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aev [14]
3 years ago
11

The steps in writing f(x) = 18x + 3x2 in vertex form are shown, but a value is missing in the last step. Write the function in s

tandard form. f(x) = 3x2 + 18x Factor a out of the first two terms. f(x) = 3(x2 + 6x) Form a perfect square trinomial. f(x) = 3(x2 + 6x + 9) – 3(9) Write the trinomial as a binomial squared. f(x) = 3(x + ______)2 – 27 What is the missing value in the last step?
Mathematics
2 answers:
zimovet [89]3 years ago
8 0

the answer would be 3

vaieri [72.5K]3 years ago
7 0
<span>y = 3x² + 18x

factor out the leading coefficient
y = 3(x²+6x)

Complete the square
 coefficient of the x term: 6
 divide it in half: 3
 square it: 3²
 use 3² to complete the square:
y = 3(x²+6x + 3²) - 3·3²
 = 3(x+3)² - 3·3²
 = 3(x+3)² - 27
vertex (-3, -27)</span>
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The perimeter of a triangle is 57 centimeters. The longest side is 3 ​centimeter(s) less than the sum of the other two sides. Tw
Setler79 [48]
Let's say x is longest side, y is shortest side and z is the other side. So we have some equations such that

x+y+z=57 (by the first sentence)

x=(y+z) -3 (by the second sentence)

2y=x-15  (by the third sentence)

By the second equation, we have y+z=x+3 and if we use it in the first equation, then x+y+z=x+(x+3)=57. So x=27

Since x=27, if we use it in the third equation the we have 2y=x-15=27-15=12 then y=6

Therefore z=24


5 0
3 years ago
70.63 + 4.7 (show ur work take a pic)
Lisa [10]

Answer:

75.33

Step-by-step explanation:

70.63

<u>+4.7     </u>

75.33

4 0
2 years ago
Read 2 more answers
At the beginning of an environmental study, a forest covered an area of 1500 km. Since then, this area has decreased by 7.25% ea
WITCHER [35]

\qquad \textit{Amount for Exponential Decay} \\\\ y=P(1 - r)^t\qquad \begin{cases} y=\textit{current amount}\\ P=\textit{initial amount}\dotfill &1500\\ r=rate\to 7.25\%\to \frac{7.25}{100}\dotfill &0.0725\\ t=\textit{elapsed time}\dotfill &t\\ \end{cases} \\\\\\ y=1500(1-0.0725)^t\implies y=1500(0.9275)^t

5 0
2 years ago
Amma hikes 2and3/4 miles of nature trail in 1 hour and 15 minutes. How many miles does Amman hike per hour?
LekaFEV [45]
Formula
====
d = r * t

Givens
======
d = 2 3/4
t = 1 hour 15 minutes 
r = ????

Calculations
==========
You need to convert the 15 minutes to hours.
1 hour = 60 minutes
x hour = 15 minutes

1/60 = x/15
x = 15/60
x = 0.25 hours
so the time = 1 hours + 0.25 hours
t = 1.25 hours

Now you need to do something with the distance.
3/4 mile = 0.75 of a mile
So the distance = 2 + 0.75 = 2.75 miles

Now you are ready for the answer.
d = r * t you are looking for r
2.75 = r * 1.25
r = 2.75/1.25
r = 2.2 miles / hour

Note you could do this with fractions.
2 3/4 = 11/4
1 1/4 =  5/4

r = 11/4 // 5/4 =11/5 = 2 1/5 which is the same thing as 2.2. If your calculator can handle fractions (those kind of calculators cost about 10 dollars in Canada. It should be 8 in the US) that might be the way to do this problem.
6 0
3 years ago
Which set or ordered pairs represents y as a unction Or X!
Zepler [3.9K]

A relation is said to be a function when every element in the domain has one and only one distinct image in the co- domain.

In the first three options , one single element in domain has more than one image.

(-2,3), (-2, 2), (-2, 1), (-2, 0)

here -2 as an element in the domain has 3,2,1,0 has image-----> so not a function

(10, 15), (5, 1), (10, 6), (6, 10)

Here 10 , an element in the domain has 15,6 as image-----> so not a function

(-11, 2), (3,8), (3, 2), (2, 2)

Here 3, as an element in the domain has 8 and 2 as image-----> so not a function

So, OPTION D

(1,6), (2, 5), (10, 5), (-17, 8)

7 0
2 years ago
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