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3 years ago

Which of the following is the equation of a line in slope-intercept form for a line with slope = 5 and y-intercept at (0, -3)?

Mathematics

2 answers:

goblinko [34]3 years ago

5 0

Answer

hello :

note : The equation of a linear function in point-slope form is : y – y1 = m(x – x1)

The point is A (x1 , y1)

Step-by-step explanation:

in this exercice : m = 5 x1 = 0 y1 = -3

the equation of a line in slope-intercept form for a line is :

y - ( -3) = 5 ( x - 0)

y +3 = 5 ( x - 0)

Zolol [24]3 years ago

4 0

Answer:

$y=5x-3$

Step-by-step explanation:

the equation of a line in slope-intercept form for a line with slope = 5 and y-intercept at (0, -3)

Slope intercept form of a line is $y=mx+b$

where m is the slope and b is the y intercept

given slope =5 and y intercept $b=-3$

now plug in the values in the slope intercept for $y=mx+b$

$y=5x-3$

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How do you simplify this? x²y+xy² / y²+2/5 × xy

polet [3.4K]

$\huge \boxed{\mathbb{QUESTION} \downarrow}$

How do you simplify this?
x²y+xy² / y²+2/5 × xy

$\large \boxed{\mathbb{ANSWER\: WITH\: EXPLANATION} \downarrow}$

$\sf\frac{ { x }^{ 2 } y+x { y }^{ 2 } }{ { y }^{ 2 } + \frac{ 2 }{ 5 } \times xy } \\$

Factor the expressions that are not already factored.

_____

How to factorise :-

NUMERATOR $\downarrow$

$\sf \: x ^ { 2 } y + x y ^ { 2 }$

Factor out xy.

$\sf \: xy\left(x+y\right)$

DENOMINATOR $\downarrow$

$\sf{ y }^{ 2 } + \frac{ 2 }{ 5 } \times xy \\$

Factor out 1/5.

$\sf \: {\frac{1}{5}y\left(2x+5y\right)} \\$

_____

Continuing...

$\sf\frac{xy\left(x+y\right)}{\frac{1}{5}y\left(2x+5y\right)} \\$

Cancel out y in both the numerator and denominator.

$\sf\frac{x\left(x+y\right)}{\frac{1}{5}\left(2x+5y\right)} \\$

Expand the expression.

$\sf\frac{x^{2}+xy}{\frac{2}{5}x+y} \\$

This can further simplified to as $\downarrow$

$= \boxed{\boxed{\bf\frac{5x\left(x +y\right)}{2x+5y}}}$

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3 years ago

Read 2 more answers

a 400 g of a liquid of density 1.6g/cm3 is made from mixing liquids of density 1.2g/cm3 and 1.8g/cm3 find the mass of the liquid

gogolik [260]

Answer:

133.33g

Step-by-step explanation:

Let the:

Mass of 1.2g/cm³ of liquid = x

Mass of 1.8g/cm³ of liquid = y

From our Question above, our system of equations is given as:

x + y = 400........ Equation 1

x = 400 - y

1.2 × x + 1.8 × y = 1.6 × 400

1.2x + 1.8y = 640..... Equation 2

We substitute, 400 - y for x in Equation 2

1.2(400 - y) + 1.8y = 640

480 - 1.2y + 1.8y = 640

- 1.2y + 1.8y = 640 - 480

0.6y = 160

y = 160/0.6y

y = 266.67 g

Solving for x

x = 400 - y

x = 400 - 266.67g

x = 133.33g

Therefore, the mass of the liquid of density 1.2g/cm³ is 133.33g

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