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3 years ago

Convert to vertex form: f(x) = x2 + 16x + 64

Mathematics

1 answer:

GuDViN [60]3 years ago

7 0

Answer:

Step-by-step explanation:

hello :

note : the vertex form is :

ax²+bx+c = a(x+(b)/(2a))²- delta/4a² and delta = b²- 4ac

in this exercice you have : a =1 b = 16 and c=64

continu ..........

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Triangle ABC has perimeter 22cm

ASHA 777 [7]

9514 1404 393

Answer:

not a right triangle

Step-by-step explanation:

The perimeter is 22, so we have ...

AB +BC +CA = 22

8 + 5 + CA = 22

CA = 22 -13 = 9

If this is a right triangle, the sum of the squares of the short sides will be equal to the square of the long side.

AB² +BC² = 8² +5² = 64 +25 = 89

This is not the same as ...

CA² = 9² = 81

The triangle is not a right triangle.

_____

<em>Additional comment</em>

If you're familiar with a few Pythagorean triples, you know that a couple involving a side length 5 are (3, 4, 5) and (5, 12, 13). That is, (5, 8, 9) is NOT a Pythagorean triple, so you know immediately that those side lengths do not form a right triangle. (No calculation is necessary.)

6 0

3 years ago

If f(x)=-5x +2 and g(x)=1/2x +4, find f(g(-6)).

ss7ja [257]

Answer:

-3

Step-by-step explanation:

Set up the composite function and simplify.

8 0

3 years ago

Every chemical element goes through natural exponential decay, which means that over time its atoms fall apart. The speed of eac

Lesechka [4]

Answer:

$Q(t) = 800e^{-0.0495t}$

Step-by-step explanation:

The amount of the isotope after t seconds is given by the following exponential equation:

$Q(t) = Q(0)e^{-rt}$

In which Q(0) is the initial amount and r is the decay rate.

A sample of beryllium-11 was first measured to have 800 atoms.

This means that $Q(0) = 800$

The half-life of the isotope beryllium-11 is 14 seconds.

This means that $Q(14) = 0.5Q(0)$

We use this to find r.

$Q(t) = Q(0)e^{-rt}$

$0.5Q(0) = Q(0)e^{-14r}$

$e^{-14r} = 0.5$

$\ln{e^{-14r}} = \ln{0.5}$

$-14r = \ln{0.5}$

$r = -\frac{\ln{0.5}}{14}$

$r = 0.0495$

$Q(t) = Q(0)e^{-rt}$

$Q(t) = 800e^{-0.0495t}$

8 0

4 years ago

EASY POINTS!!!!!

expeople1 [14]

Answer:

15 - 4 = 11

Step-by-step explanation:

that's literally all it is-

7 0

3 years ago

5/16 ÷ 5/12

harkovskaia [24]

Answer:

1.) 3/4

2.) 44/5 or 8 4/5

3.) 17/6 or 2 5/6

Step-by-step explanation:

1.) 5/16 ÷ 5/12

To divide a fraction by another fraction, reciprocate (put the numerator to denominator and vice versa) the divisor then change the sign to multiplication:

5/16 × 12/5

5 × 12 / 16 × 5

Cancel out 5 since both numerator and denominator has it:

12 / 16

Divide both by 4:

12 ÷ 4 / 16 ÷ 4

3/4

2.) 3 1/5 • 2 3/4

You have to convert the fractions first to improper fractions by multiplying the denominator to the whole number then adding the numerator to the product:

3 1/5 = 3×5 + 1 = 16/5

2 3/4 = 2 × 4 + 3 = 11/4

Now you can multiply the numerator to numerator then denominator to denominator:

Since 16 is a factor of 4, you can cancel it out, which leaves 4:

16 / 5 × 11/4

4 × 11 / 5 × 1

44/ 5

3.) 6 3/8 ÷ 2 1/4

Convert to improper fraction:

6 3/8 = 6× 8 + 3 = 51/8

2 1/4 = 4 × 2 + 1 = 9/4

(51 × 4)/ (9×8)

51 × 1/ 9× 2

51 / 18

Divide by 3:

17/6

4 0

4 years ago