Answer:
C. 3
Step-by-step explanation:
First, use the distributive property. Multiply 4x and 1 each by 2.
This gives us the equation 50 + 8x - 2 = 72.
Next, subtract 2 from 50 to get 48. Subtract 2 from 2 to cancel it out.
Then, we have 48 + 8x = 72.
Subtract 48 from both sides. This leaves 8x = 24.
Divide both sides by 8 to get x = 3.
solve please
A
B
c
d
Answer:
the answer is A
Hope this helps
The plane x + y + z = 1 cuts the cylinder x2 + y2 = 1 in an ellipse. We want to find the points on the ellipse that lie closest to the origin. Using Lagrange Multiplier method, set up a system of equations for such points.
The points on the ellipse that lie closest to the origin are (1, 0, 0), (0, 1, 0)
Let (x, y, z) be a point on an ellipse in which plane x + y + z = 1 cuts the cylinder [tex]$x^2+y^2=1$[/tex]
Let f(x, y, z) = [tex]$x^2+y^2+z^2$[/tex]
[tex]& g_1(x, y, z)=x^2+y^2-1=0 \\[/tex]
[tex]& g_2(x, y, z)=x+y+z-1=0[/tex]
From Lagrange Multiplier Method.
There are multiple ways to define the method of Lagrange multipliers.
Suppose f and g are two functions such that they both have continuous partial derivatives.
Let (x0, y0, z0) ∈ S := {(x, y, z) : g(x, y, z) = 0} and ∇g(x0, y0, z0) ≠ 0.
The method of Lagrange’s multipliers is an important technique applied to determine the local maxima and minima of a function of the form f (x, y, z) subject to equality constraints
[tex]& \nabla f=\lambda \nabla y_1+\mu \nabla g_2 \\[/tex]
[tex]\Rightarrow & \langle 2 x, 2 y, 2 z\rangle=\lambda\langle 2 x, 2 y, 0\rangle+\mu\langle 1,1,1\rangle \\[/tex]
[tex]\Rightarrow & \langle 2 x, 2 y, 2 z\rangle=\langle 2 x \lambda+\mu, 2 y \lambda+\mu, \mu\rangle[/tex]
[tex]2 x & =2 x \lambda+\mu-(1) \\[/tex]
[tex]2 y & =2 y \lambda+\mu \ldots(2) \\[/tex]
[tex]2 z & =\mu \quad \ldots(3)[/tex]
From equation (1) [tex]$2 x(1-\lambda)=\mu=2 z$[/tex]
From equation (2) [tex]$2 y(1-\lambda)=\mu=2 z$[/tex]
Therefore if [tex]\lambda=1$[/tex], then z = 0
if [tex]\lambda \neq 1, \quad x=y=\frac{2}{1-\lambda}[/tex]
if z = 0, then after solving.
[tex]x^2+y^2=1$\\ $2 x+y=1$[/tex]
We get two points: [tex]${(1,0,0)} \geq {(0,1,0)}$[/tex]
and if x = y.
Then:
[tex]& x^2+y^2=1 \Rightarrow x^2+x^2=1 \Rightarrow 2 x^2=1 \Rightarrow x=\pm \sqrt{\frac{1}{2}} \\ & x+y+z=1[/tex]
x + y + z = 1
[tex]\Rightarrow[/tex] x + x + z = 1
[tex]\Rightarrow[/tex] 2 = 1 - 2x
= [tex]1-2\left(\pm \sqrt{\frac{1}{2}}\right)=1 \pm \sqrt{2}[/tex]
Therefore the corresponding points on the ellipse.
[tex]P_1\left(\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}, 1-\sqrt{2}\right) \& P_2\left(-\frac{1}{\sqrt{2}}, \frac{-1}{\sqrt{2}}, 1+\sqrt{2}\right)[/tex]
Now we have four points
Closest to the origin:
1) (1, 0, 0)
2) (0, 1, 0)
The farthest to origin:
3) [tex]$\left(\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}, 1-\sqrt{2}\right)[/tex]
4) [tex]$\left(-\frac{1}{\sqrt{2}}, \frac{-1}{\sqrt{2}}, 1+\sqrt{2}\right)[/tex]
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sorry i chose the wrong image
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i just got some free money off of you kid
Let P(t) denote the population of bacteria in a
Petri disht hours after bacteria are introduced to the environment
of the Petri dish. Suppose that the initial population of bacteria
is known to be 5000, and that the bacteria population doubles
every 6 hours. Assume that the population can grow indefinitely.
