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3 years ago

the vertex form of the equation of a parabola is y=(x-5)2+16. what is the standard form of the equation

Mathematics

2 answers:

prohojiy [21]3 years ago

7 0

Answer: $y=x^2-10x+41$

Step-by-step explanation:

The standard form of a quadratic function is:

$y=ax^2+bx+c$

You need to remember the square of a binomial:

$(a-b)^2=a^2-2ab+b^2$

Applying the above, you get:

$y=(x-5)^2+16$

$y=(x^2-2(x)(5)+5^2)+16$

Simplify the expression:

$y=x^2-10x+25+16$

Now you need to add the like terms.

THerefore, you get:

$y=x^2-10x+41$

Reika [66]3 years ago

6 0

Answer:

y = x² - 10x + 41

Step-by-step explanation:

The standard form of a quadratic is ax² + bx + c : a ≠ 0

Given

y = (x - 5)² + 16 ← expand (x - 5)²

= x² - 10x + 25 + 16

= x² - 10x + 41 ← in standard form

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1 half gallon of ice cream cost 4.36 what is the unit price per quart

faltersainse [42]

Answer:

$2.18

Step-by-step explanation:

since there are 4 quarts in a gallon then there are 2 in a half gallon and therefore if you divide by 2 that would be your price per quart.

5 0

2 years ago

A survey of 1,562 randomly selected adults showed that 522 of them have heard of a new electronic reader. The accompanying techn

tester [92]

Answer:

a) We want to test the claim that 35% of adults have heard of the new electronic reader, then the system of hypothesis are.:

Null hypothesis: $p=0.35$

Alternative hypothesis: $p \neq 0.35$

And is a two tailed test

b) $z=\frac{0.334 -0.35}{\sqrt{\frac{0.35(1-0.35)}{1562}}}=-1.326$

c) $p_v =2*P(z$

d) Null hypothesis: $p=0.35$

e) Fail to reject the null hypothesis because the P-value is greater than the significance level, alpha.

Step-by-step explanation:

Information provided

n=1562 represent the random sample selected

X=522 represent the people who have heard of a new electronic reader

$\hat p=\frac{522}{1562}=0.334$ estimated proportion of people who have heard of a new electronic reader

$p_o=0.35$ is the value to verify

$\alpha=0.05$ represent the significance level

z would represent the statistic

$p_v$ represent the p value

Part a

We want to test the claim that 35% of adults have heard of the new electronic reader, then the system of hypothesis are.:

Null hypothesis: $p=0.35$

Alternative hypothesis: $p \neq 0.35$

And is a two tailed test

Part b

The statistic for this case is given :

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

Replacing the info given we got:

$z=\frac{0.334 -0.35}{\sqrt{\frac{0.35(1-0.35)}{1562}}}=-1.326$

Part c

We can calculate the p value using the laternative hypothesis with the following probability:

$p_v =2*P(z$

Part d

The null hypothesis for this case would be:

Null hypothesis: $p=0.35$

Part e

The best conclusion for this case would be:

Fail to reject the null hypothesis because the P-value is greater than the significance level, alpha.

5 0

3 years ago

The line perpendicular to y= (-3/2)x -4 and goes through (1,4)

Paladinen [302]

Answer <u>(assuming it is allowed to be in point-slope format)</u>:

$y-4 = \frac{2}{3}(x-1)$

Step-by-step explanation:

1) First, determine the slope. We know it has to be perpendicular to the given equation, $y = -\frac{3}{2} x-4$ . That equation is already in slope-intercept form, or y = mx + b format, in which m represents the slope. Since $-\frac{3}{2}$ is in place of the m in the equation, that must be the slope of the given line.

Slopes that are perpendicular are opposite reciprocals of each other (they have different signs, and the denominators and numerators switch places). Thus, the slope of the new line must be $\frac{2}{3}$ .

2) Now, use the point-slope formula, $y-y_1 = m (x-x_1)$ to write the new equation with the given information. Substitute $m$ , $x_1$ , and $y_1$ for real values.

The $m$ represents the slope, so substitute $\frac{2}{3}$ in its place. The $x_1$ and $y_1$ represent the x and y values of a point the line intersects. Since the point crosses (1,4), substitute 1 for $x_1$ and 4 for $y_1$ . This gives the following equation and answer:

$y-4 = \frac{2}{3}(x-1)$

3 0

3 years ago

She has one board that is 2 m 3 cm long and another that is 2 m 98 cm long. How long are the two boards together in meters?

miss Akunina [59]

Answer:

5 meters and 1 cm

Step-by-step explanation:

well their are 100 cm in 1 meter

so add 2m and 3 cm to 2 m and 98 cm

to get 4 m and 101 cm what is 5 meters and 1 cm

4 0

3 years ago

How can i show 5/8 is greater than 3/8

Serjik [45]

The first answer, using a number line, is a good answer.

I have two other ways:

Way #1:

5 stones is more than 3 stones.
5 gallons is greater than 3 gallons.
5 pounds is greater than 3 pounds.
5 puppies is greater than 3 puppies.
5 hamburgers is greater than 2 hamburgers.
5 schoolbuses is greater than 3 schoolbuses.

We look around us, and we see that 5 of anything
is always greater than 3 of the same thing.

There's no reason that should change if the 'things' are eighths.

Way #2:

-- Get 2 friends to help you.

-- Take one good-size veggie pizza or coconut cream pie.

-- Carefully cut it up in eight (8) equal pieces.
Now each piece is 1/8 of the pie or the pizza.

-- Give 5 pieces (5/8) to the first friend.
Give 3 pieces (3/8) to the other friend.

-- Ask them to get together and agree on who has more.

3 0

2 years ago

Read 2 more answers