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4 years ago

Solve average rate of change (4,-1) (-3,-2)

Mathematics

1 answer:

Vera_Pavlovna [14]4 years ago

7 0

Answer:

$\frac{1}{7}$

Step-by-step explanation:

The slope of the line joining the 2 points is a measure of the average rate of change.

Calculate slope m using the slope formula

m = $\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$

with (x₁, y₁ ) = (4, - 1) and (x₂, y₂ ) = (- 3, - 2)

m = $\frac{-2+1}{-3-4}$ = $\frac{-1}{-7}$ = $\frac{1}{7}$ ← average rate of change

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Help with 8 pls thanks

Masteriza [31]

Answer:

m<Y = 68°

Step-by-step explanation:

A tangent drawn to a circle makes a 90° angle with the radius that intersects it at the point of tangency. That means that m<X = 90°.

The sum of the measures of the angles of a triangle is 180°.

m<X + m<Y + m<Z = 180

90 + m<Y + 22 = 180

m<Y + 112 = 180

m<Y = 180 - 112

m<Y = 68

4 0

3 years ago

Sydney placed 10 guppies in a fish tank she recorded the number of guppies in the tank

pav-90 [236]

Answer:

$g(n) = 10 * 3^{n}$

Step-by-step explanation:

Given

See attachment for table

Required

Determine the explicit formula for the table

First, we need to check if the guppies increases at arithmetic progression or geometry progression.

For arithmetic progression:

We calculate the common difference (d)

$d = g(n) - g(n-1)$

Take n as 1

$d = g(1) - g(1-1)$

$d = g(1) - g(0)$

From the table:

$g(1) = 30\ \&\ g(0) = 10$

$d = 30 - 10$

$d = 20$

Take n as 2

$d = g(2) - g(1)$

From the table:

$g(1) = 30\ \&\ g(2) = 90$

$d = 90 - 30$

$d = 60$

The two differences are not equal. So, this

For geometry progression:

We calculate the common ratio (r)

$r = \frac{g(n)}{g(n-1)}$

Take n as 1

$r = \frac{g(1)}{g(1-1)}$

$r = \frac{g(1)}{g(0)}$

From the table:

$g(1) = 30\ \&\ g(0) = 10$

$r = \frac{30}{10}$

$r = 3$

Take n as 2

$r = \frac{g(2)}{g(1)}$

From the table:

$g(1) = 30\ \&\ g(2) = 90$

$r = \frac{90}{30}$

$r = 3$

The two ratios are equal.

So, the next step is to calculate the explicit formula using n term of a geometric progression.

Because the progression starts from 0, we make use of the following formula

$g(n) = g(0) * r^{n}$

Substitute values for g(0) and r

$g(n) = 10 * 3^{n}$

Hence:

The explicit formula is: $g(n) = 10 * 3^{n}$

7 0

3 years ago

Write an expression to represent: 3 minus the quotient of x and 4

alisha [4.7K]

The expression representing the sentence is $$3 -\frac{x}{4}$ .

We have a sentence - "3 minus the quotient of x and 4".

We have to determine the expression that represents the sentence.

<h3>Express the statement - "The difference of x and y is equal to an irrational number" in the form of expression.</h3>

The expression representing the above statement is -

x - y = π.

According to the question, we have -

3 minus the quotient of x and 4.

Using the Division Algorithm -

x = 4q + r

Substituting r = 0 by introducing decimals in the quotient, we get -

q = $$\frac{x}{4}$

Therefore -

$$3 -\frac{x}{4}$

Hence, the expression representing the sentence is $$3 -\frac{x}{4}$ .

To solve more questions on Expression modelling, visit the link below-

brainly.com/question/20876878

#SPJ2

8 0

2 years ago

Read 2 more answers

Can someone help me with this. Will Mark brainliest . Need answer and work/explanation. Thank you.

Rom4ik [11]

Answer:

Hope it helps...

Step-by-step explanation:

5 0

3 years ago

Do you capitalize "is" after "!"<br> "HELLO!" is blah

Naily [24]

No, you do not capitalize "is" after "!" unless you are forming a new and complete sentence. Do not capitilize: "Hello!" is okay to say. Capitilize: "Hello!" Is she okay, she has never greeted us before...

3 0

3 years ago