Taylor and Anya live 63 miles apart. Sometimes on a Saturday, they ride their bikes toward each other's houses and meet somewhere in between. Taylor is a very consistent rider - she finds that her speed is always very close to 12.5 miles per hour. Anya rides more slowly than Taylor, but she is working out and so she is becoming a faster rider as the weeks go by. On a Saturday in July, the two friends set out on their bikes at 8 am. Taylor rides at 12.5 miles per hour, and Anya rides at 5.5 miles per hour. After one hour, how far apart are they?

Answer:

b=20 or b=-20

Step-by-step explanation:

Keep in mind the meanings of the values of the discriminant:

If b^2-4ac=0, then the quadratic will have only 1 solution (double root)

If b^2-4ac<0, then the quadratic will have no real solutions

If b^2-4ac>0, then the quadratic will have 2 unique solutions

In this case, to get one real solution, the discriminant must be set up as b^2-4ac=0. Setting up the equation we get:

b^2-4(4)(25)=0

b^2-400=0

b^2=400

b=20 or b=-20

So the values of b would have to be either 20 or -20

The values of b will cause 4x^2+bx+25=0 to have one real solution is -20 and 20

Given the quadratic equation [tex]4x^2+bx+25= 0[/tex], for this expression to have a real solution, the discriminant must be greater than zero

D > 0

b^2 - 4ac > 0

Given that a = 4, b = b, c = 25

b^2 - 4(4)(25) > 0

b^2 - 400 > 0

b^2 > 400

b > ±20

Hence the values of b will cause 4x^2+bx+25=0 to have one real solution is -20 and 20

Learn more on discriminant here: https://brainly.com/question/24730520

Answer:

3

Step-by-step explanation:

I think ttttttttttttttttttttt

Answer:

5/3

Step-by-step explanation:

Between the two points, the line goes up 5 points and to the right 3 points. The slope is rise over run, so in this case the rise is 5 and the run is 3.

This makes our slope:

5/3

Answer:

-The graph of this sequence would pass the horizontal line test.

-Each day corresponds to a unique amount of pennies in this sequence.

Step-by-step explanation:

Answer:

B)The graph of this sequence would pass the horizontal line test.

D)Each day corresponds to a unique amount of pennies in this sequence.

Step-by-step explanation:

I took the test

Answer:

words are big and if words are big am I small

Answer:

c

Step-by-step explanation:

Answer:

D.)

Step-by-step explanation:

Answer:

DDDDDDDDD

Step-by-step explanation:

Answer:

umm i am pretty sure it is 20 to 22

Step-by-step explanation:

Every 3rd term that occurs after the first term in the second pattern (that is, the 4th term, 7th term, 10th term, 13th term, 16th term, etc.), all represent the terms of the first pattern.

Both Patterns start at 0

Pattern 1 follows the rule, add 9.

Pattern 1 has terms, 0, 9, 18, 27, 36, 45, 54, 63, 72, 81....

Pattern 2 follows the rule, add 3.

Pattern 2 has terms, 0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54...

It is evident that all of the terms of the first pattern will eventually occur in the second pattern at some regular points.

They both have the same first terms.

Both Patterns have terms that are all multiples of 3.

Every 3rd term that occurs after the first term in the second pattern (that is, the 4th term, 7th term, 10th term, 13th term, 16th term, etc.), all represent the terms of the first pattern.

For more information on mathematical relationships click on the link below:

https://brainly.com/question/17237498

#SPJ4

Answer:

[tex]y - (-2) = (-5/3)\, (x - 6)[/tex].

.Step-by-step explanation:

The [tex]x[/tex]-coordinates of the two given points are different. Therefore, the line that goes through these points would not be vertical. Likewise, this line would not be horizontal since the [tex]y[/tex]-coordinates of the given points are different.

If a line in a plane is of slope [tex]m[/tex] and goes through point [tex](x_{0},\, y_{0})[/tex], the point-slope equation of this line would be [tex]y - y_{0} = m\, (x - x_{0})[/tex].

If a line in a plane goes through the points [tex](x_{0},\, y_{0})[/tex] and [tex](x_{1},\, y_{1})[/tex] (where [tex]x_{0} \ne x_{1}[/tex],) the slope of this line would be [tex]m = (y_{1} - y_{0}) / (x_{1} - x_{0})[/tex].

Since the line in this question goes through points [tex](6,\, -2)[/tex] and [tex](0,\, 8)[/tex], the slope of this line would be:

[tex]\begin{aligned} m &= \frac{8 - (-2)}{0 - 6} \\ &= \frac{10}{(-6)} \\ &= -\frac{5}{3}\end{aligned}[/tex].

Let [tex](6,\, -2)[/tex] be the point [tex](x_{0},\, y_{0})[/tex]. The point-slope equation of this line would be:

[tex]y - (-2) = (-5 / 3)\, (x - 6)[/tex].

Answer:

-44

Step-by-step explanation:

The height of the room will be 4 meters

In the question, It is given that a room's four walls have to be covered by a 3-D paper of 3m² and 41 such papers are required for this. Also, we have been given that the room has 4 Windows of dimensions 2m * 1.75m each and 2 Doors of dimension 1m * 3.5m.

It is also stated that the tiling of the floor is done by tiles of dimension 2m * 1.5m each and 24 tiles are used for tiling.

