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2 years ago

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How many solutions are there to the system of equations? {-4x - 5y = 5 -0.08x + 0.10y = 0.10} A) no solutions B)one solution C)t

wo solutions D)an infinite number of solutions

1 answer:

SVEN [57.7K]2 years ago

5 0

Answer:

<h2>B) one solution</h2>

Step-by-step explanation:

Given the system of equations -4x - 5y = 5 and -0.08x + 0.10y = 0.10, to know the number of solutions the system of equation has, we need to solve for the values of x and y if possible.

-4x - 5y = 5... 1

-0.08x + 0.10y = 0.10... 2

Multiplying equation 2 by 100 will give -8x+10y = 10

The resulting system of equation will be;

-4x - 5y = 5 ...3 * 8

-8x + 10y = 10... 4 * 4

Using the elimination method to solve the equation, multiplying eqn 3 by 8 and eqn 4 by 4 we have;

-32x-40y = 40

-32x+40y = 40

Subtracting both resulting equations to eliminate x will give;

-40y-40y = 0

-80y = 0

y = 0

Substituting y = 0 into equation 3 to get x we have;

-4x-5(0) = 5

-4x = 5

x = -5/4

The solution to the system of equations is (0, -5/4). This shows that the system of equations only <u>has one solution</u>

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Fill out the tables for each scenario and answer the question that follows. Use $7.25 as the minimum wage and remember that empl

hichkok12 [17]

Answer:

see below for the table values
US labor cost: $115275 per year

Step-by-step explanation:

The labor charge is for (6 days/week). In Mongolia, the charge per laborer is then ...

(6 days/week)($1.10/day) = $6.60/week

The three laborers working 50 weeks/year will have a labor cost of ...

(3 laborers)($6.60/week/laborer)(50 weeks/year) = $990/year

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In the US, the labor charge per person per week is ...

(14 hr/day)(6 day/week) = 84 hr/week

That's 40 hours of straight pay and 44 hours of overtime pay, or ...

7.25(40 +1.5(44)) = 7.25(106) = 768.50

For 150 person-weeks per year, the total US labor charge is ...

($768.50/person/week)(3 persons)(50 weeks/year) = $115,275/year

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The materials cost for a year is ...

($50/rug)(12 rugs/year) = $600/year

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The revenue is ...

($2000/rug)(12 rugs/year) = $24,000/year

Profit is the difference between revenue and the total of costs:

profit = $24,000 -($990 +600 +10000) = $12410 . . . made in Mongolia

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So, the table gets filled as follows:

(labor, material, fixed cost, revenue, profit)

<u>Mongolian-made</u>

($990, $600, $10000, $24000, $12410)

<u>US-made</u>

($115275, $600, $10000, $24000, -$101,875)

The US labor cost would be $115,275.

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<em>Comment</em>

For the given selling price, the break-even labor cost is about $1.06 per hour (on average). At US labor rates, the break-even selling price is about $10,490 per rug.

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Step-by-step explanation:

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The equation 2x2 − 12x + 1 = 0 is being rewritten in vertex form. Fill in the missing step. Given 2x2 − 12x + 1 = 0 Step 1 2(x2

Bezzdna [24]

Answer:

Part 1) $2(x-3)^{2}-17=0$ (the missing steps in the explanation)

Part 3) (8, 4); The vertex represents the maximum profit

Part 4) x = 3.58, 0.42

Part 5) x = 6, x = 44; The zeros represent the number of monthly memberships where no profit is made

Part 6) 2(x − 7)2 + 118; x = $7

Part 7) The maximum height of the puck is 4 feet. −(x − 4)^2 + 6

Part 8) (x + 3)^2 − 4

Part 9) 2(x − 1)^2 = 4

Part 10) 8(x − 4)^2 + 592

Step-by-step explanation:

Part 1) we have

$2x^{2} -12x+1=0$

Convert to vertex form

step 1

Factor the leading coefficient and complete the square

$2(x^{2} -6x)+1=0$

$2(x^{2} -6x+9)+1-18=0$

step 2

$2(x^{2} -6x+9)+1-18=0$

$2(x^{2} -6x+9)-17=0$

step 3

Rewrite as perfect squares

$2(x-3)^{2}-17=0$

Part 3) we have

$f(x)=-x^{2}+16x-60$

we know that

This is the equation of a vertical parabola open downward

The vertex is a maximum

Convert to vertex form

$f(x)+60=-x^{2}+16x$

Factor the leading coefficient

$f(x)+60=-(x^{2}-16x)$

Complete the squares

$f(x)+60-64=-(x^{2}-16x+64)$

$f(x)-4=-(x^{2}-16x+64)$

Rewrite as perfect squares

$f(x)-4=-(x-8)^{2}$

$f(x)=-(x-8)^{2}+4$

The vertex is the point (8,4)

