All categories

2 years ago

The vertex of this parabola is at (2,-4). When the y value is -3, the x-value is

1 answer:

4 0

$\bf ~~~~~~\textit{parabola vertex form} \\\\ \begin{array}{llll} \stackrel{\textit{we'll use this one}}{y=a(x- h)^2+ k}\\\\ x=a(y- k)^2+ h \end{array} \qquad\qquad vertex~~(\stackrel{}{ h},\stackrel{}{ k}) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \textit{we know that } \begin{cases} h=2\\ k=-4 \end{cases}\implies y=a(x-2)^2-4 \\\\\\ \textit{we also know that } \begin{cases} y = -3\\ x = -3 \end{cases}\implies -3=a(-3-2)^2-4\implies 1=a(-5)^2 \\\\\\ 1=25a\implies \boxed{\cfrac{1}{25}=a}$

You might be interested in

In a film, an actor played an elderly uncle character is criticized for marrying a woman when he is 3 times her age. He wittily

yanalaym [24]

Answer:the uncle is 54 years old.

The woman is 18 years old

Step-by-step explanation:

Let x represent the age of the uncle.

Let y represent the age of the woman that he married.

In the film, an actor played an elderly uncle character is criticized for marrying a woman when he is 3 times her age. This means that

x = 3y

He wittily replies, "Ah, but in 18 years time I shall only be twice her age. It means that

x + 18 = 2(y + 18)

x + 18 = 2y + 36 - - - - - - - - - - 1

Substituting x = 3y into equation 1, it becomes

3y + 18 = 2y + 36

3y - 2y = 36 - 18

y = 18

x = 3y = 3 × 18

x = 54

6 0

2 years ago

Complete the statements for the graph of f(x) = |x|. The domain of the function is . The range of the function is . The graph is

ioda

Answer:

Domain of f(x): All real numbers

Range of f(x): $f(x) \geq0$ ---> [0, ∞)

The graph is over the interval (0, ∞)

Step-by-step explanation:

The function absolute value of x that is written: f(x) = | x | assigns only positive values to f(x) at any value of x.

For example, if for f(x) = | x | we make

f(-23) = | -23 | then the absolute value of x "transforms" the number -23 to +23.

Then f(-23) = | -23 | = 23

This means that f(x) will be positive for any value of x.

Therefore, we can conclude that:

Domain of f(x): All real numbers

Range of f(x): $f(x) \geq0$ ---> [0, ∞)

The graph is over the interval (0, ∞)

5 0

2 years ago

Read 2 more answers

During the summer months the water level in Marta's pool decreases by about 1/2 inch each day due to evaporation. Which equation

larisa86 [58]

Answer:

Change = -(1/2) * 30 = -15 inches

Step-by-step explanation:

If the water level decreases by 1/2 inch each day, the change in the water level in one day is -1/2 inch.

So, after t days, the total change in the water level can be calculated as:

Total change = -(1/2) * t inches

So, after 30 summer days, the total change is:

Change = -(1/2) * 30 = -15 inches

So the water level of the pool after 30 summer days has decreased by 15 inches.

8 0

2 years ago

Read 2 more answers

PROBLEM SOLVING You are participating in an orienteering competition. The diagram shows the position of a river that cuts throug

Wewaii [24]

Answer:

The shortest distance is 2.2 miles

Step-by-step explanation:

we know that

The shortest distance you must travel to reach the river is the perpendicular distance to the river

step 1

Find the slope of the line perpendicular to the river

we have

$y=3x+2$

The slope of the river is m=3

Remember that if two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is -1)

therefore

The slope of the line perpendicular to the river is

$m=-1/3$

step 2

Find the equation of the line into point slope form

$y-y1=m(x-x1)$

we have

$m=-1/3$

$point(2,1)$

substitute

$y-1=-(1/3)(x-2)$

step 3

Find the intersection point of the river and the line perpendicular to the river

we have

$y=3x+2$ ------> equation A

$y-1=-(1/3)(x-2)$ -----> equation B

Solve the system by graphing

The intersection point is (-0.1,1,7)

see the attached figure

step 3

Find the distance between the points (2,1) and (-0,1,1.7)

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

substitute

$d=\sqrt{(1.7-1)^{2}+(-0.1-2)^{2}}$

$d=\sqrt{(0.7)^{2}+(-2.1)^{2}}$

$d=2.2\ miles$

6 0

2 years ago

The drama teacher at a high school wants to conduct a survey to determine the percentage of students in the school who are willi

ElenaW [278]

Answer: Stratified sampling

Step-by-step explanation:

The stratified sampling is a sampling technique in which the entire population is divided into groups known as strata on the basis of some particular characteristics (For example colors , countries , gender ...etc ).
Then researcher select some members for his sample from these strata randomly.

Given : The drama teacher at a high school wants to conduct a survey to find the percentage of students in the school who are willing to pay a fee for participating in clubs.

Then, 10 students are selected randomly from each of the drama teacher's classes to complete the survey.

Here , strata = drama teacher's classes

Therefore , the plan is an example of stratified sampling method.

7 0

1 year ago

Read 2 more answers