Describe the translation of the point to its image.
(6,-8)→ (12,-2)

The main difference between an area variance and a use variance is that area variance allows for an exception to zoning regulations related to the physical characteristics of a property, while use variance allows for an exception to regulations related to the intended use of a property.

An area variance is typically granted when a property owner is unable to comply with zoning regulations related to setbacks, building height, lot coverage, or other physical characteristics of a property.

In contrast, a use variance allows a property owner to use their property for a purpose that is not permitted under the current zoning regulations. This may include using a residential property for commercial purposes or using a commercial property for residential purposes.

Use variances are generally more difficult to obtain than area variances, as they require a showing of a unique hardship or practical difficulty that cannot be addressed through other means.

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It would take 17 years for the value of the account to reach $2,550. The solution has been obtained by using the concept of compound interest.

What is compound interest?

The principal as well as the interest that has accrued over the previous period are both used to compute interest. Compound interest factors the principal into the calculation for determining the interest for the subsequent month, in contrast to simple interest, which does not. In mathematics, the symbol for compound interest is typically the letter C.I.

We are given the principal amount as $790 paying an interest rate of 6.9% compounded continuously.

The final balance is $2,550.

We know that formula for continuous compounding interest is

\(P(t) = P_{0} e^{rt}\)

So, using this, we get

⇒\(2550 = 790 e^{0.069*t}\)

Solving this, we get

t = 17

Hence, it would take 17 years for the value of the account to reach $2,550.

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Answer:

d

Step-by-step explanation:

6 weeks from now, you will have $215 in your bank account

The given parameters are:

b = 60 + (20+6)w

When the account balance is $215, we have

60 + (20+6)w = 215

Subtract 60 from both sides

(20+6)w = 155

This gives

26w = 155

Divide both sides by 26

w = 5.96

Approximate

w = 6

Hence, 6 weeks from now, you will have $215 in your bank account

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Answer:

y=7x

Step-by-step explanation:

When finding the slope intercept form using 2 points, we do the following.

y=mx+b (Slope intercept from)

y=7x+b (7 is slope)

Substitute the point

7=7(1)+b

7=7+b

b=0

y=7x

The slope intercept equation is y = 7x

Answer:

728

Step-by-step explanation:

2+6+18+...+486

a=2

r=6/2=3

\(a_{n}=ar^{n-1}\\486=2(3)^{n-1}\\3^{n-1}=486/2=243=3^5\\n-1=5\\n=5+1=6\\S_{6}=2\frac{3^6-1}{3-1} \\=2\frac{729-1}{2}\\=728\)

The equation of the plane is: 3x + 24y - 2z + 31 = 0

To find an equation of a plane containing three points:

We can use the fact that the normal vector to the plane is perpendicular to any vector lying in the plane. We can find the normal vector by taking the cross product of two vectors lying in the plane, and then use the equation of a plane in point-normal form.

Let's first find two vectors lying in the plane by taking the differences between the three given points:

v1 = <(-2) - (-4), 5 - 1, 1 - (-4)> = <2, 4, 5>

v2 = <(-2) - (-4), 6 - 1, 3 - (-4)> = <2, 5, 7>

Now we can take the cross product of v1 and v2 to find a normal vector to the plane:

n = v1 x v2 = <(4)(7) - (5)(5), -(2)(7) + (5)(2), (2)(5) - (4)(2)> = <-3, -24, 2>

We want the coefficient of x in the equation of the plane to be 3, so we need to scale the normal vector by a factor of -1/3:

n' = (1/3)<3, 24, -2> = <1, 8, -2/3>

Now we can use any of the three given points to write the equation of the plane in point-normal form. Let's use the first point (-4, 1, -4):

(x - (-4), y - 1, z - (-4)) · <1, 8, -2/3> = 0

Simplifying and multiplying through by 3 to eliminate the fraction, we get:

3x + 24y - 2z + 31 = 0

So an equation of the plane containing the three points (-4, 1, -4), (-2, 5, 1), (-2, 6, 3) in which the coefficient of x is 3 is 3x + 24y - 2z + 31 = 0.

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Answer: 57.8

Step-by-step explanation:48.7 seconds + 49.3 seconds.= 57.8

If the diagonals of a quadrilateral divide each other proportionally, it is a trapezium.

Let's consider a quadrilateral ABCD, where the diagonals AC and BD intersect at point E. If the diagonals divide each other proportionally, it means that AE/CE = BE/DE.

To prove that the quadrilateral is a trapezium, we need to show that one pair of opposite sides is parallel.

Using the proportionality condition, we can rewrite it as (AE/CE) = (BE/DE) = 1.

