[tex]\left( x+\frac{1}{x}\right)^{8} =\sum _{k=0}^{8}\binom{8}{k} \cdotp x^{8-k} \cdotp \left(\frac{1}{x}\right)^{k}\\\\\\ \begin{array}{l}\text{We\ wish\ to\ find\ } x^{0} :\\\\x^{8-k} \cdotp \left(\frac{1}{x}\right)^{k} =x^{0}\\\\\Longrightarrow x^{8-k} \cdotp x^{-k} =x^{0}\\\\\Longrightarrow \cancel{x}^{8-2k} =\cancel{x}^{0}\\\\\Longrightarrow 2k=8\\\\\Longrightarrow k=4\end{array}\\\\\therefore \binom{8}{4} \cdotp x^{4} \cdotp \left(\frac{1}{x}\right)^{4} =\frac{8!}{( 8-4) !\cdotp 4!}[/tex]
[tex]\binom{8}{4} \cdotp x^{4} \cdotp \left(\frac{1}{x}\right)^{4} =\frac{8\cdotp 7\cdotp 6\cdotp 5\cdotp \cancel{4!}}{\cancel{4!} \cdotp 4\cdotp 3\cdotp 2\cdotp 1}\\\\\binom{8}{4} \cdotp x^{4} \cdotp \left(\frac{1}{x}\right)^{4}=70\\\\\therefore \boxed{\boxed{\text{The\ constant\ term\ is\ } 70}}[/tex]
2) A rectangular pyramid has the base area measuring 30 m by 20 m. Given 1 point
that the volume is 7,000 m^3, find its height. *
Answer:
20x30xH=7000
11.6666 , depends on how much you need to round it. if 2 sig figs, round it to 12.
Answer:
Pyramid Height = 3 * Pyramid Volume / Base Area
Height = 3 * 7,000 / (30 * 20)
Height = 21,000 / 600
Height = 35 meters
Step-by-step explanation:
Help will give 25 Brainly points
What is the value of the underlined digit in 91,764,350?
Digit wise values.
[tex]\\ \sf\longmapsto 9=90000000[/tex]
[tex]\\ \sf\longmapsto 1=1000000[/tex]
[tex]\\ \sf\longmapsto 7=700000[/tex]
[tex]\\ \sf\longmapsto 6=60000[/tex]
[tex]\\ \sf\longmapsto 4=4000[/tex]
[tex]\\ \sf\longmapsto 3=300[/tex]
[tex]\\ \sf\longmapsto 5=50[/tex]
[tex]\\ \sf\longmapsto 0=0[/tex]
How long of a ladder is needed to reach a window sill 50 feet above the ground if the ladder rests against the building making an angle of 75∘ with the ground? Round your answer to the nearest foot and do not include units.
The length of the ladder needed to reach a window with 50 feet above the ground is 52 ft.
How to find the length of the ladder to reach the window?The angle formed with the ground and the ladder is 75 degrees.
The window is 50 ft above the ground.
The situation forms a right triangle.
Therefore, using trigonometric,
sin 75 = opposite / hypotenuse
where
hypotenuse side = length of the ladderopposite side is height of the window from the ground where the ladder head will be placed.Therefore,
sin 75 = 50 / h
cross multiply
h = 50 / sin 75
h = 50 / 0.96592582628
h = 51.763809036
h = 52 ft
Therefore, the length of the ladder needed to reach a window with 50 feet above the ground is 52 ft.
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If she wants the track to have a circumference of 150 feet,what does the radius of the track need to be
Answer:
the radius will need to be 150/2(pi) feet or roughly 23.87 feet
Step-by-step explanation:
equation for circumference is C = 2(pi)r
divide C (which is 150) by 2(pi)
150/2(pi) roughly equals 23.87.
There are 12 girls and 18 boys in a class. Teacher wants to form groups with the same
number of girls and boys in each group. What is the greatest number of groups can be
formed. How many girls and how many boys will be in each group?
Answer:
6 groups
2 girls, 3 boys
Step-by-step explanation:
To find the answer, first find the Greatest Common Factor or the GCF. The GCF in this case is 6. So, the amount of groups is 6. Then divide each number by 6, so there will be 2 girls in each group and 3 boys in each group.
A coat that normally sells for $48.50 is on sale for 12% off. What is the amount of the discount?
Answer:
The discount is 5.82
Step-by-step explanation:
To find the amount of the discount
48.50 * 12%
Change to decimal form
48.50 * .12
5.82
The discount is 5.82
HELP PLZ. A circular drum has a radius of 12.25 inches. Karen wants to glue a ribbon around the edge of the drum. If Karen has exactly enough ribbon, which measurement is closest to the length of the piece of ribbon in inches?
