Twelve identical cylindrical pop cans are placed in a box. If sand fills the space between the pop cans and the cans and the sides of the box, what volume of sand is needed?
Answer:
Step-by-step explanation:
I don't see any information on dimensions of the cans or box, so I'll assume the question wants a general solution.
Three steps will result in the volume of sand required to fill the remaining space in the box.
1. Calculate the volume of a can using the equation for the volume of a cylinder: Vol = πr²h
2. Multiply the can volume by 12. This will give the total volume of the 12 cans in the box.
3. Calculate the volume of the box: Volume = (Base)(Width)(Height)
[Make sure the units are the same as those used in calculating the can volume. E.g., if the can is calculated with cm as the measue, the box dimensions must also be cm]
4. Subtract the volume of the12 cans (from step 2) from the volume of the box.
The result from 4 will be the volume of sand required to fill the box containing 12 cans.
I'm not clear why filling the box with sand is important, but perhaps it will absorb any soda released from cans broken when the heavy box is dropped by the person shocked that 12 cans of pop could be so heavy.
If the percent of discount of an item is 25 percent and the sale price is $40 what is the original price
Answer:
$53.33
Step-by-step explanation:
40/1 - .25
40/.75 = $53.33
A right triangle has leg lengths of 9 units and 12 units. Write an equation that can be
used to determine the length of the hypotenuse, c .
The Pythagorean Theorem: [tex]a^2+b^2=c^2[/tex]
a and b are the two legs in a right trianglec is the hypotenuse (the longest side of a right triangle; opposite the 90° angle*keep in mind that this theorem applies only to right trianglesSolving the QuestionWe're given:
Legs = 9 units and 12 unitsHypotenuse = cPlug these measurements into the Pythagorean theorem:
[tex]a^2+b^2=c^2\\9^2+12^2=c^2[/tex]
⇒ Combine like terms:
[tex]81+144=c^2\\c^2=225[/tex]
Answer[tex]c^2=225[/tex]
The shorter leg of a right triangle has a measure of x + 5. The longer leg is one less than three times the length of the shorter leg. The hypotenuse is thirteen more than two times the shorter leg. The area of the triangle, A, is 2.5 times the magnitude of the perimeter.
Create a system of equations to model the situation above. Determine if there are any solutions, and, if possible, whether or not they are viable.
How many total possible solutions of the form (x, A) are there for this situation?
How many total viable solutions of the form (x, A) are there for this situation?
Answer:
Given:
[tex]\textsf{Shorter leg}=(x+5)[/tex][tex]\textsf{Longer leg}=3(x+5)-1[/tex][tex]\textsf{Hypotenuse}=2(x+5)+13[/tex][tex]\sf A=2.5P\quad \textsf{(where A is area and P is perimeter)}[/tex][tex]\begin{aligned} \textsf{Perimeter} & =\textsf{shorter leg + longer leg + hypotenuse}\\ & = (x+5)+[3(x+5)-1]+[2(x+5)+13]\\ & = x+5+3x+15-1+2x+10+13\\ & = 6x+42\end{aligned}[/tex]
[tex]\begin{aligned} \textsf{Area} & =\dfrac12\textsf{(shorter leg)(longer leg)}\\ & =\dfrac12(x+5)[3(x+5)-1]}\\ & =\dfrac12(x+5)(3x+14)\\ & = \dfrac12(3x^2+29x+70)\\ & = \dfrac32x^2+\dfrac{29}{2}x+35 \end{aligned}[/tex]
[tex]\begin{aligned} \textsf{Area} & =2.5 \sf (Perimeter)\\ \implies \dfrac32x^2+\dfrac{29}{2}x+35 & =\dfrac52(6x+42)\\ 3x^2+29x+70 & =5(6x+42)\\ 3x^2+29x+70 & =30x+210\\ 3x^2 -x-140 & =0\\ 3x^2-21x+20x-140 & =0\\ 3x(x-7)+20(x-7) &=0\\ (x-7)(3x+20)& =0\end{aligned}[/tex]
Therefore:
[tex](x-7)=0 \implies x=7[/tex]
[tex](3x+20)=0 \implies x=-\dfrac{20}{3}[/tex]
[tex]x=-\dfrac{20}{3}[/tex] is not a viable solution as when inputting this into the formula for the shorter leg, it gives a negative value:
[tex]\textsf{Shorter leg}=-\dfrac{20}{3}+5=-\dfrac53[/tex]
As distance cannot be negative, this is not a viable solution.
When x = 7:
[tex]\textsf{Shorter leg}=7+5=12[/tex]
[tex]\textsf{Longer leg}=3(7+5)-1=35[/tex]
[tex]\textsf{Hypotenuse}=2(x+5)+13=37[/tex]
[tex]\textsf{Perimeter}=6(7)+42=84[/tex]
[tex]\textsf{Area} & =\dfrac32(7)^2+\dfrac{29}{2}(7)+35=210[/tex]
Therefore, there is one viable solution. This solution in the form (x, A) is (7, 210)
The sum of two numbers is 122. The difference of the first number and twice the second number is 23. Find the two numbers.
