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3 years ago

Given the function f(x)= 3(x-2)² + 5, what is f(-1)?

Mathematics

2 answers:

motikmotik3 years ago

5 0

Answer:

Step-by-step explanation:

f(x)= 3(x-2)² + 5

Let x = -1

f(-1)= 3(-1-2)² + 5

Parentheses first

f(-1) = 3(-3)^2 +5

Exponents

f(-1)= 3*9 + 5

Multiply

f(-1) = 27+5

Add

f(-1) = 32

Anna11 [10]3 years ago

5 0

Answer: 32

=3(-1-2)^2+5
=3(-3)^2+5
=3•3^2+5
=3^3+5
=27+5
=32

Explanation: Plug in -1 for x in the function and solve.

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Each sequence below gives an explicit formula. Write the first five terms of each sequence. Then, write a recursive

Bas_tet [7]

Answer:

The first five values are 12, 14, 16, 18 and 20

The recursive formula is as follow

$\left \{ {{a_{1} =12} \atop {a_{n} =a_{n-1} } + 2} \right.$

Step-by-step explanation:

Since we need to find the first 5 values we start with n = 1 to n = 5. Note that we don't start from n = 0 as the question states that n ≥ 1.

For the first 5 values we just replace the value of n with 1, 2, 3, 4 and 5 and calculate the answer

$a_{1} = 2(1) + 10 = 12\\ a_{2} = 2(2) + 10 = 14\\ a_{3} = 2(3) + 10 = 16\\ a_{4} = 2(4) + 10 = 18\\ a_{5} = 2(5) + 10 = 20$

The first five values are 12, 14, 16, 18 and 20

A recursive formula is one that

a) Mentions the initial term

b) provides a formula connecting the previous term to the existing term.

Since we know the first term is 12, i.e $a_{1} = 12$ and we know that the difference between consecutive terms is 2 we can conclude that the recursive formula is made up of the following two formulas

$a_{1} = 12$

$a_{n} = a_{n-1} + 2$

The over all formula is as follow

$\left \{ {{a_{1} =12} \atop {a_{n} =a_{n-1} } + 2} \right.$

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3 years ago

An art academy requires there to be 3 teachers for every 60 students 4 tutors for every 48 student how many students does the ac

vfiekz [6]

Answer:

per teacher = 20 students

per tutor = 12 students

72 students = 18 tutors

Step-by-step explanation:

Divide 60 by 3 to get 20

Divide 48 by 4 to get 12

Divide 72 by 4 to get 18

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4 years ago

Find the area of the shaded region?<br> 3x + 1<br> 3x + 1

mash [69]

Im pretty sure its 3x + 1

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3 years ago

How do you do this question?

madam [21]

Answer:

Step-by-step explanation:

A left Riemann sum approximates a definite integral as:

$\int\limits^b_a {f(x)} \, dx \approx \sum\limits_{k=1}^{n}f(x_{k}) \Delta x \\where\ \Delta x = \frac{b-a}{n} \ and\ x_{k}=a+\Delta x \times (k-1)$

Here, the integral is ∫₀² 9ˣ dx, and the number of subintervals is n = 4.

So Δx = 2/n = 1/2, and x = 2(k−1)/n = (k−1)/2.

Plugging in:

∑₁⁴ 9^((k−1)/2) (1/2)

1/2 ∑₁⁴ 9^((k−1)/2)

1/2 (9^((1−1)/2) + 9^((2−1)/2) + 9^((3−1)/2) + 9^((4−1)/2))

1/2 (9^(0) + 9^(1/2) + 9^(1) + 9^(3/2))

1/2 (1 + 3 + 9 + 27)

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3 years ago

Determine the reading of the scale of the following instrument

Zanzabum

Answer: is there suppose to be a pictured inserted?

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3 years ago