Give a formula for P(t).
well, if the population is doubling from whatever they happen to be, so that means the growth rate is 100%, so if they're hmmm "g", then later they become "2g", or doubled, and the later becomes "4g" and so on, so the rate is simply 100%, because "g" plus "g" is just 2g, and "2g" plus "2g" is just 4g and so on, anyhow
[tex]\textit{Periodic/Cyclical Exponential Growth} \\\\ A=P(1 + r)^{\frac{t}{c}}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &5000\\ r=rate\to 100\%\to \frac{100}{100}\dotfill &1\\ t=hours\\ c=period\to &6 \end{cases} \\\\\\ A=5000(1 + 1)^{\frac{t}{6}}\implies A=5000(2)^{\frac{t}{6}}\implies {\Large \begin{array}{llll} P(t)=5000(2)^{\frac{t}{6}} \end{array}}[/tex]
Find the 12th term of the following geometric sequence. 2, 8, 32, 128
Step-by-step explanation:
So 2 * 4 = 8
8 * 4 = 32
32 * 4 = 128
128 * 4 = 512
512*4=2048
2048*4=8192
8192*4=32768
32768*4=131072
131072*4=524288
524288*4=2097152
2097152*4=8388608
8388608*4=33554432 and that would probably be your final answer
Write the range for the relation.
((-1, 1), (-2, 5), (-3, 7). (5, 8))
The range of a relation is the set of all possible values of the second element of the ordered pairs in the relation. In this case, the range of the relation is the set {1, 5, 7, 8}. This can be found by looking at the second element of each ordered pair in the relation and listing all the different values that appear.
20. Keith is offered an interest rate of 8.27% for a
loan with continuous compounding. Calculate
his equivalent rate with simple compounding.
[A] 0.0795 or 7.95%
[B] 0.0998 or 9.98%
[C] 0.0106 or 1.06%
[D] 0.0863 or 8.63%
[E] 0.1108 or 11.08%
Keith's equivalent rate with simple compounding is 0.0998 or 9.98%.
The Correct option is (B).
What is Compound Interest?The yearly interest rate is raised to the number of compound periods minus one, and the starting principal amount is multiplied by both of these factors. The resulting value is subsequently deducted from the loan's entire original amount.
Given:
Keith is offered an interest rate of 8.27% for a loan.
Now, using the following formula:
r = ([tex]e^{(i/n)[/tex] - 1) x n
where r is the equivalent rate with simple compounding, i is the interest rate with continuous compounding, and n is the number of compounding periods per year.
We have, i = 8.27%
Also assume that the number of compounding periods per year is 12, since many loans are compounded monthly.
Then,
r = ([tex]e^{(0.0827/12[/tex]) - 1) x 12
= (1.0082 - 1) x 12
= 0.0082 x 12
= 0.0984 or 9.84%
Hence, The equivalent rate is 0.0984 or 9.84%.
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Daliyah is given one point on a line as (3,−1) and the slope of the line as −5.
The y-intercept of the line having point (3,−1) and slope -5 is 14.
The equation of a line in the slope-intercept form is:-
y = mx+c
where 'm' is the slope and 'c' is the y-intercept.
here, m= -5
∴ y = -5x + c .........(Partial equation)
to find b substitute (3,-1) into the partial equation
where,
x= 3 and y= -1 by substituting the values,
-1 = (-5)×3 + c => c = 15 - 1
∵ c = 14
Thus, the value of the y-intercept is 14.
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The correct question is:-
Daliyah is given one point on a line as (3,−1) and the slope of the line as −5. what is the y-intercept of the line?
determine the probability of drawing either a queen or a heart? write your answer as a reduced fraction.
