How do i solve this?

Mathematics

1 answer:

Aloiza [94]3 years ago

5 0

Okay on here it has to deal with a certain theorem or postulate. The theorem states that the two angles opposite of the corresponding angle to the extended angle equal the extended angle. In other words the two given angles inside the triangle equal the outside angle so (62)+(7x+14)=15x-4

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There are 33 of them altogether and pay £311 in total. How many kids are in the family? Adults pay £15 and kids pay £7

Marrrta [24]

Answer:

Step-by-step explanation

Let x be the number of adults and y the number of kids

We can then write this two equations :

x+y= 33

15x+7y= 311

let's solve the two eaquations

to do that we should combine them both in a way that help us get rid of one of the variables.

Let's multiply the first equation by -7 to get rid of y by adding it to thr second equation

-7x-7y= -231

now add both equations .

15x+7y-7x-7y=311-231

we get : 8x = 80

as you notice y is gone and we get a classic easy equation to solve

x= 80/8

= 10

so the number of adults is 10

let's go back to the first equation ( x+y= 33) and replace x with 10

10+y= 33

y= 33-10

=23

let's check using the second equation :

(10*15)+(23*7) = 311

that is true

so :

the number of adults is 10
the number of kids is 23

4 0

4 years ago

1. The height of a missile t seconds after it has been fired is given by h=4.9t^2+44.1t. How many seconds will it take for the r

asambeis [7]

Answer:

The rocket will take 4.5 seconds to reach its maximum height.

Step-by-step explanation:

The height of a missile t seconds after it has been fired is given by h=-4.9*t²+44.1*t

This function is a quadratic function of the form f (x) = a*x² + b*x + c. In this case a=-4.9, b=44.1 and c=0

To calculate how many seconds it will take for the rocket to reach its maximum height, I must calculate the maximum of the function. The maximum of a quadratic function is the vertex of the parabola. The x coordinate of the vertex will be simply: $x=\frac{-b}{2*a}$ . The y coordinate of the vertex corresponds to the function evaluated at that point.

In this case the x coordinate of the vertex corresponds to the t coordinate. In other words, by calculating the x coordinate of the vertex, you are calculating the maximum time t it will take for the rocket to reach its maximum height. So:

$t=\frac{44.1}{2*(-4.9)}$