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Alenkasestr [34]
3 years ago
5

Find an equation of the plane that passes through the point P0 = (6, 3, 2) and is parallel to the xy-plane. g

Mathematics
1 answer:
Nutka1998 [239]3 years ago
3 0

The <em>xy</em>-plane has a normal vector of 〈0, 0, 1〉, and any plane parallel to it will have the same normal vector.

Then the equation of the plane through (6, 3, 2) that is parallel to the <em>xy</em>-plane has equation

〈<em>x</em> - 6, <em>y</em> - 3, <em>z</em> - 2〉 • 〈0, 0, 1〉 = 0

==>   <em>z</em> - 2 = 0

==>   <em>z</em> = 2

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Can someone help me with these problems? The majority of them I have answers but I don't understand them. Thanks!
zaharov [31]

Question 1:

The area of the triangle is 9\frac{5}{8} cm², if you want it rounded to the nearest whole number it will be 10 cm²

Question 2:

The area of the parallelogram is 304.5 m²

Question 3:

The ratio of grilled chicken salads sold to the total number of lunches sold is 1 : 3 in the simplest form

Question 4:

The ratio of odd to even digits in the following number:  7,208,631

is 3 : 4

Question 5:

5 tons is equal to 10,000 pounds

Question 6:

A table measures 3 feet across is 36 inches across

Step-by-step explanation:

Question 1:

The formula of the area of a triangle is A=\frac{1}{2}bh , where

  • b is the base of the triangle
  • h is the height of the triangle

∵ The base of the triangle = 5\frac{1}{2} cm

∵ The height of the triangle = 3\frac{1}{2} cm

- Change the mixed numbers to improper fractions

∵ 5\frac{1}{2} = \frac{(5*2)+1}{2}=\frac{11}{2}

∵ 3\frac{1}{2} = \frac{(3*2)+1}{2}=\frac{7}{2}

∴ A=\frac{1}{2}(\frac{11}{2})(\frac{7}{2})=\frac{77}{8} cm²

- To change the improper fraction to mixed number divide 77 by 8

∵ 77 ÷ 8 = 9 and remainder 5 (8 × 9 = 72 , 77 - 72 = 5)

∴ 77 ÷ 8 = 9\frac{5}{8}

∴ A=9\frac{5}{8} cm²

The area of the triangle is 9\frac{5}{8} cm²

If you want to round it to the nearest whole number the area will

be 10 cm²

Question 2:

The formula of the area of a parallelogram is A = b h , where

  • b is the base of the parallelogram
  • h is the height of this base of the parallelogram

∵ The base of the parallelogram = 14.5 m

∵ Its height = 21 m

∵ A = b h

∴ A = 14.5 × 21 = 304.5 m²

The area of the parallelogram is 304.5 m²

Question 3:

∵ The cafeteria sold 200 grilled cheese sandwiches, 100 tacos, and

   150 grilled chicken salads

∴ The cafeteria sold = 200 + 100 + 150 = 450 lunches

- To find the ratio between the grilled chicken salads sold to the total

   number of lunches sold divide them and simplify the answer to the

   lowest term

→  G.C.S    :    Lunches

→  150       :    450 ⇒ divide both by 10

→  15          :   45 ⇒ divide both by 5

→  3           :   9 ⇒ divide both by 3

→  1            :    3

The ratio of grilled chicken salads sold to the total number of lunches sold is 1 : 3 in the simplest form

Question 4:

The even numbers are the numbers whose one digit is 0 , 2 , 4 , 6 , 8

The odd numbers are the numbers whose one digit is 1 , 3 , 5 , 7 , 9

∵ The number is 7,208,631

∵ The odd digits are 7 , 3 , 1

∴ There are 3 odd digits

∵ The even numbers are 2 , 0 , 8 , 6

∴ there are 4 even digits

∴ The ratio of odd to even digits is 3 : 4

The ratio of odd to even digits in the following number:  7,208,631

is 3 : 4

Question 5:

∵ One ton is equal to 2000 pounds

∵ There are 5 tons

→  Ton    :    Pound

→  1           :    2000

→  5          :    x

Use the cross multiplication

∵ 1 × x = 5 × 2000

∴ x = 10,000 pounds

5 tons is equal to 10,000 pounds

Question 6:

∵ A table measures 3 feet across

∵ 1 foot = 12 inches

∴ 3 × 12 = 36 inches

A table measures 3 feet across is 36 inches across

Learn more:

You can learn more about ratio in brainly.com/question/10781917

#LearnwithBrainly

6 0
3 years ago
For the equation, complete the solution. 7x + y = −18
Alex777 [14]

Answer:

x= - 18/7 - 1/7y, y

or if you are solving for y= -18-7x, x

( SEE OTHER IMAGE)

Step-by-step explanation:

See image below:)

8 0
3 years ago
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Twice a number plus 6 times the number is -72.
katen-ka-za [31]

Answer:

The number is -9

Look at the attachment

7 0
2 years ago
Find the distance CD rounded to the nearest tenth (5-2)^2 +(6-2)^2
amid [387]

(5−2)^2+(6−2)^2 = 25

(3)^2 + (4)^2

(9) + (16) = 25

3 0
3 years ago
3
ludmilkaskok [199]

Answer: Yes

Step-by-step explanation:

Each value of y maps onto one value of x.

3 0
1 year ago
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