Higher mean absolute deviation is an example of a measure of variability and range. It give us some information about how spread out the data in a data set is. When used together with measures of center like the mean and median, they can give us a useful overview of the data set.
For an example,
A chef wants to hire someone to work in his kitchen. There are two candidates: Sally and Nader. To test their abilities, he times how long it takes them to make each of four meals and records the data in two tables.
He decides to calculate the mean time it took each candidate to make the four meals; he is planning to hire the candidate with the lower (quicker) mean time.
The mean time it takes Sally to make a meal is
= 3+5+7+9 / 4
=24/6
= 6 minutes
The mean time it takes Nader to make a meal is
= 5+6+5+8 / 4
=24/4
= 6 minutes
After having mean times same he doesn't classify which one is best he used their statical graphs.
For Sally, the mean absolute deviation of her times is the mean of the distances,
=4+1+2+3 / 4
=2.5
For Nader, the mean absolute deviation of his times is
= 1+0+1+2 / 4
=1
The chef sees that the mean absolute deviation of Nader’s times is lower than the mean absolute deviation of Sally’s times. This shows that Nader is more consistent in his cooking times and agrees with what we observed from the bar graphs.
Which means that the higher mean absolute deviation occurs less consistency in the mean absolute deviation.
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Which expression is equivalent to 3 x − 2 − 5 2 − 4 x − 2 ?
The given expression 3x + 2.5 (4x + 2) is equivalent to 13x + 5.
The given question is a polynomial in one variable. Polynomials in one variable are algebraic expressions that depend on only one variable. The given expression is also dependent only on the variable, x.
In order to find its equivalent, we need to expand it. To expand it, we multiply the terms inside the bracket with the 2.5 outside. By doing so, we will get -
= 3x + (2.5*4x) + (2.5*2)
= 3x + 10x + 5
= 13x + 5
Hence, we find out that 3x + 2.5 (4x + 2) is equivalent to 13x+5.
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Write the linear equation in slope-intercept form from the description. Use c to represent the total cost and m to represent the number of movie rentals.
The cost of a movie streaming service is $11.50, plus $1.25 per movie rental.
Answer:
Step-by-step explanation:
C=1.75m+10.50
What is the solution for x in the equation, 3/x + 7 = -5?
A. x = -4
B. x = -1/4
C. x = 3/2
D. x = 12
Answer:C
Step-by-step explanation:
The answer is c because of the following:
-5 + 7 = 2
so 3/x= 2
we can put two in x's place and x in 2 place and get 3/2= x
A group of friends wants to know how many students bike to school. There are 526 students at the school. Each friend surveys a random sample of 50 students. The box plot shows their data.
How do the samples vary? In the samples, the percent of students that bike to school varies from 5%, 10%, 20%, or 25% to 10%, 15%, 20%, or 50%
Answer:
Step-by-step explanation: 20% to 50%
In the samples, the percent of students that bike to school varies from 20% to 50%.
In the data plot, 10 is the minimum and 25 is the maximum so 10/50= 0.2 or 20%. 25/50= 0.5 or 50%. Meaning it should vary from 20% to 50%.
Two times the quantity of 6 subtracted from 13
Answer:
13 - 6(2)
Step-by-step explanation:
I found this out because, since you have to subtract the 6 from the 13, the 13 will go first:
13 -
Then, you figure out what the 6 and two times means. It means 6 x 2, or 6(2):
13 - 6(2).
May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I only need 12 more brainliest to become a genius! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
will give brainy and 25 points and a thanks if you get this right need a expert
Answer: ∠1= 60° ∠2=120° ∠3=60° ∠4=60° ∠5=120° ∠6=120° ∠7=60°
Step-by-step explanation: hope this helps!
please give brainliest!
Answer:
1. 60°
2. 120°
3. 60°
4. same as 1. 60°
5. same as 2. 120°
6. same as 2 and 5, and the angle given of 120°
7. same as 1. and 3. 60°
Step-by-step explanation:
You are given an angle of 120°
The lines are parallel, and the transversal gives you all the answers. All have to add up to 360°.
Alice has 24 apples. In how many ways can she share them with becky and chris so that each of the three people has at least two apples?
There is a total of 190 ways to share apples between them.
What is a ball-and-urn method?
The ball-and-urn method often referred to as stars-and-bars, sticks-and-stones, or dots-and-dividers is a typical combinatorial method.
It is used to resolve issues of the following type: in how many different ways can one divide 'k' undifferentiable items into 'n' distinct bins?
Use the ball-and-urn method, Let Alice get 'x' apples, Becky get 'y' apples, and Chris get 'z' apples.
⇒x + y + z = 24
We can manipulate this into an equation that can be solved using the ball-and-urn method
All of them get at least 2 apples, so we can subtract 2 from x, 2 from y, and 2 from z.
