Answer:
Volume = 30 cm³
Step-by-step explanation:
The formula for the volume of a box is:
V = width x length x height
Plug in the values given:
V = 2 x 5 x 3
V = 30
Answer:
30 cm
Step-by-step explanation:
Area= length x width x height
5 x 2 x 3
10 x 3 = 30
Apply Conversion Factors to Measurements
When converting a measurement from one unit to another, the conversion factor is a ratio of equal measurements.
In this instance, we are determining the corresponding lengths in centimetres, metres, and inches.
We must locate the conversion factors and use them in order to finish the table of equivalent measurements. We multiply by 100 to convert Metres to centimetres.
We multiply by 0.01 to change from centimetres to metres.
We can write 2.54cm to represent the number of centimetres needed to equal one inch. One centimetre is equal to 0.39 inches in terms of inches.
We can convert 3 inches to centimetres by using the conversion factor from issue 4. 7.62 centimetres are equal to 3 inches times 2.54 centimetres per inch.
In issue number four, the conversion factors are inches to centimetres and centimetres to inches.
The conversion factor for centimetres to inches is 0.39 and for inches to centimetres is 2.54.
We can convert 10 centimetres to inches by using the conversion factor from issue 4. 3.9 inches are equal to 10 centimetres times the unit's 0.39 inch.
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[tex]12x^3-3x^2=0\\[/tex]12x^3-3x^2=0
The solutions of 12x³ - 3x² , a cubic polynomial of one variable x ,using method of factorisation is 0 , 0 and [tex]\frac{1}{4}[/tex].
What is polynomial?
Variables, coefficients, addition, subtraction, multiplication, and non-negative integer exponents are all components of a polynomial, which is a type of mathematical statement. The "language" of mathematics and algebra includes polynomials extensively. As a result of mathematical operations, they are employed to express numbers in almost every area of mathematics. In other kinds of mathematical expressions, including rational expressions, polynomials are also used as "building blocks." Polynomials having number of solutions equal to its degree. Numbers that evenly split into another number are called a number's factors. A number is written as the sum of smaller numbers when it is factorised.
Given polymonial function=12x³ - 3x²
Taking factors of each term:
1st term= 12x³
factors=2. 2 . 3 . x . x . x
2nd term= 3x²
factors=3 . x . x
The highest common factor of both terms= 3 . x . x
Taking common factor out of each term, we get:
12x³ - 3x² = 0
3 . x . x(4x) - 3 . x . x(1) = 0
3x² (4x) - 3x²(1) = 0
3x² [ 4x - 1] = 0
This is factorised form of given equation.
To find solution, equate each factor to zero
3x²=0 and [ 4x - 1] = 0
Using 3x²=0, we get x =0
Using [ 4x - 1] = 0, we get x = [tex]\frac{1}{4}[/tex].
The total solutions must be 3 as the highest power of polynomial is 3.
Solutions are 0,0, [tex]\frac{1}{4}[/tex].
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Refer to attachment for complete question
Which expression can be rewritten
Answer:
A
Step-by-step explanation:
[tex] - \sqrt{ \frac{ {g}^{5} }{ {h}^{5} } } = - {( \frac{ {g}^{5} }{ {h}^{5} }) }^{ \frac{1}{2} } = - {( \frac{g}{h} )}^{ \frac{5}{2} } [/tex]
Pleas help real quick thank you
Answer:
[tex]y = 2x+1[/tex]
Step-by-step explanation:
Let y = mx + b.
We can find two points, (0, 1) and (1, 3).
Substituting both into the equation:
[tex]\left \{ {{1 = 0m + b} \atop {3 = m+b}} \right.[/tex]
We find that b = 1, m = 2.
Thus, y = 2x + 1.
The maximum of 4 8 12 16 20 24 28 32 36
Answer:
36
Step-by-step explanation:
It's the biggest number.
you just hired a new employee to work in your bakeshop. In one hour the employee burned 55 chocolate chip cookies. if this represented 15% of the days production, how many cookies did you plan on producing that day?
Solving the equation we get the number of production is ≈366.67
What is equation?
In mathematics, an equation is a mathematical statement that is built by two expressions connected by an equal sign('='). For example, 3x – 8 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 8.
you just hired a new employee to work in your bakeshop. In one hour the employee burned 55 chocolate chip cookies. if this represented 15% of the days production.
Let , I planned to produce x cookies on that day.
15% is burned.
