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3 years ago

(03.04) For the function f(x) = (x − 2)2 + 4, identify the vertex, domain, and range.

Mathematics

1 answer:

aleksklad [387]3 years ago

8 0

Vertex: (2,4)
domain: all real numbers
range: y is greater than or equal to 4

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The amount in kilograms, a, of a radioactive element that remains after t hours can be modeled by the equation a= 0.65(0.92)to t

elena-14-01-66 [18.8K]

Answer:

The rate of decrease is 8%

Step-by-step explanation:

we know that

The general equation for the radioactive decay can be written as:

$a=a_0(1-r)^t$

where

a is the amount in kilograms after time t.

a_0 is the original amount of the substance or y-intercept of the function

r is the decay rate, written in decimals.

t is the time

In this problem we have

$a=0.65(0.92)^t$

$a_0=0.65\\(1-r)=0.92$

solve for r

$r=1-0.92=0.08$

Convert to percentage

$0.08(100)=8\%$

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3 years ago

Factor the expression completely. 625x4 - 256y4

scoundrel [369]

Answer:

(625 • (x4)) - 28y4

54x4 - 28y4 3.1 Factoring: 625x4-256y4

Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)

Proof : (A+B) • (A-B) =

A2 - AB + BA - B2 =

A2 - AB + AB - B2 =

A2 - B2Note : AB = BA is the commutative property of multiplication.

Note : - AB + AB equals zero and is therefore eliminated from the expression.

Check : 625 is the square of 25

Check : 256 is the square of 16

Check : x4 is the square of x2

Check : y4 is the square of y2

Factorization is : (25x2 + 16y2) • (25x2 - 16y2) 3.2 Factoring: 25x2 - 16y2

Check : 25 is the square of 5

Check : 16 is the square of 4

Check : x2 is the square of x1

Check : y2 is the square of y1

Factorization is : (5x + 4y) • (5x - 4y)this is the answer: (25x2 + 16y2) •(5x + 4y) • (5x - 4y)

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3 years ago

In simplest racial form what are the solutions to the quadratic equation 0= -3x-4x+5

givi [52]

Answer:

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

Johnny spend 1/7 of his income on Food, 1/10 of his income on gas, and 3/8 of his income on rent. What percentage of his income

Agata [3.3K]

Answer:

38.2%

Step-by-step explanation:

1/7 ≈ 14.29%

1/10 = 10.00%

3/8 = 37.50%

The total that Johnny has allocated for food, gas, and rent is ...

14.29% + 10.00% + 37.50% = 61.79%

So, the remaining amount is ...

100% -61.79% = 38.21%

About 38.2% of Johnny's income remains.

7 0

3 years ago

Please help me with #4 (10 points )

myrzilka [38]

Answer:

40 feet

Step-by-step explanation:

We are given a right isosceles triangle having lengths of two sides 12 feet and 16 feet.

Since, the triangle is an isosceles triangle i.e. two sides of the triangle are equal.

That is, the three sides of the triangle are 12 feet, 12 feet and 16 feet.

We know that, Perimeter of a triangle = Sum of the sides

Thus, Perimeter of the given triangle = 12 + 12 + 16 = 24 + 16 = 40 feet.

Hence, the total length of the fencing needed is 40 feet.

8 0

3 years ago