The probability that the card drawn is either a queen or a heart is 4/13
According to the given information
Consider the random experiment of picking one card from a deck of 52 cards that has been expertly shuffled, as well as the subsequent occurrences.
A queen is the card that was drawn.
H: the heart card was shown.
The chance that "the card drawn is a queen" is P(Q) = 4/52 = 1/13 because there are four queens.
The probability that the card selected will be a heart is P(H) = 13/52, or 1/4, because there are 13 hearts in the deck. Because the queen of hearts is one of the deck's cards, events Q and H are inclusive events. P(Q and H) = 1/52 is the likelihood that "the card picked is a queen and a heart (the queen of hearts)".
Four queens and thirteen hearts are included in the chance that "the card picked is a queen or a heart," but we do not want to count the queen of hearts twice. There are so 16 different methods to depict a queen.
The probability that the card drawn is either a queen or a heart
P(Q or H) = P(Q) + P(H) - P(Q and H)
= [tex]\frac{4}{52} + \frac{13}{52} - \frac{1}{52}[/tex]
= [tex]\frac{16}{52}[/tex]
= [tex]\frac{4}{13}[/tex]
The probability that the card drawn is either a queen or a heart is 4/13
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If BA BD, the value of x is:
4.
9.
10.
None of these choices are correct.
g what would need to be known about the pivot columns in an augmented matrix in order to know that the linear system is consistent and has a unique solutionwhat would need to be known about the pivot columns in an augmented matrix in order to know that the linear system is consistent and has a unique solution
There are no free variables for the pivot columns in an augmented matrix in order to know that the linear system is consistent and has a unique solution.
Define the term unique solution?Identical to a coefficient matrix, an augmented matrix has an additional column that contains the values from the right side of a linear system of equations. A number of equations must match the number of unknowns if a system of equations does have a single unique solution (variables).For the stated question-
It is necessary to know that a system is consistent (i.e., there is no pivot in the last column of the augmented matrix) and that there are no free variables in order to determine whether it has a unique solution (like a pivot position in every column of the coefficient matrix).
Also take note that this rules out having fewer rows than columns.
Thus, there are no free variables for the pivot columns in an augmented matrix in order to know that the linear system is consistent and has a unique solution.
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A 8-inch candle burns down in 4 hours. Assuming the candles are the same thickness and make (that is, directly proportional), how long would it take a 12-inch candle to burn down?
Answer:
To determine how long it would take a 12-inch candle to burn down, we need to first determine the relationship between the length of the candle and the time it takes to burn down. Since the candles are the same thickness and make, we can say that the time it takes for a candle to burn down is directly proportional to its length. This means that we can write an equation to represent the relationship between the length of the candle and the time it takes to burn down as follows:
t = k * l
where t is the time it takes for the candle to burn down, k is the proportionality constant, and l is the length of the candle.
We can use the information given in the problem to find the value of k. We know that an 8-inch candle burns down in 4 hours, so we can substitute these values into the equation above to find the value of k, as follows:
4 = k * 8
Solving for k, we get:
k = 0.5
Now that we know the value of k, we can use the equation above to determine how long it would take a 12-inch candle to burn down. Substituting the values for t, k, and l into the equation, we get:
t = (0.5) * (12) = 6
This means that it would take a 12-inch candle 6 hours to burn down.
A. 2.9 inches
B. 40 inches
C. 3.2 inches
D. 2.1 inches
The required measure of length of the box is 2.9 inches. Option A is correct.
What is volume?Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.
Here,
according to the question,
h = 3l - 2.5
w = 3/4l
The volume of the box,
40 = l × w × h
40 = l × 3/4l × [3l-2.5]
40 = 3/4l²[3l - 2.5]
40 = 9/4l³ - 7.5/4l²
9/4l³ - 7.5/4l² - 40 = 0
t = 2.91932
t ≈ 2.9 inches
Thus, the length of the box must be at least 2.9 inches. Option A is the right answer.