The length of a ribbon that will cover the edge of the circular drum is 76.98 in
The given parameter:
radius of the circular drum, r = 12.25 inchesTo find:
the length of a ribbon that will cover the edge of the circular drumThe length of a ribbon that will cover the edge of the circular drum is equal to the circumference of the circular drum.
The circumference of the circular drum = 2πr
The circumference of the circular drum = 2 x 3.142 x 12.25
The circumference of the circular drum = 76.98 in
Thus, the length of a ribbon that will cover the edge of the circular drum is 76.98 in
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Subtract using a number line.
1.4−1.7
Plot the minuend and the difference on the number line.
The difference between the numbers 1.4 and 1.7 is -0.3 after using the number line.
What is a number line?It is defined as the representation of the numbers on a straight line that goes infinitely on both sides.
It is given that:
As we can see in the number line:
1.4 < 1.7
If we take the difference between these two numbers
From the number line:
= 1.4 - 1.7
= -0.3
The arithmetic operation can be defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
After using the arithmetic operation concept:
The difference between the numbers:
= 1.4 - 1.7
= -0.3
Thus, the difference between the numbers 1.4 and 1.7 is -0.3 after using the number line.
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Evelina is shopping for back-to-school clothes. She bought 3 skirts, 2 pairs of
jeans, and 4 sweaters. Write and evaluate an expression to find out how much she
spent.
Answer:
3a + 2b + 4c = D
D = Amount Spent
Step-by-step explanation:
The perimeter of an equilateral triangle is 3 (+ 5). The perimeter of a rectangle is 2 (2x - 3) + 2(2). If the perimeters of the two figures are equal, then what is the value of r?
Answer:
3.25
Step-by-step explanation:
Perimeter of triangle = 3(5) = 15 cm
Perimeter of rectangle = 2(2x - 3 + 4)
Perimeter = 2(2x + 1)
Perimeter = 4x + 2
4x + 2 = 15
4x = 15 - 2
4x = 13
x = 13/4
x = 3.25
n - 5.5 = 8.3 please help ASAP
Answer:
= 2.8
Step-by-step explanation:
8.3 - 5.5 = 2.8
= 2.8
What’s the answer please, and that’s a division sign in the middle of the parentheses. It’s supposed to be a synthetic division problem.
9514 1404 393
Answer:
-6x^3 +5x^2 -x -2
Step-by-step explanation:
The synthetic division is shown in the attachment.
help please will mark brainliest
Step-by-step explanation:
option number B.......
Answer:
A) Translating 20 units right
Step-by-step explanation:
The triangle is in the same orientation as it would be on the other side of n. It would be translated 20 units instead of 10 because you reflected the triangle twice so you would need to multiply 10 by 2. The 10 also represents the triangle only being reflected once. It would be to the right because the triangle moved to the right.
Rotation 180 degrees about the origin
Answer:
Rule for rotation 180° about the origin:
(x, y) → (-x, -y)Given coordinates:
U(1, 0), V(4, -1), T(1, -3)Coordinates of the image, apply the rule above:
U'(-1, 0), V'(-4, 1), T'(-1, 3)COME ON HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP LOSING POINTSS HERE!!!!!
Answer:
The 1st one for the first pic and I'm not sure but c for the 2nd one
Answer:
a and c
Step-by-step explanation:
Asher pays $156 every 6 weeks for piano lessons. what is the price for per year for piano lesson?
24k to the power of 9 over 6k to the power of 6
How many solutions does the following equation have 3(X + 9) = 2x + 54
Answer:
One solution.
Step-by-step explanation:
3(x + 9) = 2x + 54
3x + 27 = 2x + 54
3x + 27 - 2x = 2x + 54 - 2x
x + 27 = 54
x + 27 - 27 = 54 - 27
x = 27
Write the standard form of the equation of the line through the pair of points (6,3) and (-7,7)
Step-by-step explanation:
steps are in the picture above.
Note:if you need to ask any question please let me know.anybody know how 1 5/8 would be drawn as a model/picture?
Answer:
nope I have no idea heheheheheheheh
Matthew through he could make 19 free throws, but he only made 13. What was his percent error?
Answer:
the percent error was 73%
Question 9 of 10
If f(x) = 2x^2+ 1 and g(x) =x^2 - 7, find (f – g)(x).
O A. 3x2 + 8
B. 3x2 - 6
C. x2 - 6
D. x2 + 8
Answer:
x2 + 8
Step-by-step explanation:
The value of the composite function (f - g)(x) is x² + 8.
