The quadrilateral WXYZ is a square. The coordinates of the vertices W and X are (-3, 2) and (5, 3) respectively. Click to match each side of
the square with its slope.

Answer:

y = 2x + 2.

Step-by-step explanation:

The equation of a line with gradient "m" can be represented as y = mx + b, where b is the y-intercept. To find the equation of a line that passes through the point (1, 4) and has a gradient of 2, we can use the point-slope form of a line:

y - y1 = m(x - x1), where (x1, y1) is the point on the line and m is the gradient.

Plugging in the values for the gradient (m = 2), point (x1 = 1, y1 = 4), we have:

y - 4 = 2(x - 1)

Expanding the right side, we get:

y - 4 = 2x - 2

Adding 4 to both sides, we get:

y = 2x + 2

So the equation of the line that has a gradient of 2 and passes through the point (1, 4) is y = 2x + 2.

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Hope this helps :)

If there were 132 crayons in John's backpack, the number of blue crayons is equal to blue crayons.

In Mathematics, a proportion simply refers to an equation which is typically used to represent the equality of two (2) ratios. This ultimately implies that, proportions can be used to establish that two (2) ratios are equivalent and solve for all unknown quantities.

By applying direct proportion to the given information, we have the following mathematical expression:

3 crayons = 8 blue crayons

132 crayons = X blue crayons

By cross-multiplying, we have the following:

3x = 132 × 8

3x = 1,056

x = 1,056/3

x = 352 blue crayons.

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0.025285 km is 2528.5 cm. 0.02528 km as significant figures.

The given centimeters:

2528.5 cm

To convert kilometers to cm, we first need to convert the given number in centimeters to meters and then to kilometers.

To convert from centimeters to meters:

1 cm = 1/100 m

2528.5 cm = (2528.5 / 100) = 25.285 m

To convert meters to kilometers:

1 m = (1/ 1000) km

25.285 m = (25.285 / 1000) km = 0.025285 km

Since, 2528.5 cm has 5 significant figures, we can write 0.025285 km as 0.02528 km in 5 significant figures.

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The 6 distinct possible areas can the rectangle have.

Given the perimeter of a rectangle, we can find the length (l) and width (w) using the formula:

The perimeter of a rectangle is defined as the sum of all the sides of a rectangle. In case of a rectangle, the opposite sides of a rectangle are equal and so, the perimeter will be twice the width of the rectangle plus twice the length of the rectangle and it is denoted by the alphabet “p”.

Let us derive the formula for its perimeter and area

2l + 2w = 24

Solving for l and w, we get:

l + w = 12

l and w can be any combination of positive integers that add up to 12. The possible combinations are:

(1, 11), (2, 10), (3, 9), (4, 8), (5, 7), (6, 6)

Therefore, there are 6 distinct possible combinations of length and width for a rectangle with a perimeter of 24 inches, and therefore 6 distinct possible areas.

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The reliability corresponds to the design factor of 1. 2 is R=0.9616 and d=1.02, for 1.5 R=0.9999 and d=1.14.

To find the reliabilities we first have to find z. There is a formula to find z.

[tex]z=\frac{n_d-1}{\sqrt{n_d^2C_s^2+C_s_d^2} }[/tex]

Factor c is defined as:

C=sd/u

For the strength, this is simply because we are given μs and sd's so we have

[tex]C_s=\frac{6.59kpsi}{95.5kpsi}[/tex]

Cs=0.069

For the stress, it's a bit different since we are given the μp and sd p:

sd=4P/πd².

The standard deviation is:

σ=4/πd²*σP

From this we have:

Cσ=σP/⁻P

=5kip/65kip

Cσ=1/13

For nd=1.2 we have:

[tex]z=-\frac{1.2-1}{\sqrt{1.2^2(0.069)^2+(1/13)^2} }[/tex]

z=-1.77

from table A-10 we see that the probability of failure is 0.0384, meaning the reliability is

R=1-F

R=1-0.0384

R=0.9616

We can express the diameter from 2 equations for stress:

[tex]\frac{4P}{\pi d^2} =\frac{S}{n_d} - > d=\sqrt{\frac{4Pn_d}{\pi S} } \\\\d=\sqrt{\frac{4.65kips.1.2}{\pi .95.5kpsi} }[/tex]

d=1.02

from nd=1.5 we have:

