Answer:
Step-by-step explanation:
t2 = a*r
t2 = 6
t5 = a*r^4
t5 = 162
162/6 = ar^4 / ar
r^3 = 27
r = 3
6 = a*3
2 = a
Sum = a(r^n - 1)
=======
r - 1
n = 5
a = 2
r = 3
Sum = 2(3^5 - 1)
=======
2
Sum = 242
The diameter of a cylinder is 4 m. If the height is triple the radius, which is the closest to the
?volume of the cylinder
75.40 m3 o
251.33 m3 o
100.53 m3 o
613.19 m3 o
WILL MARK BRAINLIEST OR WHATEVER NEEDED ASAP
Answer:
A. 75.40 m³
Step-by-step explanation:
Diameter of cylinder (d) = 4 m
Radius (r) = ½(d) = ½(4) = 2 m
Height (h) = 3 × r = 3 × 2 = 6 m
Volume of cylinder = πr²h
Substitute the values
Volume of cylinder = π*2²*6
Volume of cylinder = π*4*6
Volume = π*24
Volume = 75.40 m³
Classify the following polynomials according to the number of terms. Combine any like terms first.
x^2 + 3x + 2x
x^2 + 5x = Binomial
x^3 + x + 3x^2 - x
x^3 + 3x^2 = Binomial
4x^3 + x + x^2 - 2x
4x^3 + x^2 - x = Trinomial
3x^4 + x - 3x^4 - x
0 = No Polynomial/Zero Polynomial
Hope this helps!
The first given polynomial is binomial.
The second given polynomial is binomial.
The third given polynomial is binomial.
The fourth given polynomial is monomial.
What is polynomial?Polynomials are algebraic expressions that consist of variables and coefficients.
What is monomial?A monomial is an algebraic expression that has only one term.
What is binomial?Binomial is an algebraic expression that contains two different terms connected by addition or subtraction.
What is trinomial give?A trinomial is an algebraic expression that has three non-zero terms.
According to the given question.
We have some polynomials.
If we take the polynomial:
[tex]x^{2} +3x+2x[/tex]
The above polynomial can be written as
[tex]x^{2} + 5x[/tex]
Since, the above polynomial has only two terms therefore it is a binomial.
[tex]x^{3} +x+3x^{2} -x = x^{3} +3x^{2}[/tex]
The above polynomial has only two terms. Hence, the given polynomial is binomial.
[tex]4x^{2} + x + x^{2} -2x\\=5x^{2} -x[/tex]
The given polynomial has only two terms therefore it is binomial.
[tex]3x^{4} + x - 3x^{4} -x\\= 0[/tex]
The given polynomial has only one term therefore it is monomial.
Find out more information about classification of polynomials here:
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The sum of two rational numbers is 9 and one of them is − 3, then the other is_.( ) 10
Answer:
12
Step-by-step explanation:
let the rational number be x
x+(-3) = 9
x = 9+3 = 12
Answer:
12
Step-by-step explanation:
x + y = 9
x = -3
=>
-3 + y = 9
y = 12
Find the missing length.
Answer:
hello,
Step-by-step explanation:
12²=(x-16)*16
9=x-16
x=25
Relation metric in a right triangle
xpower4 minus 16 bracket b minus c whole power 4
Answer
6372 - power 4
Step-by-step explanation:
In how many ways can 10 people be divided into three groups of 2, 3, and 5 people respectively
Given:
Total number of people = 10
To find:
The number of ways in which 10 people can be divided into three groups of 2, 3, and 5 people respectively.
Solution:
We know that the number of ways to select r items form n times is:
[tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]
The number of ways to select 2 people from 10 is [tex]^{10}C_2[/tex].
The number of remaining people is [tex]10-2=8[/tex].
The number of ways to select 3 people from 8 is [tex]^{8}C_3[/tex].
The number of remaining people is [tex]8-3=5[/tex].
The number of ways to select 5 people from 5 is [tex]^{5}C_5[/tex].
