Hello and Good Morning/Afternoon:
Let's take this problem step-by-step:
What does the problem want us to find:
slopey-interceptLet's gather the information:
⇒ the information given: y = 1/5 x - 8
⇒ the line is in slope-intercept form
⇒ means:
⇒ coefficient in front of 'x' is the slope
⇒ constant is the y-intercept
slope is 1/5y-intecept is -8Answer:
Slope is 1/5y-intercept is -8Hope that helps!
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Hi!
The equation that we're working with is provided to us in Slope-Intercept Form:
[tex]\diamondsuit~~~\large\boldsymbol{y=mx+b}[/tex]
In the formula, the letter "m" denotes the slope, and it always comes before x; b is the y-intercept, and it's basically a number that is either added or subtracted from x.
Now let's identify the slope of the line given to us, that is:
[tex]\boldsymbol{\underline{\underline{y=1/5x-8}}}[/tex]
Slope = number before x,
Y-intercept = number added/subtracted from the slope
Therefore,
[tex]\stackrel{\heartsuit}{\boxed{\boxed{\textsc{Answers:}\begin{cases}\bold{Slope:\displaystyle\frac{1}{5}}\\\bold{Y-intercept:-8}\end{cases}}}}[/tex]
I hope it helped! Let me know if you need any explanation or clarification! I'm always happy to help. :D
graph the solution set of this inequality 3x-2y <_ 12
The graph of the solution set for the inequality can be seen below.
How to graph the solution set?Here we have the inequality:
3x - 2y < -12
If we isolate y, we get:
3x + 12 < 2y
(3x + 12)/2 < y
(3/2)x + 6 < y
Now, we just need to graph the line y = (3/2)x + 6 with a dashed line (because the points on the line are not solutions).
And then we need to shade the region above the line.
The graph of the solution set can be seen below.
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Area of Rectangle: A = length*width
One side of a rectangle is twelve kilometers longer than three times another side of the rectangle. Find the
sides if we also know that the area of the rectangle is 135 km².
shorter side:
longer side:
Answer:
shorter side: 5 km
longer side: 27 km
Step-by-step explanation:
So you're already given the formula for the area of a rectangle, the next thing to do is assign length and width in terms of some unknown variable, which for convenience, I'll just say is x. So let's say one of the sides is x, the one that's the shorter side, since the longer side can be related to the shorted side, which is x. The longer side is 12km longer than 3 times the other side, so since the other side is x, it's length is (3x+12). So we simply multiply this by x, to get the area which is 135
"Known" Values: one side=x, other side=3x+12, area=135 km^2
[tex]135=x(3x+12)[/tex]
Distribute the x
[tex]135=3x^2+12x[/tex]
Subtract 135 from both sides
[tex]0=3x^2+12x-135[/tex]
Now since the equation is equal to zero, we can use the quadratic equation. In this case a=3, b=12, and c=-135
[tex]x=\frac{-12\pm\sqrt{12^2-4(3)(-135)}}{2(3)}[/tex]
Simplify denominator and multiply inside of the radical
[tex]x=\frac{-12\pm\sqrt{144+1,620}}{6}[/tex]
If you're confused where the negative went in the radical, it canceled out when multiply -4 by -135. Now add the stuff in the radical
[tex]x=\frac{-12\pm\sqrt{1,764}}{6}[/tex]
Simplify the radical
[tex]x=\frac{-12\pm 42}{6}[/tex]
Now you might think there are two solutions to this equation, but the thing is that one of the sides simply cannot have a "negative length", because in this context, x must be positive. So it's easy to see you have to use the positive sign, since using the negative sign would result in -12-42 over 6 which is certainly negative. So we can ignore that solution as it doesn't mean anything in this context. We only need the positive solution
[tex]x=\frac{-12+42}{6}[/tex]
Add values
[tex]x=\frac{30}{6}[/tex]
Divide
[tex]x=5[/tex]
Since the shorter side was 5, that's the solution to the shorter side, now to find the longer side we plug in 5 into the equation: [tex]3x+12[/tex] which becomes 3(5) + 12 = 15+12 = 27. This means the two lengths are 5 and 27
Step-by-step explanation:
let x = length of shorter side
[tex](3x + 12)(x)= 135[/tex] This is the equation
[tex]3x^2+12x=135[/tex] use distributive property to multiply out
[tex]3x^2+12x-135=0[/tex] subtract 135 from both sides to get in position to factor
[tex]3(x^2+4x-45)[/tex] factor out a 3
[tex]3(x-5)(x-9)[/tex] factor the resulting expression
[tex]x=5,9[/tex] two answers (we want one so see which one works)
Check both values of x
[tex]5*3+12=27[/tex]
[tex]27*5=135[/tex]
Therefore, we know the shorter side is 5 km and the longer side is 27 km.
