Answer:
The missing value in last step is 3
Step-by-step explanation:
Given the function f(x)
[tex]f(x)=18x+3x^2[/tex]
Here some steps are given to write the above function in vertex form.
Step 1: Factor a out of the first two terms
[tex]f(x)=3(x^2+6x)[/tex]
Step 2: Form a perfect square trinomial.
[tex]f(x) = 3(x^2 + 6x + 9) - 3(9)[/tex]
Write the trinomial as a binomial squared.
By the identity of binomial square
[tex]a^2+2ab+b^2=(a+b)^2[/tex]
[tex]x^2 + 6x + 9=x^2+2(x)(3)+3^2[/tex]
[tex]\text{Put a=x and b=3 in the identity, we get}[/tex]
[tex]x^2+2(x)(3)+3^2=(x+3)^2[/tex]
[tex]x^2 + 6x + 9=(x+3)^2[/tex]
Hence, the f(x) can be written as
[tex]f(x) = 3(x+3)^2 - 3(9)[/tex]
Therefore, the missing value in last step is 3
In the set of real numbers, the first number less than -3 is -4.
True
False
Could someone help with 14 I know it’s not a Consecutive interior but it could be A) alternate interior B) alternate exterior C) corresponding D) exterior
A student has selected 8 books that she likes, but she has money only for 3 books. how many possible selections does she have?
HELP ME PLEASE
Olga deposited $1500 in a savings account that pays 7.5% interest compounded quarterly. What is the balance in her account at the beginning of the third quarter?
A. $1,590
B. $1,560
C. $1,585.97
D. $1,591.81
ok let me make one thing clear: i have put up questions like this before but i am NOT TRYING TO JUST GET ANSWERS. I legit want to learn this. It is just hard for me i guess.. so sorry if this answer seems simple to you but its not to me so if you could please explain your answer CLEARLY, in particular with "compound quarterly." please explain so i can use the principles later on. Thank you!
What is the inverse of the conditional statement “If a number is divisible by 6, then it is divisible by 3”?
I need help finding v
Kristin is 20 miles behind a truck that is driving 50 miles per hour. How long will it take her to catch up to the truck? How far will she go in that time
It will take Kristin 24 minutes to catch up to the truck. She will travel a distance of 20 miles in that time.
Explanation:To calculate how long it will take for Kristin to catch up to the truck, we can use the equation: time = distance / speed. Since Kristin is 20 miles behind the truck, she will need to cover a distance of 20 miles to catch up to the truck. Assuming she drives at a constant speed, we can use her speed as the truck's speed since she needs to match it to catch up.
Time to catch up = 20 miles / 50 miles per hour = 0.4 hours = 24 minutes.
In that time, Kristin will travel the same distance as the truck. So, she will go 20 miles in 24 minutes.
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You are paid $82.50 for 7 1/2 hours of work. What is your rate of pay?
Katherine owns the trendy boutique where Clara works as a shop assistant. Deanne loves the clothes in Katherine's boutique and shops there often. Which of these three people is a consumer?
Answer:
Deanne
Step-by-step explanation:
Deanne is a consumer
How many ways are there to distribute six different toys to three different children such that each child gets at least one toy?
What is the number in scientific notation? 409,200,000,000
A car travels 83 7/10 miles on 2 1/4 gallons of fuel. Which is the best estimate of the number of miles the car travels on one gallon of fuel
round miles up to 84
round gallons down to 2
and divide
84 /2 = 42 miles per gallon ( estimate)
How to find the measure of an exterior angle given the measure of the interior angle?
true or false circumference is the distance around the outside of a circle.
PLEASE HELP!!!
1. The coordinates of the vertices of triangle ABC are A(-1,3), B(1,2) and C(-3,-1).
Determine the slope of each side of the triangle and use that information to determine if the triangle is a right triangle or not.
2.The coordinates of the vertices of quadrilateral JKLM are J(-3,2), K(4,-1), L(2,-5) and M(-5,-2).
Find the slope of each side of the quadrilateral and determine if the quadrilateral is a parallelogram
If you're going 80 miles per hour how long does it take to go 80 miles answer
If one candy bar weighs 3 ounces what is the weight of 11 candy bars
Final answer:
The weight of 11 candy bars is calculated by multiplying the weight of one candy bar, which is 3 ounces, by 11. The total weight for 11 candies is equal to 33 ounces.
Explanation:
If one candy bar weighs 3 ounces, the weight of 11 candy bars can be found by multiplying the weight of one candy bar by the number of candy bars. The calculation would be as follows:
Multiply the weight of one candy bar by the number of candy bars: 3 ounces × 11 = 33 ounces.
Therefore, the weight of 11 candy bars is equal to 33 ounces.
A train fare costs £23.55
All train fares are increased by 2.8%
Work out the new fare.
[2 marks]
Answer.......
4 A savings account pays 3.6% per annum simple interest.
Heidi puts £400 into the account.
How much will she have in the account after 5 years?
[2 marks]
Answer .............
5 In one week the mass of a puppy increases from 1.8 kg to 2.25 kg
Work out the percentage increase of the mass.
[2 marks]
Answer............
