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zaharov [31]
2 years ago
5

Triangle ABC is shown with line DE running horizontally through the center of the figure.

Mathematics
1 answer:
vichka [17]2 years ago
3 0

Answer:

If triangle ABC is dilated by a scale factor of three about the center of the triangle, dilated line D'E' will be parallel to the original line. As the triangle is dilated, the line will move up. This is because the center of the triangle does not lie on DE.

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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.

4 0
2 years ago
Help please!!!!! I don't really get this, help asap.
Greeley [361]
1 box = 6 granola bars
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3 0
3 years ago
Read 2 more answers
Tia is making lemonade for a baseball tournament. The recipe calls for 2/3 cup of strawberries for each gallon of lemonade. She
antoniya [11.8K]

Given:

The recipe calls for \dfrac{2}{3} cup of strawberries for each gallon of lemonade.

Tia has 6 cups of strawberries.

To find:

The number of gallons of lemonade she can make.

Solution:

We have,

\dfrac{2}{3} cup of strawberries for = 1 gallon of lemonade

1 cup of strawberries for = \dfrac{1}{\frac{2}{3}} gallons of lemonade

                                        = 1\times \dfrac{3}{2} gallons of lemonade

                                       = \dfrac{3}{2} gallons of lemonade

6 cup of strawberries for = 6\times \dfrac{3}{2} gallons of lemonade

                                         = \dfrac{18}{2} gallons of lemonade

                                        = 9 gallons of lemonade

Therefore, 9 gallons of lemonade she can make by using 6 cups of strawberries.

7 0
2 years ago
What is an equation of the line in slope intercept form? M=2/3 and y intercept is (0,-3)
lana66690 [7]

Answer:

y= (2/3)x -3

Step-by-step explanation:

M is equal to the slope in y=mx+b form. And the y intercept is equal to (0, -3), therefore the b part of the formula is -3.

6 0
3 years ago
What is a gradient of a line
Dennis_Churaev [7]
(slope) The higher the gradient<span> of a graph at a point, the steeper the </span>line<span> is at that point.</span>
4 0
3 years ago
Read 2 more answers
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