At this point, we do not even need to check x=9
Find three consecutive odd integers whose sum is 489
Answer:
162, 163, and 164.
Step-by-step explanation:
Here we will use algebra to find three consecutive integers whose sum is 489. We start by assigning X to the first integer. Since they are consecutive, it means that the 2nd number will be X + 1 and the 3rd number will be X + 2 and they should all add up to 489. Therefore, you can write the equation as follows:
(X) + (X + 1) + (X + 2) = 489
To solve for X, you first add the integers together and the X variables together. Then you subtract three from each side, followed by dividing by 3 on each side. Here is the work to show our math:
X + X + 1 + X + 2 = 489
3X + 3 = 489
3X + 3 - 3 = 489 - 3
3X = 486
3X/3 = 486/3
X = 162
Which means that the first number is 162, the second number is 162 + 1 and the third number is 162 + 2. Therefore, three consecutive integers that add up to 489 are 162, 163, and 164.
162 + 163 + 164 = 489
We know our answer is correct because 162 + 163 + 164 equals 489 as displayed above.
Answer:
161, 163, 165
Step-by-step explanation:
x + x+2 + x +4 =489.
This is how we calculate three consecutive odd integers!
Combine like terms:
3x+6=489
3x=483
x=161
Three numbers are:
161, 161+2, 161+4.
161, 163, 165
If you stand 100 feet away from a flagpole, and the angle of elevation to the top of the pole is 31°, what is the height of the flagpole?
The height of the flagpole with an angle of elevation to the top of the pole of 31° is 60.086 feet
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Trigonometric ratio is used to show the relationship between the sides and angles of a triangle.
Let h represent the height of the flagpole, hence:
tan(31) = h/100
h = 60.086 feet
The height of the flagpole with an angle of elevation to the top of the pole of 31° is 60.086 feet
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What is the percentage of salt in the solution made of 9 on of water and 3 lb of salt
The percentage composition of salt in the solution is; 84.2%.
What is the percentage composition of salt?Since, it follows that there are 16 ounces in 1 pound. Then the 3 lb of salt is equivalent to; 3×16 = 48ounces.
Consequently, the percentage of salt in the solution as described is;
{48/57} × 100%
Percentage composition of salt is therefore;
= 84.2%.
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At noon, ship A is 20 nautical miles due west of ship B. Ship A is sailing west at 17 knots and ship B is sailing north at 21 knots. How fast (in knots) is the distance between the ships changing at 3 PM? (Note: 1 knot is a speed of 1 nautical mile per hour.)
The distance between the ships is 26.65.
How to illustrate the distance?Based on the information given, after 3 hours, the distance of ship B will be:
= 20 + (17 × 3)
= 71.
A = 21 × 3 = 63
Well calculate the square root which will be:
A² + B² = 71² + 63²
= 5041 + 3969
= 9010
Therefore, ✓9010 = 94.92
Finally, the distance will be:
= (63 × 21) + (71 × 17) / 94.92
= (1323 + 1207)/94.92
= 26.65
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A. 2
C
C. 3
5
4
3
-3-2 A-10
-1
2
-2
-3
B
1
N
D
3 4
5
E
6
F
In the similarity
transformation of AACB
to AEFD, AACB was dilated by
a scale factor of [?], reflected
across the [ ], and moved
through the translation [ ].
