Deacrease 250 by 15%

A nature museum has 2008 specimens of early birds, some with 222 wings and some with 444 wings. The specimens have a total of 40

ludmilkaskok [199]

Let's assume

number of birds with 2 wings is x

number of birds with 4 wings is y

A nature museum has 2008 specimens of early birds

so,

$x+y=2008$

Total of wings of 2 wings bird =2x

Total of wings of 4 wings bird =4y

The specimens have a total of 4384 wings

so, we get

$2x+4y=4384$

we can divide both sides by 2

$x+2y=2192$

so, we get system of equations as

$x+y=2008$

$x+2y=2192$

we can solve for x and y

We can subtract both equations

$2008-y+2y=2192$

$y=184$

$x=2008-184$

$x=1824$

$y=184,\:x=1824$

so,

number of birds with 2 wings is 1824

number of birds with 4 wings is 184.............Answer

5 0

3 years ago

A ball is thrown into the air from a height of 4 feet at time t = 0. The function that models this situation is h(t) = -16t2 + 6

katrin2010 [14]

Answer:

Part a) The height of the ball after 3 seconds is $49\ ft$

Part b) The maximum height is 66 ft

Part c) The ball hit the ground for t=4 sec

Part d) The domain of the function that makes sense is the interval

[0,4]

Step-by-step explanation:

we have

$h(t)=-16t^{2} +63t+4$

Part a) What is the height of the ball after 3 seconds?

For t=3 sec

Substitute in the function and solve for h

$h(3)=-16(3)^{2} +63(3)+4=49\ ft$

Part b) What is the maximum height of the ball? Round to the nearest foot.

we know that

The maximum height of the ball is the vertex of the quadratic equation

so

Convert the function into a vertex form

$h(t)=-16t^{2} +63t+4$

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$h(t)-4=-16t^{2} +63t$

Factor the leading coefficient

$h(t)-4=-16(t^{2} -(63/16)t)$

Complete the square. Remember to balance the equation by adding the same constants to each side

$h(t)-4-16(63/32)^{2}=-16(t^{2} -(63/16)t+(63/32)^{2})$

$h(t)-(67,600/1,024)=-16(t^{2} -(63/16)t+(63/32)^{2})$

Rewrite as perfect squares

$h(t)-(67,600/1,024)=-16(t-(63/32))^{2}$

$h(t)=-16(t-(63/32))^{2}+(67,600/1,024)$

the vertex is the point (1.97,66.02)

therefore

The maximum height is 66 ft

Part c) When will the ball hit the ground?

we know that

The ball hit the ground when h(t)=0 (the x-intercepts of the function)

so

$h(t)=-16t^{2} +63t+4$

For h(t)=0

$0=-16t^{2} +63t+4$

using a graphing tool

The solution is t=4 sec

see the attached figure

Part d) What domain makes sense for the function?

The domain of the function that makes sense is the interval

[0,4]

All real numbers greater than or equal to 0 seconds and less than or equal to 4 seconds

Remember that the time can not be a negative number

6 0

3 years ago

Write the inequality!! Connie’s dog Fido weighs 35 pounds. Her vet placed Fido on a diet. What inequality can you write to find

Butoxors [25]

Answer: $\frac{35-28}{x} \leq 6$

Step-by-step explanation:

Let x be the average number of pounds Fido must loss.

Since, the initial weight of Fido is 35 pounds.

And, After losing the weight, the new weight of Fido in pounds = 28 pounds.

Then the time taken for losing the weight

= $\frac{\text{ The weight it losses}}{\text{ Average of losing weight per month}}$

= $\frac{35-28}{x}$

According to the question, it must lose weight within 6 months,

Thus, $\frac{35-28}{x}\leq 6$

Which is the required inequality to find the average number of pounds per month.

By solving it we, get, $x\geq \frac{7}{6}$

6 0

3 years ago

Josh rented a truck for one day. There was a base fee of$14.99,and there was an additional charge of81cent for each mile driven.

BigorU [14]

$117.05
- $ 14.99
-------------
$102.46 left

Divide 102.46 by 0.81, and you get 126, which makes it 126 miles.

Hope this helps!

7 0

3 years ago

Read 2 more answers

Mary Grace has 3 more Jolly Ranchers than Isabella. If Isabella has 10 Jolly Ranchers, how many do they have total?

PilotLPTM [1.2K]

Answer:23

Step-by-step explanation:

10+3=13 so that means that mary has 13 and isabella has 10

Then if you add 13+10=23

so they have 23 jolly ranchers in all.

5 0

2 years ago

Read 2 more answers