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3 years ago

Give the property that justifies each step.

Mathematics

1 answer:

hjlf3 years ago

5 0

Answer:

Please check the explanation below.

Step-by-step explanation:

Some of the properties are defined as:

Distributive property

a(b+c) = ab+ac

For example,

suppose a=1, b=2, c=3

1(2+3) = 1(2) + 1(3)

5 = 2+3 = 5

Subtraction property of Equality

if (a=b), then a-c = b-c

For example,

suppose a=1, b=1, c=3

if a = b ⇒ 1 = 1

then a-c = b-c ⇒ 1-3 = 1 - 3 ⇒ -2 = -2

Addition property of Equality

if (a=b), then a+c = b+c

For example,

suppose a=1, b=1, c=3

if a = b ⇒ 1 = 1

then a+c = b+c ⇒ 1+3 = 1+3 ⇒ 4 = 4

Multiplicative property of Equality

if (a=b), then a×c = b×c

For example,

suppose a=1, b=1, c=3

if a = b ⇒ 1 = 1

then a×c = b×c ⇒ 1×3 = 1 × 3 ⇒ 3 = 3

Division property of Equality

if (a=b), then a÷c = b÷c

For example,

suppose a=1, b=1, c=3

if a = b ⇒ 1 = 1

then a÷c = b÷c ⇒ 1÷3 = 1 ÷ 3 ⇒ 1/3 = 1/3

Let's solve the given equation using the above properties.

5(x+10) = 20 Given

5x+50 = 20 1) Distriburive property ∵ a(b+c) = ab+ac

5x = -30 2) Subtraction property of Equality ∵ if (a=b), then a-c = b-c

x = -6 3) Division property of Equality ∵ if (a=b), then a÷c = b÷c

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If EF = x + 5, DC = 2x + 4, and AB = 2x + 2. Find EF.

bonufazy [111]

Answer:

B *second one down.

Step-by-step explanation:

EF = 1/2(AB + CD)

x+5 = 1/2 (2x + 2 + 2x+4) Combine the like terms on the right.

x+5 = 1/2 (4x + 6) Remove the brackets.

x+5 = 1/2*4x + 1/2*6

x+5 = 2x + 3 Subtract x from both sides

5 = 2x-x + 3

5 = x + 3 Subtract 3 from both sides

5-3 = x

x = 2

EF = x + 5

EF = 2 + 5

EF = 7

The answer is B

3 0

3 years ago

you are making curtains by alternating strips of solid colored fabric and patterned fabric. the solid colored fabric costs 99¢ p

weeeeeb [17]

Hello,

to find the total cost (c) of the colored strips we have to multiply the number of strips (n) by the cost of each color strip (99¢), that as an algebraic function is:

$\boxed{c= n*99}$ [¢]

Now, if we use 3 solid color strips, that means that we use 4 patterned strips, so:

$Cost=3*0.99+4*1.25 \\ \boxed{Cost= 7.97}$

Answer: c=n*99 and Cost per curtain= $7.97

4 0

3 years ago

At Billy‘s preschool they have bicycles and tricycles with a total of 57 wheels. The number of bicycles is three less than three

ikadub [295]

Use b for bicycles b and t for tricycles.

We know that each bicycle has 2 wheels, and each tricycle has 3 wheels, and if the entire number of wheels is 57, that means the

equation would be: 2b + 3t = 57

We can "separate" b by calling it "25 - t" as an alternative,

2(25 - t) + 3t = 57, or

50 - 2t + 3t = 57,

or 50 + t = 57, so

t = 7 So there must be 18 bicycles and 7 tricycles.

CHECKING:You can check this out by multiplying 7 tricycles x 3 wheels, which is 21,

and 18 bicycles x 2 wheels, which is 36

36 + 21 = 57

6 0

3 years ago

What is 7 and 1/4% of 89.75?

BlackZzzverrR [31]

6.506875 is the answer because 7.25% out of 100 is .0725 and 89.75 times that is 6.506875

3 0

3 years ago

Factor the quadratic expression in the equation y=2x^2+28x+96 and use the factors to find the zeros of the equation. Then, use t

gavmur [86]

Answer:

$x=-7$

Step-by-step explanation:

We have been given an equation $y=2x^2+28x+96$ . We are asked to find the zeros of equation by factoring and then find the line of symmetry of the parabola.