By the Converse of the Basic Proportionality Theorem, we know that if two lines are cut by a transversal such that corresponding angles are equal, then the lines are parallel. In this case, AE is parallel to CD, and BE is parallel to AD.

Therefore, we have shown that AB || CD, which is the definition of a trapezium.

If the diagonals of a quadrilateral divide each other proportionally, it can be concluded that the quadrilateral is a trapezium.

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Check the picture below.

Make sure your calculator is in Degree mode.

If his beard  was 8 millimeter long and each passing week it grew 2 additional millimeters, the graph that represents the relationship between the length of his beard in millimeter and time in week has been plotted

The initial length of the beard = 8 millimeter

The length of beard grow in each week = 2 millimeter

Consider the number of week as x

Therefore the linear relationship will be

The length of the beard y = 2x + 8

Plot the graph using the equation

Hence, If his beard  was 8 millimeter long and each passing week it grew 2 additional millimeters, the graph that represents the relationship between the length of his beard in millimeter and time in week has been plotted

The complete question is

Rip van Winkle fell asleep for a very long time. When he fell asleep, his beard was 8 millimeters long, and each passing week it grew 2additional millimeters.

Graph the relationship between the length of Rip van Winkle's beard (in millimeters) and time (in weeks).

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Answer:

B works it satisfies the equation to both 1 ⅔ i = 1 ⅔ i

The value of x from the given triangle is 7√2 units.

The sides and angles of a right-angled triangle are dealt with in Trigonometry. The ratios of acute angles are called trigonometric ratios of angles. The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).

From the given triangle, one of the angle in right angle triangle is 45°, opposite side is 7 units and hypotenuse is x units.

We know that, sinθ =Opposite/Hypotenuse

sin45°=7/x

1/√2=7/x

x=7√2 units

Therefore, the value of x is 7√2 units.

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Answer:1440

Step-by-step explanation:

A score of x = 60 on an exam with μ = 72 and σ = 12 is comparatively better than a score of x = 70 on an exam with μ = 82 and σ = 8.

To compare the two scores, we can convert them to z-scores, which tell us how many standard deviations a particular value is from the mean. The formula for z-score is:

z = (x - μ) / σ

where x is the value, μ is the mean, and σ is the standard deviation.

For the first score of x = 70 on an exam with μ = 82 and σ = 8, the z-score is:

z = (70 - 82) / 8 = -1.5

For the second score of x = 60 on an exam with μ = 72 and σ = 12, the z-score is:

z = (60 - 72) / 12 = -1.0

The z-score for the first score is lower than the z-score for the second score, which means that the first score is further below its mean than the second score is below its mean. Therefore, we can say that a score of x = 60 on an exam with μ = 72 and σ = 12 is comparatively better than a score of x = 70 on an exam with μ = 82 and σ = 8.

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The statement that shows a discrepancy between the check register and bank statement is: C. Gavin: The balance in his check register is $500 and the balance in his bank statement is $510.

The check register shows a balance of $500, while the bank statement shows a balance of $510.

In the case of Gavin, where the balance in his check register is $500 and the balance in his bank statement is $510, there is a $10 discrepancy between the two.

A possible explanation for this discrepancy could be outstanding checks or deposits that have not yet cleared or been recorded in either the check register or the bank statement.

For example, Gavin might have written a check for $20 that has not been cashed or processed by the bank yet. Therefore, the check register still reflects the $20 in his balance, while the bank statement does not show the deduction. Similarly, Gavin may have made a deposit of $10 that has not yet been credited to his account in the bank statement.

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The magnitude of the electric field at the origin due to the given charges is 2.98×10^4 N/C, and its direction is 139.5 degrees counterclockwise from the positive x-axis. The magnitude of the instantaneous acceleration of a proton placed at the origin is 5.97×10^14 m/s^2, and its direction is 139.5 degrees counterclockwise from the positive x-axis.

To determine the electric field at the origin, we need to calculate the contributions from each charge and then sum them up. The electric field due to a point charge can be found using Coulomb's law, which states that the electric field magnitude (E) is equal to the charge (Q) divided by the distance squared (r^2), multiplied by a constant (k) equal to 8.99×10^9 Nm^2/C^2. Considering the first charge, the distance from the origin (0, 0) to (0, -2) is 2 cm. Using the formula, we find that the electric field magnitude due to this charge is 1.12×10^4 N/C, pointing along the positive y-axis.

For the second charge, the distance from the origin to (3, 0) is 3 cm. Calculating the electric field magnitude for this charge yields 3.32×10^4 N/C, pointing along the positive x-axis. Lastly, the third charge at (3, 4) creates an electric field magnitude of 2.24×10^4 N/C, directed at an angle of 53.13 degrees from the positive x-axis.

