Answer:
A. 500 transistors
B. 50,000 capacitors
C. 100 capacitors
Step-by-step explanation:
The width of one transistor =0.004 mm
The total length filled by the 0.004 mm transistors is 2 mm.
A. In 2 mm there are: 2 mm/ 0.004 mm/transistor =500 transistors.
B. In 2 mm there are 2 mm/ 0.00004 mm/capacitor= 50,000 Capacitors.
C. The number of capacitors to fit in one transistor is given by the quotient between the width of a transistor and the width of a capacitor.
=0.004 mm ÷0.00004 mm
=100 capacitors/transistor
Thus only 100 capacitors can fit into 1 transistor
Match the polynomial to the correct description :
(X+4)(x-1)(x-2)(x-4)
A. The related polynomial equation has a total of four roots;all four roots are real.
B. the related polynomial equation has a total of four roots,all four roots are real and one root has a multiplicity of 2.
C. The related polynomial equation has a total of four roots, two roots are complex and two roots are real.
D. The related polynomial equation has a total of two roots, both roots are real and have a multiplicity of 2.
E. The related polynomial equation has a total of three roots, two roots are complex and one root is real.
F. The related polynomial equation has a total of four roots, two roots are complex and one root is real with a. Multiplicity of 2.
Answer:
A
Step-by-step explanation:
The polynomial (x+4)(x-1)(x-2)(x-4) has zeros at x=-4,1,2,4.
The related polynomial equation is (x+4)(x-1)(x-2)(x-4)=0.
In order for this equation to be true at least one of the factors must by 0 that is the only way a product can be zero (if one of it's factors is).
So you wind up needing to solve these 4 equations:
x+4=0 x-1=0 x-2=0 x-4=0
x=-4 x=1 x=2 x=4
First equation, I subtracted 4 on both sides.
Second equation, I added 1 on both sides.
Third equation, I added 2 on both sides.
Fourth equation, I added 4 on both sides.
-4,1,2,4 are all integers
Integers are real numbers.
So A.
The polynomial (X+4)(x-1)(x-2)(x-4) corresponds to option A: The related polynomial equation has a total of four roots; all four roots are real, with no root having a multiplicity. Hence the correct answer is A.
To match the polynomial (X+4)(x-1)(x-2)(x-4) to the correct description, we can look at its factors to determine the roots. Each factor of the form (x - c) represents a real root at x = c. For this polynomial, the factors indicate there are four roots: -4, 1, 2, and 4. These roots all come from different factors, so there is no repeated root, implying no multiplicity among them. Hence, the correct description must state that there are four real roots and none of them is repeated.
Since options B, C, E, and F suggest either roots with multiplicity, a mixture of real and complex roots, or fewer than four roots, they are not correct. Therefore, this leaves us with option A as the correct match: The related polynomial equation has a total of four roots; all four roots are real. None of the roots are repeated, there are no complex roots, and all roots can be identified directly from the given factors of the polynomial.
3(-4n - 9) = 21 plc solve
[tex]\huge{\boxed{n=-4}}[/tex]
Explanation:[tex]\begin{array}{cc}\begin{flushright}\text{Divide both sides of the equation by 3.}\end{flushright}&\begin{flushleft}-4n-9=7\end{flushleft}\\\begin{flushright}\text{Add 9 on both sides.}\end{flushright}&\begin{flushleft}-4n=16\end{flushleft}\\\begin{flushright}\text{Divide both sides by -4.}\end{flushrigh}&n=-4\end{array}[/tex]
Answer:
[tex]\Huge \boxed{n=-4}[/tex]
Step-by-step explanation:
First thing you do is divide by 3 from both sides of equation.
[tex]\displaystyle \frac{3(-4n-9)}{3}=\frac{21}{3}[/tex]
Simplify.
[tex]\displaystyle -4n-9=7[/tex]
Then add by 9 from both sides of equation.
[tex]\displaystyle -4n-9+9=7+9[/tex]
Simplify.
[tex]\displaystyle 7+9=16[/tex]
[tex]\displaystyle -4n=16[/tex]
Divide by -4 from both sides of equation.
[tex]\displaystyle \frac{-4n}{-4}=\frac{16}{-4}[/tex]
Simplify, to find the answer.
[tex]\displaystyle 16\div-4=-4[/tex]
[tex]\huge\boxed{\textnormal{N=-4}}[/tex], which is our answer.
-2k-(-5)+1 like terms
Answer:
-2k + 6
Step-by-step explanation:
-2k - (-5) + 1 //-1 times -5 = 5 ( - - gives +)
-2k + 5 + 1 //Combine like terms
-2k + 6
Remember you can't add or sub -2k with 6 since -2 is multiplying with k (which is constant and you don't know it's value)
//Hope this helps
Answer:
-2k+6
Step-by-step explanation:
Solve for x: 2 over 10 equals 3 over quantity x minus 9
Answer:
24
Step-by-step explanation:
2/10=3/x-9
2(x-9)=30
2x-18=30
2x=30+18
2x=48
x=24
Answer:
The value of x in the given phrase is 24.
Step-by-step explanation:
Given phrase,
2 over 10 equals 3 over quantity x minus 9
[tex]\frac{2}{10}=\frac{3}{x-9}[/tex]
By cross multiplication,
[tex]2x-18=30[/tex]
Adding 18 on both sides,
[tex]2x=48[/tex]
Divide both sides by 2,
[tex]x=24[/tex]
Hence, the value of x is 24.
Find the quotient.
8.24 = 1.7=
Answer:
4.847
Step-by-step explanation:
divide 8.24 by 1.7
8.24 /1.7 = 4.847
For this case we have the following operation:
[tex]\frac{8.24} {1.7}[/tex]
We must find the final result after the division.
To do this, we can use a calculator or a computer program.
We then have to do the division:
[tex]\frac{8.24} {1.7} = 4.94[/tex]
Answer:
The total ratio is given by: 4.94.
If a cube has side lengths of 8 centimeters, what is the volume of the cube? cubic centimeters
Answer:
V = 512 cm³Step-by-step explanation:
The formula of a volume of a cube:
[tex]V=a^3[/tex]
a - edge
We have a = 8cm.
Substitute:
[tex]V=8^3=512\ cm^3[/tex]
Answer:
512 square centimeters
Step-by-step explanation:
have a great day :)
What is the answer please
Step-by-step explanation:
[tex]1a.\\ 8-y=2\qquad\text{subtract 8 from both sides}\\-y=-6\qquad\text{change the signs}\\\boxed{y=6}\\\\1b.\\11-9=2-b\\2=2-b\qquad\text{subtract 2 from both sides}\\0=-b\to \boxed{b=0}\\\\2a.\\5=\dfrac{c}{3}\qquad\text{multiply both sides by 3}\\15=c\to \boxed{c=15}\\\\2b.\\2=5-t\qquad\text{subtract 5 from both sides}\\-3=-t\qquad\text{change the signs}\\3=t\to\boxed{t=3}\\\\3a.\\5n=10\qquad\text{divide both sides by 5}\\\boxed{n=2}\\\\3b.\\a+6=12\qquad\text{subtract 6 from both sides}\\\boxed{a=6}[/tex]
[tex]4a.\\v-10=7\qquad\text{add 10 to both sides}\\\boxed{v=17}\\\\4b.\\7=7n+7n\\7=14n\qquad\text{divide both sides by 14}\\\dfrac{7}{14}=n\\\boxed{n=\dfrac{1}{2}}\\\\5a.\\m+11=12\cdot4\\m+11=48\qquad\text{subtract 11 from both sides}\\\boxed{m=37}\\\\5b.\\6y=7+5\\6y=12\qquad\text{divide both sides by 6}\\\boxed{y=2}\\\\6a.\\b-8=3\qquad\text{add 8 to both sides}\\\boxed{b=11}\\\\6b.\\1+c=8\qquad\text{subtract 1 from both sides}\\\boxed{c=7}[/tex]
Write the equation 8y = 1/12 x – 0.8 in standard form. Identify A, B, and C.
Answer:
The equation is 10x - 960y = 96
A = 10 , B = -960 , C = 96
Step-by-step explanation:
* Lets explain the standard form of the linear equation
- The standard form of the linear equation is :
AX + BY = C , where A , B , C are constant
- A is a positive integer, and B, and C are integers
- The slope of the line is -A/B
- The y-intercept is C/A
- Lets solve the problem
∵ The equation of the line is 8y = 1/12 x - 0.8
- At first multiply the equation by 12 to make the coefficient of x integer
∴ (8 × 12) y = (1/12 × 12) x - (0.8 × 12)
∴ 96y = x - 9.6
- Multiply the two sides of the equation by 10 to make 9.6 integer
∴ (96 × 10) y = (1 × 10) x - (9.6 × 10)
∴ 960y = 10x - 96
- Add the two sides by 96
∴ 960y + 96 = 10x
- Subtract 960y from both sides
∴ 96 = 10x - 960y
∴ The standard form of the equation is 10x - 960y = 96, where
A = 10 , B = -960 , C = 96
a lottery costs $1 per ticket. the player selects a sincle letter from A to T and a single digit from 0 to 9. if both the letter and the digit match the letter and digit picked on that day, the player wins $250. what is the expected value of a lottery ticket/
================================================
Explanation:
The letter T is the 20th letter in the English alphabet. This means that there are 20 letters to pick from to go with the 10 single digit numbers to pick from. We have 20*10 = 200 different combinations (eg: one combination is K4).
Out of these 200 combinations, there is exactly one winning match.
The probability of winning is therefore P(W) = 1/200 = 0.005 and the probability of losing is P(L) = 1-P(W) = 1-0.005 = 0.995 where W and L represent winning and losing respectively.
The net value of winning is V(W) = 250 - 1 = 249 because the player wins $250 but they lose $1 (which is the cost of the ticket). The net value of losing is V(L) = -1, indicating the player has lost that $1 and hasn't gained any money at all.
-----------
To summarize so far:
P(W) = 0.005
P(L) = 0.995
V(W) = 249
V(L) = -1
Multiply the probability P values with the corresponding net values V, then add up the products to get the expected value:
E(X) = P(W)*V(W) + P(L)*V(L)
E(X) = 0.005*249 + 0.995*(-1)
E(X) = 0.25
The expected value is 0.25 dollars or 25 cents
This positive expected value means that the game is favored toward the player, because over the long run, the player gains an average of 25 cents each time they play. On the other side of the spectrum, the lottery company loses on average 25 cents each time. The nonzero expected value means that the game is not fair.
how to find equation of line passing through the points (x,y)
First you must acknowledge that you are dealing with a line therefore you must write linear equation or linear function in this case.
Linear function has a form of,
[tex]y=mx+n[/tex]
Then calculate the slope m using the coordinates of two points. Let say A(x1, y1) and B(x2, y2),
[tex]m=\dfrac{\Delta{y}}{\Delta{x}}=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Now pick a point either A or B and insert coordinates of either one of them in the linear equation also insert the slope you just calculated, I will pick point A.
[tex]y_1=mx_1+n[/tex]
From here you solve the equation for n,
[tex]
y_1=mx_1+n\Longrightarrow n=y_1-mx_1
[/tex]
So you have slope m and variable n therefore you can write down the equation of the line,
[tex]f(x)=m_{slope}x+n_{variable}[/tex]
Hope this helps.
r3t40
Hep with this
Math homework
Answer:
a) 16.7
b) 13.5
Step-by-step explanation:
AC and DE are parallel, so ∠CAB and ∠EDB are corresponding angles, and ∠ACB and ∠DEB are corresponding angles.
Therefore, ΔABC and ΔDBE are similar triangles. We can use this to write a proportion.
a)
(25 + x) / (18 + 12) = x / 12
12 (25 + x) = x (18 + 12)
300 + 12x = 30x
300 = 18x
x = 16.7
b)
x / (7 + 2) = 3 / 2
x = 13.5
What is the range of rooms in Henry's histogram?
The houses surveyed had between 1 and 10 rooms.
The histogram shows a range of 5 to 6 rooms.
The houses surveyed had between 0 and 6 rooms.
The histogram shows a range of 1 to 5 rooms.
Answer:
The houses surveyed had between 1 and 10 rooms ..
Step-by-step explanation:
We can see from the histogram that the minimum number of rooms any house had was 1 and the maximum number of rooms were 10.
Range is the difference between highest and lowest value of a data set.
Hence, the range from the given histogram can be determined as:
The houses surveyed had between 1 and 10 rooms ..
Answer: The houses surveyed had between 1 and 10 rooms.
Step-by-step explanation:
The range of any data gives us a interval which contains all the data values and provides an indication of the dispersion of data its from minimum value to the maximum value.From the histogram, the minimum number of rooms = 1
The maximum number of rooms = 10
Hence, the range of rooms in Henry's histogram is between 1 and 10 rooms.
How do I solve this question ?
49/b - 5 = 2
First add 5 to both sides:
49/b = 7
Multiply both sides by b:
49 = 7b
Divide both sides by 7:
b = 49/7
b = 7
bicycles 14mph with no wind. Against the wind, bikes 10 mi in
the same time it takes to bike 20 mi with the wind. What is the speed of
the wind?
recall your d = rt, distance = rate * time.
w = speed of the wind.
14 = speed of the bicycle without wind.
now, against the wind, the bicycle is not really going 14 mph fast, is really going "14 - w", since the wind is eroding speed from it, likewise, when the bicycle is going with the wind is not going 14 mph fast either, is really going "14 + w" due to the wind adding speed, let's say it took "t" hours against and also "t" hours with it.
[tex]\bf \begin{array}{lcccl} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ \cline{2-4}&\\ \textit{against the wind}&10&14-w&t\\ \textit{with the wind}&20&14+w&t \end{array}~\hfill \begin{cases} 10=(14-w)t\\ \frac{10}{14-w}=\boxed{t}\\ \cline{1-1} 20=(14+w)t \end{cases}[/tex]
[tex]\bf 20=(14+w)t\implies \cfrac{20}{14+w}=t\implies \stackrel{\textit{substituting in the 2nd equation}}{\cfrac{20}{14+w}=\boxed{\cfrac{10}{14-w}}} \\\\\\ 280-20w=140+10w\implies 280=140+30w\implies 140=30w \\\\\\ \cfrac{140}{30}=w\implies \cfrac{14}{3}=w\implies 4\frac{2}{3}=w[/tex]
32' 1566" is the same as _
Round to the nearest hundredth of a degree
Answer:
32.27°
Step-by-step explanation:
Convert 32° 15' 66'' to the nearest hundredth of a degree
we know that
1 degree=60 minutes
1 minute=60 seconds
1 degree=3,600 seconds
step 1
Convert 15' to degrees
15'=15/60=0.25°
step 2
Convert 66'' to degrees
66''=66/3,600=0.02°
substitute
32° 15' 66''=32° +0.25°+0.02°=32.27°
HELP ASAP PLS!!!
A power outage occurs 6 min after the ride started. Passengers must wait for their cage to be manually
cranked into the lowest position in order to exit the ride. Sine function model: h = 82.5 sín 30t +0.5) +97.5
where h is the height of the last passenger above the ground measured in feet and t is the time of operation of
the ride in minutes.
(a) What is the height of the last passenger at the moment of the power outage? Verity your answer by
evaluating the sine function model.
(b) Will the last passenger to board the ride need to wait in order to exit the ride? Explain.
Answer:
I will assume
h = 82.5 sin (3 pi (t+0.5) )+97.5 , (you had no equation and no h)
so when t = 6
h = 82.5 sin (3π(6.5)) + 97.5
= 82.5(-1) + 97.5 = 15
check: period = 2π/(3π) = 2/3 minutes (that is a fast ride considering how huge it is)
So 6 ÷(2/3) = 9 , at the 6 minute mark, the last passenger has just completed 9 rotations.
the min height of the basket is -82.5 + 97.5 = 15
( the min value of 82.5 sin(anything) = 82.5(-1) )
so the last passenger must be at the platform level.
how did you get 79 ???
