The equation that can be used to find the volume V of the container is: Option A. [tex]V = 12 \pi}[/tex]
To find the volume V of the popcorn container, which is an inverted cone, we use the formula for the volume of a cone:
[tex]\[ V = \frac{1}{3} \pi r^2 h \][/tex]Given:
The diameter of the circular opening is 4 inches, so the radius [tex]\( r \) is \( \frac{4}{2} = 2 \) inches.[/tex]The height h of the cone is 9 inches.Now substitute these values into the formula:
[tex]\[ V = \frac{1}{3} \pi (2)^2 (9) \][/tex]Calculate [tex]\( (2)^2 \):[/tex]
[tex]\[ (2)^2 = 4 \][/tex]Now substitute r = 2 and h = 9 into the formula:
[tex]\[ V = \frac{1}{3} \pi[/tex] × 4 × 9Simplify the multiplication:
[tex]\[ V = \frac{1}{3} \pi[/tex] × 36Now calculate [tex]\( \frac{1}{3}[/tex] x 36
[tex]\[ \frac{1}{3}[/tex] x 36 = 12Full Question
A popcorn container is the shape of an inverted cone. It is 9 inches tall, and the circular opening has a diameter of 4 inches.
A. [tex]V = 12 \pi}[/tex]
B. V=(4)(9) 3
C. V=(4)(9)²
D. V-(2)(9)² wr
if k is a constant, what is the value of k such that the polynomial k^2x^3 - 6kz+9 is
divisible by x-1?
The value of k that makes the polynomial k^2x^3 - 6kz + 9 divisible by x-1 is 3. This is found using the Remainder Theorem and substituting x=1 into the polynomial and solving the resulting equation.
Explanation:The question asks for the value of k such that the polynomial k2x3 - 6kz + 9 is divisible by x-1. To find the value of k, we use the Remainder Theorem, which states: if a polynomial f(x) is divisible by x-c, then f(c) = 0.
Applying this theorem, we set x=1 and solve for k:
Therefore, the value of k that makes the polynomial divisible by x-1 is 3.
What’s the slope of y=-7x+5
Answer:
m=-7
Step-by-step explanation:
The slope intercept form is y=mx+b.
So, the variable that represents slope is x.
If your plug your equation in, -7 would be the slope.
A builder is putting floor tiles on each of the 15 kitchen floors in an apartment building. Each floor uses 40 tiles. Each floor tile costs $7.
How much does the builder spend on the floor tiles?
Answer:
$4200
Step-by-step explanation:
15 floor times 40 tiles
15 X 40 = 600 tiles
so 600 tiles times 7 dollars
600 X 7 = 4200 dollars
Final answer:
To find the total cost of floor tiles for 15 kitchen floors, multiply the total number of tiles by the cost per tile. The builder will need 600 tiles (15 floors × 40 tiles) and with each tile costing $7, the total cost comes to $4200.
Explanation:
The student is asking about the total cost of floor tiles needed for an apartment building project. To calculate this, we need to find the total number of tiles used and then multiply this by the cost per tile. There are 15 kitchen floors, with each floor using 40 tiles. Each tile costs $7.
First, let's find out how many tiles are needed in total:
Number of floors × Number of tiles per floor = Total number of tiles
15 floors × 40 tiles per floor = 600 tiles in total
Next, let's calculate the total cost:
Total number of tiles × Cost per tile = Total cost
600 tiles × $7 per tile = $4200
Therefore, the builder spends a total of $4200 on floor tiles for the 15 kitchen floors.
Solve by factoring:
4x² - 8x=0
Answer:
Step-by-step explanation:
4x² - 8x= 0
4x(x -2) = 0
: 4x = 0 or x - 2 = 0
4x = 0
Dividing by 4
x = 0/4
x = 0
And
x - 2 = 0
x = 2
find the approximate area of the shaded region below, consisting of a right triangle with a circle cut out of it. Use 3.14 as an approximation for pi.
Answer:
2794 m^2
Step-by-step explanation:
Area of Triangle - Area of Circle
1/2bh - piR^2
4050 - 1256
= 2794
The approximate area of the shaded region is, 2794 m²
What is Area?Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.
Given a right triangle with a circle cut out of it,
Area of circle = π*Radius²
Area of triangle = 1/2*base*height
Area of circle = π*20² = 1256 m²
Area of triangle = 1/2*90*90 = 4050 m²
Area of the shaded region = Area of triangle - Area of circle
Area of the shaded region = 4050 - 1256 = 2794 m²
Hence, The approximate area of the shaded region is, 2794 m²
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What is the sum of 197+413 in expression
Answer:
197+413
=197+413
=610
Step-by-step explanation:
this is how i was taught
Find the value of x. Round your answer to the nearest tenth.
A.) 52.6
B.) 52.9
C.) 6.2
D.) 6.5
Answer:
Option A: 12.5
Step-by-step explanation:
We use trigonometric ratios on this right angled triangle.
[tex]$ cos \hspace{1mm} \theta = \frac{adj}{hyp} $[/tex]
we get:
[tex]$ cos \hspace{1mm} 28^{\circ} = \frac{11}{x} $[/tex]
Also cos 28° = 0.88
Therefore, x = [tex]$ \frac{11}{0.88} $[/tex]
[tex]$ = \frac{100}{8} =\textbf{12.5} $[/tex]
OPTION A is the answer.
Need to show my work
Answer:
[tex]\large\boxed{x=\dfrac{5}{4},\ y=\dfrac{15}{16}}[/tex]
Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}y=\dfrac{3}{4}x&(1)\\\dfrac{5}{2}x+2y=5&(2)\end{array}\right\\\\\text{Substitute}\ (1)\ \text{to}\ (2):\\\\\dfrac{5}{2}x+2\left(\dfrac{3}{4}x\right)=5\\\\\dfrac{5}{2}x+\dfrac{3}{2}x=5\\\\\dfrac{5+3}{2}x=5\\\\\dfrac{8}{2}x=5\\\\4x=5\qquad\text{divide both sides by 4}\\\\x=\dfrac{5}{4}[/tex]
[tex]\text{Put the value of}\ x\ \text{to (1)}\\\\y=\dfrac{3}{4}\cdot\dfrac{5}{4}\\\\y=\dfrac{15}{16}[/tex]
Answer:
Step-by-step explanation:
y = 3x/4 .........(1)
5x/2 + 2y = 5 .......(2)
Putting (1) into (2)
5x/2 + 2(3x/4) = 5
5x/2 + 3x/2 = 5
Multiply each term by 2
5x + 3x = 10
8x = 10
x = 10/8
x = 5/4
x = 1 1/4
And y = 3x/4
y = 3(5/4) ÷ 4
y = 15/4 ÷ 4
y = 15/(4×4)
y = 15/16
What is the value of x?
Enter your answer in the box.
°
Answer:
x = 111
Step-by-step explanation:
Sum of interior angles= (n-2)*180= (7-2)*180 = 5*180 = 900
x + 139 + 121 + 125 + 126 + 158 + 120 = 900
x + 789 = 900
x = 900 - 789 = 111
x = 111
Tina has $220 in her account. Cliff has $100 in his account. Starting in July, Tina adds $25 to her account on the first of each month, while Cliff adds $35 to his. How many dollars will they have in their accounts when the amounts are the same
Answer:
Both accounts will have $450
Step-by-step explanation:
Tina y= 25x+220
Cliff y= 35x+100
we can use substitution to solve this problem so the formatting would be:
25x+220=35x+100
subtract 25x from both sides
220=10x+100
Subtract 100 from both sides
120=10x
Divide both sides by 10
12=x
now that we have an x value we can plug it into either equation.
y=100+35(10)
y=100+350
y=450
Hank has eight action figures this is 12 less than the quotient of 60 and the number figures palo has
Answer:
6
Step-by-step explanation:
hold up hold up so you are saying 60 less than what quotient I'm guessing 68 divided by 12 so the answer would be 6
For which value of x is the equation 3x + x = 2x + 24 true?
A) 3
B) 4
C) 6
D) 12
do you guys know the answer?
Answer:
D) 12
Step-by-step explanation:
3x+x=2x+24
4x=2x+24
4x-2x=24
2x=24
x=24/2
x=12
The sum of two numbers is 52. The larger number is 8 more than the smaller number. What are the numbers?
Answer:
The smaller number is 22
The larger number is 30
Step-by-step explanation:
L + S = 52
L = S + 8
Set both equations equal to L.
S + 8 = -S + 52
+S +S
2S + 8 = 52
- 8 - 8
2S = 44
S = 22
To find the larger number, plug 22 in as S into the equations.
L = 30
Final answer:
The two numbers are 22 and 30, with the smaller number being 22 and the larger one being 30 (which is 8 more than the smaller number).
Explanation:
The sum of two numbers is 52, and the larger number is 8 more than the smaller number. Let's denote the smaller number as x and the larger number as x + 8. The equation to represent their sum is:
x + (x + 8) = 52
By combining like terms, the equation simplifies to:
2x + 8 = 52
Subtract 8 from both sides of the equation to isolate the term with x:
2x = 44
Divide by 2 to solve for x:
x = 22
Now that we have the value of the smaller number, we can find the larger number:
x + 8 = 22 + 8 = 30
So, the two numbers are 22 and 30.
the graph of f(x)=|x| is reflected across the x-axis, moved 2 units to the right and 7 units down. What is the function?
The transformed function after reflecting f(x)=|x| across the x-axis, moving it 2 units to the right, and 7 units down is f(x)=-|x-2|-7.
Explanation:The original function is f(x)=|x|.
When the graph of the function is reflected across the x-axis, it changes the sign of the output or y-coordinate.
Thus, the absolute value function becomes f(x)=-|x|.
When this function is moved 2 units to the right, it results in a shift in the coordinate of x within the function, thus becoming f(x)=-|x-2|.
Lastly, when the function is moved 7 units down, 7 is subtracted from the function, resulting in the final equation of f(x)=-|x-2|-7.
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Pls help me x+4=__+24 I don’t know the answer pls I really need this 200 points I give you
Answer:
x-20
Step-by-step explanation:
x+4=y+24
x=y+24-4
x=y+20
y=x-20
A video game system costs $185 and one video game costs $14.95. You can spend no more than $280 on the system and games. set up and solve an inequality to calculate the maximum number of games you can purchase
Answer:
Therefore the maximum number of video games that we can purchase
is 6.
Step-by-step explanation:
i) Let us say the number of video game system we can buy that costs $185
is x and the number of video games of cost $14.95 is y.
ii) The total amount we can spend on the purchase of the video game
system is $280.
iii) Now with the amount of $280 mentioned in ii) we can see that the
number of game systems that can be bought is 1.
Therefore x = 1.
Therefore the equation we can write to equate the number of video
games and video game system is given by $185 + $14.95 × y ≤ 280
Therefore 14.95 × y ≤ 280 - 185 = 95
Therefore y ≤ 95 ÷ 14.95 = 6.355
Therefore the maximum number of video games that we can purchase
is 6.
what is the slope of (1,2) and (4,11)
Answer:
slope = 3
Step-by-step explanation:
Calculate the slope m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (1, 2) and (x₂, y₂ ) = (4, 11)
m = [tex]\frac{11-2}{4-1}[/tex] = [tex]\frac{9}{3}[/tex] = 3
Answer:
3
Step-by-step explanation:
y2 - y1/ X2 - X1
11 - 2/ 4-1
9/3
= 3
What is the values of x and y?
(5x) + (9y)
Answer:
x=5 y=9
Step-by-step explanation:
hope this helps :) have a nice day :) :) :)
M - 2 3/4 = 6 1/2 what does the m equal
Answer:
Step-by-step explanation:
6 1/2 + 2 3/4=M
M=9 1/4
What is the length of the radius, r?
Answer:
18 cm
Step-by-step explanation:
The circumference (C) of a circle is calculated as
C = 2πr ← r is the radius
Given
C = 36π, then
2πr = 36π ( divide both sides by 2π )
r = [tex]\frac{36\pi }{2\pi }[/tex] = 18
2 litre 450 ml mustard oil was used from a can of 5 litre in a month. How much is left? For how many months in all can it be used?
Answer:
Step-by-step explanation:
1 liter = 1000 ml....so 2 liters and 450 ml = (2* 1000) + 450) = 2450 ml
5 liters = (5 * 1000) = 5000 ml
5000 ml - 2450 ml = 2550 ml or 2 liters and 550 ml <== this is how much is left
so he used 2450 ml in 1 month....and he has 5000 ml
5000/2450 ≈ 2.04 months <=== it will be all used up
Answer:
Step-by-step explanation:
1 litre = 1000 ml
5 liter = 5 * 1000 = 5000 ml
2 liter 450 ml = 2 liter + 450 ml = 2000 ml + 450 ml = 2450 ml
Oil left = 5000 - 2450 = 2550 ml
2550 - 2450 = 100 ml
4 liter 900ml is used in two months and 100 ml will be left over
Identify the following equation as that of a line, a circle, an ellipse, a parabola, or a hyperbola. x^2 + 2y^2 = 2
This is an equation representing the ellipse
Explanation:
The general equation for an ellipse is [tex]\frac{x^{2} }{a^{2} } + \frac{y^{2} }{b^{2} } = 1[/tex] so, when you simplify it according to the characteristics of a and b, you would end up in the similar form of the equation givenwhere a represents half the length of the major axis and b represents half the length of the minor axis. The easiest method to identify, look at whether both the variables are squared, and also the coefficient of x and y should be positive but different.Quadrilateral ABCD has 2 sets of parallel sides, 4 congruent angles, and 4 congruent
sides. What are all the classifications for Quadrilateral ABCD? Mark all that apply.
Parallelogram
Rectangle
Trapezoid
Square
Kite
Rhombus
Answer:
It can be a parallelogram, a square, a rectangle and rhombus too.
Answer:
There are many special types of quadrilateral.
A parallelogram is a quadrilateral in which both pairs of opposite sides are parallel .
