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2 years ago

8x + 20y = 20 14x + 35y = k For the above system of equations to be consistent, k must equal

Mathematics

1 answer:

Goshia [24]2 years ago

7 0

Answer:

Step-by-step explanation:

The equations will be "consistent" when they describe lines that are not parallel.

<h3>Slopes</h3>

The slope of a line whose equation is written in this form is the opposite of the ratio of the y-coefficient to the x-coefficient:

line 1 slope = -8/20 = -2/5

line 2 slope = -14/35 = -2/5

These lines have the same slope, so will be parallel unless they have the same y-intercept.

<h3>Y-intercept</h3>

The y-intercept of each line is the ratio of the constant to the y-coefficient:

line 1 y-intercept = 20/20 = 1

line 2 y-intercept = k/35

We want these lines to have the same y-intercept so that they are not inconsistent. This requires ...

k/35 = 1

k = 35

For the equations to be consistent, we must have k = 35.

<em>Additional comment</em>

Linear equations are generally categorized as "consistent" or "inconsistent," and "dependent" or "independent."

Equations are "inconsistent" if there are no values of the variables that satisfy all of the equations. They are "dependent" if they describe exactly the same relation between the variables. "Consistent" equations may be "dependent" (describing the same line, as here), or "independent" (describing lines with different slopes.)

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2 years ago

Write the ratios for sin X and cos X. Given that sin is opposite over hypotenuse and

Romashka-Z-Leto [24]

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3 years ago

Help on #3 above??? I will give brainliest!

Leona [35]

Answer:

$f(x)\rightarrow 1\ \text{as}\ x\rightarrow\pm\infty$

Step-by-step explanation:

"End behavior" generally refers to the behavior as the independent variable (x) gets large in the positive or negative directions. Here, the curve for large magnitude x flattens out and approaches 1. So, we say ...

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3 years ago

Write the sum or difference in the standard form a + bi.

REY [17]

Answer:

Sum = 13+ 4i Difference = -5 - 8i

Step-by-step explanation:

Given complex number as (4 -2i) and (9 + 6i)

Sum of these complex number is

(4 -2i) + (9 + 6i) = ( 4 +9) + (6i -2i)

= 13 +4i

Difference of these complex number is

(4 -2i) - (9 + 6i) = (4 -9) - (2i +6i)

= -5 - 8i

Hence the sum and Difference of given complex numbers are

Sum = 13+ 4i Difference = -5 - 8i Answer

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3 years ago

What is an equation of the line that passes through the points (0, -7) and (-8, 3)?

avanturin [10]

Answer <u>(assuming it can be in slope-intercept form)</u>:

$y = -\frac{5}{4} x-7$

Step-by-step explanation:

1) First, find the slope of the line by using the slope formula, $m = \frac{y_2-y_1}{x_2-x_1}$ . Substitute the x and y values of the given points into the formula and solve:

$m = \frac{(3)-(-7)}{(-8)-(0)}\\m = \frac{3+7}{-8-0} \\m = \frac{10}{-8} \\m = -\frac{5}{4}$

So, the slope is $-\frac{5}{4}$ .

2) Now, use the point-slope formula $y-y_1 = m (x-x_1)$ to write the equation of the line in point-slope form. Substitute real values for the $m$ , $x_1$ , and $y_1$ in the formula.

Since $m$ represents the slope, substitute $-\frac{5}{4}$ in its place. Since $x_1$ and $y_1$ represent the x and y values of one point the line intersects, choose any one of the given points (either one is fine, it will equal the same thing at the end) and substitute its x and y values into the formula as well. (I chose (0, -7), as seen below.) Then, isolate y to put the equation in slope-intercept form and find the following answer:

$y-(-7) = -\frac{5}{4} (x-(0))\\y + 7 = -\frac{5}{4} x\\y = -\frac{5}{4} x-7$

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2 years ago