use properties of logarithms to condense logc Yc X
(x^2+ 6x + 9) / (x-3)
Answer:
Simplify:
[tex]\frac{( {x}^{2} + 6x + 9) }{x - 3} [/tex]
Factoring:
[tex] {x}^{2} + 6x + 9[/tex]
The first term is, x2 its coefficient is 1 .
The middle term is, +6x its coefficient is 6 .
The last term, "the constant", is +9
Step-1 : Multiply the coefficient of the first term by the constant 1 • 9 = 9
Step-2 : Find two factors of 9 whose sum equals the coefficient of the middle term, which is 6 .
-9 + -1 = -10
-3 + -3 = -6
-1 + -9 = -10
1 + 9 = 10
3 + 3 = 6 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 3 and 3
[tex] {x}^{2} + 3x + 3x + 9[/tex]
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x+3)
Add up the last 2 terms, pulling out common factors :
3 • (x+3)
Step-5 : Add up the four terms of step 4 :
(x+3) • (x+3)
Which is the desired factorization.
Multiply (x+3) by (x+3)
The rule says : To multiply exponential expressions which have the same base, add up their exponents.
In our case, the common base is (x+3) and the exponents are :
1 , as (x+3) is the same number as [tex](x+3) {}^{1}[/tex]
and 1 , as (x+3) is the same number as[tex](x + 3) {}^{1} [/tex]
The product is therefore, [tex](x + 3) {}^{(1 + 1)} = (x + 3) {}^{2} [/tex]
Events A and B are disjoint. Find P(AorB) when P(A) = 0.55 and P(B) = 0.2
P (A or B)=
Answer:
0.75 = P(A or B)
Step-by-step explanation:
Since the events are disjoint, we can find the probability of one or the other occurring merely by adding P(A) and P(B): 0.55 + 0.2 = 0.75 = P(A or B)
As Sandra drives, her music player randomly selects music from her playlist. Sandra’s playlist contains:
3 traditional country songs
6 traditional rock songs
4 hip-hop rap songs
5 contemporary country songs'
1 Latin rap song
3 traditional pop songs
What is the probability that the player will select some rap music next?
Answer:
the probability will be 18.18%
(3x+8)(x+4)
Expand and simplify
Answer:
Step-by-step explanation:
(3x+8)(x+4), distribute 3x over the second parenthesis first and then the 8
3x² + 12x + 8x + 32 , combine like terms
3x² + 20x + 32
Answer:
3x^2 + 20x + 32
Step-by-step explanation:
Distribute 3x over the second parenthesis first and then the 8.
#CarryOnLearning
What is the length of the radius of a circle if the equation for the circle is (x + 2)2 + (y - 9)2 = 22.09?
Answer:
The radius is 4.7 units.
Step-by-step explanation:
To answer this we need only find the square root of 22.09: 4.7
The radius is 4.7 units.
The number of ways to choose three different pizza toppings from a group of six is called a ?
Answer:
Uh, 16.
Step-by-step explanation:
We need to choose three different toppings. So here we need to find the number of ways in which we can choose three different toppings out off. 16. So a number of ways are takes three at a time, from a total of 16. That is civilians combination. Here are formula for combination is 16 factorial over three factorial into 16 minus three. Factorial this candidate and a 16 factorial over three factorial into 16 minus trees. 13. Authority in factorial, now 16. Factory converted on a 16 in 2 15 into 14 into 13. Factorial over three factorial into 30. In fact, a real as we can see that 13 factorial is common toward denominator and numerator so we can get through this. Now I remaining times are 16 into 15 into 14. Over three in Toto into one has three factories, three in tow, one So calculating this ticket. Find 60 Soviet 56 TVs to select three different topics. Talked to select three different toppings out off 16 on a bizarre
(b+3)(b+7) FOIL method
Step-by-step explanation:
(b + 3)(b + 7) = ...
= b² + (3 + 7)b + (3•7)
= b² + 10b + 21
PLEASE HURRY THIS IS TIMED !!!!
Answer:
c
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
you could give away 70 coffee mugs without charging anything.
If you charge $10.00, nobody will buy the coffee mugs. You also figured out that your sales will be decreasing
following straight line. Your job is to find the maximum possible revenue from selling the coffee mugs.
Answer the following questions:
1. Graph the linear relationship between the price of coffee mugs p, and the number of coffee mugs sold S.
Hint: To give away 70 coffee mugs means when the price p=0, S(0) = 70. Plot that point on the graph. Find one
more point using the other given condition. Keep in mind S(p) is a linear function. Be careful what will be
represented on the x-axis, and what will be represented on the y-axis.
2. Find the equation of the linear function S(p) that describes the quantity sold as a function of the price p.
3. The revenue is determined by R = Sp. Express the revenue as a function of the price p.
Help: You may look at the examples from the power point for section 2.6
4. Graph the revenue function. Make sure to label the x - and the y - axis with the appropriate units.
5. At which price per coffee mug do you not make any money?
6. Find the price per coffee mug that makes the most revenue.
7. How many coffee mugs must be sold to maximize the revenue?
8. What is the maximum revenue?
9. What price per coffee mug you should charge to collect at least $70 in revenue?
Your project will be graded based on the following:
1. Turned in a hard copy, and an electronic version as a PDF file on Blackboard on time (due date Dec 7
or before ) (5pts. deduction per day)
2. Completeness (no missing part, show all of your work, calculations, formulas used etc.
3. Precision ( correct answers )
4. Complete graph
the graph has a title
the axes are labeled ( make sure you have included the units of measurement)
-
At $ 10 per mug you will not get any money; the maximum possible revenue is $ 175, which will be obtained by selling the mugs for $ 5; and to get at least $ 70 in revenue the mugs must be sold for $ 2.
Since you could give away 70 coffee mugs without charging anything, and if you charge $ 10.00, nobody will buy the coffee mugs, and you also figured out that your sales will be decreasing following straight line, and your job is to find the maximum possible revenue from selling the coffee mugs, to determine at which price per coffee mug do you not make any money; the price per coffee mug that makes the most revenue; how many coffee mugs must be sold to maximize the revenue; what is the maximum revenue; and what price per coffee mug you should charge to collect at least $ 70 in revenue; the following calculations must be performed:
70 = 0 0 = 10 35 = 5 63 x 1 = 63 56 x 2 = 112 49 x 3 = 147 42 x 4 = 168 35 x 5 = 175 28 x 6 = 168
Therefore, at $ 10 per mug you will not get any money; the maximum possible revenue is $ 175, which will be obtained by selling the mugs for $ 5; and to get at least $ 70 in revenue the mugs must be sold for $ 2.
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What is an equation in point-slope form for the line that passes through the points (4,-1) and (-3,4)?
y-3= (x+4)
y–4= (x+3)
y+4= (x+3)
y+4= (x+3)
The diagram below shows how the tables and chairs are arranged in the school cafeteria. A table seats 3 people and the tables can be pushed together. When two tables come together, 4 people can sit around the table. Complete this table to show the relationship between the number of tables, n, and the number of students, S, who can sit around the table.
Answer:
well in theory on tabe has to be smaller so I guess the number of people in all is 4 and the difference between the tables are size
What is the inverse of the function f(x) =√x-2
Louise spins the spinner twice. Which probabilities are correct? Check all that apply.
Write the equation of the line in point-slope form that has slope 3 and passes through (2, -5).
Answer:
y+5=3(x-2).
Step-by-step explanation:
1) according to the condition m=3; x₁=2; y₁= -5, then
2) the required equation is y+5=3(x-2).
In the figure, lines j and k intersect to form the
angles shown. What is the measurements of angle 1
The graph f(x)=(x+2)^2-7is translated 5 units left, resulting in the graph g(x). Which equation represents the new function, g(x)?
Answer: G(x)=(x-3)^2-7
Step-by-step explanation: Translated 5 units to the left is a negative change and a change in the X axis
The equation represents the new function, g(x) will be G(x)=(x-3)²-7. The correct option is A.
What is translation?The process of changing the location of the image on the coordinate system will be known as the translation. A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.
It is given that the graph f(x)=(x+2)²-7 is translated as 5 units left, resulting in the graph g(x).
Translated 5 units to the left are a negative change and a change in the X axis. The graph is also attached with the answer below.
The equation represents the new function, g(x) will be G(x)=(x-3)²-7.
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#SPJ5
please need help answering this
9514 1404 393
Answer:
2
Step-by-step explanation:
Between the points at (x, y) = (-5, 4) and (-4, 6), the graph rises 2 units for a horizontal run of 1 unit. The average rate of change between the two points is ...
m = rise/run = 2/1 = 2
The average rate of change on the interval [-5, -4] is 2.
40
X
5. A health-food business would like to create a high-potassium blend of dried fruit in the form
of a box of fruit bars. It decides to use dried apricots, which have 407 mg of potassium per
serving, and dried dates, which have 271 mg of potassium per serving.
4
y
The company can purchase its fruit through www.driedfruitbaskets.com in bulk for a
reasonable price. Dried apricots cost $3.33/serving and dried dates cost $2/serving. The company
would like the box of bars to have at least the recommended daily potassium intake of about
4700 mg, but would like to keep it under twice the recommended daily intake. In order to
minimize cost, how many servings of each dried fruit should go into the box of bars?
5
Objective Function:
Constraints:
Corner Points & Answer:
Thus, the values corresponding to the function and constraints will be:
Objective Function:[tex]C=3.33X+2.00Y[/tex]
Constraints:[tex]407X+271Y\geq 4700\\407X+271Y\leq 9400[/tex]
We begin by defining the variables. Let call:
X = of servings of dried apricots
Y= of servings of dried dates
For apricots, there are 3 servings in one pound. This means that the cost per serving is $9.99/3 = $3.33. The cost for X:
[tex]3.33X[/tex]
For dates, there are 4 servings per pound. This means that the cost per serving is $7.99/4=$2.00. The cost for Y:
[tex]2.00Y[/tex]
The total cost would be:
[tex]C=3.33X+2.00Y[/tex]
Product must contain at least 4700mg of potassium
[tex]407X+271Y\geq 4700\\407X+271Y\leq 9400[/tex]
So now with the equations set it is possible to see that the desired values are between 9400 and 4700. Then using the critical points X=0, Y=0 for the two given equations. This will inform the points of interest for X and Y if this analysis is needed for the exercise.
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what slope is parallel to m = 3/4
Answer:
3/4
Step-by-step explanation:
For lines to be parallel, only their y-intercepts have to be different.
Answer:
3/4
Step-by-step explanation:
Ricardo camina 2 km
en 2 hora. ¿Cuántos
minutos tardará si
DESCANSO
A 2KM
camina 12 km?
The time it will take ricardo to walk 12km is 12 hours
If Ricardo walks 2 km in 2 hours, the speed of Ricardo is expressed as:
Speed = Distance/Time
Speed = 2km/2hr
Distance = 1km/hr
To find the time it will take to walk 12km, we will use the same formula:
Time = Distance/Speed
Time = 12km/1km/hr
Time = 12hours
Hence the time it will take ricardo to walk 12km is 12 hours
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The weight of a full steel bead tire is approximately 800 grams, while a lighter wheel weighs only 700 grams. What is the weight of each tire in pounds? There are 453.592 grams in one pound. Round answers to 2 decimal places.
800 grams = (How many?)
pounds
700 grams = (How many?)
pounds
Answer:
Here they are unrounded
800 grams = 1.7637
700 grams = 1.54324
Step-by-step explanation:
Hope this helps
Keith wants to buy an IPad for $500. He wants to earn enough money delivering pizzas to cover at least two-fifths of the cost.
Part A.
If he earns $12.50 per hour at work, write an inequality that represents how many hours Keith's needs to work
Part B
Solve your inequality? Justify your answer.
Answer:
Step-by-step explanation:
500 / 5 = 100 (that's 1 fifth, so 2 fifths will be 200)
200 / 12.5 = 16 (he will have to work 16 hours to get $200)
the inequality would be:
x * 12.5 >= 500 * 0.4 (something like that)
Two of the angles in a triangle measure 154° and 20°. What is the measure of the third angle?
Answer:
6°
Step-by-step explanation:
The angles in a triangle always add up to 180°. Let’s call the third angle x. That means that:
154 + 20 + x = 180 ->
174 + x = 180 ->
x = 180 - 174 ->
x = 6°
Hope that help! :)
Help?????????????????
Answer:
the first option is the answer
Step-by-step explanation:
"15 is always equal to the product of a number and 5" translates to a mathematical equation.
O True
O False
Answer:
This is True
Step-by-step explanation:
I know this because it is like dividing you just divide 15 by 5 and the it will be equal
What is the quotient of 4/5÷1/3
The quotient of a division, is the result of the division, for example, 3 divided by 3, the result is 1, that is the quotient.
[tex]\sf \displaystyle \sf \frac{4}{\:5}\div \frac{1}{3}\\\\\\\sf \frac{4}{5}\times \frac{3}{1}\\\\\\\sf \frac{4\times \:3}{5\times \:1}\\\\\\\sf \frac{12}{5\times \:1}\\\\\\\sf \frac{12}{5}\approx\boxed{\sf 2,2\ll Quotient}[/tex]
Okay?!A car's value depreciates by 18% in its first year and is now worth £6789.
What was the original price of the car?
Answer:
£8279.27
Step-by-step explanation:
The given relationship is ...
(original price) × (1 - 18%) = £6789
Dividing by the coefficient of the original price, we find it to be ...
original price = £6789/0.82 = £8279.27
The original price of the car was £8279.27.
Which number line represents the solution set for the inequality 3(8 – 4x) < 6(x - 5)?
-
o
-5
-4
-3
-1
0
1
2
3
4
5
f
.
-5
-4
-3
-2.
-1
o
3
o
1
2
4
5
+
+
-4
-5
-3
-2
-1
+
1
o
+
2.
+
3
+
4
5
Ол
O
3
-5
-4
-3
-2
-1
o
1
2.
3
4
5
Answer:
3 8-4× less than 6 ×-5 and then you solve the equation
Jack and Jill, trying to do math and chill, when they ran into a problem. They can't agree on what the answers should be, so now it's up to you to solve them.
In class, Jack thought as Jill she sought solve an absolute value... she removed the sign from her negative nine and said "the problem should be just about through".
But Jack he said, "no Jill you misread, the negative is on the outside". Still Jill didn't budge, so you be the judge, does this mean that the teacher lied?
Here's the problem Jack and Jill are trying to solve: -|9| = ?Jack thinks the answer is -9, because the negative is outside the absolute value signs. Jill thinks the answer is 9, because the teacher said absolute value is always positive.
Who is right and why? Explain your steps using sentences.
Answer:
-9
Step-by-step explanation:
the teacher was right