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4 years ago

Which is the slope of the line that passes through the points (4,2) and (6,7)

Mathematics

1 answer:

Anastasy [175]4 years ago

5 0

The slope is 5/2. You can find the slope by using y2-y1/x2-x1. 7-2/6-4= 5/2.

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A restaurant offers diet soda and regular soda. In one day they sold 14 diet sodas. If the ratio of diet sodas sold to regular s

finlep [7]

Answer: 26 sodas.

Step-by-step explanation:

Let be "x" the number of regular sodas that were sold in that day.

You know that the the ratio of diet sodas sold to regular sodas sold was:

$7 : 6$

This ratio can also be written as a fraction:

$\frac{7}{6}$

Knowing that in that day they sold 14 diet sodas, you can write the following proportion:

$\frac{7}{6}=\frac{14}{x}$

Now solve for "x":

$(x)(\frac{7}{6})=14\\\\x=(14)(\frac{6}{7})\\\\x=12$

Then the total number of sodas sold that day is:

$Total=14\ sodas+12\ sodas=26\ sodas$

6 0

3 years ago

Is the value of the 8 in 12.984 the same as the value of the 8 in 7.38? Justify your response.

FinnZ [79.3K]

Answer:

Yes because they are both in the hundredths place

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

A hurricane was detected in the Atlantic around 5 a.m. The National Weather Service determined that it will make landfall at a l

solniwko [45]

Answer:

The correct option is;

A) Components: [0.30, 0.70], magnitude: 0.76

Step-by-step explanation:

The given parameters are;

The path of the of the airplane at 5 a.m. given by The National Weather Service = [3, 7]

The location of the hurricane at 6 a.m. = 1/10 of the total distance between the point where it was detected to the point where it is predicted to make land fall

Therefore;

The components of the vector at 6.00 a.m. = 1/10 × [3, 7] = [0.3, 0.7]

The magnitude of the vector at 6.00 a. m. = √(0.3² + 0.7²) ≈ 0.76.

6 0

3 years ago

Read 2 more answers

Find a positive number for which the sum of it and its reciprocal is the smallest (least) possible. Let x be the number and let

Allisa [31]

Answer:

$S(x) = x + \frac{1}{x}$ --- Objective function

Interval = $\{x:x=1\}$

Step-by-step explanation:

Given

Represent the number with x

The required sum can be represented as:

$x + \frac{1}{x}$

Hence, the objective function is:

$S(x) = x + \frac{1}{x}$

To get the the interval, we start by differentiating w.r.t x

<em>Using first principle, this gives:</em>

$S'(x) = 1 - \frac{1}{x^2}$

Equate S'(x) to 0 in order to solve for x

$0 = 1 - \frac{1}{x^2}$

Subtract 1 from both sides

$0 -1 = 1 -1 - \frac{1}{x^2}$

$-1 = - \frac{1}{x^2}$

Multiply both sides by -1

$1 = \frac{1}{x^2}$

Cross Multiply

$x^2 * 1 = 1$

$x^2 = 1$

Take positive square root of both sides because x is positive

$\sqrt{x^2} = \sqrt{1$

$x = 1$

Representing x using interval notation, we have

Interval = $\{x:x=1\}$

To get the smallest sum, we substitute 1 for x in $S(x) = x + \frac{1}{x}$

$S(1) = 1 + \frac{1}{1}$

$S(1) = 1 + 1$

$S(1) = 2$

<em>Hence, the smallest sum is 2</em>

3 0

3 years ago

According to the 2008 U.S. census, California had a population of approximately 4 × 10^7 people and Florida had a population of

KIM [24]

Answer:

A. The population of California was approximately two times the population of Florida.

Step-by-step explanation:

According to the 2008 U.S. census, population of Florida = 2 × $10^{7}$

Population of California = 4 × $10^{7}$

= 2 × 2 × $10^{7}$

= 2 × population of Florida

Hence, the population of California was approximately two times the population of Florida and the correct option is A.

5 0

3 years ago

Read 2 more answers