B. 1/2
D. 1/3
Answer: x-axis
Step-by-step explanation:
If you visualize the line of reflection, it must be vertical. Option A is the only option that has a vertical line.
Which expression is equivalent to
The expression that is equivalent to the given expression is 16⁴
Evaluating an ExpressionFrom the question, we are to determine the expression that is equivalent to the given expression
The given expression is
[tex](\frac{1}{16} )^{-4}[/tex]
Evaluating
[tex](\frac{1}{16} )^{-4}[/tex]
[tex]= (16^{-1} )^{-4}[/tex]
[tex]= 16^{-1 \times -4}[/tex]
[tex]= 16^{4}[/tex]
Hence, the expression that is equivalent to the given expression is 16⁴
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The term can also be written as:
The correct expansion is the one in option b:
[tex]Log_9(\frac{6}{11}) = Log_9(6) - Log_9(11)[/tex]
How to rewrite the term?Here we must use the logarithmic property:
[tex]Log(a) -Log(b) = Log(\frac{a}{b})[/tex]
Our expression in this case is:
[tex]Log_9(\frac{6}{11})[/tex]
Using the above property, we can rewrite the expression as:
[tex]Log_9(\frac{6}{11}) = Log_9(6) - Log_9(11)[/tex]
From this, we conclude that the correct option is B.
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suppose that there are two types of tickets to show; advance and same -day. Advance tickets cost $35 and same-day tickets cost $30. For one performance, there were 50 tickets sold in all, and the total amount paid for them was $1650. How many tickets of each type were sold?
Answer:
#of advanced tickets (x) = 30
#of same-day tickets (y) = 20
Step-by-step explanation:
x-#of advanced tickets
y-#of same-day tickets
[tex]x+y=50,\\35x+30y=1650[/tex]
5x+30(x+y)=1650
5x+30(50)=1650
5x=150
x=30
y=20
Volume and surface area
Answer: 290.6
Step-by-step explanation:
The volume of the cone is [tex]\frac{1}{3}(\pi)(5.6^{2})(13.8-7)=\frac{26656}{375}\pi[/tex].
The volume of the cylinder is [tex](\pi)(5.6^2)(7)=219.52\pi[/tex].
Adding these together gives the exact volume to be [tex]\frac{108976}{375}\pi[/tex], which is 290.6 to the nearest tenth.
Find the locus of a point P which moves so that the sum of squares of squares of its distance A(3,0)and B(-3,0) is 4 times the distance between A and B
Based on the calculations, the equation for the locus of these points is equal to x² + y² = 9.
How to find the locus of a point?First of all, we would determine the distance between points A and B as follows:
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Distance = √[(-3 - 3)² + (0 - 0)²]
Distance = √[-9² + 0]
Distance = √81
Distance = 9.
Four (4) times the distance between points A and B is given by:
Distance = 9 × 4
Distance = 36.
Translating the word problem into a mathematical expression, we have:
a² + b² = 36
Also, from the distance formula we have:
a = √[(h + 3)² + (k - 0)²]
a² = h² + 6h + 9 + k²
Similarly, b² is given by:
b = √[(h - 3)² + (k - 0)²]
b² = h² - 6h + 9 + k²
Equating the equations, we have:
a² + b² = 36
h² + 6h + 9 + k² + h² - 6h + 9 + k² = 36
2h² + 2k² = 36 - 18
2h² + 2k² = 18
Dividing both sides by 2, we have:
h² + k² = 9 ⇒ x² + y² = 9.
