An expression has numbers, variables, and mathematical operations. The factors of the expression 4x³+x²-8x-2 by grouping are x²(4x+1)-2(4x+1).
What is an Expression?
In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The factors of the expression by grouping can be done as,
[tex]4x^3+x^2-8x-2[/tex]
Take x² as the common factor from the first two terms while -2 from the last two terms,
[tex]4x^3+x^2-8x-2\\\\=x^2(4x+1)-2(4x+1)[/tex]
Thus, the factors of the expression 4x³+x²-8x-2 by grouping are x²(4x+1)-2(4x+1).
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A) Convert the exponential function, 12^3=x^4 y^3 z^6, to its corresponding logarithmic function.
B) Write the log form from Part A into the expanded log form. **expression must be fully expanded for full credit**
The logarithmic function is ㏒ 12³ = ㏒ x⁴ · y³ · z⁶. The equation into the expanded logarithmic form is 3 · ㏒ 12 = 4 · ㏒ x + 3 · ㏒ y + 6 · ㏒ z.
How to apply logarithms on a exponential function
Logarithms are the reciprocal of exponential functions. In this question we must apply logarithms and its properties to obtain a linear-like expression in the following lines. The logarithm properties are summarized below:
㏒ₐ (b/c) = ㏒ₐ b - ㏒ₐ c (1)
㏒ₐ (b · c) = ㏒ₐ b + ㏒ₐ c (2)
㏒ₐ bⁿ = n · ㏒ₐ b (3)
a) To obtain the corresponding logarithmic function we apply logarithms on both sides of the expression:
㏒ 12³ = ㏒ x⁴ · y³ · z⁶ (4)
The logarithmic function is ㏒ 12³ = ㏒ x⁴ · y³ · z⁶. [tex]\blacksquare[/tex]
b) The expanded logaritmic form of (4) consists in the addition and subtraction of logarithms of non-power numbers, whose formed could be found, if possible, by logarithm properties:
㏒ 12³ = ㏒ x⁴ · y³ · z⁶
㏒ 12³ = ㏒ x⁴ + ㏒ y³ + ㏒ z⁶
3 · ㏒ 12 = 4 · ㏒ x + 3 · ㏒ y + 6 · ㏒ z
The equation into the expanded logarithmic form is 3 · ㏒ 12 = 4 · ㏒ x + 3 · ㏒ y + 6 · ㏒ z. [tex]\blacksquare[/tex]
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4x^2- 4x-1=0 i need the awnser
Answer:
See below
Step-by-step explanation:
Do you know how to use the Quadratic Formula with
a = 4 b = -4 c = -1
results in x = 1/2 +- sqrt(2) / 2
Can anyone help me with my homework
Answer:
Below in bold.
Step-by-step explanation:
When x = -3, y = -(-3) - 2 = 3-2 = 1.
When x = 0, y = -0 - 2 = -2.
When x = 4, y = -4 - 2 = -6.
To draw the graph plot the 3 points and you should be able to draw a straight line through them.
Answer:
The first y value with -3, is 1.
The second y value with 0, is -2.
The third y value with 4, is -6.
A graph is shown below.
Step-by-step explanation:
It states that the rule is y = -x-2. So all we do is plug in the values shown in the table.
y = -(-3)-2
y = 1
The first point of intersection is at (-3,1)
y = -(0)-2
y = -2
The second point of intersection is at (0,-2)
y = -(4)-2
y = -6
The third point of intersection is at (4,-6)
So now, we plot the points, and draw a line connecting them all.
how many days are in 3 weeks??
Answer:
21
Step-by-step explanation:
because 7 day or in a week so 7 time 3 = 21
Answer:
21
Step-by-step explanation:
Becasue there are 7 days in a week, So use and time 7x3 and you will get 21 multiplication.
What is the completely factored form of the expression 16x2 8x 32? 4(4x2 2x 8) 4(12x2 4x 28) 8(2x2 x 4) 8x(8x2 x 24)
An expression is defined as a set of numbers, variables, and mathematical operations. The factored form of the expression 16x²+8x+32 is 8(2x²+x+4).
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The completely factored form of the expression can be written as,
[tex]16x^2+8x+32\\\\=8(2x^2+x+4)[/tex]
Thus, the factored form of the expression 16x²+8x+32 is 8(2x²+x+4).
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pls explain why and how the answer u got is proportional
Answer:
A
Step-by-step explanation:
This is because to find out if a table is proportional you have to do y divided by x. Whatever table has the same answer on all of the table sections when you divide y by x, that is proportional.