So the amount of burned cookies are (15x)/100
It is given that the amount of burned cookies are 55.
Equating both values we get,
(15x)/100= 55
So the equation is
(15x)/100= 55
Solving the equation we get,
x= (55×100)/15
≈366.67
Hence, the number of production is ≈366.67.
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Identify the graph of m(x)=√x+5.
Determine when the function is nositive. negative, increasing. or decreasing. Then describe the end behavior of the function..
Therefor option C graph for this identity will be best . This function has all real numbers as its domain and all real numbers as its range.
what is domain?The collection of all potential input values (typically denoted by x) for which a mathematical function is specified is known as the domain of the function. For instance, the domain of a function f(x) = 1/x, with the exception of x = 0, is all real numbers. This is due to the illogical nature of division by zero.
Another illustration is the formula g(x) =.(x - 2). All real numbers larger than or equal to 2 fall under the domain in this situation. This is due to the fact that a negative number cannot be squared.
A cube root function is the one with the formula m(x) = x + 5. Similar to a square root function, but more spread out, is the graph of a cube root function. This function has all real numbers as its domain and all real numbers as its range.
We can start by locating a few points on the graph in order to graph this function for example,
when x = 0, m(x) = ∛0 + 5 = 5.
When x = 1, m(x) = ∛1 + 5 ≈ 6.
When x = -1, m(x) = ∛(-1) + 5 ≈ 4.
We can plot these points on a coordinate plane and connect them with a smooth curve to get the graph of the function.
Therefor option C graph for this identity will be best
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The circle below is centered at the point (1, 2) and has a radius of length 2. Write the equation for the circle.
The equation of the circle is x²2 - 2x + y²2 - 4y = -3.
How to solve?
The equation for a circle centered at the point (h, k) with a radius of length r is given by:
(x - h)²2 + (y - k)²2 = r²2
In this case, the circle is centered at the point (1, 2) and has a radius of length 2. So, we have:
h = 1
k = 2
r = 2
Substituting these values into the equation, we get:
(x - 1)²2 + (y - 2)²2 = 2²2
Simplifying and expanding the squared terms, we get:
(x²2 - 2x + 1) + (y²2 - 4y + 4) = 4
Moving the constant term to the right-hand side, we get:
(x²2 - 2x) + (y²2 - 4y) = -1
Adding 1 to both sides, we get the final equation of the circle in standard form:
(x²2 - 2x + 1) + (y²2 - 4y + 4) = 4
x²2 - 2x + y²2 - 4y = -3
The equation of the circle is x²2 - 2x + y²2 - 4y = -3.
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What is the range of
A piecewise function g of x, where part 1 is x squared minus 5 for x less than 2 and part 2 is 2 times x for x greater than or equal to 2.?
The range of a function refers to the set of all possible output values. To find the range of the given piecewise function g(x), we need to consider the two cases separately:
Case 1: x < 2
In this case, g(x) = x^2 - 5. The graph of this function is a parabola that opens upward and has a vertex at (0,-5). Since the parabola is open upward, the minimum value of g(x) occurs at the vertex and is g(0) = -5. As x increases, g(x) increases without bound. Therefore, the range of g(x) for x < 2 is (-5, ∞).
Case 2: x ≥ 2
In this case, g(x) = 2x. The graph of this function is a line with slope 2 and y-intercept 0. Since the line has a positive slope, g(x) increases as x increases. Therefore, the range of g(x) for x ≥ 2 is [4, ∞).
To find the overall range of g(x), we need to consider the union of the two ranges, which is (-5, ∞).
6) In circle C, mAB = 72. Find m
a) 72
b) 108
7 Find th
c) 144
Sindr
d) 180
D
72
B (#6)
Please help me question number 6 with the diagram.
Using the central angle theorem, the measure of angle BCD in the circle given is: b. 108°.
How to Apply the Central Angle Theorem of a Circle?The central angle theorem of a circle states that the measure of a central angle of a circle is equal to the measure of the arc that it cuts off.
In other words, if you know the measure of an arc in a circle, you can find the measure of the central angle that intercepts that arc, and vice versa.
m(BD) = 180 - m(AB)
Substitute:
m(BD) = 180 - 72
m(BD) = 108°
m<BCD = m(BD) [based on the central angle theorem]
Substitute:
m<BCD = 108°
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PLEASE HELP ME DONT ANSWER IF YB
(Surface Area of Cylinders MC)
A makeup artist purchased some lipsticks and wants to wrap them individually with gift wrap. Each lipstick has a radius of 0.4 inch and a height of 2.2 inches. How many total square inches of gift wrap will the makeup artist need to wrap 5 lipsticks? Leave the answer in terms of π.
