Please help
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 standard 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?
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
what is the true hourly wage of a job that pays $18 per hour and allows 20 hours of paid time off for every 500 hours worked ? show your work
The true hourly wage of a job is:
$ 18.72 per hour
Step-by-step explanation:The pay per hour is: $ 18
Also, it is given that: The job allows 20 hours of paid time off for every 500 hours worked.
This means he will be paid for 520 hours of work
but the true hourly wage will be calculated on the basis of 500 hours.
The wage for 520 hours of work will be: $ (18×520)= $ 9360
and the true hourly wage is:
Ratio of wage for 520 hours to 500 hours
i.e.
[tex]=\dfrac{9360}{500}\\\\\\=\dfrac{936}{50}\\\\=\$\ 18.72\ \text{per\ hour}[/tex]
Which of the following elements is the most reactive?
Chlorine
Bromine
Fluorine
Helium
Solve for n.
3(n+6)≥3n+8
no solution
all real numbers
n≥7
n≥23
Answer:
The correct option is B) all real numbers.
Step-by-step explanation:
Consider the provided inequity.
[tex]3(n+6)\geq 3n+8[/tex]
We need to solve the inequity for n.
[tex]3(n+6)\geq 3n+8[/tex]
[tex]3n+18\geq 3n+8[/tex]
Subtract 3n from both sides
[tex]3n-3n+18\geq 3n-3n+8[/tex]
[tex]18\geq 8[/tex]
Which is true for any real number. As 18 is greater than 8.
Hence, the value of n is all real numbers.
Thus the correct option is B) all real numbers.
Write the equation of a line in slope intercept form that goes through the point (-2,10 with a slope of -3
If a+bi is a zero of a function and the coefficients of the polynomial are real, what will be the other complex zero of the function?
1. -a + bi
2. a - bi
3. -a - bi
4. a
There were 67 candles on grandmas bBirthday cake and 26 left in the box how many candles birthda birthday cake and 26 left in the box how many candles were there in all
To find the total number of candles, you have to add the number of candles on your grandma's birthday cake, which are 67, to the number of candles left in the box, which are 26. This brings the total to 93 candles.
Explanation:The question involves a mathematical process known as addition. In this situation, you have 67 candles on your grandma's birthday cake and 26 more in a box. To find the total number of candles, you simply need to add the number of candles on the cake to the number of candles in the box.
So, 67 (candles on the cake) + 26 (candles in the box) = 93 candles in total. Hence, you have 93 candles in all.
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What conversion factor fraction is used to convert inches to feet?
Answer:
C
Step-by-step explanation:
Notice that on C 24:2, 48:4 72:6, etc
Which value is equivalent to the problem in the pic?
If, P(x,y) is a point on the unit circle determined by real number δ, then tanδ = what
What is the area of the rectangle?
The mass of the sun is about 2x10^27 metric tons or 2x10^30 kilograms. How many kilograms are in one metric ton
simplify 7-(-12)-5
a -10
b 0
c 14
d 24
Two tourists went on a hike at dawn. One went from a to b and another one went from b to a. They met at noon but did not stop and continued walking maintaining same speed for the whole trip. One finished his hike at 4pm in B and another one came to A at 9 pm. At what hour was dawn that day?
What are the roots of the quadratic equation 0 = 2x^2 + 12x –14?
2, 12, –14
–7, 1
–1, 7
1, 6, –7
Can you explain what it is wanting or asking?
Answer:
-7, 1
Step-by-step explanation:
Given quadratic equation,
[tex]2x^2+12x-14=0[/tex]
By middle term splitting,
[tex]2x^2+(14-2)x-14=0[/tex]
[tex]2x^2+14x-2x-14=0[/tex]
[tex]2x(x+7)-2(x+7)=0[/tex]
[tex](2x-2)(x+7)=0[/tex]
By the zero product property,
[tex]2x-2=0\text{ or }x+7=0[/tex]
[tex]\implies x=1\text{ or }x=-7[/tex]
Hence, the roots of the given equation are -7 and 1.
Second option is correct.
There are three consecutive odd integers whose sum is 159. what are the three numbers?
By graphing the system of constraints, find the values of x and y that maximize the objective function. x+y<=11 2y=>x x=>0 y=>0 maximum for p=3x+2y a. p=10 1/3 b. p=7 1/3 c. p=21 d. p=29 1/3
Find the measure of an angle whose measure is 18 degrees less than one-half of the measure of its complement.Find the measure of an angle whose measure is 18 degrees less than one-half of the measure of its complement.
The measure of the angle in question is 18 degrees, as found by setting up an equation based on the relationship between an angle and its complement, and solving for the angle.
To find the measure of an angle that is 18 degrees less than one-half of the measure of its complement, first let's define the angle as x. Since the angle and its complement add up to 90 degrees, the complement is 90 - x. The given information tells us that x is 18 degrees less than half of its complement. Therefore, we can set up the equation:
x = (1/2)(90 - x) - 18
Doubling both sides gives:
2x = 90 - x - 36
Adding x to both sides and adding 36 to both sides gives:
3x = 54
Dividing by 3, we find that:
x = 18 degrees.
