What two numbers add up to 1 but multiply to -2

Answers

Answer 1

Answer: Negative 1 and positive 2 will add up to 1 and will multiply to -2.

-1 + 2 = 1

-1 * 2 = -2

The two numbers are -1 and 2.

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Translate the phrase into a mathematical expression and then evaluate it. Four squared divided by two cubed.

Answers

As an expression, it is 4² ÷ 2³. The answer to the expression is 2.

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Answer:

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The population of a local species of dragonfly can be found using an infinite geometric series where a1 = 42 and the common ratio is three fourths. Write the sum in sigma notation and calculate the sum that will be the upper limit of this population.

Answers

Answer:

The sum in sigma form is $\sum_(i=1)^(\infty)42((3)/(4))^(i)$

The upper limit of the population is 168.

Step-by-step explanation:

We are given that,

Population of dragonfly is represented by the series with,

First term, $a_(1)=42$

Common ratio, $r=(3)/(4)$

So, we see that,

The sum in sigma form is given by $\sum_(i=1)^(\infty)a_(1)r^(i)$

That is, $\sum_(i=1)^(\infty)42((3)/(4))^(i)$

Now, the infinite sum of the series is $S=(a_1)/(1-r)$

So, the sum is $S=(42)/(1-(3)/(4))$

i.e. $S=(42* 4)/(4-3)$

i.e. $S=(168)/(1)$

Thus, the upper limit of the population is 168.

Hello,

$\lim_(n \to \infty) \sum_(i=0)^(i=n) a_1*((3)/(4))^i =42*4=168$

Fill in the blanks to the picture above

Answers

Middle one is the answer

Answer:

The answer is B, 6x^2 - 21x + 15

Step-by-step explanation:

= (3x + − 3) (2x + − 5)

= (3x) (2x) + (3x) (− 5) + ( − 3) (2x) + ( − 3) ( − 5)

= 6x^2 − 15x − 6x + 15

= 6x^2 − 21x + 15

- I don't know how you want me to fill the boxes exactly but here's the step by step explanation. I hope I helped.

A boat travels at 15 km/hr in still water. In travelling 45 km downstream from town A to town Bit completes the journey in 75 minutes less than it takes for the return journey. At what speed does the river flow?

Answers

Let the speed of river be x km/hr down stream.

Time = Distance / speed

Since river flows downstream, speed of boat down stream = Speed of boat + speed of river = (15 + x).

Since river flows downstream, speed of boat upstream = Speed of boat - speed of river = (15 - x).

Time Upstream - Time Downstream = 75 minutes

Time Upstream = 45 / (15 - x)

Time Downstream = 45 / (15 + x)

75 minutes = 75/60 = 5/4 hours

Time Upstream - Time Downstream = 75 minutes = 5/4 hours

45 / (15 - x) - 45 / (15 + x) = 5/4 Divide both sides by 45

1 / (15 - x) - 1 / (15 + x) = (5/4)*(1/45)

1 / (15 - x) - 1 / (15 + x) = 1/36

((15 + x) - (15 -x)) / (15-x)(15+x) = 1/36

(15 +x - 15 +x) / (15-x)(15+x) = 1/36

2x / (15-x)(15+x) = 1/36

(15-x)(15+x) = 2x*36

(15-x)(15+x) = 72x

225 - x² = 72x

0 = x² + 72x -225

x² + 72x -225 = 0 This is a quadratic function, use a calculator that can solve the function, by inputting the function.

x = 3, or -75. Since we are solving for speed, we can not have negative values.

x = 3 is the only valid solution.

Speed of the river = 3 km/hr downstream.

Copyright.

Which measurement is the best estimate for the distance between New York City and Washington, D.C.?:A : 331 mm

B : 331 cm

C : 331 m

D : 331 Km

Answers

The best estimate would be D: 331 km

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