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3 years ago

10 POINTS!! Any answers help!!

Mathematics

1 answer:

Paraphin [41]3 years ago

7 0

10. 15

11. 18

12. yes; scale factor: 2.5

13. no

14. no

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Find the smallest positive integer k such that 3240/k is a square number

sashaice [31]

Answer:

Step-by-step explanation:

First, factorize the number 3,240:

$3,240=2\cdot 1,620=2\cdot 2\cdot 810=2\cdot 2\cdot 2\cdot 405=2\cdot 2\cdot 2\cdot 2\cdot 5\cdot 81=2^3\cdot 5\cdot 9^2$

So,

$3,240=2^2 \cdot 2\cdot 5\cdot 9^2=18^2\cdot 10$

Now consider the fraction

$\dfrac{3,240}{k}=\dfrac{18^2\cdot 10}{k}$

If k = 10, then

$\dfrac{3,240}{k}=\dfrac{18^2\cdot 10}{10}=18^2$

is a square number.

For all k < 10, the fraction tex]\dfrac{3,240}{k}[/tex] is not a square number (this follows from factorization).

Or you can simply check the values of the fraction for all k < 10:

k = 1, $\dfrac{3,240}{1}=3,240$ is not a square number;
k = 2, $\dfrac{3,240}{2}=1,620$ is not a square number;
k = 3, $\dfrac{3,240}{3}=1,080$ is not a square number;
k = 4, $\dfrac{3,240}{4}=810$ is not a square number;
k = 5, $\dfrac{3,240}{5}=648$ is not a square number;
k = 6, $\dfrac{3,240}{6}=540$ is not a square number;
k = 7, $\dfrac{3,240}{7}$ is not a square number;
k = 8, $\dfrac{3,240}{8}=405$ is not a square number;
k = 9, $\dfrac{3,240}{9}=360$ is not a square number.

5 0

3 years ago

Need help!!!!!!!!!!!!!

xeze [42]

Answer:

m = $14/day

w = $6/day

Step-by-step explanation:

See attached image.

7 0

2 years ago

19, find the direction angle of vector v to the nearest tenth of a degree

labwork [276]

The vector v is given by:
v = (7, 2) - (-5, 0)
v = ((7 - (- 5)), (2-0))
v = ((7 + 5), 2)
v = (12, 2)
Then, the angle is given by:
tan (theta) = 2/12
theta = atan (2/12)
theta = 9.46 degrees
Answer:
The direction angle of vector to the nearest tenth of a degree is:
theta = 9.5 degrees

6 0

3 years ago

Dean put together first boxes for 5 of his neighbors. Each box cost $1.00 and contained a plant and a $3.00 pair of gardening gl

Scorpion4ik [409]

(5 Neighbors) x (($1.00 Box) + (? Plant) + ($3.00 Gloves)) = 42.50

5 x (1 + x + 3) = 42.50

Combine in parens.

5 x (4 + x) = 42.50

Distribute.

20 + 5x = 42.50

Subtract 20 from both sides.

5x = 22.50

Divide both sides by 5.

x = 4.50

Thats the cost of each plant.

Check.

5 x (1 + 4.50 + 3)

5 x 8.50 = 42.50

3 0

3 years ago

A contractor digs a hole for the basements of a new house that is 40 feet long and 10 1/2 feet deep. What is the width of the ho

34kurt

D. 15.5

40*10.5 = 420

6510/420 = 15.5

7 0

3 years ago