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vesna_86 [32]
3 years ago
10

Which expression is equivalent to 1/4 (8-6x+12)

Mathematics
1 answer:
Dovator [93]3 years ago
6 0
So:

Let us simply the parenthesis first.

So we have \sf{(8-6x+12)}

We can rearrange the terms and get:

\sf{(8+12-6x)}

Which is equal to

\sf{(20-6x)}

So now we have to complete it by multiplying it all by 1/4 which is basically dividing it by 4.

So:

\sf{\frac{20-6x}{4}}

Simplifying that, we get:

\sf{5-\frac{6}{4}x}

And reducing that farther we finally get:

\sf{5-\frac{3}{2}x}

Which is your final answer :)
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Use the Multiplication Property of Equality to complete the following statement: If , 4x divided by 2 = 4
vovangra [49]

Answer:

then x = 2.

Step-by-step explanation:

4 multiplied by 2 = 8

8 divided by 2 equals 4

Putting it together:

4(2)/2=4

4 0
3 years ago
Read 2 more answers
Given: mAngleEDF = 120°; mAngleADB = (3x)°; mAngleBDC = (2x)° Prove: x = 24 3 lines are shown. A line with points E, D, C inters
N76 [4]

Answer:

" Vertical angles are congruent " ⇒ 2nd answer

Step-by-step explanation:

* <em>Look to the attached figure </em>

- There are three lines intersected at point D

- We need to find the missing in step 3

∵ Line FA intersects line EC at point D

- The angles formed when two lines cross each other are called

 vertical angles

- Vertical angles are congruent (vertical angles theorem)

∴ ∠ADC and ∠FDE are vertical angles

∵ Vertical angles are congruent

∴ ∠EDF ≅ ∠ADC

∴ m∠EDF ≅ m∠ADC

∵ m∠EDF = 120° ⇒ given

∵ m∠ADC = m∠ADB + m∠BDC

∴ m∠ADB + m∠BDC = 120°

∵ m∠ADB = (3x)° ⇒ given

∵ m∠BDC = (2x)° ⇒ given

∴ 3x + 2x = 120 ⇒ add like terms

∴ 5x = 120 ⇒ divide both sides by 5

∴ x = 24

Column (1)                                                     Column (2)

m∠EDF = 120°                                               given

m∠ADB = 3 x                                                 given

m∠BDC = 2 x                                                 given

∠EDF and ∠ADC are vertical angles           defin. of vert. ∠s

∠EDF is congruent to ∠ADC                        vertical angles are      

                                                                        congruent  

m∠ADC = m∠ADB + m∠BDC                        angle add. post.

m∠EDF = m∠ADC                                          defin. of cong.

m∠EDF = m∠ADB + m∠BDC                         substitution

120° = 3 x + 2 x                                               substitution

120 = 5 x                                                         addition

x = 24                                                              division  

∴ The missing reason is " vertical angles are congruent "

- From the explanation above ∠ADC and ∠FDE are vertical

 angles then they are congruent according to vertical angle

 theorem

6 0
3 years ago
Read 2 more answers
Given that α and β are the roots of the quadratic equation <img src="https://tex.z-dn.net/?f=2x%5E%7B2%7D%20%2B6x-7%3Dp" id="Tex
siniylev [52]

Answer:

\large \boxed{\sf \ \ \ p=-11 \ \ \ }

Step-by-step explanation:

Hello,

\alpha \text{ and } \beta \text{ are the roots of the following equation}

   2x^2+6x-7=p

It means that

   2\alpha^2+6\alpha-7=p \\\\2\beta ^2+6\beta -7=p \\\\

And we know that

\alpha= 2\cdot \beta

So we got two equations

   2(2\beta)^2+6\cdot 2 \cdot \beta -7=p \\\\8\beta^2+12\beta -7=p\\\\ and \ 2\beta ^2+6\beta -7=p \ So \\\\\\8\beta^2+12\beta -7 = 2\beta ^2+6\beta -7\\\\6\beta^2+6\beta =0\\\\\beta(\beta+1)=0\\\\ \beta =0 \ or \ \beta=-1

For \beta =0, \ \ \alpha =0, \ \ p = -7

For \beta =-1, \ \ \alpha =-2, \ \ p= 2-6-7=-11, \ p=2*4-12-7=-11

I assume that we are after two different roots so the solution for p is p=-11

b) \alpha +2 =-2+2=0 \ and \ \beta+2=-1+2=1

So a quadratic equation with the expected roots  is

x(x-1)=x^2-x

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

3 0
2 years ago
A girl is Snorkeling 1 meter below sea level and then dives down another 0.5 meter. How far below sea level is the girl NEED THE
OLga [1]
1.5 meters will be your answer.
3 0
3 years ago
If a circle has circumference 100pi units, what is it’s area
const2013 [10]

Answer:

2500pi^2 units

Step-by-step explanation:

Circumference = pi * diameter

Circumference = pi * 100

Radius = diameter/2

Radius = 50

Area = pi * radius^2

Area = pi * 50^2

Area = pi * 2500

Area = 2500pi^2 units

8 0
2 years ago
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