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2 years ago

Ella completed the following work to test the equivalence of two expressions.

2 answers:

6 0

Answer:

The expressions are not equivalent because Ella did not know that you can’t use substitution to test for equivalence.

Step-by-step explanation:

Equivalent algebraic expressions are those expressions which on simplification give the same resulting expression.

Two algebraic expressions are said to be equivalent if their values obtained by substituting any values of the variables are same.

Two expressions 3f+2.6 and 2f+2.6 are not equivalent, because when f=1,

3f + 2.6 = 3.1 + 2.6 = 3 + 2.6 = 5.6

2f + 2.6 = 2.1 + 2.6 = 2 + 2.6 = 4.6

5.6 = 4.6

Method of substitution can only help her to decide the expresssions are not equivalent, but if she wants to prove the expressions are equivalent, she must prove it for all values of f.

3f + 2.6 = 2f + 2.6

3f = 2f

3f - 2f = 0

f = 0

This is true only when f=0.

Hence,

The expressions are not equivalent because Ella did not know that you can’t use substitution to test for equivalence.

Brrunno [24]2 years ago

5 0

Answer:

The expressions are not equivalent because Ella did not know that you can’t use substitution to test for equivalence.

Step-by-step explanation:

Equivalent algebraic expressions are those expressions which on simplification give the same resulting expression.

Two algebraic expressions are said to be equivalent if their values obtained by substituting any values of the variables are same.

Two expressions 3f+2.6 and 2f+2.6 are not equivalent, because when f=1,

Method of substitution can only help her to decide the expresssions are not equivalent, but if she wants to prove the expressions are equivalent, she must prove it for all values of f.

This is true only when f=0.

Hence,

The expressions are not equivalent because Ella did not know that you can’t use substitution to test for equivalence.

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Hiro has a stack of cards with one number from the set 1, 1, 2, 2, 3, 3, 3, 4 written on each card. What is the probability that

professor190 [17]

Answer:

Therefore, the probability is P=3/32.

Step-by-step explanation:

We know that Hiro has a stack of cards with one number from the set 1, 1, 2, 2, 3, 3, 3, 4 written on each card.

We calculate the probability that he pulls out a 3 first and then pulls out a 2 without replacing them.

The probability that he pulls out a 3 first is 3/8.

The probability of a second card being 2 is 2/8.

We get:

$P=\frac{3}{8}\cdot \frac{2}{8}\\\\P=\frac{6}{64}\\\\P=\frac{3}{32}$

Therefore, the probability is P=3/32.

7 0

2 years ago

the area of a rectangle banquet hall is 7400 square feet. the length of one side of the hall is 82 feet. explain how you can use

Vadim26 [7]

We are given that the hall has a rectangular shape.
Area of rectangle can be calculated using the following rule:
Area of rectangle = length * width

We are also given that:
Area = 7400 square feet
length = 82 feet

Substitute with the givens in the above equation to get the width as follows:
Area of rectangle = length * width
7400 = 82 * width
width = 7400 / 82
width = 90.24390244 feet

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2 years ago

Question 14. A carousel makes one complete revolution every 75 seconds. Levi sits on the carousel 4 feet from its center. If the

garik1379 [7]

Answer:

The correct option is;

H. 32·π

Step-by-step explanation:

The given information are;

The time duration for one complete revolution = 75 seconds

The distance from the center of the carousel where Levi sits = 4 feet

The time length of a carousel ride = 5 minutes

Therefore, the number of complete revolutions, n, in a carousel ride of 5 minutes is given by n = (The time length of a carousel ride)/(The time duration for one complete revolution)

n = (5 minutes)/(75 seconds) = (5×60 seconds/minute)/(75 seconds)

n = (300 s)/(75 s) = 4

The number of complete revolutions - 4

The distance of 4 complete turns from where Levi seats = 4 ×circumference of circle of Levi's motion

∴ The distance of 4 complete turns from where Levi seats = 4 × 2 × π × 4 = 32·π.

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2 years ago

762,508 expanded form using exponents

r-ruslan [8.4K]

762,508 in expanded form using exponents is given as:

$7 \times 10^5 + 6 \times 10^4 + 2 \times 10^3 + 5 \times 10^2 +0 \times 10^1 + 8 \times 10^0$

<h3><u>Solution:</u></h3>

Given that we have to write 762, 508 in expanded form using exponents

Expanded form or expanded notation is a way of writing numbers to see the math value of individual digits

<h3><u>Write 762508 in Expanded form</u></h3>

Let us first find the place value of digits

Place value can be defined as the value represented by a digit in a number on the basis of its position in the number.

Place value of 7 = 700000

In 762508, 7 is in hundred-thousands place

Place value of 6 = 60000

In 762508, 6 is in ten-thousands place.

Place value of 2 = 2000

In 762508, 2 is in thousands place

Place value of 5 = 500

In 762508, 5 is in hundreds place

Place value of 0 = 0 x 10 = 0

In 762508, 0 is in tens place

Place value of 8 = 8

In 762508, 8 is in ones place

Therefore, the expanded form is given as:

700,000 + 60,000 + 2,000 + 500 + 0 + 8

<u><em>Using exponents we can write as,</em></u>

$7 \times 10^5 + 6 \times 10^4 + 2 \times 10^3 + 5 \times 10^2 +0 \times 10^1 + 8 \times 10^0$

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2 years ago

Triangle KLM represents a section of a park set aside for picnic tables. The picnic area will take up approximately 400 square y

svetoff [14.1K]

Given triangle KLM with two sides given as 45 yd and 20 yd and a 25 degree angle opposite the 20 yd side.

We find the angle made at the opposite of the 45 yd side using the sine rule as follows.
$\frac{\sin{A}}{a} = \frac{\sin{B}}{b} \\ \frac{\sin{25^o}}{20} = \frac{\sin{B}}{45} \\ \sin{B}= \frac{45\sin{25^o}}{20} = \frac{19.0178}{20} =0.9509 \\ B=\arcsin{(0.9509)}=71.97^o$

Thus, the third angle is given by 180 - 25 - 71.97 = 83.03 degrees.

We also use the sine rule to find the third side of the triangle as follows.
$\frac{\sin{A}}{a} = \frac{\sin{C}}{c} \\ \frac{\sin{25^o}}{20} = \frac{\sin{83.03^o}}{c} \\ c= \frac{20\sin{83.03^o}}{\sin{25^o}} = \frac{19.8522}{\sin{25^o}} =46.97 yds$

Therefore, amount of fencing needed to surround the perimeter of the picnic area = 45 + 20 + 46.97 = 111.97 ≈ 120 yds

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2 years ago

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