Write the following quadratic expression in vertex form x^2+4x+10

Mathematics

1 answer:

AysviL [449]3 years ago

7 0

9514 1404 393

Answer:

(x +2)^2 +6

Step-by-step explanation:

We can add and subtract the square of half the x-coefficient.

x^2 +4x +10 = (x^2 +4x +2^2) +10 -2^2

= (x +2)^2 +6

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Explain how the expression 8.3√2+7.9√2 can be simplified using the distributive property.

IceJOKER [234]

Answer:

$\sqrt{2}(16.2)$

Step-by-step explanation:

The distributive property says that the answer of multiplying two numbers is the same as multiplying the first number by the sum or subtraction of two numbers that result in the second number.

What we have to do is to simpligy the ecuation, this mean, making it shorter.

First we take out the common term of the ecuation: $\sqrt{2}$ .

By distributive property $8.3\sqrt{2} +7.9\sqrt{2} =\sqrt{2}(8.3+7.9)$

then $\sqrt{2} (16.2)$ .

3 0

3 years ago

a sociologist develops a test to measure attitudes towards public transportation and 27 randomly selected subjects are given the

horsena [70]

Answer:

The 95% confidence interval for the mean score is:

$\mu$ ∈ $(67.73,\ \ 84.67)$

Step-by-step explanation:

We want to estimate the population mean, that is, the average score of all the subjects.

An estimator for the population mean μ is ${\overline {x}}$

Since the sample size is $27$ then we use the statistic $t_{\frac{\alpha}{2}}$ with $27-1 = 26$ degrees of freedom

The confidence interval for the mean is:

$({\displaystyle {\overline {x}}} + t_{\frac{\alpha}{2}}\frac{S}{\sqrt{n}},\ \ {\displaystyle {\overline {x}}} - t_{\frac{\alpha}{2}}\frac{S}{\sqrt{n}})$