According to triangle inequality theorem a triangle with two sides 7 units and 17 units, has a third side which measures 10 units.
What is Triangle Inequality Theorem?
According to triangle inequality theorem, the sum of the lengths of any two sides of a triangle is greater than the length of the third side.
The two sides of a triangle are -
a=7, b=x and c=17, where a, b and c are the sides of the triangle.
As, 17 is a bigger number so let it be the biggest side.
Now, according to triangle inequality theorem -
a + b = c
7 + x = 17
x = 17 -7
x = 10
Therefore, the third side of the triangle measures 10 units.
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What role does place value have in finding 10% and 1% of a number? Write at least two complete sentences.
The fractions of the numbers are found as follows:
10% of a number is found moving the decimal digit one unit right.1% of a number is found moving the decimal digit two units right.How to divide a number by powers of 10?To divide a number by the nth power of 10, the decimal digit in the number is moved n units to the right.
The fraction that represents 10% of a number is given as follows:
10/100 = 1/10.
Meaning that the number is divided by 10, which is the first power of 10, and thus the decimal digit is moved one unit right in the number.
The fraction that represents 1% of a number is given as follows:
1/100.
Meaning that the number is divided by 100, which is the second power of 10, and thus the decimal digit is moved two units right in the number.
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What is the solution to the system of equations 3x 2y 7 and Y 3x 11?
The solution to the system of equations is x = 4 and y = 5.
3x + 2y = 7
y = 3x - 11
Substitute 3x - 11 for y in the first equation:
3x + 2(3x - 11) = 7
Simplify:
3x + 6x - 22 = 7
Combine like terms:
9x - 22 = 7
Add 22 to both sides:
9x = 29
Divide both sides by 9:
x = 29/9
x = 4
Change x in the second equation to 4:
y = 3(4) - 11
Simplify:
y = 12 - 11
y = 1
The solution to the system of equations is x = 4 and y = 1.
The solution to the system of equations 3x + 2y = 7 and y = 3x - 11 is x = 4 and y = 1. To solve this system, we first substituted 3x - 11 for y in the first equation. We then simplified the equation and combined like terms to get 9x - 22 = 7. We then added 22 to both sides, divided both sides by 9, and got x = 29/9 which is x = 4. We then substituted 4 for x in the second equation, simplified, and got y = 1. Thus, the solution to the system of equations is x = 4 and y = 1.
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at the same time that a 60 foot tall buidling casts s shadow hat is 21.5 feet long a nearby tree casts a shadow that is 18 feet long, Which measure is closest to the height of the tree
The height of the tree is closest to 40 feet.
We can use the proportion of similar triangles to determine the height of the tree.
Let h be the height of the tree and s be the length of the shadow cast by the tree.
We know that the height of the building is 60 feet and the length of its shadow is 21.5 feet. So:
(h/s) = (60/21.5)
We also know that the length of the shadow cast by the tree is 18 feet.
So we can substitute that into the proportion and solve for h:
h = (60/21.5) * 18
h = (60*18)/21.5
h ≈ 40
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Could someone help me
[tex]\cfrac{6a^2 + 21a}{3a^2}\implies \cfrac{6a^2 }{3a^2}+\cfrac{21a}{3a^2}\implies 2+\cfrac{7}{a}[/tex]
You have $12 to spend at a vending machine. A pack of Starbursts cost $1 and a pack of M&M chocolates cost $2. You want to buy at least three packs of Starbursts.
a. Write a system of linear inequalities that represents this situation.
b. How many packs of each type of candy can you possibly purchase?
Answer:yes
Step-by-step explanation:
yes
Answer:
Starbursts = 12 dollars
M&M = 2 dollars
1. Make Startbursts and M&Ms into "x"
(a) 1x + 2x = 12
2. 3*1= 3
4+2x=12
(b) 4 packs
If A=(7,9) and B=(3,12) what is the length of AB
The distance between two points A and B is 5 units.
