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3 years ago

12

Mario earned three times as much money last year as his wife Elena. The total amount that the two earned was $11,000. How much m

oney did Mario earn?

1 answer:

OLEGan [10]3 years ago

6 0

Mario earns $8.250. Solution:
Elena = x
MArio = 3x

Equation:
x + 3x = 11,000
4x = 11,000
x = 2,750

Mario = 3x ; 3(2,750) = 8,250

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The opposite of a negative is positive, the opposite of a positive is a negative.

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3 years ago

Let W= { (x, y, z) |x=1|; y, z ∈ℝ } Prove that W is a subspace of ∈ℝ<br> How can I resolve this ?

Nataly [62]

Answer:

W is not a subspace.

Step-by-step explanation:

Notice that (-1,2,2) and (-1,5,3) are both elements of W. Because its x coordinate, x = -1, satisfy the condition |x| = 1.

but (-1,2,2) + (-1,5,3) = (-2,7,5) do not belongs to W. Because its first coordinate, x =-2, do not satisfy |x| = 1.

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3 years ago

Evaluate the expression \dfrac{x^5}{x^2} x 2 x 5 start fraction, x, start superscript, 5, end superscript, divided by, x, squa

Elza [17]

Answer:

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Step-by-step explanation:

Fill in the variable value and do the arithmetic.

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Of course, the fraction can be simplified first:

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7 0

3 years ago

Hello! Can someone please help me with this question ? I’ll mark brainly thanks ! :)

NikAS [45]

Answer:

$\Large\boxed{\text{Perpendicular Equation:} \ y = -\frac{2}{7}x + \frac{22}{7}}$

$\Large\boxed{\text{Parallel Equation:} \ y = \frac{7}{2}x -12}$

Step-by-step explanation:

In order to find the equations that are parallel/perpendicular to the line $y = \frac{7}{2}x - 4$ , we need to note a couple things about the relationships between lines and their parallel/perpendicular lines.

A) If a line is perpendicular to another, the slopes will be opposite reciprocals (for instance $-2$ and $\frac{1}{2}$ - multiplied, they equal -1.)
B) If a line is parallel to another, they will have the exact same slope.

<h2>Perpendicular:</h2>

We know that the slope of a perpendicular line will be the the opposite reciprocal of the line we're comparing it to.

Since the slope of our base line is $\frac{7}{2}$ , we can find the reciprocal, then the opposite of that.

Reciprocal of $\frac{7}{2} = \frac{2}{7}$
Opposite of $\frac{2}{7} = -\frac{2}{7}$

So the slope of this line will be $-\frac{2}{7}$ , making our equation $y = -\frac{2}{7}x+ b$

However, y-intercepts will not stay the same. In order to find this, we can substitute the point (4, 2) into our equation to solve for b.

$2 = -\frac{2}{7} \cdot 4 + b$
$2 = -\frac{8}{7} + b$
$b = 2+\frac{8}{7}$
$b = 2 \frac{8}{7}$
$b=\frac{22}{7}$

Now we know the y-intercept of this equation is $\frac{22}{7}$ . We can now finish off our equation of the line by substituting that in to what we already have, $y = -\frac{2}{7}x+ b$ .

$y = -\frac{2}{7}x+ \frac{22}{7}$

<h2>Parallel:</h2>

As mentioned earlier, parallel lines will have the exact same slope but not the same y-intercept. Since the slope of our original equation is $\frac{7}{2}$ , the slope for this one will also be $\frac{7}{2}$ .

So we now know the equation looks something like $y = \frac{7}{2}x + b$ .

In order to solve for b, we apply the same logic we did in the perpendicular line and substitute in the point (4, 2) into the equation.

$2 = \frac{7}{2} \cdot 4 + b$
$2 = \frac{28}{2}+b$
$2 = 14+b$
$b = 2-14$

$b =-12$

Now that we know the slope and the y-intercept, we can finish off our equation as $y = \frac{7}{2}x -12$ .

Hope this helped!

3 0

3 years ago