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2 years ago

Which statements are true about the graph of the function f(x) = 6x - 4 + x2? Select two options

Mathematics

2 answers:

yulyashka [42]2 years ago

5 0

Answer:

2 and 4

Step-by-step explanation:

Basile [38]2 years ago

3 0

Answer:

only: The vertex of the function is (-3, -13

Step-by-step explanation:

function f(x) = 6x - 4 + x2?

x^2 + 6x - 4

= xx + 6x + 9 - 9 - 4

= (x + 3)^2 - 13

vertex is at (-3, -13)

f(x) does cross the x-axis

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Part A: During what interval(s) of the domain is the water balloon's height increasing?

Advocard [28]

Answer:

The answer is below

Step-by-step explanation:

The linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time, x, measured in seconds: A linear model with ordered pairs at 0, 60 and 2, 75 and 4, 75 and 6, 40 and 8, 20 and 10, 0 and 12, 0 and 14, 0. The x axis is labeled Time in seconds, and the y axis is labeled Height in feet. Part A: During what interval(s) of the domain is the water balloon's height increasing? (2 points) Part B: During what interval(s) of the domain is the water balloon's height staying the same? (2 points) Part C: During what interval(s) of the domain is the water balloon's height decreasing the fastest? Use complete sentences to support your answer. (3 points) Part D: Use the constraints of the real-world situation to predict the height of the water balloon at 16 seconds.

Answer:

Part A: During what interval(s) of the domain is the water balloon's height increasing?

Between 0 and 2 seconds, the height of the balloon increases from 60 feet to 75 feet

Part B: During what interval(s) of the domain is the water balloon's height staying the same?

Between 2 and 4 seconds, the height remains the same at 75 feet. Also from 10 seconds the height of the balloon is at 0 feet

Part C: During what interval(s) of the domain is the water balloon's height decreasing the fastest?

Between 4 and 6 seconds, the height of the balloon decreases from 75 feet to 40 feet (i.e. -17.5 ft/s)

Between 6 and 8 seconds, the height of the balloon decreases from 40 feet to 20 feet (i.e. -10 ft/s)

Between 8 and 10 seconds, the height of the balloon decreases from 20 feet to 0 feet (i.e. -10 ft/s)

Hence it decreases fastest from 4 to 6 seconds

Part D: Use the constraints of the real-world situation to predict the height of the water balloon at 16 seconds

From 10 seconds, the balloon is at the ground, so it remains at the ground (0 feet) even at 16 seconds

6 0

2 years ago

The average time taken to complete an exam, X, follows a normal probability distribution with mean = 60 minutes and standard dev

k0ka [10]

Answer: b. 0.8413

Step-by-step explanation:

Given : The average time taken to complete an exam, X, follows a normal probability distribution with $\mu=60\text{ minutes}$ and $\sigma=30\text{ minutes}$ .

Then, the probability that a randomly chosen student will take more than 30 minutes to complete the exam will be :-

$P(x>30)=P(z>\dfrac{30-60}{30})\ \ [\because\ z=\dfrac{x-\mu}{\sigma} ]\\\\=P(z>-1)=P(z-z)=P(Z$

[using z-value table]

Hence, the probability that a randomly chosen student will take more than 30 minutes to complete the exam = 0.8413

3 0

2 years ago

In 2008, the price of a gallon of unleaded gasoline was $4.02. In 1990, it was only $1.37 per gallon. What is the increase expre

liubo4ka [24]

First get the difference between the 2008 price and 1990 which is $4.02-$1.37= $2.65. Then the difference you've got which is $2.65, divide it to the current market price which is $4.02 to get the how many percentage it increased since then, $2.65/$4.02= 0.65920398 then multiply it to 100. It would be 65.92 or 66% if rounded off to whole number.

6 0

2 years ago

A helicopter flies 8 km due north from A to B. It then flies 5 km from B to C and returns to A as shown in the figure. Angle ABC

In-s [12.5K]

Please consider the attached graph.

We have been given that a helicopter flies 8 km due north from A to B. It then flies 5 km from B to C and returns to A as shown in the figure. The measure of angle ABC is 150°. We are asked to find the area of triangle ABC.

We will use trigonometric area formula to solve our given problem.

$A=\frac{1}{2}a\cdot c\cdot\text{sin}(b)$ , where angle b is angle between sides a and c.

For our given triangle $a=5,c=8$ and measure of angle b is 150 degrees.

$A=\frac{1}{2}(5)\cdot (8)\cdot\text{sin}(150^{\circ})$

$A=5\cdot 4\cdot(0.5)$

$A=10$

Therefore, the area of the triangle ABC is 10 square kilo-meters and option 'c' is the correct choice.

6 0

2 years ago

Recently, 18.3% of visitors to the travelocity web site hailed from the google search engine. a random sample of 130 visitors on

kaheart [24]

In your problem:
p = 18.3% = 0.183
n = 130

The standard error can be calculated by the formula:
SE = √[p · (1 - p) / n]
= √[0.183 · (1 - 0.183) / 130]
= 0.0339

The standard error of the proportion is 0.034.

7 0

2 years ago