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Trava [24]
3 years ago
14

Vertex form is f(x)=a(x-p)^2 +q. How do i determine a?

Mathematics
1 answer:
slamgirl [31]3 years ago
8 0
Y1 is the simplest parabola.  Its vertex is at (0,0) and it passes thru (2,4).  This is enough info to conclude that y1 = x^2.

y4, the lower red graph, is a bit more of a challenge.  We can easily identify its vertex, which is (-4,0), and several points on the grah, such as (2,-3).

Let's try this:  assume that the general equation for a parabola is 
y-k = a(x-h)^2, where (h,k) is the vertex.  Subst. the known values,

-3-(-4) = a(2-0)^2.  Then 1 = a(2)^2, or 1 = 4a, or a = 1/4.

The equation of parabola y4 is   y+4 = (1/4)x^2

Or you could elim. the fraction and write the eqn as 4y+16=x^2, or

4y = x^2-16, or    y = (1/4)x - 4.  Take your pick!  Hope this helps you find "a" for the other parabolas.


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Moby sold half his toy car collection, and then bought 12 more cars the next day. He now has 48 toy cars. How many cars did he h
castortr0y [4]

Answer: 72 cars.

Step-by-step explanation:

Let be "x" the number of toys that Moby had to start with.

According to the information given in the exercise, Moby sold half his toy car collection. This can be represented with the following expression:

\frac{1}{2}x

Then he bought 12 more cars, giving a total amount of 48 toy cars.

Therefore, the equation that represents this situation is the equation shown below:

x-\frac{1}{2}x+12=48

Now you must solve for "x" in order to find its value.

You get that this is:

\frac{1}{2}x+12=48\\\\\frac{1}{2}x=48-12\\\\\frac{1}{2}x=36\\\\x=(36)(2)\\\\x=72

7 0
4 years ago
What is the length of segment AE?
nexus9112 [7]

Answer:

AE=\frac{50}{3}\ units

Step-by-step explanation:

step 1

In the right triangle ABC

Applying the Pythagoras Theorem fin the hypotenuse AC

AC^{2} =AB^{2}+BC^{2}

substitute

AC^{2} =6^{2}+8^{2}

AC^{2} =100

AC =10\ units

step 2

we know that

If two figures are similar, then the ratio of its corresponding sides is equal

so

\frac{AB}{CD}=\frac{AC}{CE}

substitute and solve for CE

\frac{6}{4}=\frac{10}{CE}\\ \\CE=4*10/6\\ \\CE=\frac{20}{3}\ units

step 3

Find the length of segment AE

AE=AC+CE

substitute the values

AE=10\ units+\frac{20}{3}\ units=\frac{50}{3}\ units

6 0
3 years ago
Recall that Rn denotes the right-endpoint approximation using n rectangles, Ln denotes the left-endpoint approximation using n r
pogonyaev

Answer:

R_5=1.12

Step-by-step explanation:

We want to calculate the right-endpoint approximation (the right Riemann sum) for the function:

f(x)=x^2+x

On the interval [-1, 1] using five equal rectangles.

Find the width of each rectangle:

\displaystyle \Delta x=\frac{1-(-1)}{5}=\frac{2}{5}

List the <em>x-</em>coordinates starting with -1 and ending with 1 with increments of 2/5:

-1, -3/5, -1/5, 1/5, 3/5, 1.

Since we are find the right-hand approximation, we use the five coordinates on the right.

Evaluate the function for each value. This is shown in the table below.

Each area of each rectangle is its area (the <em>y-</em>value) times its width, which is a constant 2/5. Hence, the approximation for the area under the curve of the function <em>f(x)</em> over the interval [-1, 1] using five equal rectangles is:

\displaystyle R_5=\frac{2}{5}\left(-0.24+-0.16+0.24+0.96+2)= 1.12

3 0
3 years ago
Can you use elimination to solve a system of linear equations with three equations
crimeas [40]
You can use elimination to solve systems of equations with 3 equations. I know how to solve systems of equatons with 3 equations, but I use a different process, I don't know how to use the elimination method.
7 0
3 years ago
Read 2 more answers
A survey of 46 college athletes found that 24 played volleyball, while 22 played basketball. a) If we pick one athlete survey pa
PSYCHO15rus [73]

Answer:

A) \dfrac{11}{23}

B) \dfrac{88}{345}

Step-by-step explanation:

A survey of 46 college athletes found that

  • 24 played volleyball,
  • 22 played basketball.

A) If we pick one athlete survey participant at random,  the probability they play basketball is

P_1=\dfrac{22}{46}=\dfrac{11}{23}

B) If we pick 2 athletes at random (without replacement),

  • the probability we get one volleyball player is \dfrac{24}{46}=\dfrac{12}{23};
  • the probability we get another basketball player is \dfrac{22}{45} (only 45 athletes left).

Thus, the probability we get one volleyball player and one basketball player is

P_2=\dfrac{12}{23}\cdot \dfrac{22}{45}=\dfrac{88}{345}

5 0
4 years ago
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