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3 years ago

Rectangle 30 ft wide and 70 feet long. How long would diagonal corners be?

Mathematics

1 answer:

jonny [76]3 years ago

5 0

Answer:

around 76.16

Step-by-step explanation:

30 squared + 70 squared = 5800

square root of 5800 = 76.16

a squared + b squared = c squared

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The sum of three consecutive even numbers is 114. what is the smallest of the three numbers?

saul85 [17]

Answer:

Step-by-step explanation:

Let's let n be any number.

If we multiply n by 2, we get 2n. Since anything multiplied by 2 is even, 2n <em>must</em> be even. Therefore, let 2n be our first number.

So, the consecutive even number will be (2n+2) followed by (2n+4).

We know that their sum must be 114. Therefore, we can write the following equation:

$(2n)+(2n+2)+(2n+4)=114$

Solve for n. Combine like terms on the left:

$6n+6=114$

Subtract 6 from both sides:

$6n=108$

Finally, divide both sides by 6. Therefore, the value of n is:

$n=108/6=18$

Therefore, our first even number is 2n or 2(18) which equates to 36.

And the consecutive even numbers will be 38 and 40.

So, the smallest of them, the first term, is 36.

4 0

3 years ago

Read 2 more answers

1.) What is the equation of the path of firework #1? Write your equation in general form.

valina [46]

1. I'm assumig that the paths are perfect parabolas

this means that their general forms can be written in $y=ax^2+bx+c$

it's easier to find vertex form first then expand to get general form

vertex form is $y=a(x-h)^2+k$ where the vertex is (h,k) and a is a constant

firework #1

vertex is (10,50), so (h,k)=(10,50) and h=10, k=50

$h_1=a(t-10)^2+50$

to find the value of $a$ , subsitute another point

(0,0)

$0=a(0-10)^2+50)$

$0=100a+50$

$a=\frac{-1}{2}$

so the equation in vertex form is $h_1=\frac{-1}{2}(t-10)^2+50$

expand to get general form

$h_1=\frac{-1}{2}(t^2-20t+100)+50$

$h_1=\frac{-1}{2}t^2+10t-50+50$

$h_1=\frac{-1}{2}t^2+10t$

same as last time

vertex is (10,72) so (h,k)=(10,72) so h=10 and k=72

equation is $h_2=a(t-10)^2+72$

find $a$

use another point

(0,22)

$22=a(0-10)^2+72$

$22=100a+72$

$-50=100a$

$a=\frac{-1}{2}$

so the equation in vertex form is $h_2=\frac{-1}{2}(t-10)^2+72$

range is the numbers that h is allowed to be

think about what h represents. it represents the height of the rocket

from the graph, we can see that the lowest possible height is 0yd and the highest height is 50yd

so range is 0 to 50 or 0≤h≤50

domain is the numbers that t is allowed to be

think about what t represents. it represents how long the rocket has been flying

it will stop flying when it hits the ground or at t=20

it starts flying at t=0

so domain is from 0 to 20 or 0≤t≤20

3 0

3 years ago

Help me with this table

Damm [24]

I believe the anwser would be -B

6 0

3 years ago

Which equation is in slope intercept form and represents a line with slope 0 through the point (2,3)

Neko [114]

The slope is m = 0 and the line goes through the point (x,y) = (2,3). So x = 2 pairs up with y = 3.

Plug m = 0, x = 2, y = 3 into the equation below. Then solve for b
y = mx+b
3 = 0*2+b
3 = 0+b
3 = b
b = 3

So if m = 0 and b = 3, then
y = mx+b
y = 0*x+3
y = 0+3
y = 3
is the equation of this line. This line is completely horizontal going through points like (0,3), (1,3), (2,3), etc. Every point on this line has a y coordinate of 3. The x coordinate can be any number you want.

Answer: Choice C) y = 3

4 0

4 years ago

Read 2 more answers

Johnny Awesome and his band is raising money to save the world. He is having a concert and charging

Andre45 [30]

Answer:

9375

Step-by-step explanation:

5 0

3 years ago