To determine the net electric field at the origin, we must vectorially add the electric field contributions from each charge. By adding the x-components and y-components separately, we find that the resultant electric field magnitude is 2.98×10^4 N/C, at an angle of 139.5 degrees counterclockwise from the positive x-axis.

Now, let's calculate the instantaneous acceleration of a proton at the origin. Since the proton has a positive charge, it will experience a force in the opposite direction to the electric field. We can use Newton's second law, F = ma, where F is the force experienced by the proton, m is its mass, and a is its acceleration. The force experienced by the proton is given by the electric field strength multiplied by its charge. The mass of a proton is approximately 1.67×10^-27 kg, and its charge is 1.6×10^-19 C. Substituting these values, we find that the acceleration of the proton is approximately 5.97×10^14 m/s^2, pointing at an angle of 139.5 degrees counterclockwise from the positive x-axis, which is the same as the direction of the electric field at the origin.

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Graph A.

Graph A has a line passing through (0,4).

.............................................................................

Answer:

Given equation are 3x+4y=11 and 2x+3y=8

Comparing with a

1

x+b

1

y+c

1

=0 and a

2

x+b

2

y+c

2

=0 we have

a

1

=3,b

1

=4,c

1

=−11 and a

2

=2,b

2

=3,c

2

−8

Now , x=

a

1

b

2

−a

2

b

1

b

1

c

2

−b

2

c

1

and y=

a

1

b

2

−a

2

b

1

c

1

a

2

−c

2

a

1

⇒x=

3×3−2×4

4x(−8)−3×(−11)

and y=

3×3−2×4

−11×2−(−8)×3

⇒x=

9−8

−32+33

and y=

9−8

−22+24

⇒x=1 and y=2

Answer:

I think it's c sorry if im wrong

Answer: (5,11)

Step-by-step explanation:

Answer:

k = \(\frac{1}{2}\)

Step-by-step explanation:

The equation of proportionality is

y = kx ← k is the constant of proportionality

To find k use any coordinate point lying on the graph

Using (12, 6 ), then

6 = 12k ( divide both sides by 12 )

k = \(\frac{6}{12}\) = \(\frac{1}{2}\)

Answer:

126305.622 is the town's population after 2 years on percentage  7.4.

Step-by-step explanation:

Answer:

you will asume this rate is constant. so put it into y=mx+b form y=1.74*2+109,500

Step-by-step explanation:

Answer:

NL is congruent to US.

Answer:

d. NL ≅US

Step-by-step explanation:

ΔMNL ≅ ΔTUS

follow the order in ≅ statement meaning that MN ≅ TU,NL ≅US, ML ≅ TS

Answer:

VW = √2

Step-by-step explanation:

y = x+1

x²+y²+2x+2y+1=0          (x²+2x+1) + (y²+2y+1) = 1

(x+1)² + (y+1)² = 1  : Circle: (x-h)² + (y-k)² = r²     Center (O): (h , k) = (-1 , -1) r = 1

solve for roots: x²+(x+1)²+2x+2(x+1)+1=0

2x² + 6x + 4 = 0          x²+3x+2=0

(x+1)(x+2)=0

x = -1 or x = -2

y = 0 or y = -1

V and W: (-1 , 0) and (-2 , -1)  forms a 90° center angle

√vw = √1²+1² = √2

The value for R in the table which is most likely to indicate an association between the conditional variables is 0.79.

The association between the conditional variables, exist when the relative frequencies between the two variables are not similar.

The more the difference in the values shows the stronger the association between two.

The table given in the problem is attached below. The given option for the R value in the table is, 0.09,  0.10,  0.13, and 0.79.

As it is known that the bigger the difference, gives the stronger the association. Here, the R value with 0.79 is the most opposite to the value above the R.

Hence, the value for R in the table which is most likely to indicate an association between the conditional variables is 0.79.

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Answer:

D)

Step-by-step explanation:

Step-by-step explanation:

-9/8 is it's resiprocal

Answer:

7 hours

Step-by-step explanation:

20.00 + 10x = 90

10x = 70

x = 7

Answer:

20 + 10x = 90  (where x is the number of hours spent raking leaves)

7 hours

Step-by-step explanation:

let x = number of hours spent raking leaves

Given:

20 + 10x = 90

To solve:  20 + 10x = 90

Subtract 20 from both sides:

⇒ 10x = 70

Divide both sides by 10:

⇒ x = 7

Therefore he spent 7 hours raking the leaves.