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shtirl [24]
9 months ago
15

If the range of the function y = f(x) is {y | y ≥ 11, y ∈ R}, then the range of the new function g(x) = f(x + 2) - 3 is

Mathematics
1 answer:
mafiozo [28]9 months ago
3 0

Answer:

y ≥ 8

Explanation:

Note that if f(x) is transformed into f(x + a) - b

The original functions is shifted a units to the left and b units downward.

Horizontal shifting will not affect the range of the function, only vertical shifting will change its range.

From the given, g(x) is the transformation of f(x) with

g(x)=f(x+2)-3_{}

f(x) is shifted 2 units to the left and 3 units downward, we will disregard the horizontal shifting.

Since f(x) has a range of y ≥ 11, and g(x) is 3 units downward, the range will also move 3 units downward.

y ≥ 11 - 3

The answer is y ≥ 8

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0.5

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Help ..<br><br><br><br> 3(x+2)=5x+1-2x+5
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Answer:

All real numbers are solutions

Step-by-step explanation:

Let's solve your equation step-by-step

3(x+2)=5x+1−2x+5

Step 1: Simplify both sides of the equation

3(x+2)=5x+1−2x+5

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3x+6=3x+6

3x+6=3x+6

Step 2: Subtract 3x from both sides

3x+6−3x=3x+6−3x

6=6

Step 3: Subtract 6 from both sides

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8 0
2 years ago
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2 years ago
From a boat ont he lake, the angle of elevation to the top of a cliff is 11° 50'. If the base of the cliff is 1568 feet from the
Marizza181 [45]

Answer:

328 feet

Step-by-step explanation:

From a boat ont he lake, the angle of elevation to the top of a cliff is 11° 50'. If the base of the cliff is 1568 feet from the boat, how high is the cliff (to the nearest foot)

Step 1

Note that

that 11°50' is just 11 degrees and 50 minutes

60 minutes = 1 degree,

thus 50 minutes = x degree

50/60 degrees

= 0.83°

Hence: 11°50' = 11.83°.

Step 2

We solve using Trigonometric function of tan

tan theta = Opposite/Adjacent

theta = 11.83°

Adjacent = 1568 feet

Opposite = Height of the cliff = x

tan 11.83° = x/1568

Cross Multiply

x = tan 11.83 × 1568

x = 328.429195 feet

Approximately = 328 feet

The height of the cliff is 328 feet

8 0
3 years ago
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