Now, the total number of ways is:
[tex]Total=^{10}C_2\cdot ^{8}C_3\cdot ^{5}C_5[/tex]
[tex]Total=\dfrac{10!}{2!(10-2)!}\cdot \dfrac{8!}{3!(8-3)!}\cdot \dfrac{5!}{5!(5-5)!}[/tex]
[tex]Total=\dfrac{10\times 9\times 8!}{2\times 1\times 8!}\cdot \dfrac{8\times 7\times 6\times 5!}{3\times 2\times 1\times 5!}\cdot 1[/tex]
[tex]Total=45\cdot 56\cdot 1[/tex]
[tex]Total=2520[/tex]
Therefore, the total number of ways is 2520 to divide 10 people into three groups of 2, 3, and 5 people respectively.
Using only the values given in the table for the function f(x) = x^3 - 3x - 2 what is the interval of x-values over which the function is decreasing?
Answer:
3 = 3(x² - 1) We know, any Function f(x) decrease s in interval [a, b] when f'(x) < 0 ... -1 < x < 1. Hence, function f(x) = x³ - 3x - 2 , is decreased in (-1, 1).
pls answer my question from the above picture
Answer:
Step-by-step explanation:
[tex]a^{m}* a^{n}=a^{m+n}\\\\\\(\frac{-1}{2})^{-19}*(\frac{-1}{2})^{8}=(\frac{-1}{2})^{-2x +1}\\\\(\frac{-1}{2})^{-19+8}=(\frac{-1}{2})^{-2x+1}\\\\\\(\frac{-1}{2})^{-11}=(\frac{-1}{2})^{-2x+1}[/tex]
As bases are equal in boht sides, we can compare the exponents.
-2x + 1 = -11
Subtract 1 form both sides
-2x = -11 - 1
-2x = -12
Divide both sides by -2
x = -12/-2
x = 6
In parallelogram QRST if RU=17 find UT.
help me fast plzzzzzz
Answer:
has been saving is the correct answer I believe
Answer:
"has been saving" is the right answer.
pls help me i really need it!
Answer:
A
Step-by-step explanation:
make g the subject 4m+2g=p
Step-by-step explanation:
4m+2g=p
2g=p-4m
g=(p-4m)/2
Answer:
g = p/2 - 2m
Step-by-step explanation:
4m +2g = p
Subtract 4m from each side
4m -4m +2g = p-4m
2g = p -4m
Divide each side by 2
2g/2 = p/2 - 4m/2
g = p/2 - 2m
On a unit Circle, the terminal point of 0 is (sqrt3/2, 1/2) what is 0?
This is a point, so it has x- and y-coordinates. Both of these coordinates are positive, therefore the point must be in the first quadrant.
The pattern for the points on a unit circle is 3 - 2 - 1 starting at 0 and up to pi/2. The pattern for the radian denominators on a unit circle is 6 - 4 - 3 starting at 0 and up to pi/2.
(sqrt(3) / 2, 1/2) = pi / 6 radians
Hope this helps!
Answer:
A. pi/6 radians
Step-by-step explanation:
The ratio of the lengths of the sides of a 30-60-90 triangle is
1/2 : sqrt(3/2) : 1
sin theta = opp/hyp
tan theta = 1/2 / 1
tan theta = 1/2
theta = pi/6 radians
Answer: A. pi/6 radians
State the equation, in slope-intercept form, of each of the following graphs of linear relations.
Explain how the equation was determined.
Answer: y=80/5x+80
Step-by-step explanation:
At one point graph goes from (0,400) to (25,800). So the y intercept is 400 because that’s where the line was at x=0. 0 to 25 is 25. 400 to 800 is 400. So the equation would be y=400/25x+400. But you can divide all of it by 5 to get y=80/5x+80.
SEE QUESTION IN IMAGE
Answer:
42Required probability:
P(≤4) = (18 + 14 + 20 + 16)/(18 + 14 + 20 + 16 + 15 + 17) = 68/100 = 0.6843Required probability:
P(>3) = (20 + 16 + 15 + 17) / (18 + 14 + 20 + 16 + 15 + 17) = 68/100 = 0.6844At least 2 students pass:
P(2 or 3) = (3/5)² + (3/5)³ = 9/25 + 27/125 = 72/125 = 0.57645Number of x's:
x/108 = 4/27x = 108*4/27x = 16hlp pleassssssssssssssssssssss
Answer:
Volume of a cube is s×s×s
hence 7 cube=343
343 is the answer. Hope this helps you. Good luck^_^
A taxi fare is $3 and then $0.40 for every kilometre. A taxi fare is $9 . How far has the taxi travelled?
