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statuscvo [17]
2 years ago
13

Write a formula for function g in terms of function h.

Mathematics
1 answer:
viva [34]2 years ago
4 0

Answer:

  • g(x) = h(x + 7) + 5

Step-by-step explanation:

Compare the corresponding points, the best is vertices

  • y = h(x) ⇒ (- 2, - 7)
  • y = g(x) ⇒ (5, - 2)

Find the difference of coordinates, the rule of translation right and up

  • x = 5 - (-2) = 7
  • y = - 2 - (- 7) = 5

<u>The formula of g(x) in therms of h(x) is:</u>

  • g(x) = h(x + 7) + 5
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Can y = sin(t2) be a solution on an interval containing t = 0 of an equation y + p(t) y + q(t) y = 0 with continuous coefficient
JulsSmile [24]

Answer:

Step-by-step explanation:

y = sin(t^2)

y' = 2tcos(t^2)

y'' = 2cos(t^2) - 4t^2sin(t^2)

so the equation become

2cos(t^2) - 4t^2sin(t^2) + p(t)(2tcos(t^2)) + q(t)sin(t^2) = 0

when t=0, above eqution is 2. That is, there does not exist the solution. so y can not be a solution on I containing t=0.

7 0
2 years ago
43.
aleksklad [387]

Answer:

4.12 kg

Step-by-step explanation:

Regular cakes:

1 dozen normal sponge cakes: 264 g plain flour

Vegetarian cakes:

1 dozen cakes: 264 g plain flour

4 eggs are replaced by 4 * 30 g of flour = 120 g flour

total flour for 1 dozen vegetarian cakes = 264 g + 120 g = 384 g

Proportion for regular cakes:

12 cakes to 264 g flour = 100 cakes to x grams flour

12/264 = 100/x

12x = 26400

x = 2200

2200 g flour for 100 regular cakes

Proportion for vegetarian cakes:

12 cakes to 384 g flour = 60 cakes to y grams flour

12/384 = 60/y

12y = 384 * 60

12y = 23040

y = 1920

1920 g flour for 60 vegetarian cakes

Total flour needed:

2200 g + 1920 g = 4120 g

4120 g * 1 kg/(1000 g) = 4.12 kg

Answer: 4.12 kg

4 0
3 years ago
Look at the picture and answer question <br> Quick and simple respond pls
gogolik [260]

Answer:

It is not a good model because neither point lies on the line.

Step-by-step explanation:

We can test each point on the equation of the line.

7x - 10y = 3

Point: (8, 5)

7(8) - 10(5) = 56 - 50 = 6

The left side equals 6, not 3, so point (8, 5) is not on that line.

Point: (-12, -9)

7(-12) - 10(-9) = -84 + 90 = 6

The left side equals 6 again, but the right side is 3, not 6.

Answer: It is not a good model because neither point lies on the line.

6 0
2 years ago
How to solve this trigonometric equation cos3x + sin5x = 0
mrs_skeptik [129]

Answer:

  x = {nπ -π/4, (4nπ -π)/16}

Step-by-step explanation:

It can be helpful to make use of the identities for angle sums and differences to rewrite the sum:

  cos(3x) +sin(5x) = cos(4x -x) +sin(4x +x)

  = cos(4x)cos(x) +sin(4x)sin(x) +sin(4x)cos(x) +cos(4x)sin(x)

  = sin(x)(sin(4x) +cos(4x)) +cos(x)(sin(4x) +cos(4x))

  = (sin(x) +cos(x))·(sin(4x) +cos(4x))

Each of the sums in this product is of the same form, so each can be simplified using the identity ...

  sin(x) +cos(x) = √2·sin(x +π/4)

Then the given equation can be rewritten as ...

  cos(3x) +sin(5x) = 0

  2·sin(x +π/4)·sin(4x +π/4) = 0

Of course sin(x) = 0 for x = n·π, so these factors are zero when ...

  sin(x +π/4) = 0   ⇒   x = nπ -π/4

  sin(4x +π/4) = 0   ⇒   x = (nπ -π/4)/4 = (4nπ -π)/16

The solutions are ...

  x ∈ {(n-1)π/4, (4n-1)π/16} . . . . . for any integer n

5 0
2 years ago
Help!!! Just those two, please
Lunna [17]

A. Multiply the area of the original store by the percent increase then add that to the original amount.

1200 x 0.75 = 900

1200 + 900 = 2100

Answer: 2,100 square feet.

B. 2000 x 0.30 = 600

2000 + 600 = $2,600

2600 x 0.05 = 130

2600 + 130 = 2,730

Rent :$2,730

4 0
2 years ago
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