Can someone please tell me

The reflection of the point \(\( (4,2,4) \)\) is the point\(\( (a,b,c) \)\), where \(\( a=\frac{-17}{5} \), \( b=\frac{56}{5} \), and \( c=\frac{-6}{5} \).\)

The reflection of a point in a plane can be found by finding the perpendicular distance from the point to the plane and then moving twice that distance along the line perpendicular to the plane.

The equation of the plane is given as ( 2x + 9y + 7z = 11 ). The normal vector to the plane is \(\( \mathbf{n} = (2,9,7) \)\). The point to be reflected is \(\( P = (4,2,4) \).\)

The perpendicular distance from point P to the plane is given by the formula:

\(d = \frac{|2x_1 + 9y_1 + 7z_1 - 11|}{\sqrt{2^2 + 9^2 + 7^2}}\)

where \(\( (x_1,y_1,z_1) \)\) are the coordinates of point P.

Substituting the values of point P into the formula gives:

\(d = \frac{|2(4) + 9(2) + 7(4) - 11|}{\sqrt{2^2 + 9^2 + 7^2}} = \frac{53}{\sqrt{110}}\)

The unit vector in the direction of the normal vector is given by:

\(\mathbf{\hat{n}} = \frac{\mathbf{n}}{||\mathbf{n}||} = \frac{(2,9,7)}{\sqrt{110}}\)

The reflection of point P in the plane is given by:

\(P' = P - 2d\mathbf{\hat{n}} = (4,2,4) - 2\left(\frac{53}{\sqrt{110}}\right)\left(\frac{(2,9,7)}{\sqrt{110}}\right)\)

Simplifying this expression gives:

\(P' = \left(\frac{-17}{5}, \frac{56}{5}, \frac{-6}{5}\right)\)

So the reflection of the point\(\( (4,2,4) \)\)in the plane \(\( 2x+9y+7z=11 \)\) is the point \(\( \left(\frac{-17}{5}, \frac{56}{5}, \frac{-6}{5}\right) \).\)

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Answer:

6, 3

Step-by-step explanation:

Main answer:A set of values that shows the exact position of a point in a two-dimensional coordinate plane

supporting answer:  

what is coordinate system?

An arrangement of reference lines or curves used to locate points in space. The Cartesian (after René Descartes) system is the most common two-dimensional system.

body  of the answer:

final answer: by following the above steps we can find the coordinates

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A set of values that shows the exact position of a point in a two-dimensional coordinate plane

What is a coordinate system?

An arrangement of reference lines or curves used to locate points in space. The Cartesian (after René Descartes) system is the most common two-dimensional system.

Navigate to the coordinate graph with the lines X'OX, Y'OY.

Determine which quadrant of the graph contains an ordered pair or a point.

Measure the distance between the point and the x-axis to get the abscissa.

Similarly, to obtain the ordinate value, measure the point's distance from the y-axis.

By following the above steps we can find the coordinates.

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Answer:

Use 1 equation plus the 2 equation

5x + x + y - y = 24

6x = 24

x = 4

4 + y = 15

y = 11

Answer:

x = 4

y = 11

Step-by-step explanation:

 x + y = 15           Eq. 1

5x  - y =  9           Eq. 2

_________

6x + 0  = 24

6x = 24

x = 24/6

x = 4

From Eq. 1:

x + y = 15

4 + y = 15

y  =  15 - 4

y = 11

Check:

From Eq. 2

5x - y = 9

5*4 - 11 = 9

20 - 11 = 9

The number of square inches of cloth cut from the square will be 1,017.36 square inches. Then the correct option is A.

It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.

Let r be the radius of the circle. Then the area of the circle will be

A = πr² square units

The radius is given as,

r = 36 / 2

r = 18 inches

The area of the circle is given as,

A = π x (18)²

A = 3.14 x 324

A = 1,017.36 square inches

The number of square inches of cloth cut from the square will be 1,017.36 square inches. Then the correct option is A.

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The complete question is given below.

A circle is cut from a square piece of cloth, as shown:

A square, one side labeled as 36 inches, has a circle inside it. The circle touches all the sides of the square. The portion of the square outside the circle is shaded.

How many square inches of cloth is cut from the square?

(π = 3.14)

1,017.36 in2

1,489.24 in2

1,182.96 in2

1,276.00 in2

Answer:

D (12, 21); B (11, 17); C (18,28); D (42); C (8).

