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3 years ago

For an upcoming concert, each customer may purchase up to 3 child tickets and 3 adult tickets. Let C be the

Mathematics

1 answer:

Rainbow [258]3 years ago

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1. Write the standard form of the line that passes through the given points. (7, -3) and (4, -8)

Sveta_85 [38]

Answer:

1. $-5x+3y+44=0$

2. $2x+y-2=0$

3. $2x+y-4=0$

Step-by-step explanation:

Standard form of a line is $Ax+By+C=0$ .

If a line passing through two points then the equation of line is

$y-y_1=m(x-x_1)$

where, m is slope, i.e., $m=\dfrac{y_2-y_1}{x_2-x_1}$ .

The line passes through the points (7,-3) and (4,-8). So, the equation of line is

$y-(-3)=\dfrac{-8-(-3)}{4-7}(x-7)$

$y+3=\dfrac{-5}{-3}(x-7)$

$y+3=\dfrac{5}{3}(x-7)$

$3(y+3)=5(x-7)$

$3y+9=5x-35$

$-5x+3y+9+35=0$

$-5x+3y+44=0$

Therefore, the required equation is $-5x+3y+44=0$ .

We need to find the equation of the line, in standard form, that has a y-intercept of 2 and is parallel to $2 x + y =-5$ .

Slope of the line : $m=\dfrac{-\text{Coefficient of x}}{\text{Coefficient of y}}=\dfrac{-2}{1}=-2$

Slope of parallel lines are equal. So, the slope of required line is -2 and it passes through the point (0,2).

Equation of line is

$y-2=-2(x-0)$

$y-2=-2x$

$2x+y-2=0$

Therefore, the required equation is $2x+y-2=0$ .

We need to find the equation of the line, in standard form, that has an x-intercept of 2 and is parallel to $2x + y =-5$ .

From part 2, the slope of this line is -2. So, slope of required line is -2 and it passes through the point (2,0).

Equation of line is

$y-0=-2(x-2)$

$y=-2x+4$

$2x+y-4=0$

Therefore, the required equation is $2x+y-4=0$ .

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3 years ago

A clothing store put a sales price of $48 on a purse. Before the markup, the store paid $40 for the purse. What percent markup d

Nimfa-mama [501]

Answer:

20% mark up

Step-by-step explanation:

[(48-40)/40]×100%= 20%

8 0

3 years ago

Look at the two expressions. 3x−18 3⋅(x−6) Are the two expressions equivalent?

Ivanshal [37]

Yes because if you distribute the 3 and multiply it with 3 • x and 3• 6 you’ll get 3x-18

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3 years ago

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Is the following shape a triangle? How do you know

Arte-miy333 [17]

Answer:

Depends

Step-by-step explanation:

All triangles have 3 sides no more no less Hope this helps

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3 years ago

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Find the domain of the function (f/g)(x) where f(x)=√x+1, g(x)=√x-9

nadya68 [22]

Answer:

4x + 9. Given f(x) = 2x + 3 and g(x) = –x2 + 5, find (g o g)(x). (g o g)(x) = g(g(x)) ... Given f (x) = sqrt(x) and g(x) = x – 2, find the domains of ( f o g)(x) and (g o f )(x). Since f (x) involves a square root, the inputs have to be non-negative. ... Given h(x) = (x + 1)2 + 2(x + 1) – 3, determine two functions f (x) and g(x

Step-by-step explanation:

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4 years ago