Answer:
1
Step-by-step explanation:
The cone is sliced by a plane, which produces a smaller cone on top. This cone is similar to the original cone. Therefore:
R / H = r / h
2 / 8 = r / 4
r = 1
The radius of the circle at the intersection of the plane and the cone is 1.
To find the radius of the circle at the intersection of the plane and the cone, we start by understanding the geometry of the cone and the slicing plane.
Given:
- Cone height ( h = 8 )
- Cone radius ( r = 2 )
- The plane slices the cone halfway along its height, so the distance from the vertex to the plane is [tex]\( \frac{8}{2} = 4 \)[/tex].
Let's denote:
- ( R ): Radius of the circle at the intersection of the plane and the cone.
At height ( h ) from the vertex of the cone, the radius ( R ) of the circle formed by the intersection with the plane is related to the similar triangles formed by the cone and the slice plane.
The ratio of corresponding sides of similar triangles gives us:
[tex]\[ \frac{R}{r} = \frac{h - 4}{h} \][/tex]
Substitute the given values:
[tex]\[ \frac{R}{2} = \frac{8 - 4}{8} = \frac{4}{8} = \frac{1}{2} \][/tex]
Now, solve for ( R ):
[tex]\[ R = 2 \cdot \frac{1}{2} = 1 \][/tex]
Therefore, the radius of the circle at the intersection of the plane and the cone is [tex]\( \boxed{1} \).[/tex]
:
A plumber charges a one-time fee of $75 plus a fixed hourly rate, h, in dollars. The plumber works at a customer’s house for 2 hours and charges a total of $205.
Part A
Which tape diagram represents this situation?
A
B
C
D
Answer:
$65/hour
Step-by-step explanation:
Let C(h) represent the total amount payable to the plumber. Then:
C(h) = $75 + (rate)(2 hr) = $205. Solve for the "fixed hourly rate."
Subtracting $75 from both sides, we get:
(rate)(2 hr) = $130.
Dividing both sides by (2 hr) results in (rate) = $65/hour
The total bill of $205 is composed of a $75 fixed charge and $130 for the 2 hours worked. This implies that the plumber charges an hourly rate of $65. A representative tape diagram would show these components separately, with 2 equal blocks for the hourly rate totaling to the overall cost of $205.
Explanation:The situation described is a basic arithmetic problem dealing with a fixed cost ($75) and a variable cost (hourly rate, represented as h). The equation that represents this problem is 75+2h=205, derived from the fixed cost plus two times the hourly rate (since the plumber worked for 2 hours). To solve for h (the hourly rate), we subtract 75 from both sides which leaves us with 2h=130, then divide by 2, giving us h=65. This means the hourly rate, h, the plumber charges is $65.
Without seeing the options A, B, C, and D, I can't explicitly say which tape diagram would best represent this situation. However, ideally, the tape diagram should illustrate $75 as a fixed cost and then two equal blocks (each equivalent to $65) to represent the cost of each hour worked. The total of all blocks combined should equal $205, the total cost.
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x/20=4/5 what’s us the Poportion
Answer:
For this question, x = 16
Step-by-step explanation:
x/20 = 4/5
if we cross multiply, we will have
x × 5 = 4 × 20
5x = 80
x = 80/5
x = 16
Answer: 16
Step-by-step explanation:
X/20 = 4/5
Cross multiply
(5×X) = (20×4)
5x = 80
x = 80/5
x = 16
Ariana Grande is coming to North Gulfport Middle School for a fundraising benefit concert! Nevaeh is selling tickets. This week, she sold 3 kids tickets and 9 adult tickets for a total of $75. Last week, she sold 8 kids tickets and 5 adult tickets for $67. How much was each adult ticket, and how much was each kids ticket?