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Can someone help me fully simplify this step by step pleaseeeee
[tex]2x - 7x + 2 + 1 - 2[/tex]
[tex]2x - 7x + 3 - 2[/tex]
[tex] - 5x + 1[/tex]
Select the correct answer from each drop-down menu. Which system of equations is represented by this graph? Graph shows system of equations plotted on a coordinate plane. A line goes through (minus 6, 0) and (0, minus 3). Another line goes through (0, 3) and (minus 4, minus 5). y = x + 3 y = x − 3 Reset
The equation of the line going through (-6, 0) and (0, -3) is y = -(1/2)x - 3
The equation of the line going through (0, 3) and (-4, -5) is y = 2x + 3
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
The equation of the line going through (-6, 0) and (0, -3) is:
y - 0 = [(-3 - 0) / (0- (-6)](x - (-6))
y = -(1/2)x - 3
The equation of the line going through (0, 3) and (-4, -5) is:
y - 3 = [(-5 - 3) / (-4 - 0)](x - 0)
y = 2x + 3
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Answer:
2
-1/2
Step-by-step explanation:
20. Find the solution to the system of linear equations below:
x - 3y = -5
2x + 5y = 12
O (-5, 12)
O (3,2)
O (-2,7)
O (1,2)
Answer:
The last option
Step-by-step explanation:
When you plug in 1 for the x and 2 for y, the answer is -5 for the first equation and is 12 for the second equation. I hope that helps!
Write an equation that represents the transformations formed by the following items: (a) horizontally shifting the graph of f(x) = square root over x, 9 units to the right and then vertically shrinking the graph by a factor of 2/3.
(b) vertically stretching the graph of f(x) = square root over x by a factor of 8 and then vertically shifting the graph 4 units down.
(c) horizontally stretching the graph of f(x) = square root over x, by a factor of 7 and then vertically shifting the graph 5 units up
(d) reflection of the graph of f(x) square root over x, across the y-axis and then vertically shifting the graph 10 units down. Answer:
The equations of the transformed graphs are [tex]f(x) = \frac 23\sqrt{x - 3}[/tex], [tex]f(x) = 8\sqrt{x }-3[/tex], [tex]f(x) = \sqrt{\frac x7} + 5[/tex] and [tex]f(x) = \sqrt{-x} - 10[/tex]
How to transform the functions?The function #1
The function is given as::
[tex]f(x) = \sqrt{x}[/tex]
It is shifted right by 3 units.
So, we have:
[tex]f(x) = \sqrt{x - 3}[/tex]
It is shrunk vertically by a factor of 2/3
[tex]f(x) = \frac 23\sqrt{x - 3}[/tex]
Hence, the equation of the transformed graph is [tex]f(x) = \frac 23\sqrt{x - 3}[/tex]
The function #2
The function is given as::
[tex]f(x) = \sqrt{x}[/tex]
It is stretched vertically by a factor of 8
[tex]f(x) = 8\sqrt{x }[/tex]
It is shifted down by 3 units.
So, we have:
[tex]f(x) = 8\sqrt{x }-3[/tex]
Hence, the equation of the transformed graph is [tex]f(x) = 8\sqrt{x }-3[/tex]
The function #3
The function is given as::
[tex]f(x) = \sqrt{x}[/tex]
It is stretched horizontally by a factor of 7
[tex]f(x) = \sqrt{\frac x7}[/tex]
It is shifted up by 5 units.
So, we have:
[tex]f(x) = \sqrt{\frac x7} + 5[/tex]
Hence, the equation of the transformed graph is [tex]f(x) = \sqrt{\frac x7} + 5[/tex]
The function #4
The function is given as::
[tex]f(x) = \sqrt{x}[/tex]
It is reflected across the y-axis
[tex]f(x) = \sqrt{-x}[/tex]
It is shifted down by 10 units.
So, we have:
[tex]f(x) = \sqrt{-x} - 10[/tex]
Hence, the equation of the transformed graph is [tex]f(x) = \sqrt{-x} - 10[/tex]
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Jenny is preparing a roast chicken dinner in honour of her daughter coming back for the holidays after studying abroad. Her daughter will be on Flight BM1264. Jenny will arrive at the airport ten minutes before the flight arrives and will leave with her daughter fifteen minutes after it lands. Her journey to the airport takes 25 minutes. Jenny wants to do all the preparation for the meal before leaving for the airport. It takes 30 minutes to prepare. She will leave for the airport straight after finishing the preparation. Jenny has bought a 2.4kg chicken. It takes 35-45 minutes per kg plus an additional 30 minutes to cook the chicken. Jenny will start cooking five minutes after getting back from the airport. QUESTION IS: HOW LATE CAN THEY EAT DINNER, ALSO PLANE ARRIVES AT 4PM
The addition is one of the four fundamental mathematical operations. Jenny can have dinner at 7 pm and 7.5 mins.
