Given that k=cd2 + e find the value of c when k=3 ,d=2 and e = 5

The steps that should be followed to create a copy of cab are listed below in the correct order. Mark a point X. Use a straightedge to draw a ray with endpoint X.

Place the compass point at X and draw an arc intersecting the ray. Mark the point Y at the intersection. Without changing the setting, place the compass point at Y and draw an arc. Label the point Z where the two arcs intersect.

Use a straightedge to draw XZ. Place the compass point at A. Draw an arc that intersects both rays of ZA. Label the points of intersection B and C. Place the compass point at C and open the compass to the distance between B and C. The above-mentioned steps should be followed in the given order to create a copy of cab.

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The process to create a replication of the cab includes marking a point x, drawing rays, drawing arcs with a compass, and repeating this process with several different points. The steps are done in a sequential, specific order.

To create a copy of the cab, the steps would be rearranged in this order:

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Step-by-step explanation:

here,

principal (p)=£6000

Rate (R)=. 3.4%

time (t)=3 yrs

now,

total investment is compound amount i.e CA

here,

\(CA = p(1 + \frac{r}{100} ) ^{t} \)

=£6000(1+3.4/100)^3

=£6633.044

here he will get his total investment as £6633.044 in compound interest of 3.4%

h= |x/3| equation that represents a horizontal stretch by a factor of 3 of the graph of g(x)=|x| .

Translation is the process of reworking text from one language into another to maintain the original message and communication.

The parent function is: g(x)=|x|

we stretch the parent function y = |x| by a factor of 3.

h= |x/3|

If the constant is between 0 and 1, we get a horizontal stretch

if the constant is greater than 1, we get a horizontal compression of the function.

Hence h= |x/3| equation that represents a horizontal stretch by a factor of 3 of the graph of g(x)=|x| .

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Answer:

Bottom Left

Step-by-step explanation:

Bottom Left

Answer:

thats a little complex

Step-by-step explanation:

advanced math?

Answer:

(7, 23).

Step-by-step explanation:

y=x+16

y=5x-12

Subtract the equations

0 = x - 5x + 16 - (-12)

-4x + 28 = 0

4x = -28

x = 7

plug x = 7 in first equation:

y = 7 + 16 = 23.

Solution :

Given :

a = (1, 2, 3, 4) ,    b = ( 4, 3, 2, 1),    c = (1, 1, 1, 1)     ∈   \(R^4\)

a). (a.2c)b + ||-3c||a

Now,

(a.2c) = (1, 2, 3, 4). 2 (1, 1, 1, 1)

         = (2 + 4 + 6 + 6)

         = 20

-3c = -3 (1, 1, 1, 1)

     = (-3, -3, -3, -3)

||-3c|| = \($\sqrt{(-3)^2 + (-3)^2 + (-3)^2 + (-3)^2 }$\)

        \($=\sqrt{9+9+9+9}$\)

       \($=\sqrt{36}$\)

        = 6

Therefore,

(a.2c)b + ||-3c||a = (20)(4, 3, 2, 1) + 6(1, 2, 3, 4)  

                          = (80, 60, 40, 20) + (6, 12, 18, 24)

                         = (86, 72, 58, 44)

b). two vectors \(\vec A\) and \(\vec B\) are parallel to each other if they are scalar multiple of each other.

i.e., \(\vec A=r \vec B\)   for the same scalar r.

Given \(\vec p\) is parallel to \(\vec a\), for the same scalar r, we have

\($\vec p = r (1,2,3,4)$\)

\($\vec p = (r,2r,3r,4r)$\)   ......(1)

Let \(\vec q = (q_1,q_2,q_3,q_4)\)   ......(2)

Now given \(\vec p\)  and  \(\vec q\) are perpendicular vectors, that is dot product of \(\vec p\)  and  \(\vec q\) is zero.

\($q_1r + 2q_2r + 3q_3r + 4q_4r = 0$\)

\($q_1 + 2q_2 + 3q_3 + 4q_4 = 0$\)  .......(3)

Also given the sum of \(\vec p\)  and  \(\vec q\) is equal to \(\vec b\). So

\(\vec p + \vec q = \vec b\)

\($(r,2r,3r,4r) + (q_1+q_2+q_3+q_4)=(4, 3,2,1)$\)

∴ \($q_1 = 4-r , \ q_2=3-2r, \ q_3 = 2-3r, \ q_4=1-4r$\)   ....(4)

Putting the values of \(q_1,q_2,q_3,q_4\) in (3),we get

\(r=\frac{2}{3}\)

So putting this value of r in (4), we get

\($\vec p =\left( \frac{2}{3}, \frac{4}{3}, 2, \frac{8}{3} \right)$\)

\($\vec q =\left( \frac{10}{3}, \frac{5}{3}, 0, \frac{-5}{3} \right)$\)

These two vectors are perpendicular and satisfies the given condition.

c). Given terminal point is \(\vec a\) is (-1, 1, 2, -2)

We know that,

Position vector = terminal point - initial point

Initial point = terminal point - position point

                  = (-1, 1, 2, -2) - (1, 2, 3, 4)

                  = (-2, -1, -1, -6)

d). \(\vec b = (4,3,2,1)\)

Let us say a vector \(\vec d = (d_1, d_2,d_3,d_4)\)  is perpendicular to \(\vec b.\)

Then, \(\vec b.\vec d = 0\)

     \($4d_1+3d_2+2d_3+d_4=0$\)

     \($d_4=-4d_1-3d_2-2d_3$\)

There are infinitely many vectors which satisfies this condition.

Let us choose arbitrary \($d_1=1, d_2=1, d_3=2$\)

Therefore, \($d_4=-4(-1)-3(1)-2(2)$\)

                      = -3

The vector is (-1, 1, 2, -3) perpendicular to given \(\vec b.\)

The area of the bases of the second triangular pyramid will be 3 times the first one.

What is a triangular pyramid?

A tetrahedron is a four-sided, three-dimensional object that is also known as a triangular pyramid. Its triangular base is formed by three triangles, the sides of which meet at the apex above the base.

We are given that a triangular pyramid with a volume of 90 cubic inches has a height of 15 inches.

So, area of the bases is

⇒ Volume = \(\frac{1}{3}\) * A * H

⇒ 90 = \(\frac{1}{3}\) * A * 15

⇒ 90 = A * 5

⇒ A = 18 square inches.

Similarly, another pyramid with a volume of 270 cubic inches has a height of 15 inches.

So, area of the bases is

⇒ Volume = \(\frac{1}{3}\) * A * H

⇒ 270 = \(\frac{1}{3}\) * A * 15

⇒ 270 = A * 5

⇒ A = 54 square inches.

Hence, the area of the bases of the second triangular pyramid will be 3 times the first one.

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Answer:

{u,v} = {4,1}

Step-by-step explanation:

Answer: 147.2 miles

Step-by-step explanation:

We can answer this by knowing the formula \(speed=\frac{distance}{time}\). Here, the speed is 46 miles/hour and the time is 3.2 hours. Let's put these values into the formula and solve for distance.

\(46=\frac{distance}{3.2}\\46*3.2=\frac{distance}{3.2}*3.2\\d=147.2\)

Alex traveled 147.2 miles.

Answer:

\(-5xy -13xy=-18xy\)

\(m^8n^1 * m^3n^5=m^{11} n^6\)

Step-by-step explanation:

\(-5xy -13xy=-18xy\)

\(m^8n^1 * m^3n^5\)

\(m^{8+3} =m^{11}\)

\(n^{1+5} =n^6\)

\(m^{11} n^6\)

Hope this helps!