[tex]z=-\frac{1.5-1}{\sqrt{1.5^2(0.069)^2+(1/13)^2} }[/tex]

z=-3.88

from table A-10 we see that the probability of failure is 0.0001, meaning the reliability is:

R=1-F

R=1-0.0001

R=0.9999

The diameter is:

[tex]d=\sqrt{\frac{4.65kips.1.5}{\pi .95.5kpsi} }[/tex]

d=1.14

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Based on the slope of -1/2, we have:

   y = -1/2 x + b

Substitute in (6,-5), we have:

  -5 = -1/2 (6) + b

We can solve this for b:

  -5 = -3 + b

  -2 = b

Now we have the equation:

  y = -1/2 x - 2

Answer:

An isosceles triangle because it will have two side lengths that are equal.

Step-by-step explanation:

Answer:

110 miles

Step-by-step explanation:

See the attached worksheet.  A spreadsheet was used to add each of the mileage options to the start of 18981 and observe which one was a palindrome.  110 miles added to 18981 is 19091, a palindrome.

Alicia was paid $ 51.25.

According to the question,

Let the amount that Alicia was paid by Y.

If she already spent $10.25 of her paycheck and this is 20% of her paycheck, then

    20 % of  Y =  10.25

   ⇒ [tex]\frac{20}{100} * Y[/tex] = 10.25

    ⇒0.2 * Y = 10.25

     ⇒  Y = [tex]\frac{10.25}{0.2}[/tex]  ( by using division)

       ∴ Y =  51.25

So, Alicia was paid $ 51.25.

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My best guess is that the sequence an= 5n2 n3 5 has an infinite limit. The definition of a limit, which indicates that as n gets closer to infinity, the limit of an= 5n2 n3 5 is also infinite, can be used to demonstrate this.

My best guess is that the sequence an= 5n2 n3 5 has an infinite limit. The definition of a limit, which indicates that as n gets closer to infinity, the limit of an= 5n2 n3 5 is also infinite, can be used to demonstrate this. In other words, when n increases without limit, the value of a will also increase until it reaches infinity. We can examine the value of a for various values of n to illustrate this. The value of a rises sharply as n rises. As an illustration, an equals 12500 when n = 5 and 250000 when n = 10. The value of a rises exponentially as n rises, proving that the sequence's limit, an= 5n2 n3 5, is truly infinite. Additionally, we may provide a formal demonstration for this using the limit definition. The limit of the sequence an= 5n2 n3 5 is in fact infinity when n = is substituted into the expression, yielding a = 523 ,5 = ∞, which proves that the limit of the sequence an= 5n2 n3 5 is indeed infinity.

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Answer:

7

Step-by-step explanation:

If the bell tolls every 30mins on the hour and at half past the hour, then the bell will toll at 12 noon, 12:30pm, 1pm, 1:30pm, 2pm, 2:30pm and 3pm which is 7 times.

i hope is help

The meaning of the y-intercept of the linear function is given as follows:

The tablet starts with 80 percent of battery remaining.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The graph of the function touches the y-axis at y = 80, hence the intercept b is given as follows:

b = 80.

As the output variable is the battery percentage, it represents the initial battery percentage.

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The meaning of the y-intercept of the linear function is given as follows:

The tablet starts with 80 percent of battery remaining.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The slope m represents the rate of change of the output variable relative to the input variable.

The intercept b represents the value of y when the graph of the function touches of crosses the y-axis.

The graph of the function touches the y-axis at y = 80, hence the intercept b is given as follows:

b = 80.

As the output variable is the battery percentage, it represents the initial battery percentage.

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Answer: e is the correct option.

Step-by-step explanation:

Option e  If z = xy, then z = 2.

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Answer:at the end of the day u have 34 dollars

the amount that u carry around is 4 dollars.

Step-by-step explanation: $27-14=13

13-9=4.

4+30=34.

Hope this helped.

Answer:

circumference= 28.26

Area= 63.585

Step-by-step explanation: So, to do this question you have to know the formula for both circumference and the area. So to find the circumference you have to do

                   2*3.14*4.5 -(9/2)

                  = 28.26

And to find the area you have to do.

              3.14*4.5^2

              = 63.585

Therefore, those are the answers. Please let me know if they are wrong.

Answer:

V = 8446.9 in³

Step-by-step explanation:

Just use the cylinder formula.