Step-by-step explanation:
Set up a systems of equations (x = kids, y = adults)
3x+9y=75 --> 15x+45y=375
8x+5y=67 --> 72x+45y=603
Subtract the two equations
57x = 228
x = 4
A KID'S TICKET IS $4
Plug that in for x
4(3)+9y=75
12+9y=75
9y=63
y=7
AN ADULT'S TICKET IS $7
Three less than two times x is y
Step-by-step explanation:
The Mathematical transformation of the given statement would be:
[tex]2x - 3 = y[/tex]
Solve this: 2x+y=-7y Y=x+10
Answer:
In this equation, when x = -8 , Y = 2
Answer check using either equation =
(1) 2x + y = -7y ===> 2(-8) + 2 = -7(2) ===> -14 = -14
(2) Y= x + 10 ===> 2 = -8 + 10 ===> 2 = 2
Step-by-step explanation:
Assuming that you are looking for "x" and "y", Let
2x + y = -7y ................. (1)
Y= x + 10 ................. (2)
From equation (2), Y = x + 10, therefore substitute for "Y" in equation (1) to get the value of "x"
2x + x + 10 = -7(x + 10)
3x + 10 = -7x - 70
gather like terms on each side.
3x + 7x = -70 - 10
10x = -80
divide through by 10
x = -8
Now substitute for "x" in equation (2)
Y = x + 10
Y = -8 + 10
Y = 2
Amanda uses a rectangular canvas for a painting. The length is 6x - 3 centimeters.
The width is 2x + 6 centimeters, and is of the length. What are the dimensions
of the canvas?
Answer:
Length:15 cm
Width: 12 cm
Step-by-step explanation:
The complete question is
Amanda uses a rectangular canvas for a painting. The length is 6x - 3 centimeters. The width is 2x + 6 centimeters, and is 4/5 of the length. What are the dimensions of the canvas?
Let
L ----> the length of the rectangular canvas
W ---> the width of the rectangular canvas
we know that
The width is 4/5 of the length
so
[tex]W=\frac{4}{5}L[/tex] ----> equation A
substitute the given values in equation A
[tex](2x+6)=\frac{4}{5}(6x-3)[/tex]
solve for x
[tex]10x+30=24x-12\\24x-10x=30+12\\14x=42\\x=3[/tex]
Find the dimensions of the canvas
substitute the value of x
[tex]L=6(3)-3=15\ cm[/tex]
[tex]W=2(3)+6=12\ cm[/tex]
What is the product of 10 and 9radical 72 in simplest radical form
Step-by-step explanation:
[tex]10 \times 9 \sqrt{72} \\ = 90 \sqrt{36 \times 2} \\ = 90 \times 6 \sqrt{2} \\ = 540\sqrt{2} [/tex]
Final answer:
To find the product of 10 and 9√72, simplify √72 to 6√2, then multiply the outside coefficients (10 and 9) to get 90, and attach the simplified radical. The final answer is 90√2.
Explanation:
The question asks to find the product of 10 and 9√72 in simplest radical form. First, recognize that the square root of 72 can be simplified by factoring out perfect squares. The square root of 72 is equal to the square root of 36 times 2, which simplifies to 6√2. Now, multiply the outside coefficients (10 and 9) and then multiply the result by the simplified radical. The final simplification is 90√2, which is the product of 10 and 9√72 in simplest radical form.
write down the first five terms of the sequence start at 26 and subtract 3 B start at -3 and add 10
Step-by-step explanation:
Sequence 1:
term1=26
term2=26-3=23
term3=23-3=20
term4=20-3=17
term5=17-3=14
sequence2:
term1=-3
term2=-3+10=7
term3=7+10=17
term4=17+10=27
term5=27+10=37
The first sequence starts at 26 and subtracts 3 to find the next terms: 26, 23, 20, 17. The second sequence starts at -3 and adds 10 to find the next terms: -3, 7, 17, 27.
Explanation:The first term of the sequence is 26. To find the next term, subtract 3 from 26, which gives you 23. Continuing this pattern, the second term is 23. To find the third term, subtract 3 from 23, which gives you 20. The fourth term is 20. To find the fifth term, subtract 3 from 20, which gives you 17. The fifth term is 17.
The first term of the second sequence is -3. To find the next term, add 10 to -3, which gives you 7. Continuing this pattern, the second term is 7. To find the third term, add 10 to 7, which gives you 17. The fourth term is 17. To find the fifth term, add 10 to 17, which gives you 27. The fifth term is 27.