Chapter 3 Lesson 4 Arithmetic Sequence
Answer:
Step-by-step explanation:
1) 1,15,29,43,57,.....
here, 15-1 =14 and 29-15=14
therefore,it is an arithmetic sequence with common difference = 14
2) 3,6,9,15,17,....
here, 6-3=3, 9-6=3 , 15-9=6
therefore,it is not an arithmetic sequence.
3) 93,86,79,72,65,......
here, 86-93=-7 , 79-86=-7 and 72-79=-7
therefore,it is an arithmetic sequence with common difference = -7
4) 37,34,31,29,26,......
here, 34-37 = -3,31 - 34 = -3,29 - 31 =-2
therefore,it is not an arithmetic sequence.
A line is perpendicular to y = x + 3
and intersects the point (-2, 4).
What is the equation of this
perpendicular line?
y = − ²x + [ ]
Hint: Use the Point-Slope Form:y-y₁ = m(x - X1)
Then write the equation in slope-intercept form.
Enter
Answer:
y =x+3
y =-x²+[?]
Find the gradient;
What is the formula for the gradient of a graph?
Finding the gradient of a straight-line graph
X2 = 2
Y2 = 7
ΔX = 4
ΔY = 3
θ = 36.869897645844°
Equation of the line:
y = 0.75x + 5.5
When x=0, y = 5.5
When y=0, x = -7.3333333333333
OR
X2 = -6
Y2 = 1
ΔX = -4
ΔY = -3
θ = 216.86989764584°
Equation of the line:
y = 0.75x + 5.5
When x=0, y = 5.5
When y=0, x = -7.3333333333333
A line has a slope of – 1/7 and passes through the point (4,5). What is its equation in point-slope form?
Answer:
y-5=-1/7(x-4)
Step-by-step explanation:
The equation of the line in point-slope form is y-5=-1/7(x-4)
Answer:
y = -1/7 x + 39/7
Step-by-step explanation:
An equation in point slope form is
y = mx+b where m is the slope and b is the y intercept
We are given the slope
y = -1/7 x + b
Substitute in the point for x and y and solve for b
5 = -1/7(4) +b
5 = -4/7 +b
5 + 4/7 = b
5*7/7 + 4/7 = b
35/7 + 4/7 = b
39/7 = b
The equation is
y = -1/7 x + 39/7
3) Camile offers you a challenge. Are the triangles below similar? Examine them and tell how
you know.
a) Use a flowchart to organize your explanation.
b) Camile says, "These triangles aren't just similar-they're congruent!" Is Camile
correct? What special value in your flowchart indicates that the triangles are
congruent?
a) The flowchart for the congruency of triangles is given below.
b) The triangles are congruent as DQ ≅ XZ, PQ ≅ XY, and ∠PQD ≅ ∠ZXY.
What is congruency?
The word 'congruent' means 'exactly equal' in terms of shape and size. Even when we turn, flip, or rotate the shapes, they remain equal.
In the given diagram, it can be seen that -
Line segment DQ = Line segment XZ.
Similarly, Line segment PQ = Line segment XY.
Since, the two sides of the triangle are equal, hence the third side must also be equal.
Line segment PD = Line segment ZY.
Also, in the diagram it can be seen that ∠PQD ≅ ∠ZXY.
Therefore, the triangles PDQ and ZXY are equal and congruent.
The flowchart for the same is given below.
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Jay wants to go paddleboarding at least 8 hours each week. If he averages 2 hours per day, write and solve an inequality to find how many days he will have to go kayaking.
An inequality to find how many days he will have to go kayaking. is; d ≥ 4
How to solve Inequality word problems?We are told that Jay wants to go paddle boarding at least 8 hours each week. This means greater than or equal to 8. That is the minimum number of hours each week is 8 hours.
Now, we are told that he averages 2 hours per day. If the number of days is given by d, then we have the inequality as;
2d ≥ 8
Divide both sides by 2 to get;
d ≥ 4
That is the domain of the number of days required to go kayaking
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T h e r e a r e 235 seven t h - g r a d e st u d e n t s g o i n g o n a fi e l d t r i p . T h e sc h o o l h a s 5 b u se s t o t a k e t h e st u d e n t s. E a c h b u s h a s 22 se a t s, a n d 2 st u d e n t s c a n si t i n e a c h se a t . B a se d o n t h i s i n f o r m a t i o n , h o w m a n y st u d e n t s w i l l n o t b e a b l e t o r i d e o n a b u s f o r t h e fi e l d t r i p ?