V = πr²h

V = (3.14)(21)²(6.1)

V = 8446.9 in³

The required match of the given reasons with the statement is,
1. AR = AS                       [equal sides of the isosceles triangle]
2. AM = AM                    [common side]
3. MR = MS                     [As median bisect the line RS]

△RAM ≅ △SAM             (SSS, Reflexive, Definition of isosceles triangle
                                          Definition of the median, Given)

In congruent geometry, the shapes that are so identical. can be superimposed to themselves.

Here,
Triangle RAS is isosceles, AM is a median
Consider triangle RAM and SAM

1. AR = AS                       [equal sides of the isosceles triangle]
2. AM = AM                    [common side]

3. MR = MS                     [As median bisect the line RS]
△RAM ≅ △SAM             (SSS, Reflexive, Definition of an isosceles triangle, Definition of the median, Given)

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Answer:(a) The smallest possible distance between the two towns would be 12km (the distance to Bergville) + 15km (the distance to Reddington) = 27km. The largest possible distance would be 12km + 15km + 1km (the margin of error for each distance being given to the nearest kilometer) = 28km.

(b) The possible difference in the distance the two walkers walk would be the difference in the distances given on the sign, which is 15km - 12km = 3km. However, this difference would also be affected by the margin of error of 1km for each distance given on the sign, so the possible difference in distance could range from 2km to 4km.

A quadratic function for the area of a figure can be represented as [tex]A(x) = ax^2 + bx + c,[/tex] where a, b, and c are constants and x is the side length of the figure.

[tex]A(x) = x^2 - 6x + 9\\A(7) = (7^2) - (6\times 7) + 9 \\= 49 - 42 + 9 = 16[/tex]

In this case, the given value of x is 7, so the area of the figure can be found by plugging 7 into the equation. [tex]A(7) = a(7^2) + b(7) + c = 49a + 7b + c.[/tex]

Therefore, the area of the figure for [tex]x = 7 , 49a + 7b + c.[/tex]

The quadratic equation can also be used to calculate the area of the figure for any given value of x.

To do this, simply plug in the desired value of x into the equation and solve for the area.

For example, if we want to find the area of the figure for x = 4, then we would plug 4 into the equation and solve for the area. [tex]A(4) = 16a + 4b + c[/tex].

This shows that the area of the figure for x = 4 is 16a + 4b + c.

In summary, the quadratic equation [tex]A(x) = ax^2 + bx + c[/tex] can be used to calculate the area of a figure for any given value of x.

For the given value of x = 7, the area of the figure is calculated to be [tex]49a + 7b + c.[/tex]

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Complete question -

Write a quadratic function for the area of the figure. Then, find the area for the given value of x.

x=7

A quadratic function for the area of the figure is A(x)= (Simplify your answer.).

The solution of the given initial value problem y'' + y = f(t), y(0) = 7, y'(0) = 4 where f(t) = [tex]\left\{\begin{matrix}1, & 0\leq t\leq \frac{\pi}{2}\\ 0, & \frac{\pi}{2}\leq t < \infty\end{matrix}\right.[/tex] is 1 + 6cost + 4sint + u(t - π/2)(cos(t - π/2) - 1).

The initial value problem y'' + y = f(t), y(0) = 7, y'(0) = 6 where

f(t) = [tex]\left\{\begin{matrix}1, & 0\leq t\leq \frac{\pi}{2}\\ 0, & \frac{\pi}{2}\leq t < \infty\end{matrix}\right.[/tex]

Now f(t) = 1[u(t-0) - u(t-π/2)]

f(t) = u(t) - u(t-π/2)

Laplace transformation of f(t) is

L{f(t)} = L{u(t)} - L{u(t-π/2)}

L{f(t)} = 1/S - [tex]e^{\pi S/2}[/tex]/S

Now taking the Laplace transformation on both side to the equation y'' + y = f(t).

