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2 years ago

What is the solution for r in the following system of equations? 2x + 3y = 16 2 + 2y = 10

Mathematics

1 answer:

klio [65]2 years ago

8 0

Answer:

(2,4)

*View attached graph*

Step-by-step explanation:

2x + 3y = 16

2 + 2y = 10

-2 - 2

2y = 8

/2 /2

y = 4

2x + 3y = 16

2x + 3(4) = 16

2x + 12 = 16

- 12 - 12

2x = 4

/2 /2

x = 2

(x,y) -> (2,4)

Hope this helps!

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Factor 8a^2-2a^2 form of the polynomial ????

Naily [24]

$8a^2-2a^2$

$= 6a^2$

6 0

3 years ago

The total area of the figure to the right is 299 cm². Use this fact to write an equation involving x. Then solve the

Sliva [168]

Answer:

i. $x^{2}$ + 26x + 144 - 299 = 0

ii. x = 5

Step-by-step explanation:

The area of the figure = 299 cm²

The figure has a shape of a rectangle, so that;

Area of rectangle = length x width

length of the figure = 18 + x

width of the figure = 8 + x

Area of the figure = (18 + x) x (8 + x)

299 = (18 + x) x (8 + x)

299 = $x^{2}$ + 26x + 144

$x^{2}$ + 26x + 144 - 299 = 0

$x^{2}$ + 26x - 155 = 0

applying the trigonometric formula;

x = (-b ± $\sqrt{b^{2} - 4ac}$ ) ÷ 2a

= (-26 ± $\sqrt{(26)^{2} - 4(1*-155)}$ ) ÷ 2

= (-26 ± $\sqrt{676 +620}$ ) ÷ 2

= (-26 ± $\sqrt{1296}$ ) ÷ 2

= (-26 ± 36) ÷ 2

x = (-26 + 36) ÷ 2 OR x = (-26 -36) ÷ 2

= 10 ÷ 2 OR -62 ÷ 2

= 5 OR -31

Thus, x = 5

5 0

3 years ago

A study conducted by the Center for Population Economics at the University of Chicago studied the birth weights of 637 babies bo

hoa [83]

he;lfvpfk2ewl;9kvebnmhicojbmh3jkiodjhbsws4xAnswer:

Step-by-step explanation:

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4 0

3 years ago

The price p (in dollars) that a camera manufacturer is able to charge for a camera is given by p = 100 - 10x² where x is the num

Alla [95]

Answer:

10x^3-70x+60=0

x=1, x=2.

Step-by-step explanation:

x is the number (in millions) of cameras produced

The price is p=100 - 10x²

Profit= 60 (in millions)

It costs 30 to make a camera.

So we have:

Profit=x(price-cost)

60=x( [100-10x²] - 30)

60=100x-10x^3 -30x

60=70x-10x^3

10x^3-70x+60=0

⇒x^3 -7x+6=0 is the equation we were looking for.

Solving:

The independent term of the equation is 6.

the divisors of 6 are {1,-1, 2,-2, 3,-3, 6,-6}

Substituting each divisor in the equation we have:

x=1

(1)^3 -7(1)+6=0

1-7+6=0

0=0

⇒x=1 is a solution.

x=-1

(-1)^3 -7(-1)+6=0

-1+7+6=0

12=0 this is not true

⇒x=1 is not a solution.

x=2

(2)^3 -7(2)+6=0

8-14+6=0

0=0

⇒x=2 is a solution.

x=-2

(-2)^3 -7(-2)+6=0

-8+14+6=0

12=0 this is not true

⇒x=-2 is not a solution.

x=3

(3)^3 -7(3)+6=0

27-21+6=0

12=0 this is not true

⇒x=2 is not a solution.

x=-3

(-3)^3 -7(-3)+6=0

-27+21+6=0

0=0

⇒x=-3 is a solution.

x=6

(6)^3 -7(6)+6=0

216-42+6=0 this is not true

⇒x=6 is not a solution.

x=-6

(-6)^3 -7(-6)+6=0

-216+42+6=0 this is not true

⇒x=-6 is not a solution.

The solutions of the equation are x=-3,x=1,x=2.

However, it is not possible to produce -3 millions of cameras.

So the only possible solutions are x=1 and x=2.

4 0

2 years ago

Read 2 more answers

The ratio of the number of dolls Jacky had to the number of dolls Peter had was 5 : 2 but, after Jacky gave 15 dolls to Peter, t

tester [92]

Answer:

35 [$]

Step-by-step explanation:

1) if Peter's sum is p and Jacky's is j, then the ratio 5:2 in the condition can be written j/p=5/2;

2) the phrase 'after Jacky gave 15 dolls to Peter, they have an equal number of dolls' can be written as j-15=p;

3) using the two above it is possible to make up the system of two equations:

$\left \{ {{\frac{j}{p} =5/2} \atop {j-15=p}} \right. \ = > \ \left \{ {{j=2.5p} \atop {j-15=p}} \right. \ = > \ \left \{ {{j=25} \atop {p=10}} \right.$

4) finally, the have together 10+25=35 doll-s.

8 0

1 year ago