A parallelogram also has the following properties:
Opposite angles are congruent;
Opposite sides are congruent;
Adjacent angles are supplementary;
The diagonals bisect each other.
A rectangle is a parallelogram with four right angles, so all rectangles are also parallelograms and quadrilaterals. On the other hand, not all quadrilaterals and parallelograms are rectangles.
A rectangle has all the properties of a parallelogram, plus the following:
The diagonals are congruent.
A rhombus is a parallelogram with four congruent sides. The plural of rhombus is rhombi . (I love that word.)
A rhombus has all the properties of a parallelogram, plus the following:
The diagonals intersect at right angles.
A square can be defined as a rhombus which is also a rectangle – in other words, a parallelogram with four congruent sides and four right angles.
A trapezoid is a quadrilateral with exactly one pair of parallel sides. (There may be some confusion about this word depending on which country you're in. In India and Britain, they say trapezium ; in America, trapezium usually means a quadrilateral with no parallel sides.)
Step-by-step explanation:
you should be able to find your answer in this i rlly hope it helps you
PLEASEEE HELPPP ASAPP! THANK YOU LOTS!! <3 (7TH GRADE MATH)
btw January: -5/8 and July: 6 5/8
Answer:
Therefore the change in water level over the course of 9 months is a drop in level of 3.4 cm (= -3.4 cm)
Step-by-step explanation:
i) change in water level over the course of 9 months =
[tex]- \frac{5}{8} - 0.4 - 0.4 - 6 - 2.9 + 3.2 + 6\frac{5}{8} - 3.2 + 0.3[/tex]
= [tex]-0.625 - 0.4 - 0.4 - 6 - 2.9 + 3.2 + 6.625 - 3.2 + 0.3[/tex]
= -3.4
Therefore the change in water level over the course of 9 months is a drop in level of 3.4 cm (= - 3.4 cm)
F(x)=2x+6
G(x)=-5x-9
Find the product of f and g.
A.-10x^2-54
B.-10x^2-48x-54
C.-10x^2-12x-54
D.-10x^2+48x-54
Answer:
Step-by-step explanation:
F(x) = 2x + 6
G(x) = - 5x - 9
product of F and G .....the product is the result of multiplication
(2x + 6)(-5x - 9) =
-10x^2 - 18x - 30x - 54 =
-10x^2 - 48x - 54 <====
Five times a number , subtracted from ten , is triple the number . Find the number.
The value of the variable number x will be 1.25.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.
Let x be the number. Then the Five times a number is written as 5x. Then the expression will be
⇒ 10 - 5x
The triple number is written as 3x. Then the equation is given below.
10 - 5x = 3x
Simplify the equation, then we have
10 = 3x + 5x
10 = 8x
x = 10 / 8
x = 1.25
The value of the variable number x will be 1.25.
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Final answer:
The algebraic equation set up from the problem 10 - 5x = 3x leads us to find that x = 1.25. Thus, the number in question is 1.25.
Explanation:
The question describes an algebraic problem where we are trying to find a particular number. According to the problem, five times this number, when subtracted from ten, equals three times the number. To find the number, we set up the equation based on the given information:
10 - 5x = 3x
Where x is the number we are trying to find. Now, we will solve for x:
Add 5x to both sides of the equation to get all x terms on one side:
10 = 3x + 5x
Combine like terms on the right side:
10 = 8x
Divide both sides by 8 to solve for x:
x = 10/8
Simplify the fraction:
x = 1.25
So, the number we were seeking is 1.25.
Which function models the sequence -5, -7,-9, -11, ...?
Answer:
-13
Step-by-step explanation:
add two but put a negative .
What is an equation of the line that passes through the points (7,-6)(3,-6)
Answer:
Step-by-step explanation:
Since both points have their y coordinate as -6, and this is a line,
Then your answer would be y = -6
Suppose we want to choose 2 objects, without replacement from the objects pencil, eraser and desk
The question is about finding the number of ways to choose 2 items without replacement from a set of 3 items using combinatorics, and there are 3 different ways to do so.
The question deals with the concept of combinations in probability and combinatorics. When choosing 2 objects from a set of 3 items (a pencil, an eraser, and a desk) without replacement, we can use the combination formula C(n, k) = n! / (k!(n-k)!), where n is the total number of items and k is the number of items to choose.
In this case, we have 3 items and we want to choose 2, so we plug the values into the formula to get the number of combinations without replacement.
Using the combination formula, C(3, 2) = 3! / (2! × (3-2)!) = 3.
Therefore, there are 3 different ways to choose 2 objects from the set of a pencil, an eraser, and a desk.
what is n/8=11/5 solve for n
Answer:
n = 17.6
Step-by-step explanation:
Cross-multiply and you have:
5 * n = 11 * 8
5n = 88
n = 88/5 = 17.6