What is Addition?The addition is one of the four fundamental mathematical operations, the others being subtraction, multiplication, and division. When two whole numbers are added together, the total quantity or sum of those values is obtained.
The time can be calculated as,
Time taken for preparation = 30 minTime is taken to travel to airport = 25 minsShe will wait for 10 mins before the flight arrive = 10 minFlight lands at 4 pm
She will leave 15 mins after the flight lands = 15 minsIt takes 25 mins to travel back home ⇒ 15 + 25 minsShe will start cooking after 5 mins ⇒ 15+25+5 minJenny has bought a 2.4kg chicken. It takes 35-45 minutes per kg plus an additional 30 minutes to cook the chicken. Time needed for cooking the chicken = (2.5×45 + 30) = 142.5 min
⇒ 15+25+5+142.5 min
Thus, the total time it takes for Jenny to cook the food starting when the flight lands are ⇒ 187.5 mins = 3 hours 7.5 mins
Since the flight lands at 4 pm
⇒ 4 pm + 3 hours 7.5 mins
⇒ 7 pm and 7.5 mins
Hence, Jenny can have dinner at 7 pm and 7.5 mins.
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add 37 +31 by counting in tens
Answer:
(30+30) +(7+1) = 68
Step-by-step explanation:
hope this helps you (ʘᴗʘ✿)
An automobile travels 140 miles in 4 hours. Find the average rate of speed
Answer:
35mph
Step-by-step explanation:
divide 140/4=35
3,900,000,000,000,000,000,000,000,000,000,000 X 245,000
Answer:
955,500,000,000,000,000,000,000,000,000,000,000,000
or 9.555 x 10^38
Step-by-step explanation:
multiply 245 x 39 first and then add all the zeros from both numbers after
factorize it
evaluate it
factorise it
evaluate
factorize
Answer:
[tex](x^2+y^2+xy)(x^2+y^2-xy)[/tex]
Step-by-step explanation:
Rewrite the middle term.
[tex]x^4+2x^2y^2-x^2y^2+y^4[/tex]
Rerrange terms.
[tex]x^4+2x^2y^2+y^4-x^2y^2[/tex]
Factor first three terms by perfect square rule.
[tex](x^2+y^2)^2-x^2y^2[/tex]
Rewrite [tex]x^2y^2[/tex] as [tex](xy)^2[/tex].
[tex](x^2+y^2)^2-(xy)^2[/tex]
Since both terms are perfect squares, factor using the difference of squares formula, [tex]a^2-b^2=(a+b)(a-b)[/tex] where [tex]a=x^2+y^2[/tex] and [tex]b=xy[/tex].
[tex](x^2+y^2+xy)(x^2+y^2-(xy))[/tex]
Remove parentheses.
[tex](x^2+y^2+xy)(x^2+y^2-xy)[/tex]
Match the systems of equations with their solution sets. y + 12 = x2 + x x + y = 3 y − 15 = x2 + 4x x − y = 1 y + 5 = x2 − 3x 2x + y = 1 y − 6 = x2 − 3x x + 2y = 2 y − 17 = x2 − 9x -x + y = 1 y − 15 = -x2 + 4x x + y = 1 Solution Set Linear-Quadratic System of Equations {(-2, 3), (7, -6)} arrowRight {(-5, 8), (3, 0)} arrowRight {(-2, 5), (3, -5)} arrowRight {(2, 3), (8, 9)} arrowRight
The System of Equations 1, 2, 3, and 4 have solutions corresponding to the option B, A, C, and D.
What is a System of Equations?A system of equations is a set of equations that have a common solution.
The first system of equations is
y+12 = x² +x
x+y = 3
To determine the solution, the equations are plotted on the graph and the intersection of the equations gives the solution.