Step-by-step explanation:

First:

Let I represent Isabel and M represent Marie.

We know that currently, Isabel is 9 years older than Marie, or:

I=9+M.

In three years, Isabel will be six years less than twice of Marie's age. In other words:

(I+3)= 2(M+3)-6

Now solve. Substitute I.

(9+M+3)=2M+6-6

12+M=2M

M=12; I=21. Marie is 12 while Isabel is 21.

Second:

Let I represent Isabel and M represent Marie.

Isabel is 6 years older than Marie; in other words: I=6+M

In 4 years, Isabel will be 9 years less than twice Marie's age. Or:

(I+4)=2(M+4)-9

Solve. Substitute I.

(6+M+4)=2(M+4)-9

10+M=2M+8-9

10+M=2M-1

11=M; I=17; Marie is 11 while Isabel is 17.

Third:

Let I represent Isabel and M represent Marie.

Isabel is 10 years older than Marie, or: I=10+M

In 2 years, twice Isabel's age is three times Marie's age. Or:

2(I+2)=3(M+2)

Solve. Substitute for I.

2(10+M+2)=3(M+2)

24+2M=3M+6

18=M; I=28. Marie is 18 while Isabel is 28.

Fourth:

Let M represent Mary and A represent Ann.

Mary is 3 time as old as Ann. Or: M=3A

7 years ago Mary was 5 times as old as Ann. In other words:

(M-7)=5(A-7)

Solve for this system. Substitute M.

(3A-7)=5A-35

-2A=-28

A=14; M=42; Mary is 42.

Fifth:

Let T represent Tammy and L represent Laurel.

We know that Tammy is 42 while Laurel is 9. In other words:

T=42 and L=9.

We need to find in how many years will 3 times Laurel's age be 1 more than Tammy's age. In other words, let's let y represent the amount of years. Thus:

3(L+y)=(T+y)+1

We already know L and T:

3(9+y)=(42+y)+1

27+3y=43+y

2y=16

y=8

In 8 years, when Laurel is 17 and Tammy is 50. (3 times 17 is 51, one more than 50).

Step-by-step explanation:

Since we have the answers no need to write an equation and solve it

the answer is A

b is the answer

C is the answer

So the answer is D

The answer is c

Answer:

1/2

Step-by-step explanation:

y2 - y1. over. x2 - x1

Answer:

2 ft

Step-by-step explanation:

Perimeter = 4 * sides

8 ft = 4 * s

side = 2 ft

Answer:

2 ft

Step-by-step explanation:

8/4 = 2

Answer: 14 inches

Step-by-step explanation:

If one is 4 times the length of the other, then you'll have to divide by 5 because that's how many times there are in total. So 70/5 would be 14 which is the length of the smaller one. 70-14= 56 which is the length of the normal one.

Answer:

Company C

Step-by-step explanation:

Company A sells 12 tigers for $33.24.

Cost per tiger = $33.34 / 12

= $2.78

Company B sells 16 tigers for $44.80. Company

Cost per tiger = $44.80 / 16

= $2.8

C charges $41.10 for 15 tigers.

Cost per tiger = $41.10 / 15

= $2.74

The company that has the best buy is company C that charges $2.74 per tiger

\(the \: right \: answer \: is \: of \: option \: d \\ hope \: it \: helps \\ good \: luck \: on \: your \: assignment\)

The percentage of the sugar in the concentration is 28.57%.

Percentage is defined as the parts of a number per fraction of 100.

We have to divide a number with it's whole and then multiply with 100 to calculate the percentage of any number. It is usually denoted by the symbol '%'.

Given that,

A syrup is made of 10 kg of water and 4 kg of sugar.

Weight of water = 10 kg

Weight of sugar = 4 kg

Total weight of the mixture = 14 kg

Fractional content of sugar = 4 / 14 = 0.2857

Percentage of sugar in the concentration = 0.2857 × 100 = 28.57%

Hence 28.57% of sugar is in the concentration.

