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DIA [1.3K]
3 years ago
5

Complete the equation of the line whose y-intercept is (0, -1) and slope is 4. (Khan academy)

Mathematics
1 answer:
vagabundo [1.1K]3 years ago
5 0

Answer:

y = 4x - 1

Step-by-step explanation:

y = mx + b

Here m is slope and b is y-intercept

m = 4;  b = -1  

y = 4x - 1

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For what values of the variable, do the following fractions exist: y^2-1/y+y/y-3
ale4655 [162]

Answer:

Remember that the division by zero is not defined, this is the criteria that we will use in this case.

1) \frac{y^2 - 1}{y}  + \frac{y}{y - 3}

So the fractions are defined such that the denominator is never zero.

For the first fraction, the denominator is zero when y = 0

and for the second fraction, the denominator is zero when y = 3

Then the fractions exist for all real values except for y = 0 or y = 3

we can write this as:

R / {0} U { 3}

(the set of all real numbers except the elements 0 and 3)

2) \frac{b + 4}{b^2 + 7}

Let's see the values of b such that the denominator is zero:

b^2 + 7 = 0

b^2 = -7

b = √-7

This is a complex value, assuming that b can only be a real number, there is no value of b such that the denominator is zero, then the fraction is defined for every real number.

The allowed values are R, the set of all real numbers.

3) \frac{a}{a*(a - 1) - 1}

Again, we need to find the value of a such that the denominator is zero.

a*(a - 1) - 1 = a^2 - a - 1

So we need to solve:

a^2 - a - 1 = 0

We can use the Bhaskara's formula, the two values of a are given by:

a = \frac{-(-1) \pm \sqrt{(-1)^2 + 4*1*(-1)}  }{2*1}  = \frac{1 \pm \sqrt{5} }{2}

Then the two values of a that are not allowed are:

a = (1 + √5)/2

a = (1 - √5)/2

Then the allowed values of a are:

R / {(1 + √5)/2} U {(1 - √5)/2}

7 0
2 years ago
Find the measure of the central angle with an arc length equaling 29.21 and a circumference = 40.44
Dima020 [189]

measure of central angle is 4.607 radians with an arc length equaling 29.21 and a circumference = 40.44

Step-by-step explanation:

Arc length = 29.21

Circumference = 40.44

Central angle = ?

The formula used to find central angle is:

s=r\theta

where s = arc length, r= radius and Ф=central angle.

We need to find radius from circumference

c=2\pi r\\r=\frac{c}{2\pi } \\Putting\,\,values:\\r=\frac{40.44}{2*3.14}\\r=6.43

So, radius = 6.34

Now, finding central angle:

s=r\theta\\29.21=6.34\,\,\theta\\\theta=\frac{29.21}{6.34}\\\theta=4.607\,\,radians

So, measure of central angle is 4.607 radians with an arc length equaling 29.21 and a circumference = 40.44

Keywords: Central angle of circle

Learn more about Central angle of circle at:

  • brainly.com/question/8618791
  • brainly.com/question/2115496
  • brainly.com/question/10610299

#learnwithBrainly

5 0
2 years ago
The graph shows the height of a hiker above sea level.
dimaraw [331]

The <u>correct answer</u> is:


B) The variables are height and time. For the first part of the graph, the height is increasing slowly, which means the hiker is walking up a gentle slope. Flat parts of the graph show where the elevation does not change, which means the trail is flat here. The steep part at the end of the graph shows that the hiker is descending a steep incline.


Explanation:


The variables are marked on the graph. Time is marked along the x-axis, which means it is the independent variable. Height is marked along the y-axis, which means it is the dependent variable.


The first part of the graph rises slowly. This means the elevation does not change much over the time; this would be consistent with a gentle slope being climbed.


The flat areas are where the elevation does not change. This would be consistent with the hiker resting.


The steep decrease at the end shows that the elevation goes down quickly. This is consistent with the hiker climbing down a steep slope.

3 0
3 years ago
Read 2 more answers
40 pts!! Simplify the expression in the picture.
tino4ka555 [31]

Answer:

D.   (27x^6y^9) / x^9.

Step-by-step explanation:

(3x^2y^3 / z^3 )^3

=  3^3 x^(2*3)y(3*3) / z^(3^3)

= 27 x^6y^9 / x^9.

4 0
3 years ago
Read 2 more answers
I need help plz real onez plz
melamori03 [73]
The mean is 10.
To find the mean you add up all the numbers and divide by how many sets of numbers there were.
8+10+11+8+13=50
50/5=10.
6 0
2 years ago
Read 2 more answers
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