Write an algebratic expression for the quotient of 95 and x is

If there is a triangle and the sides are 8&12 and 14 what is the missing angle

rewona [7]

Answer:

8/12 = 14/x

Cross multiplication so

8x=14×12

8x=168

X=168/8

X=21

8 0

2 years ago

You have $3000 to enclose a rectangular piece of property with a fence. The fence costs $9 per foot. A scale drawing of the prop

son4ous [18]

Answer:

Step-by-step explanation:

C=9P

P=2(L+W)

C=18(L+W)

C=18(8(12)+7(12))

C=18(96+84)

C=18(180)

C=$3240

So you do not have enough money to enclose the property.

8 0

2 years ago

18

asambeis [7]

Answer:

B

Step-by-step explanation:

When we have a horizontal translation on the x-axis, it means the translation in question would be affecting only the x component of our function

With respect to the question, what we have here is that we are going to take out some values from x (or add some values) to it

Thus;

f(x) = x^2 would be;

g(x) = (x-4)^2

Corresponding to a shift to the right of upto 4 units on the x axis

7 0

2 years ago

Find x?<br> In 3x - In(x - 4) = ln(2x - 1) +ln3

earnstyle [38]

Answer:

$x = \displaystyle \frac{5 + \sqrt{17}}{2}$ .

Step-by-step explanation:

Because $3\, x$ is found in the input to a logarithm function in the original equation, it must be true that $3\, x > 0$ . Therefore, $x > 0$ .

Similarly, because $(x - 4)$ and $(2\, x - 1)$ are two other inputs to the logarithm function in the original equation, they should also be positive. Therefore, $x > 4$ .

Let $a$ and $b$ represent two positive numbers (that is: $a > 0$ and $b > 0$ .) The following are two properties of logarithm:

$\displaystyle \ln (a) + \ln(b) = \ln\left(a \cdot b\right)$ .

$\displaystyle \ln (a) - \ln(b) = \ln\left(\frac{a}{b}\right)$ .

Apply these two properties to rewrite the original equation.

Left-hand side of this equation:

$\begin{aligned}&\ln(3\, x) - \ln(x - 4)= \ln\left(\frac{3\, x}{x -4}\right)\end{aligned}$

Right-hand side of this equation:

$\ln(2\, x- 1) + \ln(3) = \ln\left(3 \left(2\, x - 1\right)\right)$ .

Equate these two expressions:

$\begin{aligned}\ln\left(\frac{3\, x}{x -4}\right) = \ln(3(2\, x - 1))\end{aligned}$ .

The natural logarithm function $\ln$ is one-to-one for all positive inputs. Therefore, for the equality $\begin{aligned}\ln\left(\frac{3\, x}{x -4}\right) = \ln(3(2\, x - 1))\end{aligned}$ to hold, the two inputs to the logarithm function have to be equal and positive. That is:

$\displaystyle \frac{3\ x}{x - 4} = 3\, (2\, x - 1)$ .

Simplify and solve this equation for $x$ :

$x^2 - 5\, x + 2 = 0$ .

There are two real (but not rational) solutions to this quadratic equation: $\displaystyle \frac{5 + \sqrt{17}}{2}$ and $\displaystyle \frac{5 - \sqrt{17}}{2}$ .

However, the second solution, $\displaystyle \frac{5 - \sqrt{17}}{2}$ , is not suitable. The reason is that if $x = \displaystyle \frac{5 - \sqrt{17}}{2}$ , then $(x - 4)$ , one of the inputs to the logarithm function in the original equation, would be smaller than zero. That is not acceptable because the inputs to logarithm functions should be greater than zero.

The only solution that satisfies the requirements would be $\displaystyle \frac{5 + \sqrt{17}}{2}$ .

Therefore, $x = \displaystyle \frac{5 + \sqrt{17}}{2}$ .

7 0

3 years ago

The student-to-faculty ratio at a small college is 17 to 3. The total number of students and faculty is 740. How many faculty me

ryzh [129]

17+3=20

740/20=37 Classes

37 classes x 3 faculty members=111

3 0

3 years ago