The expression after factorisation is 4w⁴x² (7y⁷ + 3w⁵x⁶)
What is an Expression ?An expression is defined as a mathematical statement consisting of variables , constants and mathematical operators.
The expression given is
28w⁴x²y⁷+12w⁹x⁸
Factors of the given expression will be the common terms in both the terms
w⁴x² is common in the variable term
The HCF of 28 and 12 is 4
4w⁴x² (7y⁷ + 3w⁵x⁶)
The expression after factorisation is 4w⁴x² (7y⁷ + 3w⁵x⁶)
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a²-b when a = 8 and b = 7
Answer:
[tex]57[/tex]
Step-by-step explanation:
You just plug in 8 as a, and 7 as b. This gives you the following equation: [tex](8)^2-7[/tex] which becomes [tex]64-7[/tex] by squaring the 8, Then subtract 7 and you get [tex]57[/tex]
Answer:
57
Step-by-step explanation:
a = 8
b = 7
a² - b
= 8² - 7
= (8*8) - 7
= 64 - 7
= 57
Chana and Josiah started skating at the same time in the same direction, but Josiah had a head start 10 meters past the starting line. Chana skated 3 meters per second and Josiah skated 2 meters per second.
What does point H represent in this context?
CORRECT (SELECTED)
Chana's and Josiah's distance from the starting line at the time when Chana catches up with Josiah
Explanation: Point HHH is on line aaa, so it represents Josiah's distance at a certain time. Point HHH is also on line bbb, so it represents the same distance and time for Chana.
The point that is labeled H on this graph is the point where Chana's and Josiah's distance from the starting line at the time when Chana catches up with Josiah.
How to solve for the point H.At the point H, there is an intersection between the distance covered by both of these individuals.
This point is the point where we are shown that Chana has caught up with Josiah as they are skating.
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I need some help please
What is the domain of the function f(x) = √(x+3)²?
Answer: Option 1
Step-by-step explanation:
The domain is the set of x values that make the radicand non-negative. Since the radicand is a perfect square, it will always be non-negative for any real value of x.
Find the solutions of each equation on the interval [0,2pi)
sin(3pi/2+ x)+sin(3pi/2 +x)= -2
Answer:
x=0
Step-by-step explanation:
You can combine the equation to get 2sin(3/2 +x) = -2
divide both sides by 2 and you get the equation equal to -1. sin is equal to -1 when the value inside is 3/2 so this is the answer.
x+6y=28, solve for y
Answer:
[tex]y = -\frac{x}{6} + \frac{14}{3}[/tex]
Step-by-step explanation:
So when you're solving for y you want to get y by it self meaning there should be nothing with y, including any coefficients. The first step is to usually move any terms to the other side and then divide by the coefficient of y so y "technically doesn't" have a coefficient, while it does, but that coefficient 1, so it doesn't really mean much.
Subtract x from both sides
[tex]6y = -x+28[/tex]
Divide both sides by 6
[tex]y = -\frac{x}{6} + \frac{14}{3}[/tex]
The given equation solved for y as y = (28 - x)/6.
The given equation is x+6y=28.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The given equation can be solved for y as follows
Here, x+6y=28
⇒ 6y = 28 - x
⇒ y = (28 - x)/6
Therefore, the given equation solved for y as y = (28 - x)/6.
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On a road, a bike sign in the shape of an isosceles trapezoid is to be painted. The sign and its dimensions are shown below. What is the area of the sign?
A right trapezoid is shown with height labeled 5 feet and one of the bases labeled as 9 feet, and the other base is labeled as 7 feet.
The area of the given right trapezoid is 40 ft².
What is the area of the trapezium?Area of the trapezium = ½(a + b) × h
Given;
base 1 = 9 feet
base 2 = 7 feet
Height h = 5 feet
Area of the trapezium = ½(a + b) × h
Area = (9 + 7) x 5/2
Area = 16 x 5/2
Area = 8 x 5
Area = 40 Square feet.
Hence, the area of the given trapezium is 40 ft².
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Which of the following best represents the altitude, h, of the triangle shown? (5 pts.) A. tan 75° B. 11.5 sin 75° C. D. 23 cos 75° 23 sin 75° M21 R 23* 759
The height of a triangle with a hypotenuse of 23 and angle between base and hypotenuse of 75° is h= 23sin(75)
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Trigonometric ratio shows the relationship between the sides and angles of a right angle triangle.
Let us assume that the right triangle has a altitude h, hypotenuse of 23 and angle between base and hypotenuse is 75°, hence:
sin(75) = h/23
h= 23sin(75)
The height of a triangle with a hypotenuse of 23 and angle between base and hypotenuse of 75° is h= 23sin(75)
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Barbara worked on a straight 7% commission. Her friend worked on a salary of $600 plus a 5% commission. In a particular month, they both sold $21,600 worth of merchandise.
Step 1 of 2 : How much did Barbara earn for this month? Follow the problem-solving process and round your answer to the nearest cent, if necessary.
The amount Barbara earned this month is $1512.
How much did Barbara earn?
Percentage can be described as a fraction of an amount expressed as a number out of hundred.
Barbara's earnings = percentage commission x worth of goods sold
7% x 21,600
0.07 x 21,600 = $1512
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Whats the correct answer answer asap for brainlist
The distance between two towns on a
map is 6.25 cm.
The scale on the map is 1 cm = 30 miles.
What is the actual distance between the
two towns?
Answer:
Actual distance=187.5miles
Step-by-step explanation:
1cm=30miles
6.25cm=6.25*30miles
=187.5miles
The distance between the two towns using the map scale is 187.5 miles.
What is a Measurement unit?A measurement unit is a unit to measure certain quantities.
For example, the mass can be measured in kilograms, length can be measured in meter and time can be measured in seconds.
To find the measurement of a new quantity known units can be used in operation. As to find the unit for speed we use m/s as a unit, where, m is the unit of distance and s is the unit of time.
Given that,
The distance between the towns on map is 1 cm.
And, the scale of map is 1 cm = 30 miles.
As per the problem the actual distance can be found by using the scale of the map as follows,
The distance between two towns is 6.25 × 30 = 187.5 miles.
Hence, the actual distance between the two towns is 187.5 miles.
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The maximum capacity of a bird's lungs varies directly with it size. If a robin with a mass of 310 grams has a lung capacity of 46,5 mL, how much lung capacity does a 1270-gram hawk have? round it to the nearest tenth.
Thus, the required capacity lung capacity of hawk is 190.5ml.
robin with a mass of 310 grams has a lung capacity of 46.5 mL
let lung capacity of a 1270-gram hawk = x
Volume, is defined as the ratio of the mass of object to its density.
Here,
The maximum capacity of a bird's lungs varies directly with it size.
So the proportion can be given as
⇒ 310/46.5 = 1270/x
= 190.5
Thus, the required capacity lung capacity of hawk is 190.5ml.
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You enter a room. 2 dogs, 4 horses, 1 giraffe, and a duck are lying on the bed. 3 chickens are flying over a chair.
How many legs are on the ground?
Answer:
36
Step-by-step explanation:
I think it’s a trick question because “legs” can also mean like chair legs that hold it up. Therefore:
2 dogs = 8 legs
4 horses = 16 legs
1 giraffe = 4 legs
And a bed: 4 legs(things that hold it up)
And a chair: 4 legs (things that hold it up)
This is assuming that the bed is a normal bed with stools holding it up
And the chair has 4 piles aswell as no missing legs in the animals… lol
Can i get a solution for this?
the effects of the given transactions on the accounting equation are:
increase in assets and increase in equity.increase in assets and increase in liabilities.no change increase in assets and increase in equity.decrease in assets and decrease in liabilities. decrease in assets and decrease in equity. decrease in assets and decrease in equity. decrease in assets and decrease in equity. no change increase in assets and increase in liabilities. how is the accounting equation affected?an investment would increase assets (cash) and also increase equity. every expense such as salaries would decrease assets and equity.
incurring debt would increase assets and liabilties while paying off debt would decrease both asset (cash) and liabilities.
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Which graph represents the function of f(x) = the quantity of 4 x squared minus 16, all over 2 x minus 4 ? (2 points) graph of 2 x plus 4, with discontinuity at negative 2, 0 graph of 2 x plus 4, with discontinuity at 2, 8 graph of 2 x minus 4, with discontinuity at negative 2, negative 8 graph of 2 x minus 4, with discontinuity at 2, 0
We can simplify the given rational function into a linear one, the graph is below.
Which graph represents the function?
Here we have the rational function:
[tex]f(x) = \frac{4x^2 - 16}{2x - 4}[/tex]
Factorization the numerator, we get:
4x² - 16 = 0
4x² = 16
x² = 16/4 = 4
x = ±√4 = ±2
Then the numerator can be written as:
4*(x - 2)*(x + 2)
And the denominator can be rewritten as:
2x - 4 = 2*(x - 2)
Then the function becomes:
[tex]f(x) = \frac{4*(x + 2)*(x - 2)}{2*(x - 2)} \\\\f(x) = 2*(x + 2) = 2x + 4[/tex]
So we have just a linear equation, so the graph that represents the function is the graph of a line, the one you can see below.
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Your best friend is really struggling with their math class. You passed the same class last term with an A, so you’ve been helping them do practice problems and double-checking their homework. The professor has given them a take-home exam for their mid-term, and they want your help completing the exam. Is this an academic integrity violation? Why or why not? How would you handle this situation, and why would you handle it in that way?
Answer:
no
Step-by-step explanation:
you have done your part by helping in their study session,if you help them cheat you will suffer the consequences if he/she is caught,
This is an academic integrity violation because it is against honesty rules, the best would be to offer assistance to your friend.
Is this an academic integrity violation?Academic integrity encompasses principles of honesty, fairness, and trustworthiness in academic pursuits. It generally includes a commitment to originality and independent work. Assisting someone in completing an exam, especially a take-home exam, where individual effort and understanding are expected, would likely violate academic integrity policies.
Handling this situationHandling the situation ethically and responsibly would involve respecting the academic rules and ensuring fairness for all students. Instead of directly completing the exam for your friend, you can offer assistance by explaining concepts, providing guidance on problem-solving approaches, or reviewing their completed work to identify errors or areas for improvement. This way, you can help your friend learn the material and develop their own understanding, without compromising academic integrity.
Encourage your friend to seek additional help from their professor, teaching assistants, or tutoring services provided by the institution. They can also engage in group study sessions or form study groups with classmates, which promote collaborative learning while maintaining individual effort.
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You are playing an online game with your friend and they are on level 4. You are on level 6 and can beat, on average, 4 levels per hour. If your friend can beat 5 levels per hour, how many hours will it take for you and your friend to be on the same level? Think about how you would solve this question. Write at least two sentences about how you would attempt this problem. You can think about a new method of solving or use methods that you already have learned.
It would take 2 hours for me at level 6 to be on the same level with my friend which is initially at level 5.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let t represent the time it would take to be on the same level with your friends. I am at level 6 and my friend is on level 4, hence:
5t = 4t + 2
t = 2 hours
It would take 2 hours for me at level 6 to be on the same level with my friend which is initially at level 5.
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Write an equation of the line that passes through a pair of points:
(2, 3), (4, negative 2)
a.
y = Negative five-halvesx – StartFraction 1 Over 8 EndFraction
c.
y = Negative five-halvesx + 8
b.
y = Negative five-halvesx – 8
d.
y = Five-halvesx + 8
The equation of line that passes through a pair of points: (2, 3), (4, -2).is option B. y = -5/2 x + 8.
What is the equation of a line passing through two given points in 2 dimensional plane?Suppose the given points are (x_1, y_1) and (x_2, y_2),
then the equation of the straight line joining both two points is given by
[tex](y - y_1) = \dfrac{y_2 - y_1}{x_2 - x_1} (x -x_1)[/tex]
We need to find the equation of the line that passes through a pair of points: (2, 3), (4, -2).
So, the equation would be
[tex](y - y_1) = \dfrac{y_2 - y_1}{x_2 - x_1} (x -x_1)[/tex]
[tex](y - 3) = \dfrac{-2 - 3}{4- 2} (x -2)\\\\\\(y - 3) = \dfrac{-5}{2} (x -2)\\\\\\2(y - 3) = -5 (x -2)\\\\2y - 6 = -5x + 10\\\\2y = -5x + 16\\\\y = -5/2 x + 8[/tex]
Hence, the equation of line is option B. y = -5/2 x + 8.
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Answer:B
Step-by-step explanation:
Im trying to figure out the answer
Step-by-step explanation:
[tex]\sqrt{35} =\sqrt{5} *\sqrt{7};[/tex]
all the details are in the attachment.
Please help me answer this question in khan academy
The interval that function f(x)=x³-9x has a positive average rate of change is [ -4, -1 ].
Option D) is the correct answer.
Over which interval does f have a positive rate of change?To determine whether the average rate of change is positive, f(max) - f(min) must be greater than zero.
Given the function; f(x) = x³ - 9x
We determine f(max) - f(min)
At interval [ -2, 1 ]
(x³ - 9x) - ( x³ - 9x )
( (1)³ - 9(1) ) - ((-2)³ - 9(-2))= -8 - 10 = -18 NOT POSITIVE
At interval [ -2, 3 ]
(x³ - 9x) - ( x³ - 9x )
( (3)³ - 9(3) ) - ((-3)³ - 9(-3))= 0 - 0 = 0 NOT POSITIVE
At interval [ -1, 2 ]
(x³ - 9x) - ( x³ - 9x )
( (2)³ - 9(2) ) - ((-1)³ - 9(-1))= -10 - 8 = -18 NOT POSITIVE
At interval [ -4, -1 ]
(x³ - 9x) - ( x³ - 9x )
( (-1)³ - 9(-1) ) - ((-4)³ - 9(-4))= 8 - (-28) = 36 POSITIVE
Therefore, the interval that function f(x)=x³-9x has a positive average rate of change is [ -4, -1 ].
Option D) is the correct answer.
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Find the real numbers x and y.
27+yi= 11-x + 4i
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:x = -16 [/tex]
[tex]\qquad \tt \rightarrow \: y =4 [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \: 27 + yi = 11 - x + 4i[/tex]
[tex]\qquad \tt \rightarrow \: yi + x = 11 + 4i - 27[/tex]
[tex]\qquad \tt \rightarrow \: x + yi = - 16 + 4i[/tex]
By equating both equations we get :
[tex]\qquad \tt \rightarrow \: x = - 16[/tex]
[tex]\qquad \tt \rightarrow \: y = 4[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Factor completely.
x^2+5x+6
Enter your answer in the box.
Answer:
(x+3)(x+2)
Step-by-step explanation:
x^2 + 5x+6
To factor this problem, we need to determine which two numbers multiply to 6 and add to 5
3*2 = 6
3+2 -5
(x+3)(x+2)
Step-by-step explanation:
x² + 5x + 6
= x² + 2x + 3x + 6
= x ( x + 2 ) + 3 ( x + 2 )
= ( x + 2 ) ( x + 3 )
Hence factorized.
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The system of equation that will represent her purchase is as follows:
1.39b + 2.49m = 50.73
1.29b + 2.69m = 51.63
How to represent system of equation?At store A she will pay a total sum of $50.73 for bread and milk.
At store B she will pay a total sum of $51.63 for bread and milk.
Therefore, the system of equation that will represent her purchase is as follows:
where
b = number of bread
m = number of milk
Therefore,
1.39b + 2.49m = 50.73
1.29b + 2.69m = 51.63
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Please help!
If a student (represented by initials) was chosen at random, find P(HH|C).
P(HH|C)=2/5
P(HH|C)= 13/16
P(HH|C)=9/16
P(HH|C)=3/5
Answer:
a.) P(HH|C)=2/5
Explanation:
Given following:
P(HH) = 7P(C) = 10P(HH ∩ C) = 4P(HH ∪ C) = 13Solving steps:
[tex]\sf P(HH|C) = \dfrac{P(HH \cap C) }{P(C)}[/tex]
[tex]\sf P(HH|C) = \dfrac{4 }{10}[/tex]
[tex]\sf P(HH|C) = \dfrac{2 }{5}[/tex]
Will is 30% taller than Wanda, so Will's height is ____% of Wanda's height.
Will's height is % of Wanda's height.
Thus we can conclude that if Will is 34% higher than Wanda, then Will's height is 134% (100% + 34%) of Wanda's height.
Will is 34% taller than Wanda, so Will's height is 134% of Wanda's height.
If Will is 34% of Wanda's height, we can conclude that he has all of Wanda's height plus 34% of that height.
All the height of Wanda represents 100% as it is referring to a complete system.
What is the height?
Height is a way to measure someone or something from base to top or head to toe.
From this, we can conclude that Will is 100% more than 34% of Wanda's height.
Thus we can conclude that if Will is 34% higher than Wanda, then Will's height is 134% (100% + 34%) of Wanda's height.
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PLS help!!! MARKING BRAINLIST IF ANSWER IS CORRECT( explanation required) What number should be placed in the box to help complete the division calculation?
.
Which equation represents a circle that contains the point (-2, 8) and has a center at (4, 0)?
Distance formula: √(x₂-x₁)² + (V2 - V₁)²
O(x-4)² + y² = 100
O(x-4)2 + y² = 10
O x² + (y-4)² = 10
O x² + (y-4)² = 100
Answer:
(x-4)² + y² = 100
Step-by-step explanation:
The only circles that have a center at (4 , 0) are :
(x-4)² + y² = 100
(x-4)² + y² = 10
……………………
• (-2 - 4)² + 8² = (-6)² + 64 = 36 + 64 = 100 ≠ 10
Then
The circle (x-4)² + y² = 10 doesn’t contain the point (-2, 8)
• (-2 - 4)² + 8² = 100
Then
The circle (x-4)² + y² = 100 contains the point (-2, 8)
A bank loaned out $11,000, part of it at the rate of 8% per year and the rest at 18% per year. If the interest received in one year totaled $1500, how much was loaned at
The amount loaned at 8% is $4800.
The amount loaned at 18% is $6,200.
What are the linear equations that represent the question?a + b - 11,000 equation 1
0.08a + 0.18b = 1500 equation 2
Where:
a = amount loaned at 8%
b = amount loaned at 18%
How much was loaned at 8 and 18%?Multiply equation 1 by 0.08
0.08a + 0.08b = 880 equation 3
Subtract equation 3 from equation 2
0.10b = 620
b = 620 / .10
b = $6200
a = 11,000 - 6200 = $4800
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a rectangular fish tank is 50 cm long, 40 cm wide, and 30 cm high.
a) how many cubic centimeters of water will the tank hold?
b) how many milliliters of water will the tank hold?
c) how many liters of water will the tank hold?
Answer:
a) 60,000 cubic cm; b) 60,000 mL; c) 60 L
Step-by-step explanation:
a) V = l x w x h
V = 50 cm x 40 cm x 30 cm = 60,000 cubic cm
b) 1 cubic cm = 1 mL, therefore 60,000 cubic cm = 60,000 mL
c) 1000 mL = 1 L; 60,000 mL = 60 L
Mr. Zuro finds the mean height of all 15 students in his statistics class to be 67.0 inches. Just as Mr. Zuro finishes explaining how to get the mean, Danielle walks in late. Danielle is 63.8 inches tall. What is the mean height of the 16 students in the class?
Answer: 66.8
Step-by-step explanation:
Let the mean height of 16 students in the class = X
Therefore,
[tex]\frac{15*67+63.8}{16} =X[/tex]
[tex]X=\frac{334}{5}[/tex]
X = 66.8