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I need help I don’t know how to do this question on ixl
Estimation Gabe goes to the mall. If k is the number of items he bought, the
expression 12.92k + 27 gives the amount he spent in dollars at one store. Then he
spent 20 dollars at another store. Find the expression which represents the amount
Gabe spent at the mall. Then estimate how much Gabe spent if he bought 2 items.
The total spent at the mall by Gabe is $72.84 and the expression which represents the amount is 12.92 k + 27 + 20 or 12.92 k + 47.
What is expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.
Given:
12.92 k + 27, where k is the number of items bought,
Calculate the expression which represents the amount Gabe spent at the mall as shown below,
Total amount = Amount spent in one store + Amount spent in the second store
Total amount = 12.92 k + 27 + 20
Calculate the estimate of Gabe spent by putting k = 2,
Total spent in mall = 12.92 × 2 + 27 + 20
Total spent in mall = 25.84 + 47
Total spent in mall = $72.84
Therefore, the total spent at the mall by Gabe is $72.84, and the expression which represents the amount is 12.92 k + 27 + 20 or 12.92 k + 47.
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Xavier makes a conjecture that the sum of two odd integers is always an even integer. Which choice is the best proof of his conjecture?.
The correct option A: Let 2a + 1 be one odd number, and let 2b + 1 be the other odd number. (2a + 1) + (2b + 1) = 2a + 2b + 2 = 2(a + b + 1). Because 2(a + b + 1) is evenly divisible by 2, it is an even number.
Explain the term even integer?Odd numbers cannot be divided by two exactly, whereas even numbers were integers that can be divided by two exactly. Even number examples include 2, 6, 10, 20, 50, etc.The statement made by Xavier that the product of two odd integers always results in an even integer should be noticed.
For the given case, conjecture that the sum of two odd integers is always an even integer is -
Let 2a + 1 be one odd number, and let 2b + 1 be the other odd number. (2a + 1) + (2b + 1) = 2a + 2b + 2 = 2(a + b + 1). Because 2(a + b + 1) is evenly divisible by 2, it is an even number.To know more about the even integer, here
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The complete question is-
Xavier makes a conjecture that the sum of two odd integers is always an even integer. Which choice is the best proof of his conjecture?
Select option;
A: Let 2a + 1 be one odd number, and let 2b + 1 be the other odd number. (2a + 1) + (2b + 1) = 2a + 2b + 2 = 2(a + b + 1). Because 2(a + b + 1) is evenly divisible by 2, it is an even number.
B: Look at these different examples: 3 + 5 = 8, 13 + 5 = 18, 23 + 5 = 28. So the sum of two odd numbers must be even.
C: Let a and b both represent odd numbers, and let a + b be an even number. Therefore, a + b = b + a, which shows that the sum of two odd numbers is even.
D: Every time you add two odd numbers, the sum is an even number.
Pleaseeee helppppp meeeeee
Answer:
C
Step-by-step explanation:
You can do trial and error since it is a multiple ans question
Answer:
c
Step-by-step explanation:
do trial and error it's right the answer is c
Name the x- and y - intercepts for the equation:
5x - 3y = 15
Answer:
Red=X-Int: (3,0) Y-int: (0,-5)
Step-by-step explanation:
To find the y and x intercepts you have to plug in the 0 for the variable. You'd get 5(0)-3y=15 you get this by plugging in the 0 for x and then you solve. 5 x 0 is 0 so you'd get -3y=15 divide -3 on both sides and get y=--5 meaning that is the y-intercept. You'd do the same when you look for the x-int. Just that you'd plug in a 0 for y instead of x. Which is 5x-3(0)=15. -3 x 0 is 0. So you'd have 5x=15 divide both sides by 5 and you'd get x=3 meaning that is the x intercept.
(Hopefully you were able to understand how I got the x and y intercepts for this equation)
A statistics professor would like to build a model relating student scores on the first test to the scores on the second test. The test scores from a random sample of 21 students who have previously taken the course are given in the table.
