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2 years ago

Given the graph of y=f(x), shown as a red dashed curve, drag the movable blue point to obtain the graph of y=f(x−4)+3.

Mathematics

2 answers:

Sergeeva-Olga [200]2 years ago

6 0

Answer:

See graph in attachment.

Step-by-step explanation:

The graph of $y=f(x)$ is a parabola that has its vertex at the origin.

The equation of the transformed graph is

$y=f(x-4)+3$

The vertex of this transformed function is

$(4,3)$

Drag the blue graph up so that the vertex will now be at (4,3).

See graph in attachment.

Cloud [144]2 years ago

6 0

The graph of the function f(x),which is in the shape of parabola has vertex at (0,0).

→y=x²

f(x)=x²

Now, the graph of f(x) is translated by 2 units in horizontally right Direction.

→ y=(x-2)²

f(x-2)=(x-2)²

Now, we have to obtain the graph of the function

→y=f(x-4)+3

y=(x-4)²+3

The function , f(x-2) is shifted , 2 unit right in Horizontal right direction and, 3 unit up in vertically Upward direction.

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Consider a sample with data values of 10, 20, 12, 17, and 16. Compute the z-score for each of the five observations. If required

Mila [183]

Answer:

$\begin{tabular}{c|ccccc}{$x$&10&12&16&17&20&z&-1.397&-0.839&0.2795&0.559&1.397&\end{tabular}$

Step-by-step explanation:

z-score is denoted by:

$z=\dfrac{x-\mu}{\sigma}$

here,

$\mu$ : mean

$\sigma$ : standard deviation (or the square root of the variance)

so first we need to find the means of our sample:

$\mu=\dfrac{10+20+12+17+16}{5}\\\mu = 15\\$

Now to find the standard deviation we first need to find the variance of the sample. The variance is the sum of the squares of the differences of each value from the mean.

$\sigma^2 = \dfrac{(10-15)^2+(20-15)^2+(12-15)^2+(17-15)^2+(16-15)^2}{5}\\\sigma^2 = 12.8$

the standard derviation is simply the square root of the variance!

$\sigma = \sqrt{\sigma^2} \\\sigma = \sqrt{12.8} \\\sigma = 3.5778$

Now that we all the values for our z-score formula. we can plug it in!

$z=\dfrac{x-\mu}{\sigma}$

$z=\dfrac{x-15}{3.5778}$

Finally we'll use each value in place of x from our sample into the formula to find the z-score of each value.

$z=\dfrac{10-15}{3.5778} = -1.397$

$z=\dfrac{20-15}{3.5778} = 1.397$

$z=\dfrac{12-15}{3.5778} = -0.839$

$z=\dfrac{17-15}{3.5778} = 0.559$

$z=\dfrac{16-15}{3.5778} = 0.2795$

We can even display the z-scores in a table: (the x-values are in ascending order)

$\begin{tabular}{c|ccccc}{$x$&10&12&16&17&20&z&-1.397&-0.839&0.2795&0.559&1.397&\end{tabular}$

5 0

3 years ago

Arrange the steps to solve the equation \sqrt(x+3)-\sqrt(2x-1)=-2 solve for x

kirill115 [55]

I hope this helps you

x+3/2x-1=-2

x+3= -2 (2x-1)

x+3= -2.2x-2. (-1)

x+3= -4x+2

x+4x=2-3

5x= -1

x= -1/5

3 0

2 years ago

Jackie filled the blue water balloon with 12.25 ounces of water and the red water balloon with 5.5 ounces of water. How much mor

tekilochka [14]

All you do is subtract 5.5 oz from 12.25 oz, so the answer is that the blue balloon has 6.75 more oz than the other balloon.

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3 years ago

Help me the questions and answer choices are in the picture

Anika [276]

Using the Triangle Inequality Theorem

The sum of two side lengths of a triangle is always greater than the third side

first one: 6, 22 , 10
6 + 22 > 10 : yes
22 + 10 > 6 : yes
6 + 10 > 22 : No because 16 < 22
These 3 lengths could NOT be lengths of sides of a triangle

second one: 8 , 15 , 22
8 + 15 > 22 : yes
15 + 22 > 8 : yes
8 + 22 > 15 : yes
These 3 lengths could be lengths of sides of a triangle

Answer:
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3 years ago

7. Solve the formula M=2P+3Q for the variable Q.

vichka [17]

The answer is Q=(M−2P)/3

M = 2P + 3Q

Subtract 2P from both sides:
M - 2P = 2P + 3Q - 2P
M - 2P = 3Q

Divide both sides by 3:
(M - 2P)/3 = 3Q/3
(M - 2P)/3 = Q

7 0

3 years ago