There are 3080 ways 3 men and 2 women can be chosen if they are equally considered, using the multiplication principle of counting

The multiplication principle states that if there are m ways to perform one task and n ways to perform another task, then there are m x n ways to perform both tasks together.

To find the number of ways to choose 3 men from the 12 men, we can use the formula for combination, which is: ⁿCᵣ = n! / (r! (n-r)!).

where n is the total number of men and r is the number of men chosen

so, the number of ways to choose 3 men from the 12 men = ¹²C₃ = 1.

Similarly, we evaluate the number of ways to choose 2 women from the 8 women

as = ⁸C₂ = 14

Now, using the multiplication principle, we can find the total number of ways 3 men and 2 women be chosen if they are equally considered.

220 x 14 = 3080

Therefore, there are 3080 ways 3 men and 2 women can be chosen if they are equally considered, using the multiplication principle of counting

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The argument states that since all paintings by Matisse are beautiful and the museum has a painting by Matisse, the museum must have a beautiful painting.

The argument presented is an example of a logical fallacy known as affirming the consequent. It follows the form of a logical fallacy known as the fallacy of the converse. The fallacy of the converse occurs when one assumes that if the consequent (in this case, having a painting by Matisse) is true, then the antecedent (in this case, the painting being beautiful) must also be true. However, this is not a valid logical inference.

While it is true that the argument assumes that all paintings by Matisse are beautiful, it does not necessarily follow that the museum's painting by Matisse is also beautiful. There may be exceptions to the generalization that all Matisse paintings are beautiful. Additionally, beauty is subjective, and what one person finds beautiful, another may not.

Therefore, based on the argument presented, we cannot conclude with certainty that the museum has a beautiful painting solely because it possesses a painting by Matisse. The argument relies on a logical fallacy and does not provide sufficient evidence to support the claim that the museum's painting is beautiful.

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The area inside the loop of the limacon given by the polar equation r = 7 - 14sin(θ) is 294π square units.

To find the area inside the loop of the limacon given by the polar equation r = 7 - 14sin(θ), we need to evaluate the integral for half of the area and then double the result.

The curve of the limacon has a loop when 0 ≤ θ ≤ π, so we integrate from 0 to π. The area can be calculated as follows:

A = 2 ∫₀^π 1/2 r² dθ

Using the equation for r given, we can substitute and simplify:

A = 2 ∫₀^π 1/2 (7 - 14sin(θ))² dθ

A = 2 ∫₀^π 1/2 (49 - 196sin(θ) + 196sin²(θ)) dθ

A = ∫₀^π (98 - 392sin(θ) + 392sin²(θ)) dθ

Using the trigonometric identity 1 - cos(2θ) = 2sin²(θ), we can simplify further:

A = ∫₀^π (98 - 392sin(θ) + 196 - 196cos(2θ)) dθ

A = ∫₀^π (294 - 392sin(θ) - 196cos(2θ)) dθ

Integrating with respect to θ:

A = [294θ + 392cos(θ)sin(θ) + 98sin(θ)]₀^π

Evaluating at the limits of integration, we get:

A = [294π + 0 + 0] - [0 + 392cos(0)sin(0) + 98sin(0)]

A = 294π - 0 - 0 = 294π

Therefore, the area inside the loop of the limacon r = 7 - 14sin(θ) is 294π square units.

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For a straight line graph, the point at which the line crosses the y axis is called the y intercept. From the information given, the line crosses the y axis at - 5. This means that the y intercept is - 5

We would write the equation in the slope intercept form whicg is expressed as

y = mx + c

Where m represents the slpoe

We would substitute x = 2, y = 3 and c = - 5 in the equation above to determine the slope, m. It becomes

3 = m * 2 - 5

3 = 2m - 5

3 + 5 = 2m

2m = 8

m = 8/2

m = 4

The equation would be

y = 4x - 5y interceptF

Answer:

80√3c+12√5c⁴

Step-by-step explanation:

You gave 2√10c (4√30 + 3√2c³) so...