Test Scores
Student First Test Grade Second Test Grade
1 50 70
2 91 58
3 55 74
4 58 65
5 79 60
6 70 60
7 97 48
8 51 73
9 51 73
10 59 66
11 69 67
12 56 70
13 56 73
14 41 76
15 49 72
16 58 68
17 58 73
18 99 53
19 87 58
20 95 50
21 97 55
Using statistical software, estimate the parameters of the model
Second Test Grade=β0+β1(First Test Grade)+εiSecond Test Grade=β0+β1(First Test Grade)+εi.
Enter a negative estimate as a negative number in the regression model. Round your answers to 4 decimal places, if necessary.
Sum of multiplied differences= -962.676 and β1 = -962.676 / ((-18.381)^2 + (22.619)^2 + (-13.381)^2 + (-10.381)^2 + (10.619)^2 + (2.619)^2 + (28.619)^2 + (-17.381)^2 + (-17.381)^2 + (-9.381)^2 + (0.619).
To estimate the parameters of the model, we can use the following steps:
Calculate the mean of the first test scores and the mean of the second test scores.
Calculate the difference between each student's first test score and the mean first test score, and the difference between each student's second test score and the mean second test score.
Multiply the differences from step 2 together for each student, and sum the results.
Divide the sum from step 3 by the sum of the squares of the differences from step 2. This will give us the value of β1.
Calculate β0 by substituting the values of β1 and the mean first and second test scores into the equation: Second Test Grade = β0 + β1(First Test Grade)
Using these steps, we can calculate the estimates of the parameters as follows:
Mean first test score = (50+91+55+58+79+70+97+51+51+59+69+56+56+41+49+58+58+99+87+95+97)/21 = 68.381
Mean second test score = (70+58+74+65+60+60+48+73+73+66+67+70+73+76+72+68+73+53+58+50+55)/21 = 64.762
Difference between student 1's first test score and mean first test score = 50 - 68.381 = -18.381
Difference between student 1's second test score and mean second test score = 70 - 64.762 = 5.238
Difference between student 2's first test score and mean first test score = 91 - 68.381 = 22.619
Difference between student 2's second test score and mean second test score = 58 - 64.762 = -6.762
Sum of multiplied differences = (-18.3815.238) + (22.619-6.762) + (-13.3818.238) + (-10.381-0.762) + (10.619*-6.238) + (2.619*-7.238) + (28.619*-16.762) + (-17.3819.238) + (-17.3819.238) + (-9.381*-0.762) + (0.619*-0.238) + (-2.3816.238) + (-2.3817.238) + (-27.38116.238) + (-18.3813.238) + (-10.381*-3.762) + (-10.3815.238) + (-10.3815.238) + (30.619*-11.762) + (18.619*-6.762) + (26.619*-14.762) + (28.619*-9.762) = -962.676
β1 = -962.676 / ((-18.381)^2 + (22.619)^2 + (-13.381)^2 + (-10.381)^2 + (10.619)^2 + (2.619)^2 + (28.619)^2 + (-17.381)^2 + (-17.381)^2 + (-9.381)^2 + (0.619)
Thus, Sum of multiplied differences= -962.676 and β1 = -962.676 / ((-18.381)^2 + (22.619)^2 + (-13.381)^2 + (-10.381)^2 + (10.619)^2 + (2.619)^2 + (28.619)^2 + (-17.381)^2 + (-17.381)^2 + (-9.381)^2 + (0.619).
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Which of the equations listed below would be parallel to the line divon by y= -4x + 3
Answer: A
A. y=-4x-2. Two lines are parallel if they have the same slope. In this case, the line given by y = -4x + 3 has a slope of -4, so the equation of the line that is parallel to it must also have a slope of -4. The equation y = -4x - 2 has a slope of -4, so it is the equation of a line that is parallel to the line given by y = -4x + 3.
6. The solid line is the parent function, f(x). Which of the following dotted line graphs shows the translation f(x) = f(x)
The function that is gotten after transformation is; f(x - 1) = -2x - 4
How to Interpret the Graph Transformation?We are told that the parent function is f(x).
Now, after transformation, the function becomes;
f(x) = f(x - 1)
Now, the solid line graph has;
y-intercept = -2
x intercept = 1
Slope = -2/1 = -2
Thus, equation is;
f(x) = -2x - 2
Thus, for f(x - 1), what it means is that we will plug in (x - 1) for x in the parent function to get;
f'(x - 1) = -2(x - 1) - 2
= -2x -2 - 2
= -2x - 4
The graph that represents the function after transformation is as attached.
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Complete question is;
The solid line is the parent function, f(x). Which of the following dotted line graphs shows the translation f(x) = f(x - 1)?
what is the angle of rotation that maps point P to point Q?
Answer:225 degrees
Step-by-step explanation:
I need the answer now
Please help me
I’ll give you the Brainiest
There is a close relationship between the air pressure inside a hurricane and its maximum sustained wind speed: Y-1.15x + 1190 where
x is the air pressure in millibars (kPa) and y is the wind speed in knots (nautical miles per hour). Using the model, what would be the wind
speed of a hurricane with an air pressure of 956 kPa? Round your answer to the nearest knot
A) 50 knots
B) 75 knots
C) 115 knots
D) 91 knots
The wind speed of a hurricane with an air pressure of 956 kPa will be 2289.4 knots.
What is a mathematical function, equation and expression?function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.Given is that relationship between the air pressure inside a hurricane and its maximum sustained wind speed → y = 1.15x + 1190, where [x] is the air pressure in millibars (kPa) and [y] is the wind speed in knots (nautical miles per hour).
The air pressure inside a hurricane and its maximum sustained wind speed are related as → y = 1.15x + 1190
For x = 956 kpa of pressure, we can write -
y = 1.15 x 956 + 1190
y = 2289.4 knots
Therefore, the wind speed of a hurricane with an air pressure of 956 kPa will be 2289.4 knots.
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Nadia typically type 32 word per minute, but her rate may vary by a much a 5 word per minute. Let x be the actual rate at which Nadia type. What i the range of rate, in word per minute, that Nadia could type?
The range of rate that Nadia can type is 27 to 37.
We will calculate the lower and upper limit stating the minimum and maximum number of words Nadia can type in a minute. It will depict the range of rate.
Minimum number of words = 32 - 5
Performing subtraction on Right Hand Side of the equation
Minimum number of words = 27
Maximum number of words = 32 + 5
Performing subtraction on Right Hand Side of the equation
Minimum number of words = 37
Hence, Nadia's range of word typing is 27 to 37 per minute.
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. The flashlight shown below has no batteries. Instead, it is operated by squeezing and letting go of the handle
Inside the body of the flashlight are gears.
A Kinetic → electrical → light
8 Kinetic chemical → light
C. Chemical -kinetic light
D chemical- electrical → light
The sequence of the energy conversion is; Kinetic → electrical → light Option A
What is energy conversion?From the first law of thermodynamics, we know that energy can neither be created nor destroyed but it can be converted from one form to the other. We have been told that in this case, the flashlight shown below has no batteries. Instead, it is operated by squeezing and letting go of the handle.
The letting go of the handle is kinetic energy which would lead to electrical energy that is then converted into the visible light energy.
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A hotel ha food proviioned for 30 day to erve 80
people. If 40 more men join the hotel, the ame proviion
would have lat for how many day?
By using the formula, days = (original number of people / new number of people) * original number of days, the same food would last for 20 days.
What is number?A number is a mathematical concept that refers to a quantity or value that can be represented by a symbol. Numbers can be used to represent quantities in various contexts, such as counting, measuring, and quantifying.
What is irrational numbers?Irrational numbers are numbers that cannot be expressed as the ratio of two integers (e.g. pi, the square root of 2).
days = (original number of people / new number of people) * original number of days
In this case, we can plug in the values as follows:
days = (80 / (80 + 40)) * 30
days = (80 / 120) * 30
days = 2/3 * 30
days = 20
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What’s the surface area of this prism ?
The surface area of the triangular prism is 191 cm².
What is a triangular prism?A triangular prism is a polyhedron made up of two triangular bases and three rectangular sides. It is a three-dimensional shape that has three side faces and two base faces, connected to each other through the edges.
We know the surface area of a triangular prism is (S₁ + S₂ + S₃)/l + bh.
The given triangular prism has a surface area from the given diagram we determine, 3(D×A) + 2(B×C) [area of rectangles and triangles],
= 3(8×4) + 2(10×6).
= 3(24) + 2(60).
= 71 + 120.
= 191 cm².
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if f(x)=-2x+5, find x so f(x)=3
Answer:
f(x)=-2x+5
f(x)=3
then,
f(x)=-2x+5
or, 3=-2x+5
or, 2x=5-3
or,2x=2
or, x=2÷2
x=1
so, the value of x is 1
Answer:
x=1
Step-by-step explanation:
3= -2x+5
-5. -5
-2= -2x
/-2. /-2
1=x
hopes this helps
Tanisha has 51 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 304 square
meters. List each set of possible
dimensions (length and width) of the
field.
Possible dimensions #1:
meters by
meters.
Possible dimensions #2:
meters by
meters.
Answer:
Two sets of dimensions are possible:
L(m) W(m) Area(m^2) Fence (m) Perimeter
Set 1 19 16 304 51
Set 2 32 9.5 304 51
Step-by-step explanation:
Let's set L and W for the Length and Width of the perimeter. We know that:
Area = L*W
Area = 304 m^2
Perimeter = 51 m
Let's say that the side bounded by the river is the length side. No fence is required for that portion, so the fencing for the perimeter is given by:
Perimeter, P = L + 2W
P = 51 m
We can write: L+2W=51 m
Rearrange to isolate one of the two variables. Lets pick L:
L+2W=51
L=51-2W
L = (51-2W)
Now use this in the area equation:
304 m^2 = L*W
304 m^2 = (51-2W)*W
304 m^2 = (51-2W)*W
304 m^2 = 51W-2W^2
Arrange this in the standard form of a quadratice equation and solve:
-2W^2+51W-304 m^2 = 0
W = 16 and 9.5 meters
W = 16 m
Since L=51-2W
L=51-2*(16)
L = 51-32
L = 19 m
Area = L*W
L*W = 304 m^2
(19m)W = 304 m^2
W = 16 m
Check:
Does a length (L) of 19 m and a width (W) of 16 m give an area of 304 m^2 and a fencing perimeter of 51 m if one of the L sides is the river?
Area = (19 m)*(16 m) = 304 m^2 YES
Per. = 2*(16)+ 19 = 51 m YES
W = 9.5 m
Ding the same calculation for a width of 9.5 m also satisfies all the equations, as per above.
Both values of W are valid, so the twos sets of possible dimensions are:
L(m) W(m) Area(m^2) Fence (m) Perimeter
Set 1 19 16 304 51
Set 2 32 9.5 304 51
find f. f ''(x) = x−2, x > 0, f(1) = 0, f(3) = 0
Answer:
Step-by-step explanation:
Here we have the second derivative of a function and we need to go back to the original function. This situation is inverse of taking derivative which is called antiderivative or integral. But because we have the second derivative, we have to integrate twice because the first integral will give me the first derivative then the second integral will give me the function itself.
1. Let's start taking the 1st integral of x-2 which is x²/2-2x+C1
2. Take the 2nd integral which is the integral of the 1st one
x³/6-2x²/2+C1x+C2
remember: the integral is the inverse of derivative, that means we have to add 1 to the power of x and divide by that power. I did that in steps 1 and 2.
3. After simplifying the second term, f(x)=x³/6-x²+C1x+C2 this is the function, but I have to find C1 and C2 the constants. We can use the two conditions given. the 1st one means that when x=1 , y=0
0=1/6-1+C1+C2 now combine like terms and move them to the left side of the equation C1+C2=5/6
the 2nd condition means that when x=3 , y=0
0=27/6-9+3C1+C2 after simplifying 3C1+C2=9/2
4. We got 2 equations with 2 variables C1 and C2, we can solve these system of equations. You can eliminate C2 and find C1 which is 11/6 then plug in C1 in any of the two equations to find C2, which is -1
5. Last step substitute C1 and C2 in the function from step 3 and you will get f(x)=x³/6-x²+11x/6-1