Which is the following is equivalent to 60^1/2

I need help with this because I don’t understand

GalinKa [24]

Answer:

x=1+√5 or x=1−√5

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

: A coin is thrown 30 times.

mel-nik [20]

The relative frequency of it landing on tails is 20/30 or 2/3 or 0.667

7 0

3 years ago

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Which expression is a factor of 10x^2+11x+3

Ulleksa [173]

Answer:

The factors are (5x + 3) and (2x + 1)

Step-by-step explanation:

When you need to factor a quadratic, and the coefficient of the x² is not 1, use the slide and divide method.

The general form of a quadratic is ax² + bx + c

Factor: 10x² + 11x + 3

Here a = 10, b = 11, and c = 3

Step 1: Multiply ac, we SLIDE a over to c. Notice the 10 is gone for now..

x² + 11x + 30

Step 2: Factor this (this step will always factor)

x² + 11x + 30 = (x + 5)(x + 6)

So the factors are (x + 5)(x + 6), but we now need to DIVIDE by a, since we multiplied it into c before. We divide the constants in the factors...

(x + 5/10 )(x + 6/10 )

Now reduce the fractions as much as possible...

(x + 1/2 )(x + 3/5)

*If they don't reduce to a whole number, SLIDE the denominator over as a coefficient of x....

(2x + 1)(5x + 3) *2 slide over in front of x, 5 slide over in front of x, the fractions are gone!

These are our factors!

5 0

4 years ago

Surface Area Of Cylinders <br><br> Please show work<br><br> It would make my year if you helped

jeka94

Answer:

1st cylinder: 3541.9 square mm

2nd cylinder: 439.6 square cm

Step-by-step explanation:

$s = 2\pi r^{2} + 2\pi rh\\s = 2(3.14)(12)^{2} + 2(3.14)(12)(35)\\s = 6.28(144) + 6.28(420)\\s = 904.32 + 2637.6\\s = 3541.92\\s = 3541.9$

Second cylinder.

$s = 2\pi r^{2} + 2\pi rh\\s = 2(3.14)(7)^{2} + 2(3.14)(7)(3)\\s = 6.28(49) + 6.28(21)\\s = 307.72 + 131.88\\s = 439.6$

7 0

2 years ago

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Use Cramer’s rule to solve for x: x + 4y − z = −14 5x + 6y + 3z = 4 −2x + 7y + 2z = −17

V125BC [204]

Looks like the system is

x + 4y - z = -14

5x + 6y + 3z = 4

-2x + 7y + 2z = -17

or in matrix form,

$\mathbf{Ax} = \mathbf b \iff \begin{bmatrix} 1 & 4 & -1 \\ 5 & 6 & 3 \\ -2 & 7 & 2 \end{bmatrix} \begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} -14 \\ 4 \\ -17 \end{bmatrix}$

Cramer's rule says that

$x_i = \dfrac{\det \mathbf A_i}{\det \mathbf A}$

where $x_i$ is the solution for i-th variable, and $\mathbf A_i$ is a modified version of $\mathbf A$ with its i-th column replaced by $\mathbf b$ .

We have 4 determinants to compute. I'll show the work for det(A) using a cofactor expansion along the first row.

$\det \mathbf A = \begin{vmatrix} 1 & 4 & -1 \\ 5 & 6 & 3 \\ -2 & 7 & 2 \end{vmatrix}$

$\det \mathbf A = \begin{vmatrix} 6 & 3 \\ 7 & 2 \end{vmatrix} - 4 \begin{vmatrix} 5 & 3 \\ -2 & 2 \end{vmatrix} - \begin{vmatrix} 5 & 6 \\ -2 & 7 \end{vmatrix}$

$\det \mathbf A = ((6\times2)-(3\times7)) - 4((5\times2)-(3\times(-2)) - ((5\times7)-(6\times(-2)))$

$\det\mathbf A = 12 - 21 - 40 - 24 - 35 - 12 = -120$

The modified matrices and their determinants are

$\mathbf A_1 = \begin{bmatrix} -14 & 4 & -1 \\ 4 & 6 & 3 \\ -17 & 7 & 2\end{bmatrix} \implies \det\mathbf A_1 = -240$

$\mathbf A_2 = \begin{bmatrix} 1 & -14 & -1 \\ 5 & 4 & 3 \\ -2 & -17 & 2 \end{bmatrix} \implies \det\mathbf A_2 = 360$

$\mathbf A_3 = \begin{bmatrix} 1 & 4 & -14 \\ 5 & 6 & 4 \\ -2 & 7 & -17 \end{bmatrix} \implies \det\mathbf A_3 = -480$

Then by Cramer's rule, the solution to the system is

$x = \dfrac{-240}{-120} \implies \boxed{x = 2}$

$y = \dfrac{360}{-120} \implies \boxed{y = -3}$

$z = \dfrac{-480}{-120} \implies \boxed{z = 4}$

5 0

2 years ago