All categories

2 years ago

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

Mathematics

1 answer:

Romashka [77]2 years ago

8 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.

this what i know

You might be interested in

Jared is using a 100 ft rope to set up a kite-shaped area for food vendors. He has started roping off the area as shown below, a

marishachu [46]

Jared has already used 30+30=60 ft of rope.

A kit shape has 2 pairs of 2 lines that are the exact same length. We can use x to represent this unknown length.

60+2x=100

Subtract 60 from both sides
2x=40

Divide both sides by 2
x=20

Final answer: He can use all the rope by using 20 ft for each of the other sides that are left.

8 0

1 year ago

Read 2 more answers

The gross income of Maurice Vaughn is $785 per week.His deductions are $42.25,FICA tax,$90.33,income tax,2% state tax,1% city ta

boyakko [2]

Gross income : 785 per week

deductions are :
FICA : 42.25
income tax : 90.33
2% state tax : 0.02(785) = 15.70
1% city tax : 0.01(785) = 7.85
3% retirement : 0.03(785) = 23.55
total deductions are : 42.25+90.33+15.70+7.85+23.55 = 179.68

gross pay - deductions = net pay
785 - 179.68 = net pay
605.32 = net pay <====

7 0

1 year ago

Read 2 more answers

A square is constructed on side AD of quadrilateral ABCD such that FA lies on AB, as shown in the figure.

Elza [17]

Answer: The co-ordinates of F are (4.4, -4.6) and the co-ordinates of D are (4.4, -1.4).

Step-by-step explanation: Given that a square is constructed on side AD of quadrilateral ABCD such that FA lies on AB as shown in the figure. The co-ordinates of A are (6, -3) and the co-ordinates of B are (10, 1).

Also, AD : AB = 2 : 5 and the co-ordinates of the point E are (2.8, -3).

We are to select the correct co-ordinates of the points F and D.

Let, (a, b) are the co-ordinates of F and (c, d) are the co-ordinates of D.

Since ADEF is a square, so we have

AD = DE = EF = FA.

Given that

AD : AB = 2 : 5, so FA : AB = 2 : 5.

That is, \left(\dfrac{c+4.4}{2},\dfrac{d-4.6}{2}\right)=\left(\dfrac{2.8+6}{2},\dfrac{-3-3}{2}\right)

We have, after applying the internal division formula that

$\left(\dfrac{2\times 10+5\times a}{2+5},\dfrac{2\times 1+5\times b}{2+5}\right)=(6,-3)\\\\\\\Rightarrow \left(\dfrac{20+5a}{7},\dfrac{2+5b}{7}\right)=(6,-3)\\\\\\\Rightarrow \dfrac{20+5a}{7}=6,~~~~~\dfrac{2+5b}{7}=-3\\\\\\\Rightarrow 20+5a=42,~~~~\Rightarrow 2+5b=-21\\\\\\\Rightarrow 5a=22,~~~~~~~~~~\Rightarrow 5b=-23\\\\\\\Rightarrow a=4.4,~~~~~~~~~~~\Rightarrow b=-4.6.$

So, the co-ordinates of F are (4.4, -4.6).

Now, since ADEF is a square, and the diagonals of a square bisect each other.

So, the mid-points of both the diagonals are same.

That is,

$\textup{mid-point of DF}=\textup{mid-point of AE}\\\\\\\Rightarrow \left(\dfrac{c+4.4}{2},\dfrac{d-4.6}{2}\right)=\left(\dfrac{2.8+6}{2},\dfrac{-3-3}{2}\right)\\\\\\\Rightarrow \left(\dfrac{c+4.4}{2},\dfrac{d-4.6}{2}\right)=\left(\dfrac{8.8}{2},\dfrac{-6}{2}\right)\\\\\\\Rightarrow \dfrac{c+4.4}{2}=\dfrac{8.8}{2},~~~~~~\dfrac{d-4.6}{2}=-\dfrac{6}{2}\\\\\\\Rightarrow c+4.4=8.8,~~~~~\Rightarrow d-4.6=-6\\\\\Rightarrow c=4.4,~~~~~~~~~~~~\Rightarrow d=-1.4.$

So, the co-ordinates of D are (4.4, -1.4).

Thus, the co-ordinates of F are (4.4, -4.6) and the co-ordinates of D are (4.4, -1.4).

7 0

1 year ago

Read 2 more answers

Solve 2sinx + √2 = 0

stepladder [879]

Attached you will see the solution using the trig plane and general solutions.

3 0

1 year ago

Tony wants to plant no more than 400 acres of corn and soybeans. He earns $300 per acre of soybeans and $200 for corn. He needs

inna [77]

In this item, we let x be the number of corns and Y represent soybeans. The sum of these variables is 400. This is represented by the equation,
x + y = 400
The amount that needs to be earn by Tony is then represented by,
200x + 300y ≥ $60,000

9 0

1 year ago