For what value of k are the two lines 2x + ky = 3 and x + y = 1 parallel?

Answers

Answer 1

Answer: Remember that: the slope-intercept form of a
line is
1 of 3
y= m. x+c
where m is the slope of the line.
The equation for the first line is 2x + ky = 3
To find the slope, we simply have to rewrite the
given equation into its slope-intercept form.
Start by subtracting 2a from both sides
KY
=
-22 +3
Divide both sides by k
y =
2
•It
3
K
K
The above equation is now in slope-intercept
form, and the coefficient of a is -2/k, so that
is the slope for the first line.

Answer 2

Answer:

Final answer:

The two lines 2x + ky = 3 and x + y = 1 are parallel when the value of k equals 2, as parallel lines have equal slopes.

Explanation:

To determine the values of k for which these two lines are parallel, we need to first understand that parallel lines have the same slope. The slope is the coefficient, or number, with the variable x in the equation of the line.

The first line 2x + ky = 3 can be rewritten in slope-intercept form (y = mx + b) as:

y = -2/kx + 3/k

Here, the slope is -2/k. The second line x + y = 1 can also be rewritten in slope-intercept form as:

y = -x + 1

Here, the slope is -1.

Since the slopes of parallel lines are equal, we equate -2/k to -1:

-2/k = -1

Solving this equation, we find that k = 2. So, the two given lines are parallel when k = 2.

Learn more about Parallel Lines here:

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Answers

I am not sure...but....
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Let f(x)=8x and g(x)=8x+5+1.Which transformations are needed to transform the graph of f(x to the graph of g(x)?

Select each correct answer.

horizontal translation 1 unit left

vertical translation 1 unit down

vertical translation 5 units up

vertical translation 1 unit up

horizontal translation 5 units right

horizontal translation 5 units left

Answers

Transformation involves changing the form of a function

The transformations are:

vertical translation 1 unit up .
horizontal translation 5 units left.

The functions are given as:

$\mathbf{f(x) = 8x}$

$\mathbf{g(x) = 8(x + 5) + 1}$

Considering f(x), we have:

$\mathbf{f(x) = 8x}$

Start by translating the function 5 units left.

The rule of this translation is:

$\mathbf{f'(x) = f(x + 5)}$

So, we have:

$\mathbf{f'(x) = 8(x + 5)}$

Next, translate the function 1 unit up

The rule of this translation is:

$\mathbf{f''(x) = f'(x) + 1}$

So, we have:

$\mathbf{f''(x) = 8(x + 5) + 1}$

Rewrite as:

$\mathbf{g(x) = 8(x + 5) + 1}$

Hence, the transformations are: vertical translation 1 unit up and horizontal translation 5 units left

Answers

Answer:

The first and 3rd are functions, but the second and fourth are not functions.

Step-by-step explanation:

To see if something is a function, use the vertical line test. If there are multiple y coordinates for a singular point for x, it is not a function.

Estimate 6.1 DIVIDED 8

Answers

Estimate 6.1 DIVIDED 8
When you say estimate, meaning you have to round off the decimal to its nearest whole number to solve it easily
=> 6.1 = 6
=> 6 / 8 = 0.75 is the quotient of the given equation.

$(6.1)/(8)$ ≈0.8

You round off to one decimal place.

The lengths of the sides of a triangle are 7. and 10. If the length of the longest side of a similar triangle is 25. what is the length of the shortest side of this triangle?

Answers

Answer: 17.5

Step-by-step explanation:

7:10 = x:25

times both sides by 25

25(7/10) =x

than solve for x

X = 25 × (7/10)

X = 17.5

A motorcycle can travel 70 miles per gallon. Approximately how many gallons of fuel will the motorcycle need to travel 60 km?

Answers

We have the following given
mileage = 70 miles per gallon
distance = 60 km

Required: amount of fuel in gallons

First, we must convert the distance to miles, so
60 km (1 mi/1.6 km) = 37.5 mi

So, the amount of fuel is
37.5 mi / (70 mi/gal) = 0.54 gallons

Answer:

0.54 gallons

Step-by-step explanation:

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