Step-by-step explanation:
Please explain how to answer this!
[tex]\huge{\boxed{66}}[/tex]
Start by substituting in the values. [tex]3(2)+6(8+2)[/tex]
Add. [tex]3(2)+6(10)[/tex]
Multiply. [tex]6+60[/tex]
Add. [tex]\boxed{66}[/tex]
Answer:
Step-by-step explanation:
3a+6(b+2)
=3(2)+6(8+2)
=6+6(10)
=6+60
=66
a fashion stylist wants to know if her clients are happy with her. She decides to survey a sample of her clients. What method would be best for choosing a random sample that is a fair representation of her clients?
Answer:
Assign numbers to each client and then use a random number generator to choose one hundred clients to survey.
Step-by-step explanation:
I think the best method would be:
Assign numbers to each client and then use a random number generator to choose one hundred clients to survey.
It is the best way to choose a random sample as it is a fair representation of her all customers. In this sample all of her costumers will be assigned numbers and will be chosen randomly. ...
What number is missing in the solution to the system of equations:
4x-3y=1
5x+4y = 9
(1.11
First you must solve system of equations.
Multiply the first equation by 4 and second one by 3.
You result with,
[tex]
16x-12y=4 \\
15x+12y=27
[/tex]
Add the equations so y terms cancel out.
[tex]31x=31\Longrightarrow x=1[/tex]
Insert x that was found in either one of the equations. I'll pick first one.
[tex]4\cdot1-3y=1[/tex]
Solve for y.
[tex]
-3y=-3 \\
y=1
[/tex]
The solutions to the system of equations are,
[tex]\boxed{x=1},\boxed{y=1}[/tex]
Therefore the number missing is 1.
Hope this helps.
r3t40
Answer:
(1,1)
Step-by-step explanation:
Which statement about perfect cubes is true?
Answer: C.
Step-by-step explanation: A cube’s volume is Length x Width x Height. Since a cube has all equal sides, a perfect cube would have 3 of the same numbers being multiplied, 8 x 8 x 8.
Option c is correct, 512 is a perfect cube because 512=8×8×8 is a correct statement about perfect cube.
What is Number system?A number system is defined as a system of writing to express numbers.
A perfect cube of a number is a number that is equal to the number, multiplied by itself, three times.
25 is not a perfect cube but it is a perfect square
30 is not a perfect cube
512 is a perfect cube because 8³=512
512=8×8×8
1875 is not a perfect cube.
Hence, 512 is a perfect cube because 512=8×8×8 id a correct statement about perfect cube.
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The Chesapeake Bay tides vary between 4 feet and 6 feet. The tide is at its lowest point when time (t) is 0 and completes a full cycle in 12 hours. What is the amplitude, period, and midline of a function that would model this periodic phenomenon?
Amplitude = 1 foot; period = 12 hours; midline: y = 5
Amplitude = 2 feet; period = 6 hours; midline: y = 1
Amplitude = 2 feet; period = 12 hours; midline: y = 5
Answer:
Amplitude = 1 foot; period = 12 hours; midline: y = 5
Step-by-step explanation:
The Chesapeake Bay tides vary between 4 feet and 6 feet.
This means the range is
[tex]4 \leqslant f(t) \leqslant 6[/tex]
The period is the length of the interval on which the function completes one full cycle.The tide is at its lowest point when time (t) is 0 and completes a full cycle in 12 hours.
The interval is [0,12] and its length is 12, hence the period is 12.
The midline
[tex]y = \frac{min + max}{2} [/tex]
[tex]y = \frac{4 + 6}{2} = 5[/tex]
The amplitude is the distance from the midline to the peak.
The amplitude is |5-4|=|5-6|=1
The first choice is correct.
The amplitude of the function modeling the Chesapeake Bay tides is 1 foot, the period is 12 hours, and the midline is at y = 5 feet.
