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3 years ago

The sum of five times a number and 6 is 21. What is the number?

Mathematics

2 answers:

Nataliya [291]3 years ago

6 0

Answer: it’s 3

Step-by-step explanation:

steposvetlana [31]3 years ago

6 0

5x + 6 = 21
-6 -6
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5x = 21
(divide 5 on both sides to get rid of the number to get the variable by itself on both sides which makes X = 4.2

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A Triangle has an area of 36cm^2. The base and height are scaled by a factor of 5. What is the area of the resulting triangle?

Finger [1]

Answer:

Area of resulting triangle will be 900 $cm^2$ .

Step-by-step explanation:

When sides of any polygon if scaled by a factor of k

then area is scaled by $k^2$

According to the above statement

therefore here in the question since area of original triangle was 36 $cm^2$

and both base and height are scaled by a factor of 5.

therefore area of scaled triangle will be $5^2$ times of the original

that is 25 x 36 which gives 900 $cm^2$

So area of resulting triangle will be 900 $cm^2$

7 0

3 years ago

Can someone help me with this problem

Naily [24]

<h3>Answer: Choice A</h3><h3>The point Z ' is at (8,4)</h3><h3>The point Y ' is at (0,4)</h3>

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Explanation:

The key thing here is that point Z does not move. Why not? Because this is where the center of dilation occurs. The center point is fixed. Everything around the center will expand away from, or contract toward, the center.

In this case, the scale factor is 4/5 = 0.8 which is less than 1. So points will contract toward the center. The old pre-image shrinks to make the image smaller.

Note how point Y = (-2,4) is 10 units away from point Z. You can count out the spaces or subtract the x coordinates. Use an absolute value to make sure the result is positive

|x1-x2| = |-2-8| = |-10| = 10

|x2-x1| = |8-(-2)| = |8+2| = |10| = 10

So 0.8 times this distance is therefore 0.8*10 = 8 meaning that point Y' is going to be 8 units away from point Z' or Z.

Subtract 8 from the x coordinate of point Z to get x-8 = 8-8 = 0.

The y coordinate stays the same at y = 4 the whole time.

----------------------------------------

In short, point Y starts at (-2,4) and moves to (0,4)

Distance from Y to Z is 10 units

Distance from Y' to Z' is 8 units

8/10 = 4/5 = 0.8 is the scale factor

Point Z does not move. So Z and Z' are at the same location.

5 0

3 years ago

Read 2 more answers

Rewrite the following statements less formally, without using variables. Determine, as best as you can, whether the statements a

Anni [7]

Answer:

The answer is given below

Step-by-step explanation:

a) Let u and v be real numbers. The sum of u and v = u + v and the difference between u and v = u - v.

u + v < u - v means the sum of two real numbers is less than the difference between the two numbers.

There exist two real numbers such that their sum is less than the difference between them

This is true when atleast one of the numbers is negative, for example u = 2 and v = -2

u + v = 2 + (-2) = 0 , u - v = 2 - (-2) = 4

u + v < u - v.

b) Let x be a real number and x² be the square of the real number

x² < x means that the square of a real number is less than the real number

We can rewrite the statement as: There exist a real number such that its square is smaller than itself.

The statement is true for x is between 0 and ±1

E.g. for x = 1/2, x² = (1/2)² = 1/4

1/4 < 1/2

c) Let n represent all positive integers. n² is the square of n.

n²≥n means that the square of n is greater or equal to n.

We can rewrite the statement as: For all positive integer numbers, the square of the number is greater than or equal to the number itself

The statement is true.

1² ≥ 1, 2² ≥ 2 e.t.c

d) Let a and b be real numbers. The sum of a and b = a + b. |a| is the absolute value of a and |b| is the absolute value of b

|a+b|≤|a|+|b| means the absolute value of the sum of two real numbers is less than or equal to the sum of their individual absolute value.

We can rewrite the statement as: For two real numbers, the absolute value of their sum is less than or equal to their individual absolute value sum.

This statement is true for all real numbers.

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3 years ago

Jin’s soccer team has 4 coaches and 22 players, and his twin sister’s team has 2 coaches and 11 players. If the relationship bet

nikklg [1K]

Question : Jin’s soccer team has 4 coaches and 22 players, and his twin sister’s team has 2 coaches and 11 players. If the relationship between the number of players and coaches is proportional throughout the league, which ordered pair could represent the total number of coaches and players in the entire league?

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Answer :

<u>26 coaches and 143 players</u>

<u />

4 0

3 years ago

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Given the following system of equations: 2x + 6y = 12 4x + 3y = 15 Which action creates an equivalent system that will eliminate

Charra [1.4K]

Option A and B are correct.

Step-by-step explanation:

We are given the following systems of equation:

$2x + 6y = 12 \\4x + 3y = 15$

We need to identify the action creates an equivalent system that will eliminate one variable when they are combined.

Checking the options:

a) Multiply the second equation by −2 to get −8x − 6y = −30

If we add equation(1) and the new equation(2) the variable y will be eliminated. So, this is the correct option.

b) Multiply the first equation by 2 to get 4x + 12y = 24.

If we subtract new equation(1) and equation(2), the variable x will be eliminated. So, this is the correct option.

c) Multiply the second equation by −4 to get −16x − 12y = −60

By adding or subtracting, none of the variable is eliminated. So, it is not the correct option.

d) Multiply the first equation by −4 to get −8x − 24y = −48.

By adding or subtracting, none of the variable is eliminated. So, it is not the correct option.

So, Option A and B are correct.

Keywords: Solve System of equations

Learn more about solving system of equations at:

#learnwithBrainly

7 0

3 years ago

Read 2 more answers