The line integral for the path of the semicircular arc is -5/3.
C is the arc such that-
x = cost, y = sin t, 0 ≤ t ≤ π/2
and c is the line segment such that-
x = −t, y = 1, 0 ≤ t ≤ 1
Along curve C we have
F · r' = {(cos²t + sin²t)i + 2 cost sint j} · (− sint i + cost j)
= − sin t + 2 sin t cos²t
Hence,
[tex]\int\limits_C F \, dr = \int\limits^a_b {(-sin t + 2sint t cos^{2} t)} \, dt[/tex]
where a = π/2 and b = 0
= [cos t - 2cos³ t/3]
= -1/3
Moreover, along curve c we have
F · r' = ((−t)² + 1²)i + 2(−t)j)· (−1)i
= −(t² + 1).
Hence,
[tex]\int\limits_c {F} \, dr = \int\limits^1_0 {-(t^{2}+ 1) } \, dt[/tex]
= −4/3.
Finally, we obtain the line integral as follows-
[tex]\int\limits_C {F} \, dr + \int\limits_c {F} \, dr[/tex]
= -1/3 -4/3
= -5/3
The line integral for the path of the semicircular arc is -5/3
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Solve each of the quadratic equations.
0 = 5x2 - 2x + 6
(1) prompt the user to enter four numbers, each corresponding to a person's weight in pounds. store all weights in a list. output the list. (2 pts)
A prompt is one to three sentences that pose a problem or a query that you must address in an essay.
In the given question we have to prompt the user to enter four numbers, each corresponding to a person's weight in pounds and store all weights in a list and output the list.
(1) weights = [float(input('Enter weight 1: \n')),
float(input('Enter weight 2: \n')),
float(input('Enter weight 3: \n')),
float(input('Enter weight 4: \n'))]
print("Weights:", weights)
(2) weights = [float(input('Enter weight 1:\n')),
float(input('Enter weight 2:\n')),
float(input('Enter weight 3:\n')),
float(input('Enter weight 4:\n'))]
print("Weights:", weights)
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The right question is given below:
Write an equivalent fraction to 5/8 with a denominator of 40
Step-by-step explanation:
So you have 5/8 and you want the equivalent fraction to have a denominator of 40. You put 5/8=X/40 and find for x.
First, multiply both sides by 40
5/8*40=x
Express 5/8 * 40 as a single fraction.
5*40/8=x
Multiply 5 40 to get 200.
200/8=x
Divide 200 by 8 to get 25.
25=x
Swap sides so that all variable terms are on the left-hand side.
x=25
(10 points) Find the height y and length of a side of its base x of a square pyramid with congruent isosceles triangle sides whose volume is cubic meters and whose lateral surface area is as small as possible. (The lateral surface area includes the sides but excludes the base of the pyramid.) Justify that the dimensions you found give minimum lateral surface area.
The minimum lateral surface area of the prism is approximately 1.194 square units.
The given base and height of the prism is y and x respectively.
Hence volume of the prism
V = 1/3 x²y
again 1/3 x²y = 1/6
or, y = 1/2x²
The lateral surface area of the prism is given by :
F = √(4y²+x²)
By the equation 1 we get :
F = x √ (1/x⁴ + x²)
Now we will use differentiation:
[tex]\frac{df}{dx} = \frac{2x^6-1}{x^4(x^2+\frac{1}{x^2} )}[/tex]
Now for the critical points we have to take df/dx = 0
hence solving the equation for x we get :
[tex]x = (\frac{1}{2} )^{\frac{1}{6}}[/tex]
Hence the values of x is [tex](\frac{1}{2} )^{\frac{1}{6}}[/tex] and the value of y will be [tex]\frac{1}{2^\frac{2}{3}}[/tex] units,
And the lateral surface are will be :
F (min ) = √(4y²+x²)
= √ (0.795 + 0.633)
= 1.194 square units
The approximate values of x and y are
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use euler's method with step size 0.5 to compute the approximate y-values y1, y2, y3 and y4 of the solution of the initial-value problem y' = y-2x, y(2) = 1.
For y1, im getting 1+0.5(1-2(2))= -4.5 but that answer isnt correct and I dont know what I'm doing wrong
The values are y₁=-0.5, y₂=-3.25, y₃=-7.825 and y₄=-15.3125 when the initial - value problem y' = y-2x. y(2)=1.
Given that,
Use Euler's method with step size 0.5 to compute the approximate y-values y₁, y₂, y₃ and y₄ of the solution of the initial - value problem y' = y-2x. y(2)=1.
We have to find the values y₁
We know that,
What is Euler approximation?At Euler's approach, the curve of the solution can be roughly approximated at steps of h by the tangent in each interval (i.e., by a series of brief line segments). In general, using a short step size improves approximation accuracy.
By Euler approximation,
y₁ = y₀+hf(x₀,y₀)
=1+0.5(1-2(2))
=1-1.5
y₁=-0.5
Similarly,
y₂=-3.25, y₃=-7.825 and y₄=-15.3125
Therefore, The values are y₁=-0.5, y₂=-3.25, y₃=-7.825 and y₄=-15.3125 when the initial - value problem y' = y-2x. y(2)=1.
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I've gotten stuck on this problem: "Let f(z) be the branch to z13+z14, which is defined on the entire complex plane except on the negative imaginary axis, for which f(1)=0. Find f(-1)."
I started by writing z13+z14 as e13(ln|z|+iθ(z)+i2nπ)+e14(ln|z|+iθ(z)+i2mπ) but when I try to solve f(1)=0 I just get the relationship between n and m, which means I won't get a specific branch. I am also not sure how to use the condition "not defined on the negative imaginary axis"
In order to find the value of f(-1), you can start by finding the value of f(1) and then proceed for the next step.
As you have already noted, writing z13+z14 as e13(ln|z|+iθ(z)+i2nπ)+e14(ln|z|+iθ(z)+i2mπ) will not give you a specific branch. Instead, you can write z13+z14 as follows:
(z-1)(z12+z11+z10+...+1)
Then, you can use the fact that f(1)=0 to solve for the value of z12+z11+z10+...+1. This will give you a specific value for f(1).
To find the value of f(-1), you can use the following relationship:
f(-1) = f(1) * (-1)13 * (-1)14
Substituting the value you found for f(1) and evaluating the expression will give you the value of f(-1).
As for the condition "not defined on the negative imaginary axis", this means that the branch of f(z) is not defined for any complex number with a negative imaginary part. This is because the 13th and 14th roots of a complex number are not unique when the imaginary part is negative, so the function is not defined for these values.
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Find the value of x for which l is parade to m. The diagram is not to scale
The value of x for which l is parallel to m is 41°
What is meant by an angle?An angle is a figure in Euclidean geometry made up of two rays that share a terminal and are referred to as the angle's sides and vertices, respectively. The meeting of two planes can also create an angle. These are referred to as dihedral angles. The angle formed by the rays lying perpendicular to the two intersecting curves at their point of intersection can likewise be used to establish an angle between two intersecting curves.
In the depicted figure, l and m are parallel. A transversal crosses parallel lines, creating the appropriate angles. The angles created when two parallel lines cross any other line, whether they are corresponding or matching corners to the transversal.
(3x-43)°=80°
3x=80°+43°
3x=123°
x=41°
Therefore, the value of x is 41°
Hence, the value of x for which l is parallel to m is 41°.
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Please help ASAP! its due today! ill give brainlist..
The volumes aren't the same as the first cylinder has a bigger volume.
How to calculate the volume?Based on the information given, it should be noted that the first cylinder has circumference of 11 inches. The radius will be calculated thus:
2πr = 11
2 × 3.14 × r = 11
6.28r = 11
Divide
r = 11 / 6.28
r = 1.75 inches
The volume of the cylinder will be:
= πr²h
= 3.14 × 1.75² × 8.5
= 81.74 inches³
For the second cylinder, circumference is 8.5 inches. The radius will be calculated thus:
2πr = 8.5
2 × 3.14 × r = 8.5
6.28r = 8.5
Divide
r = 8.5 / 6.28
r = 1.35 inches
The volume of the cylinder will be:
= πr²h
= 3.14 × 1.35² × 11
= 63 inches³
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which of the following number lines shows the solution to the inequality given below? 4x + 7 _< -37 or 5x + 3 > -7
The graph of the compound inequality can be seen in the image at the end.
Which number line shows the solution set for the inequality?
Here we have a compound inequality which is:
4x + 7 ≤ -37
5x + 3 > -7
First we need to isolate x in both of these inequalities, on the first one we will get:
4x + 7 ≤ -37
4x ≤ -37 - 7
4x≤ -44
x ≤ -44/4
x ≤ -11
The other inequality gives:
5x + 3 > -7
5x > -7 - 3
5x > -10
x > -10/5
x > -2
So the compound inequality is:
x > -2
x ≤ -11
To graph this we need to have a open circle at x = -2, and we need to graph a line to the right. And a closed circle at x = -11 and a line that goes to the left.
The number line is below
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the temperature of city changed by total of -12 degrees Celsius over 2 weeks period. the temperature changed by the same amount each week. Part A write an expression to show the average change in the temperature of the city each week. Part B simply the expression and explain, using words, what your answer mean
Answer:
The number of degrees Celsius goes down 6 every week. (-6)
Step-by-step explanation:
If the city's temperature changed the same every week, and over the period of 2 weeks it changed -12 degrees Celsius, we need to figure out how much it changed every week (c). We can do this by dividing the number of weeks (w), by the total number of Celsius it changed (t).
The equation will look something like this:
w ÷ t = c
Fitting the numbers into this equation will look something like this:
2 ÷ -12 = -6
Every week, it changed -6 degrees Celsius.
Simplifying the expression, every week it changed -6 degrees Celsius. We know this because the temperature changes the same amount every week. So if the total amount is -12, we have to divide that by 2 to get -6.
Which of the following does not represent a relation that is a function?
A) The graph of the relation passes the vertical line test.
B) In a table of values, each input has exactly one output.
C) In a table of values, each input has one or more outputs.
D)The equation of the relation is in the form y = mx or y = mx + b.
Answer:B
Step-by-step explanation: I did the test
The function is set of ordered pairs in which each X element has only a Y element.
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that;
The correct statement which does not represent a relation that is a function.
Since,
The vertical line test is used to determine the function exists or not. If the vertical line is moved across the graph one point of the graph is a function. The line moving from point to point is a function.
Hence the option A is correct.
Thus, The function is set of ordered pairs in which each X element has only a Y element.
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the triangles are similar solve for x
Answer:
show the whole question
Step-by-step explanation:
NO LINKS!! Please help me with this problem. Part 1ff
Answer:
[tex]\textsf{a)} \quad A=\dfrac{x(2x+22)}{x-4}[/tex]
[tex]\textsf{b)} \quad x > 4[/tex]
[tex]\begin{aligned}\text{c)} \quad x &= 11.75\; \sf in\\y &= 68.98\; \sf in \end{aligned}[/tex]
Step-by-step explanation:
Part (a)Print area (blue rectangle):
width = (x - 4) inlength = (y - 2) inarea = 30 in²Create an equation for the print area using the given values and rearrange to isolate y:
[tex]\implies (x-4)(y-2)=30[/tex]
[tex]\implies y-2=\dfrac{30}{x-4}[/tex]
[tex]\implies y=\dfrac{30}{x-4}+2[/tex]
Total area of the page is:
[tex]\implies A=xy[/tex]
Substitute the found expression for y to write an equation for the total area of the page in terms of x:
[tex]\implies A=x\left(\dfrac{30}{x-4}+2\right)[/tex]
[tex]\implies A=x\left(\dfrac{30+2(x-4)}{x-4}\right)[/tex]
[tex]\implies A=x\left(\dfrac{2x+22}{x-4}\right)[/tex]
[tex]\implies A=\dfrac{x(2x+22)}{x-4}[/tex]
Part (b)If x < 4 then A < 0.
If x = 4 then A is undefined.
Therefore, given the physical constraints of the problem, x has to be greater than 4.
Part (c)Using a graphing utility, graph the function for area from part (a) when x > 4 (see attachment). (Note: The x-axis of the attached graph crosses the y-axis at y = 50 for ease of inspection).
The values of x and y that use the least amount of paper are the coordinates of the minimum point of the graph.
From inspection of the graph, the minimum point is:
x = 11.75 iny = 68.98 inwrite down in trems of n an expression for the nth term in the following sequences 1 8 15 22 29
The expression which represents the nth term of the given sequence, in terms of n as required in the task content is; T (n) = 1 + 7(n - 1).
Which expression represents the nth term of the expression in terms of n?It follows from the task content that the expression which represents the nth term of the given sequence, in terms of variable, n be determined.
According to the task content, the first term, a of the sequence is; 1.
Also, since; 8 - 1 = 15 - 8 = 22 - 15 = 29 - 22 = Common difference, d = 7.
Consequently, the required expression is an arithmetic sequence which can be modelled by;
T (n) = a + d (n - 1)
Since the constant common difference of consecutive terms in the sequence is; 7,
Therefore, the expression for the nth term of the expression is;
nth = 1 + 7(n -1)
On this note, the required expression which represents the nth term of the arithmetic sequence in discuss is; T (n) = 1 + 7 (n -1).