Answer:
One is 89 , the other is 33.
Step-by-step explanation:
Set up a system of 2 equations:
x + y = 122
x - 2y = 23 Subtracting:
0 + 3y = 99
y = 33.
So:
x + 33 = 122
x = 122 -33 = 89.
Answer:
first number= 89 and second number= 33
Step-by-step explanation:
here, let the first number be X and the second number be y,then
From the question,
x + y = 122 ---- eq i
x -2y = 23 ----- eq ii
From substitution method,
From eq i,
x + y = 122
or, x =122 - y
Now, putting the vale of x in eq ii,we get,
122 -y -2y = 23
or, -3y = 23-122
or, -3y = -99 (cut minus sign in both sides)
or, y=99/3
or, y = 33
Again, putting the value of y in eq i,we get,
x + 33 = 122
or, x= 122-33
or, x=89
From first principle, find the derivative of y=2x^3+x²+4x with respect to X
Answer:
[tex]derivative \: of \: y = 6 {x}^{2} + 2x + 4[/tex]
Step-by-step explanation:
we know that
[tex] \frac{d}{dx} {x}^{n} = n {x}^{n - 1} [/tex]
Now the derivative of y=2x³+x²+4x
[tex] \frac{dy}{dx} = \frac{d}{dx} (2 {x}^{3} + {x}^{2} + 4x)[/tex]
[tex] \frac{dy}{dx} = \frac{d}{dx} (2 {x}^{3} ) + \frac{d}{dx}( {x}^{2} ) + \frac{d}{dx} (4x)[/tex]
[tex]\frac{dy}{dx} = 2(\frac{d}{dx} {x}^{3} ) + \frac{d}{dx} {x}^{2} + 4(\frac{d}{dx} x)[/tex]
here
[tex]\frac{d}{dx} {x}^{3} = 3 {x}^{2} [/tex]
[tex]\frac{d}{dx} {x}^{2} = 2x[/tex]
[tex]\frac{d}{dx} x = 1[/tex]
Now
[tex]\frac{dy}{dx} = 2(3 {x}^{2} ) + 2x + 4(1)[/tex]
[tex]\frac{dy}{dx} = 6 {x}^{2} + 2x + 4[/tex]
I hope it helped you
WILL GIVE BRAINLIEST!!!
Solve 3(2x - 3) = 15. Explain ALL steps.
Answer:
x=4
Step-by-step explanation:
distributive property goes first.
you get 6x-9=15
add 9 on both sides so 9 cancells out on the left side.
you get 6x=24
divide by 6 and you get x=4
Super Sandwiches offers 4 kinds of breads, 3 kinds of meats, 5 cheeses, and 7 dressings for a sandwich. How many possible combinations would there be for making a sandwich
Answer:
19
Step-by-step explanation:
Answer:
420
Step-by-step explanation:
Need help with khan geometry no link pls just answer
Angles ABC and CBD are complementary - they add up to 90°. This means
(4x + 52°) + (8x - 10°) = 90°
Solve for x :
12x + 42° = 90°
12x = 48°
x = 4°
It follows that angle CBD has measure
4 • 4° + 52° = 16° + 52° = 68°
Using the tree diagram below, what is the probability of getting tails and an even number?
hi the awnser us defiantly going to be that I 56
Step-by-step explanation:
edge
The equation y = 8x 12, where x is the number of hours and y is the total cost, represents what the surf instructor charges for lessons. use this information to describe how to draw the line on a graph.
Answer:
Use points (0,12) and (1,20) on graphing paper or a program to find final answer.
Step-by-step explanation:
In the problem, I was unable to understand the equation so I am presuming the equation actually means y=8x+12
Whenever you graph a Linear Function you always need two points. The first point is always easy to acquire.
You can plug in any value for x, which will be your x cordinate and the output (solution) of the equation will be you y cordinate.
I'm plugging in 0 for X first.
y=8x+12
y=8(0) +12
y=12
We have our first point as (0,12)
Now you can plug in any other number for X other then Zero.
I choose 1 this time for X.
y=8x+12
y=8(1)+12
y=8+12
y=20
We now have our second point (1,20). Two points will be enough to graph this graph, you can graph these two points and then draw a line if on paper or use an application and get the line that way.
Answer:
Use the rise/run strategy to draw the line. Start at the y-intercept (0, 12), and count 8 up and 1 to the right to the point (1, 20). Then, draw a line through the points. Test the point (3,36) in the equation y = 8x + 12 to verify that the line is correct.
