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3 years ago

What is the advantage of using function notation instead of using y?

1 answer:

6 0

The advantage of using function notation is that you can see the input and the output in the answer. For Example: if f(x)=2x + 1 then f(3)=7

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How many solutions does the system of equations below have?

soldier1979 [14.2K]

Answer:

One solution

Step-by-step explanation:

5x + y = 8

15x + 15y = 14

Lets solve using substitution, first we need to turn "5x + = 8" into "y = mx + b" or slope - intercept form

So we solve for "y" in the equation "5x + y = 8"

5x + y = 8

Step 1: Subtract 5x from both sides.

5x + y − 5x = 8 − 5x

Step 2: 5x subtracted by 5x cancel out and "8 - 5x" are flipped

y = −5x + 8

Now we can solve using substitution:

We substitute "-5x + 8" into the equation "15x + 15y = 14" for y

So it would look like this:

15x + 15(-5x + 8) = 14

Now we just solve for x

15x + (15)(−5x) + (15)(8) = 14(Distribute)

15x − 75x + 120 = 14

(15x − 75x) + (120) = 14(Combine Like Terms)

−60x + 120 = 14

Step 2: Subtract 120 from both sides.

−60x + 120 − 120 = 14 − 120

−60x = −106

Divide both sides by -60

$\dfrac{ -60x }{ -60 } = \dfrac{ -106 }{ -60 }$

Simplify

$x = \dfrac{ 53 }{ 30 }$

Now that we know the value of x, we can solve for y in any of the equations, but let's use the equation "y = −5x + 8"

$\mathrm{So\:it\:would\:look\:like\:this:\ y = -5 \left( \dfrac{ 53 }{ 30 } \right) +8}$

$\mathrm{Now\:lets\:solve\:for\:"y"\:then}$

$y = -5 \left( \dfrac{ 53 }{ 30 } \right) +8}$

$\mathrm{Express\: -5 \times \dfrac{ 53 }{ 30 }\:as\:a\:single\:fraction}$

$y = \dfrac{ -5 \times 53 }{ 30 } +8$

$\mathrm{Multiply\:-5 \:and\:53\:to\:get\:-265 }$

$y = \dfrac{ -265 }{ 30 } +8$

$\mathrm{Simplify\: \dfrac{ -265 }{ 30 } \:,by\:dividing\:both\:-265\:and\:30\:by\:5} }$

$y = \dfrac{ -265 \div 5 }{ 30 \div 5 } +8$

$\mathrm{Simplify}$

$y = - \dfrac{ 53 }{ 6 } +8$

$\mathrm{Turn\:8\:into\:a\:fraction\:that\:has\:the\:same\:denominator\:as\: - \dfrac{ 53 }{ 6 }}$

$\mathrm{Multiples\:of\:1: \:1,2,3,4,5,6}$

$\mathrm{Multiples\:of\:6: \:6,12,18,24,30,36,42,48}$

$\mathrm{Convert\:8\:to\:fraction\:\dfrac{ 48 }{ 6 }}$

$y = - \dfrac{ 53 }{ 6 } + \dfrac{ 48 }{ 6 }$

$\mathrm{Since\: - \dfrac{ 53 }{ 6 }\:have\:the\:same\:denominator\:,\:add\:them\:by\:adding\:their\:numerators}$

$y = \dfrac{ -53+48 }{ 6 }$

$\mathrm{Add\: -53 \: and\: 48\: to\: get\: -5}$

$y = - \dfrac{ 5 }{ 6 }$

$\mathrm{The\:solution\:is\:the\:ordered\:pair\:(\dfrac{ 53 }{ 30 }, - \dfrac{ 5 }{ 6 })}$

So there is only one solution to the equation.

5 0

2 years ago

Can someone help me please

Ad libitum [116K]

Answer:

a) = 8

Step-by-step explanation:

You add up all the numbers then divide that number by how many numbers you had. 4+5+7+11+13=40 40/5.

Do you want the rest?

3 0

3 years ago

Read 2 more answers

Juanita usually spends $3 more than twice her transportation costs on groceries. if x is the amount she spends on transportation

ruslelena [56]

<h3>Answer: It's a linear equation.</h3><h3>It's not a proportional relationship.</h3><h3>Juanita spend $63 on groceries if she spent $30 on transportation.</h3>

Step-by-step explanation: Given equation y=2x+3.

Where x is the amount she spends on transportation, and y is the amount she spends on groceries.

<em>We can see that given equation is in slope-intercept form y=mx+b.</em>

So, it's a linear equation and y=2x+3 is the relationship between x and y linear.

<em>Also, a linear linear equation represents a proportion relationship if y-intercept is 0.</em>

But for the given equation y=2x+3, y-intercept is 3.

Therefore, it's not a proportional relationship.

Now, in order to find how much would Juanita spend on groceries if she spent $30 on transportation, we need to plug x= 30 in given equation.

Therefore,

y = 2(30) +3 = 60+3 = 63.

<h3>So, Juanita spend $63 on groceries if she spent $30 on transportation.</h3>

7 0

3 years ago

Two plants, plant A and B, are being grown in a science experiment. Plant A is 6 cm tall and growing at a rate of 4 cm/day. Plan

Irina18 [472]

By the second day of growth

6 0

3 years ago

What's 1 + 1<br><br> What's 1 + 1

miskamm [114]

Answer:

the awnser would be 2

Step-by-step explantion

u have 1 apple and get 1 from a friend and that adds up to 2

4 0

2 years ago

Read 2 more answers