To calculate an increase, multiply the original value by the percentage increase. For simple interest, use the formula Interest = Principal * Rate * Time. Percentage increase in mass can be found with the formula: [(Final mass - Initial mass) / Initial mass] * 100%. These methods result in a new train fare of £24.21, a bank balance after 5 years of £472, and a 25% increase in the puppy's mass.
Explanation:1. To work out the new fare, we first need to calculate how much the fare has increased by. 2.8% of £23.55 is found by multiplying 23.55 by 0.028, which comes out to £0.66 (rounded to the nearest penny). Adding this increase to the original fare gives us a new fare of £24.21.
2. The simple interest can be calculated using the formula Interest = Principal * Rate * Time. In this case, Heidi's investment of £400 (the principal) is earning 3.6% (the rate) in interest every year for 5 years (the time). So, the interest Heidi earns equals £400 * 3.6% * 5 = £72. Adding this to the original amount gives us £472.
3. The percentage increase in the puppy's mass is calculated as follows: [(2.25 kg - 1.8 kg) / 1.8 kg] * 100%. So, the mass has increased by 25%.
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Evaluate the expression when =m6 m2-18
Help me with this please
Given B = {a, l, g, e, b, r} and C = {m, y, t, h}, find B ∪ C
Find the simple interest on a loan of $3,500 at 7.8% interest for 9 months
Rewrite the expression as a polynomial in standard form.
The expression (2x² - x³ - 9x + 1) - (x³ + 7x - 3x² + 1) can be rewritten in standard form as -2x³ + 5x² - 16x
How did we get the value?To rewrite the expression (2x² - x³ - 9x + 1) - (x³ + 7x - 3x² + 1) as a polynomial in standard form, we can combine like terms.
First, let's distribute the negative sign in front of the parentheses:
(2x² - x³ - 9x + 1) - x³ - 7x + 3x² - 1
Next, let's group the like terms together:
2x² + 3x² - x³ - x³ - 9x - 7x + 1 - 1
Now, let's combine the terms:
(2x² + 3x²) + (-x³ - x³) + (-9x - 7x) + (1 - 1)
5x² - 2x³ - 16x + 0
Finally, the expression (2x² - x³ - 9x + 1) - (x³ + 7x - 3x² + 1) can be rewritten in standard form as:
-2x³ + 5x² - 16x
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If you study hard, then you can pass the tests.
If you pass the tests, then you can pass the class.
What conclusion can be draw from the statements above?
A) Studying hard will allow you to pass the class.
B) Only students who pass tests study hard.
C) If you have passed the class, you must not have studied very hard.
D) Not passing tests means that you did not study.
Answer:
A) Studying hard will allow you to pass the class.
Problem page the sum of two numbers is 56 . the smaller number is 16 less than the larger number. what are the numbers?
which fraction is less than 7/15
A: 5/9
B: 6/11
C: 1/2
D: 4/9
A 14.5-gallon gasoline tank is 3 — 4 full. how many gallons will it take to fi ll the tank?
It would take 3.625 gallons of gasoline to fill a 14.5-gallon tank that is already 3/4 full.
Explanation:The question asks how many gallons of gasoline are needed to fill a 14.5-gallon tank that is already 3/4 full. To find the amount needed to fill the tank, we first determine how much gasoline is currently in the tank by multiplying 14.5 gallons by 3/4:
14.5 gallons × 3/4 = 10.875 gallons
This means that there are 10.875 gallons of gasoline in the tank at the moment. To find out how much more gasoline is needed to fill the tank, we subtract this amount from the tank's total capacity:
14.5 gallons - 10.875 gallons = 3.625 gallons
Therefore, it would take 3.625 gallons of gasoline to fill the tank.
Each of my daughters has as many brothers as sisters, but each of my sons has three times as many sisters as brothers. How many children do I have?
The family has 3 sons and 3 daughters, for a total of 6 children.
Explanation:
The question is a problem in basic algebra which can be solved using simple logical reasoning. We are given that each daughter in the family has as many brothers as sisters, and each son has three times as many sisters as brothers.
Let's start by saying that the number of daughters is D and the number of sons is S.
If each daughter has the same number of brothers as sisters, that means D = S. But, each son has three times as many sisters as brothers, which we can express as S = 3*(D - 1), because the number of sisters for each son is the number of daughters minus one (each son doesn't count himself as a sister).
By substituting D from the first equation into the second, we get S = 3 * (S - 1), which simplifies to S = 3, and thus D = 3 as well.
So, the family has 3 sons and 3 daughters, for a total of 6 children.
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Using the speaking outline, how many times should you practice? five or more three two one
According to the speaking outline, it is recommended to practice your speech at least five times or more.
According to the speaking outline, you should practice your speech "five or more" times. Practicing your speech multiple times helps you become more familiar with the content, improve your delivery, and gain confidence in your presentation. The more you practice, the better prepared you'll be to deliver a successful speech.
Therefore, it is recommended to practice your speech at least five times or more.
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According to the speaking outline, it is recommended to practice your speech at least five times or more.
According to the speaking outline, you should practice your speech "five or more" times.
Practicing your speech multiple times helps you become more familiar with the content, improve your delivery, and gain confidence in your presentation.
The more you practice, the better prepared you'll be to deliver a successful speech.
Therefore, it is recommended to practice your speech at least five times or more.
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if x^2+14x-95=(x+a)(x+b), then the numerical value for ab is