In which quadrant does point T (−5, 10) lie?

What are the coefficient(s) in the expression: 3x+2r-7

strojnjashka [21]

Answer:

3

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

What are the solutions of x^2-2x+5=0

sweet [91]

The solution of $x^{2}-2 x+5=0$ are 1 + 2i and 1 – 2i

Solution:

Given, equation is $x^{2}-2 x+5=0$

We have to find the roots of the given quadratic equation

Now, let us use the quadratic formula

$x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$ --- (1)

Let us determine the nature of roots:

Here in $x^{2}-2 x+5=0$ a = 1 ; b = -2 ; c = 5

$b^2 - 4ac = 2^2 - 4(1)(5) = 4 - 20 = -16$

Since $b^2 - 4ac < 0$ , the roots obtained will be complex conjugates.

Now plug in values in eqn 1, we get,

$x=\frac{-(-2) \pm \sqrt{(-2)^{2}-4 \times 1 \times 5}}{2 \times 1}$

On solving we get,

$x=\frac{2 \pm \sqrt{4-20}}{2}$

$x=\frac{2 \pm \sqrt{-16}}{2}$

$x=\frac{2 \pm \sqrt{16} \times \sqrt{-1}}{2}$

we know that square root of -1 is "i" which is a complex number

$\begin{array}{l}{\mathrm{x}=\frac{2 \pm 4 i}{2}} \\\\ {\mathrm{x}=1 \pm 2 i}\end{array}$

Hence, the roots of the given quadratic equation are 1 + 2i and 1 – 2i

6 0

3 years ago

A rectagle has a height of 5x and a width of x+2 area=???

astra-53 [7]

Answer: $Area=5x^2+10x$

Step-by-step explanation:

The area of a rectangle:

$a=h$ × $w$

$a=5x(x+2)$

$a=5x$ × $x+5x$ × $2$

$a=5x^2+10x$

-Result:

$a=5x^2+10x$

5 0

3 years ago

Home Videos Inc. surveys 450 households and finds that the mean amount spent for renting or buying videos is P135 a month and th

adell [148]

SOLUTION:

Case: Hypothesis testing

Step 1: Null and Alternative hypotheses

$\begin{gathered} H_0:\mu=P127.50 \\ H_1:\mu\leq P127.50 \end{gathered}$

Step 2: T-test analysis

$\begin{gathered} t=\frac{\hat{x}-\mu}{\frac{s}{\sqrt{n}}} \\ t=\frac{135-127.5}{\frac{75.25}{\sqrt{450}}} \\ t=2.144 \end{gathered}$

Step 3: t-test with the significance level

$\begin{gathered} t_{\alpha}=? \\ \alpha=0.05 \\ From\text{ }tables \\ t_{0.05}=1.654 \end{gathered}$

Step 4: Comparing

$t>t_{\alpha}$

So tail to reject the null hypothesis. There is enough evidence at a 0.05 level of significance to claim that the mean spent is greater than P127.50.

Final answer:

Yes, there is evidence sufficient to conclude that the mean amount spent is greater than P127.50 per month at a 0.05 level of significance.

6 0

1 year ago

A circle is centered on point B, Points A, C and D lie on its circumference. if ABC measures 46 degrees, what does ADC measures?

den301095 [7]

Answer: 23 degrees

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Explanation:

Using the inscribed angle theorem we can connect the central angle ABC and the inscribed angle ADC. The reason why is because they both cut off the minor arc AC

Angle ABC is given to be 46 degrees, the formula we use is shown below

central angle = 2*(inscribed angle)
angle ABC = 2*(angle ADC)
46 = 2*(angle ADC)
46/2 = 2*(angle ADC)/2 ... divide both sides by 2
23 = angle ADC
angle ADC = 23 degrees

5 0

3 years ago