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Part A: What is the group of points labeled X called? What is the point labeled Y called? Give a possible reason for the presence of point Y. (3 points) Part B: Describe the association between a student’s test scores and the number of homework assignments submitted. (2 points)
a) The group of points labeled X are the non-outlier scores, while point Y is an outlier score.
b) The association between the variables is positive.
How to classify the association between variables?There are two possible classifications for the associations between variables, as follows:
Positive association: as one variable increases, the other variable also increases.Negative association: as one variable increases, the other variable decreases.For this problem, the variables are given as follows:
Input: Number of homework assignments submitted.Output: Test scores.As the number of assignments submitted increases, the test scores also increases, hence there is a positive relationship between these two variables.
The point Y is an outlier, as the student got a considerably worse grade than expected, meaning that combined with his low score on the assignments, the student may have considerable difficulties in the subject.
Missing InformationThe graph is given by the image shown at the end of the answer.
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Suppose that a steel company views the production of its continuous caster as a continuous income stream with a monthly rate of flow at time t given by
f(t)=12,000e^0.04t (dollars per month).
Find the total income from this caster in the first year. (Round your answer to the nearest dollar.)
The Total Income from this caster in the first year = $184,822 approximately
What is Total Income?
Total income is the sum of all earnings, save those specifically mentioned in Section 12 of this Act, that a person receives during a certain accounting period, before any deductions are taken into account.
Given that : f(t)=12,000e^0.04t (dollars per month)
We could calculate our twelve calculations and evaluate this function once a month, but it would take some time. Instead, we should keep in mind that a continuous function can be represented by an integral. This indicates that we can simplify our calculation by simply taking the integral of this function between 0 and 12.
∫₀¹² 12000e⁰·⁰⁴t dt
Since we will transform this integrand into something for which we have the antiderivative, we may utilise u-substitution to simplify the calculation of this integral.
u=0.04t
du=0.04
dt0.04(0)=0
0.04(12)=0.48
To get the substitute for d u, we must slightly modify our integrand. This can be accomplished by adding 0.04 inside and canceling it outside by its reciprocal. The Fundamental Theorem of Calculus will then be used to calculate this definite integral.
12000 (1/0.04) ∫₀¹² 0.04e⁰·⁰⁴t dt = 30000 ∫₀⁰·⁴⁸ e⁴du
30000[tex]e^{u}[/tex] | ₀ ⁰·⁴⁸
30000(1.61607 -1)
184822.32
Therefore, the total income over the first year is approximately $184,822.
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Reasoning Kareem cannot decide which of two washing machines to buy. The selling price of each is $550. The first is marked down by 40%. The second is marked down by 30% with an additional
10% off. Find the sale price of each washing machine.
The sale price of each washing machine is $330.
How to find the sale price of each washing machine?
Discount is defined as a deduction from the usual cost of something
The first washing machine is marked down by 40%, so its sale price is 100% - 40% = 60% of the original price.
This means that the sale price is 60/100 × $550 = $330.
The second washing machine is marked down by 30%, with an additional 10% off, for a total discount of 30% + 10% = 40%.
Its sale price is 100% - 40% = 60% of the original price.
This means that the sale price is 60/100 × $550 = $330.
Therefore, the sale price of each washing machine is $330.
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11(b). Karen has a spinner. When the spinner is spun once, the probability that it will land on yellow is Karen spins the spinner 30 times. Work out an estimate for the number of times the spinner lands on yellow. This is my exam question. May i know the answer of this? plss
Step-by-step explanation:
we would need the number for the probability to get yellow.
without that I can only tell you the general approach :
you need to multiply the probability by the number of tries (30).
if the probability is given as %, you need to divided this number by 100 (e.g. for 20% the probability factor is 0.2).
so,
probability × tries (30) = the expected number the spinner lands on yellow.
Which type of set square has two sides with equal length?
Answer:
Step-by-step explanation:
n the reading you learned about five concepts related to variables. Line 3 is ______________. More than one answer may be required.
double c = 3.15;
The five concepts related to variables that are mentioned in the prompt are:
Declaration: This is the process of creating a new variable and giving it a name. In the given line of code, "double c" is the declaration of a new variable named "c".Data type: This is the type of data that a variable can hold. In the given line of code, the data type of the variable "c" is "double", which means that it can hold a decimal value.Assignment: This is the process of giving a value to a variable. In the given line of code, "c = 3.15" is the assignment of the value "3.15" to the variable "c".Initialization: This is the process of declaring and assigning a value to a variable at the same time. In the given line of code, "double c = 3.15" is the initialization of the variable "c".Value: This is the data that is stored in a variable. In the given line of code, the value of the variable "c" is "3.15".To learn more about variables, visit:
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What is represented on the x-axis of this graph?
