use the properties of logarithms to expand the following expression as much as possible.
Answers
1. Factor the expression in parenthesis:
[tex]\begin{gathered} 2x^2+8x+8 \\ \\ =2(x^2+4x+4) \\ =2(x+2)\placeholder{⬚}^2 \end{gathered}[/tex]2. Rewrite the expression using the factors above:
[tex]\log_2(2(x+2)\placeholder{⬚}^2)[/tex]3. Use the next properties to expand the expression:
[tex]\begin{gathered} \log_a(x*y)=\log_ax+\log_ay \\ \log_aa=\frac{\log_a}{\log_a}=1 \\ \log_a(b^c)=c*\log_ab \end{gathered}[/tex][tex]\begin{gathered} \log_2(2(x+2)\placeholder{⬚}^2) \\ =\log_22+\log_2((x+2)\placeholder{⬚}^2) \\ =1+2\log_2(x+2) \end{gathered}[/tex]Then, the given expression is equal to:[tex]\log_2(2x^2+8x+8)=1+2\log_2(x+2)[/tex]Related Questions
What is the value of the expression? (10 1/4 +6 1/4) – (3 3/5 - 3 1/2) Enter your answer in the box as a mixed number in simplest form.
Answers
Step-by-step explanation:
Answer: 16 2/5
Step-by-step explanation:
1. 10 1/4+6 1 /4 Turn into a mixed number.
2. 41/4+25/4= 66/4 Simplify by 2= 33/2
Next question
1. 3 3/5 - 3 1/2 Turn into a mixed number
2. 18/5 - 7/2= 1/10 This is its simplest form in fraction.
3. Now that we have our answers, we are now going to subtract them.
4. 33/2- 1/10= 164/10 Simplify = 82/5 Divide it. Your remainder is 2 and our answer is 16 we keep our denominator 5 so we get: 16 2/5
Hope this helps :)
Is this a valid argument?
Given: If I drive over 60 miles an hour, then I am breaking the law.
If I am breaking the law, then I could go to jail.
Conclusion: If I drive over 60 miles an hour, then I could go to jail.
1. No. This is an improper use of the Law of Syllogism
2. No. This is an improper use of the Law of Detachment.
3. Yes. This argument uses the Law of Detachment.
4. Yes. This argument uses the Law of Syllogism.
Answers
Answer:
4. Yes. This argument uses the Law of Syllogism.
Step-by-step explanation:
Law of Syllogism:
Statement 1: If p, then q.
Statement 2: If q, then r.
Statement 3: If p, then r.
p = "If I drive over 60 miles an hour"
q = "I am breaking the law"
r = "I could go to jail"
Using the answer choices provided, complete the proof.
Answers
Since two lines AC and BD intersect at point E
we have proved
∠DEC = ∠AEB
Proof:Given,
The straight line has a 180-degree angle.
The two lines AC and BD intersect at E.
consider AEB : BEC = 9: 11.
If BEC is x, then AEB is 9x / 11 and AEC + BEC
= 180 degree (9 x /11) + x = 180.
9x + 11x = 11 * 180
20x = 11 * 180 x = 99
BEC is 99 degrees and AEB is 81 degrees.
Because angle AED is vertically opposite angle BEC, angle AED = 99 degrees.
Because angle DEC is vertically opposite angle AEB, angle DEC equals 81 degrees.
Hence ∠DEC = ∠AEB.
Hence proved
To learn more about intersecting angles refer to :
https://brainly.com/question/23732231
#SPJ13
square root of negative 108
Answers
We must evaluate the following:
[tex]\sqrt[]{-108}[/tex]We can write the argument of the square root in the following way:
[tex]undefined[/tex]Which pair of radicals is a pair of like radicals?
O 5√6 and 6√5
O 9√2 and -9√/3
O 3√7 and 11√7
O 7√5 and 7√3
Answers
Correct option is C. The pair of radical is 3√7 and 11√7
A number system is what?
A way to express or represent numbers is through the number system.
The Number System includes any of the several sets of symbols and the rules for using them to represent numbers.
From all the pairs,
5√6 and 6√5
9√2 and -9√/3
3√7 and 11√7
7√5 and 7√3
Only 3√7 and 11√7 is a radical as it has same value of under root.
To learn more about radicals from given link
https://brainly.com/question/3253643
#SPJ9
1 + 1
I’ll mark brainliest if explanation included!!
Answers
Answer: 1+1=1
Step-by-step explanation: because just like in multiplication for infinity
1x1 will always equal one and if you flip the x sign it will be a plus sign so 1+1=1
I'm so smart :)
The distance between City A and City B is 200 miles. A length of 1.7 feet represents this distance on a certain wall map. City C and City D are 4.25 feet apart on this map. What is the actual distance between City C and City D?
The actual distance between City C and City D is
Answers
The actual distance between City C and City D is 500 miles .
In the question ,
it is given that ,
the distance of 200 miles between City A and City B is represented by 1.7feet on the map .
the scale factor of map is 1.7 feet = 200 miles
So , 1 feet = 200/1.7 miles
= 117.64 miles
So , on map, 1 feet is 117.64 miles of actual distance .
Given that the distance between City C and City D on the map is 4.25 feet .
So , in actual
4.25 feet = 4.25*117.64
= 499.97
≈ 500
we get , 4.25 feet = 500 miles .
Therefore , The actual distance between City C and City D is 500 miles .
Learn more about Scale Factor here
https://brainly.com/question/4526389
#SPJ1
6) A ferris wheel can accommodate 45 people in 30 minutes. How many peoplecould ride the ferris wheel in 3 hours? What was that rate per hour?
Answers
The ferris well can accomodate 45 people in 30 minutes.
You need to calculate how many people you can accomodate in 3 hours.
To do so the first step is to express the 3 hours in minutes:
You know that 1 hour has 60 minutes, multiply 60 by 3 to determine how many minutes there are in 3 hours:
[tex]60\cdot3=180[/tex]3 hours equal to 180 minutes
Now you can use cross multiplication to determine the number of people that can ride the ferris well in three hours.
30 min_____45 people
180min_____x people
[tex]\begin{gathered} \frac{45}{30}=\frac{x}{180} \\ x=(\frac{45}{30})180 \\ x=270 \end{gathered}[/tex]The ferris well can accomodate 270 persons in 3 hours.
I need the answers to the question
Answers
Given
we have
[tex]P(x)=x^3+2x^2+x+2[/tex]Required
we need to write it in terms of linear factors.
Explanation
Here
[tex]\begin{gathered} P(x)=x^3+2x^2+x+2 \\ =x^2(x+2)+x+2 \\ =(x+2)(x^2+1) \\ =(x+2)(x+i)(x-i) \\ so\text{ }P(x)=(x+2)(x+i)(x-i) \\ so\text{ }P(x)=(x+2)(x+\sqrt{-1})(x-\sqrt{-1}) \\ \end{gathered}[/tex]the answer is (x+2)(x+i)(x-i)
What is the value of 21 + 62 – (35 – 8) • 3?
Answers
Answer:
Step-by-step explanation:
21+62-(35-8)x3
=83−(35−8)(3)
=83−(27)(3)
=83−81
=2
Answer: 56
Step-by-step explanation:
21+62=83 -(36-8) =56
the temperature at jebel jais on a particular winter morning is "-3c" at 5 am . if the temperature drops 2 degree at 6am and rises 7 degree ar 8am and again drops 1 at 9am . what is the temperature at 6am and 9am
Answers
The temperature at jebel jais at 6 a.m. will be -5 °C and the temperature at 9 a.m will be 1 °C.
What is temperature?A temperature is a unit of hotness or coldness that can be described in terms of a variety of arbitrary scales. It also indicates the direction in which heat energy will naturally flow, i.e., from a hotter body to a colder body (one at a lower temperature). Temperature is not the same as the energy of a thermodynamic system; for instance, an iceberg has a considerably higher temperature than a burning match, but it has a far larger total heat energy than a match.
