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3 years ago

What is the slope of the line that passes through the points (1, 1) and (–1, –5)?

Mathematics

1 answer:

GalinKa [24]3 years ago

6 0

$Slope = \frac{-5-1}{-1-1}$
$Slope = \frac{-6}{-2}$
$Slope = 3$

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Dina and Masha start cycling on a 20 km bike path at the same time. When Dina reaches the end of the path, Masha still has 4 km

sammy [17]

Answer:

0.5 hour

Step-by-step explanation:

Given

Speed of Dina = 10 km/h

Distance = 20 km

So the time Dina taken to complete the track is:

$Speed=\frac{distance}{time}\\10=\frac{20}{time}\\time=\frac{20}{10}\\ time=2\ hours$

The time taken by Dina is 2 hours. As masha started with dina but she was 4 km of the path left to cycle,

her distance covered in 2 hours was:

$Distance\ covered\ by\ Masha\ in\ 2\ hours=20-4\\=16 km$

So we know the time and distance:

Now,

$Speed\ of\ Masha=\frac{distance}{time}\\ =\frac{16}{2}\\ =8\ kilometer\ per\ hour$

We have to calculate the time that will be needed by MAsha to complete the track:

As we know the speed and remaining distance

$Speed=\frac{distance}{time}\\8=\frac{4}{time}\\ time=\frac{4}{8}\\time=0.5\ hours$

Masha needs 0.5 hour to complete the track ..

7 0

3 years ago

Read 2 more answers

Simplify the following expression and then write down the coefficient of x²: x² + x² + x² + x²

lapo4ka [179]

Answer:

The expression is 4x² and coefficient is 4.

Step-by-step explanation:

All have the same variables, x², so you add up together :

$1{x}^{2} + 1{x}^{2} + 1{x}^{2} + 1{x}^{2}$

$= 4 {x}^{2}$

7 0

3 years ago

12) Add the fractions, and simplify if possible.<br><br> (y+7)/(y^2-y-12) - 2/(y^2-9)

lianna [129]

Answer:

$\dfrac{y^2+2y-13}{(y-4)(y+3)(y-3)}$

Step-by-step explanation:

Given the expression

$\dfrac{y+7}{y^2-y-12}-\dfrac{2}{y^2-9}$

First, factor each denominator:

1. $y^2-y-12=y^2-4y+3y-12=y(y-4)+3(y-4)=(y-4)(y+3)$

2. $y^2-9=(y-3)(y+3)$

Now the expression is

$\dfrac{y+7}{(y-4)(y+3)}-\dfrac{2}{(y-3)(y+3)}$

Now, multiply the first numerator by (y-3) and the second by (y-4) and write the result as a fraction with denominator $(y-4)(y+3)(y-3):$

$\dfrac{(y+7)(y-3)-2(y-4)}{(y-4)(y+3)(y-3)}=\dfrac{y^2-3y+7y-21-2y+8}{(y-4)(y+3)(y-3)}=\dfrac{y^2+2y-13}{(y-4)(y+3)(y-3)}$

This fraction cannot be simplified more.

3 0

3 years ago

At a soccer tournament there are (16x+30) boys and (5x-12) more girls if x= 5 how many girls are at the tournament

VikaD [51]

16(5)+30
16x5=80
80+30=110

5(5)-12
5x5=25
25-12=13

110x13=1430

There are 1430 girls at the soccer tournament.

Hope this helps!

3 0

4 years ago

The proper interpretation of a 95% confidence interval is: A. We are 95% confident that the point estimate is between the lower

soldier1979 [14.2K]

Answer: B. We are 95% confident that the population parameter is between the lower confidence limit and upper confidence limit.

Step-by-step explanation:

In statistics, we know that the interpretation of $(1-\alpha)\%$ level of confidence interval is that we are $(1-\alpha)\%$ sure that the true population parameter lies in it.

Therefore, the proper interpretation of a 95% confidence interval is that we are 95% confident that the population parameter is between the lower confidence limit and upper confidence limit.

4 0

3 years ago