10) what is the algebraic expression for the following word phase : the sum of 5 and 2x?

X-intercept (3,0) and y-intercept (0,-6) point slope form please.

Viktor [21]

Answer:

$y+6=2x$

Step-by-step explanation:

we have

x-intercept (3,0) and y-intercept (0,-6)

step 1

Find the slope

The slope is

$m=(-6-0)/(0-3)=2$

step 2

Find the equation of the line into point slope form

The equation is equal to

$y-y1=m(x-x1)$

we have

$m=2$

$(0,-6)$

substitute

$y+6=2(x-0)$

$y+6=2x$ ----> equation of the line into point slope form

5 0

3 years ago

What two numbers have a product of -36 and a sum of 5?

natima [27]

Answer: 9, -4

Step-by-step explanation:

We can write an equation:

xy=-36

x+y=5

Factors of -36 are: 1, -36, -1, 36, 2, -13, -2, 13, 4, -9, -9, 4, 6, -6

There are only 2 factors here that add up to -36: 9 and -4

5 0

3 years ago

Why is the answer to this integral's denominator have 1+pi^2

ss7ja [257]

It comes from integrating by parts twice. Let

$I = \displaystyle \int e^n \sin(\pi n) \, dn$

Recall the IBP formula,

$\displaystyle \int u \, dv = uv - \int v \, du$

Let

$u = \sin(\pi n) \implies du = \pi \cos(\pi n) \, dn$

$dv = e^n \, dn \implies v = e^n$

Then

$\displaystyle I = e^n \sin(\pi n) - \pi \int e^n \cos(\pi n) \, dn$

Apply IBP once more, with

$u = \cos(\pi n) \implies du = -\pi \sin(\pi n) \, dn$

$dv = e^n \, dn \implies v = e^n$

Notice that the ∫ v du term contains the original integral, so that

$\displaystyle I = e^n \sin(\pi n) - \pi \left(e^n \cos(\pi n) + \pi \int e^n \sin(\pi n) \, dn\right)$

$\displaystyle I = \left(\sin(\pi n) - \pi \cos(\pi n)\right) e^n - \pi^2 I$

$\displaystyle (1 + \pi^2) I = \left(\sin(\pi n) - \pi \cos(\pi n)\right) e^n$

$\implies \displaystyle I = \frac{\left(\sin(\pi n) - \pi \cos(\pi n)\right) e^n}{1+\pi^2} + C$

6 0

2 years ago

Let C be between D and E. Solve for x DC = 5x + 8 CE = 3x + 5 DE = 61

morpeh [17]

DE/2 = 30.5
CE=30.5
DC=30.5

3x + 5 = 30.5
3x = 30.5 - 5
3x = 25.5
25.5/3 =8.5
x=8.5

8 0

3 years ago

William and Stephanie are playing a rather dangerous game of catch on the rooftops of skyscrapers in downtown Chicago. William i

olasank [31]

The question involves the concept & equations associated with projectile motion.

Given:
y₁ = 1130 ft
v₁ = +46 ft/s (note positive sign indicates upwards direction)
t = 6.0 s
g = acceleration due to gravity (assumed constant for simplicity) = -32.2 ft/s²

Of the possible equations of motion, the one we'll find useful is:

y₂ = y₁ + v₁t + 1/2gt²

We can just plug and chug to define the equation of motion:

y = (1130 ft) + (46 ft/s)t + 1/2(-32.2 ft/s²)t²

(note: if you were to calculate y using t = 6.0 s, you'd find that y = 826.4 ft, instead of 830 ft exactly because of some rounding of g and/or the initial velocity)

7 0

4 years ago