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4 years ago

Solve each system by substitution.4x+2y=10x-y=13

Mathematics

2 answers:

emmainna [20.7K]4 years ago

5 0

x-y=13

x=13+y--(1)

4x+2y=10

2x+y=5

26+2y+y=5

3y=-21

y=-7

Substituting value of y in equation (1)

x=13-7

x=6

Bond [772]4 years ago

3 0

Answer:

Step-by-step explanation:

$\left\{\begin{array}{ccc}4x+2y=10\\x-y=13&\text{add y to both sides}\end{array}\right\\\\\left\{\begin{array}{ccc}4x+2y=10&(1)\\x=y+13&(2)\end{array}\right\\\\\\\text{Substitute (2) to (1):}\\\\4(y+13)+2y=10\qquad\text{use the distributive property}\\\\(4)(y)+(4)(13)+2y=10\\\\4y+52+2y=10\qquad\text{subtract 52 from both sides}\\\\6y=-42\qquad\text{divide both sides by 6}\\\\\boxed{y=-7}\\\\\text{Put the value of y to (2):}\\\\x=-7+13\\\\\boxed{x=6}$

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Stuck on this it's Algebra 2 12x^{3} -3x^{2} =0

olchik [2.2K]

Answer:

Exact Form:

x = 0, 1/4

Decimal Form:

x = 0, 0.25

Step-by-step explanation:

Step 1: Factor 3x^2 out of 12x^3 - 3x^2

Factor 3x^2 out of 12x^3:

3x^2 (4x) - 3x^2 = 0

Factor 3x^2 out of -3x^2:

3x^2 (4x) + 3x^2 (-1) = 0

Factor 3x^2 out of -3x^2 (4x) + 3x^2 (-1) :

3x^2 (4x-1) = 0

Step 2: Divide each term by 3 and simpify

divide each term in 3x^2 (4x-1) = 0 by 3.

3x^2 (4x-1) / 3 = 0 / 3

simplify 3x^2 (4x-1) / 3.

Cancel the common factors.

3 x^2 (4x -1) / 3 = 0 / 3

divide x^2 (4x-1) by 1.

x^2 (4x-1) / 3 = 0 / 3

Apply the Distributive Property

Reorder.

Rewrite using the commutative property of multiplication.

4x^2 x + x^2 · -1 = 0 / 3

Move -1 to the left of x^2

4x^2 x -1 · x^2 = 0 / 3

Simplify each term

multiply x^2 by x^2 by adding the exponents.

Move x

4 (x · x^2) -1 · x^2= 0 / 3

Multiply x by x^2

Rase x to the power of 1.

4 (x^1 · x^2) -1 · x^2= 0 / 3

Use the power rule a^m a^n = a^m+n to combine exponents

4x^1+2 -1 · x^2= 0 / 3

Add 1 and 2.

4x^3 -1 · x^2= 0 / 3

Rewrite -1x^2 as -x^2.

4x^3 -x^2= 0 / 3

Divide 0 by 3

4x^3 -x^2= 0

Step 3: Factor x^2 out of 4x^3 -x^2.

Factor x^2 out of 4x^3

x^2 (4x) -x^2 = 0

Factor x^2 out of -x^2

x^2 (4x) x^2 · -1 = 0

Factor x^2 out of x^2 (4x) x^2 · -1

x^2 (4x -1) = 0

If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0

x^2 = 0

4x -1 = 0

Set x^2 equal to 0 and solve for x

x = 0

Set 4x -1 equal to 0 and solve for x

x = 1/4

The final solution is all the values that make x^2 (4x-1) = 0 true

x= (0, 1/4)

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3 years ago

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Answer:

Step-by-step explanation:

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3 years ago

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3 years ago

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The temperature, H, in degrees Celsius, of a cup of coffee placed on the kitchen counter is given by H = f(t), where t is in min

Deffense [45]

Answer:

f'(t) is negative

The unit is degC/min

At 35 minutes after the coffee was put on the counter, its temperature is 68 and will decrease by about 0.75 in the next 30 seconds.

Step-by-step explanation:

From the question we are told we are told that

The equation for the temperature of a cup of coffee place on a counter is

$H= f(t)$

Here t is the time in minutes the coffee was put on the counter

Generally f(t)' is the derivative of f(t) at it represents the change of the temperature of the cup of coffee with respect to time

Generally for the coffee placed on the counter after a couple of minutes the temperature will decrease hence f(t)' is negative

Generally the unit of the temperature is in degrees Celsius while that of time is in minutes

So the change in temperature with time f(35)' will be in degrees Celsius/minutes (i.e degC/min)

From the question we are told that

$|f(35)'| = 1.5$

i.e the rate of change of temperature after 35 minutes is 1.5

and

$|f(35)| = 68$

i.e the temperature of the cup of coffee after 35 minutes is 67 degC

Now after another t= 30 seconds = $\frac{30}{60}= 0.5 \ minutes$ the rate of change of the temperature of the cup of coffee is

$R = |f(35)'| * t$

=> $R = 1.5 * 0.5$

=> $R = 0.75$

At 35 minutes after the coffee was put on the counter, its temperature is 68 and will decrease by about 0.75 in the next 30 seconds.

5 0

3 years ago

Solve each system by substitution.4x+2y=10x-y=13​

Solve each system by substitution.4x+2y=10x-y=13