Maria drove 258.6 miles in 4.5 hours. On average, how many miles per hour did she drive? Round the answer to the nearest tenth?

17. Scott cuts his birthday cake into nine equal pieces and eats two of them.

Roman55 [17]

Answer:

A. 0.2222

B. Repeat indefinitely

Step-by-step explanation:

A. We have that Scott has 9 pieces in total and he eats 2 of them. That means he eats 2 <em>out of </em>the 9, so we have 2 ÷ 9. (see attachment)

The decimal form is: 0.2222.

B. Clearly, we can see that throughout the long division, we keep getting 20 - 18 = 2, which makes another 20 and so on. So, this will repeat indefinitely.

7 0

3 years ago

When does expanding and simplifying a(b+c) result in a positive value for ac

TiliK225 [7]

Answer:

Step-by-step explanation:

(ab + bc)(ab + bc)

Simplifying

(ab + bc)(ab + bc)

Multiply (ab + bc) * (ab + bc)

(ab(ab + bc) + bc(ab + bc))

((ab * ab + bc * ab) + bc(ab + bc))

Reorder the terms:

((ab2c + a2b2) + bc(ab + bc))

(ab2c + a2b2 + (ab * bc + bc * bc))

(ab2c + a2b2 + (ab2c + b2c2))

Reorder the terms:

(ab2c + ab2c + a2b2 + b2c2)

Combine like terms: ab2c + ab2c = 2ab2c

(2ab2c + a2b2 + b2c2)

7 0

3 years ago

Which of the following points could you remove so that the resulting graph is the graph of a function?

larisa [96]

Answer:

(1, -3) can be removed so that the resulting graph represents a function. A relation from a set X to a set Y is called a function if each element of X is related to exactly one element in Y

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

What is the circumstance of 12cm ?

konstantin123 [22]

Answer:

37.68 cm

Step-by-step explanation:

The formula for circumference is C= 2* (3.14) r

First you can actually cut 12 by 1/2

12 * 1/2 is 6. This works because 12 is an even number.

2 * 3.14 (6) gives you 37.68 cm.

So i believe the answer is 37.68 cm.

8 0

3 years ago

Solve the given initial-value problem. x^2y'' + xy' + y = 0, y(1) = 1, y'(1) = 8

Kitty [74]

Substitute $z=\ln x$ , so that

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{\mathrm dy}{\mathrm dz}\cdot\dfrac{\mathrm dz}{\mathrm dx}=\dfrac1x\dfrac{\mathrm dy}{\mathrm dz}$

$\dfrac{\mathrm d^2y}{\mathrm dx^2}=\dfrac{\mathrm d}{\mathrm dx}\left[\dfrac1x\dfrac{\mathrm dy}{\mathrm dz}\right]=-\dfrac1{x^2}\dfrac{\mathrm dy}{\mathrm dz}+\dfrac1x\left(\dfrac1x\dfrac{\mathrm d^2y}{\mathrm dz^2}\right)=\dfrac1{x^2}\left(\dfrac{\mathrm d^2y}{\mathrm dz^2}-\dfrac{\mathrm dy}{\mathrm dz}\right)$

Then the ODE becomes

$x^2\dfrac{\mathrm d^2y}{\mathrm dx^2}+x\dfrac{\mathrm dy}{\mathrm dx}+y=0\implies\left(\dfrac{\mathrm d^2y}{\mathrm dz^2}-\dfrac{\mathrm dy}{\mathrm dz}\right)+\dfrac{\mathrm dy}{\mathrm dz}+y=0$
$\implies\dfrac{\mathrm d^2y}{\mathrm dz^2}+y=0$

which has the characteristic equation $r^2+1=0$ with roots at $r=\pm i$ . This means the characteristic solution for $y(z)$ is

$y_C(z)=C_1\cos z+C_2\sin z$

and in terms of $y(x)$ , this is

$y_C(x)=C_1\cos(\ln x)+C_2\sin(\ln x)$

From the given initial conditions, we find

$y(1)=1\implies 1=C_1\cos0+C_2\sin0\implies C_1=1$
$y'(1)=8\implies 8=-C_1\dfrac{\sin0}1+C_2\dfrac{\cos0}1\implies C_2=8$

so the particular solution to the IVP is

$y(x)=\cos(\ln x)+8\sin(\ln x)$

4 0

3 years ago