1.) Distribute
You will then get 8√300c+6√20c⁴

2.) Simplify the radical expression and you will get
8x10√3c+6x2√5c⁴

3.) Calculate
80√3c+12√5c⁴

And that is your answer

Answer:

80√3c+12√5c⁴

Step-by-step explanation:

2√10c (4√30 + 3√2c³) so first things first:

1.) Distribute

You will then get 8√300c+6√20c⁴

2.) Simplify the radical expression and you will get

8x10√3c+6x2√5c⁴

3.) Calculate

80√3c+12√5c⁴

The equation is exact, and its solution is given by\((4/3)x^3 - x^2y + 5x + 2y^2 = (5/3)y^3 - x^2y + 4y + (5/2)x^2 + C\), where C is a constant..

The given equation is exact. To determine if an equation is exact, we check if the partial derivative of the function with respect to y is equal to the partial derivative of the function with respect to x. In this case,\(\frac{{\partial}}{{\partial y}}(4x^2 - 2xy + 5) = -2x \quad \text{and} \quad \frac{{\partial}}{{\partial x}}(5y^2 - x^2 + 4) = -2x\). Since the partial derivatives are equal, the equation is exact.

To find the solution, we integrate the coefficient of dx with respect to x and the coefficient of dy with respect to y. Integrating \(4x^2 - 2xy + 5\) with respect to x gives \((4/3)x^3 - x^2y + 5x + g(y)\), where g(y) is the constant of integration with respect to x. Then, integrating \(5y^2 - x^2 + 4\) with respect to y gives \((5/3)y^3 - x^2y + 4y + h(x)\), where h(x) is the constant of integration with respect to y.

To obtain the solution, we equate the mixed partial derivatives:\(\frac{{\partial}}{{\partial y}}\left(\frac{4}{3}x^3 - x^2y + 5x + g(y)\right) = \frac{{\partial}}{{\partial x}}\left(\frac{5}{3}y^3 - x^2y + 4y + h(x)\right)\). By comparing the terms, we find that g'(y) = 4y and h'(x) = 5x. Integrating both equations gives g(y) =\(2y^2 + C1\)and h(x) = \((5/2)x^2 + C2\), where C1 and C2 are constants of integration. Thus, the general solution to the exact equation is\((4/3)x^3 - x^2y + 5x + 2y^2 = (5/3)y^3 - x^2y + 4y + (5/2)x^2 + C.\)

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The equation, in slope-intercept form, of the line that is parallel to the given line and passes through the point (0, 12) is y = -5x + 1

A line is the distance between two points

Given the equation of a line expressed as 10x + 2y = -2. Determine the slope

2y = -10x -2

y = -5x - 1

Slope of the line is -5

The equation of a line in point-slope form is y - y1 = m(x-x1)

Substitute the point and the slope of the parallel line

y - 12 = -5(x  - 0)
y - 12 = -5x
y = -5x + 12

Hence the equation, in slope-intercept form, of the line that is parallel to the given line and passes through the point (0, 12) is y = -5x + 12

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Answer:

its d

Step-by-step explanation:

i got it

Answer:

Number of Muhammad's swim suits = k - 8

Step-by-step explanation:

Given:

Number of Charlie's swim suits = K

Number of Muhammad's swim suits = 8 less than Charlie

Find:

Expression [Number of Muhammad's swim suits]

Computation:

Number of Muhammad's swim suits = 8 less than Charlie

Number of Muhammad's swim suits = k - 8

Step-by-step explanation:

The given number is 7,594,000,000.

To convert it into scientific notation,

First move the decimal point places to the left to find a number that is greater than or equal to 1 and less than 10. Then multiply by 10 , using an exponent on 10 that equals the number of places you moved the decimal. The exponent is negative if the original no was <1 and the exponent is positive, if the original number was  > 1.

In 7,594,000,000, we move the decimal point places to the left before 5. It means we have moved 9 digits left.