A)The percentage of surviving individuals, using a normal (non-logarithmic) scale
B)The percentage of surviving individuals, using a logarithmic scale
C)The type of survivorship curve
D)Individuals' life spans as a percentage of the maximum life span for the species
The x-axis of this graph is D) Individuals' life spans as a percentage of the maximum life span for the species.
In mathematics, "graph" can refer to (at least) two different things. The word "graph" in elementary mathematics refers to a plot or a function graph.
A graph is, in the language of mathematicians, a set of points and the connections between some subset of those points (which may be empty).
Making a diagram that shows the link between two or more objects is known as developing a graph. Create a graph by placing a series of bars on graph paper.
Depending on age, survival curves display the likelihood of survival in a population. The y-axis represents the number of survivors (on a log scale), while the x-axis represents time (indicating relative age). The graph's x-axis (horizontal line) should contain the independent variable, and the y-axis should contain the dependent variable. At the origin, where the coordinates are, the x and y axes intersect.
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What are the prime factors that 27 and 36 share?
_______ and _______
Answer:
The prime factors are 3 and 3
Newsweek performed a poll in which 500 American parents were asked the question, “Would you prefer to have your child taught by a male or female for grades K-2?” Only 40% responded that they would prefer to have their child taught by a male in grades K-2. Construct a 95% confidence interval for the poll.
Newsweek performed a poll in which 500 American parents were asked the question, “Would you prefer to have your child taught by a male or female for grades K-2?” 95% confidence interval for the poll is
(38.88%, 41.12%)
What is a confidence interval?Generally, To construct a 95% confidence interval for the poll, we need to first calculate the margin of error. The margin of error for a poll is a measure of the precision of the estimate and is calculated based on the sample size, the level of confidence, and the standard deviation of the population.
In this case, the sample size is 500, the level of confidence is 95%, and the standard deviation of the population is unknown. We can approximate the standard deviation using the sample proportion of 40% as an estimate of the population proportion.
Using these values, the margin of error can be calculated as follows:
Margin of error = z * standard error
Where z is the critical value from the standard normal distribution for the desired level of confidence (in this case, 1.96 for a 95% confidence interval) and the standard error is calculated as:
Standard error = √(p * (1 - p) / n)
Where p is the sample proportion (40% in this case) and n is the sample size (500 in this case).
Substituting these values into the formula for the margin of error, we get:
Margin of error = 1.96 * √(0.4 * (1 - 0.4) / 500)
= 1.96 * sqrt(0.16 / 500)
= 1.96 * √(0.000032)
= 1.6 * 0.005656854
= 0.011168
So the margin of error for this poll is approximately 0.011168 or 1.12%.
To construct the 95% confidence interval, we need to add and subtract the margin of error from the sample proportion. The 95% confidence interval for the poll is, therefore:
40% ± 1.12%
= (38.88%, 41.12%)
This means that we can be 95% confident that the true population proportion of parents who would prefer to have their child taught by a male in grades K-2 lies within the interval between 38.88% and 41.12%.
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The length and height of room & 6m and 3m and its volume is 90m cube then find the breadth and cost of carpenting the floor the rate of Rs. 12 per square meter.
The cost of the carpentering of the floor at the rate 12 rupees per square meter is 60 rupees.
What is cuboid?A cuboid is a solid in three dimensions with six rectangular faces, eight vertices, and twelve edges. Three dimensions, including length, breadth, and height, define a cuboid. A cuboid with integer edges is referred described as being perfect.
We have the room as a cuboid.
And its length is 6 meters and height is 3 meters.
The volume of the cuboid = length x height x width
90 = 6 x 3 x width
width = 90 / 18
width = 5 meter.
To find the cost of carpentering the floor, the rate of Rs. 12 per square meter.:
12 x width = 12 x 5 = 60 rupees.
Therefore, at the rate of 12 rupees per square meter, the cost of the carpentering of the floor is 60 rupees.
