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Solnce55 [7]
3 years ago
14

Evaluate 2d + 3 when d = 8

Mathematics
1 answer:
vlada-n [284]3 years ago
7 0

Answer:

19

Step-by-step explanation:

2d+3

=2(8)+3

2*8

=16+3

=19

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An architect built a scale model of a sports stadium using a scale in which 2 inches represents 30 feet. The height of the sport
bija089 [108]
The height of the model in inches would be 6. if you multiply 30 until it reaches 180 you will have 6.
7 0
2 years ago
Find the equation of a parabola with a focus at (0,-1) and a directrix at y = 4.
Anastasy [175]

Answer:

  y = -1/10x^2 +2.5

Step-by-step explanation:

The distance from focus to directrix is twice the distance from focus to vertex. The focus-directrix distance is the difference in y-values:

  -1 -4 = -5

So, the distance from focus to vertex is p = -5/2 = -2.5. This places the focus 2.5 units below the vertex. Then the vertex is at (h, k) = (0, -1) +(0, 2.5) = (0, 1.5).

The scale factor of the parabola is 1/(4p) = 1/(4(-2.5)) = -1/10. Then the equation of the parabola is ...

  y = (1/(4p))(x -h) +k

  y = -1/10x^2 +2.5

_____

You can check the graph by making sure the focus and directrix are the same distance from the parabola everywhere. Of course, if the vertex is halfway between focus and directrix, the distances are the same there. Another point that is usually easy to check is the point on the parabola that is even with the focus. It should be as far from the focus as it is from the directrix. In this parabola, the focus is 5 units from the directrix, and we see the points on the parabola at y=-1 are 5 units from the focus.

5 0
3 years ago
Emily wants to watch her intake of fat per day.
AfilCa [17]

Answer:

One variable equation that is (4800/x) represents percentage of Emily's dinner fat intake compared to total daily allowance of x gram.

Step-by-step explanation:

lets assume the variable for total daily allowance

lets say total daily allowance of fat = x grams

Fat consumed at dinner = 48 grams

Fat consumed at dinner in percentage = (Fat consumed at dinner/total daily allowance of fat) × 100

= (48 grams/x grams)×100=(4800/x)%

so (4800/x)%  

So one variable equation that is (4800/x) represents percentage of Emily's dinner fat intake compared to total daily allowance of x gram.

lets take one example

lets says total daily allowance of fat for Emily = 100gm

so from derived equation that is 4800/x , we can get required percentage by putting x =  total daily allowance of fat = 100gm

=4800/100 = 48%.

you can change value of variable x according to total daily allowance and get the required dinner intake percentage by equation 4800/x.


6 0
3 years ago
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mel-nik [20]

Answer:

y=5/1 - 3

Step-by-step explanation:

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8 0
2 years ago
Find an equation of a line that is tangent to the graph of f and parallel to the given line. Please see picture
ivanzaharov [21]

Answer:

y = 3x - 2 (smaller y-intercept)

y = 3x + 2 (larger y-intercept)

Step-by-step explanation:

First let's write the generic equation of a line:

y = ax + b

This line needs to be parallel to the line 3x - y + 5 = 0, so it needs to have the same slope of this line.

The line 3x - y + 5 = 0 has a slope of 3, so our line has a = 3:

y = 3x + b

Now we need to find the values of b that make this line tangent to the function f(x) = x^3

Let's first find the derivative of f(x) in relation to x:

df(x)/dx = 3x^2

This derivative is the slope of the tangent line to the function for any value of x. We need a slope of 3, so:

3x^2 = 3

x^2 = 1

x = ±1

Now, to find the y-values, we have:

f(1) = 1^3 = 1

f(-1) = (-1)^3 = -1

So, using the points (1,1) and (-1,-1) in our parallel line, we have:

first line using (1,1) : 1 = 3*1 + b

b = -2

second line using (-1,-1) : -1 = -3*1 + b

b = 2

The value of b is the y-intercept of the line, so the line with smaller y-intercept is y = 3x - 2, and the line with larger y-intercept is y = 3x + 2

8 0
3 years ago
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