10.4π square inches
4.8π square inches
2.08π square inches
1.76π square inches
Answer:
A would be correct
Step-by-step explanation:
the answer is A.
write the following set by listing its element (a/a en an odd number)
The elements of the set after listing is:
(i) A = {1, 3, 5, 7, 9, ...}
(ii) B = {x: -8 < x < 2/9}
(iii) C = {0, 1, 2}
(iv) D = {L, O, Y, A}
(v) E = {April, June, September, November}
(vi) F = {b, c, d, f, g, h, j}
What is integer?An integer is a whole number, meaning it does not have any fractional or decimal parts. It can be positive, negative, or zero. Examples of integers are -3, 0, 2, and 7. Integers are a subset of the real numbers and are often denoted by the symbol ℤ (which comes from the German word "Zahlen" meaning "numbers"). Integers have a number of important properties, such as closure under addition and multiplication, and they play a central role in many areas of mathematics and computer science.
(i) A={x:x is an odd natural number}={1,3,5,7,9.....}
(ii) B={x:x is an integer,−1/2 <x< 9/2}
Since, −1/2 = -0.5 and 9/2 = 4.5
∴B = {0,1,2,3,4}
(iii) C={x:x is an integer; x² ≤ 4}
It can be seen that
(−1)² = 1 ≤ 4
;(−2)² = 4 ≤ 4
;(−3)² = 9>4
0² = 0≤4
1² = 1≤4
2² = 4≤4
3² = 9>4
∴C = {−2,−1,0,1,2}
(iv) D={x:x is a letter in the word LOYAL}={L,O,Y,A}
(v) E={x:x is a month of a year not having 31 days}
={February, April, June, September, November}
(vi) F={x:x is a consonant in the English alphabet which precedes k}={b,c,d,f,g,h,j}
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If you have a quadratic equation in vertex form and it has values of a=3, h = -4 and k = 1, what equation would represent a line that would be its axis of symmetry ? TIMED!!!
All points on this line are equidistant from the two arms of the parabola, and the line passes through the vertex of the parabola.
What is quadratic equation?
A quadratic equation is a second-degree polynomial equation in a single variable, where the variable is typically denoted by x.
According to question:
A quadratic equation's vertex form is provided by:
y = a(x - h)² + k
where an is a constant that governs the parabola's shape and (h, k) is the parabola's vertex.
In this case, the vertex form of the quadratic equation with a = 3, h = -4, and k = 1 is:
y = 3(x + 4)² + 1
To find the equation of the axis of symmetry, we need to determine the x-coordinate of the vertex, which is given by -h. In this case, -h = -(-4) = 4.
The line that represents the axis of symmetry has the following equation, then:
x = 4
This is because all points on this line are equidistant from the two arms of the parabola, and the line passes through the vertex of the parabola.
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Suppose that the weight of navel oranges is normally distributed with a mean of μ=6
ounces and a standard deviation of σ=0.8
ounces.
Find the weight below that one can find the lightest 90%
of all navel oranges. Use Excel, and round your answer to two decimal places.
The weight below which one can find the lightest 90% of all navel oranges is approximately 4.83 ounces.
What is standard deviation?Standard deviation is a statistical measure that represents the amount of variability or dispersion in a set of data. It measures how spread out the data is from the mean or average value.
A small standard deviation indicates that the data points tend to be close to the mean, while a large standard deviation indicates that the data points are more spread out.
In the given question,
We can use Excel's NORM.INV function to find the weight below which we can find the lightest 90% of all navel oranges, given the mean and standard deviation of the weight distribution.
The NORM.INV function takes three arguments: the probability value (in this case, 0.9 for the lightest 90%), the mean value (μ), and the standard deviation value (σ). The function returns the corresponding z-score, which can be multiplied by the standard deviation and added to the mean to get the weight value.
Using Excel, the formula to find the weight below which we can find the lightest 90% of all navel oranges is:
=6 - 0.8 * NORM.INV(0.9,0,1)
This gives us a result of 4.83 ounces (rounded to two decimal places).
Therefore, the weight below which one can find the lightest 90% of all navel oranges is approximately 4.83 ounces.
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How do you simplify 9z³ + 19u ?
Answer: 172z + 19u
Step-by-step explanation: To look up to the power of, use: "^"
2^6
4^5 etc.
1. Complete the table.
2. Write an addition equation and draw a number line diagram for B. Include the starting elevation,
change, and final elevation in your diagram.
The completed table is shown below:
starting elevation (feet)
change (feet)
final elevation (feet)
A
+200
75 up
275
B
+200
75 down
125
C
+200
200 down
0
D
+200
+25
225
the additional equation for B is:
final elevation for B = +200 feet - 75 feet
c. The line diagram is attached below.
How do we calculate?We can use the formula, to write an addition equation for B
final elevation = starting elevation + change
final elevation for B = +200 feet - 75 feet
We simplify this equation as:
final elevation for B = +125 feet
We draw a number line diagram for B, we can start at +200 feet (the starting elevation) and then move 75 units down (since the elevation is decreasing by 75 feet).
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A stainless steel patio heater is a square pyramid. The length of one side of the base is 22.6 The slant height of the pyramid is 88.6 What is the height of the pyramid?
Answer: The height of the pyramid is approximately 87.58 units.
Step-by-step explanation:
Is (1, 9) a solution to this system of equations? y = 5x + 4 y = 2x + 7 yes or no
Answer:
Yes (1, 9) is a solution
Step-by-step explanation:
Plug in 9 for y and 1 for x. (x, y) = (1, 9)
y = 5x + 4
9 = 5 (1) + 4
9 = 9 true
y = 2x + 7
9 = 2(1) + 7
9 = 9 true
A farmer counts the chickens and pigs in one field on the farm. The farmer finds that the ratio of chickens to pigs is 5:8. Approximately what percent of the animals counted are pigs?
Let's assume that the farmer counted 5x chickens and 8x pigs, where x is a positive integer.
The ratio of chickens to pigs is 5:8, which means that the total number of animals counted is 5x + 8x = 13x.
To find the percentage of animals that are pigs, we need to divide the number of pigs by the total number of animals and then multiply by 100:
(Number of pigs / Total number of animals) x 100
Substituting 8x for the number of pigs and 13x for the total number of animals, we get:
(8x / 13x) x 100 = (8/13) x 100
Simplifying, we get:
(8/13) x 100 ≈ 61.5%
Therefore, approximately 61.5% of the animals counted are pigs.
Brainliest? This took a long time :)
Conduct a survey to know the favourite colour of students among grey, green, blue, pink and yellow. Write the result in the tabular form. Also represent it in Pie chart.
pls answer to my question.....
Answer: Sure, here's an example survey result in tabular form:
Color Number of Students
Grey 10
Green 20
Blue 35
Pink 15
Yellow 20
Total 100
Step-by-step explanation:
Queisha spent 1/3 hour answering nine homework questions for the history class she spent the same amount of time on each question what fraction of an hour does it take f Queisha to answer each question?
The fraction of an hour does it take Queisha to answer each question is 1/27 hour.
What is fraction?
Part of a whole is a fraction. The quantity is written as a quotient in mathematics, where the numerator and denominator are divided. Each is an integer in a simple fraction. Whether it is in the numerator or denominator, a complex fraction contains a fraction. The numerator and denominator of a correct fraction are opposite each other.
Here the time taking to complete 9 home work = 1/3 hour.
Then time taking for completing 1 home work = x.
Then,
=> 9 = 1/3
1 = x
=> x = [tex]\frac{\frac{1}{3}}{9}[/tex]
=> x = 1/27
Hence fraction of an hour does it take Queisha to answer each question is 1/27 hour.
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HELP PLEASE!!! WILL GIVE BRAINLIEST
A linear relationship is shown in the table.
Time (hours) 2 4 6 8
Distance (miles) 4 8 12 16
Is the linear relationship also proportional? Explain.
No, the constant of proportionality is 2.
Yes, the constant of proportionality is 2.
No, there is no constant of proportionality.
Yes, there is no constant of proportionality.
Answer:
Yes, the c.o.p. is 2.
Step-by-step explanation:
The question of proportionality is answered by directly dividing each y-value (distance) by its associated x-value (time). If ALL of the related pairs give the same quotients, the relationship is proportional and the common quotient is the constant of proportionality.
4/2=2
8/4=2
12/6=2
16/8=2
NEED help on questions 11-14 Please and Thank you
Answer:
11. (D) 90 degrees
12. (C) 93
13. (D) 90 degrees
14. (C) 46
Step-by-step explanation:
11. this is a square so each angle is 90 degrees.
12. as each side is the same, we create the equation 9x + 3 = 11x - 17. Solve.
13. With diagonals, MGQ, QGE, QEO, QOM, QMG become 45 degrees, while the intersection of the diagonals become 90 degrees
Hope this answers your question
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You received a score of 3.4 on your annual review. Merit increases are given out at .5% at a score of 2.6 and it goes up 1% every .4 points. What is the increase you can expect to receive?
You can expect to receive the increase of percentage that is 2.5%.
What do you mean by percentage?The term "percentage" in mathematics can refer to either numbers or ratios that are stated as fractions of 100. In most cases, they are indicated by "%" or "percent."In mathematics, a percentage is a number or ratio that is expressed as a fraction of 100. A% is a number that has neither dimensions nor a defined unit of measurement.
Given,
You received a score of 3.4 on annual review. Merit increases are given out at .5% at a score of 2.6 and it goes up 1% every .4 points.
Score received in the beginning = 2.6
Increase in score as a percentage equals 0.5%
Score increases by 1% for every 0.4 points.
The following rise will occur at 2.6 + 0.4 = 3.0 points.
Increase in percentage: 0.5 + 1= 1.5%
Score = 3.0 + 0.4 = 3.4 points will be the following point increment.
Score increase as a percentage: 1.5 + 1 = 2.5%
You can expect to receive the increase 2.5%
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pls help i'm dead if i get this wrong.
Answer:
41.59 square meters
Step-by-step explanation:
You want the surface area of a rectangular prism with dimensions ...
L = 2.1 mW = 1.45 mH = 5 mYou are given the formula ...
SA = 2LW +2WH +2LH
AreaYou find the area by replacing the variables in the formula with the given values, then doing the arithmetic.
We find there is less typing involved and fewer calculator operations if we rearrange the formula first. We can factor some terms, so we have ...
SA = 2(LW +WH +LH) . . . . factor out 2
SA = 2(LW +H(L +W)) . . . . . factor H from the last two terms
The attached calculator screen shows the use of this formula with the given numbers.
SA = 2(2.1·1.45 +5(2.1 +1.45)) = 41.59 . . . . square meters
The surface area is 41.59 m².
Answer:
41.59
Step-by-step explanation:
The equation given is SA= 2(lw)+2(wh)+2(lh)
What you should do in this case is input all the values first. So you should have:
SA= 2(2.1*1.45)+ 2(1.45*5)+ 2(2.1*5)
SA=6.09+14.5+21
SA= 41.59
Please help if you can!
According to chances:
10. different ways, to all sit together in a row of 6 empty seats is 720.11. 21 possible ways to purchase 5 different flavors of hot sauce.12. (a) 1/15,504., (b) 1/3,584,000.How to calculate probabilities?10. If you and your five friends are sitting together in a row of 6 empty seats, then you can be seated in any of the 6 seats, your first friend can be seated in any of the remaining 5 seats, your second friend can be seated in any of the remaining 4 seats, and so on. Therefore, the total number of ways in which you all can sit together in a row of 6 empty seats is given by:
6 x 5 x 4 x 3 x 2 x 1 = 720
Hence, there are 720 different ways in which you all can sit together in a row of 6 empty seats.
11. Since you can purchase 5 out of 7 different flavors of hot sauce, the number of possible ways of purchasing the hot sauces can be calculated using the combination formula. The number of ways to choose 5 sauces out of 7 is given by:
C(7,5) = 7! / (5! x 2!) = 21
Therefore, there are 21 possible ways for you to purchase 5 different flavors of hot sauce.
(a) If the order of the five numbers does not matter, then we need to find the number of combinations of 5 numbers that can be selected from 20 numbers. This can be calculated using the combination formula, and is given by:
C(20,5) = 20! / (5! x 15!) = 15,504
Therefore, the probability of winning the lottery is 1/15,504.
(b) If the order of the five numbers matters, then we need to find the number of permutations of 5 numbers that can be selected from 20 numbers. This can be calculated using the permutation formula, and is given by:
P(20,5) = 20! / 15! = 3,584,000
Therefore, the probability of winning the lottery is 1/3,584,000.
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Image transcribed:
10. You and five of your friends go to the local theatre to watch a famous orchestra perform. In how many, different ways, can you all sit together in a row of 6 empty Seats? (7pts)
11. A local grocery store has 7 different kinds of hot sauce that you would love try. However, you only have enough money to purchase 5 of the different flavors. How many of the flavors of hot sauce are possible for you to purchase? (7 pts)
12. You are testing your recent luck and want to find out how unlikely it is to win a lottery with a jackpot $1, 000, 000. In order to win, you must correctly select 5 numbers where each is an integer between 0-19 inclusive. Find the probability that you randomly select a lottery ticket and win if: (6 pts each)
(a) The order of the five numbers does not matter.
(b) The order of the five numbers do matter.
What is the value of P(X= 2 or X = 0)?
Enter your answer in the box.
P(X= 2 or X = 0) =
X
0
1
2
3
4
5
P
0.3
0.05
0.1
0.15
0.15
0.25
So, the value of P (X=2 or X=0) is 0.4.
What does probability mean?Probability is a measure of the likelihood or chance of an event occurring. It is a numerical value between 0 and 1, with 0 indicating that an event is impossible, and 1 indicating that it is certain to occur.
For example, if you flip a fair coin, the probability of it landing on heads is 0.5 or 50%, as there are only two possible outcomes (heads or tails) and they are equally likely to occur.
Probability is used extensively in fields such as statistics, mathematics, and science to model and analyze uncertainty and randomness. It is also used in practical applications such as gambling, risk assessment, and decision making.
o find the probability of X being 2 or 0, we need to add the probabilities of the two events.
P(X=2 or X=0) = P(X=2) + P(X=0)
From the given table, we can see that:
P(X=2) = 0.1
P(X=0) = 0.3
Therefore,
[tex]P (X=2 or X=0) = 0.1 + 0.3 = 0.4[/tex]
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Find the surface area of a c shaped figure with all right angles.
width: 1ft
hight: 4ft
full hight: 15ft
hight:4ft
length:7ft
length: 7ft
Answer:
Step-by-step explanation:
,
A four-sided figure is resized to create a scaled copy. The lengths of its four sides change as in the table below. Original Figure Scaled Copy 6 10 12 39 65 78 Find the constant of proportionality from the original figure to the scaled copy. Express your answer as a fraction in reduced terms.
So, the constant of proportionality from the original figure to the scaled copy is indeed 5/3.
To find the constant of proportionality from the original figure to the scaled copy, we need to find the ratio of the corresponding side lengths. Let's take the first pair of corresponding side lengths, 6 and 10, from the table.
To get from 6 to 10, we multiply by a constant factor. Let's call this constant factor "k". Then:
[tex]6 * k = 10[/tex]
Solving for k, we get:
[tex]k = 10/6 = 5/3[/tex]
So, the constant of proportionality from the original figure to the scaled copy is 5/3.
We can check this for the other pairs of corresponding side lengths in the table as well. For example, taking the second pair of corresponding side lengths, 12 and 39:
[tex]12 *k = 39[/tex]
Solving for k, we get:
[tex]k = 39/12 = 13/4[/tex]
We can see that this also satisfies the other pair of corresponding side lengths:
[tex]6 * (13/4) = 39[/tex]
and
[tex]10 * (13/4) = 65[/tex]
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a linear function has an x intercept of -8 and a y intercept of 4. which of these is an equation of the linear function?
2x+y=-12
x+2y=0
2x-y=-20
x-2y=-8
Here, x-2y=-8 is an equation of the linear function.
What is Equation?An equation is a mathematical statement that shows that two expressions are equal. It typically contains variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division.
To find the equation of a linear function given its x-intercept and y-intercept, we can use the slope-intercept form:
y = mx + b
where m is the slope and b is the y-intercept.
We are given that the x-intercept is -8, which means that the point (-8, 0) is on the line. We are also given that the y-intercept is 4, which means that the point (0, 4) is on the line. Using these two points, we can find the slope of the line:
m = (y₂ - y₁) / (x₂ - x₁)
m = (4 - 0) / (0 - (-8))
m = 4 ÷ 8
m = 1/2
Now that we know the slope is 1/2 and the y-intercept is 4, we can write the equation of the line in point slope form:
y - y₁ = m(x - x₁)
y - 4 = 1/2(x - 0)
y - 4 = 1/2(x - 0)
y = 1/2(x - 0) + 4
y = 1/2x + 4
Multiply all by -2
y = 1/2x + 4
-2y = -x -8
x -2y = -8
Therefore, The other equations do not have the same slope and/or y-intercept as the linear function except x -2y = -8.
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