The solution is (-5,8) (3,0)
The second system of equation is
y-15 = -x² +4x
x+y = 1
The solution to the system is (7,-6) (-2,3)
The third system of equation is
y+5 = x²-3x
2x+y = 1
The solution to the system is (3,-5) (-2,5)
The fourth system of equation is
y-17 = x²-9x
-x+y =1
The solution to the system is (2,3) , (8,9)
Therefore, the System of Equations 1, 2, 3, and 4 have solutions corresponding to the option B, A, C, and D.
The graphs are attached with the answer.
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solve for x
[tex]\bold{4x - 64 = 0}[/tex]
ty! ~
Answer:
[tex]\tt x = 16[/tex]
Step-by-step explanation:
[tex]\tt 4x-64=0[/tex]
Add 64 to both sides.
[tex]\tt 4x - 64 + 64 = 0+ 64[/tex]
Simplify.
[tex]\tt 4x = 64[/tex]
Divide both sides by 4.
[tex] \tt \cfrac{4x}{4} = \cfrac{64}{4} [/tex]
Simplify.
[tex]\tt x = 16[/tex]
Done!!!
[tex]\Large\maltese\star\underline{\textbf{What is Asked}}\star\maltese[/tex]
Solve for x. [tex]\bf{4x-64=0}[/tex].[tex]\Large\maltese\star\underline{\textbf{The required answer is below -:}}\star\maltese[/tex]
First we need to add 64 to both sides. That way, we will be one step closer to solving this in terms of x.
[tex]\bf{4x-64+64=0+64}[/tex] | on the left side the 64's sum to zero
[tex]\bf{4x=0+64}[/tex] | the right side is now 64
[tex]\bf{4x=64}[/tex] | divide the equation by 4
[tex]\bf{x=16}[/tex]
[tex]\cline{1-2}[/tex]
[tex]\gray\star\bf{Result / Required\;Answer:}[/tex]
[tex]\star\blacksquare\Large\boxed{\boxed{\bf{X=16.}}}\blacksquare\star[/tex]
Key to solving this problem -:When you're solving an equation in terms of x, or any other variable, use inverse operations to solve it. For instance, if something is added to x, use subtraction. If something is subtracted to x, use addition.
If x is multiplied by something, use division. If x is divided by something, use multiplication.
[tex]\infty\LARGE\boxed{\bf{\brace aesthetic\not1\theta\ell}}\infty[/tex]
First accurate answer gets brainliest
Answer: [tex]20x^2 + 47x+24[/tex]
Step-by-step explanation:
We just multiply the values on the edges like we are finding the area of a square, L * L = area.
4x * 5x = 20x^2
4x * 8 = 32x
3 * 8 = 24
3 * 5x = 15x
Next add the answers together
20x^2 + 47x + 24
Answer:
option 3
Step-by-step explanation:
you need to times (4x+3) by (5x+8)
so you basically need to expand the brackets and collect like terms
What is the equation of a parabola that has intercepts of x=-2 and x=6 and passes through point (8,6)?
Step-by-step explanation:
general form of a parabola :
y = ax² + bx + c
we have 3 points of the parabola to calculate the 3 variables :
the 2 intercepts are actually
(-2, 0)
(6, 0)
and then
(8, 6)
so, we get the 3 equations
0 = a(-2)² + b×-2 + c = 4a - 2b + c
0 = a×6² + b×6 + c = 36a + 6b + c
6 = a×8² + b×8 + c = 64a + 8b + c
from the 1st equation we get
c = -4a + 2b
using that in the 2nd equation we get
0 = 36a + 6b - 4a + 2b = 32a + 8b = 4a + b
b = -4a
therefore,
c = -4a + 2b = -4a + 2×-4a = -4a - 8a = -12a
using all that in the 3rd equation we get
6 = 64a + 8×-4a + -12a = 64a - 32a - 12a = 20a
a = 6/20 = 3/10 = 0.3
b = -4a = -4×3/10 = -12/10 = -1.2
c = -12a = -12×3/10 = -36/10 = -3.6
so, we have
y = 3/10 x² - 12/10 x - 36/10 = 3/10 × (x² - 4x - 12)
How many surgeon are either office-based or ophthalmologist.?
Answer:
Is there a graph related to this question?
