CAN SOMEONE PLEASE HELP!!!

marissa [1.9K]

Answer:

$y=\frac{4}{5}x-\frac{18}{5}$

Step-by-step explanation:

Hi there!

Linear equations are typically organized in slope-intercept form: $y=mx+b$ where m is the slope and b is the y-intercept (the value of y when x is 0).

1) Determine the slope (m)

$m=\frac{y_2-y_1}{x_2-x_1}$ where two points on the line are $(x_1,y_1)$ and $(x_2,y_2)$

In the graph, the points (-3,-6) and (2,-2) are plotted clearly, so we can use these to help us find the slope. Plug them into the equation:

$m=\frac{-6-(-2)}{-3-2}\\m=\frac{-6+2}{-3-2}\\m=\frac{-4}{-5}\\m=\frac{4}{5}$

Therefore, the slope of the line is $\frac{4}{5}$ . Plug this into $y=mx+b$ :

$y=\frac{4}{5}x+b$

2) Determine the y-intercept (b)

$y=\frac{4}{5}x+b$

Typically, given a graph, we could look at where exactly the line crosses the y-axis to determine b. However, because it appears ambiguous on this graph, we must solve it algebraically.

Plug in one of the given points (2,-2) and solve for b:

$-2=\frac{4}{5}(2)+b\\-2=\frac{8}{5}+b$

Subtract $\frac{8}{5}$ from both sides to isolate b

$-2-\frac{8}{5}=\frac{8}{5}+b-\frac{8}{5}\\-\frac{18}{5} =b$

Therefore, the y-intercept of the line is $-\frac{18}{5}$ . Plug this back into $y=\frac{4}{5}x+b$ :

$y=\frac{4}{5}x+(-\frac{18}{5})\\y=\frac{4}{5}x-\frac{18}{5}$

I hope this helps!

8 0

3 years ago

I need help on 13. Please someone help me. Don’t put a link. Please help me.

Viktor [21]

Answer and Step-by-step explanation:

How to know if the side lengths can form a triangle:

Add together two of the lowest numbers. If it is greater than the largest number, it can form a triangle.

13. Yes, these side lengths can form a triangle.

-- 4 + 5 = 9.

-- 9 is greater than 7, the largest length.

14. No, these side lengths can't form a triangle.

-- 2 + 3 = 6

-- 6 is equal to 6, not greater than.

15. Yes, these side lengths can form a triangle.

-- 2 + 4 = 6

-- 6 is greater than 5, the largest number.

16. Yes, these side lengths can form a triangle.

-- Don't get confused when you see that there are two side lengths that are the same (it means that this is an isosceles triangle); the rules still apply.

-- 2 + 8 = 10

-- 10 is greater than 8, the largest number.

17. Yes, these side lengths can form a triangle.

-- 5 + 6 = 11

-- 11 is greater than 9, the largest number.

18. Yes, these side lengths can form a triangle.

-- 4 + 5 = 9

-- 9 is greater than 8, the largest number.

I hope this helps!!

#teamtrees #PAW (Plant And Water)

5 0

3 years ago

Find the dimensions of the rectangle of largest area that has its base on the x-axis and its other two vertices above the x-axis

stealth61 [152]

Complete question is;

Find the dimensions of the rectangle of largest area that has its base on the x-axis and its other two vertices above the x-axis and lying on the parabola. (Round your answers to the nearest hundredth.) y = 6 - x²

Answer:

height = 4 and base = 2√2

Step-by-step explanation:

Area of a rectangle is given by;

A = base(b) × height(h)

To start off, we will first have to consider half of the rectangle.

Due to the fact that it is bounded by a parabola which is symmetric over the y-axis, it means that the rectangle will have the same area on the right and left hand sides.

So if we maximize the area of the first quadrant, it means that we are also maximizing the area of the entire rectangle.

Now, since we are dealing with the base and other 2 vertices on the x-axis, it means that the base(b) of this half rectangle will be x.

The height of this rectangle is the y coordinate of the corner that is directly above the x coordinate, which is also on the rectangle.

Therefore, the coordinates of the upper corner will be (x, y), or (x, 6 - x²). Thus our half base is x and full height is 6 - x². Area will be;

A = x(6 - x²)

A = 6x - x³

We will maximize this area by finding the derivative and equating to zero.

Thus;

A' = 6 - 3x²

At A' = 0,we have;

6 - 3x² = 0

3x² = 6

x² = 6/3

x² = 2

x = √2

Thus, from y = 6 - x², we have;

y = 6 - (√2)²

y = 6 - 2

y = 4

Since x is half base, it means our full width is 2x = 2 × √2 = 2√2

So, height = 4 and base = 2√2

8 0

3 years ago

What is the point-slope form of a line that has a slope of –4 and passes through point (–3, 1)?

svet-max [94.6K]

Answer:

y - 1 = - 4(x + 3)

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

Here m = - 4 and (a, b) = (- 3, 1), thus

y - 1 = - 4(x - (- 3)), that is

y - 1 = - 4(x + 3)

7 0

3 years ago

In triangle ABC, the right angle is at vertex C, a = 714 cm and the measure of angle A is 78° . To the nearest cm, what is the l

rewona [7]

Answer:

c = 730cm

Step-by-step explanation:

The first thing we would do is to draw the diagram using th given information.

Find attached the diagram.

a = 714 cm

the measure of angle A = 78°

To determine c, we would apply sine rule. This is because we know the opposite and we are to determine the hypotenuse

sin78 = opposite/hypotenuse

sin 78 = 714/c

c = 714/sin 78 = 714/0.9781

c= 729.99

c≅ 730 cm ( nearest cm)

7 0

4 years ago