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3 years ago

Does this equation represent a direct variation? X + 3y = 15 No Yes

Mathematics

1 answer:

Vladimir79 [104]3 years ago

8 0

Answer:

Step-by-step explanation:

This answer is no because we have no variable to use for X

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A sporting goods store wants to display 64 sneakers in rows.Each row must contain the same amount of sneakers. Which arrangement

GenaCL600 [577]

Answer:

Step-by-step explanation:

3 rows of 21 sneakers.

If you add 21+21 it equals 42, which is two rows. If you add that last row, 42+21, you end up with 63.

3 0

2 years ago

Two forces act on an object. The first Force has a magnitude of 400 Newtons and acts at an angle of 30 degrees as measured from

Sedaia [141]

ANSWER

Option D is correct

EXPLANATION

We resolve the forces into component forms.

$F_1 = 400 \cos(30) i + 400 \sin(30) j$

$F_1 = 200 \sqrt{3} i +200j$

Also the second is resolved to obtain,

$F_2= 280 \cos(135) i + 280 \sin(135) j.$

$F_2= - 140 \sqrt{2} i + 140 \sqrt{2} j$

To find the resultant vector, V, We add the corresponding components of the two forces to get:

$V=F_1+F_2$

$\implies \: V = (200 \sqrt{3} - 140 \sqrt{2} )i + (200 + 140 \sqrt{2})j$

The correct answer is D.

3 0

3 years ago

A bacteria culture starts with 160 bacteria and grows at a rate proportional to its size. After 5 hours there will be 800 bacter

Leona [35]

Answer:

Step-by-step explanation:

Let the rate at which the bacteria grow be represented by the exponential equation

P(t) = P0e^kt

P(t) is the population of the bacteria after time t

P0 is the initial population

k is the constant of variation

t is the time

If the initial Population is 160 bacteria's, them the equation becomes;

P(t) = 160e^kt

b) if After 5 hours there will be 800 bacteria, this means

at t = 5 p(t) = 800

Substitute and get k

800 = 160e^5k

800/160 = e^5k

5 = e^5k

Apply ln to both sides

Ln5 = lne^5k

ln5 = 5k

k = ln5/5

k = 0.3219

Next is to calculate the population after 7hrs i.e at t = 7

P(7) = 160e^0.3219(7)

P(7) = 160e^2.2532

P(7) = 160(9.5181)

P(7) = 1522.9

Hence the population after 7houra will be approximately 1523populations

c) To calculate the time it will take the population to reach 2790

When p(t) = 2790, t = ?

2790 = 160e^0.3219t

2790/160 = e^0.3219t

17.4375 = e^0.3219t

ln17.4375 = lne^0.3219t

2.8587 = 0.3219t

t = 2.8587/0.3219

t = 8.88 hrs

Hence it will take approximately 9hrs for the population to reach 2790

7 0

3 years ago

5x – 12y – 17 = 0 1*9(x + 2) - (y + 1) + 3 = 0

valentina_108 [34]

Answer: $x=\frac{12y+17}{5}$

$y=\frac{-5x+17}{-12}$

$x=\frac{y-20}{9}$

y=9x+20

Step-by-step explanation:

5x-12y-17=0 (plus 17 from both sides)

5x-12y=17 (plus 12y from both sides)

5x=12y+17 (divide 5 from everything)

$x=\frac{12y+17}{5}$

5x-12y-17=0 (plus 17 from both sides)

5x-12y=17 (minus 5x from both sides)

-12y=-5x+17 (divide everything by -12)

$y=\frac{-5x+17}{-12}$

1*9(x+2)-(y+1)+3=0 (distribute 9 to x and to 2) (distribute -1 to y and to 1)

1*9x+18-y-1+3=0 (times 9x by 1)

9x+18-y-1+3=0 (combine like terms)

9x-y+20=0 (minus 20 from both sides)

9x-y=-20 (plus y to both sides)

9x=y-20 (divide 9 from both sides)

$x=\frac{y-20}{9}$

1*9(x+2)-(y+1)+3=0 (distribute 9 to x and to 2) (distribute -1 to y and to 1)

1*9x+18-y-1+3=0 (times 9x by 1)

9x+18-y-1+3=0 (combine like terms)

9x-y+20=0 (minus 20 from both sides)

9x-y=-20 (minus 9x from both sides)

-y=-9x-20 (divide -1 from everything)

y=9x+20

3 0

3 years ago

4x+6+ 3=-8 2 What is x? 4x+6 <<<< 2 <<< It’s a fraction

Andreas93 [3]

Answer:

-17/4

Step-by-step explanation:

4x+6+3=-8

4x+9=-8

-9 -9

4x=-17

÷4 ÷4

X=-17⁄4

6 0

3 years ago