A math class is having a discussion on how to determine if the expressions 4 x minus x + 5 and 8 minus 3 x minus 3 are equivalent using substitution. The class has suggested four different methods.

Which describes the correct method?
Both expressions should be evaluated with one value. If the final values of the expressions are both positive, then the two expressions must be equivalent.
Both expressions should be evaluated with one value. If the final values of the expressions are the same, then the two expressions must be equivalent.
Both expressions should be evaluated with two different values. If for each substituted value, the final values of the expressions are positive, then the two expressions must be equivalent.
Both expressions should be evaluated with two different values. If for each substituted value, the final values of the expressions are the same, then the two expressions must be equivalent.

To determine the surface area of a model pyramid that has been scaled down, we must first compute the area of the original pyramid, and then multiply that area by the square of the scale factor.

To find the surface area of a square pyramid we first calculate the area of the base which is side squared (152 = 225 sq ft), and then calculate the area of the four triangular faces. For the latter we can use the formula 0.5 x base x height, where base is the side of the pyramid (15 ft) and height is the slant height. The slant height can be calculated using Pythagoras' theorem which constitutes of half of the base and the height of the pyramid, this will give us the slant height, which then can be used in the surface area formula.

Next, if the pyramid is scaled down by a factor of 0.5, both lengths and areas are reduced by that factor. Hence, multiply the original area by 0.52 = 0.25 to find the surface area of the model pyramid.

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Answer:

Step-by-step explanation:

hi

Answer:

a = 2, b = -5,  c = 3

Step-by-step explanation:

The standard form of the quadratic equation is   a*x^2 + bx + c = 0

Looking at the equation you have, we should correspond the coefficients with the standard form I wrote above.

so.   a = 2, b = -5,  c = 3

Answer:

c

Step-by-step explanation:

the like terms are 5x and 2x

The like terms in the given equation are 5x and 2x. Therefore, option C is the correct answer.

Like terms are those terms whose variables and their exponent power are the same. The coefficient of these variables can be different. Algebraic-like terms are terms that are similar to each other.

The given equation is 5x+3y+2x+3z=27.

In the given equation like terms are 5x and 2x and unlike terms are 3y and 3z.

Therefore, option C is the correct answer.

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Answer:

6 and 3/250

Step-by-step explanation:

The whole number part is 6, obviously

Then you have the fraction part, which in decimal form is 0.012 which is 12 thousandths which is 12/1000.

Simplify by dividing both the num. and denom. by 4 and you get 3/250. ;p

Answer:

6 3/250

Step-by-step explanation:

The correct equation that expresses how much each book cost is C.5x + 4 = 129, where x represents the price of one book.

The student asked which equation expresses how much each book cost if Tim bought a magazine for $4 and five books that all cost the same amount, spending a total of $129. The correct equation would account for the magazine's cost and the total cost of the five books. The equation that represents this scenario is C.5x + 4 = 129, where x represents the cost of one book, 5x represents the total cost of the five books, and 4 is the cost of the magazine. To find the cost of each book, you need to subtract the magazine's cost from the total and then divide by the number of books. The equation 5x + 4 = 129 does this correctly because when we subtract 4 (the cost of the magazine) from 129 (total amount spent), and then divide that result by 5, we find the cost of a single book.

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Answer:

D and B

Step-by-step explanation:

Answer:

$823.2

Step-by-step explanation:

Interest = 700 × 4.4/100 × 4

= 123.2

Balance = principle + interest

700 + 123.2

823.2

Answer:

A =823.20

Step-by-step explanation:

A = P (1 + rt)

Where A is the amount in the account

P is the principle,  r is the rate and t is the time

A = 700(1+4.4% *4)

Change to decimal form

A = 700(1+.044 *4)

A = 700(1+.176)

A =823.20

Answer:

negative,1800 feet , y=16.25x+1,800

Step-by-step explanation:

The correlation, y-intercept, and equivalent representations of given points all depend on the data's plot on the graph. The correlation is classified as positive, negative, or none based on the scatter pattern of points. The y-intercept is where the line intersects the y-axis, and it could be any of the provided options. The equation representing the line of best fit depends on the slope (gradient) and y-intercept of the line.

