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2 years ago

Two joggers set out at the same time from their homes 21 miles apart. They agree to meet at a point somewhere in

1 answer:

3 0

The two joggers who are 21 miles apart travel at a speed 8 mph and 6 mph respectively and would meet after one and half hours.

<h3>What is an equation?</h3>

An equation is an expression used to show the relationship between two or more variables and numbers.

Let a represent the speed of the faster jogger and represent the speed of the other jogger. Hence:

a = b + 2 (1)

Also:

In one and half hour (1.5 h):

a = d₁/1.5

d₁ = 1.5a

b = d₂/1.5

d₂ = 1.5b

d₁+ d₂ = 21

1.5a + 1.5b = 21 (2)

From both equation 1 and 2:

a = 8, b = 6

The speed of the joggers is 8 mph and 6 mph respectively.

Find out more on equation at: brainly.com/question/2972832

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Express f(x) in the form a(x-h)^2+k for f(x)=x^2-8x+21

Vlad [161]

X^2-8x+21

=x^2-2(4)(x) +16+5
=(x-4)^2+5

here a=1
h=4
k=5

3 0

3 years ago

The annual net income of a company for the period 2007–2011 could be approximated by P(t) = 1.6t2 − 11t + 44 billion dollars (2

son4ous [18]

Answer:

$P'(t) = 3.2 t -11$

And we can set equal this derivate to 0 in order to find the critical point and we got:

$3.2 t-11= 0$

$t = \frac{11}{3.2}= 3.4375$

And we can calculate the second derivate and we got:

$P''(t) = 3.2 >0$

So then w can conclude that the value of t = 3.4375 represent the minimum value for the function and we can replace in the original function and we got:

$P(3.4375) = 1.6(3.4375)^2 - (11*3.4375) +44 = 25.094$

So then the minimum annual income occurs at t = 3.43 (between 2008 and 2009) and the value is 25.094

Step-by-step explanation:

For this case we have the following function:

$P(t) = 1.6 t^2 -11t +44$

Where P represent the annual net income for the period 2007-2011 and $2 \leq t \leq 7$

And t represent the time in years since the start of 2005

In order to find the lowet income we need to use the derivate, given by:

$P'(t) = 3.2 t -11$

And we can set equal this derivate to 0 in order to find the critical point and we got:

$3.2 t-11= 0$

$t = \frac{11}{3.2}= 3.4375$

And we can calculate the second derivate and we got:

$P''(t) = 3.2 >0$

So then w can conclude that the value of t = 3.4375 represent the minimum value for the function and we can replace in the original function and we got:

$P(3.4375) = 1.6(3.4375)^2 - (11*3.4375) +44 = 25.094$

So then the minimum annual income occurs at t = 3.43 (between 2008 and 2009) and the value is 25.094

5 0

3 years ago

What is the solution to the system of equations?

Ann [662]

Substitute x = -2 in the equation

y = 2/3x + 3

y = (2/3 x 2) + 3

y = 13/3

answer is choice D

7 0

4 years ago

W<br>hat is 101/2 dived by 21/4

DerKrebs [107]

The quotient is 202/21 simplified 9 13/21

7 0

3 years ago

Four consecutive positive prime numbers have a sum that is divisible by three. What is the smallest possible value of this sum?

LuckyWell [14K]

Answer:

Step-by-step explanation:

1 + 3 + 5 + 7 = 16

3 + 5 + 7 + 11= 26

These consecutive positive prime numbers above have sums that are not divisible by three.

5 + 7 + 11 + 13 = 36

This consecutive positive prime numbers above has a sum that is divisible by three: 36.

36 : 3 = 12

4 0

4 years ago