A music store sold 103 CDs and 102 CD players. If each CD costs $12
and each CD player costs $35, what was the store's total earnings?
$15,500
© $36,200
$24,500
0 $47.000

If these vectors are to be linearly independent, then there exists some not-all-zero choice for scalars [tex]c_1,c_2,c_3,c_4[/tex] such that

[tex]c_1(1,1,0,-1) + c_2(1,k,1,1) + c_3(5,1,k,1) + c_4(-1,1,1,k) = (0,0,0,0)[/tex]

We can recast this as a system of linear equations,

[tex]\begin{bmatrix}1&1&5&-1\\1&k&1&1\\0&1&k&1\\-1&1&1&k\end{bmatrix}\begin{bmatrix}c_1\\c_2\\c_3\\c_4\end{bmatrix} = \begin{bmatrix}0\\0\\0\\0\end{bmatrix}[/tex]

This system has a solution if the coefficient matrix on the left side is not singular. So we attempt to find k such that it *is* singular, i.e. the determinant is zero:

• A cofactor expansion along the first column gives

[tex]\begin{vmatrix}1&1&5&-1\\1&k&1&1\\0&1&k&1\\-1&1&1&k\end{vmatrix} = \begin{vmatrix}k&1&1\\1&k&1\\1&1&k\end{vmatrix} - \begin{vmatrix}1&5&-1\\1&k&1\\1&1&k\end{vmatrix} + \begin{vmatrix}1&5&-1\\k&1&1\\1&k&1\end{vmatrix}[/tex]

• Cofactor expansions along the first columns of the remaining 3x3 matrices give

[tex]\begin{vmatrix}k&1&1\\1&k&1\\1&1&k\end{vmatrix} = k \begin{vmatrix}k&1\\1&k\end{vmatrix} - \begin{vmatrix}1&1\\1&k\end{vmatrix} + \begin{vmatrix}1&1\\k&1\end{vmatrix} = k^3-3k+2[/tex]

[tex]\begin{vmatrix}1&5&-1\\1&k&1\\1&1&k\end{vmatrix} = \begin{vmatrix}k&1\\1&k\end{vmatrix} - \begin{vmatrix}5&-1\\1&k\end{vmatrix} + \begin{vmatrix}5&-1\\k&1\end{vmatrix} = k^2-4k+3[/tex]

[tex]\begin{vmatrix}1&5&-1\\k&1&1\\1&k&1\end{vmatrix} = \begin{vmatrix}1&1\\k&1\end{vmatrix} - \begin{vmatrix}5&-1\\k&1\end{vmatrix} + \begin{vmatrix}5&-1\\1&1\end{vmatrix} = -k^2 - 6k + 7[/tex]

It follows that

[tex]\begin{vmatrix}1&1&5&-1\\1&k&1&1\\0&1&k&1\\-1&1&1&k\end{vmatrix} = (k^3-3k+2) - (k^2-4k+3) + (-k^2 - 6k + 7) \\\\ \begin{vmatrix}\cdots\end{vmatrix} = k^3 - 2k^2 - 5k + 6 = (k-3)(k-1)(k+2)[/tex]

which makes the coefficient matrix singular if k = 3, k = 1, or k = -2.

Then the four vectors are linearly independent for

[tex]\left\{ k\in\mathbb R \mid k\not\in\{-2,1,3\}\right\}[/tex]

Answer:

No

Step-by-step explanation:

To write 97/1000 as a decimal you have to divide numerator by the denominator of the fraction.

We divide now 97 by 1000 what we write down as 97/1000 and we get 0.097

And finally we have:

97/1000 as a decimal equals 0.097

Answer:

answer it's c)24...

Step-by-step explanation:

i think helping you..... please tell correct or no...

9514 1404 393

Answer:

  $9072

Step-by-step explanation:

Put the given numbers in the given formula and do the arithmetic.

  A = MN . . . . . . M = payment = $189. N = number of payments = 48.

  A = $189 × 48 = $9072

The total amount paid is $9072.

9514 1404 393

Answer:

  p = -3/4b -3/4

Step-by-step explanation:

Vectors are perpendicular when their dot product is zero.

  A·B = p(4) +b(3) -3(-1) = 4p +3b +3

We want this to be zero, so ...

  4p +3b +3 = 0

  4p = -3b -3

  p = -3/4b -3/4 . . . . the value of p that makes A⊥B

Answer:

acute

Step-by-step explanation:

Angles between 0 and less than 90 are acute

A 90 degree angle is right

Greater than 90 and less than 180 is obtuse

180 degree angles are straight

45 degrees is less than 90 so it is acute

Answer: acute

Step-by-step explanation: if angle is between 0 and 90 degrees, it is acute

Answer:

Howard spent $27.25 for each baseball card.

Step-by-step explanation:

1 dozen = 12

Set up an equation:

327 ÷ 12

27.25

Answer:

27.25

Step-by-step explanation:

Answer:

g(f(x))=x^2 + 14x + 48

Step-by-step explanation:

you insert (x+7) into every x in the g(x) equation, so g(x)=(x+7)^2 - 1. then you simplify it by doing (x+7)(x+7) which gets you x^2 + 14x + 49. then you subtract the 1 from the equation to get g(f(x))=x^2 + 14x + 48.

(g o f) (x) = g ( f(x) )

= (x+7)² – 1

= x² + 14x+49 – 1

= x² + 14x+48

If you want, (f o g ) (x) below is the solution ^_^

(f o g ) (x) = f ( g(x) )

= g(x) + 7

= x²-1 +7

= x² +6

I hope I helped you^_^

Step-by-step explanation:

all steps are in picture

Answer:

1/4

Step-by-step explanation:

9514 1404 393

Answer:

  (C)  g = f(-x)

Step-by-step explanation:

g is a reflection of f over the y-axis. Such a reflection replaces x with -x.

  g(x) = f(-x) . . . . . matches choice C

_____

Additional comment

(A) leaves the function unchanged.