Hence, \(7,594,000,000=7.59\times 10^9\) is the scientific notation.

Zack should use a line with one arrowhead to map an abandoned line of reasoning.

A line with one arrowhead is commonly used in diagrams to represent the direction of a process or flow of information. In the case of mapping an abandoned line of reasoning, the line can be used to show the original train of thought that was pursued but later abandoned.

The arrowhead can indicate the point at which the reasoning was abandoned or diverted. Therefore, using a line with one arrowhead would be the most appropriate shape for Zack to use. The other shapes listed (orange oval, green rectangle, red) do not provide a clear representation of a line of reasoning and would not be suitable for this purpose.

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Answer:

0.22 square units

Step-by-step explanation:

Area of the left over fabric = Area of the square piece - Area of the circle

let the side length of the square piece be 1 unit

Area of the square piece = 1 * 1

Area of the square piece = 1 square units

Area of the circle = πd²/4

d is the diameter of the circle = 1 unit (equivalent to the side length of the square)

Area of the circle = π(1)²/4

Area of the circle = 3.14/4

Area of the circle = 0.785square units

Area of the left over fabric = 1- 0785

Area of the left over fabric = 0.215 square units

Hence the amount of fabric that would be leftover is 0.22 square units

Answer:

0.22 square units

Step-by-step explanation:

Hope this helps

Noote that the measure of angle R is 27°. Here is how we got that.

Since the largest triangle is right triangle, the vertical segment is the perpendicular bisector of right angle with vertex at the center of circle.

Then we have

m∠R + 18° = 90°/2

m∠R + 18° = 45°

m∠R = 45° - 18°

m∠R = 27°

Note that the angle on the top of the triangle is right angle, 90 deg. Its altitude is the vertical segment, which is also angle bisector. It bisects the right angle and each formed angle measures 90/2 = 45°

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Full Question:

Although part of your question is missing, you might be referring to this full question:

See the attached iamge.

Answer: 7/6 ft or 14 in

Step-by-step explanation:

Mouth to eye ratio ==> 18:11

18/6-11/6=7/6 ft or 14 in

Answer: 2,620 meatballs.

Step-by-step explanation:

Initially, Harold had 150 meatballs. Sarah ate 30 of them, so there are 150 - 30 = 120 meatballs left. The waiter then brought 2,500 more meatballs. Therefore, the total number of meatballs now is 120 + 2,500 = 2,620 meatballs.

5761.4 feet is the height of the mountain prior to construction

Given: 1.1h – 622.5 = 5,675

This is an algebraic equation, we need to solve for h

1.1h – 622.5 = 5675

collect like terms:

1.1h =  5675 + 622.5

Add like terms:

1.1h = 6337.5

Divide both sides by 1.1:

h = 6337.5/1.1

h = 5761.4 feet

Therefore,  the height of the mountain prior to construction is 5761.4 feet

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The main difference between the crime statistics reported under the traditional UCR program and the new UCR/NIBRS is the level of detail provided.

The traditional UCR program only collects information on the most serious offense in any given incident, while the new UCR/NIBRS collects information on all offenses involved in an incident. The new UCR/NIBRS also collects information on the location of an incident, the types of weapons used, and the number of victims and offenders involved. Additionally, the new UCR/NIBRS collects information about any arrests that were made in connection with an incident. This level of detail allows for more thorough analysis of crime trends and patterns, and helps police and other law enforcement agencies better understand the causes and motivations behind criminal activity.

The main difference between the traditional UCR program and the new UCR/NIBRS is the level of detail collected, with the new program collecting information on all offenses, location, weapons used, victims and offenders, and any arrests made in connection with an incident. This level of detail allows for more thorough analysis of crime trends and patterns.

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Imagine that a survey of randomly selected people finds that people who used sunscreen were more likely to have been sunburned in the past year.

