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3 years ago

Identify the property used in the first four steps to solve the equation 4(x-7)=2x-6

Mathematics

1 answer:

myrzilka [38]3 years ago

4 0

Answer:

x = 11

distributive law

additive law

multiplication property

Step-by-step explanation:

Given in the question an equation

4(x-7) = 2x-6

Distributive law

a(b+c) = ab +ac

4x - 4(7) = 2x - 6

4x -28 = 2x - 6

Use the addition property of equality to reduce the 2x on the right.

4x - 2x - 28 = 2x - 2x -6

4x -2x -28 = -6

Use the addition property of equality to reduce -28 to zero on the left.

4x - 2x- 28 + 28 = -6 + 28

2x = 22

Use the multiplication property of equality to reduce 2x to just x

2x2 = 22/22

x = 22/2

x = 11

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3 years ago

The Law and Order detectives enter a house at 11:30 am and found a man on the floor murdered. They take his body temperature fin

taurus [48]

Answer:

Time of murder = 10:39 am

Step-by-step explanation:

Let the equation of exponential function representing the final temperature of the body after time 't' is,

f(t) = $a(e)^{nt}$

Here, a = Initial temperature

n = Constant for the change in temperature

t = Duration

At 11:30 am temperature of the body was 91.8°F.

91.8 = $98.6(e)^{nt}$ --------(1)

Time to reach the body to the morgue = 12:30 pm

Duration to reach = 12:30 p.m. - 11:30 a.m.

= 1 hour

Therefore, equation will be,

84.4 = $91.8(e)^{n\times 1}$

eⁿ = $\frac{84.4}{91.8}$

ln(eⁿ) = ln(0.9194)

n = -0.08403

From equation (1),

91.8 = $98.6(e)^{-0.08403t}$

$(e)^{0.08403t}=\frac{98.6}{91.8}$

$ln[(e)^{0.08403t}]=ln[\frac{98.6}{91.8}]$

0.08403t = 0.07146

t = 0.85 hours

t ≈ 51 minutes

Therefore, murder was done 51 minutes before the detectives arrival.

Time of murder = 11:30 - 00:51

= 10:90 - 00:51

= 10:39 am

7 0

2 years ago

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dimaraw [331]

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3 years ago

As – 16a,<br> as – 4a3,<br> 2a3 + 8a - 4a2 - 16

vfiekz [6]

Answer:

1) as-16a

taknig a as common

=a(s-16)

2)as-4a³

taking a as common

=a(s-4a²)

3)2a³+8a-4a²-16

taking common terms

=2a(a²+4)-4(a²+4)

=(2a-4)(a²+4)

again taking common

=2(a-2)(a²+4)

i hope this will help you :)

7 0

3 years ago

Simplify the following completely, show all work. √-45

scoray [572]

Answer:

$3\sqrt{5}i$

Step-by-step explanation:

$\sqrt{-45}$

$\sqrt{-9*5}$

$\sqrt{-9}\sqrt{5}$

$3i\sqrt{5}$

$3\sqrt{5}i$

7 0

2 years ago