Explanation:The amplitude of a function that models a periodic phenomenon, like the tides in this case, is half of the total variation in height. Since the tides vary between 4 feet and 6 feet, the total variation is 2 feet (6 feet - 4 feet), and thus, the amplitude is 1 foot (2 feet / 2).
The period of the function is the time it takes for the tidal cycle to repeat itself. Given that the tide completes a full cycle in 12 hours, the period of the function is 12 hours.
The midline represents the average value around which the tide oscillates. It can be found by averaging the maximum and minimum tide levels. Therefore, the midline is (4 feet + 6 feet) / 2 = 5 feet.
Considering these calculations, the correct amplitude is 1 foot, the period is 12 hours, and the midline is y = 5 feet for the function that would model the periodic phenomenon of the Chesapeake Bay tides.
The bill for Dino's lunch was $19.45. He wanted to leave 20% of the total bill as a tip. How much should the tip be?
You could multiply 19.45 by 0.2 to solve for it, but if you're not using a calculator, then 19.45/5 would be much more convenient and easier.
0.2 is 1/5 in fraction form, which is why we can do that.
19.45/5 = 3.89
Dino should leave $3.89 as a tip.
Answer:
$3.89
Step-by-step explanation:
X = 20
19.45 = 100
19.45*20=389
389/100=$3.89
Deanna has $150.00 in her account.At the end of each week, she plans to take $15.00 out of her account for her spending money. Write an equation to show the relationship between the number of weeks and the balance in the account
Let the balance = Y and the number of weeks = x
She takes out 15 per week, so multiply 15 by x ( the number of weeks) to get 15x.
You would then want to subtract that from the amount she started with in her account.
The equation becomes: Y = 150 - 15x
A bakery's production is modeled by function f(x), where f(x) is the number of donuts made in a day and x is the number of bags of flour needed. Choose the ordered pair that represents a possible domain and range of the function.
(−1, 15)
(5, 92.75)
(10, 100)
(−5, 110.5)
ANSWER
(10,100) is the correct answer
Answer:
The correct option is 3. The possible domain and range of the function is (10, 100).
Step-by-step explanation:
It is given that a bakery's production is modeled by function f(x), where
f(x) = The number of donuts made in a day
x = The number of bags of flour needed.
The number of donuts made in a day and the number of bags of flour needed can not be a fraction value of a negative number. So, the values of x and f(x) can not defined by negative or decimal numbers.
In ordered pair (-1,15), the value of x is negative, so option 1 is incorrect.
In ordered pair (5,92.75), the value of y is in decimal, so option 2 is incorrect.
In ordered pair (10,100), both coordinates are positive integers, so option 3 is correct.
In ordered pair (-5,110.5), the value of x is negative and the value of y is in decimal, so option 4 is incorrect.
The possible domain and range of the function is (10, 100). Therefore the correct option is 3.
What is the length of DE?
A. 10
B. 22
C. 18
D. 12
Answer:
C. 18
Step-by-step explanation:
Both triangle are same (compared with angles), but are different size.
This is based on simple ratio.
AB/AC = DE/DF
27/15 = x/10 //Multiply both sides by 10
270/15 = x
x = 18
Therefore DE is 18.
Hence, the length of DE is 18.
What is length?Length is defined as the measurement or extent of something from end to end. In other words, it is the larger of the two or the highest of three dimensions of geometrical shapes or objects.
How to solve?It can be observed that the given 2 triangles are similar.
we know, for similar triangles, the ratio of corresponding sides is equal.
Hence,
[tex]\frac{15}{10} = \frac{27}{x}[/tex]
[tex]x = 18[/tex]
Therefore, the value of x is 18.
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How would you do this problem?
