Final answer:
The height of the cone is equal to the slant height plus 1.
Explanation:
To find the height of the cone, we can use the formula for the surface area of a cone: S = πr^2 + πrl, where r is the radius of the base and l is the slant height. Since the problem states that the surface area is equal to the volume, we can set S equal to V and solve for h, the height of the cone.
Here's the step-by-step calculation:
S = V
πr² + πrl = V
πr² + πrl = πr²h
πr² + πrl - πr²h = 0
Combine like terms: πr²(1 - h) + πrl = 0
Divide both sides by πr to solve for h: 1 - h + l = 0
Subtract l from both sides: 1 - h = -l
Subtract 1 from both sides: -h = -l - 1
Multiply both sides by -1 to solve for h: h = l + 1
So, the height of the cone is h = l + 1.
What is the slope-intercept form of a linear equation? explain why this form is called the slope-intercept form?
Answer: The slope intercept form of a linear equation has the following form where the equation is solved for y in terms of x: y = a + bx. b is the slope. a is a constant term. It is the y intercept, the place where the line crosses the y axis.
Hope this helps:)
Enter an inequality that represents the graph in the box.
PLEASE HELP ME!
its actually y=>3x-1 because it's shaded below the line.
below the line: < or <=
above the line: > or>=
Write the point-slope form of the equation of the line with a slope of - 2 and an x-intercept of - 1. Include your work in your final answer.
Please helps and show how.
Answer:
y= -2x-2
Step-by-step explanation:
point slope- y=mx+b
y-y1=m(x-x1)
you have the point (-1,0) and you have to use (x1, y1)
your slope is -2
Substitute
y-0= -2(x +1)
Distribute
y-0=-2x-2
+0 +0
y= -2x-2
Help! I'm not sure how you would graph x = -6. There's no other information available for this question.
The total amount of money in cents in 3x nickels 4x dimes and 3x quarters
1.30 or 130
Step-by-step explanation:
The measure of the vertex angle in an isosceles triangle is six less than four time the measure of the base angle. find the measure of the vertex angle
What is the measure of angle S?
132 + 56 + 79 = 267
360 - 267 = 93
answer is 93 degrees
Twice the number n is no less than 10 units from -1
The mathematical equation 'Twice the number n is no less than 10 units from -1' can be solved as two inequalities, yielding a solution of n ≤ -5.5 or n >= 4.5.
Explanation:This is a math problem asking about the absolute value inequality of an equation. The question states 'Twice the number n is no less than 10 units from -1'. This can be written as |2n + 1| >= 10. To solve it, we'll divide it into two inequalities: 2n + 1 >= 10 and -2n - 1 >= 10. Solving the first inequality yields n >= 4.5, and solving the second inequality yields n <= -5.5. Thus, the solution to the equation is n ≤ -5.5 or n >= 4.5.
Learn more about Absolute Value Inequality here:https://brainly.com/question/33786594
#SPJ3
Problem page the perimeter of a rectangular garden is 274 feet. if the width of the garden is 63 feet, what is its length?
(3^-2)^4 *3^3 divided by 3^-3
How can you find the measure of a distance that you cannot measure directly?
What is 7 1/5 written as a percent
1) if the sum of two prime numbers is divisible by 7 and is a perfect square, what is a possible product of these numbers?
2) If it takes 5 pipes 2 hours to fill 2 pools and they output water at the same rate, how many hours will it take 1 pipeto fill 1 pool?
3) On a test with 30 questions, Ron got 6 questions wrong. What is his score expressed as a percentage?
4)35 percent of a class voted to go to the museum. If 7 students chose to go to the museum, how many students are there in the class?
5)Katie is 2 years younger than her brother. In 12 years, her brother will be twice as old as she is now. How old is Katie?
1) There are no prime numbers whose sum is divisible by 7 and is a perfect square.
2) 1 pipe will take 2 hours to fill 1 pool, as it fills at the same rate as all 5 pipes combined.
3) Ron's score is 20%.
4) There are 20 students in the class.
5) Katie is 14 years old.
Let's evaluate each of the statements you provided:
1) The sum of 2 prime numbers is ALWAYS even, so if x and y are prime numbers, then (x+y)/7 = z².
In this case either x = 2 or y = 5 (or vice versa). This is the only possibility to be divisible by 7.
Then (5+2)/7 = 1² = 1.
The first part is correct; the sum of two prime numbers is always even. However, the statement about (x+y)/7 = z² doesn't hold true for all prime numbers. It might work for the specific values of x and y you mentioned, but it's not a general rule.
5 pipes → 2 hours → 2 pools, then 1 pipe takes (5x2) 10 hours to fill 2 pools, or 1 pipe takes (10/2) 5 hours to fill 1 pool.
This is a correct interpretation of the information provided. If 5 pipes can fill 2 pools in 2 hours, then each pipe alone takes 10 hours to fill 2 pools, or 5 hours to fill 1 pool.
It's 6/30 = 0.2 or 20%.
Correct, 6/30 simplifies to 0.2, which is equivalent to 20%.
35% represents 7 students, and 100% of the class represents x students. Therefore, 35%/7 = 100%/x. Cross-multiplying, we get 0.35x = 7, and x = 7/0.35, which simplifies to x = 20 students.
Let K be the age of Katie, and B her brother's age. K + 2 = B (Today). In 12 years, B+12 will be twice K (remember K = B-2):
B+12 = 2(K) OR B+12 = 2(B-2)
B+12 = 2(B-2)
B+12 = 2B - 4
12 + 4 = B, and B = 16. If the brother is 16, then Kate is 14.