The correct option is D.
What is a composite function?Any function that is created by combining two or more other functions is referred to as a composite function. To put it another way, given two functions, f, and g, the composite function of f and g, denoted as f(g(x)), is a new function that applies g to the input x before applying f to the output of g (x).
Given:
f(x) = 2x² + 1 and g(x) = x² - 7.
To find (f – g)(x), we need to subtract g(x) from f(x):
(f - g)(x) = f(x) - g(x)
where f(x) = 2x² + 1 and g(x) = x² - 7.
Substituting these expressions into the equation, we get:
(f - g)(x) = (2x² + 1) - (x² - 7)
Simplifying the expression on the right-hand side by distributing the negative sign, we get:
(f - g)(x) = 2x² + 1 - x² - 7)
Combining like terms, we get:
(f - g)(x) = x² + 8.
Therefore, (f - g)(x) = x² + 8.
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[tex]-2b-(-7)=11[/tex]
[tex] - 2b - ( - 7) = 11 \\ \\ - 2b + 7 = 11 \\ \\ - 2b = 11 - 7 \\ \\ - 2b = 4 \\ \\ b = \frac{4}{ 2} \\ \\ b = 2[/tex]
Hope it help youAnswer:
b = -2
Step-by-step explanation:
[tex] - 2b - ( - 7) = 11[/tex]
[tex] - 2b + 7 = 11[/tex]
[tex] - 2b + 7 - 7 = 11 - 7[/tex]
[tex] - 2b = 11 - 7[/tex]
[tex] - 2b = 4[/tex]
[tex]b = 4 \div( - 2) = - 4 \div 2 [/tex]
[tex]\boxed{\green{b = - 2}}[/tex]
1 square meters to square centimeters
*16. Camping Norman's camping tent has a volume of 72.576 cubic inches. What is the
volume of the tent in cubic feet?
1 square meter is equivalent to 0.0001 square centimeter
72.576 cubic inches. in cubic feet is 0.042 cubic feet
Conversion in math is a way of changing the value of an expression using units.
1) In order to change 1 square meter to square centimeters, we will use the conversion
1m = 0.01cm
Taking the square of both sides
(1m)² = (0.01cm)²
1m² = 0.01cm * 0.01cm
1m² = 0.0001cm²
This shows that 1 square meter is equivalent to 0.0001 square centimeter
2) We are to convert 72.576 cubic inches to cubic feet. Using the conversion factor:
1 cubic inch = 0.000578704 cubic feet
72.576 cubic inches = x
Cross multiply
x = 72.576 * 0.000578704
x = 0.042 cubic feet
This shows that 72.576 cubic inches. in cubic feet is 0.042 cubic feet
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how can you find out the mass of a marble
3. Which of the following graphs shows the solution set to 4x - 5 2 3 or 5- X > 8?
Inequalities are used to show the relationship between unequal expressions.
See attachment for the graph of [tex]4x - 5\ge 3[/tex] or [tex]5 - x > 8[/tex]
Given that:
[tex]4x - 5\ge 3[/tex] or [tex]5 - x > 8[/tex]
First, we solve for x.
[tex]4x - 5\ge 3[/tex]
Collect like terms
[tex]4x \ge 3+5[/tex]
[tex]4x \ge 8[/tex]
Divide by 4
[tex]x \ge 2[/tex]
[tex]5 - x > 8[/tex]
Collect like terms
[tex]-x > 8 - 5[/tex]
[tex]-x > 3[/tex]
Divide by -1
[tex]x < -3[/tex]
So, we have:
[tex]4x - 5\ge 3[/tex] or [tex]5 - x > 8[/tex] becomes
[tex]x \ge 2[/tex] or [tex]x < -3[/tex]
The graphs are not given. So, I've added as an attachment, the graphs of [tex]x \ge 2[/tex] or [tex]x < -3[/tex]
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Sandy can read 25 words in 5 seconds. At that
rate
Answer:
5 words a second because 5÷25 is 5 so in 1 second she reads 5 words
What is [tex]|x-6|[/tex] given that [tex]x \geq 6[/tex]
9514 1404 393
Answer:
x - 6
Step-by-step explanation:
For values of x greater than or equal to 6, the difference x-6 is non-negative, so the absolute value function does nothing. The value is ...
x -6
In the band, there are 2 vocalists and 5 musicians. What is the ratio of musicians to vocalists
Answer:
The answer is D. 5 to 2
Step-by-step explanation:
It sounds like they want the ratio to be given in that order.
Hope that helps!
