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Svetach [21]
3 years ago
12

Bob thought of an even and odd number, multiplies the numbers together, added 6, divided by 5, and subtracted 3 to give an answe

r of 1. What was the odd number he started with?
Mathematics
1 answer:
Marina CMI [18]3 years ago
7 0

Answer:

  7

Step-by-step explanation:

Working backward, we can find Bob's initial product.

We subtracted 3 to get 1, so we had 4.

We divided by 5 to get 4, so we had 20.

We added 6 to get 20, so we had 14

After Bob multiplied the two numbers together, he had 14. We know that 14 is the product of 2 and 7. The odd number is 7.

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Verify that the points are the vertices of a parallelogram, and find its area. A(1, 1, 3), B(2, −5, 6), C(4, −2, −1), D(3, 4, −4
almond37 [142]

Answer:

Area = 71.3 sq unit

Step-by-step explanation:

a) We will use properties of parallelogram to verify the given vertices.

Property: Have a pair of parallel opposite sides

Hence, vectors AB AD BD BC CD AC. A pair should be parallel:

vectors

AB = A - B = (1, 1 , 3) - ( 2 , -5 , 6 ) = (-1 , 6 , -3)

AD = A - D = (1, 1 , 3) - (3, 4 , -4) = (-2 , -3 , 7)

BC = B - C = (2 , -5 , 6) - (4, -2 , -1) = (-2 ,-3 , 7)

CD = C - D = (4, -2 , -1) - (3, 4 , -4) = (1 , -6 , 3)

Hence we can see  that AB //CD and AD // BC as their unit vector co-efficents are identical/scalar multiple of each other.

b)

Equation of line AB = (1,1,3) + t*(-1 , 6 , -3 )

Point E = (1-t , 1+6t , 3 -3t) ... denotes an position of point E on line AB.

Choose a point on line CD, lets suppose C = ( 4 , -2 , -1 )

Vector EC = ( 1-t , 1+6t , 3-3t ) - (4 , -2 , -1 ) = (-3 -t , 3 +6t , 4 -3t)

For EC to be perpendicular to AB then dot product of AB . EC = 0

Hence,

EC . AB = -1 * (-3-t) -2*(3+6t) -3*(4-3t) = 0

3 + t -6 -12t -12+9t = 0

-2t-3 = 0

t = -3/2

Vector EC = (-3 -t , 3 +6t , 4 -3t) = (-1.5 , -6 , 8.5)

Area = magnitude (AB) * magnitude (EC)

Area = sqrt ((-1)^2 + 6^2 + (-3)^2) * sqrt ((-1.5)^2 + 6^2 + (8.5)^2)

Area = sqrt (46) * sqrt (442) / 2

Area = 71.3 unit^2

6 0
3 years ago
Answer this and i will never forget about you. ever.
trasher [3.6K]

Answer:

I believe that A is the correct answer.

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
A package of 30 Oreos cost $3.60. Kennedy says the unit rate is 0.12. Mason says the unit rate is 8.33. Who is right?
Alekssandra [29.7K]

Answer:

360 \div 30 = 12

Step-by-step explanation:

so Kennedy is right

8 0
2 years ago
These graphs depict the price and output levels of apples under perfect competition and monopoly market structures. what is the
Ksivusya [100]

The extra amount that Mary would pay for apples under a monopoly instead of perfect competition is B. $3

<h3>Calculations and Parameters:</h3>

From the complete information,

There are images of the prices that can be gotten under a monopoly and the ones that can be gotten in a perfect competition by Mary.

The marginal cost which is graphed against the pound of apples and the price shows Mary would pay $15 and the marginal revenue shows that Mary would pay $12.

Hence, the difference between them, which is the extra amount to be paid would be $15-$12

=$3

Read more about perfect competition here:

brainly.com/question/3914700

#SPJ4

6 0
2 years ago
I need help with this mathh​
Tju [1.3M]

Answer:

M=5

Step-by-step explanation:

2 ( 2m ) + 4 ( 4m + 2 ) = 108

step 1. do distributive property

4m + 16m + 8 = 108

step 2. add 4m and 16m and subtract 8 from 108

20m = 100

step 3. divide 100 by 20

m = 5

5 0
3 years ago
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