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kari74 [83]
3 years ago
15

A line is parallel to y = 5x + 9 and

Mathematics
1 answer:
ch4aika [34]3 years ago
5 0

Answer:

y = 5x + 7

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 5x + 9 ← is in slope- intercept form

with slope m = 5

Parallel lines have equal slopes, thus

y = 5x + c ← is the partial equation

To find c substitute (- 2, - 3) into the partial equation

- 3 = - 10 + c ⇒ c = - 3 + 10 = 7

y = 5x + 7 ← equation of parallel line

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During a phone call, Beyunka was told of the most recent transactions in her company's business account. There were deposits of
Norma-Jean [14]

Answer:

The amount of change in the balance of the account is an increase of $3160.57.

Step-by-step explanation:

i) first deposit is given as $1250

ii) second deposit is given as $3040.57

iii) first withdrawal is given as $400

iv) second withdrawal is given as $400

v) third withdrawal is given as $400

vi) first penalty removed is $35

vii) second penalty removed is $35

viii) therefore the change to the balance is given by

$1250 + $3040.57 - $400 - $400 - $400 + $35 + $35 = $3160.57

viii) Therefore the amount of change in the balance of the account is an increase of $3160.57.

4 0
3 years ago
PLEASE HELP!!! I know it’s a lot of questions but I’m just trying to get this done, but I can’t because I’m clueless. I tried gr
artcher [175]

Answer:

a) The graph shifted to the left by 3 units and up 1 unit.

b) Domain = x ∈ R    Range = y ∈ R

(Domain (x) = All real numbers     Range (y) = All real numbers)

c) (-4, 0)

d) (0, 2.442)

~Hope this helps! If you have any questions, please let me know!~

6 0
3 years ago
Factor completely. <br> <img src="https://tex.z-dn.net/?f=x%5E%7B8%7D-%5Cfrac%7B1%7D%7B81%7D" id="TexFormula1" title="x^{8}-\fra
Eduardwww [97]

We have 3⁴ = 81, so we can factorize this as a difference of squares twice:

x^8 - \dfrac1{81} = \left(x^2\right)^4 - \left(\dfrac13\right)^4 \\\\ x^8 - \dfrac1{81} = \left(\left(x^2\right)^2 - \left(\dfrac13\right)^2\right) \left(\left(x^2\right)^2 + \left(\dfrac13\right)^2\right) \\\\ x^8 - \dfrac1{81} = \left(x^2 - \dfrac13\right) \left(x^2 + \dfrac13\right) \left(\left(x^2\right)^2 + \left(\dfrac13\right)^2\right) \\\\ x^8 - \dfrac1{81} = \left(x^2 - \dfrac13\right) \left(x^2 + \dfrac13\right) \left(x^4 + \dfrac19\right)

Depending on the precise definition of "completely" in this context, you can go a bit further and factorize x^2-\frac13 as yet another difference of squares:

x^2 - \dfrac13 = x^2 - \left(\dfrac1{\sqrt3}\right)^2 = \left(x-\dfrac1{\sqrt3}\right)\left(x+\dfrac1{\sqrt3}\right)

And if you're working over the field of complex numbers, you can go even further. For instance,

x^4 + \dfrac19 = \left(x^2\right)^2 - \left(i\dfrac13\right)^2 = \left(x^2 - i\dfrac13\right) \left(x^2 + i\dfrac13\right)

But I think you'd be fine stopping at the first result,

x^8 - \dfrac1{81} = \boxed{\left(x^2 - \dfrac13\right) \left(x^2 + \dfrac13\right) \left(x^4 + \dfrac19\right)}

6 0
3 years ago
What is the relationship between the values of the 4 in this number 4438
galben [10]
They do not mean the same thing:
4 in 4000 stands for 4 thousands
4 in 400 stands for 4 hundreds.
You can see, that first '4' means 4 000, while the second one means 400, so the first one is 10 times greater.
5 0
3 years ago
Read 2 more answers
A central angle θ in a circle of radius 5 m is subtended by an arc of length 6 m.
Marina86 [1]

Answer:

θ=1.2 rad=68.7549°

Step-by-step explanation:

Given

  • Circle of radius 5
  • Arc of length 6 subtends angle of θ

\text{Arc Length}=\text{Radius}\times \text{Angle Subtented(in rad)}

⇒

6= 5\times \text{O}\\

θ=\frac{6}{5} =1.2rad

Therefore θ=1.2 rad

(π rad= 180°)

Therefore 1.2 rad= 68.7549°

7 0
3 years ago
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