Classify the triangle as acute, right, or obtuse and classify it as equilateral, isosceles, or scalene.
The triangle is Obtuse and scalene , Option C is the correct answer.
What is a Triangle ?A triangle is a polygon with three sides , three angles and three vertices.
A triangle can be classified as Acute , Right or Obtuse on the basis of the angle in a Triangle .
and it is classified as scalene , equilateral and isosceles on the basis of the length of the sides of a triangle.
The triangle given in the question has all the sides different , so it is a scalene triangle.
One of the angle is obtuse angle and so it can be classified as a Obtuse Angle Triangle.
Therefore , Option C is the correct answer.
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Answer:
right angle
Step-by-step explanation:
Find the volume of a cone with a diameter of 12 m and a height of 7m.
A. 84 m^3
B. 84π m^3
C. 336 π m^3
D. 252 π m^3
Answer Fast!
I am giving 100 points and brainliest!
Answer:
84π m^3
Step-by-step explanation:
1. The formula of a cone is: (1/3) · π · r^2 · h
2. The radius is 6m. (Diameter / 2)
3. (1/3) * π * (6^2) * 7
4. Multiply all numbers besides pi to get the answer in terms of pi
5. (36 / 3 ) = 12 * 7 = 84
6. 84π
[tex] \Large \purple \maltese \Huge\: \underline {\rm {{{\color{cyan}{Given...}}}}} \: [/tex]
Diameter = 12 Radius = 12/2 = 6mHeight = 7m[tex] \Large \purple \maltese \Huge\: \underline {\rm {{{\color{cyan}{To \: Find ...}}}}} \: [/tex]
Volume of cone[tex] \Large \purple \maltese \Huge\: \underline {\rm {{{\color{cyan}{Formula \: Using ...}}}}} \: [/tex]
[tex]\Large❏ \: \Large\begin{gathered} {\underline{\boxed{ \sf {{\large {\tt {{{\color{blue}{Volume_{ \red{( cone)}}}}}}}\large\orange\implies \tt \large \: \frac{1}{3}\pi {r}^{2} h}}}}}\end{gathered}[/tex]
Where,
r is radiush is height[tex] \Large \purple \maltese \Huge\: \underline {\rm {{{\color{cyan}{Solution ...}}}}} \: [/tex]
Substituting the given values in formula.
[tex]\large {\tt {{{\color{blue}{Volume_{ \red{( cone)}}}}}}}\large\orange\implies \tt \large \: \frac{1}{3}\pi {r}^{2} h[/tex]
[tex]\large {\tt {{{\color{blue}{Volume_{ \red{( cone)}}}}}}}\large\orange\implies \tt \large \: \frac{1}{3}\pi {(6)}^{2} \: \times \: 7[/tex]
[tex] \large {\tt {{{\color{blue}{Volume_{ \red{( cone)}}}}}}}\large\orange\implies \tt \large \: \frac{1}{ \cancel3}\pi \: \times \: \cancel{ 36} \: \: ^{ \pink{12}} \: \times \: 7 \\ [/tex]
[tex]\large {\tt {{{\color{blue}{Volume_{ \red{( cone)}}}}}}}\large\orange\implies \tt \large \:\pi \: \times \: 12 \: \times \: 7 \\ [/tex]
[tex]\large {\tt {{{\color{blue}{Volume_{ \red{( cone)}}}}}}}\large\orange\implies \tt \large \: 84 \pi \: {m}^{3} [/tex]
Hence , option b is the correct answer
i need to get this done, please help
The expression that is a sum of cubes is given as follows:
[tex]-27a^3b^6 + 8a^9b^12[/tex]
What is a sum of cubes?An expression that is a sum of cubes is given as follows:
a³ + b³.
For the sum, all numeric factors have to be powers of 3, while all exponents have to be multiples of 3. Hence the expression that is a sum of cubes is given as follows:
[tex]-27a^3b^6 + 8a^9b^12[/tex]
More can be learned about a sum of cubes at https://brainly.com/question/26726803
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write the zeros of this function: f(x) = 25 - 75x - 100x^2