Skylar is driving on a long road trip. She currently has 9 gallons of gas in her car.

Question 45 A length of pipe that weighs 45 pounds is cut into two pieces. One of the pieces is 3 feet long and weighs 18 pounds

dmitriy555 [2]

Answer: 4.5 pounds.

Step-by-step explanation:

Given : Weight of original pipe =45 pounds

Weight of first piece = 18 pounds

Then, Weight of other piece = 45- 18 = 27 pounds

Length of first piece = 3 feet

Let x be the length of other piece.

As length is directly proportional to weight.

Then, $\dfrac{x}{27}=\dfrac{3}{18}$

$\Rightarrow\ \dfrac{x}{27}=\dfrac{1}{6}\\\\\Rightarrow\ x=\dfrac{1}{6}\times27 =4.5$

Hence, the he length of the other piece = 4.5 pounds.

7 0

3 years ago

One positive number is one-fifth of another number. The difference between the two numbers is 260, find the numbers.

Tasya [4]

Answer:

x = 325 and y = 65

Step-by-step explanation:

Let the numbers be x and y.

$y = \frac{1}{5} x$

x - y = 260

Now substituting value of y in the second equation

$x - \frac{1}{5} x = 260\\$

4x = 1300

x = 325

y = 65

5 0

3 years ago

I need help please, I am so confused.

vazorg [7]

Answer:

$\begin{tabular}{| c | c | c |}\cline{1-3} Equation & x-intercepts & x-coordinate of vertex\\\cline{1-3} $y=x(x-2)$ & $x=0, x=2$ & $x=1$\\\cline{1-3} $y=(x-4)(x+5)$ & $x=-5, x=4$ & $x=-0.5$\\\cline{1-3} $y=-5x(x-3)$ & $x=0, x=3$ & $x=1.5$\\\cline{1-3} \end{tabular}$

Step-by-step explanation:

x-intercepts are when the curve intercepts the x-axis, so when y =0.

Therefore, to find the x-intercepts, substitute y = 0 and solve for x.

The vertex is the turning point: the minimum point of a parabola that opens upward, and the maximum point of the parabola that opens downward. As a parabola is symmetrical, the x-coordinate of the vertex is the midpoint of the x-intercepts.

Equation: $y=x(x-2)$

$\implies x(x-2)=0$

$\implies x=0$

$\implies (x-2)=0 \implies x=2$

Therefore, the x-intercepts are x = 0 and x = 2

The midpoint of the x-intercepts is x = 1, so the x-coordinate of the vertex is x = 1

Equation: $y=(x-4)(x+5)$

$\implies (x-4)(x+5)=0$

$\implies (x-4)=0 \implies x=4$

$\implies (x+5)=0 \implies x=-5$

Therefore, the x-intercepts are x = -5 and x = 4

The midpoint of the x-intercepts is x = -0.5, so the x-coordinate of the vertex is x = -0.5

Equation: $y=-5x(3-x)$

$\implies -5x(3-x)=0$

$\implies -5x=0 \implies x=0$

$\implies (3-x)=0 \implies x=3$

Therefore, the x-intercepts are x = 0 and x = 3

The midpoint of the x-intercepts is x = 1.5, so the x-coordinate of the vertex is x = 1.5

$\begin{tabular}{| c | c | c |}\cline{1-3} Equation & x-intercepts & x-coordinate of vertex\\\cline{1-3} $y=x(x-2)$ & $x=0, x=2$ & $x=1$\\\cline{1-3} $y=(x-4)(x+5)$ & $x=-5, x=4$ & $x=-0.5$\\\cline{1-3} $y=-5x(x-3)$ & $x=0, x=3$ & $x=1.5$\\\cline{1-3} \end{tabular}$

4 0

2 years ago

What is the slope of the line?<br> y + 5 = 2(x + 1)<br> Choose 1 answer:

nlexa [21]

Answer:

2

Step-by-step explanation:

y + 5 = 2x +2

y = 2x -3

slope is 2

4 0

4 years ago

Hasan has an annual income of $24,000. He decides to take classes on line and at night so that he can continue to work. After 3

Korolek [52]

Answer:

$36,000

Step-by-step explanation:

The difference in income is $6000. After 6 years, the extra income totals to $36,000. So that was the cost of the investment.

7 0

3 years ago