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sergey [27]
3 years ago
9

The distance a spring will stretch varies directly with how much weight is attached to the spring. If a spring stretches 5 inche

s with 50 pounds attached, how far will it stretch with 170 pounds attached?
Mathematics
1 answer:
Step2247 [10]3 years ago
5 0
There is a few ways to do this but I am going to use the variation equation.

Variation Equation:
y = kx
First we need to find k, which is the constant of variation
5 = k50
5/50 = k
1/10 = k
k= 1/10

Now that we have found the constant of variation, we can find how much the spring will stretch with 170 pounds.
y = kx
y = (1/10) times 170 = 17 inches

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The graph shows the dilation of quadrilateral MNOP with the origin as its center. Which rule describes this transformation?
lana66690 [7]

Answer:

D) (x, y) → (1/3x , 1/3 y)

Step-by-step explanation:

A dilation is a change of size, if the dilation factor is greater than 1, then the figure is enlarged.  If the dilation factor is smaller than 1, the figure is shrinked.  In both cases, the coordinates are MULTIPLIED by the dilation factor.

Among the 4 choices, only 2 are dilations.  One is with a dilation factor of 3 (A), which means the shape was enlarged.  And the other is with  dilation factor of 1/3, meaning the shape was shrinked.

Since we went from MNOP (LARGE one) to M'N'O'P' (small one), the dilation factor was < 1... so 1/3 is the answer.

Answers B and  C show a translation/movement of the shape, not a dilation.

8 0
3 years ago
What property is shown in this equation? (2 X 1/2) + 8 = 1+8
Julli [10]
The property shown in the following equation is 9 beacause simply we know 9=1 +8 so its easy
5 0
3 years ago
Seven times a number plus the number is 24. what is the number​
katrin2010 [14]

Answer:

x=3 is the number

Step-by-step explanation:

Suppose number be "x".

Equation will be

7x + x = 24

8x = 24

x = 24/8

x = 3

5 0
3 years ago
Read 2 more answers
The coordinates of LMN are L (4,5), M (5,-2), and N (0,0). If the triangle is rotated 270° about point N, what are the coordinat
tester [92]

Answer: (-2,-5)

Step-by-step explanation:

The rotation rule for rotating a figure about 270^{\circ} is given by :-

(x,y)\to (y,-x) , where (x,y) is the coordinates for pre-image and (y,-x) is the coordinates for image.       (1)

Given : The coordinates of LMN are L (4,5), M (5,-2), and N (0,0).

If the triangle is rotated 270° about point N

Then, the coordinates of M , will be :

(5,-2)\to (-2,-5)   (Using the rule described in (1))

Hence, the coordinates of M after rotated 270° about point N=(-2,-5).

8 0
3 years ago
The graph below shows the height of a tunnel f(x), in feet, depending on the distance from one side of the tunnel x, in feet:
denis23 [38]
Part A) x-intercepts simply show that when the value of the function is zero. Vertex coordinates show that when the function obtains its maximum value. When x=50, function obtains its maximum value and it's 75. The function is increasing in the interval (0, 50) and decreasing in the interval (50, 100). In regard to the height and distance of the tunnel, these numbers show that decreasing and increasing intervals are symmetric. Each number from the intervals has its own pair in the corresponding interval and they are located in the same distance from the midpoint (50,75)

Part B) In order to calculate the average rate of change, we can first write the function. Using the information about the x-intercept and the vertex coordinates, we find that our function is f(x)=-0.03x^{2}+3x.
Plugging 15 and 35 in x, we can find the values of the function, i.e. 
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Then, the average change is \frac{68.25-38.25}{35-15}=1.5
4 0
3 years ago
Read 2 more answers
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