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3 years ago

What are the steps to solving systems of equations and inequalities

Mathematics

1 answer:

Black_prince [1.1K]3 years ago

7 0

Step 1: Line up the equations so that the variables are lined up vertically.

Step 2: Choose the easiest variable to eliminate and multiply both equations by different numbers so that the coefficients of that variable are the same.

Step 3: Subtract the two equations.

Step 4: Solve the one variable system.

Step 5: Put that value back into either equation to find the other equation.

Step 6: Reread the question and plug your answers back in to check.

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Z=(x+y)ex,x=3t,y=2−t2, find dz/dt using the chain rule. assume the variables are restricted to domains on which the functions ar

luda_lava [24]

$z=(x+y)e^x$
$\begin{cases}x=3t\\y=2-t^2\end{cases}$

$\dfrac{\mathrm dz}{\mathrm dt}=\dfrac{\partial z}{\partial x}\dfrac{\mathrm dx}{\mathrm dt}+\dfrac{\partial z}{\partial y}\dfrac{\mathrm dy}{\mathrm dt}$
$\dfrac{\mathrm dz}{\mathrm dt}=(e^x+(x+y)e^x)(3)+e^x(-2t)$
$\dfrac{\mathrm dz}{\mathrm dt}=3(1+x+y)e^x-2te^x$
$\dfrac{\mathrm dz}{\mathrm dt}=3(1+3t+2-t^2)e^{3t}-2te^{3t}$
$\dfrac{\mathrm dz}{\mathrm dt}=3(3+t-t^2)e^{3t}$

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4 years ago

Write an equation in slope-intercept form for the line that passes through (4, 7) and is perpendicular to the y-axis.

Goshia [24]

Slope intercepetion by aerodynamic

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3 years ago

Read 2 more answers

After a storm damage is the community center sent Kiya and her friends hold fundraising events to help pay for repairs after the

andrew-mc [135]

Answer: the total amount of money that they wanted to raise is $2400

Step-by-step explanation:

Let x represent the total amount of money that Keelan and her friends want to raise.

After the first event they raise $240 which is 10% of the total amount they want to raise. The amount of money that raised after the first event is expressed as

10/100 × x = 0.1 × x = 0.1x

Therefore,

0.1x = 240

Dividing both sides of the equation by 0.1, it becomes

x = 240/0.1

x = $2400

7 0

3 years ago

Factor each.<br><br><br> Please help!

Naddika [18.5K]

Answer:

1) The factors of $x^2-3x+2=0$ are $\mathbf{(x-1)(x-2)=0}$

Option C is correct.

3) The factors of $x^2+2x-8=0$ are $\mathbf{(x-2)(x+4)=0}$

Option B is correct.

Step-by-step explanation:

1) Factor : $x^2-3x+2=0$

For factoring we need to break the middle term, such that there sum is equal to middle term of expression and product is equal to product of first and last term.

The middle term : -3x

We can break them as (-2x)( -x)

Solving:

$x^2-3x+2=0\\x^2-2x-x+2=0\\x(x-2)-1(x-2)=0\\(x-1)(x-2)=0$

So, factors of $x^2-3x+2=0$ are $\mathbf{(x-1)(x-2)=0}$

Option C is correct.

3) Factor: $x^2+2x-8=0$

For factoring we need to break the middle term, such that there sum is equal to middle term of expression and product is equal to product of first and last term.

The middle term : 2x

We can break them as (4x)( -2x)

Solving

$x^2+2x-8=0\\x^2+4x-2x-8=0\\x(x+4)-2(x+4)=0\\(x-2)(x+4)=0$

So, factors of $x^2+2x-8=0$ are $\mathbf{(x-2)(x+4)=0}$

Option B is correct.

7 0

3 years ago

Jody, a statistics major, grows tomatoes in her spare time. She measures the diameters of each tomato. Assume the Normal model

lina2011 [118]

Answer:

Zscore = 0.5

Step-by-step explanation:

If we assume a normal distribution, we mean that the diameters of each tomato follow a normal distribution. This is N~ (0,1).

By that, we mean that the mean (μ) = 0 and variance ( $\sigma^{2}$ ) = 1. Thus, since we are told that one tomato was in the 50th percentile. This implies the median. And is 0.5. And if the distribution is normal, the mean and median and mode should be equal.

Thus:

==> Z score = $\frac{x-\mu}{\sigma}$ = $\frac{0.5 - \mu}{\sigma} = \frac{0.5-0}{1} = 0.5$

8 0

3 years ago