The number of students who will not be able to ride on the bus for the school trip is given by the equation A = 15 students
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
The total number of students for the trip = 235 students
The number of buses = 5 buses
The number of students in a bus be = B
Now , each seat on the bus can occupy = 2 students
So , 22 seats can occupy = 22 x 2 students
22 seats in the bus can occupy = 44 students
So , the number of students in a bus B = 44 students
And , the total number of students in 5 buses = 5 x number of students in a bus B
Substituting the values in the equation , we get
The total number of students in 5 buses = 5 x 44
The total number of students in 5 buses = 220 students
So , the remaining number of students A = total number of students for the trip - total number of students in 5 buses
Substituting the values in the equation , we get
The remaining number of students A = 235 - 220
The remaining number of students A = 15 students
Therefore , the value of A is 15 students
Hence , the number of students is 15 students
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1. Marta walked 6 miles in 1.5 hours. At this rate how long will it take her to walk 16 miles?
2. Lionel typed 320 words in 4 minutes. At this rate, how long will it take him to type 800 words?
Answer for no.2: 800
Step-by-step explanation:
Barrett earns $15 per hour cutting grass and $10 per hour tutoring reading. In one month, Barrett
needs to save at least $400 for a new lawnmower but does not want to work more than 35 hours.
Part A: Let x represent the hours cutting grass and y represent the hours tutoring. Given x ≥ 0 and
y ≥ 0, select all the inequalities that represent the situation.
A. x + y ≥ 35
B. 15x + 10y ≤ 400
C. x + y ≤ 35
D. 15x + 10y ≥ 400
E. 25x + 25y ≤ 400
F. 15x + 10y ≤ 35
Part B: Determine whether each point is a viable or nonviable solution according to the above scenario.
Viable Nonviable
(10, 25)
(10, 20)
(20, 12)
(35, 0)
(20, 20)
The inequalities that represent the situation are 15x + 10y ≥ 400 and x + y ≤ 35 and the viable solutions are (10, 25), (20, 12), (35, 0) and (20, 20)
The inequalities that represent the situation.From the question, we have the following parameters that can be used in our computation:
Earnings from cutting = $15Earning from tutoring = $10Number of hours = not more than 35Total earnings = At least $400These parameters above mean that
15x + 10y = Total earnings
x + y = Number of hours
So, we have
15x + 10y ≥ 400
x + y ≤ 35
The above represent the inequalities of the situation
The viable solutionsIn (a), we have
15x + 10y ≥ 400
x + y ≤ 35
Next, we test the options
(10, 25)
15 * 10 + 10 * 25 ≥ 400 ⇒ 400 ≥ 400
10 + 25 ≤ 35 ⇒ 35 ≤ 35
True
(10, 20)
15 * 10 + 10 * 20 ≥ 400 ⇒ 350 ≥ 400
10 + 20 ≤ 35 ⇒ 30 ≤ 35
False
(20, 12)
15 * 20 + 10 * 12 ≥ 400 ⇒ 420 ≥ 400
20 + 12 ≤ 35 ⇒ 32 ≤ 35
True
(35, 0)
15 * 35 + 10 * 0 ≥ 400 ⇒ 525 ≥ 400
35 + 0 ≤ 35 ⇒ 35 ≤ 35
True
(20, 20)
15 * 20 + 10 * 20 ≥ 400 ⇒ 500 ≥ 400
20 + 20 ≤ 35 ⇒ 40 ≤ 35
False
Hence, the viable solutions are (10, 25), (20, 12), (35, 0) and (20, 20)
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If triangle NPZ ~ triangle HBZ find the measure of angle B.
Please show the steps
The measure of angle B is m ∠B = 107°.
What is similar triangles?
Triangles that are similar in shape but differ in size are known as similar triangles. Examples of related objects include all equilateral triangles and squares with any side length. To put it another way, if two triangles are similar, then their corresponding angles and sides are congruent and equal in size.
