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3 years ago

Solve. x^2-15x+50 (x-5)(x+10) (x+5)(x+10) (x-10)(x-5) (x-10)(x+5)

Mathematics

1 answer:

fgiga [73]3 years ago

7 0

C.)<span>(x-10)(x-5)
and that is grouping the factors </span>

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What is an equation of the line, in point-slope form, that passes through (8, -8); slope: 3

gavmur [86]

Answer:

you're answer will be y+8=3(x-8)

3 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

2 years ago

A steamer going downstream traveled the distance between two ports in 3 hours. The return trip took 3 hours 40 minutes. Find the

lapo4ka [179]

Answer:

1.8 mph

Step-by-step explanation:

Speed of the steamer in still water is 18 mph.

Speed of the current = x mph.

1. The steamer going downstream traveled the distance between two ports in 3 hours. Traveling downstream the current "helps" the steamer, then the speed is 18 + x mph.

The distance traveled downstream = 3(18 + x) miles.

2. The steamer going upstream traveled the distance between two ports in 3 hours 40 minutes that is $3\frac{2}{3}$ hours. Traveling upstream the current "interferes" the steamer, then the speed is 18 - x mph.

The distance traveled upstream $3\dfrac{2}{3}(18-x)$ miles.

3. The distances are the same, so

$3(18+x)=3\dfrac{2}{3}(18-x)$

Solve this equation:

$3(18+x)=\dfrac{11}{3}(18-x)\\ \\9(18+x)=11(18-x)\\ \\162+9x=198-11x\\ \\9x+11x=198-162\\ \\20x=36\\ \\x=1.8\ mph$

6 0

3 years ago

You have made two of the exact same necklaces that cost you a total of $15 in supplies. You have chosen to mark up the price by

tatyana61 [14]

Answer:

A) The selling price for each necklaces is $8.625

B) The profit mark in each necklaces is 15%

Step-by-step explanation:

Given as :

The total cost of two necklaces = c.p = $15

The markup percentage for the necklaces = m = 15%

Let The selling price for both necklaces = s.p

A ) <u>Now, From markup method</u>

m% = $\dfrac{s.p - c.p}{c.p}$

or, 15% = $\dfrac{s.p - 15}{15}$

or, 15% = $\dfrac{s.p}{15}$ - 1

or, $\dfrac{s.p}{15}$ = 1 + 15%

or, $\dfrac{s.p}{15}$ = 1 + $\dfrac{15}{100}$

or, $\dfrac{s.p}{15}$ = $\dfrac{100 + 15}{100}$

or, $\dfrac{s.p}{15}$ = $\dfrac{115}{100}$

∴ s.p = $\frac{15\times 115}{100}$

I.e s.p = $17.25

So, selling price of two necklaces = s.p = $17.25

or, selling price of one necklaces = s.p = $\dfrac{17.25}{2}$ = $8.625

Hence, The selling price for each necklaces is $8.625

<u>Now, Again</u>

B) ∵ The total cost of two necklaces = c.p = $15

So, The cost price of one necklaces = $\dfrac{15}{2}$ = $7.5

∴ profit% for each necklace = $\dfrac{s.p - c.p}{c.p}$

i.e profit% for each necklace = $\dfrac{8.625 - 7.5}{7.5}$

Or, profit% for each necklace = $\dfrac{1.125}{7.5}$

Or, profit% for each necklace = 0.15

So, The profit make in each necklaces = 15%

Hence, The profit mark in each necklaces is 15%

Answer

8 0

3 years ago

What is the equation of the line for this function? (0, 0), (2, 1), (4, 2), (6, 3).

aleksley [76]

The equation of the line is $y=\frac{1}{2}x$

Explanation:

Given that the set of ordered pairs is (0,0), (2,1), (4,2), (6,3)

We need to determine the equation of the line.

<u>Slope:</u>

The slope of the line can be determined using the formula,

$m=\frac{y_2-y_1}{x_2-x_1}$

Let us substitute any two coordinates in the formula.

Thus, substituting the coordinates (2,1) and (6,3) in the above formula, we have,

$m=\frac{3-1}{6-2}$

$m=\frac{2}{4}$

$m=\frac{1}{2}$

Thus, the slope of the line is $m=\frac{1}{2}$

<u>Equation of the line:</u>

The equation of the line can be determined using the formula,

$y-y_1=m(x-x_1)$

Let us substitute any one of the coordinates and the slope in the above formula.

Hence, substituting $m=\frac{1}{2}$ and the coordinate (0,0), we get,

$y-0=\frac{1}{2}(x-0)$

$y=\frac{1}{2}x-0$

$y=\frac{1}{2}x$

Hence, the equation of the line is $y=\frac{1}{2}x$

7 0

3 years ago