Answer:
y = 3 + 0.40x
Step-by-step explanation:
Fixed cost of taxi fare = $3
Additional cost = $0.40
Let
y = Total cost
x = number of kilometers
The equation:
Total cost = Fixed cost of taxi fare + (Additional cost * number of kilometers)
y = 3 + 0.40x
Simplify
Rewrite the expression in the form 9^n
(9^2)^5
Answer:
9^10
Step-by-step explanation:
(a^b)^c = a^(b×c)
hihi
Please help me
A person starts walking from home and walks: 6 miles East 6 miles Southeast 3 miles South 5 miles Southwest 2 miles East This person has walked a total of 22Correct miles Find the total displacement vector for this walk: If this person walked straight home, they'd have to walk miles
Answer:
1) The total displacement vector is ((16 + √2)/2, -(6+11·√2)/2)
2) The number of miles they'd have to walk is approximately 13.856 miles
Step-by-step explanation:
1) The distance, direction, and location of the path of the walk the person takes, are listed as follows;
Start location, (0, 0)
6 miles East walk to location, (6, 0)
6 miles Southeast to location, (6 + 3·√2, -3·√2)
3 miles South to location, (6 + 3·√2, -3·√2 - 3)
5 miles Southwest to location, (6 + 3·√2 - 2.5·√2, -3·√2 - 3 - 2.5·√2)
2 miles East to location, (6 + 3·√2 - 2.5·√2 + 2, -3·√2 - 3 - 2.5·√2)
(6 + 3·√2 - 2.5·√2 + 2, -3·√2 - 3 - 2.5·√2) = ((16 + √2)/2, -(6+11·√2)/2)
Therefore the destination coordinates is ((16 + √2)/2, -(6+11·√2)/2)
The total displacement vector, [tex]\underset{d}{\rightarrow}[/tex] = ((16 + √2)/2, -(6+11·√2)/2)
d = (16 + √2)/2)·i - (6+11·√2)/2)·j
2) If the person walked straight home, the number of miles they'd have to walk, [tex]\left | \underset{d}{\rightarrow} \right |[/tex], is given as follows;
[tex]\left | \underset{d}{\rightarrow} \right | = \sqrt{\left(\dfrac{16 +\sqrt{2} }{2} \right)^2 + \left(-\dfrac{6 + 11 \cdot \sqrt{2} }{2} \right)^2 } = \sqrt{134 + 41 \cdot \sqrt{2} }[/tex]
Therefore;
If the person walked straight home, the number of miles they'd have to walk [tex]\left | \underset{d}{\rightarrow} \right | \approx 13.856 \ miles[/tex]
If the triangle on the grid below is translated three units left and nine units down, what are the coordinates of C"?
Write the equation of the line with a slope of 4 that contains the point (5, 8).
Answer:
y = 4x - 12
Step-by-step explanation:
y = 4x + b
8 = 4(5) + b
8 = 20 + b
-12 = b
[tex] \green{ \boxed{\boxed{\begin{array}{cc} \maltese \bf \: \: \: we \: know \: that \: \\ \sf \: if \: any \: equation\:of \: line \: which \: slope (m) \\ \sf \: and \: passes \: through \: (x_1,y _1) \: \: then \: its \\ \sf equation \: is \: : \\ \\ \red{ \boxed{ \bf y - y_1 = m(x - x_1)}}\bf\end{array}}}}[/tex]
Given that,
A equation of the line with a slope of m = 4 and that contains / passes through the point (5, 8).
So,
[tex] \green{ \boxed{\boxed{\begin{array}{cc} \bf \: x_1 = 5 \: \: \: \\ \bf y_1 = 8 \\ \bf \: m \: = 4 \: \: \end{array}}}}[/tex]
NOW,
The equation is :
[tex] \green{ \boxed{\boxed{\begin{array}{cc} \bf \: y - 8 = 4(x - 5) \\ \\ = > \bf \: y - 8 = 4x - 20 \\ \\ = > \pink{ \boxed{\bf\:4x - y - 12 = 0}} \end{array}}}}[/tex]
Rewrite the expression in the form x^n:
x^-10/3
---------
x^3
Answer:
x^ (-19/3)
Step-by-step explanation:
x ^ (-10/3) ÷ x^3
We know a^b ÷ a^c = a^(b-c)
x ^ (-10/3) ÷ x^3 = x^(-10/3 - 3) = x^(-10/3 - 9/3) = x^ (-19/3)
Which of the following shapes is the cross-section for a cone?
