All categories

2 years ago

Find the value of r in (4, r), (r, 2) so that the slope of the line containing them is −53

Mathematics

2 answers:

Elan Coil [88]2 years ago

7 0

Answer:

C) 7

===========================================

Work Shown:

Use the slope formula

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

Plug in the given slope we want m = -5/3 and also the coordinates of the points. Then isolate r

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

-5/3 = (2-r)/(r-4)

-5(r-4) = 3(2-r) .... cross multiplying

-5r+20 = 6-3r

-5r+20+5r = 6-3r+5r .... adding 5 to both sides

20 = 6+2r

20-6 = 6+2r-6 ....subtracting 6 from both sides

14 = 2r

2r = 14

2r/2 = 14/2 .... dividing both sides by 2

r = 7

The slope of the line through (4,7) and (7,2) should be -5/3, let's check that

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

m = (2-7)/(7-4)

m = -5/3

The answer is confirmed

Brut [27]2 years ago

5 0

Answer:

C) 7

Correct answer

Step-by-step explanation:

You might be interested in

Vera is an ecologist who studies the change in the bear population of Siberia over time. The relationship between the elapsed ti

rewona [7]

Answer:

Every year, the bear population shrinks by a factor of 2/3 .

Explanation:

The concrete question and the function or data were omitted.

I found the complete question on the internet. Please, find attached the picture with the complete question

You must complete the sentence about the yearly rate of change of the bear population, telling whether it grows or shrinks and by what factor.

Thus, the goal is to interpret the rate of change in an exponential model.

The exponential model is:

$N(t)=2187\cdot \bigg(\dfrac{2}{3}\bigg)^t$

Let's analyze that function.

When t = 0, (2/3)⁰ = 1 and N(0) = 2,187 × 1 = 2,187

Thus, the population of bears starts with 2,187 individuals.

For t = 1, the population will be N(1) = 2,187 × (2/3).

For t = 2, the population will be N(2) = 2,187 × (2/3)²

And so on, every year the population of bears is multiplied by a factor of 2/3.

Since, 2/3 is less than 1, every year the population will be decreasing (decaying), by a factor of 2/3.

Thus, the answer, i.e. the complete sentence, is:

Every year, the bear population shrinks by a factor of 2/3 .

6 0

3 years ago

Read 2 more answers

Jeff lives 12 miles east of Stan. Jeff lives 16 miles north of Wei. What is the shortest distance that Stan and Wei can live fro

Greeley [361]

| \
| \
| 16 \
| \
|______\
12

Envision this as a right triangle, with one leg of 12 miles, and the other 16 miles. Solve using the Pythagorean Theorem a²+b²=c²:

12²+16²=c²
400 = c²
20=c...they live at least 20 miles from each other.

7 0

3 years ago

Alondra says that (12 + 31) × 5 is equivalent to 12 + 31 × 5 because of the associative property. Determine if Alondra is correc

MAXImum [283]

Answer:

Step-by-step explanation:

(12 + 31) × 5 = 215

12 + 31 × 5 = 167

order of operations are the rules that state the sequence in which the multiple operations in an expression should be solved.

Order of Operations :

1. Parentheses

2. Exponents

3. Multiplication and Division

4. Addition and Subtraction

7 0

1 year ago

At a red-tag sale, all items with red tags have been marked down by 49%. What should be the sale price of a DVD player having a

ss7ja [257]

The answer is 119.8245. 49% of $234.95 is 115.1255 (.49 • 234.95 = 115.1255). Subtract $115.1255 from $234.95 to get the answer to get 119.8245 (234.95 – 115.1255 = 119.8245).

6 0

2 years ago

Katie bought 2 one gallon bottles for a party. Her guest drank 5/4 gallons of juice. What is the fraction of juice leftover? Sho

frosja888 [35]

Answer:

3/4 gallons of juice

Step-by-step explanation:

Katie bought 2 one-gallon bottles for a party.

2 one-gallon bottles = 2-gallon bottles of juice

We are told that:

Her guest drank 5/4 gallons of juice.

The fraction of juice leftover is calculated as:

2 gallons of juice - 5/4 gallons of juice

2 - 5/4

Lowest Common Denominator = 4

2/1 - 5/4

= 8 - 5/4

= 3/4 gallons of juice

Therefore, the fraction of juice leftover is 3/4 gallons of juice

7 0

2 years ago