(B) is a reflection over the x-axis

(C) is a reflection over the y-axis (applicable here)

(D) is a reflection over the origin (both x- and y-axes)

Answer:

2

Step-by-step explanation:

1+1×5−6+8×(4+4)−62 =

1+1x5-6+8x(8)-62 =

1+5-6+64-62 =

2

Hope this helps! :)

Answer:

-16,200

Step-by-step explanation:

162×(-92)-(-162)×(-5)-162×3

-14,904 - 810 - 486 = -16,200

Answer:

-16200 is your answer....

Answer:

x = 36

Step-by-step explanation:

multiply 4 and 9.5 to get the total amount.

38 = 14.5 + (-8) + (-4.5) + x; hence x is 36.

Answer: x=36

Step-by-step explanation:

To solve this question, we first want to know what mean is. Mean is the same as the average. You take the sum and divide it by the amount. Since we know there are 4 numbers and the mean, we can easily find the value of x.

[tex]\frac{14.5-8-4.5+x}{4} =9.5[/tex]               [multiply both sides by 4]

[tex]14.5-8-4.5+x=38[/tex]       [combine like terms]

[tex]2+x=38[/tex]                          [subtract both sides by 2]

[tex]x=36[/tex]

Now, we know that x=36.

A glucose molecule is the smallest type of protein monomer of starch and cellulose largest of the carbohydrate polymers fundamental unit of genetic material.

A glucose molecule is the monomer of starch and cellulose.

Step-by-step explanation:

So from this, we can conclude that A glucose molecule is the monomer of starch and cellulose.

Learn more about glucose here:

brainly.com/question/13593795?referrer=searchResults

brainly.com/question/13159416?referrer=searchResults

The guitar's volume was amplified, but it was hard to hear the notes since it was so loud.

What word or phrase is a signal word that a context clue might be nearby to help determine the meaning of "amplified"?

Step-by-step explanation:

Here we want to see if the statement:

"A proper use of units can help us to determine the meaning of the slope of a linear function" is true or false.

We will see that it is true.

First, a general linear equation can be written as:

y = a*x + b

Where a is the slope, x is the independent variable, y is the dependent variable, and b is the y-intercept.

The proper use of units is:

y and b must have the same units.

x can have any type of units

The slope must have the quotient between the units of y and the units of x.

Where the proper use of units means that we have the same units on both sides of the expression.

Now, assume that we know the units of y and x.

For example:

y is miles  (then b is also in miles)

x is in hours

Then, with the proper use of units, we can see that the units of the slope are:

miles/hour, or miles per hour.

With this (only knowing the units of x and y) we can see that the slope will be a speed.

So yes, the proper use of units is really important, as this has a lot of information (particularly, the meaning of the slope in a linear equation)

Thus, the statement is true.

If you want to learn more, you can read:

https://brainly.com/question/20286983

Answer:

[tex]{ \underline{ \sf{x \: is \: \: \{ \frac{ - 5 + i \sqrt{35} }{10} \} } \: \: and \: \: \{ \frac{ - 5 - i \sqrt{35} }{10} \}} }[/tex]

Step-by-step explanation:

[tex]5 {x}^{2} + 4x + 3 = 0 [/tex]

from quadratic formular:

[tex]{ \sf{x = \frac{ - b± \sqrt{ {b}^{2} - 4ac } }{2a} }} [/tex]

general equation:

[tex] {ax}^{2} + bx + c = 0[/tex]

a is 5, b is 4 and c is 3:

substitute in formular:

[tex]{ \sf{x = \frac{ - 5± \sqrt{ {5}^{2} - (4 \times 5 \times 3) } }{(2 \times 5)} }} \\ \\ { \sf{x = \frac{ - 5± \sqrt{ - 35} }{10} }}[/tex]

but from complexes, i² = -1

[tex]{ \sf{x = \frac{ - 5± \sqrt{35 {i}^{2} } }{10} }} \\ \\ = { \sf{x = \frac{ - 5±i \sqrt{35} }{10} }}[/tex]

Hi! I'm happy to help!

To solve for the area of a semi-circle, we just need to find the area of a circle, and divide it by 2.

The equation for area of a circle is A=[tex]\pi[/tex]r²

It says we can use 3.14 for pi, so we can write our equation like this:

A=3.14(r²)

Since we are dealing with half of a circle, we can  write this as:

A=[tex]\frac{1}{2}[/tex](3.14(r²))

Our radius is a straight line going from the edge of the circle to the center. We have the diameter, which is just the radius doubled (because it goes from the edge to the center point then back to the edge). So, we divide our diameter by 2 to get our radius.

14÷2=7

Our radius is 7, so we can plug that into our equation:

A=[tex]\frac{1}{2}[/tex](3.14(7²))

Now all we have to do, is solve:

A=[tex]\frac{1}{2}[/tex](3.14(49))

A=[tex]\frac{1}{2}[/tex](153.86)

A=76.93

So, our area is 76.93 units².

I hope this was helpful, keep learning! :D

Answer:

Step-by-step explanation:

Step-by-step explanation:

Please mark me as brainlyest

Answer:

9/25

Step-by-step explanation:

36% = 36/100

Simplify the fraction and you'll have:

9/25

Answer:

9/25

Step-by-step explanation:

36% = 0.36 = 36/100 = 18/50 = 9/25

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

4.  3,52  - Tenths                

   0.352 - Hundredths

5.  65.09 - Ones

   7.005 - Thousandths

6.  753.4 - Tens

    0.051 -  Hundredths

Answer:

1833 miles is the total distance if the model airplane.