The calculations and logic are correct. If Katie's brother is 16, then Katie is indeed 14 years old.
for such more question on prime numbers
https://brainly.com/question/145452
#SPJ12
If m is the midpoint of pq, what is the relationship between pm and pq
Midpoint, as the word suggests, means the point which lies in the middle of something. If m is the midpoint of PQ then PM will be half of PQ.
What does a midpoint mean?Midpoint, as the word suggests, means the point which lies in the middle of something. The midpoint of a line segment means a point that lies in the mid of the given line segment.
Given that m is the midpoint of PQ. Therefore, it will divide PQ into two equal parts. Therefore, we can write,
PQ = PM + MQ
But since PM = MQ,
PQ = PM + PM
PQ = 2 PM
PM = PQ/2
Hence, if m is the midpoint of PQ then the relationship between PM and PQ will be half of PQ.
Learn more about Midpoint here:
https://brainly.com/question/5127660
#SPJ2
64 ounces in 8 cups unit rate
what is 100/6 as a decimal
For what values of x is the quantity x−9 negative?
The value of x is the quantity x−9 negative would be negative for all values of x less than 9.
What is algebra?Algebra is the analysis of mathematical representations, while logic is the manipulation of those symbols.
What is inequality?
Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
To determine the values of x is the quantity x−9 negative
As per the given condition, translate the phrase into an algebraic expression:
⇒ x - 9 < 0
Add 9 to both sides of the inequality,
⇒ x - 9 + 9 < 9
⇒ x < 9
So x - 9 is negative for all values of x less than 9.
Hence, the value of x is the quantity x−9 negative would be negative for all values of x less than 9.
Learn more about inequalities here:
brainly.com/question/20383699
#SPJ2
Victor is walking at a rate of 1 mile every 17 minutes. sarah is walking at a rate of 1 mile every 14 minutes. if they are 10 miles apart and are approaching each other along a straight road, how many hours will it take them to meet, rounded to the nearest hundredth?
Rectangle ABCD is graphed in the coordinate plane. The following are the vertices of the rectangle: A(5, 1), B(7,1) C(7, 6), and D(5, 6). What is the perimeter of rectangle ABCD?
The perimeter of the rectangle ABCD is 14 units after using the distance formula.
What is a rectangle?It is defined as the two-dimensional geometry in which the angle between the adjacent sides is 90 degrees. It is a type of quadrilateral.
The area of a rectangle can be calculated using the following formula:
Rectangle area = length x width
The missing figure is in the picture, please attached to the picture.
We have:
Rectangle ABCD is graphed in the coordinate plane.
As we know,
The distance formula: it can be defined as the formula for finding the distance between two points. It has given the shortest path distance between two points.
The distance formula can be given as:
[tex]\rm d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
After using the distance formula:
The perimeter of the rectangle = AB + BC + CD + DA
The perimeter of the rectangle = 2 + 5 + 2 + 5
The perimeter of the rectangle = 14 units
Thus, the perimeter of the rectangle ABCD is 14 units after using the distance formula.
Learn more about the rectangle here:
https://brainly.com/question/15019502
#SPJ2
4(-3)(15/3)
20 points
Which of the following describes the correct process for solving the equation 3x + 6 = 21 and arrives at the correct solution? Divide both sides by 6 and then add 3. The solution is x = 5. Add 6 to both sides of the equation and then divide by 3. The solution is x = 9. Subtract 6 from both sides of the equation and then divide by 3. The solution is x = 8. Subtract 6 from both sides of the equation and then divide by 3. The solution is x = 5.
If ab= 37 and xy =1/37, what is the value of the product x x b x y x a
In this case, we are simply asked to find for the value of:
xbya or abxy
Since we know that given values of ab and xy, therefore abxy is:
abxy = 37 * (1 / 37)
abxy = 37 / 37
abxy = 1
Three friends rented a kayak. It cost $4 per hour per person to rent the kayak, plus $2 for each life jacket, and $3 to park the car. It cost $57 in all. How many hours did they spend kayaking? Write an equation and solve.
is -2.75 greater than -2.5 please explain your answer
20 point question!!! Please help me! Number 4.
Which mathematical property is demonstrated?
If w = - 8 and - 8 = u, then w = u.
Question 4 options:
symmetric property of equality
transitive property of equality
closure property of addition
closure property of multiplication
The circumference of a circle is 25.12 yards. What is the radius of the circle?
You are making identical gift bags using 24 candles and 36 bottles of lotion .what is the greatest number of gift bags you can make with no items left over. Show your work
Answer: 12
Step-by-step explanation:
Given : You are making identical gift bags using 24 candles and 36 bottles of lotion .
Then, the greatest number of gift bags you can make with no items left over= greatest common factor of 24 and 36
Prime factorization of 24 and 36 :_
[tex]24=2\times2\times2\times3\\\\ 36=2\times2\times3\times3[/tex]
GCF(24 , 36)= [tex]2\times2\times3=12[/tex]
Hence, the greatest number of gift bags you can make with no items left over =12
ABCD is a rectangle. The length of BD is 8 units, and m angle ABD is 67°. The length of AC is units, and m angle CDB is °.
Answer:
cbd is 23 degrees
Step-by-step explanation:
Ali currently has $25. He is going to start saving $5 every week.
Which equation represents this situation?
y = 25x – 5
y = 5x + 25
y = 25x + 5
y = 5x – 25