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3 years ago

Is the equation's graph opening up or down?

Mathematics

1 answer:

Inessa05 [86]3 years ago

5 0

Answer:

Step-by-step explanation:

Your "y=2xsquared-12x+10" translates into y = 2x^2 - 12x + 10. This factors into y = 2(x^2 - 6x + 5).

Setting this = to 0 results in y = 2(x - 5)(x - 1) = 0, so that the x-intercepts are (5, 0) and (1, 0). The x-coordinate of the vertex lies halfway between x = 1 and x = 5, that is, at x = 3. Using synthetic division to evaluate y = 2x^2 - 12x + 10 at x = 3, we get

3 2 -12 10

6 -18

------------------

2 -6 -8

Therefore, the vertex is located at (3, -8).

Setting x = 0 results in the y-intercept: y = 2(0)^2 - 12(0) + 10 => (0, 10)

You might be interested in

Fairfield Homes is developing two parcels near Pigeon Fork, Tennessee. In order to test different advertising approaches, it use

evablogger [386]

Answer:

(1) Null Hypothesis, $H_0$ : $\mu_1 = \mu_2$

Alternate Hypothesis, $H_1$ : $\mu_1\neq \mu_2$

(2) Test statistics = -1.48

(3) At the 0.05 significance level, Fair field conclude that the population means are same.

Step-by-step explanation:

Let $\mu_1$ = mean annual family income for 12 people making inquiries at the first development

$\mu_2$ = mean annual family income for 24 people making inquiries at the second development

$s_1$ = standard deviation of annual family income for 12 people making inquiries at the first development

$s_2$ = standard deviation of annual family income for 24 people making inquiries at the second development

$n_1$ = sample of people of first development i.e. 12

$n_2$ = sample of people of second development i.e. 24

(1) Null Hypothesis, $H_0$ : $\mu_1 = \mu_2$ {population means are same}

Alternate Hypothesis, $H_1$ : $\mu_1\neq \mu_2$ {population means are different}

DECISION RULE ;

If the test statistics is less than the critical value of t from table at 5% significance level, then we will accept null hypothesis, $H_0$ .
If the test statistics is more than the critical value of t from table at 5% significance level, then we will reject null hypothesis, $H_0$ .

(2) The test statistics is given by;

$\frac{(X_1bar -X_2bar) - (\mu_1-\mu_2)}{s_p\sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }$ ~ $t_n__1+n_2-2$

where, $X_1bar$ = Sample mean income of people at first development

= $153,000

$X_2bar$ = Sample mean income of people at second development = $171,000

$s_1$ = $42,000 and $s_2$ = $30,000

$s_p= \sqrt{\frac{(n_1-1)s_1^{2}+(n_2-1)s_2^{2} }{n_1+n_2-2}}$ = $\sqrt{\frac{(12-1)42000^{2}+(24-1)30000^{2} }{12+24-2}}$ = 34344.30

Test statistics = $\frac{(153000 -171000) - 0}{34344.30\sqrt{\frac{1}{12}+\frac{1}{24} } }$ ~ $t_3_4$

= -1.48

(3) At 5% level of significance, t table gives critical value of 2.032 at 34 degree of freedom.Since our test statistics is less than the critical value of t so considering our decision rule, we will accept null hypothesis.

And conclude that population means are same.

4 0

4 years ago

PLSSS HELP IF YOU TURLY KNOW THISS

xxMikexx [17]

Answer:

2 1/2

Step-by-step explanation:

Turn both fractions into improper fractions, multiply the whole number by the denominator and add the numerator.

4 3/4

4 * 4 + 3 = 19

19/4

2 1/4

2 * 4 + 1 = 9

9/4

Now since she drank 2 1/4 gallons of juice, subtract 9/4 from 19/4.

19/4 - 9/4 = 10/4

Now turn back into a mixed fraction, do this by putting 4 into ten twice and taking the remainder and putting it as numerator:

4 * 2 = 8

10 - 8 = 2

2 1/2

8 0

3 years ago

How yo resolve x/-3-2=9

liq [111]

X/-3-2=9
Step 1: Add ~ x/-3-2+2=9+2
Step 2: Substitute ~ x/-3=11
Step 3: Multiply ~ x/-3(-3)=9(-3)
step 4: Substitute ~ x=-27

6 0

3 years ago

Question 2 (2 points)

hoa [83]

Answer:

4) The limit does not exist.

General Formulas and Concepts:

Calculus

Limits

Right-Side Limit: $\displaystyle \lim_{x \to c^+} f(x)$
Left-Side Limit: $\displaystyle \lim_{x \to c^-} f(x)$

Limit Rule [Variable Direct Substitution]: $\displaystyle \lim_{x \to c} x = c$

Step-by-step explanation:

*Note:

For a limit to exist, the right-side and left-side limits must be equal to each other.

Step 1: Define

Identify

$\displaystyle f(x) = \left\{\begin{array}{ccc}5 - x ,\ x < 5\\8 ,\ x = 5\\x + 3 ,\ x > 5\end{array}$

Step 2: Find Left-Side Limit

Substitute in function [Left-Side Limit]: $\displaystyle \lim_{x \to 5^-} 5 - x$
Evaluate limit [Limit Rule - Variable Direct Substitution]: $\displaystyle \lim_{x \to 5^-} 5 - x = 5- 5 = 0$

Step 2: Find Left-Side Limit

Substitute in function [Right-Side Limit]: $\displaystyle \lim_{x \to 5^+} x + 3$
Evaluate limit [Limit Rule - Variable Direct Substitution]: $\displaystyle \lim_{x \to 5^+} x + 3 = 5 + 3 = 8$