Answer:
A
Step-by-step explanation:
The product of the expression [tex]\frac{x^2 - 16}{2x + 8} * \frac{x^3 - 2x^2 + x}{x^2 + 3x - 4}[/tex] is [tex]\frac{x(x- 1)(x - 4)}{x(x + 4)}[/tex]
What is an expression?An expression is an algebraic term used for a mathematical statement that include variables and mathematical operations
Below is how to calculate the product
The product expression is given as:
[tex]\frac{x^2 - 16}{2x + 8} * \frac{x^3 - 2x^2 + x}{x^2 + 3x - 4}[/tex]
Express x^2 - 16 as a difference of two squares
[tex]\frac{(x - 4)(x + 4)}{2x + 8} * \frac{x^3 - 2x^2 + x}{x^2 + 3x - 4}[/tex]
Divide the expression
[tex]\frac{x - 4}{2} * \frac{x^3 - 2x^2 + x}{x^2 + 3x - 4}[/tex]
Factorize the other fraction
[tex]\frac{x - 4}{2} * \frac{x(x^2 - 2x + 1)}{(x -1)(x + 4)}[/tex]
Further factorize
[tex]\frac{x - 4}{2} * \frac{x(x- 1)(x - 1)}{(x -1)(x + 4)}[/tex]
Divide
[tex]\frac{x - 4}{2} * \frac{x(x- 1)}{x + 4}[/tex]
Multiply the fractions
[tex]\frac{x(x- 1)(x - 4)}{x(x + 4)}[/tex]
Hence, the product of [tex]\frac{x^2 - 16}{2x + 8} * \frac{x^3 - 2x^2 + x}{x^2 + 3x - 4}[/tex] is [tex]\frac{x(x- 1)(x - 4)}{x(x + 4)}[/tex]
Read more about algebraic expressions at:
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The diameter of a pipe is 6 cm. If the pipe is 26 cm long, what is its volume?
Use the value 3.14 for π , and round your answer to the nearest whole number.
Be sure to include the correct unit in your answer.
i think this question answer is 734.76cm^3
There are 4 consecutive integers that sum to 394. What is the least of these integers?
Answer: 97
Step-by-step explanation:
394 / 4 = 98.5, so the 4 numbers must be around 98.5.
97 + 98 + 99 + 100 = 394
Find the common ratio of the geometrie sequence 6, 24, 96,
Answer:
4
Step-by-step explanation:
To find the common ratio, take the second term and divide by the first term
24/6 = 4
Check by taking the third term and dividing by the second term
96/24 = 4
The common ratio is 4
Judith randomly selected 20% of the
seventh-grade students in her school
and asked them their favorite genre of
music. Of these students surveyed 41
chose pop music as the favorite music
genre. Based on the data, what is the
most reasonable prediction of the
number of seventh-grade students in
her school who would choose pop
music as their favorite genre?
Group of answer choices
60
80
200
160
Answer:
200
Step-by-step explanation:
41 x 5 = 205
20% x 5 = 100%
Solve the following system algebraically.
y = x2 +x
y = -x - 1
A) (-2,3)
B) (-1,0)
C) (0,0)
D) (-5,2)
Answer:
B
Step-by-step explanation:
-x - 1 = x^2 + x
x^2 + 2x + 1 = 0
(x+1)(x+1) = 0
x = -1 (double soution)
y = 1-1 =
y =0
(-1,0) = double solution
A coffee cup keeps coffee at 175 degrees for 2 hours each quarter hour after that the coffee loses 15 degrees of warmth what will the temperature of the coffee be after 4 hours who ever actually helps get brainliest and random answers will be reported.
Answer:
I believe the answer is 55 degrees.
Plz don't report me if i'm wrong.
Step-by-step explanation:
Me puedes ayudar es para hoy porfavor
Answer:
mira a las base de las figuras y busca cual base matchs con la figuras de la figura prinsipal
Step-by-step explanation:
como el cono va con la del toda la izquierda de la de la mitad
HELP PLZZ TIMED TEST 5 MIN LEFT!
Step-by-step explanation:
answer: 135 degrees for the missing side
Parallelogram JKLM shown below is going to be rotated 270° clockwise to create J'K'L'M'. Which rule describes this transformation? K M F. (x, y) = (-y, x)
G. (x, y) = (-x. -Y)
H. (x, y) = (y, -x)
J. (x,y) → (-x, y) c
Answer:
F. (x, y) = (-y, x)
Step-by-step explanation:
270º clockwise transformation:
The 270° clockwise transformation of a point (x,y) is:
(x,y) -> (-y,x)
Thus, as we just apply the rule in this conceptual question, the correct answer is given by:
F. (x, y) = (-y, x)
PLEASE HELP ALL LINKS GIVEN WILL BE REPORTED
Answer:
- 13
Step-by-step explanation:
[tex]log \frac{ {a}^{6} {b}^{6} }{ {c}^{7} } \\ \\ = log( {a}^{6} {b}^{6} ) - log {c}^{7} \\ \\ = 6log \: a + 6log \: b - 7log \: c \\ \\ = 6(2) + 6( - 3) - 7(1) \\ \\ = 12 - 18 - 7 \\ \\ \therefore \: log \frac{ {a}^{6} {b}^{6} }{ {c}^{7} } = - 13[/tex]
Can anyone help ?
Kim rolls a dice and flips a coin.
a) Calculate the probability that she
gets a 2 and a head.
b) Work out the probability that she
gets an even number and a tail.
What would b be
Answer:
a) 1 / 12
b) 1 / 4
Step-by-step explanation:
The events are independent since they do not affect each other. The total probability of two independent events is the product of the probabilities of the two events.
a) When rolling a die, there are 6 outcomes, the numbers 1 - 6. There is only 1 outcome where you can get a 2. Therefore, the probability of rolling a two is 1/6.
When flipping a coin, there are two ways it can land: heads or tails. And there is one outcome with heads. The probability of getting head would be 1 / 2.
To find the the total, you multiply the probabilities of the two events: 1 / 6 * 1 / 2 = 1 / 12
b) As stated before, when rolling a die, there are 6 outcomes, the numbers 1 - 6. There are 3 outcomes where she can roll an even number: the numbers 2, 4, or 6. So, the probability of rolling an even number is 3 / 6 or 1 / 2.
When flipping a coin, there are two ways it can land: heads or tails. And there is one outcome with tails. The probability of getting tails would be 1 / 2.
Now, you multiply the two probabilities to get the total probability: 1 / 2 * 1 / 2 = 1 / 4
Can somebody help me seriously
Answer: b
Step-by-step explanation:
I don't know but i am right
Due to budget cuts the Fire Department only has one ladder which is 35 feet long. While rescuing a damsel from a burning house the ladder must be 12 feet from the base of the house. How high up the house can the ladder reach?
a. Draw a diagram that models the situation. Be sure to label it.
b. Write an equation that models the situation and solve it.
Answer:
good luck always brings luck the answer is 12
Step-by-step explanation:
If a fair coin is tossed 4 times, what is the probability, to the nearest thousandth, of getting exactly 3 tails?
Answer:
000.3
Step-by-step explanation:
The probability of getting exactly 3 tails is 0.25 If a fair coin is tossed 4 times, what is the probability.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
We have a coin if it is tossed 4 times.
Then the probability of getting exactly 3 tails is:
[tex]=\rm 4 C_3(\frac{1}{2} )^3\times (1-\frac{1}{2} )^1[/tex]
[tex]=\rm 4\times \frac{1}{16}[/tex]
= 1/4
= 0.25
Thus, the probability of getting exactly 3 tails is 0.25 If a fair coin is tossed 4 times, what is the probability.
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A soccer ball is kicked from the top of a 64 ft building into the air at an initial speed of 48 ft/sec. Its flight as a functions of time can be modeled by: h(t)=−16t2+48t+64. After how many seconds, will the soccer ball hit the ground (h=0)?
Answer:
t = 4 seconds
Step-by-step explanation:
The height of a soccer ball as a function of time is given by :
[tex]h(t)=-16t^2+48t+64[/tex]
We need to find the time when the ball hit the ground i.e. h = 0
Put h = 0 in above equation. So,
[tex]-16t^2+48t+64=0\\\\16(-t^2+3t+4)=0\\\\-t^2+3t+4=0[/tex]
It is a quadratic equation such that,
t = -1 s and t = 4 s
Neglecting -1 s, the ball will hit the ground after 4 seconds.
Subtract 8−2x from 3−6x .
Answer in this format:
Answer:
[tex]4x + 5[/tex]
Step-by-step explanation:
[tex](8 - 2x) - (3 - 6x)[/tex]
[tex]8 - 2x - 1 \times 3 - (6x)[/tex]
[tex]8 - 2x - 3 + 6x[/tex]
[tex] - 2x + 5 + 6x[/tex]
[tex]4x + 5[/tex]
Hope it is helpful....Which interval is the graph of the parent absolute vale function f(x)=|x| decreasing
Answer:
(-∞,0)
Step-by-step explanation:
The graph of ƒ(x) = |x| is below.
The function is decreasing on (-∞,0) .
A is wrong. The function both decreases and increases on (-∞,∞).
C is wrong. The function is decreasing on (-6,0), but that is only a portion of the interval.
D is wrong. the function is increasing on (o,∞)
Kim got a "40" in a class and I make a 70 on a test. How much does the grade goes up?
Answer:
30%
Step-by-step explanation:
A marathon had 567 runners registered. Of these runners, about 0.7% completed the race in under 2 h 12 min. How many runners completed the race in this time?
