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Juliette [100K]

2 years ago

8

On the number line below, P represents a number. What is the value of the opposite of that number?

1 answer:

Alex787 [66]2 years ago

7 0

1.5 that is the correct answer

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- 4x + 9y = 9<br> x - 3y = -6

egoroff_w [7]

Answer:

it is -12

Step-by-step explanation:

4 0

2 years ago

For what value of k is there one solution to the given quadratic equation (k+1)x²+4kx+2=0.

andriy [413]

Answer:

If $k = 1$ or $k = -\frac{1}{2}$ , there is only one solution to the given quadratic equation.

Step-by-step explanation:

Given a second order polynomial expressed by the following equation:

$ax^{2} + bx + c, a\neq0$

This polynomial has roots $x_{1}, x_{2}$ such that $ax^{2} + bx + c = (x - x_{1})*(x - x_{2})$ , given by the following formulas:

$x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}$

$x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}$

$\bigtriangleup = b^{2} - 4ac$

The signal of $\bigtriangleup$ determines how many real roots an equation has:

$\bigtriangleup > 0$ : Two real and different solutions

$\bigtriangleup = 0$ : One real solution

$\bigtriangleup < 0$ : No real solutions

In this problem, we have the following second order polynomial:

$(k+1)x^{2} + 4kx + 2 = 0$ .

This means that $a = k+1; b = 4k; c = 2$

It has one solution if

$\bigtriangleup = 0$

$b^{2} - 4ac = 0$

$16k^{2} -8(k+1) = 0$

$16k^{2} - 8k - 8 = 0$

We can simplify by 8

$2k^{2} - k - 1 = 0$

The solution is:

$k = 1$ or $k = -\frac{1}{2}$

So, if $k = 1$ or $k = -\frac{1}{2}$ , there is only one solution to the given quadratic equation.

4 0

2 years ago

Find the sample standard deviation of the following data set, using the statistical functions on your calculator.0.2315 0.4725 0

Nonamiya [84]

Answer:

Option C) 0.2358

Step-by-step explanation:

We are given the following data set:

0.23105, 0.4725, 0.8765, 0.4865, 0.5326, 0.7976

Formula:

$\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}$

where $x_i$ are data points, $\bar{x}$ is the mean and n is the number of observations.

$Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}$

$Mean =\displaystyle\frac{3.39675}{6} = 0.566125$

Sum of squares of differences = 0.1122752556 + 0.008765640625 + 0.09633264063 + 0.006340140625 + 0.001123925625 + 0.05358067562 = 0.2784182787

$S.D = \sqrt{\frac{0.2784182787}{5}} = 0.2358$

Thus, the standard deviation for given data is

Option C) 0.2358

7 0

2 years ago

If he = 7x -27 find the value of x

Amiraneli [1.4K]

$\\ \sf\longmapsto 7x-27=1$

$\\ \sf\longmapsto 7x=1+27$

$\\ \sf\longmapsto 7x=28$

$\\ \sf\longmapsto x=\dfrac{28}{7}$

$\\ \sf\longmapsto x=4$

5 0

2 years ago

Charlotte pays $24 for 3 yards of landscaping fabric and 6 yards of chicken wire. Kami pays $30 for 6 yards of landscaping fabri

vlabodo [156]

Answer: the price of 1 yard of chicken wire is $2

Step-by-step explanation:

Let x represent the cost of one yard of landscaping fabric.

Let y represent the cost of one yard of chicken wire.

Charlotte pays $24 for 3 yards of landscaping fabric and 6 yards of chicken wire. This means that

3x + 6y = 24 - - - - - - - - - - 1

Kami pays $30 for 6 yards of landscaping fabric and 3 yards of chicken wire. This means that

6x + 3y = 30 - - - - - - - - -2

Multiplying equation 1 by 6 and equation 2 by 3, it becomes

18x + 36y = 144

18x + 9y = 90

Subtracting

27y = 54

y = 54/27 = 2

Substituting y = 2 into equation 1, it becomes

3x + 6×2 = 24

3x = 24 - 12 = 12

x = 12/3 = 4

4 0

2 years ago

Read 2 more answers