Step-by-step explanation:
got it right
Manuel works out at the gym 2 days each week for 3/4 hour each day
how many hours does manuel work out each week?
2 x 3/4 =
Answer:
1.5, so an hour and thirty minutes
Step-by-step explanation:
Simplify 3/4 as 0.75. 0.75 times 2 is 1.5.
What’s the area of the circle?
r= 4m
Answer:
50.3
Set A to the value of pi times the radius squared.
[tex]4^2 = 4 * 4 = 16\\\\A = \pi *r^2(4^2) = 50.26548245...[/tex]
Given the following graph, define a) the vertex, b) the intercepts, c) the axis of symmetry, and the sign of the lead coefficient.
Answer:
Option D is correct
[tex]Slope[/tex] [tex]of[/tex] [tex]AC=Slope[/tex] [tex]of[/tex] [tex]DF[/tex]
Step-by-step explanation:
Given:
1.
ΔABC and ΔDEF are similar
Property of similar states that corresponding sides are in proportion.
2.
[tex]\frac{BC}{EF}=\frac{AB}{DE}[/tex] [By property of similar triangles]
Property of proportions allows you to cross multiply the equation.
then;
3.
[tex]\frac{AB}{BC}=\frac{DE}{EF}[/tex] [Property of proportion]
Definition of slope: Slope is described as the steepness and direction of line.
then by definition of slope;
4.
[tex]Slope[/tex] [tex]of[/tex] [tex]AC=\frac{BC}{AB}[/tex]
5.
[tex]Slope[/tex] [tex]of[/tex] [tex]DF=\frac{EF}{DE}[/tex]
6.
Substitution property of equality states that:
If a = b then a can be substituted in place of b in any equation or vice-versa.
then;
[tex]Slope[/tex] [tex]of[/tex] [tex]AC= Slope[/tex] [tex]of[/tex] [tex]DF[/tex]
Therefore, the missing step in 6 we get,
[tex]Slope[/tex] [tex]of[/tex] [tex]AC= Slope[/tex] [tex]of[/tex] [tex]DF[/tex]
what is x if 1/4x = 9?
Answer:
x is 36
Step-by-step explanation:
the way to find out is 1/4 multiplied by what gives you 9. 9 divided by 1/4 is 36. 36 1/4's gives you 9.
Answer: 2
Step-by-step explanation:first u subtract 1-9=8then u divide 4/8=2 tell me if wrong
(WILL MARK BRAINLIST)
Write an inequality to represent the graph.
у
-5
4
3
(0, 2)
2 1
x
x
-5 -4 -3 -2 -1 0
-1
2
4 5 6 7 8 9 10
(4,-1)
-2
-3
-4
-51
-6
-7
-8
-9
-Previous Question
Question 1 (Answered)
PLS I really need this a have 40 questions due tomorrow :( (please help anyone) 16 points
Two angles are supplementary. The larger angle is 15 more than 10 times the smaller angle. FInd the measure of each angle.
[tex]\text{Larger angle} =x\\\\\text{Smaller angle} =y\\ \\\text{According to the condition,}\\\\x=10y+15\\\\\text{The two angles are supplementary, so their sum is}~ 180^{\circ} \\\\x+y=180\\\\\implies 10y+15 +y = 180\\\\\implies 11y = 180-15\\\\\implies 11y=165\\\\\implies y = \dfrac{165}{11}\\\\\implies y = 15\\\\\text{So,} ~x =180-15 = 165\\\\\text{Hence the larger angle is}~ 165^{\circ}~ \text{and the smaller angle is }15^{\circ}[/tex]
a fishing tackle box is 13 inches long 6 inches wide and 2 1/2 inches high. what is the volume of the tackle box
Answer:
195 cubic inches
Step-by-step explanation:
A fishing tackle box is 13 inches long, 6 inches wide, and inches high. What is the volume of the tackle box? SOLUTION: The volume of the tackle box is 195 cubic inches.
The sum of 5 times a number and 7 equals 8
Answer:
0.2
Step-by-step explanation:
the sum of 5 times 0.2 and 7 equals 8
At the beginning of the year, Mrs. Wilkinson's class had 19 packages of colored paper. So far, the class has used 401 pieces of colored paper.
If each package of colored paper contained 75 pieces, how many pieces of colored paper does the class have left?
I need help
Answer:
1024 pages left
Step-by-step explanation:
19 pack * 75 page/pack - 401 page =
x2 +9 x- 22,
Which graph shows the solution set of
20?
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HoHHHHHHH |
-10
-8
-4
0
4
8
OO
01
니아 中
아 | || |||||| +
-14
-10
-8
-4
0
4
8
+ |
|||||| || + +
-14
-10
-4
0
과
|| ||||||||
X
-14
-10
-8
-4
0
4
B
Answer...
