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3 years ago

The function f(x) = x2 + 10x - 3 writers in vertex form is f(x) = (x + 5)2 - 28. What are the coordinates of the vertex?

Mathematics

1 answer:

andrey2020 [161]3 years ago

3 0

General formula of the parabola in vertex form is

f(x) =(x-h)² +k, where (h,k) is a vertex of the parabola.

f(x) = (x + 5)²- 28

h= -5, k = -28,

so (-5, -28) is a vertex of the given parabola.

Answer is A.

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Two lines intersect at a point, forming ∠1 , ∠2 , ∠3 , and ∠4 .

Ad libitum [116K]

The answer is: [B]: " 60° " .
________________________________________
Because at whatever location, ∠2 and ∠4 are vertical angles;

and all vertical angles have equal measurements.

Given: m∠1 is 120°, and ∠1 is supplementary to ∠2 ;

then m∠1 + m∠2 = 180° .

So, m∠2 = (180 - 120)° = 60° .

As aforementioned:

m∠4 = m∠2 = 60° ; which is: Answer choice: [B]: " 60° " .
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3 years ago

you plant 15 tulip bulbs and 10 of them grow into flowers to bloom. If you plant 21 more re tulips bulbs, predict how many of th

harina [27]

Answer:

14 more flower would bloom if 21 more tulip bulb is planted.

Step-by-step explanation:

Given ratio for tulip bulbs and flowers is 15:10.

Now, finding number of flower to bloom if 21 tulip bulb are planted.

Assume if 21 tulip bulbs are planted then number of flower would bloom be"x"

ratio given: $\frac{Tulip\ bulbs}{ Flower} = \frac{15}{10} = \frac{21}{x}$

Cross multiplying the ratio to get:

⇒x= $\frac{21\times 10}{15} = \frac{210}{15}$

∴ $x= 14\ flowers$

Hence, 14 flowers would bloom if 21 tulip bulb are planted.

If total tulip bulb is $15+21= 36$ , then $10+14= 24\ flowers$ would bloom.

5 0

3 years ago

A small business owner estimates his mean daily profit as $970 with a standard deviation of $129. His shop is open 102 days a ye

Katena32 [7]

Answer:

The probability that the shopkeeper's annual profit will not exceed $100,000 is 0.2090.

Step-by-step explanation:

According to the Central Limit Theorem if we have a population with mean μ and standard deviation σ and we select appropriately huge random samples (n ≥ 30) from the population with replacement, then the distribution of the sum of values of X, i.e ∑X, will be approximately normally distributed.

Then, the mean of the distribution of the sum of values of X is given by,

$\mu_{x}=n\mu$

And the standard deviation of the distribution of the sum of values of X is given by,

$\sigma_{x}=\sqrt{n}\sigma$

The information provided is:

μ = $970

σ = $129

n = 102

Since the sample size is quite large, i.e. n = 102 > 30, the Central Limit Theorem can be used to approximate the distribution of the shopkeeper's annual profit.

Then,

$\sum X\sim N(\mu_{x}=98940,\ \sigma_{x}=1302.84)$