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3 years ago

Solve above question

Mathematics

2 answers:

Mandarinka [93]3 years ago

7 0

Y=2−3x

2 Substitute
y
=
2
−
3
x
y=2−3x into
x
+
y
=
7
x+y=7.
−
2
x
+
2
=
7
−2x+2=7

3 Solve for
x
x in
−
2
x
+
2
=
7
−2x+2=7.
x
=
−
5
2
x=−
2
5

4 Substitute
x
=
−
5
2
x=−
2
5

into
y
=
2
−
3
x
y=2−3x.
y
=
19
2
y=
2
19

5 Therefore,
x
=
−
5
2
y
=
19
2

x=−
2
5

y=
2
19

melisa1 [442]3 years ago

5 0

Answer:

x=-2.5,y=7.5

Step-by-step explanation:

Solution,

3x+y=2.....(1)

x+y=7

or,y=7-x......(2)

Now,by putting the value of y from equation 2 to equation 1,we get

3x+y=2

or,3x+(7-x)=2

or,3x+7-x=2

or,2x+7=2

or,2x=2-7

or,2x=-5

or,x=-5/3

or,x=-2.5

Again,

by putting the value of x in equation 2,we get

x+y=7

or,-2.5+y=7

or,y=7+2.5

or,y=7.5

I HOPE THIS WILL HELP U

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the straight line L has the equation 4y=5x+3. Point A has the coordinates (3,-2) Find the equation of the line straight line tha

Aleonysh [2.5K]

Answer:

y = - $\frac{4}{5}$ x + $\frac{2}{5}$

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 )

Rearrange 4y = 5x + 3 into this form by dividing the 3 terms by 4

y = $\frac{5}{4}$ x + $\frac{3}{4}$ ← in slope- intercept form

with slope m = $\frac{5}{4}$

Given a line with slope m then the slope of a line perpendicular to it is

$m_{perpendicular}$ = - $\frac{1}{m}$ = - $\frac{1}{\frac{5}{4} }$ = - $\frac{4}{5}$ , thus

y = - $\frac{4}{5}$ x + c ← is the partial equation

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

- 2 = - $\frac{12}{5}$ + c ⇒ c = - 2 + $\frac{12}{5}$ = $\frac{2}{5}$

y = - $\frac{4}{5}$ x + $\frac{2}{5}$ ← equation of perpendicular line

4 0

3 years ago

Giving 100 points.

Nitella [24]

Answer:

1. Cost per customer: 10 + x

Average number of customers: 16 - 2x

$\textsf{2.} \quad -2x^2-4x+160\geq 130$

3. $10, $11, $12 and $13

Step-by-step explanation:

Given information:

$10 = cost of buffet per customer
16 customers choose the buffet per hour
Every $1 increase in the cost of the buffet = loss of 2 customers per hour
$130 = minimum revenue needed per hour

Let x = the number of $1 increases in the cost of the buffet

Part 1

Cost per customer: 10 + x

Average number of customers: 16 - 2x

Part 2

The cost per customer multiplied by the number of customers needs to be at least $130. Therefore, we can use the expressions found in part 1 to write the inequality:

$(10 + x)(16 - 2x)\geq 130$

$\implies 160-20x+16x-2x^2\geq 130$

$\implies -2x^2-4x+160\geq 130$

Part 3

To determine the possible buffet prices that Noah could charge and still maintain the restaurant owner's revenue requirements, solve the inequality:

$\implies -2x^2-4x+160\geq 130$

$\implies -2x^2-4x+30\geq 0$

$\implies -2(x^2+2x-15)\geq 0$

$\implies x^2+2x-15\leq 0$

$\implies (x-3)(x+5)\leq 0$

Find the roots by equating to zero:

$\implies (x-3)(x+5)=0$

$x-3=0 \implies x=3$

$x+5=0 \implies x=-5$

Therefore, the roots are x = 3 and x = -5.

Test the roots by choosing a value between the roots and substituting it into the original inequality:

$\textsf{At }x=2: \quad -2(2)^2-4(2)+160=144$

As 144 ≥ 130, the solution to the inequality is between the roots:

-5 ≤ x ≤ 3

To find the range of possible buffet prices Noah could charge and still maintain a minimum revenue of $130, substitute x = 0 and x = 3 into the expression for "cost per customer.

[Please note that we cannot use the negative values of the possible values of x since the question only tells us information about the change in average customers per hour considering an increase in cost. It does not confirm that if the cost is reduced (less than $10) the number of customers increases per hour.]

Cost per customer:

$x =0 \implies 10 + 0=\$10$