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Mrs. Lowe gave a countries project to three of her students George, Martin, and Andrew. Use an organized list to show all the possible orders the three students can present their projects.
Answer:
GeorgeMartinAndrewGeorgeAndrew MartinAndrewGeorge MartinAndrew MartinGeorgeMartinAndrewGeorgeMartinGeorgeAndrewStep-by-step explanation:
Find the volume of a cone that has a radius of 3 inches and a height of 9 inches. Use 3.14 for pi and round your answer to the nearest hundredth.
Volume of the cone is 100 in³
Step-by-step explanation:
Step 1: Volume of a cone = 1/3 πr²h. Find volume of the cone where r = 3 inches and h = 9 inches.Volume = 1/3 × 3.14 × 3² × 9
= 84.78 in³ ≈ 100 in³ (rounding off to nearest hundredth)
Final answer:
The volume of a cone with a radius of 3 inches and a height of 9 inches is approximately 84.78 cubic inches.
Explanation:
To find the volume of a cone with a radius of 3 inches and a height of 9 inches, you can use the formula for the volume of a cone, which is:
[tex]V = (1/3)\pi r^2h[/tex]
Plugging the given values into the formula gives us:
[tex]V = (1/3) * 3.14 * (3 inches)^2 * 9 inches[/tex]
Now, calculate the square of the radius:
[tex]V = (1/3) * 3.14 * 9 * 9[/tex]
Next, multiply all the numbers together:
[tex]V = 3.14 * 27[/tex]
V = 84.78 cubic inches
Therefore, the volume of the cone is approximately 84.78 cubic inches, rounded to the nearest hundredth.
The first hexagon is dilated to form the second hexagon.
Select answers from the drop-down menus to correctly complete the statements.
The scale factor is
.
This represents
Answer:
The scale factor is 1.25 and this represents an enlargement.
Step-by-step explanation:
As shown at the figure
The side length of the first hexagon = 5
The side length of the second hexagon = 6.25
So, the scale factor = 6.25/5 = 1.25
and the second hexagon is larger than the first hexagon.
So,
The scale factor is 1.25 and this represents an enlargement.
Answer:
Step-by-step explanation:
How many obtuse angles are in an obtuse triangle
Answer:
ONE
Step-by-step explanation:
Only one. Since a triangle's angles must sum to 180° in Euclidean geometry, no Euclidean triangle can have more than one obtuse angle.
Answer: ONE
The required, an obtuse triangle is a triangle that has one angle measuring more than 90 degrees. By definition, an obtuse triangle has exactly one obtuse angle.
An obtuse triangle, by definition, contains one obtuse angle, which is an angle greater than 90 degrees but less than 180 degrees. The obtuse angle is the largest angle in an obtuse triangle, while the other two angles are acute angles (less than 90 degrees).
Since there is only one angle in an obtuse triangle that qualifies as an obtuse angle, we can conclude that there is exactly one obtuse angle in an obtuse triangle. The remaining two angles are acute angles.
It's important to note that the sum of the angles in any triangle is always 180 degrees. In the case of an obtuse triangle, the obtuse angle occupies a portion of that sum greater than 90 degrees, leaving the remaining acute angles to share the remaining portion of the 180-degree total.
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ANSWER PLEASE! SHOW WORK
Answer:
Use compatible numbers that are close to the actual numbers
Choose 36 for 35 3/4 and 6 for 5 7/8 because the divide evenly.
Step-by-step explanation:
Compatible numbers are numbers that are close to the actual values of a particular number. They make estimating easier when yo udo the different operations.
