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2 years ago

Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.

Mathematics

1 answer:

torisob [31]2 years ago

7 0

Answer: Brian & Derek will earn $25 If they sell 8 and 12.

Step-by-step explanation:

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mr. Smith is putting in a new floor in his bathroom he has already filled 25 ft.² of floor measuring 10‘ x 6‘ what percent has h

Salsk061 [2.6K]

Answer:

41.67%

Step-by-step explanation:

$tiled \: percent = \frac{25}{10 \times 6} \times 100 \\ \\ = \frac{2500}{60} \\ \\ = 41.6666667\% \\ \\ \approx \: 41.67\% \\$

7 0

2 years ago

The equation of a parabola is y=x2+6x+9. Write the equation in vertex form.

nignag [31]

Answer:

Step-by-step explanation:

Vertex form is accomplished by completing the square on the quadratic. Do this by first setting the parabola equal to 0 then moving the constant over to the other side:

$x^2+6x=-9$

Now take half the linear term, square it, and add it to both sides. Our linear term is 6. Half of 6 is 3, and 3 squared is 9:

$x^2+6x+9=-9+9$

The reason we do this is to create a perfect square binomial on the left:

$(x+3)^2=0$ (obviously the 0 results from the addition of 9 and -9). Move the 0 back over to the other side and set the quadratic back equal to y:

$(x+3)^2+0=y$

This gives you a vertex of (-3, 0), which is a minimum value, since the parabola opens upwards.

6 0

2 years ago

6. Identify the recursive formula for the sequence 3, –15, 75, –375, . . .

vlada-n [284]

Answer:

first option

Step-by-step explanation:

There is a common ratio r between consecutive terms in the sequence, that is

r = - 15 ÷ 3 = 75 ÷ - 15 = - 375 ÷ 75 = - 5

The recursive formula allows a term in the sequence to be found by multiplying the previous term by r , thus

f(n) = - 5f(n - 1) if n > 1

with f(1) = 3 ← first term

4 0

3 years ago

514 divided by 9 as remainder

lesantik [10]

Answer:

57 and a remainder of 1 or 0.11.

Step-by-step explanation:

514dividedby9=57.1

6 0

2 years ago

A colony of bacteria is grown under ideal conditions in a laboratory so that the population increases exponentially with time. A

Naddik [55]

Answer:

Initial bacterias = 6006000

Altought I believe is safe to assume that the values were 192,000 and 384,000 instead of 192,192,000 and 384,384,000, in that case the initial bacterias is 6000

Step-by-step explanation:

A exponential growth follows this formula:

Bacterias = C*rⁿ

C the initial amount

r the growth rate

n the number of time intervals

Bacterias (55 hours) = 192,192,000

Bacterias (66 hours) = 384,384,000

$Bacterias(55hours)=C*r^{{\frac{55-t}{t}}} \\Bacterias (66hours) = C*r^{\frac{66-t}{t}}}$

If you divide both you can get the growth rate:

$\frac{Bacterias (66hours)}{Bacterias(55hours)}=\frac{C*r^{\frac{66-t}{t}}}{C*r^{{\frac{55-t}{t}}}} \\\frac{384,384,000}{192,192,000} =r^{\frac{66-t}{t} -\frac{55-t}{t} } \\2 =r^{\frac{11}{t}}$

So with that r = 2 and each time interval correspond to 11 years

Then replacing in one you can get the initial amount of C

$Bacterias (55hours)=C*2^{\frac{55-11}{11} } 192,192,000 = C*32\\C= 6006000$

7 0

2 years ago