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3 years ago

2 Solve the equation for x: 3x – 5 = 5x + 2x. Show your work.

Mathematics

1 answer:

Galina-37 [17]3 years ago

8 0

Answer:

—5/4 or —1 1/4

Step-by-step explanation:

3x – 5 = 5x + 2x

Collect like terms

—5 = 5x + 2x — 3x

—5 = 4x

Divide both side by the coefficient of x i.e 4

x = —5/4 or —1 1/4

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Kody made a deposit into an account that earns 4% annual compound interest. After 24 months, the value of his account was $2163.

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$1176.671

Step-by-step explanation:

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3 years ago

Write an equation of a parabola that passes through (3,-30) and has x-intercepts of -2 and 18. Then find the average rate of cha

Nookie1986 [14]

Answer:

The equation of the parabola is $y = \frac{2}{5}\cdot x^{2}-\frac{32}{5}\cdot x -\frac{72}{5}$ . The average rate of change of the parabola is -4.

Step-by-step explanation:

We must remember that a parabola is represented by a quadratic function, which can be formed by knowing three different points. A quadratic function is standard form is represented by:

$y = a\cdot x^{2}+b\cdot x + c$

Where:

$x$ - Independent variable, dimensionless.

$y$ - Dependent variable, dimensionless.

$a$ , $b$ , $c$ - Coefficients, dimensionless.

If we know that $(3, -30)$ , $(-2, 0)$ and $(18, 0)$ are part of the parabola, the following linear system of equations is formed:

$9\cdot a +3\cdot b + c = -30$

$4\cdot a -2\cdot b +c = 0$

$324\cdot a +18\cdot b + c = 0$

This system can be solved both by algebraic means (substitution, elimination, equalization, determinant) and by numerical methods. The solution of the linear system is:

$a = \frac{2}{5}$ , $b = -\frac{32}{5}$ , $c = -\frac{72}{5}$ .

The equation of the parabola is $y = \frac{2}{5}\cdot x^{2}-\frac{32}{5}\cdot x -\frac{72}{5}$ .

Now, we calculate the average rate of change ( $r$ ), dimensionless, between $x = -2$ and $x = 8$ by using the formula of secant line slope:

$r = \frac{y(8)-y(-2)}{8-(-2)}$

$r = \frac{y(8)-y(-2)}{10}$

$x = -2$

$y = \frac{2}{5}\cdot (-2)^{2}-\frac{32}{5}\cdot (-2)-\frac{72}{5}$

$y(-2) = 0$

$x = 8$

$y = \frac{2}{5}\cdot (8)^{2}-\frac{32}{5}\cdot (8)-\frac{72}{5}$

$y(8) = -40$

$r = \frac{-40-0}{10}$

$r = -4$

The average rate of change of the parabola is -4.

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3 years ago

How do you solve 235+123 using a number line?

Scrat [10]

You would either start at 0 and go over 235 then you would go over 123 more

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3 years ago

1. At the gym on Monday, Larry is told to up his weight on the bench-press by 15% from last week. Last week he was bench-pressin

QveST [7]

Answer:

300 lbs

Step-by-step explanation:

We know that Larry bench pressed 200 lbs last week, and that he is supposed to increase by 15%. We know that any number times one is that same numbers. That means a number that is increaseing has to be greater than 1. So, we have to convert 15% into a decimal. That is 0.15. That plus one is 1.15. Now we just have to multiply 1.15 with 200. We get 300.

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2 years ago

In a school, 60% of the students are boys. if the number of girls is 120, what is the number of boys in that school?

Luden [163]

There are 180 boys in the school.
40% of the students are girls.
120/40 = x/60
multiply 120 by 60
divide 7200 by 40

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3 years ago