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3 years ago

Find the x and y intercepts of 6x+3y=30

Mathematics

2 answers:

VladimirAG [237]3 years ago

7 0

6x+3y=30
x+1/2y=5

x-intercepts when y=0,
x+0=5, x=5

y-intercepts when x=0.
0+1/2y=5, y=10

OlgaM077 [116]3 years ago

3 0

X intercept is 5,0
y intercept is 0,10

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NNADVOKAT [17]

Answer:

y=250x-4

Step-by-step explanation:

If y represents the amount of money made in a week, y=250.

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3 years ago

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4 years ago

Read 2 more answers

Lim x-1 x³-2x²+3x-2/(2x^4-3x+1)

UkoKoshka [18]

Since the limit becomes the undetermined form

$\displaystyle \lim_{x\to 1} \dfrac{x^3-2x^2+3x-2}{2x^4-3x+1} \to \dfrac{0}{0}$

it means that both polynomials have a root at $x=1$ . So, we can fact both numerator and denominator:

$x^3-2x^2+3x-2 = (x-1)(x^2-x+2)$

$2x^4-3x+1 = (x-1)(2x^3+2x^2+2x-1)$

So, the fraction becomes

$\dfrac{(x-1)(x^2-x+2)}{(x-1)(2x^3+2x^2+2x-1)} = \dfrac{x^2-x+2}{2x^3+2x^2+2x-1}$

Now, as x approaches 1, you have no problems anymore:

$\displaystyle \lim_{x\to 1} \dfrac{x^2-x+2}{2x^3+2x^2+2x-1} \to \dfrac{2}{5}$

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3 years ago

Having exactly the same shape and size

e-lub [12.9K]

Answer:

If two things have the same shape and size then they are congruent to one another. If they are only the same shape but not size, then they are similar.

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2 years ago

The parent function of the function represented in the table is

kondor19780726 [428]

Answer:

$y=3^x+10$

f(x)-values

decreased by 4

(4,87)

Step-by-step explanation:

The table shows the exponential growth function

$y=a\cdot b^x +c$

substitute some values to find $a,b,c:$

$13=a\cdot b^1+c\\ \\19=a\cdot b^2 +c\\ \\37=a\cdot b^3+c$

Subtract these equations:

$ab^2+c-ab-c=19-13\Rightarrow ab(b-1)=6\\ \\ab^3+c-ab^2-c=37-19\Rightarrow ab^2(b-1)=18$

Divide them:

$\dfrac{ab^2(b-1)}{ab(b-1)}=\dfrac{18}{6}\Rightarrow b=3$

Then

$3a(3-1)=6\Rightarrow a=1$

Hence,

$13=1\cdot 3+c\Rightarrow c=10$

Therefore, the parent function is $y=3^x+10$

If this function would be translated 4 units down, its expression will be

$y=3^x+10-4\\ \\y=3^x+6$

This means that f(x)-values decreased by 4.

Then the table for translated function is

$\begin{array}{cccccc}x&1&2&3&4&5\\ \\f(x)&9&15&33&87&249\end{array}$

The graph of translated function passes through the point (4,87)

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3 years ago