We choose 36 for 35 3/4 because 36 is closer to its value that 34. Conveniently, 5 7/8 is closer to 6 than 5, and they divide evenly. So a best estimate for the number of rows Holly can make would be:
36/6 = 6 rows.
the average daily attendance
Answer: 94.3%
Step-by-step explanation:
Average daily attendance = total sum of attendance ÷ frequency
=754.4/8
= 94.3%
Is 40(2x-16y) equivalent to 42-56y
Answer:
No, 40(2x - 16y) is not equivalent to 42 - 56y
Step-by-step explanation:
40(2x -16y)
If we expand the above expression, we will have
80x - 16y which is not equivalent to 42 - 56y
belle put the muffins she baked on six plates, four of which are red and two of which are yellow. the four red plates each have 5 muffins. the two yellow plates each have the same number of muffins write an expersion for the total number of muffins belle baked if each yellow plate has 8 muffins,find how many muffins belle baked in all
Answer:
36 total muffins
Step-by-step explanation:
5*4=20
8*2=16
20+16=36
Hey there!
To write an expression to represent this:
We know that the four red plates each have 5 muffins, and 4 x 5 = 20.
So we can say 20 + 2y is the expression, because we add 20 to the muffins on the two yellow plates.
The number of muffins on each yellow plate is represented by the variable y.
If each yellow plate has 8 muffins, so y = 8, the expression will look like this:
20 + 2(8)
Multiply 2 x 8.
20 + 16
Add 20 + 16.
36
Belle baked 36 muffins total.
Hope this helps!
solve equation for solution
4=5x
Answer:
X=0.8 or x=4/5
Step-by-step explanation:
Answer:
x = 0.8
Step-by-step explanation:
Step 1: Divide both sides by 5
4 / 5 = 5x / 5
0.8 = x
Answer: x = 0.8
Answer please? Its a bit confusing
Answer:
160 beads
Step-by-step explanation:
let x be the number of beads to make a bracelet, then
It requires 5x beads to make a necklace and the sum is
x + 5x = 192, that is
6x = 192 ( divide both sides by 6 )
x = 32
Number of beads to make a necklace = 5x = 5 × 32 = 160
Answer:
160 beads
Step-by-step explanation:
Beads for bracelet: b
Beads for necklace: 5b
b + 5b = 192
6b = 192
b = 32
Beads for necklace: 5b = 5(32)
= 160
what are two workout habits you are proud of?
Answer: Warming up and drinking enough water
Step-by-step explanation:
You should really ask yourself this, but you can talk about your perserverance, and not being afraid to try something new.
For which value of x is in the row in the table of values in correct? help please I’m tryna graduate
Answer:
x = 5 is incorrect
Step-by-step explanation:
12 1/2 should be -12 1/2
A jacket costs $34.85 plus sales tax. After sales tax, the jacket costs $37.29.
What is the approximate sales tax rate?
0.07%
1.07%
7%
70%
Equation:
37.29 = 34.85 + 34.85(x)
Solving:
37.29 = 34.85 + 34.85x
2.44 = 34.85x
x = 0.07
The approximate sales tax rate is 7%.
Hope this helps!! :)
Answer:
im pretty sure its 0.07
Step-by-step explanation:
The grid shows a diagram for a planned parking lot. Each unit on the grid represents 5 millimeters in length. Based on the scale, what will be the area of the actual parking lot?
A .1,080 square meters
B. 5,400 square meters
C.32,400 square meters
D. 38,880 square meters
Number 10 find x
I don’t know how to find the answers
Answer:
x= 33.8
Step-by-step explanation:
Please see attached picture for full solution.
write the repeating decimal as a fraction; 0.858585...
Answer:
85/99
Step-by-step explanation:
[tex]\frac{171717}{200000}[/tex]
URGENT MULTIPLE CHOICE - The numbers 1 through 15 are written on cards. One card is chosen at random. Event A is choosing a multiple of 5. Event B is choose an odd number. What is the probability of choosing an even number?
o 7/15
o 4/5
o 2/15
o 3/5
Step-by-step explanation:
even number cards is 7 cards (2,4,6,8,10,12,14)
so probability is 7/15
The probability of pulling out an even number from a set of 15 numbers (1-15) is 8/15, but none of the provided multiple choice options match this answer.
Explanation:The correct answer to this question could be found using the basic concepts of probability. Here, you have 15 cards in total. Among these 15, there are 8 even numbers: 2, 4, 6, 8, 10, 12, 14. The probability of choosing an even number (Event E) is thus Number of favourable outcomes (Event E) divided by Total number of outcomes.