Answer:
3
Step-by-step explanation:
The angle of elevation to the top of the Empire State Building in New York is found to be 11° from the ground at a distance of 5281 feet from the base of the building. Using this information, find the height of the Empire State Building in feet. Use the dimensions given in the diagram to give an equation and solve. Round two decimal places.
Answer:
The height of the building is of 1026.52 feet.
Step-by-step explanation:
This situation is modeled by a right triangle, in which the length of the opposite side to the angle of 11º is the height of the building, while the length of the adjacent side is of 5281 feet.
Tangent:
In a right triangle, the tangent of an angle is the length of the opposite side divided by the length of the adjacent side.
In this question:
[tex]\tan{(11)} = \frac{x}{5281}[/tex]
[tex]x = 5281*\tan{(11)}[/tex]
Using a calculator, we have that the tangent of 11 degrees is: 0.1944. Thus:
[tex]x = 5281*\tan{(11)} = 5281*0.1944 = 1026.52[/tex]
The height of the building is of 1026.52 feet.
If Samuel travels twenty kilometers north, fifty kilometers south, and forty kilometers west, what is the approximate magnitude of his total displacement, in kilometers? Find the solution by drawing a diagram. km
Answer:
108.75km
Step-by-step explanation:
please find attached the diagram
total displacement can be determined by using Pythagoras theorem
The Pythagoras theorem : a² + b² = c²
where a = length
b = base
c = hypotenuse
length of x =
20² + 40²
= 400 + 1600
2000
square root of 2000
= 44.72km
length of y
40² + 50²
1600 + 2500 = 4100
square root of 4100
64.03km
total displacement = 44.72 + 64.03 = 108.75
x = 15, x = 5; (0.75)
Answer:
12
Step-by-step explanation:
12 is 75 of 15 %^%^%^%^^^___<<<7<
Amanda is 10 years old. She wants to
start saving for college. She saves $450
this year and wants to double her money every year after. Write an equation to model this situation. How much money will she have when she is 18 years old?
Answer:
7200
Step-by-step explanation:
450 x 2 = 900
900 x 8 =7200
Question 17 (1 point)
Bicycle, a company that makes dice, is looking to change the size of the dice they produce. The current dice have edge lengths of 5mm, and the company wants to increase them to 15mm. How will the volume of the dice be effected if this change is made?
Question 17 options:
30x larger
3x larger
10x larger
27x larger
Answer:
3x
Step-by-step explanation:
what is the value of x ?
Answer:
x = 19
Step-by-step explanation:
The two angles form a right angle
A right angle has a measure of 90 degrees
Thus, x + 14 + 3x = 90
^This is the equation we will use to solve for x
x + 14 + 3x = 90
step 1 combine like terms
x + 3x = 4x
we now have 4x + 14 = 90
step 2 subtract 14 from each side
90 - 14 = 76
14 - 14 cancels out
we now have 76 = 4x
step 3 divide each side by 4
4x / 4 = x
76 / 4 = 19
we're left with x = 19
How are these triangles congruent ?
- HL
- AAA
- ASA
Marie grew 10 plants with 2 seed packets. How many seed packets does Marie need to have a total of 15 plants in her backyard? Solve using unit rates
Answer:
he need 3 seeds to plant a 15 plant
how do i do this? i don’t know how
The 3 inside angles of a triangle need to equal 180 degrees.
Add the 3 together to equal 180:
X + 2x + x+ 14 = 180
Combine like terms:
4x + 14 = 180
Subtract 14 from both sides:
4x = 166
Divide both sides by 4
X = 41.5
Answer:
Fraction form: x = 83/2
Decimal form: x = 41.5
Step-by-step explanation:
The 3 angles inside the triangle will always add up to 180 degrees.
So that gives us the equation:
x + 14 + x + 2x = 180
Combine like terms:
4x + 14 = 180
Subtract on both sides:
4x = 166
Divide:
41.5
Pls help I’ll brainlest
▬▬▬▬▬▬▬▬▬▬▬▬▬▬
Law of Exponents ⸔
→ aᵐ × aⁿ = aᵐ＋ⁿ
→ aᵐ ÷ aⁿ = aᵐ－ⁿ
→ (aᵐ)ⁿ = aᵐⁿ
→ aᵐ × bᵐ = (ab)ᵐ
→ a⁰= a¹
→ aᵐ/bᵐ = (a/b)ᵐ
Question's solution ⸔
→ 5⁰
→ 1 [a⁰ = 1]
▬▬▬▬▬▬▬▬▬▬▬▬▬▬
I own 1 mini fish and 2 giant fish each giantfish weighs 3 times as much as minfish. If my mini fish eats my two giantfish, then how many times more weight will my mini fish have now than before
Answer: 6 pounds
Step-by-step explanation:
Answer:
The mini fish would weigh 6 times its original amount hypothetically but if we were talking realistically then you would need more information to figure that out. But even then there's no way of determining the specific weight.
Step-by-step explanation: