What is the equation of the line passing through the points (2, –1) and (5, –10) in slope-intercept form?

y=-3x-5


y=-3x+5

y=3x-5
y=3x+5,

Answer:

20.40

Step-by-step explanation:

Test Yourself

Final answer:

To find the value of the dependent variable, we use the point-slope form of the linear equation. Using the given slope of 5 and point (-7, 5), we first find the y-intercept to be 40. We then calculate the dependent variable's value to be 50 when the independent variable is 2.

Explanation:

The student has asked about the value of the dependent variable when the independent variable is 2 for a given linear function that has a slope of 5, and passes through the point (–7, 5). To find this value, one should use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept.

First, using the given point (–7, 5), we can find the y-intercept by substituting the slope and point into the equation:

y = 5x + b

5 = 5(-7) + b

b = 5 + 35

b = 40

So the equation of the line is y = 5x + 40. Now, to find the value of y when x is 2:

y = 5(2) + 40

y = 10 + 40

y = 50

Therefore, the value of the dependent variable when the independent variable is 2 is 50.

The decimal 0.135 can be written as 27/200 in fractions.

A fraction is a number that can be expressed as p/q, where q is not equal to zero.

It is defined as part of the whole.

0.135 is a decimal and to convert into a fraction it has to be written as

=135/1000

On simplifying the fraction

=27/200

Therefore, the decimal 0.135 can be written as 27/200 in fractions.

To know more about Fraction

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Answer:

The correct options are 1 and 2.

Step-by-step explanation:

From the given graph it is clear that it is a graph of an exponential function and the graph passes through the points (0,100) and (1,150).

The general form of an exponential function is

[tex]y=ab^x[/tex]            .... (1)

Where, a is the initial value and b is growth rate.

The initial value is 100 because the y-intercept of the graph is 100.

The graph passes through (1,150). Put y=150, a=100 and x=1 in the above formula to find the value of b.

[tex]150=100b^1[/tex]

Divide both the sides by 100.

[tex]1.5=b[/tex]

The value of b is 1.5.

Substitute a=100 and b=1.5 in equation (1).

[tex]y=100(1.5)^x[/tex]

It means the value is 1.5 times larger in every unit of time.

It can be written as

[tex]y=100(1+0.5)^x[/tex]

It means the initial value increased by 50% per unit of time.

So, the required scenarios are

1. The amount of money in a bank account increased by 505 per year.

2. The amount of a substance is one and a half times larger after every minute.

Therefore the correct options are 1 and 2.

Answer C

to calculate mean absolute deviation, we need to use the formula = (∑|x-mean|)/n

where x is each term given in data set

n is number of terms = 7

mean = sum of terms / n = (112+134+150+98+120+68+116)/7 = 114

now find (∑|x-mean|) = 138

MAD = (∑|x-mean|) / n = 138 /7 = 19.714 = 20

Answer:

The value of n is 4.

Step-by-step explanation:

Theorem of intersection of two cords : If two cords AB and CD intersecting at point P, then

[tex]|AP|\times |PB|=|CP|\times |PD|[/tex]

Using the theorem of intersection of two cords, we get

[tex](n-2)\times 16=8\times (n+8)[/tex]

Use distribution property,

[tex]16n+32=8n+64[/tex]

[tex]16n-8n=64-32[/tex]

[tex]8n=32[/tex]

Divide both sides by 8.

[tex]n=\frac{32}{8}[/tex]

[tex]n=4[/tex]

Therefore the value of n is 4.

The equation a² + b² = c² represents the Pythagorean theorem, which describes the relationship between the sides of a right triangle. It states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. For example, in a triangle with legs of 3 and 4 units, the hypotenuse would be 5 units.

The equation a² + b² = c² represents the Pythagorean theorem in mathematics. This theorem is used to describe the relationship between the lengths of the sides of a right triangle.

Pythagorean Theorem

In a right triangle:

a and b are the lengths of the legs (the two sides that form the right angle).

c is the length of the hypotenuse (the side opposite the right angle).

The theorem states that the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides:

a² + b² = c²

This can also be expressed as c = √(a² + b²).

For example, if one leg of the triangle is 3 units and the other leg is 4 units, you can find the hypotenuse as follows:

Question:

what does a^2+b^2=C^2 formula mean ?

ANSWER

[tex](x + 2)(3x + 4)[/tex]

EXPLANATION

The given expression is

[tex]3x(x + 2) + 4(x + 2)[/tex]

We can see that (x+2) is the greatest common factor.

We factor to obtain;

[tex](x + 2)( 3x + 4)[/tex]

The correct choice is C.

Answer:

(x + 2) (3x + 4)

Step-by-step explanation:

I got it correct on my test

Final answer:

To find the ordered pairs that are solutions to the inequality 2x+3y≥−1, we can solve the inequality and substitute different x-values to find corresponding y-values.

Explanation:

To find the ordered pairs that are solutions to the inequality 2x+3y≥−1, we can use a graph or a table of values.

Let's solve the inequality for y:

2x + 3y ≥ -1

3y ≥ -1 - 2x

3y ≥ -2x - 1

y ≥ (-2/3)x - 1/3

Now we can choose some x-values and substitute them into the inequality to find corresponding y-values:

Let's choose x = 0:

y ≥ (-2/3)(0) - 1/3

y ≥ 0 - 1/3

y ≥ -1/3

So one ordered pair that is a solution is (0, -1/3).

Let's choose x = 3:

y ≥ (-2/3)(3) - 1/3

y ≥ -2 - 1/3

y ≥ -7/3

So another ordered pair that is a solution is (3, -7/3).

Answer:

2%

Step-by-step explanation:

A P E X

Answer:

15 feet

Step-by-step explanation:

Given : In this fulcrum, the weights are perfectly balanced.

To Find: How far must the fulcrum be located from the 60 pound weight if the bar is 24 feet long?

Solution:

To make the weights perfectly balanced torque must be equal

[tex]Torque = Force \times d[/tex]

Where [tex]Force = Mass \times Acceleration[/tex]

Let a be the acceleration

d= Distance between the pivot and the acting point.

Let x be the distance from 60 pound weight where fulcrum is located

Since we are given that Length of bar = 24 feet.

So,Distance of fulcrum from 100 pound weight = 24-x

Now torque for 60 pound weight :

[tex]Torque = 60a \times x[/tex]

Now torque for 100 pound weight.

[tex]Torque =100a \times (24-x)[/tex]

Now to maintain the equilibrium i.e. To make the weights perfectly balanced

[tex]60a \times x =100a \times (24-x)[/tex]

[tex]60x = 2400-100x[/tex]

[tex]160x = 2400[/tex]

[tex]x = \frac{2400}{160}[/tex]

[tex]x = 15[/tex]

Hence The fulcrum must be located 15 feet from the 60 pound weight if the bar is 24 feet long.

Answer:

15

Step-by-step explanation:

Answer:

One step equations

3 + x = 5 ___x = 2

Y + 14 = 20____x = 6

Equations with Fractions

4/5q = 32___q = 40

3/4x = 6___x = 8

Equation with decimals

3.2x – 2.7 = 1.2x___x = 1.35

Equation with distributive Property

7x + 3 (x + 1) = 10x + 3

Infinitely Many solutions

Real World Problem

Monica knows that she should spend no more than  1/3 of her income on her rent. She really wants to move into a cool condo downtown and has found a great place where the rent is $2,300 per month. Based on that, how much should Monica earn each month to afford the rent on her cool new place?

Hope This Helps!

Answer:

people who toil

Step-by-step explanation:

The above lines have been taken from the poem "The Lady of Shalott" written by Alfred, Lord Tennyson. The poem is about the mysterious Lady of Shalott who lives on the Island of Shalott. People who wanted to see her have never got the opportunity to see her. On the other hand, the people who work in the fields have listened to her singing an eerie song. The song which the lady sings echoes all over the river Camelot.