Without the actual data points, it's hard to definitively answer, but I'll provide some general guidance. The correlation of data points can be categorized as positive, negative, or none depending on how they are scattered on the graph. A positive correlation means as one variable increases, the other increases too, while a negative correlation means as one variable increases, the other decreases. When there's no pattern to the points, the correlation is none.

In terms of y-intercept, it's the point where the line crosses the y-axis. If we assume y-intercept as one of the options provided, e.g. 800 feet, 1200 feet, 1800 feet, and 2200 feet, it depends on how the line fits on the graph.

Similarly, the equivalent representation like Y=800 or Y=-17.5x+2200, Y=-16.25x+1800, or Y=-6.25x+1200 is dependent on the actual pattern of the data points. These representations are equations of straight lines where '-17.5', '-16.25', and '-6.25' represent the slope and '2200', '1800', '1200' respectively are the y-intercepts.

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Answer:

0.942 ft/s

Step-by-step explanation:

The rate of descent is the rate at which the hot air balloon is descending, that is, how fast it is descending.

We calculate this by finding how far it has moved and then dividing it by the time it took it to descend.

It moved from 5275 ft to 3128 ft. The displacement is:

5275 - 3128 = 2147 ft

The time taken is 38 minutes. In seconds, it is:

38 * 60 = 2280 seconds.

Therefore, the rate of descent is:

2147 / 2280 = 0.942 ft/s

Answer:

3m(4-5m)

Step-by-step explanation:

1) m is common in both terms so lets take it out:

m(12-15m)

since 12 and 15 are both divisible by 3 lets take 3 out:

3m(4-5m)

Hope this helps!

The factor of the expression 12m - 15m² is 3(4 - 5m).

Factorization in mathematics is the process of dividing a large number into smaller ones that, when multiplied together, give you the original number. Factorization is the process of dividing a number into its components or divisors.

Given:

An expression, 12m - 15m².

To factor the expression:

Using factorization method.

12m - 15m²,

= 3(4 - 5m)

Therefore, the factor is  3(4 - 5m).

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Answer:

x = 1586130/4778591

Step-by-step explanation:

4363x + 637 - 6282x = 562x/5262 - 282

4363x-6282x+637 = 562x/5262 - 282

-1919x+637 = 562x/5262 - 282

-1919x+637 = 562x/5262 - 282

        -637                           -637

-1919x = 281x/2490 - 637

-1919x * 2490 = 281x/2490 - 637 * 2490

-4778310x = 281x-1586130

-4778310x = 281x-1586130

        -281x               -281x

-4778591x = -1586130

-4778591x/-4778591 = -1586130/-4778591

x = 1586130/4778591

To solve the equation 1.75n = 7, divide both sides by 1.75 to isolate n, which simplifies to n = 4. Therefore, the value of n is 4.

To solve the equation 1.75n = 7 for the value of n, you need to isolate n. This can be accomplished by dividing both sides of the equation by 1.75, the coefficient of n.

Here are the steps:

Final answer:

There are 45 students in the class.

Explanation:

If 18 girls represent 40% of a class, we can calculate the total number of students in the class using the concept of percentages. To find the total number of students, we set up a proportion, which is an equation that says two ratios are equivalent.

We know that 18 girls are to 40% what the total number of students is to 100%, since 100% would be the whole class.
We can express this relationship with the equation:

18 (number of girls) / (total number of students) = 40% / 100%
Using cross-multiplication, we can find the total number of students:
18 / x = 40 / 100
x = (18 * 100) / 40
x = 1800 / 40
x = 45
So, there are 45 students in the class list.

Answer:

All of them

Step-by-step explanation:

x² - x - 2

(x + 1)(x - 2)

x² + x - 2x - 2

x² - x - 2

(x - 0.5)² - 2.25

x² - 2(x)(0.5) + 0.5² - 2.25

x² - x + 0.25 - 2.25

x² - x - 2

Answer:

Two more (+2) than three times (3) the difference between eight and a number (8-n)

Step-by-step explanation:

hope this helps

Answer:

1: "An equilateral triangle is never an obtuse triangle" & "An equilateral triangle is never an isosceles triangle."

2: Acute Isosceles Triangle

3: False! Option B.

4: D

Step-by-step explanation:

2: Isosceles Triangles have two equal sides. An acute triangle (or acute-angled triangle) is a triangle with three acute angles (less than 90°). An obtuse triangle (or obtuse-angled triangle) is a triangle with one obtuse angle (greater than 90°) and two acute angles.

3: An equilateral triangle is a triangle in which all the sides and all the angles are equal.

4: In order for a triangle to be isosceles, it has to have two same sides. For a triangle to be equilateral, all sides and angles need to be the same. Refer to reasoning in Question 2 for next explanation.

Answer:

[tex]\frac{1}{25}[/tex]

Step-by-step explanation:

if the picture shows 4 blue, 3 green, 5 red, and 3 yellow tiles, then the total amount of tiles is 15. Divide the number of yellow tiles by the total tiles. Remember the tile is replaced, so there will be the same 15 tiles in the bag with the same probability.

[tex]\frac{3}{15} *\frac{3}{15} = \frac{9}{225}=\frac{1}{25}[/tex]

Answer: The probability is 0.5

Step-by-step explanation:

The probability will be equal to the quotient between the area of region II, and the total area of the board (supposing that the probability of hitting in any place is equal)

The total area of the figure is equal to

Area = (15' + 35')*(8' + 20') = 50'*28' = 1400 in^2

Now, the area of region II is:

Region II = 20'*35' = 700

Then the probability is:

P = 700/1400 = 1/2 = 0.5

Answer:

6y3+17y2+22y+15

Step-by-step explanation:

Answer:

6y³ + 17y² + 22y + 15

Step-by-step explanation:

(2y+3) ( 3y² +4y+5)

Keep the 'FOIL' method (first, outside, inside, last) when distributing and you'll end up with

(2y)(3y² ) + (2y)(4y)  +(2y)(5 ) +(3)(3y2) + (3)(4y) + (3)(5)

Now, multiply each set to get

6y³+8y²+10y+9y²+12y+15

From there, just simplify/combine like terms (8y² + 9y² and 10y + 12y) to get your final answer: 6y³ + 17y² + 22y + 15

Answer:

Vertical angles

Step-by-step explanation:

Answer: Vertical angles

Step-by-step explanation:

Pair of opposite angles made by two intersecting lines

Answer:

4^4 x 6^6= 11943936

Step-by-step explanation:

hope this helps

Answer:

0

Step-by-step explanation:

The slope of the line is found by

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

    = (3-3)/(20-19)

    = 0/1

    = 0

Answer:

7b+6x-9y

Step-by-step explanation:

Parentheses do not matter.

2x-9y+4x+7b=

6x-9y+7b

Answer: 6x-9y+7b

Step-by-step explanation:

Answer:

18 would be the GCF.

Step-by-step explanation:

18 | 36

6 |  18

36/2 = 18.

To find the missing probability for consuming two or more cups of coffee in the data scientist's distribution, subtract the sum of the probabilities of all other events from 1, ensuring that all probabilities in the distribution meet the criteria of summing to 1 and each being between 0 and 1.

The question pertains to constructing a probability distribution for a data scientist's daily coffee consumption at work. The random variable C stands for the number of cups of coffee she drinks on a given day. To calculate the missing probability for someone who has two or more cups of coffee, one must know the individual probabilities of all other events (0, 1, 2, etc., cups of coffee). The sum of all these probabilities must equal 1, since that represents the certain event that some outcome in the distribution will occur. To find the missing probability, one would subtract the sum of the probabilities for 0 and 1 cups (if those are the only other events) from 1.

For example, if the probability of drinking 0 cups is 0.1 and the probability of 1 cup is 0.3, then the probability of drinking two or more cups would be 1 - (0.1 + 0.3) = 0.6. Important characteristics of a discrete probability distribution include that the sum of probabilities is 1 and that each individual probability is between 0 and 1, inclusive.

Answer:

It is C 75.36. I hope it helps.

Step-by-step explanation:

Answer:

15/100= 3/20

Step-by-step explanation: