Answer:
[tex]16m^{10} -25m^{12}[/tex]
Step-by-step explanation:
hope this helps :)
The expand and combination like terms (4m^5) – 5m^6) (4m^5 + 5m^6) is -9m^12 + (16)m^10.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.
We are given that;
The equation=(4m^5) – 5m^6) (4m^5 + 5m^6)
Now,
To expand the expression, we need to multiply each term inside the first parentheses by each term inside the second parentheses. This gives us:
(4m^5 - 5m^6) (4m^5 + 5m^6) = 4m^5 * 4m^5 + 4m^5 * 5m^6 - 5m^6 * 4m^5 - 5m^6 * 5m^6
To simplify the expression, we need to use the exponent rule that a^b * a^c = a^(b + c) and combine the terms that have the same base and exponent. This gives us:
4m^5 * 4m^5 + 4m^5 * 5m^6 - 5m^6 * 4m^5 - 5m^6 * 5m^6 = 16m^(5 + 5) + 20m^(5 + 6) - 20m^(6 + 5) - 25m^(6 + 6)
To further simplify the expression, we need to add the exponents and simplify the coefficients. This gives us:
16m^(5 + 5) + 20m^(5 + 6) - 20m^(6 + 5) - 25m^(6 + 6) = 16m^10 + 20m^11 - 20m^11 - 25m^12
To combine like terms, we need to add or subtract the coefficients of the terms that have the same base and exponent. This gives us:
16m^10 + 20m^11 - 20m^11 - 25m^12 = (16 - 25)m^12 + (20 - 20)m^11 + (16)m^10
= -9m^12 + (0)m^11 + (16)m^10
= -9m^12 + (16)m^10
Therefore, the equation will be equal to -9m^12 + (16)m^10.
Learn more about equations here;
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the average of nine number is 16. the average of 4 of these number is 11. what is the average of the other five number ?
Answer:
11
Step-by-step explanation:
We know formula to find average is,
Average=
Numberofnumbers
Sumofnumbers
Since the average of 10, so the sum of numbers is 5×10=50
As the fifth number is given 6, so rest 4 numbers will be = 50−6=44
Average of first four numbers will be Average=
4
44
=11
Find the value of X. If necessary write in radical form
Answer:
Step-by-step explanation:
[tex]a^{2} +b^{2} =c^{2} \\6^{2} +7^{2} =x^{2} \\\sqrt{85} = x[/tex]
Answer:
sqrt(85) =x
Step-by-step explanation:
Since this is a right triangle, we can use the Pythagorean theorem to find the hypotenuse
a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse
6^2 + 7^2 = x^2
36+49 = x^2
85 = x^2
Take the square root of each side
sqrt(85) = sqrt(x^2)
sqrt(85) =x
A boat is traveling due North at 27mph. A current is flowing at a bearing of 60° west of south at 8mph. Find the actual speed and direction of the boat written in magnitude and direction form.
Answer: [tex]24.02\ mph[/tex]
Step-by-step explanation:
Given
Boat is traveling due to north at [tex]v_{bf}=27\ mph[/tex]
The current is flowing [tex]60^{\circ}[/tex] west of south at [tex]v_f=8\ mph[/tex]
Suppose the actual velocity of boat is [tex]\vec{v_b}[/tex]
In vector notation we can write
[tex]\Rightarrow \vec{v_{bf}}=\vec{v_b}-\vec{v_f}\\\\\Rightarrow \vec{v_b}=\vec{v_{bf}}+\vec{v_f}[/tex]
Flow of current can be written as
[tex]\Rightarrow \vec{v_f}=-8\sin 60^{\circ}\hat{i}-8\cos 60^{\circ}\hat{j}[/tex]
Insert the values of vectors
[tex]\Rightarrow \vec{v_b}=27\hat{j}-8\sin 60^{\circ}\hat{i}-8\cos 60^{\circ}\hat{j}\\\\\Rightarrow \vec{v_b}=-4\sqrt{3}\hat{i}+27\hat{j}-4\hat{j}\\\\\Rightarrow \vec{v_b}=-4\sqrt{3}\hat{i}+23\hat{j}[/tex]
Magnitude of the velocity is
[tex]=\sqrt{(4\sqrt{3})^2+(23)^2}\\=\sqrt{48+529}\\=24.02\ mph[/tex]
The actual direction and magnitude of the velocity of the boat is the sum of
the velocity of the boat and the velocity of the current both in vector form.
The actual velocity and direction of the boat are approximately 24.02 m/s at a bearing of 16.76° west of north.Reasons:
Direction of the boat = North
Speed of the both = 27 mph
Direction of the current = 60° west of south
Speed of the current = 8 mph
Required:
The actual speed and direction of the boat written in magnitude and
direction.
Solution:
The velocities given in vector form are;
Velocity of the boat, [tex]\vec {v}_{boat}[/tex] = 27·j
60° west of south = 30° south of west
Therefore;
Velocity of the current, [tex]\vec{v}_{current}[/tex] = -8 × cos(30°)·i - 8×sin(30°)·j
The actual velocity of the boat, [tex]\vec{v}_{actual}[/tex] = [tex]\mathbf{\vec {v}_{boat}}[/tex] + [tex]\mathbf{\vec{v}_{current}}[/tex]
Which gives;
[tex]\vec{v}_{actual}[/tex] = 27·j - 8 × cos(30°)·i - 8 × sin(30°)·j
[tex]\vec{v}_{actual}[/tex] = 23·j - (4·√3)·i
Therefore;
[tex]\vec{v} _{actual}[/tex] = -(4·√3)·i + 23·j
Which gives;
[tex]|v_{actual}|[/tex] = √((-4·√3)² + 23²) = √(577) ≈ 24.02
The magnitude of the velocity of the boat, [tex]\mathbf{|v_{actual}|}[/tex] ≈ 24.02 m/s
The actual direction of the boat, θ, is given by the arctangent of the ratio
of the vertical to the horizontal component of the velocity as follows;
[tex]\displaystyle \theta = arctan \left(\frac{23}{-4 \cdot \sqrt{3} } \right) \approx \mathbf{-73.24^{\circ}}[/tex]
Based on the horizontal and vertical component, the above angle θ is
approximately 73.24° relative to the negative x-axis, which is 90° - 73.24° =
16.76° west of north.
Therefore;
The actual direction of the both is on a bearing of approximately 16.76° west of north.Learn more about vector quantities here:
https://brainly.com/question/1614684
2.
What is the mode of this data set?
14, 79, 77, 11, 14, 78, 77, 65, 31, 56, 16
56
14
11 and 56
14 and 77
Answer:
14
Step-by-step explanation:
Because it occurs the most frequently in the given data set
Answer:
14 and 77
Step-by-step explanation:
I just used a calculator
please answer my question
Answer:
your questions is not complete yet please send full questions and write your question ⁉️ so I will solve your problem
Decide whether there is enough information to prove that r∥s. If so, state the theroem you would use.
Answer:
C
Step-by-step explanation:
if the two lines were parallel, then the alternate, on opposite side of the trasversal, exterior, or not inside the lines, angles would be congruent. sicne they are, the line are parallel
400plus2000minus45000000
please anyone help asap
Answer:
Hi there! The correct answer should be: x is 60 degrees
Step-by-step explanation:
okay, so the equation is:
2x + 60 = 180
which we will solve:
2x + 60 - 60 = 180 - 60
2x = 120
x = 60
A play runs for five evenings. The table shows the number of tickets sold and the amount of money collected each evening.
What is the cost per ticket?
IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. What is the probability that a randomly chosen person's IQ score will be between 101 and 134, to the nearest thousandth
Answer:
Step-by-step explanation:
IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. What is the probability that a randomly chosen person's IQ score will be between 101 and 134, to the nearest thousandth
z = (x-μ)/σ, where x is the raw score,
μ is the population mean = 100
σ is the population standard deviation = 15
For x = 101
z = 101 - 100/15
z = 0.066667
Probability value from Z-Table:
P(x = 101) = 0.52658
For x = 134
z = 134 - 100/15
z = 2.26667
Probability value from Z-Table:
P(x= 134) = 0.98829
Therefore,
The circumference of a circle is 16 ft.
The radius is ?
Answer:
8/pi or approximately 2.55 ft
Step-by-step explanation:
The formula for the circumference is
C = 2 * pi *r
16 = 2 * pi *r
Divide each side by 2 pi
16 / ( 2 pi) = 2 * pi * r/ ( 2 pi)
8 / pi = r
Using 3.14 for pi
8 / 3.14 = r
2.54777 = r
2.55 =r
Answer:
Radius ≈ 2.55 ft.
Step-by-step explanation:
GIVEN :-
Circumference of circle = 16 ft.TO FIND :-
Radius of the circleFORMULAE TO KNOW BEFORE SOLVING :-
For a circle with radius 'r' & circumference 'c' ,
[tex]r = \frac{c}{2\pi }[/tex]
SOLUTION :-
[tex]Radius = \frac{Circumference}{2\pi } = \frac{16}{2\pi } = \frac{8}{\pi } = 2.55 ft. (appx)[/tex]
Find the value of x
because its isosceles so 9+9=x²
and x equal
2√3
Answer:
(3/2)√2
Step-by-step explanation:
Here the ratio of x to 3 is the sine of the 45 degree angle.
Thus:
x √2
----- = -------
3 2
Cross multiplying, we get 2x = 3√2, so that x must be (3/2)√2
need he,p pls and thank u
The temperature in Sam's home varies sinusoidal over time. Given the equation T = 4 cos(30(t − 8)) + 16 describes the temperature of the house in degrees celsius in terms of the number of hours since 12 midnight.
Answer:
The temperature is: 14.5 degrees
Step-by-step explanation:
Given
[tex]T = 4 \cos(30(t - 8)) + 16[/tex]
Required
The temperature at 4:15
We have:
[tex]t = 4:15[/tex]
Convert to hours
[tex]t = 4+\frac{15}{60}[/tex]
[tex]t = 4+0.25[/tex]
[tex]t = 4.25[/tex]
So:
[tex]T = 4 \cos(30(t - 8)) + 16[/tex]
[tex]T = 4 \cos(30(4.25 - 8)) + 16[/tex]
[tex]T = 4 \cos(30(-3.75)) + 16[/tex]
Open bracket
[tex]T = 4 \cos(-112.5) + 16[/tex]
[tex]T = 4 *-0.3826 + 16[/tex]
[tex]T = -1.5304 + 16[/tex]
[tex]T = 14.4696[/tex]
Approximate
[tex]T = 14.5^o[/tex]
Help me please!!!!!!!!!!
0.07
EXPLANATION
The number of sophmores is 2+25+3 = 30.
Of these sophmores, 2 drive to school.
So the probability that a student drives to school, given that they are a sophmore, is 2/30, or approximately 0.07.
6,2, 2/3 Find the 8th term
Answer:
2/729
Step-by-step explanation:
2/3÷3 = 2/9
2/9÷3=2/27
2/27÷3=2/81
2/81÷3=2/243
2/243÷3=2/729
Alan’s gift basket contains three oranges for every five apples. If the basket has nine oranges, how many apples does it have?
Answer:
15 apples
Step-by-step explanation:
If x= 3, then the length of AB is
Answer:
7
Step-by-step explanation:
AB = 3x-2
Let x=3
AB = 3*3 -2
= 9-2
=7
El agua de un manantial se conduce hasta unos depósitos cilíndricos que miden 12 m de radio de la base y 20 m de altura. Luego se embotella en bidones de 2.5 litros. ¿Cuántos envases se llenan con cada depósito?
Answer:
Con cada depósito se pueden llenar 3,617.28 envases.
Step-by-step explanation:
Dado que el agua de un manantial se conduce hasta unos depósitos cilíndricos que miden 12 m de radio de la base y 20 m de altura, y luego se embotella en bidones de 2.5 litros, para determinar cuántos envases se llenan con cada depósito se debe realizar el siguiente cálculo, sabiendo que el volumen de un cilindro se obtiene multiplicando pi por el radio del cilindro al cuadrado por su altura:
3.14 x (12x12) x 20 = X
3.14 x 144 x 20 = X
452.16 x 20 = X
9,043.2 = X
9,043.2 / 2.5 = X
3,617.28 = X
Por lo tanto, con cada depósito se pueden llenar 3,617.28 envases.
Please Help Me With This Problem.
A grocery store receives a shipment of potatoes weighing a total of 180-pounds. The shipment contains six 10-pound bags of potatoes and an unknown number of 5-pound bags of potatoes. Write and solve an equation so that you can describe the number of 5-pound bags of potatoes in the shipment. You got this.
Answer:
10(6) + 5x = 180
60 + 5x = 180
- 60 - 60
---------------------
5x = 120
------------
5 5
x = 24
Step-by-step explanation:
The shipment contains a total of 180 pounds of potatoes. There are two types of bags of potatoes. One weighing 10 pounds and the other weighing 5 pounds. There are 6 bags of potatoes weighing 10 pounds each and x bags of potatoes weighing 5 pounds each. Two numbers can be added up to bring a total of 180 so we can write this equation as 10(6) + 5x = 180. This problem speaks of pounds in particular so that is why 10 and five go in front of the secondary numbers. After that, just solve. The steps are shown above. ^^^ If I am wrong, please let me know. I hope this helps! :D
Determine whether the side lengths could represent a right triangle.
14, 21, 25
Answer:
No
Step-by-step explanation:
Using the given values, 25 is the largest value, so if this were a right triangle, it would be the hypotenuse.
Using Pythagoras' theorem: For this triangle to be a right triangle, √(21² + 14²) must be equal to 25.
√(21² + 14²) = 25.239 (5sf) ≠ 25
Hence the triangle formed is not right.
i dont get these questions on math help i give brainliest
Answer:
here a link to your answer
Step-by-step explanation:
https://brainly.com/question/20419046
plus the answer is b
A question "I" made.
Answer:
41.67%
Step-by-step explanation:
:)
PLEASE HELP ME PLEASE
The cost (y), in dollars, to purchase x dozen doughnuts from Bakery A and Bakery B can be found using the equations shown in the table.
Bakery Cost (y)
А y = 9x
B y = 8x
Choose all of the statements that are true based on the equations given.
A. Bakery A charges about 8 cents more per doughnut than Bakery B.
B. The cost of 2 dozen doughnuts is 2 dollars more at Bakery A than Bakery B.
C. Bakery A charges $1.33 per doughnut and Bakery B charges $1.50 per doughnut.
D. Bakery A charges $0.75 per doughnut and Bakery B charges $0.67 per doughnut.
Answer:
T
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
A tutor invited 3 students to a study group. Those 3 students each invited 3 students to the study group. Then those additional students each invited 3 students to the study group. How many total students are invited to the study group?
Answer:21 students
Step-by-step explanation: 3x7=21 students.
Brainliest to who answers first!
Select all correct conversions.
1. 53 km = 5,300 m
2. 23 cm = 2.3 mm
3. 15 m = 1,500 cm
4. 117 mm = 0.117 m
5. 79 m = 0.079 km
Answer:
correct answers
15 m=1,500
117 mm=0.117 m
79 m=0.079 km
hope it helps
Suppose the cost of electricity is $0.30 for each kilowatt-hour. Carlos's house runs on 11.4 kilowatt-hours a day. Find the cost of electricity for Carlos's house in one day.
Answer:
$3.42
Step-by-step explanation:
the cost = 11.4 × 0.30 = $ 3.42
solve for t in d =rt if d =57 and r =30. t=
57 = 30 × t
t = 57/30
t = 19 × 3 / 10 × 3
t = 19/10
t = 1.9
Answer:
t = 1.9
Step-by-step explanation:
Given
d = rt
Substitute d = 57 and r = 30 into the equation
57 = 30t ( divide both sides by 30 )
[tex]\frac{57}{30}[/tex] = t , that is
t = 1.9
PLEASEEEE HELLPPPPPPPPP
A statistics student is studying if there is a relationship between the price of a used car and the number of miles it has been driven. She collects data for 20 cars of the same model with different mileage, and determines each car’s price using a used car website. The analysis is given in the computer output. Predictor Coef SE Coef t-ratio p Constant 24157.2 2164.1 2.965 0.046 Mileage -0.181 0.024 5.377 0.000 S = 3860.7 R-Sq = 68.0% R-Sq(Adj) = 67.5% Using the computer output, what is the equation of the least-squares regression line?
Answer:
y = - 0.181x + 24157.2
Step-by-step explanation:
Equation of the regression line is given from. The table by the Coefficient of the predictor, x variable and the intercept value :
The predictor here is mileage, which has a Coefficient of - 0.181
The constant value = intercept 24157.2
The regression equation is written in the form :
y = mx + c ; m = slope = Coefficient of predictor, ; x = predictor,
Hence, we have :
y = - 0.181x + 24157.2
Answer:
A.
Step-by-step explanation:
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