Given: Δ NPZ ~ Δ HBZ
As the triangles NPZ and triangle HBZ are similar that means the corresponding angles are congruent.
⇒ ∠N = ∠H, ∠P = ∠B, ∠Z = ∠Z
Since,
∠P = (8x - 37)°, ∠Z = 42°, ∠H = (2x - 5)°
⇒ 2x - 5 = ∠H, ∠B = 8x - 37, Z = 42°
Since, the sum of three angles of triangle is 180°.
⇒ ∠H + ∠B + ∠Z = 180°
(2x - 5)° + (8x - 37)° + 42° = 180°
10x - 42° + 42° = 180°
10x = 180°
x = 18°
So,
∠B = (8x - 37)° = 8(18) - 37 = 144 - 37 = 107°.
Hence, the measure of angle B is m ∠B = 107°.
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In an amphitheater, eat are aranged in 50 emi-circular rowfacing a dome tate. The firt row contain 23 eat, and each row contain4more eat than the previou row. How many eat are in the amphitheater?
In an amphitheater, seat are arranged in 50 semi-circular row-facing a dome Tate. The first row contain 23 seat, and each row contain 4 more eat than the previous row. Therefore, there are 6050 seat are in the amphitheater.
Given that:
There are total 50 semi circular row.
In the first row there are 23 seats.
The given problem is AP series:
Arithmetic Series:
An arithmetic sequence is defined as an algebraic sequence in which each successive term has an equal difference. It is obtained by adding a constant to any preceding term. For the first term 'a' and the tolerance 'd' of the AP, here is a list of commonly used arithmetic progressions to solve various AP related problems:
Common Difference of AP: d = a2 - a1 = a3 - a2 = a4 - a3 = an - a(n-1) nth term of AP.AP: an = a + (n - 1)d of AP Sum of n terms: Sn = n/ 2( 2a+(n-1)d) = n/2(a + l),where l is the last term in the arithmetic progression.
Now,
Sum of n terms = n/2 [ 2a + (n-1)d]
= 50/2 [ 2× 23 + (50 -1)4]
= 25 [46 + 49×4]
= 25 × 242
= 6050
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A pyramid has a base area of 44cm and a height of 12. 6 cm what is the volume of the pyramid ?
Pyramids have been a symbol of great architecture inventions of the mankind. Egyptian People were the first once to design pyramids on a very large level.
Let a be the Side of Area of base of Pyramid . The base of a pyramid is a square shaped quadrilateral
The Volume of the Pyramid with base area and height is given by the equation (1)
[tex]Volume = (1/3)Ah....(1)[/tex]
[tex]A = a^{2}[/tex]
[tex]a = Side[/tex]
A = [tex]a^{2}[/tex] = [tex]44cm^{2}[/tex]
[tex]h = 12.6[/tex]
Putting these values in equation (1) we get
[tex]Volume = (1/3)X44X12.6[/tex]
[tex]Volume[/tex] [tex]= 184.8cm^{3}[/tex]
Hence , the volume of the pyramid is 184.8cm³
Convert 1.45454... into a ratio of two integers. Enter your answer as a fraction in lowest terms.
Answer:
16/11
Step-by-step explanation:
Let x = 1.45454...
Multiply both sides by 100:
100x = 145.454...
Subtract both sides by x:
100x - x = 145.454... - x
100x - x = 145.454... - 1.45454...
99x = 144
x = 144/99
The term can be simplified in lowest as 16/11. Hence, 1.45454... can be written as the ratio of two integers of 16/11
Unit 1 geometry basics Homework 2
pls help! i’ll mark brainliest
The value of AB= 24 BD is congruent to BC. BD=BC
BD = 5x – 26, BC = 2x + 1, and AC = 43
How to find value of AB?From the diagram , AC=AB+BCTo find out , we need to find BC first . For that we have to find out xWE know that BD=BC, using that we solve for x5X-26=2X+1SUBSTRACT 2X3X-26=1ADD 263x=27x=9Now we plug in 9 for x and find out BCBC=2x+1BC=2(9)+1BC=19We know AC= 43AC=AB+BC43=AB+19subtract 19AB=24To learn more about find value of AB refers to:
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solve 2x+4y=4 -2x+y=-4 using substitution 
According to the solving by using substitution method the x and y are x = 6/5 and y = -8/5 respectively.
What is a method of substitution?The algebraic approach to solving simultaneous linear equations is known as substitution method. The value of one variable through one equation is substituted in the second equation in this procedure, as the name implies.
According to the given information:given equations are 2x+4y = 4 and -2x+ y = -4
Now, simplifying -2x+y = -4
-2x+y = -4
∴ y = -4 + 2x
i.e. y = 2x - 4
By substitution method,
y = 2x - 4 in other given equation 2x+4y = 4,
2x+4y = 4
2x+4(2x - 4) = 4
∴ 2x + 8x - 8 = 4
∴ 10x = 4 + 8
∴10x = 12
∴ x = 12/10
∴ x = 6/5
Now ,
substituting x = 6/5 in y = 2x - 4,
y = 2(6/5) - 4
∴ y = - 8/5
∴ x = 6/5 & y = - 8/5.
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Consider y =f(x)=-3x+2 . Using space below, determine the equation that represents the inverse f(x)
Answer: [tex]f^{-1}(\text{x}) = \frac{2-\text{x}}{3}[/tex]
Explanation:
Swap x and y, then solve for y to get the inverse.
[tex]f(\text{x}) = -3\text{x}+2\\\\\text{y} = -3\text{x}+2\\\\\text{x} = -3\text{y}+2\\\\\text{x}-2 = -3\text{y}\\\\\text{y} = \frac{\text{x}-2}{-3}\\\\\text{y} = \frac{2-\text{x}}{3}\\\\f^{-1}(\text{x}) = \frac{2-\text{x}}{3}\\\\[/tex]
What is the perimeter of ^AEB? 16.4 ft 18.5 ft 18.7 ft 22.9 ft
The perimeter of ΔAEB is 18.5 feet.
What is Triangle Proportionality theorem?A triangle's other two sides are divided in the same proportion if a line drawn parallel to either one of its sides intersects the other two sides at two different spots.
As, side AB║DF hence we will use Triangle Proportionality theorem to calculate the length of side AE.
Since, AE/AD = EB/ BF
AE/2 = 7.2/8.4
AE = 6.5 feet
So, the perimeter of ΔAEB is
= AE + EB + BE
=6.5+4.2+7.8
=18.5 ft.
Hence, the perimeter is 18.5 feet.
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9. A triangle with a height of 12 inches has an area of 36 square inches. How long is the base of the triangle?
If anyone knows this please tell me this is due tommorow!
Answer:
Step-by-step explanation
The triangle base would be 6
A farmer took 2/3 of the trawberrie that he harveted to a market. At the the market, the farmer old 1/4 of the trawberrie. How can you find what part of the trawberrie the farmer harveted were old at the market?
There are 5/12 strawberries were left. This can be solved using the concept of fraction addition.
What is fraction?A fraction is a piece of the entire. The number is stated in arithmetic as a quotient, which signifies the numerator divided by the denominator. Both are integers in a straightforward fraction. The numerator or denominator of a complex fraction is a fraction. A suitable fraction has a numerator that is smaller than its denominator.
Three main fractional kinds exist. They come in three varieties: appropriate fractions, incorrect fractions, and mixed fractions. The numerator and denominator words are known as fractions. We define its kinds in light of these two words.
Given that,
A farmer took 2/3 of the strawberry that he harvested to a market.
At the market, the farmer sold 1/4th of the strawberry.
Now, the farmer has left no of strawberries were:
= (2/3) - (1/4)
= (8 - 3) / 12
= 5 / 12
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Which of these equations is equivalent to the following: 8/12 divided by 7/8=
Plsssss help me
Answer: o.7619
Step-by-step explanation: i used the standard algorithm i am sorry i cant do a more in depth just hard to do with words ;)
Answer: 0.7619
:)
Step-by-step explanation:
Don’t know need help
The meaning of adjoining is nearby or next to.
What is meant by adjoining?The terms neighboring, adjoining, contiguous, and juxtaposed denote close closeness. Adjacent may or may not indicate touch, but it always implies the lack of something like in between. A home with a garage attached. Adjoining means meeting and touching at some point or line. Two nearby dwellings are an example of adjacent. People on our block are typically considered our neighbors.
In the English language, “adjacent to” means “next to.” For two angles to be adjacent, they must meet the following three conditions: 1. The two angles must share (or have the same) side. 2. They must share a vertex (i.e. a common starting point for the sides).
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PS is the length of either segment multiplied by two ,PS is 38.
How to find PS?A line connecting the vertex with the middle of the other side forms the median angle. As a result, we may state that PR = QS for the provided.
By equating PR and QS, we can determine X's value.
PR = QS
5x-11 = 2x+7
Combine related terms to get 5x-2x = 7+11; divide both sides by 3 to get the x value; and last, multiply the result by 2 to get x = 6.
Find the value of PR and QS, and we'll demonstrate that two are equal as a result.
Correct: 5(6)-11 = 2(6)+7 19 = 19.
PS is the length of either segment multiplied by two, or simply the product of PR and QS.
PS = 19 x 2 = 19 + 19 = 38 (D) (D)
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There were 9 pieces of paper. Some of them were cut into 3 pieces. As a result, there
are now 15 pieces of paper. How many pieces of paper were cut?
6=3
6÷3
2 is the required answer for this question
Before taking his last test in a class, the arithmetic mean of Brian's test scores is 91. He has determined that if he scores 98 on his last test, the arithmetic mean of all his test scores will be exactly 92. How many tests, including the last test, does Brian take for this class
On solving the provided question, we can say that the mean that 6 tests including the last test brian took.
What is mean?A dataset's mean is the sum of all values divided by the total number of values, often known as the arithmetic mean (as opposed to the geometric mean). Often referred to as the "mean," this is the most often used measure of central tendency. Simply dividing the dataset's total number of values by the sum of all of those values yields this result. Both raw data and data that have been combined into frequency tables can be used for calculations. Average refers to a number's average. It is straightforward to calculate: Divide by how many digits there are after adding up all the digits. the total divided by the count.
(91n + 98) / (n + 1) = 92
91n + 98 = 92(n + 1)
91n + 98 = 92n + 92
98 = n + 92
6 = n
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If Point B represents an alternate combination of flutternutters & blank books, then how much of each product could be produced?
From the given graph, at Point B a total of 8000 fluffernutters & 500 blank books could be produced.
The study of graphs, which are mathematical constructions used to represent pairwise relationships between things, is known as graph theory in mathematics. In this context, a graph is made up of vertices connected by edges.
In discrete mathematics, a graph is made up of vertices—a collection of points—and edges—the lines connecting those vertices. In addition to linked and disconnected graphs, weighted graphs, bipartite graphs, directed and undirected graphs, and simple graphs, there are many other forms of graphs.
Straight line graphs called linear graphs are used to show the relationship between two quantities. This graph makes it easier to show a result as a collection of straight lines. The term "linear" simply means a straight line; curves, dots, bars, etc. are not used.
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Find the total surface area of a cone with a base diameter of 7cm and height of 8cm
Answer: The formula for the surface area of a cone is S = π * r * s + π * r², where r is the radius of the base and s is the slant height of the cone.
To find the surface area of a cone, you first need to find the radius of the base. Since the base diameter is given as 7cm, you can divide this by 2 to find the radius of the base:
r = 7cm / 2 = 3.5cm
Next, you need to find the slant height of the cone. You can use the Pythagorean theorem to do this.
slant height = sqrt(r^2 + h^2) = sqrt(3.5² + 8²) = sqrt(12.25 + 64) = sqrt(76.25) = 8.766cm
Now you can substitute these values into the formula for the surface area of a cone and find the surface area of the cone.
S = π * r * s + π * r² = π * 3.5cm * 8.766cm + π * 3.5² cm² = 12.571 cm² + 38.485 cm² = 51.056 cm²
So the surface area of a cone with a base diameter of 7cm and height of 8cm is 51.056 cm²
Step-by-step explanation: