Answer: the average rate of change of the function is 23.
Step-by-step explanation:
[tex]h(x)=x^2-10x+21\ \ \ \ \ -1\leq x\leq 10 \ \ \ \ A(x)=?\\\displaystyle\\A(x)=\frac{\Delta y}{\Delta x}=\frac{h(x-g)-h(x)}{g} \\g=x_{max}-x_{min}\\g=10-(-1)\\g=10+1\\g=11.\ \ \ \ \ \Rightarrow\\A(x)=\frac{(x-11)^2-10*(x-11)+21-(x^2-10x+21)}{11} \\A(x)=\frac{x^2-22x+121-10x+110+21-x^2+10x-21}{11} \\A(x)=\frac{231-22x}{11}\\ A(x)=\frac{11*(21-2x)}{11}\\ A(x)=21-2x.\\x=x_{min}\ \ \ \ \ \Rightarrow\\A(x)=21-2*(-1)\\A(x)=21+2\\A(x)=23.[/tex]
A 12m pole is buried 3.5m below the ground. What fraction of the pole is above the ground?
Answer:
8.5/12 m
Step-by-step explanation:
1. calculate the metres above the ground
total metres - metres below the ground = metres above the ground.12 m - 3.5 m = 8.5 m2. therefore, 8.5 out of the total 12 metres are above ground
8.5/12 can't be simplified any further so....answer: 8.5/12 mhope this helps :)
Find u special 4 A. 22‾√ 2 2 B. 4 C. 2 D. 2‾√
The value of u in the special triangle is 2√3
How to solve for u in the special triangle?The complete question is added as an attachment
From the attached figure, the value of u can be calculated using the following sine trigonometry ratio
sin(x) = Opposite/Hypotenuse
Where
x = 30
Opposite = u
Hypotenuse = 4√3
Substitute the known values in the above equation
sin(30) = u/4√3
Multiply both sides of the equation by 4√3
u = 4√3 * sin(30)
Evaluate the trigonometry expression sin(30)
u = 4√3 * 1/2
Evaluate the product
u = 2√3
Hence, the value of u in the special triangle is 2√3
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What is the range of the following set?
28, 45, 12, 34, 36, 45, 19, 20
A. 33
B. 57
C. 45
D. 8
Answer: A. 33
Step-by-step explanation:
40 cm³ of water is poured into an empty measuring cylinder. A stone of mass 129g is put into the cylinder. If the density of the mixture of the stone is 8.6g/cm³, find the new reading of the cylinder.
Step-by-step explanation:
I assume the measuring cylinder measures the cm³ of its normally liquid content.
because for anything else we would need more information about the dimensions of the cylinder.
and so, originally the cylinder shows 40 cm³.
after dropping the stone in, how many cm³ of water is the cylinder then showing ?
let's first mention some facts we are going to use :
water weighs 1 kg (1000 g) per liter.
and 1 liter fits exactly into a cube of
10 cm × 10 cm × 10 cm = 1000 cm³
so, 1 cm³ water weighs exactly 1 g and has therefore a density of 1 g / cm³.
the stone has a density of 8.6 g / cm³, is therefore heavier than water and sinks (and replaces water correspondingly).
how many cm³ does the stone have (and replaces water) ?
well, it has 129 g, and 8.6 g of the stone fill a cm³.
so, it has
129 / 8.6 = 15 cm³
therefore, as these 15 cm³ of stone replace 15 cm³ of water, this is the same as putting 40 + 15 = 55 cm³ of water into the measuring cylinder.
and the cylinder reads now 55 cm³.
FYI : but there is still only 40 cm³ of water in there.
this is actually used to calculate the density of objects (by first weighing and then dropping them into the water to see how much water they replace).
Answer: 55 cm³.
Step-by-step explanation:
[tex]\displaystyle\\m_{stone}=129\ g\ \ \ \ \ \rho_{stone}=8,6\ \frac{g}{cm^3} \ \ \ \ \ V_{water}=40\ cm^3\ \ \ \ \ V=?.\\ \boxed {\rho=\frac{m}{V} }\\V=\frac{m}{\rho} \\V=V_{water}+V_{stone}\\V_{stone}=\frac{m_{stone}}{\rho_{stone}} \\V_{stone}=\frac{129}{8,6}\\V_{stone }=15\ cm^3.\\V=40+15\\V=55\ cm^3.[/tex]
Given y = [tex]\frac{2x-5}{x^{2} -2}[/tex], find the value of [tex]\frac{dy}{dx}[/tex] at x = 2.
▪ [tex]\bold{\dfrac{2x-5}{x^{2} -2}}[/tex]
▪ [tex]\bold{\dfrac{dy}{dx}}[/tex]
[tex] \huge\mathbb{ \underline{SOLUTION :}}[/tex]
» [tex] \tt{For \: \: y,}[/tex]
[tex]\longrightarrow\sf{y=v \dfrac{2x - 5}{ {x}^{2} - 2} }[/tex]
[tex]\longrightarrow\sf{\dfrac{dy}{dx} = \cfrac{ ( {x}^{2} - 2)(2) - (2x - 5)(2x)}{( {x}^{2} - {2}^{2} )}}[/tex]
[tex]\longrightarrow\sf{\cfrac{2 {x}^{2} - 4 - {4x}^{2} + 10x}{ ({x}^{2} - {2}^{2} )}}[/tex]
[tex]\longrightarrow{={ \boxed{\sf \cfrac{ - 2 {x}^{2} - 4 + 10x}{ ({x}^{2} - {2}^{2} )}}}}[/tex]
» [tex] \tt{At \: \: x = 2,}[/tex]
[tex]\longrightarrow\sf{ \dfrac{ - 2(2) {}^{2} + 10(2) - 4 }{( {2}^{2} - 2 {)}^{2} } }[/tex]
[tex]\longrightarrow\sf{\dfrac{ - 8 + 20 - 4}{4} }[/tex]
[tex]\longrightarrow\sf{ \dfrac{8}{4} }[/tex]
[tex]\longrightarrow{\sf = \boxed{\sf {2}}}[/tex] ✓
[tex]\huge \mathbb{ \underline{ANSWER:}}[/tex]
◆ The value of the given differential function at [tex]\sf{x=2}[/tex] is [tex]\sf{2.}[/tex]
What is the volume of this rectangular prism? 1cm,6cm,2cm
Step-by-step explanation:
The result is 12 cm³ because to get the volume of a figure you have to multiply all the characters
Lamonte has 50 m of fencing to build a three-sided fence around a rectangular plot of land that sits on a riverbank. (The fourth side of the enclosure would be the river.) The area of the land is 288 square meters. List each set of possible dimensions (length and width) of the field.
answer 1: meters
answer 2: meters
HELP PLS
The dimensions of the rectangular plot of land that sits on a riverbank is 32 m by 9 m or 18 m by 16 m.
What is an equation?
An equation is an expression that shows the relationship between two or more numbers and variables.
An independent variable is a variable that does not depend on any other variable for its value while a dependent variable is a variable that depends on other variable.
Let x represent the length and y represent the width. Hence:
x + 2y = 50
x = 50 - 2y
Also:
xy = 288
(50 - 2y)y = 288
y = 9; and y = 16
x = 32; and x = 18
The dimensions of the rectangular plot of land that sits on a riverbank is 32 m by 9 m or 18 m by 16 m.
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Please help me with algebra 2 questions!
Answer:
5B; 7B; 1,024; see answer
Step-by-step explanation:
5.
We can see from the table that
a1 = 5
a2= 5·2 = 10
a3= 5·2·2 = 5·2² = 20
a4 = 5·2·2·2 = 5·2³ = 40
...
[tex]a_{n} = 5*2^{n-1}[/tex]
7.
Is given that the filter removes 90% of contaminated air
after run 1 :
100% air
90% contamination removed for 100% air
100% is 10%+10%+10%+10%+10%+10%+10%+10%+10%+10%
10% is still contaminated air
after run 2:
10% air
90% contamination removed for 10% air
10% is 1%+1%+1%+1%+1%+1%+1%+1%+1%+1%
1% is still contaminated air
after run 3:
1% air
90% contamination removed for 1% air
1% is .1%+.1%+.1%+.1%+.1%+.1%+.1%+.1%+.1%+.1%
.1% is still contaminated air
11.
Figure 1 = 1 piece
Figure 2 = 4 pieces
Figure 3 = 4² = 16
...
[tex]Figure 6 = 4^{(6-1)} = 4^{5} = 1024[/tex]
12.
[tex](c+d)^{6} \\[/tex]
-we know that the coefficients should be 1, 6, 15, 20, 15, 6, 1
-we start with c to the lowest power 0 and d to the highest power 6 and end with d to the lowest power 0 and c to the highest power 6
[tex](c+d)^{6} = 1*c^{0} d^{6} +6*c^{1} d^{5} +15*c^{2} d^{4} +20*c^{3} d^{3} +15*c^{4} d^{2} +6*c^{5} d^{1} +1*c^{6} d^{0}[/tex]
-we simplify to have the final answer:
[tex](c+d)^{6 } = d^{6} +6cd^{5} +15c^{2} d^{4} +20c^{3} d^{3} +15c^{4} d^{2} +6c^{5} d+c^{6}[/tex]
3-12x4-6x²
Expression in standard form:
Leading Coefficient:
Answer:
Below in bold.
Step-by-step explanation:
Standard form:
-12x⁴ - 6x² + 3.
Leading Coefficient:
-12.
What is the slope of the line that passes through
the points (2,
-4) and (5, 2)? Write your
answer in simplest form.
Answer:
2
Step-by-step explanation:
slope : ( The amount y increases , when x is increased by 1 )
slope : { y2 - y1 / x2 - x1 }
slope : y2 = 2
y1 = -4
x2 = 5
x1 = 2
You must minus the values in the formula to find the slope line that passes through the points:
slope : { y2 - y1 / x2 - x1 }
slope : (2) - (-4) / (5) - (2)
=> 2 + 3 / 3
=> 6/3
=> 2
Text explanation:
Difference between both y-coordinates. = 6
Difference between both x-coordinates. = 3
Divide the difference between y and x. =
y/x =2
Which means the slope of the line that passes through the points (2,-4) and (5,2) is 2.
Hope this helps! Sorry it took so long! ⸜(｡˃ ᵕ ˂ )⸝ xx
The slope of the line that passes through the points (2, -4) and (5, 2) is 2.
What is Slope?A slope is also known as the gradient of a line is a number that helps to know both the direction and the steepness of the line.
slope = (y₂-y₁)/(x₂-x₁)
The slope of the line that passes through the points (2, -4) and (5, 2) can be calculated as shown below,
Slope = (y₂-y₁)/(x₂-x₁) = [2 - (-4)] / (5 - 2)= 6/3 = 2
Hence, the slope of the line that passes through the points (2, -4) and (5, 2) is 2.
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A substance is tested and has a ph of 7.0. how would you classify it? a. a strong acid b. a strong base c. a weak acid d. neutral
A substance is tested and has a Ph of 7.0. It would be a weak acid.
The correct option is (c) a weak acid .
What is the nature of substance if the pH is less than 7?
Acidity is defined as pH below 7. More than 7 pH is considered basic. Each whole pH number below 7 is ten times more acidic than the next higher value since the pH scale is logarithmic. For instance, pH 4 is 100 times (10 times 10) more acidic than pH 6, while pH 5 is ten times (10 times) more acidic than pH 4.What is pH?
The pH scale determines how acidic or basic water is. The range is 0 to 14, with 7 representing neutrality. Acidity is indicated by pH values below 7, whereas baseness is shown by pH values above 7. In reality, pH is a measurement of the proportion of free hydrogen and hydroxyl ions in water.Learn more about pH
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Evaluate f(-3) for f(x) = 2^x
a. 1/8
b. -8
c. 8
d. -6
Answer:
A
Step-by-step explanation:
f(-3) = 2^-3
to get rid of a negative in an exponent, move the whole thing to the denominator.
1/(2^3)
2^3 = 2×2×2
1/(2×2×2)
1/8
PLS HELP ITS MATH PLS
[tex] \: \: \: \: \: \: \: y = \frac{ - 7x}{8} + 4 \\ \: \: \: \: \: \: multiply \: all \: by \: 8 \\ \: \: \: \: \: \: \: \: 8y = - 7x + 32 \\ \: \: \: \: \: \: \: \: \: 7x + 8y = 32[/tex]
( 7 , 8 , 32 )The numbers 1, 2, 3, 4, 5, 6, 7, and 8 are arranged to form four two-digit numbers. What is the largest amount of primes that could possibly be among these four numbers?
==========================================================
Reason:
The only even prime number is 2. The other primes are odd.
The list of the first few primes are:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43
A prime is any number that has factors of 1 and itself, and nothing else.
For instance, 13 is prime because 1 and 13 are the only factors.
-----------
As you can see, if we want a two digit prime number, then the units digit must be odd. Otherwise, 2 is a factor making it not prime (aka composite).
So far we see that the units digit is 1, 3, 5, 7, or 9. But wait, if 5 is the units digit then 5 is a factor. Eg: 5 is a factor of 35 since 5*7 = 35. Refer to the divisibility by 5 rule.
So we reduce the list of choices to 1, 3, 7, 9 for the units digit.
Unfortunately 9 is not in the list of original numbers given, so we can't use it. We really have 1, 3, or 7 as our choices to form the units digit of the two-digit number.
-----------
Let's try to build some primes.
Pick the smallest odd number 1 as the units digit. Then pick 2 as the tens digit. The number 21 is composite because 21 = 7*3, so we rule it out.
On the other hand, 31 is prime since only 1 and 31 are factors.
The problem is that now "3" is tied up and cannot be used for another prime. The good news is that 41 is prime and that's what I'll go with.
Cross 1 and 4 off the list.
The next odd number is 3 which is our units digit. The value 23 is prime.
So far we have 41 and 23 as our two primes.
Like mentioned earlier, we cannot use 5 as the units digit. The number 57 is not prime because 57 = 19*3. So we'll skip over 5.
The number 67 is prime for similar reasoning mentioned earlier.
------------
We have these primes: 41, 23, 67
The next number either 58 or 85 isn't prime
This is one way to show an example of why we're only able to get 3 primes out of this.
A company is replacing cables with fiber optic lines in rectangular casing bcde. if segment de = 2.5 cm and segment be = 3 cm, what is the smallest diameter of pipe that will fit the fiber optic line? round your answer to the nearest hundredth.
3.9 cm is the smallest diameter of pipe that will fit the fiber optic line.
What is diameter?
Diameter is the full length of the circle running from the edge, through the midpoint, all the way to the other side. That is this whole length right here. The diameter of a circle is represented by the letter d.we know that
The diameter of the circle is equal to BD
Applying the Pythagoras Theorem
BD² = BE² + DE²
substitute the given values
BD² = (3)² + (2.5)²
BD² = 9 + 6.25
BD² = 15.25
BD = √15.25
BD = 3.9 cm
Therefore , 3.9 cm is the smallest diameter of pipe that will fit the fiber optic line.
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5- Calculate the radius of a circle whose area is equal to the sum of the areas of 3 circles of radii 2cm, 3cm and 4cm
respectively.
the radius of the new circle =5cm
5cm is your answer love
During the season, the Rangers played 25 games. They won 14 of the games.
What fraction and percent of the games did they lose? Show your work in the
space below. Remember to check your solution.
Answer:
See below
Step-by-step explanation:
Out of 25 games, they won 14
Fraction won = won / total = 14 / 25
Percent won = won /total * 100 % = 14/25 * 100 = .56 * 100 % = 56 %
To find the number of games lost
25-14 = 11
Fraction won = won / total = 11 / 25
Percent won = won /total * 100 % = 11/25 * 100 = .44 * 100 % = 44 %
To check your work, the percent total should be 100
56+44 = 100
my car uses 8.5L of pertrol per 100km travelled. If I travel 400km, how many litres of petrol will my car use?
Answer:
34 L
Step-by-step explanation:
there are four 100 km(s) in 400 km
so
8.5 * 4 is what you need to do to find your answer
8.5 * 4 = 34
34 L is your answer
if a skip rope is a meter long and its a cm less how much is it pls answer
Answer:
99cm
Step-by-step explanation:
A meter is equal to 100cm
The rope is a metre (m) long but a centimetre (cm) less.
100cm - 1cm = 99cm
Which of the following is a correct interpretation of the expression -4 + 13−4+13minus, 4, plus, 13?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
The number that is 444 to the left of -13−13minus, 13 on the number line
(Choice B)
B
The number that is 444 to the right of -13−13minus, 13 on the number line
(Choice C)
C
The number that is 131313 to the left of -4−4minus, 4 on the number line
(Choice D)
D
the sum between negative 4 and 13, this can be tought as:
Stepping on -4 and moving 13 units to the right.Stepping on 13 and moving 4 units to the left.Which is the interpretation of the given expression?
The expression is just the sum:
-4 + 13
So we have the sum between negative 4 and 13, this can be tought as:
Stepping on -4 and moving 13 units to the right.Stepping on 13 and moving 4 units to the left.Now, none of the written options (a, b, and c) depict any of this, so I assume that the correct option is the one that you did not write, which is option D.
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The triathletes were offered water as they rode by the volunteer station. The volunteers handed them cones with the dimensions shown. If each triathlete sloshed 1/3 of the water out before they drank it, how many cubic cm of water did they slosh out? Round to the nearest tenth. (PLEASE ANSWER)
Answer:
29.9 cm³
Step-by-step explanation:
You want to know the volume represented by 1/3 of a cone that is 7 cm high and has a radius of 3.5 cm.
ConeThe volume of a cone is given by ...
V = 1/3πr²h
The volume of the cone of interest is ...
V = 1/3π(3.5 cm)²(7 cm) ≈ 89.797 cm³
Slosh1/3 of the volume is the amount of water that sloshed out of the cone. That volume is ...
1/3(89.797 cm³) ≈ 29.9 cm³
They sloshed out about 29.9 cm³ before they drank the water.
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Which equation shows the commutative property of addition? 4 3 = 3 4 1(3) = 3 (2 7) 12 = 2 (7 12) 4 0 = 4
The equation which shows the commutative property of addition is (A) 4+3=3+4.
What is the commutative property of addition?The commutative property is concerned with arithmetic operations such as addition and multiplication. It indicates that switching the order or position of two numbers while adding or multiplying them has no effect on the outcome. For example, 4 + 5 equals 9, and 5 + 4 equals 9.So,
The commutative property for addition states that, a + b = b + a .
Where a, b is any number.
The above condition is satisfied by the equation
4 + 3 = 3 + 47 = 7Therefore, the equation which shows the commutative property of addition is (A) 4+3=3+4.
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The correct question is given below:
Which equation shows the commutative property of addition?
A. 4+3=3+4
B. 1(3)=3
C. (2+7)+12=2+(7+12)
D. 4+0=4
A boardwalk game of chance costs $1 to play. you have a 25% chance of winning $1 back, a 20% chance of winning $2 (your $1 back, plus an additional $1), and a 10% chance to win $5 (a gain of $4). what is the expected value of playing the game if you lose your bet 45% of the time?
Expected value of playing the game = $0.8
What is cost ?
Cost denotes the amount of money that a company spends on the creation or production of goods or services. It does not include the markup for profit. From a seller's point of view, cost is the amount of money that is spent to produce a good or product.
Cost of playing = $2
Expected return
10% chance to win $1 = $1 10% = $0.1
25% chance to win back $2 = $2 25% = $0.5
50% chance to win $5 = $5 50% = $2.5
15% chance to lose $2 (being cost) = $2 15% = ($0.3)
= $0.1 + $0.5 + $2.5 - $0.3 = $2.8
Now for this we have to pay fixed cost $2
Thus, expected value of playing game = $2.8 - $2 = $0.8
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5. Mr. Griffin asked the students to form the number eighty-four million, five
hundred thirty thousand, two hundred sixteen. Ben still had the number card
with the 3. In what place was Ben standing? Show your work in the space
below. Remember to check your solution.
Answer:
Ten thousands place
Step-by-step explanation:
84 530 216
Frm here u can see that the 3 is in the ten thousands place
Given these facts, determine how many cans of paint you would need to buy to paint 2 walls.
1st wall: 20 ft. x 8ft.
2nd wall: 40ft. x 8ft.
1 can will cover 200 square feet of wall.
You will need 3 cans of paint to cover the two walls
How many cans of paint will you need?
We know that 1 can will cover 200 square feet of wall.
And here we have 2 walls, let's find the total area of these walls.
wall 1 is 20ft by 8ft, then its area is:
A = 20ft*8ft = 160ft^2
wall 2 is 40t by 8 ft, then its area is:
A' = 40ft*8ft = 320ft^2
The total area is:
160ft^2 + 320ft^2 = 480ft^2
The number of cans of paint needed is given by the quotient between the total area and the area that each can cover.
N = 480ft^2/200ft^2 = 2.4
But we can't have a 0.4 of a can, so we should round to the next whole number, which is 3.
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A cell phone carrier introduced a new strategy to increase their number of subscribers. The function below represents the increase in number of subscribers, where f(t) represents the number of subscribers and represents the time in months
The cell phone carrier had 250 subscribers before the strategy was introduced. After the new strategy is introduced, the number of staffs increased by a factor of 1.4.
What is an equation?An equation is an expression that shows the relationship between two numbers and variables.
An exponential function is in the form:
y = abˣ
Where a is the initial value of y and b is the multiplication factor.
Let f(t) represents the number of subscribers and t represents the time in months. Hence:
[tex]f(t) = 250(1.4)^t[/tex]
a = 250, b = 1.4
The cell phone carrier had 250 subscribers before the strategy was introduced. After the new strategy is introduced, the number of staffs increased by a factor of 1.4.
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Answer: 250, 1 month, and 1.4
HELP
answer the questions 61 and 62 SHOW UR WORK please i’ll mark brainliest
help me
Answer:
Step-by-step explanation:
Seven people are in an elevator which stops at ten floors. In how many ways can they get off the elevator?
The number of ways people can get off the elevator is 604800 ways.
In this question,
Number of people, n = 7
Number of floors, r = 10
The first person can leave elevator in one of 10 ways. Then second person has to choose from one of remaining 9 floors. Then third person in 8, fourth in 7 ways and so on.
Number of ways people can get off the elevator can be calculated as
⇒ [tex]nP_r=\frac{n!}{(n-r)!}[/tex]
⇒ [tex]10P_{7}=\frac{10!}{(10-7)!}[/tex]
⇒ [tex]10P_{7}=\frac{10!}{(3)!}[/tex]
⇒ [tex]10P_{7}=\frac{(10)(9)(8)(7)(6)(5)(4)3!}{(3)!}[/tex]
⇒ [tex]10P_{7}=(10)(9)(8)(7)(6)(5)(4)[/tex]
⇒ 604800 ways.
Hence we can conclude that the number of ways people can get off the elevator is 604800 ways.
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A rubber gasket has a circumference of 3.2 cm. when placed in service, it expands by a scale factor of 2. what is the circumference of the gasket when in service?
6.4 cm is the needed circumference of the gasket following dilatation with a scale factor of 2.
What does circumference mean?The boundary length of any circular shape is known as the circumference.
What is scale factor?A scale factor is a quantity multiplier (also known as a scale). The scaling factor for x, for instance, is represented by the letter "C" in the equation y = Cx. The factor would be 5 if y = 5x were the equation.
According to the given data:After scale factor 2 is applied, 6.4 cm must be the gasket's needed circumference.
It includes a rubber gasket with a 3.2 cm circumference. The circumference of the gasket has must be calculated after scaling up by factor 2.
Here,
3.2 cm is the gasket's circumference.
The circumference changed upon scale factor 2 dilatation.
Dilated gasket circumference: 2 * 3.2 = 6.4 cm
As a result, 6.4 cm is the needed circumference of the gasket following dilatation with a scale factor of 2.
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Answer:
6.4cm
Step-by-step explanation:
I Just Took the Test.
3(x - 5) = 2(x - 5) + x
Solve for x please helppp
Answer: No solution
Distribute the parenthesis
3x-15=2x-10+x
Combine like terms
3x-15=3x-10
This answer has no solution for x.