This boils down to Probability (Event E) = Number of even numbers / Total numbers = 8 / 15. As such, none of the provided multiple choice answers are correct.
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ABCD is a parallelogram If m C = 98 then what is m A
Answer:
[tex]m\angle A=98^o[/tex]
Step-by-step explanation:
we know that
In a parallelogram opposite angles are congruent and consecutive angls are supplementary
In this problem
we have the parallelogram ABCD
so
[tex]m\angle A=m\angle C[/tex] ----> by opposite angles
[tex]m\angle B=m\angle D[/tex] --> by opposite angles
and
[tex]m\angle A+m\angle B=180^o[/tex] ----> by consecutive angles
[tex]m\angle B+m\angle C=180^o[/tex] ----> by consecutive angles
we have
[tex]m\angle C=98^o[/tex]
therefore
[tex]m\angle A=98^o[/tex]
Answer:
Step-by-step explanation:
help me
Suppose you have a 42 inch TV that is 57 centimeters tall by 96 CM wide. You want to upgrade to the 60inch version of that TV. The height and width are 42in and 60 in. If you know the width of the 60 inch TV is 137 cm what is the height?
Answer:
The height is 67 cm
Step-by-step explanation:
Remember that
[tex]1\ in=2.54\ cm[/tex]
we know that
The size of a TV is measured by its diagonal
Convert 60 inches to centimeters
[tex]60\ in=60(2.54)=152.4\ cm[/tex]
Applying the Pythagorean Theorem
[tex]D^2=H^2+W^2[/tex]
where
D is the diagonal
H is the height
W is the width
we have
[tex]D=152.4\ cm\\W=137\ cm[/tex]
substitute
[tex]152.4^2=H^2+137^2[/tex]
solve for H
[tex]H^2=152.4^2-137^2\\H^2=4,456.76\\H=67\ cm[/tex]
Ethel wants to have $70000 in 20 years. How much does she need to invest today at 5.46% cc?
Find the principle and interest
Please help
[tex]\bf ~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\dotfill&\$70000\\ P=\textit{original amount deposited}\\ r=rate\to 5.46\%\to \frac{5.46}{100}\dotfill &0.0546\\ t=years\dotfill &20 \end{cases} \\\\\\ 70000=Pe^{0.0546\cdot 20}\implies 70000=Pe^{1.092}\implies \cfrac{7000}{e^{1.092}}=P \\\\\\ 23488.13 \approx P~\hfill \stackrel{~\hfill \textit{the earned interest will be}}{70000-23488.13\implies 46511.87}[/tex]
subtracting polynomials
The solution is 10x² + 7x - 1
Step-by-step explanation:
Step 1: Subtract -2x² + 3x - 9 from 8x² + 10x - 10(8x² + 10x - 10) - (-2x² + 3x - 9) = 8x² + 10x - 10 + 2x² - 3x + 9
= 10x² + 7x - 1
Step-by-step explanation:
[tex]\huge\bold\purple{ 10x^2+7x-1 }[/tex]
The scale of a map is 3 in: 45mi. Find the actual distance if the map distance between two towns is 5 in.
Answer:
75 miles
Step-by-step explanation:
We can use cross products to solve
3 in 5 in
--------------- = -------------------
45 mi x miles
3 * x = 5 * 45
3x = 225
Divide each side by 3
3x/3 = 225/3
x =75 miles
To find the actual distance between two towns on a map, use the scale provided. Set up a proportion using the scale and the map distance to find the actual distance. In this case, the actual distance is 75 miles.
Explanation:To find the actual distance between two towns on a map, you can use the scale provided. In this case, the scale is 3 in: 45 mi. This means that 3 inches on the map represents 45 miles in the real world. If the map distance between the two towns is 5 inches, you can set up a proportion to find the actual distance.
Using the scale, you can set up the equation:
3 inches / 45 miles = 5 inches / x miles
Cross-multiplying, you get:
3 * x = 5 * 45
Simplifying, you get:
x = (5 * 45) / 3
x = 75 miles
Therefore, the actual distance between the two towns is 75 miles.