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An angle on a straight line is 180 degrees
⇒ this angel is made up of two angles with measures
⇒ 'x-7' and '57'
⇒ when these two angles are added up they are equal to the larger
angle that is 180 degrees in measure
Let's set up a mathematical equation based on the information and deduction:
[tex](x-7)+57=180\\x-7+57 = 180\\x + 50=180\\x = 130[/tex]
Answer: The value of x is 130
Hope that helps!
please get this righttt!
Answer:
5/9
Step-by-step explanation:
this is the answer kinda not explainable so yeah
What is the common denominator of 2/5 and 3/10
Answer:
Answer:
10
Step-by-step explanation:
3/10~3/10
2/5
5x2=10
2x2=4
2/5=4/*10*
For problem 8, find the area of the shaded region. The polygon is a regular polygon. please show work.
Answer:
34.7791 [unit²].
Step-by-step explanation:
1) area of the circle is:
πr²;
2) area of the regular polygon is:
6*r²√3*0.25=1.5√3r²;
3) the required area:
πr²-1.5√3r²=r²(π-1.5*√3)=64*(3.1415-1.5*1.7321)=34.7791
All the dimensions of a pentagon were multiplied by the same factor, and the area of the figure changed by a factor of 25. By what factor were the dimensions of the pentagon multiplied?
12. 5
625
5
50
A bag contains 4 red, 4 blue, 4green, and 4 yellow marbles. A marbles is randomly pulled from the bag and replaced seven times. The table shows the outcome of the experiment. Which marble color’s observed frequency is closest to its expected frequency?
Answer:i think that there would not be a frequency because their is an equal chance of anycolr being pulled
Step-by-step explanation:
During geometry class, students are told that δtsr ≅ δusv. marcus states that δtsr is mapped to δusv by performing a rotation about point s. sam states that δtsr is mapped to δusv by a reflection across the line that goes through point s. determine if either student is correct. marcus is correct. sam is correct. both students are correct. neither student is correct.
Transformation involves changing the position of a shape through translation, dilation, rotation and reflection.Marcus's claim is correct.
What is transformation?A process by which one figure, expression, or function is converted into another one of similar value.
The triangles are given as: ΔTSR and ΔUSV
By comparison, we can see that point S is on both triangles, and this point on both triangles corresponds.
So, to map ΔTSR to ΔUSV, then ΔTSR must be rotated about point S to ΔUSV or rotate ΔUSV about point S to ΔTSR.
Hence, Marcus is correct, and Sam is not.
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Answer:
A. Marcus is correct.
Credits to the guy above! :))
PLEASE HELP URGENT
Maggie is walking her dog. She walks 2/3 mile in 7/10 of an hour. At this same rate, what distances can she walk? Select all that apply.
5/7 mile in 3/4 of an hour
7/10 mike in 2/3 of an hour
10/3 miles in 1 1/2 hours
32/21 miles in 1 3/5 hours
5/3 mikes in 1 9/10 hours
Calculate the perimeter of the triangle
below.
24cm
32cm
The baseball team in your community is playing for the championship. They will play seven games against the opposing team.
a. If the probability for your team to win is 74%, what is the probability for the other team to win?
b. Is this a binomial distribution? Why or why not?
c. What is the probability that your team will win 4 of the 7 games?
Answer:
a. 26%
b. It's a binomial distribution because the competition will only have two outcomes, win or lose.
c. 4/7 or 57%
Step-by-step explanation:
Hope this helps :)
PLS HELP!!! No links pls and Ty <333
Sid is making a pizza. The diameter of the pizza is 15 inches.
What is the area of the pizza (use 3.14 for pi and round to the nearest
tenth)?
Step-by-step explanation:
Your diameter is 15 and a diameter is a whole line, what your going to do it divide the 15 by 2, than mutiply the answer by 3.14 and than round ur answer :)
Can two obtuse angles be supplementary? Why or why not?
Answer:
No.
Step-by-step explanation:
Two Angles are Supplementary when they add up to 180.
Let us consider the least obtuse angle, i.e., >90
Say 91 and add it to itself.
91+91 =182
This is >180
Hence, two obtuse angles can never be supplementary.
My sister is 13 years old. My brother says that his age minus 14 is equal to my sisters age. How old is my brother?
Answer:
Brother's age = 13 years
Step-by-step explanation:
Sister's age = 13 year
Brother's age = x
Brother's age will be equal to the Sister's age when x-14
According To The Question
[tex]x - 14 = 13 \\ x = 13 + 14 \\ x = 27[/tex]
Therefore, Brother's age will be 27 years
!!PLEASE PLEASE PLEASE MARK ME THE BRAINLIEST!!
Find the GCF of 60, 96, and 156.
Answer:
GCF = 12
for the values 60, 96, 156
Step-by-step explanation:
Solution by Factorization:
The factors of 60 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
The factors of 96 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
The factors of 156 are: 1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, 156
Then the greatest common factor is 12.
Just answer the question RN im in a rush
Answer:
https://brainly.com/question/27407610
Step-by-step explanation:
Put the following items in order from most expensive to least expensive. item base price change direction blender $29.73 9% markdown hat $14.16 77% markup ink $20.17 27% markup heater $28.46 22% markdown a. blender, heater, ink, hat b. blender, ink, hat, heater c. ink, hat, blender, heater d. ink, heater, blender, hat please select the best answer from the choices provided a b c d
How many outfits can be made from five shirts three pairs of pants and two pairs of shoes?
Answer:
3*5*2=30
He can make 30 outfits.
Step-by-step explanation:
3*5*2=30
Find the slant height?
Answer:
59.94
Step-by-step explanation:
Slant height = √(height)² + (1/2 base)²
Sh = √53² + 28²Sh = √2809 + 784Sh = 59.94A space ship travels at 8 2 miles per hour and traveled for 81 8 hours.
Select the answer that represents how many miles the space ship traveled.
Answer:
D
Step-by-step explanation:
8^2 m/hr * 8^18 hr = 8^(2+18) = 8^20 miles
A rectangle has vertices (–1, 1), (–4, 1), (–1, 3), and (–4, 3). If the rectangle is reflected over the y-axis, what algebraic rule can be used to find each of the new vertices?
Select one:
A. (x,y)→(−x,−y)
B. (x,y)→(–y,–x)
C. (x,y)→(y,−x)
D. (x,y)→(−x,y)
Answer:
D. (x,y)→(−x,y)
Step-by-step explanation:
Reflecting OVER the Y axis means it will end up on the other side of the Y axis line. The Y coordinates remain unchanged while the X coordinates invert. Attaching a crude diagram to help you picture it.
In this figure, 12.2% of the area is painted blue.
How much of the area is painted blue?
1.22 cm²
3.05 cm²
4.27 cm²
5.49 cm²
The area of the figure painted blue, which is 12.2% of the total area is: 4.27 cm².
What is the Area of a Triangle and Square?Area of triangle = 1/2(b)(h)Area of Square = s²The figure is composed of a triangle and a square. Find the area of the figure.
Area of the figure = 1/2(b)(h) + s² = 1/2(5)(4) + 5² = 35 cm²
12.2% of the area of the figure = 12.2/100 × 35 = 4.27 cm²
Therefore, the area of the figure painted blue, which is 12.2% of the total area is: 4.27 cm².
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write 0.004 as a fraction in words.
Step-by-step explanation:
0.004 as a fraction is 1/250
one over two hundred and fifty
Answer:
one over Two hundred and fifty
Step-by-step explanation:
As we can see the 4 is 2 zeros away from the decimal point. This means that 4 must be in the thousandths place.
Therefore our answer is four thousandths.
Remember that we it is behind the decimal point, it becomes ths at the end.
To change this into a fraction we should get 4/1000 by taking the words literally.
Dividing both sides by 4 gives us 1/250
1/250 in words is one over Two hundred and fifty
I guess
Brainliest if helped
340 to nearest hundred
Answer:
300 - hope this helped :)
Step-by-step explanation:
340 to the nearest hundred
is 300 since thats the closest
A perfect square is a number that is the square of a whole number. For example, 25 is a perfect square because it is the square of 5: 5 × 5 = 25. How many perfect squares are greater than 0 but less than 1000?
Perfect squares are squares of integers and since 961 is the square of 31, it shows that there are 31 perfect squares greater than 0 but less than 1000
What are perfect squares?A perfect square is a number that is the square of a whole number. For instance, 36 is a perfect square being the square of 6.
Other perfect squares that are between 0 and 1000 are 1, 4, 9, 16, 25, 3649, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324... 961.
Since 961 is the square of 31, it shows that there are 31 perfect squares greater than 0 but less than 1000.
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Answer:
Since 961 is the square of 31, it shows that there are 31 perfect squares greater than 0 but less than 1000.