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3 years ago

- A total of 32 students sign up for a kayaking trip. Four more seniors (s) sign up than juniors (). Which system of linear

Mathematics

1 answer:

cricket20 [7]3 years ago

5 0

Answer:

s + j = 32

s = 4 + j

Step-by-step explanation:

The first equation that must form our system is the one that show the total of students. If both, seniors and juniors, in total are 32, we must have:

s + j = 32

The second equation must show the relation between senior and juniors students. We know that there are four MORE seniors than juniors, or in other words, the total amount of seniors equal to the amount of juniors plus 4 more students:

s = 4 + j

So, your system must be formed by

s + j = 32 (a)

s = 4 + j (b)

If you want the resolution, just replace (a) in (b). You should find s=18 and j=14.

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Step-by-step explanation:

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3 years ago

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2) Given: lines a and b are parallel Prove: m<1 = m<8

monitta

Explanation:

* Demonstrate that the related angles are the same.

* Demonstrate that different interior angles are equivalent.

* Demonstrate the adjacent interior angles are supplementary.

* Demonstrate the adjacent external angles are not mutually exclusive.

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3 years ago

What is the measure of X! Please help if you know how to do this!

deff fn [24]

Answer:

28°

Step-by-step explanation:

You're given that line DE and line FG are parallel and KL and FG are perpendicular. Then you can find out angle ∠BAC by using the vertical angles property: ∠BAC=62°. Then since KL and FG are perpendicular ∠ABC = 90°. So you find the angle ∠BCA by finding the sum of interior angles: 62+90+∠BCA=180, therefore ∠BCA is 28°. Finally, ∠x or ∠JCG = 28 because ∠JCG and ∠BCA are vertical angles and congruent.

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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:

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