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Answer:

let the third side be x

Using pythagoras theorem we get,

(58)^2 = (42)^2 + (x)^2

3364=1764+x^2

x^2=3364-1764

x^2= 1600

x=√(1,600)

x=40

\(\pink{\sf Third \: side \: of \: the \: triangle = 40}\)

As, the given triangle is a right angled triangle,

Hence, We can use the Pythagoras' Theorem,

\(\star\:{\boxed{\sf{\pink {H^{2} = B^{2} + P^{2}}}}}\)

Here,

In given triangle,

Now, by Pythagoras' theorem,

\(\star\:{\boxed{\sf{\pink {H^{2} = B^{2} + P^{2}}}}}\)

\( \sf : \implies (58)^{2} = (42)^{2} + P^{2}\)

\( \sf : \implies 58 \times 58 = 42 \times 42 + P^{2} \)

\( \sf : \implies 3364 = 1764 + P^{2}\)

\( \sf : \implies P^{2} = 3364 - 1764\)

\( \sf : \implies P^{2} = 1600\)

By squaring both sides :

\( \sf \sqrt{P^{2}} = \sqrt{1600}\)

\( \sf : \implies P^{2} = \sqrt{1600}\)

\( \sf : \implies P^{2} = \sqrt{(40)^{2}}\)

\( \sf : \implies P^{2} = 40 \)

\(\pink{\sf \therefore \: Third \: side \: of \: the \: triangle \: is \: 40}\)

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Answer:

Step-by-step explanation:

3x+ 1/3     for x<= -1

6x-27    for x >4

Answer:

110000=p(1+0.019)^168

23.62p=110000

p=4660

credit: sqdancefan

Answer:

84330

Step-by-step explanation:

The compound interest formula gives the value of an investment.

 A = P(1 +r/n)^(nt)

where principal P is invested at annual rate r compounded n times per year for t years. Using your given values, we can solve for P.

 110,000 = P(1 +0.019/12)^(12·14)

 P = 110,000/(1 +0.019/12)^(12·14) ≈ 110,000/1.00158333...^168

 P ≈ 110,000/1.30446

 P ≈ 84326.04 ≈ 84,330 . . . . dollars

Answer:

Hello friend xd

In each scenario, the choice between mean and median as a representative measure of central tendency depends on the nature of the data and the specific context..

1. Scenario: Income distribution of a population

- If the income distribution is skewed or contains extreme values (outliers), the median would be a better representation of the central tendency. This is because the median is not influenced by outliers and provides a more robust estimate of the "typical" income level. However, if the income distribution is approximately symmetric without outliers, the mean can also be an appropriate measure.

2. Scenario: Exam scores in a class

- If the exam scores are normally distributed without significant outliers, the mean would be a suitable measure as it takes into account the value of each score. However, if there are extreme scores that deviate from the majority of the data, the median may be a better representation. This is especially true if the outliers are indicative of errors or exceptional circumstances.

3. Scenario: Housing prices in a city

- In this case, the median would be a more appropriate measure to represent the central tendency of housing prices. This is because the housing market often exhibits a skewed distribution with a few high-priced properties (outliers). The median, being the middle value when the data is sorted, is not influenced by these extreme values and provides a better understanding of the typical housing price in the city.

Ultimately, the choice between mean and median depends on the specific characteristics of the data and the objective of the analysis. It is important to consider the distribution, presence of outliers, and the context in which the data is being interpreted.

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Answer:

 A) 12 cm

 B) 520 cm² (just sides); 720 cm² (sides and base)

So the mean is μ = 8 - 0.38σ = 8 - 0.38(-4.44) = 9.68 and the standard deviation is σ = 4.44. However, it's important to note that the standard deviation cannot be negative, so we must discard the negative sign in the intermediate calculation.

We know that for a normal distribution, the 90th percentile and the 30th percentile correspond to 1.28 standard deviations above the mean (z-score = 1.28) and 0.52 standard deviations below the mean (z-score = -0.52), respectively. Using this information, we can set up two equations and solve for the unknowns μ and σ.

