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Stella [2.4K]
3 years ago
11

If we transform y=x^2 by 5 units to the left and 8 units ups, what is the vertex of the resulting parabola?

Mathematics
2 answers:
sertanlavr [38]3 years ago
7 0

Answer: y = (x + 5)² + 8

<u>Step-by-step explanation:</u>

y = x²

left 5 units:       y = (x + 5)²

up 8 units:        y = (x + 5)² + 8

Burka [1]3 years ago
5 0

Answer:

(-5, 8)

Step-by-step explanation:

The vertex of y=x^2 is at the origin (0,0).

5 units to the left changes the vertex to (-5,0)

Then 8 units up makes it (-5, 8)

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If a 24-kg mass stretches a spring 15 cm, what mass will stretch the spring 10 cm
natulia [17]

Answer:

<h2>16kg</h2>

Step-by-step explanation:

 This problem is borers on elasticity of materials.

according to Hooke's law,<em> "provided the elastic limit of an elastic material is not exceeded the the extension e is directly proportional to the applied force."</em>

F= ke

where F is the applied force in N

          k is the spring constant N/m

          e is the extension in meters

Given data

mass m= 24kg

extensnion=15cm in meters= \frac{15}{100}= 0.15m

we can solve for the spring constant k

we also know that the force F = mg

assuming g=9.81m/s^{2}

therefore

24*9.81=k*0.15\\235.44=k*0.15\\k=\frac{235.44}{0.15} \\k=1569.6N/m\\

We can use this value of k to solve for the mass that will cause an extension of  10cm= 0.1m

x*9.81=1569.6*0.1\\\\x= \frac{156.96}{9.81} \\\x= 16kg

5 0
3 years ago
Brianna is getting materials for a chemistry experiment.her teacher give her a container that has 0.15 liter of a liquid in it .
Yanka [14]
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7 0
3 years ago
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A skydiver's speed during a free fall
Alekssandra [29.7K]

Answer:

Below in bold.

Step-by-step explanation:

1. 165/3.3 = 50 meters/second.

2. In 4 seconds the skydiver will fall 4*50 = 200 meters.

5 0
2 years ago
After 8 points are added to each score in a sample, the mean is found to be M= 40. What was the value for the original mean
MArishka [77]

Answer:

The value for the original mean = 32

Step-by-step explanation:

Here, we want to calculate the original value of the mean.

Let the number of samples be n

Mathematically;

mean = Total value/n

Now, we added 8 to each of values; total value added = 8 * n = 8n

Now, for the new mean of 40; we have

(Total value + 8n)/n = 40

Total value + 8n = 40n

Total value = 40n -8n

Total value = 32n

kindly recall from the beginning of the solution;

mean = Total value/n

mean = 32n/n

mean = 32

So the original value of the mean is 32

6 0
3 years ago
Consider polynomial function f(x)=(x-1)^2(x+3)^3 (+1) Use the equation to complete each statement about this function.
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Answer:

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