The vertex represent the maximum profit

Part 4) Solve for x

we have

$-2(x-2)^{2}+5=0$

$-2(x-2)^{2}=-5$

$(x-2)^{2}=2.5$

square root both sides

$(x-2)=(+/-)1.58$

$x=2(+/-)1.58$

$x=2(+)1.58=3.58$

$x=2(-)1.58=0.42$

Part 5) we have

$f(x)=-x^{2}+50x-264$

we know that

The zeros or x-intercepts are the value of x when the value of the function is equal to zero

so

In this context the zeros represent the number of monthly memberships where no profit is made

To find the zeros equate the function to zero

$-x^{2}+50x-264=0$

$-x^{2}+50x=264$

Factor -1 of the leading coefficient

$-(x^{2}-50x)=264$

Complete the squares

$-(x^{2}-50x+625)=264-625$

$-(x^{2}-50x+625)=-361$

$(x^{2}-50x+625)=361$

Rewrite as perfect squares

$(x-25)^{2}=361$

square root both sides

$(x-25)=(+/-)19$

$x=25(+/-)19$

$x=25(+)19=44$

$x=25(-)19=6$

Part 6) we have

$-2x^{2}+28x+20$

This is a vertical parabola open downward

The vertex is a maximum

Convert the equation into vertex form

Factor the leading coefficient

$-2(x^{2}-14x)+20$

Complete the square

$-2(x^{2}-14x+49)+20+98$

$-2(x^{2}-14x+49)+118$

Rewrite as perfect square

$-2(x-7)^{2}+118$

The vertex is the point (7,118)

therefore

The video game price that produces the highest weekly profit is x=$7

Part 7) we have

$f(x)=-x^{2}+8x-10$

Convert to vertex form

$f(x)+10=-x^{2}+8x$

Factor -1 the leading coefficient

$f(x)+10=-(x^{2}-8x)$

Complete the square

$f(x)+10-16=-(x^{2}-8x+16)$

$f(x)-6=-(x^{2}-8x+16)$

Rewrite as perfect square

$f(x)-6=-(x-4)^{2}$

$f(x)=-(x-4)^{2}+6$

The vertex is the point (4,6)

therefore

The maximum height of the puck is 4 feet.

Part 8) we have

$x^{2}+6x+5$

Convert to vertex form

Group terms

$(x^{2}+6x)+5$

Complete the square

$(x^{2}+6x+9)+5-9$

$(x^{2}+6x+9)-4$

Rewrite as perfect squares

$(x+3)^{2}-4$

Part 9) we have

$2x^{2}-4x-2=0$

This is the equation of a vertical parabola open upward

The vertex is a minimum

Convert to vertex form

Factor 2 the leading coefficient

$2(x^{2}-2x)-2=0$

Complete the square

$2(x^{2}-2x+1)-2-2=0$

$2(x^{2}-2x+1)-4=0$

Rewrite as perfect squares

$2(x-1)^{2}-4=0$

$2(x-1)^{2}=4$

The vertex is the point (1,-4)

Part 10) we have

$8x^{2}-64x+720$

This is the equation of a vertical parabola open upward

The vertex is a minimum

Convert to vertex form

Factor 8 the leading coefficient

$8(x^{2}-8x)+720$

Complete the square

$8(x^{2}-8x+16)+720-128$

$8(x^{2}-8x+16)+592$

Rewrite as perfect squares

$8(x-4)^{2}+592$

the vertex is the point (4,592)

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marusya05 [52]

Answer:

NOT a solution

Step-by-step explanation:

Substitute the values of x and y and see if the equation is satisfied:

3(1) -7(-1) = 3 +7 = 10 ≠ 4 . . . . . . the given point is not on the line

(1, -1) is not a solution to the equation.

_____

(-1, 1) is a solution

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3 years ago