How to evaluate s-r/-7 when r=-3 and s=4?

System of linear equation for graph below

Andrej [43]

Answer: See below

Step-by-step explanation:

For the line on top, we know the slope is negative because it is going down. We can find the slope by counting how much the point goes down and to the right. Y-intercept is the point on the y-axis.

slope: -3

y-intercept: 2

Now that we have the slope and y-intercept, we know the equation is y=-3x+2.

For the second line, we know the slope is positive because it is going up. Since slope is rise/run, we can see it rises 1 unit and runs to the right by 2 units. Y-intercept is the point on the y-axis.

slope: 1/2

y-intercept: -5

With our slope and y-intercept, we know our equation.

y=1/2x-5

5 0

3 years ago

Fill in the blank with a constant, so that the resulting quadratic expression is the square of a binomial. $\[x^2 + 22x + \under

saw5 [17]

Answer:

$\[x^2 + 22x + 121\]$

Step-by-step explanation:

Given

$\[x^2 + 22x + \underline{~~~~}.\]$

Required

Fill in the gap

Represent the blank with k

$\[x^2 + 22x + k\]$

Solving for k...

To do this, we start by getting the coefficient of x

Coefficient of x = 22

Divide the coefficient by 2

$Result = 22/2$

$Result = 11$

Take the square of this result, to give k

$k= 11^2$

$k= 121$

Substitute 121 for k

$\[x^2 + 22x + 121\]$

The expression can be factorized as follows;

$x^2 + 11x + 11x + 121$

$x(x + 11)+11(x+11)$

$(x+11)(x+11)$

$(x+11)^2$

Hence, the quadratic expression is $\[x^2 + 22x + 121\]$

8 0

3 years ago

Read 2 more answers

Why might a scientist studying water pollution work with percents less than one?

34kurt

Because, often times, water pollutants occur in small amounts. Therefore, it is likely to use small percentages (less than 1%) in comparison to the water and various other pollutants in the same sample.

7 0

3 years ago

Find all the values of x where the tangent line is horizontal. f(x) = 2x^3 + 42x^2 + 270x + 11

WITCHER [35]

Answer:

If I calculated correctly, the tangent line is horizontal where x ≈ -5.3 + 9.3i, and -5.3 - 9.3i

I'm somewhat concerned at having gotten complex numbers, and strongly recommend going through the steps to see if I missed anything. I checked it myself and don't see any errors.

Step-by-step explanation:

You can do this by taking the derivative of the function and solving for zero:

f(x) = 2x³ + 32x² + 220x + 11

f'(x) = 6x² + 64x + 220

f'(x) = 2(3x² + 32x + 110)

We can't factor that further, so let's do it the long way, starting by letting f'(x) equal zero:

0 = 2(3x² + 32x + 110)

0 = 3x² + 32x + 110

0 = 9x² + 96x + 990

0 = 9x² + 96x + 256 + 734

0 = (3x + 16)² + 734

(3x + 16)² = -734

3x + 16 = ± i√734

3x = -16 ± i√734

x = (-16 ± i√734) / 3

x ≈ (-16 + 27.9i) / 3, and (16 - 27.9i) / 3

x ≈ -5.3 + 9.3i, and -5.3 - 9.3i

I'm always wary when I end up with complex numbers. I'd suggest double checking everything here, but I'm fairly certain I did everything correctly.

8 0

3 years ago

PLEASE HELP I'LL GIVE BRAINLIEST!!! The first barn contained 3 times more hay than the second one. After 20 tons of hay were rem

shepuryov [24]

Answer:

First Barn contained = 90 tons

Second barn contained = 30 tons

Step-by-step explanation:

Let us suppose that second barn contains x tons of Hay

Now according to given condition

First Barn Contain = 3 *x = 3x

According to other condition

20 tons removed from first barn i.e. 3x - 20 and 20 tons were added to second barn i.e. x + 20

the amount of hay in second barn which is x + 20 is equal to 5 / 7 of the hay remaining in first barn which is 3x-20

So in mathematical form it could be written as

x + 20 = $\frac{5}{7}*(3x-20)$

To find hay in each barn

We have the equation

x + 20 = $\frac{5}{7}*(3x-20)$

Multiplying both sides of equation by 7

7(x+20)= $\frac{5*7}{7}*(3x-20)$

7(x+20)=5(3x-20)

7x + 140 = 15 x - 100

adding 100 on both sides gives

7x + 140 + 100 = 15x - 100 + 100

7x + 240 = 15 x

Subtracting 7x from both sides

7x + 240 - 7x = 15 x - 7x

240 = 8x

or

8x = 240

Dividing both sides by 8

8x / 8 = 240 / 8

x = 30 tons

so second barn contained = 30 tons of hay

now

First barn contained = 3 * x

as x = 30

so putting the value

First barn contained = 3 * 30

First Barn contained = 90 tons

5 0

3 years ago