What is the slope and y-intercept from the table?

The sum of 555 consecutive integers is 270270270. What is the second number in this sequence?

Simora [160]

The second number in the sequence will be 53.

Explanation

The difference between any two consecutive integers is always 1.

Suppose, the five consecutive integers are: $n$ , $n+1$ , $n+2$ , $n+3$ and $n+4$

Given that, their sum is 270. So, the equation will be......

$n+(n+1)+(n+2)+(n+3)+(n+4)=270\\\\ 5n+10=270\\\\5n=270-10=260\\ \\ n=\frac{260}{5}=52$

Thus, the second number in the sequence will be: $n+1= 52+1=53$

4 0

3 years ago

Melissa buys 212 pounds of salmon and 114 pounds of swordfish. She pays a total of $31.25, and the swordfish costs $0.20 per pou

eimsori [14]

Answer:

C. $16.60

Step-by-step explanation:

Let the cost per pound of salmon be represented by x

The cost per pound of swordfish be represented by y

Melissa buys 2 1/2 pounds of salmon and 1 1/4 pounds of swordfish. She pays a total of $31.25

2.5 × x + 1.25× y = $31.25

2.5x + 1.25y = 31.25

The swordfish costs $0.20 per pound less than the salmon.

y = x - 0.20

Hence, we substitute

2.5x + 1.25y = 31.25

2.5y + 1.25(x - 0.20) = 31.25

2.5y + 1.25x - 0.25 = 31.25

2.5x + 1.25x = 31.25 + 0.25

3.75x = 31.5

x = 31.5/3.75

x = $8.4

The cost per pound of salmon be represented by x = $8.4

y = x - 0.20

y = 8.4 - 0.20

y = $8.2

The cost per pound of swordfish be represented by y = $8.2

The cost of a pound of salmon and sword fish

= $8.4 + $8.2

=$16.60

3 0

3 years ago

A football is kicked toward an end zone with an initial vertical velocity of 30 ft/s. The function h(t) = -16+ 30t models the he

Ulleksa [173]

Answer:

A. The football does not reach a height of 15ft

Step-by-step explanation:

Given

$h(t) = -16t^2 + 30t$

Required

Determine which of the options is true

The option illustrates the height reached by the ball.

To solve this, we make use of maximum of a function

For a function f(x)

Such that:

$f(x) = ax^2 + bx + c$ :

$f(\frac{-b}{2a}) = maximum/minimum$

i.e we first solve for $\frac{-b}{2a}$

Then substitute $\frac{-b}{2a}$ for x in $f(x) = ax^2 + bx + c$

In our case:

First we need to solve $\frac{-b}{2a}$

Then substitute $\frac{-b}{2a}$ for t in $h(t) = -16t^2 + 30t$

By comparison:

$b = 30$

$c = -16$

$\frac{-b}{2a} = \frac{-30}{2 * -16}$

$\frac{-b}{2a} = \frac{-30}{-32}$

$\frac{-b}{2a} = \frac{30}{32}$

$\frac{-b}{2a} = \frac{15}{16}$

Substitute $\frac{15}{16}$ for t in $h(t) = -16t^2 + 30t$

$h(\frac{15}{16}) = -16(\frac{15}{16})^2 + 30(\frac{15}{16})$

$h(\frac{15}{16}) = -16(\frac{225}{256}) + \frac{450}{16}$

$h(\frac{15}{16}) = -(\frac{225}{16}) + \frac{450}{16}$

$h(\frac{15}{16}) = \frac{-225 + 450}{16}$

$h(\frac{15}{16}) = \frac{225}{16}$

$h(\frac{15}{16}) = 14.0625$

This implies that the maximum height reached is 14.0625ft.

So, the option that answers the question is A because $14.0625 < 15$

8 0

3 years ago

write an equation using "x" and then solve the equationThe library bought 115 new fictions, 38 non-fiction and x new reference b

oee [108]

Answer:X=21

Step-by-step explanation:

115+38+x = 174

153+ x= 174

X=174-153

X=21

3 0

3 years ago

Well, Penny, it certainly was an unusual choice to appear

Dvinal [7]

Answer:

Pretty sure it is D.

Step-by-step explanation:

How I think the narrator was thinking: I mean, yes, its a wedding on Saint Patricks, but you still need to dress appropriatley (its a wedding)

5 0

3 years ago