Therefore, the measure of the angle is 18 degrees.
Which biconditional statement is true?
A. A number is divisible by 9 if and only if it ends in 3.
B. A quadrilateral is a square if and only if it has four right angles.
C. The sum of two integers is positive if and only if the two integers are positive.
D. A number is an even number if and only if it is divisible by 2
Among the given options, the true biconditional statement is Option D: A number is an even number if and only if it is divisible by 2. This matches the true nature of a biconditional statement where both parts must have the same truth value.
The question posed is concerned with identifying the true biconditional statement among the given options. A biconditional statement is true if and only if both parts have the same truth value. We'll examine each option carefully.
Option A: A number is divisible by 9 if and only if it ends in 3. This statement is false because divisibility by 9 depends on the sum of the digits of the number, not just the last digit.Option B: A quadrilateral is a square if and only if it has four right angles. This statement is not entirely true because a rectangle also has four right angles but is not necessarily a square.Option C: The sum of two integers is positive if and only if the two integers are positive. This is false because the sum can also be positive if one integer is sufficiently larger than the negative of the other one.Option D: A number is an even number if and only if it is divisible by 2. This is a true biconditional statement. A number is considered even if it can be divided by 2 without leaving a remainder (with both having the same truth value).After reviewing the options, the correct answer is Option D.
Can I get some help on these please ?
Which of the following is the coefficient in the algebraic expression 22y3 + z
Answer:
Step-by-step explanation:
the Coefficient is 22 because its attached to the variable Y
You have a $50 bill. you and your friend ordered two cheeseburgers for $4.25 each, two fries for $1.28 each, and two colas for $1.98 each. including 4% sales tax and 15% tip, what is the change you will receive from $50?
Answer: 32.13
Step-by-step explanation:
Answer:
The answer is: $32.13
What is the value of x?
Enter your answer in the box.
Answer:
x = 9 and y = 5
Step-by-step explanation:
From the given figure :
In ΔLNM ,
LN = NM = LM
This shows that all the sides of the triangle are given to be equal.
And the triangle whose all sides are equal is called equilateral triangle and in an equilateral triangle the measure of its each angle is 60°
⇒ ∠L = ∠N = ∠M = 60°
Now, ∠N = 60°
⇒ 7x - 3 = 60
⇒ 7x = 63
⇒ x = 9
Also, ∠M = 60°
⇒ 11y + 5 = 60
⇒ 11y = 55
⇒ y = 5
Answer: x=9
Step-by-step explanation:
i did the test and got it right lol
in need some help this question please answer all my point on the line
Please Help:
Simplify. √3/10 (The square root of 3 over 10)
The simplified value of the number √3/10 will be 3/√30.
What is mean by Fraction?
A fraction is a part of whole number, and a way to split up a number into equal parts.
Or, A number which is expressed as a quotient is called fraction.
It can be written as the form of p : q, which is equivalent to p / q.
Given that;
The number is,
⇒ √3/10
Now,
Simplify the number as;
⇒ √3/10 = √3/10 x √3/3
= 3 / √30
Thus, The simplified value of the number √3/10 will be 3/√30.
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1. solve j/5=5/125.
a) 1/25
b) 1/5
c) 5
d) 25
2. state the x and y-intercepts of y=-4x-7.
a) x= -7, y= -7/4
b) x= -4, y= -7
c) x= -7/4, y= -7
d) x= -7, y= -4
3. solve b=6/13y + 12 for y.
a) y= 13/6 b-26
b) y= -6/13 b+15
c) y= -13/6b+26
d) y= 6/13 b-15
A camera manufacturer spends $2,000 each day for overhead expenses plus $9 per camera for labor and materials. The cameras sell for $17 each. a. How many cameras must the company sell in one day to equal its daily costs? b. If the manufacturer can increase production by 50 cameras per day, what would their daily profit be?
250; $400
118; $656
170; $240
250; $850
17x = 2000+9x
8x = 2000
x = 2000/8 = 250 cameras
250+50 = 300
17*50 = 850
9*50 = 450
850-450 = 400
Answer: 250, 400
Which is a graph of f(x)=4(1/2)x
In this exercise we have to be aware of the type of graph we have and identify its formula, like this:
The second graph
As it is a graph of the equation of an exponential, we have that its form is given by:
[tex]y=ab^x[/tex]
Where:
y-intercept/starting point b is the value x exponentially grows or decays.Calculating the value of X when Y is equal to 1, we have:
[tex]1=4(0.5)^x \\1/4=(1/2)^x \\log_{0.5}(1/4)=x \\x=2[/tex]
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A country's population in 1993 was 94 million. in 1999 in was 99 million. estimate the population in 2005 using the exponential growth formula. round your answer to the nearest million. P=Ae^kt
Type .00009 using scientific notation.