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3 years ago

What is the vertex f(x)= 5x^2+20x-16

1 answer:

3 0

F(x) = 5x² + 20x - 16

y = 5(x² + 4x) - 16
y + 16 = 5(x² + 4x + __)

perfect square:
x² ⇒ x * x
4x ⇒ 2*2x
2² = 4

y + 16 + 4 = 5(x² + 4x + 4)
y + 20 = 5(x+2)²

(x+2)² ⇒ (x+2)(x+2) = x(x+2) + 2(x+2) = x² + 2x + 2x + 4 = x² + 4x + 4

y = 5(x+2)² - 20

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3 less than one fourth of a number

Margaret [11]

Answer:

one fourth a number minus three

¼x-3

5 0

3 years ago

Special Triangles

Ugo [173]

Answer:

see explanation

Step-by-step explanation:

Using the cosine and tangent trigonometric ratios and the exact values

cos30° = $\frac{\sqrt{3} }{2}$ and tan30° = $\frac{1}{\sqrt{3} }$ , then

cos30° = $\frac{adjacent}{hypotenuse}$ = $\frac{6}{m}$ = $\frac{\sqrt{3} }{2}$ ( cross- multiply )

$\sqrt{3}$ × m = 12 ( divide both sides by $\sqrt{3}$ )

m = $\frac{12}{\sqrt{3} }$ ← rationalise by multiplying numerator/ denominator by $\sqrt{3}$ )

m = $\frac{12}{\sqrt{3} }$ × $\frac{\sqrt{3} }{\sqrt{3} }$ = $\frac{12\sqrt{3} }{3}$ = 4 $\sqrt{3}$

-------------------------------------------------------------------------------

tan30° = $\frac{opposite}{adjacent}$ = $\frac{n}{6}$ = $\frac{1}{\sqrt{3} }$ ( cross- multiply )

$\sqrt{3}$ × n = 6 ( divide both sides by $\sqrt{3}$ )

n = $\frac{6}{\sqrt{3} }$ ← rationalise the denominator

n = $\frac{6}{\sqrt{3} }$ × $\frac{\sqrt{3} }{\sqrt{3} }$ = $\frac{6\sqrt{3} }{3}$ = 2 $\sqrt{3}$

-----------------------------------------------------------------------------------

7 0

3 years ago

The first three terms of a Fibonacci sequence are n 3n 4n find the sixth term I FB the sequence

Amiraneli [1.4K]

Answer:

Step-by-step explanation:

In the Fibonacci sequence In mathematics, the Fibonacci numbers, commonly denoted $Fn$ , form a sequence, called the Fibonacci sequence, such that each number is the sum of the two preceding ones, starting from 0 and 1.

Given data

First term= n

second term = 3n

third term = 4n

According to Fibonacci sequence the fourth term is

$F4= F2 + F3\\F4=3n+ 4n= 7n$

the Fifth term is

$F5= f3 + f4\\f5= 4n+7n= 11n$

hence the sixth term is

$F6= F4+F5\\ F6= 7n+11n= 18n$

3 0

4 years ago

What is the length of side AB of parallelogram ABCD? units 4g - 8 B q+4

Andrews [41]

Answer:

8 units

Step-by-step explanation:

» Concepts

Parallelogram Side Theorem states that the opposite sides of a parallelogram are congruent, meaning they have the same length.

» Application

In this case, we're asked to apply the theorem to find the value of q and then find the length of AB. Thus, we have to set up the equation 4q - 8 = q + 4.

» Solving

Step 1: Subtract q from both sides.

$4q-8-q=q+4-q$
$3q-8=4$

Step 2: Add 8 to both sides.

$3q-8+8=4+8$
$3q=12$

Step 3: Divide both sides by 3.

$3q/3 = 12/3$
$q=4$

Step 4: Plug in the value of q for side AB.

$4(4)-8$
$16-8$
$8$

Therefore, the answer is 8 units.

6 0

2 years ago

Hi everyone can someone help me out with this question please

luda_lava [24]

A) After any given year the amount of money would be: [(1000*.04)x]+1000
and x stands for the number of years.
B) The interest is 4%.
C) There would be $3,480.00 after 4 years.

5 0

3 years ago