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3 years ago

Write a function rule that gives the total cost c(p) of p pounds of sugar if each pound costs $.59.

1 answer:

6 0

The total cost, c(p), to purchase sugar is equal to the product of the pound cost equal to $0.59 and the number of pounds of sugar, p. Thus, the answer to this item is,
c(p) = ($0.59)p

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Is (-2,5) a solution to the inequality y<-3x+4 show steps

Fittoniya [83]

We start with $(-2,5)$ for $y\ \textless \ -3x+4$ . $y\ \textless \ -3x+4

5\ \textless \ 6+4

5\ \textless \ 10$ Yes. This is true.

6 0

3 years ago

Gasoline costs 2.99 at the new gas station. if tom puts 8.5 gallons in his car what is the cost

SIZIF [17.4K]

$25.41. You would multiply the 2.99 by 8.5.

5 0

3 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

2 years ago

Use the diagram that awnser the questions.

CaHeK987 [17]

Part A
The first thing we must do in this case is to hide the slopes of each line.
line m:
m = (- 4-3) / (0 - (- 4))
m = -7 / 4
Line n:
n = (- 2-2) / (3-1)
n = -4 / 2
n = -2
Answer:
Lines m and n are not parallel because their slopes are different.

Part B:
We look for the slope of the K line:
k = (1 - (- 3)) / (4 - (- 3))
k = 4/7
We observe that it is true that:
k = -1 / m
Answer:
The lines are perpendicular.

8 0

3 years ago

Read 2 more answers

The number in each column are related. The goal is to determine how they are related, determine which numbers belongs in the bla

andre [41]

Answer:

If you cube the numbers in the left column, you get the numbers in the right column! We can figure this out by understanding that 1^3 = 1, 3^3 = 27, and 6^3 = 216. Then it all falls into place!

1 -> 1

2 -> 8

3 -> 27

5 -> 125

6 -> 216

11 -> 1331

8 -> 512

10 -> 1000

7 -> 343

14 -> 2744

p -> $p^{2}$

$\sqrt{q}$ -> q

8 0

3 years ago

Read 2 more answers