Answer:
6 seconds
Step-by-step explanation:
First: equalize the equation to zero
f(t) = -5t² + 20t + 60
-5t² + 20t + 60 = 0
Second: find its roots
-5(t² - 4t - 12) = 0
-5 (t - 6)(t + 2) = 0
[tex]t - 6 = 0 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: t + 2 = 0 \\ t = 6 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: t = - 2[/tex]
Time can't be negative so the answer is: it takes 6 seconds to hit the ground
PLEASE HELPPPP!!!!!! Events A and B are mutually exclusive. Events B and C are non-mutually exclusive. Which Venn diagram could represent this description? Image for option 1 Image for option 2 Image for option 3 Image for option 4
Answer:
The answer is the attached figure
Step-by-step explanation:
* Lets explain mutually exclusive and non-mutually exclusive
- The mutually exclusive means events cannot happen at the
same time
# P(A or B) = P(A) + P(B)
- The non-mutually exclusive means they have at least one
outcome in common
# P(A or B) = P(A) + P(B) - P(A and B)
* Lets solve the problem
∵ Events A and B are mutually exclusive
∵ Circle A represents the event A
∵ Circle B represents the event B
∴ There is no intersection between the two circles A and B
∵ Events B and C are non-mutually exclusive
∵ Circle C represents the event C
∴ There is an intersection between the two circles B and C
* The answer is the attached figure
Answer: D. image 4.
Just did assignment.
Solve 2x +5=12 answer?!
Answer:
x = 3.5
Step-by-step explanation:
To solve this you need to solve for x.
This is a two step equation so you need to first subtract 5 from itself and whatever you do to one side of the equation you have to do to the other side as well.
So 5 - 5 = 0
12 - 5 = 7
Then the equation becomes 2x = 12
Now it is a one step equation, so find the inverse operation of multiplication, which is division .
So 2 divided by 2 is 1 which also equals x by itself
7 divided by 2 equals 3.5
So x = 3.5
Answer:
[tex]\huge\boxed{x=\frac{7}{2}, x=3.5}[/tex]
Step-by-step explanation:
Subtract by 5 from both sides of equation.
[tex]\displaystyle 2x+5-5=12-5[/tex]
Simplify.
[tex]\displaystyle 12-5=7[/tex]
[tex]\displaystyle2x=7[/tex]
Divide by 2 from both sides of equation.
[tex]\displaystyle \frac{2x}{2}=\frac{7}{2}[/tex]
Simplify, to find the answer.
[tex]\displaystye x=\frac{7}{2}, x=3.5[/tex]
x=7/2 and x=3.5 is the correct answer.
To determine whether a graph of a relation is also a function, Shayla declares that the y-axis is a vertical line and counts the number of times that the graph intersects the y-axis. If the graph has exactly one y-intercept, Shayla concludes that the graph shows a function. In all other cases, she declares that it is not a function.
Is Shayla applying the vertical line test correctly?
Answer:
"No, because using the y-axis tests only whether x = 0 is mapped to multiple values."
Shayla's use of the vertical line test is incorrect because she is only considering the number of y-intercepts, which is not conclusive in determining if a graph is a function. The correct method is to see if any vertical line intersects the graph at more than one point.
Explanation:Shayla is not applying the vertical line test correctly. The correct use of the test involves drawing vertical lines through various points on the graph and checking to see if any vertical line intersects the graph at more than one point. A graph represents a function if, and only if, every vertical line intersects the graph at most once. The number of y-intercepts, or where the graph intersects the y-axis, is not a reliable indicator of whether a graph is a function. For example, a straight line with a slope and a y-intercept, such as in the form y = mx + b, will always be a function, regardless of the number of y-intercepts it has.
7. Suppose a student stacks 1000 congruent circles one on top of the other, and the teacher
1000 similar circles, with each circle a little smaller than the one below it.
a. What is the name of the solid formed by the stack of congruent circles?
b. Relate the dimensions of one of the congruent circles to the dimensions of this solic
c. What is the name of the solid formed by the stack of similar circles?
d. Relate the height of the stack of similar circles to a dimension of this solid.
Answer:
See below.
Step-by-step explanation:
a. That would be a cylinder.
b.The height of the cylinder will be n * thickness of one circle where n is the number of circles. The volume of the cylinder is π r^2 h where h is the height of the stack.
c. That would be a cone
d. The height of the cone will be n * thickness of one circle where n is the number of similar circles.
Volume of the cone = 1/3 * π r^2 h where h is the height of the stack of circles.