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A parachutist's rate during a free fall reaches 45 meters per second. What is this rate in feet per second?At this rate, how many feet will the parachutist fall during 2 seconds of free fall? In your computations, assume that 1 meter is equal to 3.3 feet. Do not round your answers.
Rate:
Distance fallen in 2 seconds:
a) The rate in feet per second is 148.5 feet per second
b) The distance covered after 2 feet is 360.4 feet
What is the rate?We know that the rate has to do with how much the quantity is changing per unit time. In this case, we are looking at the rate of change of the Parachute's distance per second. It is important for us to say that this rate of change of the distance can also be shown to be the speed of the object.
We would now convert the rate to feet per second and we have;
1 meter per second = 3.3 feet per second
45 meters per second = 45 * 3.3/1
= 148.5 feet per second
Then we have;
s = ut + 1/2gt^2
s =distance
u = initial velocity
g = acceleration due to gravity
t = time taken
After 2 seconds;
s = (148 * 2) + (0.5 * 32.2 * 2^2)
s = 296 + 64.4
s = 360.4 feet
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Nancy drives 20 miles to her school each day. If she drives 10 miles per hour faster, it takes her 4 minutes less to get to school. Find her new speed
Given the distance 20 miles and the fact that if she drives 10 miles per hour faster, it takes her 4 minutes less to travel the distance, Nancy's new speed is 60 miles per hour.
The relation between distance and speed is given below:
s = v . t
Where:
s = distance
v = velocity or speed
t = time
In the given problem, let:
v = first speed
t = first time periods needed to travel 20 miles, in minutes
s = distance = 20 miles
Her new speed and new time is (v + 10) and (t - 4)
Hence,
v . t / 60 = 20, or
vt = 1200
v = 1200/t
After increasing the speed, the following holds:
(v + 10) (t - 4)/60 = 20
vt + 10t - 4v - 40 = 1200
Substitute vt = 1200 and v = 1200/t
10t - 4800/t - 40 = 0
Multiply by t/10
t² - 4t - 480 = 0
(t - 24) (t+20) = 0
t = 24 or t = -20
Therefore, the time that satisfies the equation is t = 24 minutes.
Her original speed is:
v = 1200/t = 1200/24 = 50 miles per hour
Her new speed is:
v + 10 = 50 + 10 = 60 miles per hour
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1-2t=2(1-t) what is the value of t
Step-by-step explanation:
1 - 2t = 2(1 - t)
1 - 2t = 2 - 2t
there is no value for t.
Solve for X
HELPPPPPP
The value of [x] is equivalent to 9.72 units.
What is similarity of triangles?Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion.
The triangle similarity criteria are:
AA (Angle-Angle)SSS (Side-Side-Side)SAS (Side-Angle-Side)Given is a triangle as shown in the image.
The smaller triangle and the larger triangle are similar to each other. So, we can write -
3x - 4 = 10x - 72
- 4 + 72 = 10x - 3x
68 = 7x
x = 68/7
x = 9.72 units
Therefore, the value of [x] is equivalent to 9.72 units.
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Help please!!
Diana and Teri have a collection of books.
The number of books in Diana's collection can be represented with x.
Teri has four times as many books as DIana.
The total number of books is 200.
How many books does Diana have?
Answer:
Diana has 40 books in her collection.
Step-by-step explanation:
We can set up the equation 4x + x = 200 to represent the total number of books in the collection, where x is the number of books in Diana's collection and 4x is the number of books in Teri's collection. Solving for x, we get 5x = 200, so x = 40. This means that Diana has 40 books in her collection.
Answer:
Teri has 160 books
Step-by-step explanation:
1. What value of X makes this equation true?
1/2X +7=2X - 5
Record your answer and fill in the bubbles on your answer document. Be sure to use the correct place value.
The value of x is +0008.00 that make true for the equation (1/2)x + 7 = 2x - 5.
What is solution of a linear equation?
An assignment of values to the unknown variables that establishes the equality in the equation is referred to as a solution. To put it another way, a solution is a value or set of values (one for each unknown) that, when used to replace the unknowns, cause the equation to equal itself.
Given equation is
(1/2)x + 7 = 2x - 5
Subtract (1/2)x from both sides:
(1/2)x + 7- (1/2)x = 2x - 5 - (1/2)x
7 = 2x - (1/2)x - 5
Add the like terms:
7 = 3/2 x - 5
Add 5 on both sides:
7 + 5 = 3/2 x - 5 + 5
12 = 3/2 x
Multiply both sides by 2/3
12 × (2/3) = x
8 = x
x = 8
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