MATHEMATICS HIGH SCHOOL

6r+7=13+7r
how do you solve this?

Answers

Answer 1
Answer: Simplifying 6r + 7 = 13 + 7r Reorder the terms: 7 + 6r = 13 + 7r Solving 7 + 6r = 13 + 7r Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-7r' to each side of the equation. 7 + 6r + -7r = 13 + 7r + -7r Combine like terms: 6r + -7r = -1r 7 + -1r = 13 + 7r + -7r Combine like terms: 7r + -7r = 0 7 + -1r = 13 + 0 7 + -1r = 13 Add '-7' to each side of the equation. 7 + -7 + -1r = 13 + -7 Combine like terms: 7 + -7 = 0 0 + -1r = 13 + -7 -1r = 13 + -7 Combine like terms: 13 + -7 = 6 -1r = 6 Divide each side by '-1'.

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Determine what type of model best fits the given situation: The temperature of a cup of coffee decreases by 5 F every 20 minutes.

Answers

Final answer:

The situation is best modeled by a linear function, considering the steady and constant rate of temperature decrease. Although this model does not account for other factors, it lays out a fundamental understanding of the time-temperature relationship in the given scenario.

Explanation:

The situation where the temperature of a coffee decreases by 5 F every 20 minutes is best modeled by a linear function. This is because the rate of decrease is steady and constant, meaning it fits the structure of a linear function: y = mx + b, where m is the slope (rate of decrease) and b is the y-intercept (initial temperature). In this case, the slope would be -5/20, as the coffee temperature decreases by 5 F every 20 minutes.

This concept is closely related to Newton's Law of Cooling in Physics, which postulates that the rate of loss of heat from an object is proportional to the difference in temperature between the object and its surroundings, provided the temperature difference is small. However, in this case, since we are dealing with a constant rate of cooling, the linear model is more appropriate.

While this model does not account for factors such as the volume of the coffee, heat transfer to the surroundings or the specific heat capacity of the coffee, it provides a basic understanding of the relationship between time and temperature in this scenario.

Learn more about Linear Function here:

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Which of the following groups has terms that can be used interchangeably with the others?1. Percentage, Probability, and Proportion2. Critical Value, Probability, and Proportion3. Critical Value, Percentage, and Probability4. Critical Value, Percentage, and Proportion

Answers

Answer: 1) Percentage, Probability, Proportion

Step-by-step explanation:

In statistics,

▪Proportion means a fraction of the total.

▪Percentage means a number or a ratio, expressed as a fraction of 100. Here, the total is 100.

▪Probability which may look slightly different from the other two means a number between 0 and 1, showing the exact likelihood of an event happening. Which in context can mean, a number showing a fraction of an event happening out of the whole (0 to 1).

▪Critical value means a point in hypothesis testing on the test distribution that is compared to the test statistic to determine whether to reject the null hypothesis.

In the four definitions, the odd one out is Critical Value.

So the option without critical value in it is option 1) Percentage, Probability, Proportion since we can use the three interchangeable.

Answer:

1. Percentage, Probability, and Proportion

Step-by-step explanation:

Proportion means a portion of a whole e.g. 2/5

Percentage means a ratio of a number expressed as a fraction of 100 e.g 20/100

Probability- This means the likelihood of an event to occur e.g 1/2

All these three terms are usually expressed as a Fraction of a Number which makes them similar.

Square root of x to the 6th power over y to the 4th power

Answers

√((x^6)/(y^4))

x^6 indicates x to the sixth power, the same goes for y^4.

All of the following represents the same ratio except 4:3 4/3 or 3 to 4

Answers

Answer:

3 to 4

Step-by-step explanation:

cause 4:3 can be written as 4/3 or 4 to 3

but 3 to 4 is written as 3:4 or 3/4

Answer:

3 to 4

Step-by-step explanation:

All of the other ratios are 4 to 3.

Z varies jointly as x and y. If z=3 when x=3 and y=15, find z when x=6 and y=9

Answers

Answer: 6

Step-by-step explanation:

Which restriction is appropriate for the variable?3y^2 - 3y/y-1

A. no restrictions are needed
B. y= -1
C. y =1
D. y = 3 <---

Answers

Best answer is y=1
Because if the denominator is equals to 1, then the answer will be undefined and we don't want it to be undefined.
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