Solve the system of equations. 3x+5y=9 3x+2y=3

juin [17]

Answer:

$\displaystyle \large{y = \frac{1}{4} x + 1}$

Step-by-step explanation:

Whenever you solve a word problem, our first step is to read and gather the information we find.

"A line intersects the point (-8,-1) and has a slope of 1/4. What is the slope-intercept equation for this line?"

After reading the question, I am going to highlight or bold the contexts that are important to our problem-solving.

"A line intersects the point (-8,-1) and has a slope of 1/4. What is the slope-intercept equation for this line?"

First, let's understand that slope-intercept equation is in the form of y = mx+b where m = slope and b = y-intercept

After reading the context, what do we know?

a slope of 1/4
a line passes through (-8,-1)
write in slope-intercept form

We finally have the information — our first step is to write our slope-intercept equation.

$\displaystyle \large{y = mx + b}$

We know that m is slope which is 1/4 — substitute in the equation.

$\displaystyle \large{y = \frac{1}{4} x + b}$

We have used the two information which are a slope of 1/4 and slope-intercept equation.

That only leaves to one information which is a line that passes through (-8,-1).

Since the graph has to pass through the point, we substitute x = -8 and y = -1.

$\displaystyle \large{ - 1= \frac{1}{4} ( - 8)+ b}$

After using all information, it seems that we are solving for b-term or y-intercept.

$\displaystyle \large{ - 1= \frac{1}{1} ( - 2)+ b}$

From above — cross-division.

$\displaystyle \large{ - 1= 1( - 2)+ b} \\ \displaystyle \large{ - 1= - 2+ b}$

Add both sides by 2 to isolate b-term.

$\displaystyle \large{ - 1 + 2= - 2 + 2+ b} \\ \displaystyle \large{ 1= b}$

Therefore, the value of b is 1. From the equation:

$\displaystyle \large{y = \frac{1}{4} x + b}$

Substitute b = 1 in the equation.

$\displaystyle \large{y = \frac{1}{4} x + 1}$

And we're done!

8 0

3 years ago

An office building casts a 90 foot shadow. At the same time of day, a 5 foot woman standing near the building casts an 8 foot sh

professor190 [17]

The answer is 56.25ft

6 0

3 years ago

If the length of the minor axis of an ellipse is 6 units and the length of the major axis is 10 units, how far from the center a

Sedbober [7]

The distance from the center to where the foci are located exists 8 units.

<h3>How to determine the distance from the center?</h3>

The formula associated with the focus of an ellipse exists given as;

c² = a² − b²

Where c exists the distance from the focus to the center.

a exists the distance from the center to a vertex,

the major axis exists 10 units.

b exists the distance from the center to a co-vertex, the minor axis exists 6 units

c² = a² − b²

c² = 10² - 6²

c² = 100 - 36

c² = 64

$c = \sqrt{64}$

c = 8

Therefore, the distance from the center to where the foci are located exists 8 units.

To learn more about the Pythagorean theorem here:

brainly.com/question/654982

#SPJ4

3 0

1 year ago

63+81= factor each expression

dlinn [17]

63

81

24 4

the answer44

4 0

3 years ago

Sandy has 20 roses, 5 daisies, and 25 tulips. She wants to arrange all the flowers in bouquets. Each

prisoha [69]

Answer:

5 bouquets

4 roses 2 tulips 1 daisy

Step-by-step explanation:

Find a number that can be divided in to all the values given, that would be the number of groups or in this case bouquets you have. The number you get after you divide Ex: 20/5 is the amount in each group/bouquet

8 0

3 years ago