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Andrei [34K]
4 years ago
7

5x - 1 < 2x + 8 someone please help me with this.

Mathematics
2 answers:
user100 [1]4 years ago
4 0
Add 1 to both sides.  Result:  5x < 2x + 9

Subtr. 2x from both sides:  Result:  3x < 9

Div. both sides by 3.  Result:  x < 3   (Answer)
NemiM [27]4 years ago
4 0
First, you would add 1 to Both sides and get 5x-1<2x+9
Second, you would subtract 2 to both sides and get 3x<9
Lastly, you would divide 3 to Both sides
Result, X<3
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Answer:

Cost of per session the average rate is $45.

Step-by-step explanation:

It is given that a gym membership with two personal training session cost $125, while gym membership with five personal training sessions cost $260.

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Step 1 of 1

It is given that a gym membership with two personal training session cost $125, while gym membership with five personal training sessions cost $260.

To find the cost of per session calculate the average rate.

Now let $f(x)$ be the cost per session use the for the average rate of change, and the input value is the number of personal traings x.

$m=\frac{f\left(x_{2}\right)-f\left(x_{1}\right)}{x_{2}-x_{1}}$$

Now substitute, $125 for $f\left(x_{2}\right), 260 for $f\left(x_{1}\right), 2$ for $x_{1}$ and 5 for $x_{2}$ then,

$m=\frac{260-125}{5-2}$\$$\begin{aligned}&=\frac{135}{3} \\&=45\end{aligned}$$

Cost of per session the average rate is $45.

3 0
2 years ago
A quadrilateral has vertices A(3, 5), B(2, 0), C(7, 0), and D(8, 5). Which statement about the quadrilateral is true? A. ABCD is
Dima020 [189]

Hey There!!

The answer to this is: A quadrilateral has vertices A(3, 5), B(2, 0), C(7, 0), and D(8, 5). Which statement about the quadrilateral is true?" Line BC is parallel to line AD because their slopes is equal i.e. (0 - 0) / (7 - 2) = (5 - 5) / (8 - 3) which gives 0 / 5 = 0 / 5 giving that 0 = 0. We check whether line AB is parallel to line CD. Slope of line AB is given by (0 - 5) / (2 - 3) = -5 / -1 = 5. Slope of line CD is given by (5 - 0) / (8 - 7) = 5 / 1 = 5 We have been able to prove that the opposite sides of the quadrilateral are parallel which means that the quadrilateral is not a trapezoid. Next we check whether the length of the sides are equal. Length of line AB is given by sqrt[(0 - 5)^2 + (2 - 3)^2] = sqrt[(-5)^2 + (-1)^2] = sqrt(25 + 1) = sqrt(26) Length of line BC is given by sqrt[(0 - 0)^2 + (7 - 2)^2] = sqrt[0^2 + 5^2] = sqrt(25) = 5 Length of line CD is given by sqrt[(5 - 0)^2 + (8 - 7)^2] = sqrt[5^2 + 1^2] = sqrt(25 + 1) = sqrt(26) Length of line DA is given by sqrt[(5 - 5)^2 + (8 - 3)^2] = sqrt[0^2 + 5^2] = sqrt(25) = 5 Thus, the length of the sides of the quadrilateral are not equal but opposite sides are equal which means that the quadrilateral is not a rhombus. Finally, we check whether adjacent lines are perpendicular. Recall the for perpendicular lines, the product of their slopes is equal to -1. Slope of line AB = 5 while slope of line BC = 0. The product of their slopes = 5 x 0 = 0 which is not -1, thus the adjacent sides of the quadrilateral are not perpendicular which means that the quadrilateral is not a rectangle. Therefore, ABCD is a parallelogram with non-perpendicular adjacent sides. Thus, For (option A).

Hope It Helped!~ ♡

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