According to the question,
The temperature at 5 a.m = -3 °C
The temperature at drops by 2 °C at 6 a.m = -3°C - 2 °C
The total temperature at 6 a.m = -5 °C
The temperature rises by 7 °C at 8 a.m.
The net temperature by 8 a.m = -5 °C + 7 °C = 2 °C
The temperature drops by 1 °C at 9 a.m.
The net temperature at 9 a.m = 2 °C - 1 °C = 1 °C
Hence, the temperature at 6 a.m is -5 °C and the temperature at 9 a.m is 1 °C.
To get more information about temperature :
https://brainly.com/question/11464844
#SPJ1
9(c-1) + 7c please I need this
Answers
Answer:
16c-9
Step-by-step explanation:
9(c-1)+7c
9c-9+7c
What is the solution set to the equation (2x−4)(4x−5)=0? {5/4,2}{2}{−2,−5/4}{4/5,5/4}
Answers
Since the equation is written as factors, we can equate each factor to zero in order to find the solutions of the equation:
[tex]\begin{gathered} (2x-4)(4x-5)=0\\ \\ \begin{cases}2x-4=0\rightarrow2x=4\rightarrow x=2 \\ 4x-5=0\rightarrow4x=5\rightarrow x=\frac{5}{4}{}\end{cases} \end{gathered}[/tex]The solution set is {5/4, 2}, therefore the correct option is the first one.
Marco needs to buy some cat food. At the nearest store, bags of 2 food cost $9.50 How much would Marco spend on 3 bags of cat food?
Answers
Marco will have to spend $ 14.25 on 3 bags of cat food.
What is an example of a unitary method?A single or distinct unit is referred to by the word unitary. Therefore, the goal of this strategy is to establish values in reference to a single unit. The unitary technique, for instance, can be used to calculate how many kilometers a car will go on one litre of gas if it travels 44 km on two litres of fuel. The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.
Given:
Bags of 2 cat food cost $9.50
Therefore bags of 1 cat food cost $9.50 /2
=$ 4.75
Therefore bags of 3 cat food cost $ 4.75 x 3
= $ 14.25
To learn more about unitary method click on the link below:
https://brainly.com/question/24587372
#SPJ9
14x + 1 = 10x - 19 solve for x
Answers
Answer:
x = -5
Step-by-step explanation:
The image has the explanation.
(Source: Algebra Calculator, MathPapa, I suggest using it.)
Btw, could I get Brainliest? Thanks!
solve for x. A= x-y-6z
Answers
Answer: x = a + y + 6 z
Answer:
x = y + 6z + a
Please:
Please Give Brainlist
A polynomial function has zeros at -4 (multiplicity 3), -1 (multiplicity 8) and 2 (multiplicity 1). Which equation couldrepresent this function?Ax)Ax)A.B.C.D.WSelect one:O a. AO b. Bос. СO d. D
Answers
When a function has a zero with an even multiplicity, there is no sign shift for the function at that zero.
If the zero has odd multiplicity, the function shifts its sign at that point.
Since the function has zeros at -4, -1 and 2, those must be the points where the function touches the X-axis. Options A and C display this feature.
Nevertheless, the only even multiplicity is for the zero x=-1, so the function must have sign shifts at x=-4 and x=2, but no sign shift at x=-1. This is correctly displayed on option C.
Therefore, the graph that correctly represents the described function is that from option C.
I need some help with my math please
Answers
( 31.2u + 0.2 v ) is expression represents the perimeter of rectangle .
What is rectangle short answer?
A rectangle is a sort of quadrilateral with parallel sides that are equal to one another and four vertices that are all 90 degrees apart. Because of this, it is also known as an equiangular quadrilateral. Because the opposite sides of a rectangle are equal and parallel, it can also be referred to as a parallelogram.length of rectangle = ( 7.2u + 9.9v)
width of rectangle = ( 8.4u - 9.8v)
perimeter of rectangle = 2( l + b )
= 2 ( 7.2u + 9.9v + 8.4u - 9.8v )
= 2 ( 7.2u + 8.4u + 9.9v - 9.8v )
= 2 ( 15.6u + 0.1v )
= ( 31.2u + 0.2 v )
Learn more about rectangle
brainly.com/question/15019502
#SPJ13
If the divisor is a decimal then you must multiply by a power of 10 to make it a whole number. Why is it important to multiply the dividend and the divisor by the same power of 10? NEED HELP ASAP WILL GIVE BRAINLIST ALSO NO SAMPLE RESPONSE
Answers
In this example, the number being divided (15) is known as the dividend, and the number being divided by (3 in this instance) is known as the divisor. The quotient is the outcome of the division. Observe how 15 x 3 = 5 is a correct equation even if you change the quotient and divisor.
Explain about the divisor and dividend?The dividend appears to the right, or underneath, the division bracket, while the divisor is the number that appears to the left, or outside, of the division bracket.
An integer that divides another integer to obtain a result is called a divisor. The result of this division, or quotient, is the dividend, which is the original number that was divided. Quotient = Dividend Divisor.
To keep the divisor and dividend in the same proportion to one another, you multiply them by the same power.
This is true for division that is not decimal.
10 / 5 = 2.
Multiplying both sides by ten results in 100/50, which is still two.
If you merely divided by 10, you would get 100/5, which is equal to 20, or 10/50, which is equal to 1/5. Both of these throw off the ratio.
To learn more about divisor and dividend refer to:
https://brainly.com/question/28041197
#SPJ9
Graph the line with slope of 5/3 and goes through the point (2, 1).
Answers
Answer:
Point 1: (2, 1)
Point 2: (5, 6)
Step-by-step explanation:
In order to graph the line, we need to know where to start. Luckily, we have our first point given. (2, 1)
Point 1: (2, 1)
A trick I know to find point 2 is:
1. rise up the y-axis by 5 points then move to the right 3
or
2. (2, 1)
+ (3, 5)
----------
Point 2: (5, 6)
I hope this helps!
Answer:
y= 5/3x + -7/3
Step-by-step explanation:
plug in the values into y-mx+b
1=5/3 (2) + b
solve for b
What is the value of x?
0.2x(4.5-2.5x) = 7.5 +1.7x
Answers
Solve the equation.
x
=
−
4
−
i
√
359
5
,
−
4
+
i
√
359
5
x
=
-
4
-
i
359
5
,
-
4
+
i
359
5
A photo taken with a smartphone has 1,227,104 pixels. A photo taken with a camera has 11,943,936 pixels. Approximately how many times more pixels are in the photo taken with the camera?
Answers
Answer:
about 10 times more
Step-by-step explanation:
I popped it in a calculator and divided the 2 numbers and just rounded to the nearest whole number
whats the same as 2/9
Answers
Answer:4/18
Step-by-step explanation:
someone help me with this, please and thank you!
Answers
1. If two angles form a linear pair, they are supplementary angles.
2. The vertical angle theorem states that vertical angles are equal.
3. The angles are vertical angles.
4. The angles are neither vertical angles nor linear pairs.
5. The angles form a linear pair.
6. The angle ∠2 is equal to 135°.
7. The angle ∠2 is equal to 95°.
8. The angle ∠2 is equal to 150°.
9. The angle ∠3 is congruent to angle ∠1.
10. The angle ∠4 is congruent to angle ∠1.
11. The angle ∠2 is congruent to angle ∠1.
12. The angles ∠1, ∠2, and ∠3 is equal to 30°, 150°, and 30°, respectively.
13. The angles ∠1, ∠2, and ∠3 is equal to 126°, 54°, and 126°, respectively.
14. The angles ∠1, ∠2, and ∠3 is equal to 135°, 45°, and 135°, respectively.
15. The value of x is 16°.
16. The value of x is 63°.
17. The value of x is 10°.
When two lines cross at a single point, a linear pair of angles is generated. If the angles are next to each other after the two lines intersect, they are considered to be linear. The total of the angles of a linear pair is always 180°.
When two lines intersect, the angles opposite each other are called vertical angles.
To learn more about angles, visit :
https://brainly.com/question/28451077
#SPJ1
A red candle is 8 inches tall and burns at a rate of 7
10 inch per hour.
A blue candle is 6 inches tall and burns at a rate of 1
5 inch per hour.
After how many hours will both candles be the same height?
Answers
After four hours, the height of the candles will be the same.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
A red candle has an 8-inch height and burns at a 7/10-inch per hour rate. A 6-inch tall blue candle burns at a rate of 1/5 inch per hour.
Let x be the number of hours and y be the height.
y = -0.70x + 8 ...1
y = -0.20x + 6 ...2
From equations 1 and 2, then we have
- 0.20x + 6 = - 0.70x + 8
(0.70 - 0.20)x = 8 - 6
0.50x = 2
x = 4 hours
After four hours, the height of the candles will be the same.
More about the linear equation link is given below.
https://brainly.com/question/11897796
#SPJ1
Here is a diagram of a person standing next to a lorry.
The diagram shows two centimetre rulers.
The person and the lorry are drawn to the same scale.
The lorry is approximately 12.8 m in length.
Using the scale diagram, estimate the height of the person in metres.
Answers
from the diagram, we can see the Lorry is 12 cm in the model drawing, whilst in actual length is 12.8 metres, now the person on the model drawing shows as 1.5 cm, so
[tex]\begin{array}{ccll} \stackrel{cm}{model}&\stackrel{metre}{actual}\\ \cline{1-2} 12 & 12.8\\ 1.5& x \end{array} \implies \cfrac{12}{1.5}~~=~~\cfrac{12.8}{x} \\\\\\ 12x=(1.5)(12.8)\implies x=\cfrac{(1.5)(12.8)}{12}\implies x=\stackrel{metres}{1.6}[/tex]
What is the gradient of a line perpendicular to a line with a gradient of 1/3?
Answers
while playing lawn darts with his friend, jack notices that when he throws a dart up at 60 degrees it travels 11 meters. how high did the dart travel?
Answers
Answer: Approximately 9.526279 meters
======================================================
Explanation:
See the diagram below.
Draw a horizontal line to mark points A, B and C on it
A = dartboard
B = Jack's location
C = midpoint of A and B
Segment AB is the 11 meter horizontal distance from Jack to the dartboard. Half of this is BC = 11/2 = 5.5 meters.
Then just above point C, we'll have a fourth point D. Segment CD is the unknown max height of the dart. Let's call this x.
The dart will begin at point B, go upward in a parabolic arc to get to point D (the peak of the mountain), then come back down to arrive at point A.
------------------------------------
Focus on triangle BCD. Angle B = 60 degrees is the angle of elevation that Jack uses to throw the dart.
We'll use the tangent ratio to connect the opposite side x to the adjacent side 5.5
[tex]\tan(\text{angle}) = \frac{\text{opposite}}{\text{adjacent}}\\\\\tan(\text{B}) = \frac{\text{CD}}{\text{BC}}\\\\\tan(60) = \frac{\text{x}}{5.5}\\\\\text{x} = 5.5*\tan(60)\\\\\text{x} \approx 9.526279\\\\[/tex]
Make sure your calculator is in degree mode.
Segment CD is approximately 9.526279 meters which is the max height the dart reaches.
See the diagram below.
1234567890 + 0987654321
Answers
Answer:
Step-by-step explanation:
2222222211
The given table of values represents a linear equation. What is the slope?
X: 3 4 5 6
Y: 1 5 9 13
A. 3
B. 2
C. 4
D. 5
Answers
Answer: C
Step-by-step explanation:
y2 - y1/x2 - x1 = M
For example: Take the coordinates ( 3,1) and (4,5)
5-1 = 4
4-3 = 1 4/1 = 4
M=4