O A. Pentagon
O B. Square
O C. Triangle
O D. Circle
Answer:
The choose (D)
D. Circle
I hope I helped you^_^
The required cross-section for a cone is a circle. Option D is correct.
What is a conic section?A conic section is a geometric shape that is obtained by intersecting a cone with a plane. Conic sections include circles, ellipses, parabolas, and hyperbolas.
The type of conic section that is formed depends on the angle of the plane relative to the axis of the cone, as well as the distance of the plane from the vertex of the cone.
Here,
The cross-section of a cone is a circle.
A cross-section is a shape that you get when you slice a 3D object with a plane. If you slice a cone parallel to its base, you get a circle as the cross-section.
Therefore, the correct answer is option D.
Learn more about the conic section here;
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the sum of the ages of chukwu and Caroline is 45 years if the difference in their age is 3 years find the age of chukwu (chukwu is older than Caroline)
Step-by-step explanation:
let,the sum of the ages of chukwu & Caroline be X & Y.
now,
X+y=45
X-y=3
(+) (+) (-)
__________
2x=42
or,X=42/2
or,X=21
putting the value of X,
X+y=45
or, 21+y=45
or,y=45-21
or,y=24
therefore,X=21
y=24
if a = 3 and b=2,find the value of a square+2ab and (a+b)square
Answer:
a^2+2ab = 21
(a+b)^2= 25
Step-by-step explanation:
(a+b)^2 = a^+2ab+b^2
sub a=3 and b=2 and simplify
A ladder that is 17 feet long is 8 feet from the base of a wall. How far up the wall does the ladder reach?
Using Pythagoras theorem
[tex]\\ \Large\sf\longmapsto P^2=H^2-B^2[/tex]
[tex]\\ \Large\sf\longmapsto P^2=17^2-8^2[/tex]
[tex]\\ \Large\sf\longmapsto P^2=289-64[/tex]
[tex]\\ \Large\sf\longmapsto P^2=225[/tex]
[tex]\\ \Large\sf\longmapsto P=\sqrt{225}[/tex]
[tex]\\ \Large\sf\longmapsto P=15ft[/tex]
Answer:
Applying the Pythagorean theorem we have :wall length is : a²-b²=c²⇒17²-8²=c²⇒c=15(c>=0)Step-by-step explanation:
we have : the length of the ladder is the hypotenuse of the triangle ; the length of the ladder, which is far from the wall, is the right angle side of the triangle (draw your own illustration)
9) Three times a number added to 12 gives -6. Find the number.
Answer:
The number is -6.
Step-by-step explanation:
Variable x = a number
Set up an equation:
3x + 12 = -6
Isolate variable x:
3x = -18
x = -6
Check your work:
3(-6) + 12 = -6
-18 + 12 = -6
-6 = -6
Correct!
Answer:
3x +12=-6
3x=-6-12
3x=-18
x=-18/3
x=-6
Which statement can be modeled by x + 3 < 12?
Julie has 3 notebooks. Together, Mary and Julie have less than 12
notebooks
Sam sold 3 mobiles. To earn a prize, Sam must sell atleast 12 mobiles.
Frank has 3 hats. Frank and his brother Peter have more than 12 hats.
Sandy walked 3 miles yesterday. She must walk more than 12 miles.
Answer:
Step-by-step explanation: i think in my own word x+3<12 is A because it said julie only 3 notebook togerther it make itt less than 12notebook
=
-1
Use the distributive property with factoring to find the equivalent expression.
33x + 22y = 11 X + y
Answer:
22x + 21y = 0
Step-by-step explanation:
33x + 22y = 11x + y
Subtract y from both sides.
33x + 21y = 11x
Subtract 11x from both sides.
22x + 21y = 0
Please help me: 1/2(6h-4) = -5h+1
Answer:
h = 3/8
Step-by-step explanation:
1/2(6h-4) = -5h+1
Distribute
3h -2 = -5h+1
Add 5h to each side
3h-2+5h = -5h+1+5h
8h-2 = 1
Add 2 to each side
8h-2 +2 = 1+2
8h = 3
Divide by 8
8h/8 = 3/8
h = 3/8
