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Nesterboy [21]
3 years ago
6

The larger of two numbers is twice the smaller increased by five. Find the two numbers if three times the larger exceeds double

the smaller by 31
Mathematics
1 answer:
melomori [17]3 years ago
3 0

Answer:

Larger number is 13 and Smaller number is 4.

Step-by-step explanation:

Let the larger number be x.

Also let the smaller number be y.

We need to find the two numbers.

Given:

The larger of two numbers is twice the smaller increased by five.

framing in equation form we get;

x=2y+5 ⇒equation 1

Also Given:

Three times the larger exceeds double the smaller by 31

3x=2y+31 ⇒equation 2

Now Substituting the value of x from equation 1 in equation 2 we get;

3(2y+5) = 2y+31

Now Using Distributive property we get;

6y+15 = 2y +31

Combining the like terms we get;

6y-2y = 31-15

Now Using Subtraction property we get;

4y =16

Now Using Division property we get;

\frac{4y}{4}=\frac{16}{4}\\\\y =4

Now Substituting value of y in equation 1 we will find the value of x.

x=2y+5\\\\x = 2\times4+5\\\\x=8+5\\\\x=13

Hence Larger number is 13 and Smaller number is 4.

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We want to know the time, <em>t</em>, it takes the ball to reach a height (<em>y</em>) of 0.
0=-16t^2+24t
We can factor out the GCF first.  The largest number that will divide evenly into 16 and 24 is 8.  Also, both terms have a <em>t</em>, so we can factor that out as well:
0=8t(-2t+3) (-16/8 = -2 and 24/8 = 3)
Using the zero product property, we know that either 8t=0 or -2t+3=0.  Solving the first equation, we would divide both sides by 8:
8t/8=0/8
t=0
This is at 0 seconds, before the ball is in the air at all.
Solving the second equation, we start by subtracting 3 from both sides:
-2t+3-3=0-3
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Now we divide both sides by -2
-2t/-2=-3/-2
t=1.5
After 1.5 seconds, the ball will hit the ground again.
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3 years ago
manuel wanted to put a brick walkway through his backyard from door to bbq area. the walkway is going to be 6 yards long. so far
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Answer:

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Step-by-step explanation:

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3 years ago
PLEASE HELP!!!!! !!!!!!!!!!!!
valina [46]

Answer:

31.9secs

6,183.3m

Step-by-step explanation:

Given the equation that models the height expressed as;

h(t ) = -4.9t²+313t+269

At the the max g=height, the velocity is zero

dh/dt = 0

dh/dt = -9,8t+313

0 = -9.8t + 313

9.8t = 313

t = 313/9.8

t = 31.94secs

Hence it takes the rocket 31.9secs to reach the max height

Get the max height

Recall that h(t ) = -4.9t²+313t+269

h(31.9) = -4.9(31.9)²+313(31.9)+269

h(31.9) = -4,070.44+9,984.7+269

h(31.9) = 6,183.3m

Hence the maximum height reached is 6,183.3m

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