L{y''} + L{y} = L{f(t)}

S^2Y(S) - SY(0) - Y'(0) + Y(S) = 1/S - [tex]e^{\pi S/2}[/tex]/S

S^2Y(S) - 7S - 4 +Y(S) = 1/S - [tex]e^{\pi S/2}[/tex]/S

(S^2 + 1)Y(S) - 7S - 4 = 1/S - [tex]e^{\pi S/2}[/tex]/S

(S^2 + 1)Y(S) = 1/S - [tex]e^{\pi S/2}[/tex]/S + 7S + 4

Divide by (S^2 + 1) on both side, we get

[tex]Y(S) = \frac{1}{S(S^2 + 1)} -\frac{e^{\pi S/2}}{S(S^2 + 1)} + \frac{7S}{(S^2 + 1)}+\frac{4}{S^2 + 1}[/tex]

Simplify

[tex]Y(S) = \frac{1}{S}-\frac{S}{S^2 + 1} -\left[\frac{1}{S}-\frac{S}{S^2 + 1}\right]e^{\pi S/2} + \frac{7S}{(S^2 + 1)}+\frac{4}{S^2 + 1}[/tex]

Now Y(t) = [tex]L^{-1}(Y(S))[/tex]

Y(t) = [tex]L^{-1}\left[\frac{1}{S}\right]-L^{-1}\left[\frac{S}{S^2 + 1}\right] -L^{-1}\left[\frac{e^{\pi S/2}}{S}\right]-L^{-1}\left[\frac{Se^{\pi S/2}}{S^2 + 1}\right] + L^{-1}\left[\frac{7S}{(S^2 + 1)}\right]+L^{-1}\left[\frac{4}{S^2 + 1}\right][/tex]

Y(t) = 1 - cost - u(t - π/2) + cos(t - π/2) u(t - π/2) + 7cost + 4sint

Y(t) = 1 + 6cost + 4sint + u(t - π/2)(cos(t - π/2) - 1)

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The complete question is:

Find the solution of the given initial value problem y'' + y = f(t), y(0) = 7, y'(0) = 4 where f(t) = [tex]\left\{\begin{matrix}1, & 0\leq t\leq \frac{\pi}{2}\\ 0, & \frac{\pi}{2}\leq t < \infty\end{matrix}\right.[/tex]

The sum of the integrals of 175 and 1711 times the function of x is the integral of 115 times the function of x.

Calculate 175f(x)dx in step one.

∫175f(x)dx = 2.4

Calculate 1711f(x)dx in step two.

∫1711f(x)dx = 15.1

The next step is to deduct 175f(x)dx from 1711f(x)dx.

15.1 - 2.4 = 12.7

Step 4 is to add the outcome to 175f(x)dx.

2.4 + 12.7 = 15.1

In step five, take away 175f(x)dx from 115f(x)dx.

∫115f(x)dx = 15.1

By deducting the integral of 175 times the function of x from the integral of 1711 times the function of x, we get at 12.7, which is the answer to the question. The solution is 15.1, which we may obtain by adding this result to the integral of 175 times the function of x. This indicates that 15.1 is the same as the integral of 115 times the function of x.

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The average height of a tree whose age is 25 years old is 364 inches.

A linear model is an equation that describes a relationship between two quantities that show a constant rate of change.

Given that, a table giving a relation between the height and age of trees.

The linear model representing the same is given by,

y = 13.7x + 21.7, where y is the height and x is the age of a tree,

We need to find the average height of a tree whose age is 25 years old,

To find this, put x = 25 in the linear model given,

y = 13.7 × 25 + 21.7

y = 342.5 + 21.7

y = 364.2

y ≈ 364

Hence, the average height of a tree whose age is 25 years old is 364 inches.

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The time at which the velocity falls to zero can be expressed as the cube root of 5/9.

What is velocity ?

Velocity is the directional speed of an object in motion as an indication of its rate of change in position as observed from a particular frame of reference and as measured by a particular standard of time.

The velocity of an object can be found by taking the derivative of the position with respect to time.

So, the velocity can be expressed as:

v(t) = d(x(t))/dt = (-0.20)3t^2 (3.0)2t (10.0) + 6.0

The velocity of an object is zero when v(t) = 0, so we can set v(t) = 0 and solve for t:

(-0.20)3t^2 (3.0)2t (10.0) + 6.0 = 0

(-0.20)3t^2 (3.0)2t = -6.0 / (10.0)

(-0.20)3t^2 (3.0)2t = -0.6

t^2 (3.0)2t = -0.6 / (-0.20)3 = 5.0

t^3 = 5.0 / (3.0)2 = 5.0 / 9.0

t = (5.0 / 9.0)^(1/3)

So, the time at which the velocity falls to zero can be expressed as the cube root of 5/9.

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That m is odd, then the integers between 1 and m − 1 equals 2−1 mod m it must be k=1 and n = 1+m2.

Given an integer m, two integers a and b are congruent modulo m if

m| (a − b).

We write a ≡ b (mod m).

Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers.

I will also sometimes say equivalent modulo m. Notation note: we are using that "mod" symbol in two different ways.

Let n be the inverse of 2( mod m)

Where 1<n<m−1

2n≡1 ( mod m)

⇒ 2n=1+mk

Since m is odd then m=2l+1

⇒ 2n=1+(2l+1)k

Then solve for n(mod m) as that would put it within 1<n<m−1.

As an aside, we only care for 1≤n≤m−1, we don't care about strict inequalities. Indeed, if m=3 then you'd have a problem as there aren't even any integers strictly between 1 and 3−1

Supposing that m = [tex]2l+1[/tex] then [tex]2*(l+1)[/tex] = [tex]2l + 2[/tex] = m+1

We want integer n=1+mk2 between 1 and m−1.

Since m is odd, we need k to be odd, in order for 1+mk to be divisible by 2 so n is an integer.

If k≥3 then 1+mk2>m−1.

If k≤−1 then 1+mk2<1.

So it must be k=1 and n = 1+m2.

Therefore,

That m is odd, then the integers between 1 and m − 1 equals 2−1 mod m it must be k=1 and n = 1+m2.

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The required average temperature of the last summer is given as 22.10 °C.

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

Here,
Let the temperature of last summer's average be x insert,

According to the question,
21 = x - 5%x
x = 21 / 0.95
x = 22.10 °C

Thus, the required average temperature of the last summer is given as 22.10 °C.

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Answer:

-18x + -144

Step-by-step explanation:

The correct answer that is least capable of responding quickly to shifting consumer needs and of keeping a customer-focused attitude matrix.

Given that,

From given below which of the three organizational types—projectized, matrix, or functional—is least suited to providing quick responses to changing customer needs and upholding a customer-focused attitude

Matrix of the three organizational forms – projectized, matrix, or functional – is least suited for fast response to changing customer requirements and for maintaining a customer focus.

The correct answer is functional.

Functional  of the three organizational forms – projectized, matrix, or functional – is most suited for aligned project accountability and authority, and for rapid reaction to customer needs.

The correct answer is projectized.

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Answer:

Without knowing the exact number of vowels and consonants in the bag, it is not possible to accurately predict the number of vowels. However, if the bag is made up of a certain proportion of vowels and consonants and this proportion remains consistent throughout the draws, we can use the proportion of vowels and consonants in the 50 draws to estimate the proportion in the bag.

For example, if after 50 draws, there are 20 vowels and 30 consonants, we can estimate that the bag contains 40% vowels and 60% consonants. So, we can estimate the number of vowels in the bag as 42(105 x 40%).

Answer:

Step-by-step explanation:

hi

The equation of the parabola in any form is; (x + 5)² = 4(y - 4)

The general equation of a parabola is given by the expression;

y = a(x – h)² + k or x = a(y – k)² + h.

Where (h, k) denotes the coordinates of the vertex

2p = 5 - 3

2p = 2

p = 1.

Thus, the coordinates of the vertex will be;

Vertex (-5, 5 - 1) = (-5, 4)

Therefore the equation of parabola is expressed as;

(x + 5)² = 4(y - 4)

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The insurance firm will pay $45,000, claims the statement .The correct option B.

Damage to personal or real estate is known as property damage. A vehicle accident that results in damage or a chemical release on real estate might serve as examples. To guard it against possibility of property damage, property owners might get property insurance.

Personal Accident Liability Insurance for Monique provides up for $20,000 per person or $40,000 overall in coverage. Therefore, the insurance provider will cover the two passengers in the other car's medical expenditures up to a maximum of $40,000.

For damages to the other automobile, she Damage To property Liability Insurance provides up to $25,000 in coverage.

So in total, the insurance company will pay $40,000 + $25,000 = $65,000.

However, Monique's policy has a per-accident limit, so the insurance company will pay up to the policy limit, which is $45,000.

Thus, the insurance company will pay $45,000.

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The Complete Question :

Monique has 20/40 Bodily Injury Liability Insurance and $25,000 Property Damage

Liability Insurance. She causes an accident while driving. In the other car, one person

has $30,000 in medical expenses and another has $25,000 in medical expenses. The

other car has $12,000 in damage and Monique's car has $6,000 in damages.

How much will the insurance company pay?

a. $73,000

b. $45,000

c. $52,000

d. $58,000