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3 years ago

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I have Epilepsy so I tend to forget how to do multiple things! What is the equation of the line? A.y=−13x B.y=−3x C.y=13x D.y =

3x

1 answer:

vagabundo [1.1K]3 years ago

6 0

None of those seem to fit. x = -3y would work but not y = -3x or any of the other options.

We know this because when x is at 1 y is at -3.

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Find the nature of the root

GREYUIT [131]

Answer:

1) Real and same.

2) Real and distinct

3) Real and distinct

4) Real and distinct

5) Real and distinct

6) Real and distinct

7) Real and distinct

8) Real and distinct

Step-by-step explanation:

If a quadratic equation is in the form of ax² + bx + c = 0, then Discriminant of the equation D = b² - 4ac, which governs the nature of roots the equation has.

If D > 0, then there will be two different real roots.

If D = 0, then two same and real roots.

If D < 0, then two distinct but imaginary roots.

Now, 1) x² + 6x + 9 = 0 has D = 6² - 4 × 9 × 1 = 0. So, there will be two same and real roots.

2) 5x² - x = 4x² + 2

⇒ x² - x - 2 = 0

It has D = (-1)² - 4 × 1 × (-2) = 9. Therefore, the roots will be two distinct and real.

3) $\frac{2}{x} + \frac{3}{x} = x - 4$

⇒ 5 = x² - 4x

⇒ x² - 4x - 5 = 0.

So, D = (-4)² - 4 × (1) × (- 5) = 36. So, the equation has two real and distinct rools.

4) x(x - 5) = 4(5 - x)

⇒ x² - x - 20 = 0

Hence, D = (-1)² - 4 × 1 × (-20) = 81

So, the roots will be real and distinct.

5) x² + 7x + 1 = 0 has D = 7² - 4 × 1 × 1 = 45

So, the roots will be real and distinct.

6) 2x² + 9x + 3 = 0, has D = 9² - 4 × 2 × 3 = 57.

Hence, the roots will be real and distinct.

7) 5x² - 6 = 13x

⇒ 5x² - 13x - 6 = 0

So, D = (-13)² - 4 × 5 × (-6) = 289

So, the roots will be real and distinct.

8) x² - x = 3(x + 7)

⇒ x² - 4x - 21 = 0

It has D = (-4)² - 4 × 1 × (-21) = 100

So, the roots will be real and distinct. (Answer)

6 0

3 years ago

The volume of a box V is given by the formula V=lwh, where l is length, w Is width, and h is height.

Nana76 [90]

1)Original Equation: V=lwh
Divide by lw: V/w=lw/lw(h)
Answer: h= V/lw

2)Set up the equation as V=lwh
Substitute the variables for numbers: 50=10(2)h
Multiply 10*2: 50=20h
Divide 50each side by 20 to get rid of 20h: 50/20=20/20
H=2.5
The height of the box is 2.5 meters tall.

7 0

3 years ago

Read 2 more answers

How many different triangles can you make that have angels 60˚, 60˚, 60˚ ?

svet-max [94.6K]

Answer:

Infinite

Step-by-step explanation:

A triangle that has all 60-degree angles is equilateral, which means that all side lengths are the same. However, there are infinite possibilities for the side lengths!

I hope this helped, please give brainliest if this is correct! Thank you!

3 0

3 years ago

Read 2 more answers

I have an assignment and I am having trouble with it. Can someone please help ASAP???

bezimeni [28]

Answer:

A) Find the sketch in attachment.

In the sketch, we have plotted:

- The length of the arena on the x-axis (90 feet)

- The width of the arena on the y-axis (95 feet)

- The position of the robot at t = 2 sec (10,30) and its position at t = 8 sec (40,75)

The origin (0,0) is the southweast corner of the arena. The system of inequalities to descibe the region of the arena is:

$0\leq x \leq 90\\0\leq y \leq 95$

B)

Since the speed of the robot is constant, it covers equal distances (both in the x- and y- axis) in the same time.

