The point (8,1) is on the line. (Remember the line continues in both directions forever.)

Solve the inequality -5(x-7)<15 algebraically for x

babunello [35]

Answer:

x>4

Step-by-step explanation:

trust

3 0

2 years ago

when 6 is subtracted from the square of a number, the result is 5 times the number. Find the negative solution.

sveta [45]

When 6 is subtracted from the square of a number, the result is 5 times the number, then the negative solution is -1

<h3>Solution:</h3>

Given that when 6 is subtracted from the square of a number, the result is 5 times the number

To find: negative solution

Let "a" be the unknown number

Let us analyse the given sentence

square of a number = $a^2$

6 is subtracted from the square of a number = $a^2 - 6$

5 times the number = $5 \times a$

So we can frame a equation as:

6 is subtracted from the square of a number = 5 times the number

$a^2 - 6 = 5 \times a\\\\a^2 -6 -5a = 0\\\\a^2 -5a -6 = 0$

Let us solve the above quadratic equation

For a quadratic equation $ax^2 + bx + c = 0$ where $a \neq 0$

$x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$

Here in this problem,

$a^2-5 a-6=0 \text { we have } a=1 \text { and } b=-5 \text { and } c=-6$

Substituting the values in above quadratic formula, we get

$\begin{array}{l}{a=\frac{-(-5) \pm \sqrt{(-5)^{2}-4(1)(-6)}}{2 \times 1}} \\\\ {a=\frac{5 \pm \sqrt{25+16}}{2}=\frac{5 \pm \sqrt{49}}{2}} \\\\ {a=\frac{5 \pm 7}{2}}\end{array}$

We have two solutions for "a"

$\begin{array}{l}{a=\frac{5+7}{2} \text { and } a=\frac{5-7}{2}} \\\\ {a=\frac{12}{2} \text { and } a=\frac{-2}{2}}\end{array}$

We have asked negative solution. So a = -1

Thus the negative solution is -1

6 0

3 years ago

Graph the function y = |1.6x – 2| – 3.2. Over which interval is the function increasing?

klasskru [66]

You are to graph y = |1.6x – 2| – 3.2. I trust you know that the graph of y=|x| is v-shaped, opening up, with vertex at (0,0).

Let's rewrite y = |1.6x – 2| – 3.2 by factoring 1.6 out of |1.6x - 2|:

y = 1.6*|x – 2/1.6| – 3.2

This tells us that the vertex of y = |1.6x – 2| – 3.2 is at (2/1.6, -3.2). If you need an explanation of why this is, please ask.

Plot the vertex at (1.25, -3.2).
Find the y-intercept: Let x = 0 in y = |1.6x – 2| – 3.2 and find y:

y = 2-3.2 = -1.2

The y-intercept is located at 0, -1.2)

Plot this y-intercept.

Now draw a straight line from the vertex to this y-intercept. Reflect that line across the y-axis to obtain the other half of the graph.

8 0

2 years ago

Read 2 more answers

The endpoints of EF¯¯¯¯¯¯¯¯ are E(−4,12) and F(3,15). Find the coordinates of the midpoint M..

Ray Of Light [21]

Answer:

(-1/2, 27/2)

Step-by-step explanation:

Midpoint formula: (x^1 +x^2/ 2, y^1 +y^2/ 2)

(-4 +3 /2, 12+15/ 2) -> (-1/2, 27/2)

5 0

2 years ago

gary mixes a solution using two types of concentration of sale: .70 gallons of 5% and .30 gallons of 22% salt. what is the conce

wolverine [178]

Answer:

10.1%

Step-by-step explanation:

The first thing we should do is calculate the total volume of the solution when mixing them would be:

0.7 + 0.3 = 1

Now, we have that the resulting concentration (x) would be equal to the sum of the multiplications between the volumes and the concentrations to be mixed, as follows:

x * 1 = 0.7 * 0.05 + 0.3 * 0.22

x = 0.035 + 0.066

x = 0.101

That is, the concentration of the resulting mixture would be 10.1% (0.101 * 100)

5 0

3 years ago