Ok done. Thank to me >:3
A square pyramid is 6.3 in by 4 in by 4 in what is the surface area of the pyramid
Answer:
32.2 square feet
Jean estimates that her friend completes a new level of a video game on the first try 20% of the time. She conducts a simulation to predict how many times out of 80 her friend would complete a new level on the first try. Jean uses a random number generator. Every digit that is 8 or 9 represents completing the level. Examine the table.
The probability of the friend completing the new level in her first try is 22.5%
What is probability?This is a concept that is used to talk about the likelihood or the chances of an event occuring.
For the digit 8, the frequency is 7
For the digit 9, the frequency is 11
The total number of frequencies is given as
10 + 9 + 6+ 7 + 8 + 12 + 4 + 6 + 7 + 11 = 80
7 + 11 = 18
Probability = 18/80
= 0.225 x 100
= 22.5%
Read more on probability here: https://brainly.com/question/251701
Helpppp I will mark brainliest
Problem 25
Point P has the x coordinate x = -5, while point Z has the x coordinate x = 5. This is a distance of 10 units on the number line. Segment PZ is 10 units long which is the base of the triangle.
The height of the triangle is 8 units because it's the vertical distance from R to segment PZ. Notice we go from x = 4 to x = -4. The base and height are always perpendicular to one another.
Area = (base*height)/2
Area = (10*8)/2
Area = 80/2
Area = 40
Answer: 40 square units==========================================================
Problem 26
I'm not sure about this one because the instructions mention a grid, but I don't see any grid lines here. I'm not sure if the grid lines are just really faint or if your teacher forgot to put them in.
Find the solution to the system of equations.
You can use the interactive graph below to find the solution.
y= 22 + 3
y = -3.2 + 3
2=
y =
y
Answer:
Step-by-step explanation:
y=2x+3
y=-3x+3
**This is what's on the image.**
You need to aline the two together.
2x+3 = -3x+3
Add 3x both sides
3x+2x+3=3
5x+3=3
Now subtract 3 from both sides
5x=3-3
x= 0
This should be a vertical line from (0,0) to above since there is no slope you should have a straight line that is vertical.
Point P is located at (4, 6) on a coordinate plane. Point P will be reflected over the x-
axis. What will be the coordinates of the image of point P? What transformation was
performed on the given figure
1. (8,4)
2. (4-6)
3. (4,28)
4. (24,4)
Answer:
2.
Step-by-step explanation:
it's the reciprocal
so it's gonna reflect
How to solve 3x - 1/2 = 8 1/2 please no links and do it step by step
Answer:
[tex]x=\frac{3}{2}[/tex]
Step-by-step explanation:
Step 1. Put each term in [tex]3x-\frac{1}{2}[/tex] over the common denominator 2.
[tex]\frac{6x}{2}-\frac{1}{2}[/tex]
Therefore we have [tex](\frac{6x}{2}-\frac{1}{2})=4[/tex]
Step 2.
Combine [tex]\frac{6x}{2}-\frac{1}{2}[/tex] into a single fraction.
[tex]\frac{6x-1}{2}[/tex]
Therefore we have [tex](\frac{1}{2}(6x-1))=4[/tex] or [tex]\frac{6x-1}{2}=4[/tex]
Step 3.
Multiply both sides by a constant to simplify the equation.
Multiply both sides of [tex]\frac{6x-1}{2}=4[/tex] by 2:
[tex]\frac{2*(6x-1)}{2}=4*2[/tex]
Step 4.
Cancel the common terms in the numerator and denominator of [tex]\frac{2*(6x-1)}{2}[/tex]
Then we get [tex]\frac{2}{2}*(6x-1)[/tex] which simplifies to [tex](6x-1)[/tex]
So all together we have [tex](6x-1)=2*4[/tex]
Step 5.
Multiply 2 and 4 together and remove the parenthesis.
[tex]6x-1=8[/tex]
Step 6.
Isolate terms with the variable x to the left hand side.
So add 1 to both sides:
[tex]6x+(1-1)=8+1[/tex]
Evaluate [tex]1-1=0[/tex] which cancels out
Step 7.
Add the like terms on the right side:
[tex]6x=9[/tex]
Step 8.
Divide both sides by a constant to simplify the equation.
Divide both sides of [tex]6x=9[/tex] by 6.
[tex]\frac{6x}{6} =\frac{9}{6}[/tex]
Any non-zero number divided by itself is 1.
[tex]x=\frac{9}{6}[/tex] which simplifies to [tex]x=\frac{3}{2}[/tex]
what is the name of the shape
Answer:
triangular prism
Step-by-step explanation:
Have a great day!
Help asap!!! NO LINKS PLS!!
18
Solution:First, evaluate 2^3, which equals 8.Next, evaluate 4^2, which equals 16.This is the simplified expression:3/4(8+16)3/4(24)Multiply:18Hope it helps.
Do comment if you have any query.