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3 years ago

Solve the equation for x, where x is a real number (5 points): 2x^2 + 8x + 3 = 0

1 answer:

6 0

To find the solutions to this equation, we can apply the quadratic formula. This quadratic formula solves equations of the form ax^2 + bx + c = 0
                                           x = [ -b ± √(b^2 - 4ac) ] / (2a)
                                           x = [ -8 ± √((8)^2 - 4(2)(3)) ] / ( 2(2) )
                                           x = [-8 ± √(64 - (24) ) ] / ( 4 )
                                           x = [-8 ± √(40) ] / ( 4)
                                           x = [-8 ± 2*sqrt(10) ] / ( 4 )
                                           x = -2 ± sqrt(10)/2
The answers are -2 + sqrt(10)/2 and -2 - sqrt(10)/2.

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K = [ 14 -13 0 3 8 -1 -10 -2 5 ] find the determinant of K

spin [16.1K]

I suppose K is the matrix

$K = \begin{bmatrix}14 & -13 & 0 \\ 3 & 8 & -1 \\ -10 & -2 & 5\end{bmatrix}$

To compute det(K), you can use a simple cofactor expansion along the first row:

$\det(K) = 14\times\det\begin{bmatrix}8 & -1 \\-2 & 5\end{bmatrix} - (-13)\times\det\begin{bmatrix}3 & -1 \\ -10 & 5\end{bmatrix} + 0\times\det\begin{bmatrix}3 & 8 \\ -10 & -2\end{bmatrix} \\\\ \det(K) = 14\times(8\times5-(-1)\times(-2)) + 13\times(3\times5-(-1)\times(-10)) + 0 \\\\ \det(K) = 14\times38 + 13\times5 = \boxed{597}$

8 0

3 years ago

uma's salad dressing recipe calls for 1/2 cup of yogurt. She wants to triple her recipe. How much yogurt does she need?

igomit [66]

She needs 1 1/2 cups of yogurt

4 0

3 years ago

3x+y=7 6x+4y=22 can somebody help me solve this problem?

swat32

Hey there!

$\boxed{x=1;y=4}$

$3x + y = 7 \\ \\ 
 6x + 4y = 22$

$y = -3x + 7 \\ \\ Plug \ this \ in \ for \ variable \ (y) \ in \ equation \ \\ \\ 

 6x + 4*(-3x+7) = 22 \\ \\ 
 -6x = -6 \\ \\ 6x=6 \ x+1 \\ \\ x=1 \ y=-3x+7 \\ \\ \boxed{y=-3(1)+7=4} \\ \\ \boxed{\boxed{x=1;y=4}}$

I hope this helps you!

5 0

4 years ago

write an expression for the new balance using as few terms as possible. A checking account has a balance of -$126.89. A customer

Nutka1998 [239]

Answer:

New balance = -151.89 + 4.5x

(where x is the value of the smaller deposit)

Step-by-step explanation:

The inicial balance was -126.89.

Then, it were made two deposits, one with the value of x, and one that is 3 1/2 times the other, that is, 3.5x.

Then, the customer made a withdraw of $25.

So, The new balance can be calculated as:

New balance = inicial balance + x + 3.5x - 25

New balance = -126.89 + 4.5x - 25

New balance = -151.89 + 4.5x

8 0

4 years ago

Pamela is making pizzas. She has 112 pieces of pepperoni. She uses 29 pieces of pepperoni on the first pizza. If she uses the sa

Svetllana [295]

Answer:

Step-by-step explanation:

Number of pieces of pepperoni available with Pamela = 112

Number of pieces of pepperoni used in one pizza = 29

Now, number of pepperoni left after using 29 in one pizza = 112 - 29 = 83

Now, Pamela makes second pizza, so again 29 pieces of pepperoni area used.

Now, number of pepperoni left after using 29 in one pizza = 83 - 29 = 54

Now, Pamela makes third pizza, so again 29 pieces of pepperoni area used.

Now, number of pepperoni left after using 29 in one pizza = 54 - 29 = 25

To make the third pizza, another 29 pepperoni are required but only 25 are available.

Therefore, there is not enough pepperoni for making 4 more pizza.

7 0

3 years ago