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inessss [21]
3 years ago
11

if

6" align="absmiddle" class="latex-formula"> were shifted 7 units to the right and 3 down, what would be the new equation.
Mathematics
1 answer:
Elan Coil [88]3 years ago
6 0
Answer: h(x) = (2x - 14)^2 - 19

This will take the vertex from (0,-16), the original equation, to (7,-19), the new equation. This demonstrates the x-value increasing by 7, moving right on the coordinate plane, as well as the y-value decreasing by -3, going down on the coordinate plane.
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D is the midpoint of CE. If CD= 2x+10 and DE =3x-18, find x and CE<br><br> x=<br> CE=
Veseljchak [2.6K]

Answer:

<h2>x = 28</h2><h2>CE = 132</h2><h2 />

Step-by-step explanation:

|<------------- CE -------------------->|

C-------------------D-------------------E

       2x + 10              3x - 18

2x + 10 = 3x - 18

2x - 3x = -18 - 10

-x = -28

x = 28

CE = 2x + 10 + 3x - 18

CE = 2(28) + 10 + 3(28) - 18

CE = 56 + 10 + 84 - 18

CE = 132

3 0
3 years ago
In a single growing season at the smith family orchard, the average yield per apple tree is 150 apples when the number of trees
Mariana [72]

Answer:

100 trees should be planted per acre to maximize the total yield (15000 apples per acre)

Step-by-step explanation:

<u>Functions </u>

Expressing some quantities in terms of other(s) comes in handy to understand the behavior of the situations often modeled by those functions.

Our problem tells us about the smith family orchard, where the average yield per apple tree is 150 apples when the number of trees per acre is 100 (or less). But the average yield per tree decreases when more than 100 trees are planted. The rate of decrease is 1 for each additional tree is planted

Let's call x the number of trees planted per acre in a single growing season. We have two conditions when modeling:  when x is less than 100, the average yield per apple tree (Ay) is (fixed) 150.

Ay(x)=150\ ,\ x\leqslant 100

When x is more than 100:

Ay(x)=150-x\ ,\ 100< x\leqslant 150

The upper limit is 150 because it would mean the Average yield is zero and no apples are to be harvested

Part 1

We are asked what happens if the number of trees per acre was doubled, but we don't know what the original number was. Let's make it x=60

If x=60, then we must use the first function, and

Ay(60)=150

The yield per acre will be 150*60=9000 apples

If we doubled x to 120, we would have to use the second function

Ay(120)=150-x=30

The yield per acre will be 30*120=3600 apples

Note that doubling the number of trees would make the production decrease

If we started with x=30, then  

Ay(30)=150, and we would have 150*30=4500 apples per acre

We already know that for x=60 (the double of 30), our production will be 9000 apples per acre

This shows us that in some cases, increasing the number of trees is beneficial and in other cases, it is not

Part 2

The total yield is computed as

Y(x)=x.Ay(x)

This function will be different depending on the value of x

Y(x)=150x\ ,\ x\leqslant 100

Y(x)=150x-x^2\ ,\ 100< x\leqslant 150

To find the maximum total yield we take the first derivative

Y'(x)=150\ ,\ x\leqslant 100

Y'(x)=150-2x\ ,\ 100< x\leqslant 150

The first expression has no variable, so the total yield must be evaluated in the endpoints

Y(0)=0

Y(100)=15000

Now, the second expression contains variable, it will be set to 0 to find the critical point

150-2x=0

x=75

x is outside of the boundaries, we cannot find the maximum in this interval

Answer: 100 trees should be planted per acre to maximize the total yield (15000 apples per acre)

7 0
3 years ago
40 + (12) (27) + 18=
antiseptic1488 [7]

Answer:

Hey there!

40+12(27)+18

40+324+18

364+18

382

Let me know if this helps :)

6 0
3 years ago
Read 2 more answers
A square pyramid has a height of 6 units and a volume of 70 units3. if a square prism has the same base area and volume as the s
goldfiish [28.3K]

The height of the square pyramid exists 2 units.

<h3>How to estimate the area of the base of the square pyramid?</h3>

Volume of the square pyramid

$V = \frac{1}{3}BH

where B exists in the area of the base  H lives at the height of the pyramid

we have H = 6 $$unit^3

V = 70 $$unit^3

substitute in the formula and solve for B, we get

$70 = \frac{1}{3}B(6)

B = $\frac{70}{2}

= 35 $$unit^3

To estimate the height of the square prism

Volume of the square prism = Bh

Where B exists the area of the base

h exists the height of the prism

we have B = 35 and V = 70

substitute in the formula and solve for h

70 = (35)h

h = 2 units.

To learn more about square pyramid refer to:

brainly.com/question/16024003

#SPJ4

6 0
1 year ago
Read 2 more answers
A line goes through the points (8,9) and (2,4).
Nadusha1986 [10]
9-4/8-2
5/6
The slope is 5/6
y-4=5/6(x-2)
y-4=5/6x-5/3
y=5/6x+7/3
The equation of line in point-slope is y - 4 = 5/6(x - 2)
The equation of the line in slope-intercept is y = 5/6x + 7/3
4 0
3 years ago
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