Let X be a random variable following the normal distribution with mean μ and standard deviation σ. Then, we have:

X = μ + σz1 (1) where z1 = 1.28

X = μ + σz2 (2) where z2 = -0.52

We are given that X at the 90th percentile (z-score of 1.28) is equal to 12, so we can substitute these values into equation (1) and solve for μ and σ:

12 = μ + σ(1.28)

12 = μ + 1.28σ

Similarly, we are given that X at the 30th percentile (z-score of -0.52) is equal to 4, so we can substitute these values into equation (2) and solve for μ and σ:

4 = μ + σ(-0.52)

4 = μ - 0.52σ

Now we have two equations and two unknowns. We can solve for μ by adding the two equations together:

12 + 4 = μ + 1.28σ + μ - 0.52σ

16 = 2μ + 0.76σ

2μ = 16 - 0.76σ

μ = 8 - 0.38σ

Substituting this expression for μ into one of the previous equations, we can solve for σ:

4 = (8 - 0.38σ) - 0.52σ

4 = 8 - 0.9σ

0.9σ = 4 - 8

0.9σ = -4

σ = -4/0.9

σ = -4.44 (discard negative sign as σ cannot be negative)

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Answer:

Step-by-step explanation:

a. (I) x = 65

(ii) vertically opposite angles are equal.

b. (i) 71 degrees

(ii) alternate interior angles are equal

c. (i) z = 180 - 71 = 109 degrees

(ii) angles on a line add up to 180 degrees

Answer:

x = 65°, y = 71°, z = 44°

Step-by-step explanation:

x and 65 are vertical angles and congruent, thus

x = 65°

y and 71 are alternate angles and congruent, thus

y = 71°

The sum of the 3 angles in a triangle = 180°, thus

z = 180° - (65 + 71)° = 180° - 136° = 44°

Hence

x = 65°, y = 71° and z = 44°

Answer:

1:27pm

Step-by-step explanation:

52 + 8 = 1 hour

29 - 8 = 21

1 hour and 21 minutes

2:48 - 1:21

1:27pm

The turntable turns through a 45.0 degree angle, the radial line also rotates by 45.0 degrees. Therefore, the direction of the ladybug's displacement vector is 45.0 degrees counterclockwise from the positive x-axis.

Part A:
The radius of the turntable is half of the diameter, which is 6.0 in. The ladybug crawls in a straight radial line to the edge, which means its displacement vector is equal to the radius of the turntable. Therefore, the magnitude of the ladybug's displacement vector is 6.0 in.

Part B:
The direction of the ladybug's displacement vector is the same as the direction of the radial line from the center of the turntable to the edge. This direction can be described by the angle between the positive x-axis and the radial line.

Since the turntable turns through a 45.0 degree angle, the radial line also rotates by 45.0 degrees. Therefore, the direction of the ladybug's displacement vector is 45.0 degrees counterclockwise from the positive x-axis.

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The function in variable w giving the cost C (in dollars) of constructing the box is C(w) = 30w² + 270/w. The result is obtained by using the formula of volume and area of the box.

We have a rectangular storage container without a lid.

The formula of volume of the box is

V = l × w × h

Where

So, the height is

10 = 2w × w × h

10 = 2w² × h

h = 10/2w²

h = 5/w²

To find the total cost, calculate the area of base and sides of the box!

See the picture in the attachment!

The base area is

A₁ = 2w × w = 2w² m²

The sides area is

A₂ = 2(2wh + wh)

A₂ = 2(3wh)

A₂ = 6wh

A₂ = 6w(5/w²)

A₂ = 30/w m²

The total cost is

C = $15(2w²) + $9(30/w)

C = $30w² + $270/w

The function of the total cost is

C(w) = 30w² + 270/w

Hence, the function of constructing the box is C(w) = 30w² + 270/w.

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Answer:

7g - 3

Step-by-step explanation:

2g + 15 + 3g + g + g - 18

2g + 3g + g + g + 15 - 18

7g - 3

Answer:

dijkcvrhjdcrhrbfike

Step-by-step explanation:

<3

The difference in density, in pounds per cubic foot, between the box A and box B to the nearest whole number is 3. So, correct answer is option b.

The density of the body is the mass per unit volume and to find the difference in density we have to find density of each box.

Density of box A = Mass of box A / Volume of box A

= 24.6 pounds / 4 cubic feet

= 6.15 pounds per cubic foot

Density of box B = Mass of box B / Volume of box B

= 37.4 pounds / 4 cubic feet

= 9.35 pounds per cubic foot

The difference in density,

Density box A - density box B.

= (9.35- 6.15)pounds per cubic foot

= 3.2 pounds per cubic foot

To the nearest whole number, the difference in density is 3. Therefore, the answer is (b) 3.

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Answer:

The equation is linear. (-1, 5), (0, 3), (1, 1), (2, -1)