There are several possible explanations for the finding that people who used sunscreen were more likely to have been sunburned in the past year.

However, without additional context or data, it is difficult to determine the most likely explanation definitively. Here are a few possible explanations to consider:

1. Ineffective or improper use of sunscreen: It is possible that the individuals who reported using sunscreen did not apply it correctly or did not reapply it as recommended.

Inadequate application or failure to follow proper sunscreen usage guidelines could result in insufficient protection from the sun's harmful rays, leading to sunburn.

2. Self-selection bias: It is possible that individuals who have previously experienced sunburns may be more likely to use sunscreen. They may be more aware of the potential risks and take precautions, including using sunscreen.

This could create an association between sunscreen use and sunburn, even though sunscreen itself is intended to prevent sunburn.

3. Recall bias: The survey responses may be subject to recall bias, where individuals may inaccurately remember or report their sunscreen use and sunburn experiences.

Memory limitations or subjective perceptions of sunburn severity could influence the reported data and the observed association between sunscreen use and sunburn.

4. Confounding factors: There may be other factors or variables at play that are related to both sunscreen use and sunburn. For example, individuals who engage in activities that increase sun exposure or who have certain skin types may be more likely to both use sunscreen and experience sunburn.

It is important to note that further investigation, including more detailed surveys, data collection and statistical analysis, would be necessary to determine the most likely explanation for the observed association between sunscreen use and sunburn.

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Answer:

The missing fraction is 6/12

(you can further simplify this but the question requires that you don't do that)

Step-by-step explanation:

To add fractions easily, their denominators should have the same value, so the denominator should be 12,

Then, to get 16 in the numerator, we need to find a number that on adding to 10, gives 16, or,

10 + x = 16

x = 16 - 10

x = 6

So, the numerator should be 6

so we get the fraction, 6/12

We can also solve it in an alternate way,

\(10/12 + x = 16/12\\x = 16/12 - 10/12\\x = (16-10)/12\\x = 6/12\)

Trevarius' investment will grow exponentially due to the compounding effect of interest.

Compounded interest refers to the process of earning interest not only on the initial principal amount but also on the accumulated interest from previous periods.

This means that as time progresses, the interest earned becomes part of the new principal, resulting in a compounding effect.

In a linear growth scenario, the investment would grow at a constant rate over time, where the increase in value would be the same for each time period. However, in the case of compounded interest, the growth rate is not constant but rather increases over time due to the compounding effect.

As more interest is added to the principal, the subsequent interest calculations are based on a larger amount, resulting in a higher growth rate.

This compounding effect leads to exponential growth because the investment value increases at an accelerating rate over time.

Mathematically, the exponential growth of Trevarius' investment can be represented by the formula \(A = P(1 + r/n)^{(nt),\)

where A is the final amount, P is the principal, r is the interest rate, n is the number of compounding periods per year, and t is the number of years.

By continuously reinvesting the earned interest, Trevarius' investment will experience exponential growth, allowing his initial investment to grow significantly over time.

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Similar triangles have different dimensions, but their measurements have the same ratio.

In the image, we can see two triangles. A large triangle and a small triangle. These are similar. How can we tell? They share the same angles.

Now, we can set up a proportion comparing their side lengths:

\(\dfrac{82}{28}=\dfrac{(2x+8)+(5x-4)}{2x+8}\)

Theoretically, if we divide corresponding side lengths of two similar shapes, we should get the same value. This is what makes the proportion true.

Now, simplify:

\(\dfrac{82}{28}=\dfrac{(2x+8)+(5x-4)}{2x+8}\)

\(\dfrac{41}{14}=\dfrac{(2x+8)+(5x-4)}{2x+8}\)

\(41(2x+8)=14[(2x+8)+(5x-4)]\)

\(82x+328=14[2x+8+5x-4]\\82x+328=14(7x+4)\\82x+328=98x+56\)

\(328=16x+56\\272=16x\\x=17\)

x = 17