Let's look at the x-axis: the robot has covered 10 ft in 2 s and 40 ft in 8 s. There is a direct proportionality between the two variables, x and t:

$\frac{10}{2}=\frac{40}{8}$

So, this means that at t = 0, the value of x is zero as well.

Also, we notice that the value of y increases by $\frac{75-30}{8-2}=7.5 ft/s$ (7.5 feet every second), so the initial value of y at t = 0 is:

$y(t=0)=30-7.5\cdot 2 =15 ft$

So, the initial position of the robot was (0,15) (15 feet above the southwest corner)

C)

The speed of the robot is given by

$v=\frac{d}{t}$

where d is the distance covered in the time interval t.

The distance covered is the one between the two points (10,30) and (40,75), so it is

$d=\sqrt{(40-10)^2+(75-30)^2}=54 ft$

While the time elapsed is

$t=8 sec-2 sec = 6 s$

Therefore the speed is

$v=\frac{54}{6}=9 ft/s$

D)

The equation for the line of the robot is:

$y=mx+q$

where m is the slope and q is the y-intercept.

The slope of the line is given by:

$m=\frac{75-30}{40-10}=1.5$

Which means that we can write an equation for the line as

$y=mx+q\\y=1.5x+q$

where q is the y-intercept. Substituting the point (10,30), we find the value of q:

$q=y-1.5x=30-1.5\cdot 10=15$

So, the equation of the line is

$y=1.5x+15$

E)

By prolonging the line above (40,75), we see that the line will hit the north wall. The point at which this happens is the intersection between the lines

$y=1.5x+15$

and the north wall, which has equation

$y=95$

By equating the two lines, we find:

$1.5x+15=95\\1.5x=80\\x=\frac{80}{15}=53.3 ft$

So the coordinates of impact are (53.3, 95).

F)

The distance covered between the time of impact and the initial moment is the distance between the two points, so:

$d=\sqrt{(53.5-0)^2+(95-15)^2}=95.7 ft$

From part B), we said that the y-coordinate of the robot increases by 15 feet/second.

We also know that the y-position at t = 0 is 15 feet.

This means that the y-position at time t is given by equation:

$y(t)=15+7.5t$

The time of impact is the time t for which

y = 95 ft

Substituting into the equation and solving for t, we find:

$95=15+7.5t\\7.5t=80\\t=10.7 s$

G)

The path followed by the robot is sketched in the second graph.

As the robot hits the north wall (at the point (53.3,95), as calculated previously), then it continues perpendicular to the wall, this means along a direction parallel to the y-axis until it hits the south wall.

As we can see from the sketch, the x-coordinate has not changed (53,3), while the y-coordinate is now zero: so, the robot hits the south wall at the point

(53.3, 0)

H)

The perimeter of the triangle is given by the sum of the length of the three sides.

- The length of 1st side was calculated in part F: $d_1 = 95.7 ft$

- The length of the 2nd side is equal to the width of the arena: $d_2=95 ft$

- The length of the 3rd side is the distance between the points (0,15) and (53.3,0):

$d_3=\sqrt{(0-53.3)^2+(15-0)^2}=55.4 ft$

So the perimeter is

$d=d_1+d_2+d_3=95.7+95+55.4=246.1 ft$

I)

The area of the triangle is given by:

$A=\frac{1}{2}bh$

where:

$b=53.5 ft$ is the base (the distance between the origin (0,0) and the point (53.3,0)

$h=95 ft$ is the height (the length of the 2nd side)

Therefore, the area is:

$A=\frac{1}{2}(53.5)(95)=2541.3 ft^2$

J)

The percentage of balls lying within the area of the triangle traced by the robot is proportional to the fraction of the area of the triangle with respect to the total area of the arena, so it is given by:

$p=\frac{A}{A'}\cdot 100$

where:

$A=2541.3 ft^2$ is the area of the triangle

$A'=90\cdot 95 =8550 ft^2$ is the total area of the arena

Therefore substituting, we find:

$p=\frac{2541.3}{8550}\cdot 100 =29.7\%$

4 0

3 years ago

What is the unit rate of y=0.75x

Elodia [21]

The unit rate is 0.75

7 0

3 years ago