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3 years ago

What is the solution to the system of equations? 2x+4t=12

Mathematics

1 answer:

katen-ka-za [31]3 years ago

6 0

Answer:

C. $(8, -1)$

Step-by-step explanation:

{y = ¼x - 3}

{2x + 4y = 12

2x + 4[¼x - 3] = 12

2x + x - 12 = 12

3x - 12 = 12

+ 12 + 12

_________

3x = 24

__ __

3 3

$x = 8$ [Plug this back into both equations above to get the y-coordinate of −1]; $-1 = y$

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Martin is two years younger than three times his daughter Ada’s age. The sum of their ages is 54. If Ada’s age is given by a, th

liq [111]

Answer:

A. 3a-2=54

Step-by-step explanation:

3 x her age - the 2 year will equal 54

6 0

3 years ago

What is the quotient when 4x3 + 2x + 7 is divided by x + 3?

Arte-miy333 [17]

Answer:

The quotient of this division is $(4x^2 -12x + 38)$ . The remainder here would be $-26$ .

Step-by-step explanation:

The numerator $4x^3 + 2x + 7$ is a polynomial about $x$ with degree $3$ .

The divisor $x + 3$ is a polynomial, also about $x$ , but with degree $1$ .

By the division algorithm, the quotient should be of degree $3 - 1 = 2$ , while the remainder shall be of degree $1 - 1 = 0$ (i.e., the remainder would be a constant.) Let the quotient be $a\,x^2 + b\, x + c$ with coefficients $a$ , $b$ , and $c$ .

$4x^3 + 2x + 7 = \left(a\,x^2 + b\, x + c\right)(x + 3)$ .

Start by finding the first coefficient of the quotient.

The degree-three term on the left-hand side is $4 x^3$ . On the right-hand side, that would be $a\, x^3$ . Hence $a = 4$ .

Now, given that $a = 4$ , rewrite the right-hand side:

$\begin{aligned}&\left(4\,x^2 + b\, x + c\right)(x + 3) \cr =& \left(4x^2 + (b\, x + c)\right)(x + 3) \cr =& 4x^2(x + 3) + (bx + c)(x + 3) \cr =& 4x^3 + 12x^2 + (bx + c)(x + 3)\end{aligned}$ .

Hence:

$4x^3 + 2x + 7 = 4x^3 + 12x^2 + (b\,x + c)(x + 3)$

Subtract $\left(4x^3 + 12x^2\right$ from both sides of the equation:

$-12x^2 + 2x + 7 = (b\,x + c)(x + 3)$ .

The term with a degree of two on the left-hand side has coefficient $(-12)$ . Since the only term on the right hand side with degree two would have coefficient $b$ , $b = -12$ .

Again, rewrite the right-hand side:

$\begin{aligned}&\left(-12 x + c\right)(x + 3) \cr =& \left(-12 x+ c\right)(x + 3) \cr =& (-12x)(x + 3) + c(x + 3) \cr =& -12x^2 -36x + (bx + c)(x + 3)\end{aligned}$ .

Subtract $-12x^2 -36x$ from both sides of the equation:

$38x + 7 = c(x + 3)$ .

By the same logic, $c = 38$ .

Hence the quotient would be $(4x^2 - 12x + 38)$ .

6 0

3 years ago

How do I find the arc from a central angle?

Lesechka [4]

Answer:

Divide the central angle in radians by 2 and perform the sine function on it. Divide the chord length by double the result of step 1. This calculation gives you the radius. Multiply the radius by the central angle to get the arc length.

8 0

2 years ago

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The sum of two numbers is 66. the larger number is 2 more than 3 times the smaller. what are the two numbers?

Montano1993 [528]

The two numbers are 48 and 18.

66 = l + s

l = 2 + 3s

66 = 2 + 3s + s

66 = 2 + 4s

66 - 2 = 64

64 = 4s

64 / 4 = 16

66 = l + 16

66 - 16 = 50

50 - 2 = 48

16 + 2 = 18

66 = 48 + 18

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3 years ago

(3x-22)+ (4y-x-10) <br> Solve for Y

const2013 [10]

answer

Step-by-step explanation:

4 0

3 years ago