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pashok25 [27]
3 years ago
6

Which properties justify the steps taken to solve the system? {2+7b=0

Mathematics
1 answer:
BaLLatris [955]3 years ago
8 0
Step 1
Multiplication property of equality
Multiplying the first equation by 5 and the second equation by 7

Step 2
Addition property of equality
Adding the two equations you get 31a =217

step 3
Division property of equality
 Dividing both sides of the above equation by 31 to get the value of a

step 4
Substitution property of equality
Substituting a with 7 in the first equation

step 5 
Simplify
simplifying the equation got above 

step 6
 Using associative property of addition by taking 14 to the other side of the equation.
 
step 7
 Division property of equality
Dividing both side of the equation by 7 to get the value of b
 
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Find the measure of the indicated side or angle.
lozanna [386]

Answer:

60°

Step-by-step explanation:

We'll begin by calculating EC. This can be obtained as follow:

Angle EAC = 39°

Hypothenus = EA = 3.7 m

Opposite = EC =?

Sine EAC = Opposite /Hypothenus

Sine 39 = EC / 3.7

Cross multiply

EC = 3.7 × Sine 39

EC = 2.3 m

Finally, we shall determine angle BEC. This can be obtained as follow:

Adjacent = EC = 2.3 m

Hypothenus = BC = 4.6 m

Angle BEC =?

Cos BEC = Adjacent / Hypothenus

Cos BEC = 2.3 / 4.6

Cos BEC = 0.5

Take the inverse of Cos

BEC = Cos¯¹ 0.5

BEC = 60°

Thus, angle BEC is 60°

7 0
3 years ago
Eight gardeners equally share 1/2 of a pile of pine needles. What fraction of the pile does each gardener receive?
Tpy6a [65]

Answer:

Each gardner will get  <u>1/16</u> of a pile of pine needles.

Step-by-step explanation:

1/2 ÷ 8

<em>*Switch the division to multiplication and flip the 8 (or 8/1) upside-down.</em>

= 1/2 · 1/8

= 1/16

3 0
3 years ago
Can someone solve the equation?<br> n+3/4=1/4
slavikrds [6]

Answer:

n+3/4=1/4

n+3/4 - 3/4=1/4-3/4

n = -2/4 = -1/2

Step-by-step explanation:

n+3/4=1/4

n+3/4 - 3/4=1/4-3/4

n = -2/4 = -1/2

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3 years ago
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Answer:

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4 0
3 years ago
Consider the surface defined by the equation x3 + y3 + z3 = 3xyz. Use implicit differ- ∂z entiation to find ∂x. (Note z is not a
Aloiza [94]

Answer:    

   \frac{∂z}{∂x}=\frac{(3yz-3x^{2})}{3z^{2} -3xy}

Step-by-step explanation:

Given equation is x^{3}+y^{3}+z^{3}=3xyz ………………(1)

we use derivative formula \frac{d}{dx}(x^{n})  = n x^{n-1}

\frac{d}{dx}(x^{3)}  = 3 x^{2}

\frac{d}{dx}(z^{3)}  = 3 z^{2}

And also apply 'u v' formula

\frac{d}{dx}(uv})  = u\frac{d}{dx}(v)+v\frac{d}{dx}(u)

Differentiating  equation (1) partially with respective to 'x' , we treated 'y' as constant.

(3x^{2} +0+3z^{2}\frac{∂z}{∂x}) =3y(x\frac{∂z}{∂x}+z(1))   ( here y treated as constant so the derivative of constant function is zero in addition but in multiplication the constant is keep as like 'y').

on simplification , we get

(3x^{2} +0+3z^{2}\frac{∂z}{∂x}) =(3yx\frac{∂z}{∂x}+3yz)

again simplification, we get

3z^{2}\frac{∂z}{∂x}- 3yx\frac{∂z}{∂x}=3yz-3x^{2}

taking common '\frac{∂z}{∂x} on left on side , we get

(3z^{2}- 3yx)\frac{∂z}{∂x}=3yz-3x^{2}

dividing '(3z^{2}- 3yx) on both sides, we get

\frac{∂z}{∂x}=\frac{(3yz-3x^{2})}{3z^{2} -3xy}

<u>Final answer</u>:-

\frac{∂z}{∂x}=\frac{(3yz-3x^{2})}{3z^{2} -3xy}

6 0
3 years ago
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