Given that length is twice as breadth, Breadth b = x, and Length l = 2x

We know the Area of the rectangle: length * breadth

Area of tiles = 2 * 1.5 = 3m²

Area of 4 Windows = 2 * 1.75 *4 = 14m²

Area of 2 Doors = 2 * 1 * 3.5 = 7m²

On floor 24 tiles are used. So to calculate it we have : [tex]\frac{l*b}{3} = 24[/tex]

          =>  [tex]2x^{2} = 72[/tex]   => x = 6

We get x = 6. Now, Breadth = 6meters, and Length = 12meters

For covering Four walls of the room with sheets, We will find out the Curved Surface Area of the room:  2h(l+b), where h is the height of the room. We also have to exclude the area of Four Windows and Two Doors for sheets. And a total of 41 pieces of sheets are required to cover it with an area of 3m² each. So, the formula will be, [tex]\frac{2h(l+b)-14-7}{3} = 41[/tex]

          => [tex]\frac{2h(18) - 14 - 7}{3} = 41[/tex]    =>  36h = 144

         =>  h = 4 metres

Hence, the height of the room will be 4 meters.

To know more about the Area of the Rectangle, Click here :

https://brainly.com/question/2607596

#SPJ1

Answer:

3/2

Step-by-step explanation:

move the 3x to the other side and divide it by 2

Answer:

d brainest plz

Step-by-step explanation:

Answer:

2cm

Step-by-step explanation:

because?

Answer:

20

Step-by-step explanation:

Answer:

We get the value of x: x = 3

Step-by-step explanation:

Point G lies between points F and H on Line segment F H.

Space between F and G = 4x

Space between G and H = 2x

Length of FH = 18

We need to find value of x.

As point G lies between point F and H, sum of FG and GH will give FH, we can write

[tex]FG + GH = FH[/tex]

Putting values to make equation

[tex]4x + 2x = 18[/tex]

Now, solving the equation we can find value of x

[tex]4x + 2x = 18 \\6x=18\\x=\frac{18}{6}\\x=3[/tex]

So, we get the value of x: x = 3

Answer:

dlfkv

Step-by-step explanation:

[tex] \frac{3 + x}{3} = \frac{x}{2} [/tex]

[tex] \frac{3}{3} + \frac{x}{3} = \frac{x}{2} [/tex]

[tex]1 + \frac{x}{3} = \frac{x}{2} [/tex]

[tex]1 = \frac{x}{2} - \frac{x}{3} [/tex]

[tex]1 = \frac{3x}{6} - \frac{2x}{6} [/tex]

[tex]1 = \frac{x}{6} [/tex]

[tex]1 \times 6 = x[/tex]

[tex]6 = x[/tex]

The rotation of the point is (-5, 6)

The point is given as:

Point = (6,5)

The rule of 90 degrees counterclockwise rotation around the origin is

(x, y) = (-y, x)

So, we have

Image = (-5, 6)

Hence, the rotation of the point is (-5, 6)

Read more about rotation at

https://brainly.com/question/26249005

#SPJ1

Answer:

y = -3x + 30

Step-by-step explanation:

First, find the slope using the slope formula:

m = (y2 - y1) / (x2 - x1)

m = (9 - (-3)) / (7 - 11)

m = -12/4

m = -3

Next, find the y-intercept by substituding one of the two points into what the equation is so far:

y = -3x + b

(7, 9)

9 = -3(7) + b

9 = -21 + b

30 = b

Now you have the full equation:

y = -3x + 30

The percent of the time that Haddad will save by paying the extra $30.000 per month is d) 59%.

A percentage is a unit in 100, a part of a whole, or a ratio of one variable to the bigger variable.

Percentages show the quantity or value of the independent variable that is contained in a dependent variable.

Data and Calculations:

Total months to pay off a debt = 58 months

The additional amount required to reduce the payment period to 24 months = $30 per month

The savings in time = 59% (58 -24/58 x 100).

Thus, the percent of the time that Haddad will save by paying the extra $30.000 per month is d) 59%.

Learn more about percentages at https://brainly.com/question/24877689

#SPJ1

Answer:

-9 is the final answer

Step-by-step explanation:

2x-4x=-2x

so the equation would be -2x-15=3

add 15 to both sides -2x=18

divide both sides by -2

Answer:

6

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

the smallest composite number that can be written as a product of four different prime numbers is 6

Answer: y = 1/2x + 1

(4,2)

4=x1

2=y1

y = mx + b

2 = 1/2(4) + b

2 = 2 + b

b = 1

y = 1/2x + 1

Answer:

14 degrees.

Step-by-step explanation:

I am assuming that the 56 degree angle is at the centre of the circle.

The angle at the top in the circle = 1/2 * 56 = 28 degrees.

The reflex angle = 360 - 56 = 304 degrees.

If we draw a line from the vertex of the 56 degrees angle to the vertex of 28 degree angle we bisect the reflex angle and the 28  degree angle. Also the 2  triangles formed are congruent ( by SSS).

So x = 180 - 1/2 * 28 - 1/2 * 304

= 180 - 14 - 152

= 180 - 166

= 14 degrees.

Answer:

C. 7/8 days

Step-by-step explanation:

The following cases for the solutions of a system of linear equations are listed below:

In this problem we find the case of a system of linear equations with two variables, of which we must determine the nature of its dependent constants for the following three cases:

The implicit form of this system is shown below:

a · x - y = - b                (1)

c · x - y = - d                (2)

According to the linear algebra, a system of linear equations has no solutions if the determinant of the matrix of dependent coefficients is equal to zero. Then, by Cramer's law we find that:

a - c = 0

a = c

Therefore, the system of linear equations has no solutions for a = c.

Also by linear algebra, we know that the two linear equations have infinite solutions if and only if both equations are multiples of each other, then:

a · x - y + b = k · (c · x - y + d)

a · x - y + b = (k · c) · x - k · y + (k · d)

The system has infinite solutions when a = k · c and b = k · d.

Then, the system has only one solution if and only if a ≠ k · c and b ≠ k · d.

To learn more on systems of linear equations: https://brainly.com/question/19549098

#SPJ1