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3 years ago

AB=10 and BC=20 What is AC

Mathematics

2 answers:

PSYCHO15rus [73]3 years ago

7 0

Answer:

Step-by-step explanation:

A to B is 10

B to C is 20

You add them together and you get 30. A straight line is equal to 180.

You divide 30 to 180 and you get is 6.

Doss [256]3 years ago

3 0

25 I think so I may be Incorrect

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The hardcover version of a book weighs 7 ounces while its paperback version weighs 5 ounces. Forty-five copies of the book weigh

konstantin123 [22]

Answer:

33 copies were paperback and 12 were hardcover.

Step-by-step explanation:

Let h represent the number of hardcover copies and p represent the number of paperback copies.

We know that the total number of copies was 45; this gives us the equation

h+p = 45

We know that each hardcover copy is 7 ounces; this gives us the expression 7h.

We also know that each paperback copy is 5 ounces; this gives us the expression 5p.

We know that the total weight was 249 ounces; this gives us the equation

7h+5p = 249

Together we have the system

$\left \{ {{h+p=45} \atop {7h+5p=249}} \right.$

We will use elimination to solve this. First we will make the coefficients of the variable p the same; to do this, we will multiply the top equation by 5:

$\left \{ {{5(h+p=45)} \atop {7h+5p=249}} \right. \\\\\left \{ {{5h+5p=225} \atop {7h+5p=249}} \right.$

To eliminate p, we will subtract the equations:

$\left \{ {{5h+5p=225} \atop {-(7h+5p=249)}} \right. \\\\-2h=-24$

Divide both sides by -2:

-2h/-2 = -24/-2

h = 12

There were 12 hardcover copies sold.

Substitute this into our first equation:

12+p=45

Subtract 12 from each side:

12+p-12 = 45-12

p = 33

There were 33 paperback copies sold.

3 0

4 years ago

Read 2 more answers

Differential Equations - Reduction of order

iren [92.7K]

With reduction of order, we assume a solution of the form $y_2=zy_1=ze^{2x}$ , with $z=z(x)$ . Then

${y_2}'=(z'+2z)e^{2x}$
${y_2}''=(z''+4z'+4z)e^{2x}$

and substituting into the ODE gives

$x(z''+4z'+4z)e^{2x}-(2x+1)(z'+2z)e^{2x}+2ze^{2x}=0$
$x(z''+4z'+4z)-(2x+1)(z'+2z)+2z=0$
$xz''+(2x-1)z'=0$

Let $\xi(x)=z'(x)$ , so that $\xi'=z''$ . This gives the linear ODE

$x\xi'+(2x-1)\xi=0$

This equation is also separable, so you can write

$\dfrac{\xi'}{\xi}=\dfrac{1-2x}x$

Integrating both sides with respect to $x$ gives

$\ln|\xi|=-2x+\ln x+C_1$
$\xi=C_1xe^{-2x}$

Next, solve $z'=\xi$ for $z$ by integrating both sides again with respect to $x$ .

$z'=\xi$
$\implies z=\displaystyle\int C_1xe^{-2x}\,\mathrm dx$
$\implies z=C_1e^{-2x}(2x+1)+C_2$

And finally, solve for $y_2$ .

$y_2=zy_1=C_1(2x+1)+C_2e^{2x}$

and note that $y_1$ is already taken into account as part of $y_2$ , so this is the general solution to the ODE.

6 0

3 years ago

I need help with this please

Anna [14]

Multiply the base × height to find the area of each

5 0

4 years ago

Eleven less than seven times a number is five more than six times the number. Find the number.

irina1246 [14]

Answer

x = 16

Step-by-step explanation:

7x-11=6x+5

6 0

3 years ago

Is the statement "Two fundamental questions about a linear system involve existence and uniqueness" true or false? Explain.

sweet [91]

Answer:

True

Explanation:

First of all its necessary remember that a linear system is a compound of multiple equations that involve variables.

<h2>Existence:</h2>

Depending on the number of equations and the number of variables, you could determine if the linear system has a solution or not. There are 3 possibilities:

If the linear system has more equations than variables could exist infinite answers.
If the linear system has more variables than equations, it is considered an undetermined system and you neer more information to solve it.
If the linear system has the same number of equations and variables, the system is consistent and has at least one solution.

<h2>Uniqueness:</h2>

If possibility 3 is presented, it becomes necessary know if its the only one solution or exists more than one solution.

Rgds.

5 0

3 years ago