What is the gradient and y intercept of y =2-x

Find the Roots of the quadratic equation. 2x2 + 7 – 30 = 0

DIA [1.3K]

Answer:

x=−5/2,6

Step-by-step explanation:

5 0

3 years ago

Use natural logarithms to solve the equation. Round to the nearest thousandth. 3e^2x +5=27

puteri [66]

Answer:

x=0.996

Step-by-step explanation:

$3e^{2x} +5=27$

To take natural log ln , we need to get e^2x alone

Subtract 5 on both sides

$3e^{2x}=22$

Now we divide both sides by 3

$e^{2x}=\frac{22}{3}$

Now we take 'ln' on both sides

$ln(e^{2x})=ln(\frac{22}{3})$

As per log property we can move exponent 2x before ln

$(2x)ln(e)=ln(\frac{22}{3})$

The value of ln(e) = 1

$2x=ln(\frac{22}{3})$

Divide both sides by 2

$x=\frac{ln(\frac{22}{3})}{2}$

x= 0.996215082

Round to nearest thousandth

x=0.996

6 0

3 years ago

Nicolas wants to rent a carpet shampoo machine. Store A charges a flat fee of $25 plus $8 for each day a customer keeps the mach

GenaCL600 [577]

Answer:

8x+25=5x+35 (x=10/3)

Step-by-step explanation:

The equation for Store A would be: y(cost) = 8x(days) + 25

The equation for Store B would be: y = 5x + 35

So, since he wants the cost to be the same, 8x+25=5x+35

6 0

2 years ago

Given a joint PDF, f subscript X Y end subscript (x comma y )equals c x y comma space 0 less than y less than x less than 4, (1)

ioda

(1) Looks like the joint density is

$f_{X,Y}(x,y)=\begin{cases}cxy&\text{for }0$

In order for this to be a proper density function, integrating it over its support should evaluate to 1. The support is a triangle with vertices at (0, 0), (4, 0), and (4, 4) (see attached shaded region), so the integral is

$\displaystyle\int_0^4\int_y^4 cxy\,\mathrm dx\,\mathrm dy=\int_0^4\frac{cy}2(4^2-y^2)=32c=1$

$\implies\boxed{c=\dfrac1{32}}$

(2) The region in which X > 2 and Y < 1 corresponds to a 2x1 rectangle (see second attached shaded region), so the desired probability is

$P(X>2,Y$

(3) Are you supposed to find the marginal density of X, or the conditional density of X given Y?

In the first case, you simply integrate the joint density with respect to y:

$f_X(x)=\displaystyle\int_{-\infty}^\infty f_{X,Y}(x,y)\,\mathrm dy=\int_0^x\frac{xy}{32}\,\mathrm dy=\begin{cases}\frac{x^3}{64}&\text{for }0$

In the second case, we instead first find the marginal density of Y:

$f_Y(y)=\displaystyle\int_y^4\frac{xy}{32}\,\mathrm dx=\begin{cases}\frac{16y-y^3}{64}&\text{for }0$

Then use the marginal density to compute the conditional density of X given Y:

$f_{X\mid Y}(x\mid y)=\dfrac{f_{X,Y}(x,y)}{f_Y(y)}=\begin{cases}\frac{2xy}{16y-y^3}&\text{for }y$

6 0

3 years ago

Please help me with this!

DochEvi [55]

Answer:

10 is real, rational, integer, whole, natural

5/6 is real, rational

sqrt of 24 is real, irrational

0 is real, rational, integer, whole

sqrt 81 is real, rational, integer, whole, natural

Step-by-step explanation:

Classification

6 0

3 years ago

What is the gradient and y intercept of y =2-x​

What is the gradient and y intercept of y =2-x