of the boat after t years is given as follows:

[tex]A(t) = A(0)(1 - r)^t[/tex]

[tex]A(t) = 23000(1 - 0.18)^t[/tex]

[tex]A(t) = 23000(0.82)^t[/tex]

The value after 5 years will be of:

[tex]A(5) = 23000(0.82)^5 = 8527[/tex]

The value of the car after 5 years will be of $8,527.

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So to run 10km, you need to run 6.25 times the trail. (Or 7 if you only accept whole numbers as answers, we need to round up).

If you run the trail x times, then you will run:

y = x*1mi

Now remember that:

1 mi = 1.6 km

Replacing that, we get the linear equation:

y = x*1.6km

Now we want to find the value of x such that:

x*1.6km = 10km

Dividing both sides by 1.6km

x = 10km/1.6km = 6.25

So to run 10km, you need to run 6.25 times the trail. (Or 7 if you only accept whole numbers as answers, we need to round up).

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The coordinates of point C are (-9, 1)

The points are given as:

A = (-21, -7)

B = (-6, 3)

m : n = 4 : 1

The coordinates of point C is calculated as:

[tex]C = \frac{1}{m+n} *(mx_2 + nx_1, my_2+ ny_1)[/tex]

So, we have:

[tex]C = \frac{1}{4+1} *(4 * -6 + 1 * -21, 4 * 3+ 1 * -7)[/tex]

This gives

[tex]C = \frac{1}{5} *(-45, 5)[/tex]

This gives

C = (-9, 1)

Hence, the coordinates of point C are (-9, 1)

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The value of x is 0.5

The equation is given as:

(x -2)(x + 3) = (x - 2)(4 - x)

Divide both sides by x - 2

x + 3 = 4 - x

Evaluate the like terms

2x = 1

Divide by 2

x = 0.5

Hence, the value of x is 0.5

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In order to define the quantity of which of the two website produces a larger amount of content per single writer, Charlotte thought of:

Charlotte wants to know which website has more content per writer which means that she wants to know which website is more productive with writing.

One way she can do this is to check the average number of posts per writer per website. This would show her which website has a writer that writes more content on average.

Charlotte could also use average number of words per writer. This shows just how much writing the writers in each websites are doing, in terms of words. The website with the higher average words per writer is therefore providing more content.

Options for this question include:

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The answer is A

sin0 = p/h = 7/25

cos0 = b/h = -24/25

Therefore , p = 7 , b = -24

tan0 = p/b = 7 / -24 = -7/24

Answer:

Step-by-step explanation:

eq. of line is 2x-3y=-3

its slope=(-co-efficient of x/co-efficient of y)=-2/-3=2/3

slope of line perpendicular to given line=-3/2

eq. of line through (-3,0) is

y-0=-3/2 (x+3)

2y=-3x-9

3x+2y=-9

or

any eq. perpendicular to given line is

3x+2y=c where c is a constant.

it passes through (-3,0)

3(-3)+2(0)=c

c=-9

reqd. eq. is

3x+2y=-9

The given differential equation has characteristic equation

[tex]r^5 - 4r^4 + 4r^3 - r^2 + 4r - 4 = 0[/tex]

Solve for the roots [tex]r[/tex].

[tex]r^3 (r^2 - 4r + 4) - (r^2 - 4r + 4) = 0[/tex]

[tex](r^3 - 1) (r^2 - 4r + 4) = 0[/tex]

[tex](r^3 - 1) (r - 2)^2 = 0[/tex]

[tex]r^3 - 1 = 0 \text{ or } (r-2)^2=0[/tex]

The first case has the three cubic roots of 1 as its roots,

[tex]r^3 = 1 = 1e^{i0} \implies r = 1^{1/3} e^{i(0+2\pi k)/3} \text{ for } k\in\{0,1,2\} \\\\ \implies r = 1e^{i0} = 1 \text{ or } r = 1e^{i2\pi/3} = -\dfrac{1+i\sqrt3}2 \text{ or } r = 1e^{i4\pi/3} = -\dfrac{1-i\sqrt3}2[/tex]

while the other case has a repeated root of

[tex](r-2)^2 = 0 \implies r = 2[/tex]

Hence the characteristic solution to the ODE is

[tex]y_c = C_1 e^x + C_2 e^{-(1+i\sqrt3)/2\,x} + C_3 e^{-(1-i\sqrt3)/2\,x} + C_4e^{2x} + C_5xe^{2x}[/tex]

Using Euler's identity

[tex]e^{ix} = \cos(x) + i \sin(x)[/tex]

we can reduce the complex exponential terms to

[tex]e^{-(1\pm i\sqrt3)/2\,x} = e^{-x/2} \left(\cos\left(\dfrac{\sqrt3}2x\right) \pm i \sin\left(\dfrac{\sqrt3}2x\right)\right)[/tex]

and thus simplify [tex]y_c[/tex] to

[tex]y_c = C_1 e^x + C_2 e^{-x/2} \cos\left(\dfrac{\sqrt3}2x\right) + C_3 e^{-x/2} \sin\left(\dfrac{\sqrt3}2x\right) \\ ~~~~~~~~ + C_3 e^{-(1-i\sqrt3)/2\,x} + C_4e^{2x} + C_5xe^{2x}[/tex]

For the non-homogeneous ODE, consider the constant particular solution

[tex]y_p = A[/tex]

whose derivatives all vanish. Substituting this into the ODE gives

[tex]-4A = 69 \implies A = -\dfrac{69}4[/tex]

and so the general solution to the ODE is

[tex]y = -\dfrac{69}4 + C_1 e^x + C_2 e^{-x/2} \cos\left(\dfrac{\sqrt3}2x\right) + C_3 e^{-x/2} \sin\left(\dfrac{\sqrt3}2x\right) \\ ~~~~~~~~ + C_3 e^{-(1-i\sqrt3)/2\,x} + C_4e^{2x} + C_5xe^{2x}[/tex]

Se debe depositar $ 600 000 en la cuenta con 18 % de interés anual y $ 200 000 en la cuenta con 21 % de interés anual para recibir $ 150 000 en intereses.

En este problema tenemos un depósito repartido en dos cuentas, que adquiere ganancias de manera continua en el tiempo. En consecuencia, tenemos por interés compuesto la siguiente ecuación a resolver:

x · (18/100) + (800 000 - x) · (21/100) = 150 000

168 000 - (3/100) · x = 150 000

(3/100) · x = 18 000

x = 600 000

Se debe depositar $ 600 000 en la cuenta con 18 % de interés anual y $ 200 000 en la cuenta con 21 % de interés anual para recibir $ 150 000 en intereses.

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