⇒(x - 2) + (y - 2) + (z - 2) = 18
Let x' = x - 2, y' = y - 2, z' = z - 2.
⇒ x' + y' + z' = 18
We can allow either of them to equal 0, hence this can be solved by the ball-and-urn method.
By the ball-and-urn method, we get
[tex]$\binom{18 + 3 - 1}{3 - 1} = \binom{20}{2} = \ 190}$.[/tex]
Hence, there are 190 ways to split the apples among them.
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Chiamaka is 149 km from the university and drives 95 km closer every hour. Valente is 170 km from the university and drives 110 km closer every hour. Let t represent the time, in hours, since Chiamaka and Valente started driving toward the university. Complete the inequality to represent the times when Valente is closer than Chiamaka to the university. t > 7/5 hours
Using linear functions, the inequality for the times when Valente is closer than Chiamaka to the university is:
170 + 110t < 149 + 95t
What is a linear function?
Linear functions have a straight line as their graph. The following is the form of a linear function. y = f(x) + a+bx There is one independent variable and one dependent variable in a linear function.
Solution:
Considering the initial distance as the intercept and the velocity as the slope, the linear functions for the distances of each Chiamaka and Valente are given as follows:
C(t) = 149 + 95t
V(t) = 170 + 110t
Valente is closer when:
V(t) < C(t)
Hence the inequality is:
170 + 110t < 149 + 95t
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at the local college, a study found that students earned an average of 9.2 credit hours per semester. a sample of 138 students was taken. what is the best point estimate for the average number of credit hours per semester for all students at the local college?
The average number of credit hours per semester for all students at the local college is 9.2.
It is given that,
at the local college a study sound that students earned an average of 9.2 credit hours per semester.
⇒ x = 9.2 credit hours per semester
Therefore by the central limit theorem,
x = μ = 9.2 credit hours per semester
The central limit theorem states that the distribution of a sample variable approximates a normal distribution as the sample size becomes larger, assuming that all samples are identical in size, and regardless of the population's actual distribution shape.
Therefore the average number is 9.2 credit hours per semester for all students at the local college.
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A carpet that' 3/8 in. I intalled over a pad that' 1/2 in. Thick. What i the combined thickne of the carpet and pad?
The combined thickness is 7/8 inches.
The installation over the pad indicates they are joined vertically. So, the combined thickness will be sum of individual thickness of carpet and pad. Hence, calculating the thickness now.
The thickness of the carpet and pad = thickness of carpet + thickness of pad
Keep the values in equation
The thickness of the carpet and pad = 3/8 + 1/2
Taking LCM on Right Hand Side, we get 8
Adding the fractions
The thickness of the carpet and pad = (3 + (1×4))/8
The thickness of the carpet and pad = (3 + 4)/8
The thickness of the carpet and pad = 7/8
Hence, the thickness of the carpet and pad is 7/8 inches.
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geometry( check the image)
The volume and the surface area of the right cylinder are equal to 175π cubic inches and 120π square inches.
What is surface area and volume of a right cylinder?One of the fundamental three-dimensional shapes in geometry is the cylinder, which has two distant, parallel circular bases. At a predetermined distance from the center, a curved surface connects the two circular bases. The axis of the cylinder is the line segment connecting the centers of two circular bases. The height of the cylinder is defined as the distance between the two circular bases.In order to determine the volume (V) in cubic inches and the surface area (A) in square inches of the solid, we must know the dimensions of a right cylinder, whose height (h) in inches and radius (r) in inches are shown in the figure. Below is a description of the formulas:
Here Volume of the cylinder,
V = π · r² · h
Surface area of the cylinder,
A = 2π · r² + 2π · r · h
If we know that r = 5 in and h = 7 in, then the volume and the surface area of the cylinder are, respectively:
Volume is,
V = π · ( 5 in )² · ( 7 in )
V = 175 π in³
Surface area is,
A = 2π · (5 in)² + 2π · (5 in) · (7 in)
A = 120π in²
Therefore volume and surface area of cylinder is 175 π in³ and 120π in².
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FILL IN THE BLANK. the quantitative relation between two amounts showing the number of times one value contains or is contained within the other definition. ___
Ratio is the relation between two amounts that shows the number of times one value contains within the other.
What is Ratio?
A ratio in mathematics illustrates how many times one number contains another. For example, if a dish of vegetables contains eight tomato and six carrots, the tomato-to-carrot ratio is eight to six (that is, 8:6, which is equivalent to the ratio 4:3). Similarly, the proportion of carrots to tomato is 6:8 (or 3:4), while the proportion of tomato to overall fruit is 8:14. (or 4:7). A ratio's numbers can be any quantity, such as a count of persons or things, or measures of lengths, weights, time, and so forth. In most situations, both numbers must be positive.
Solution:
Ratio is the relation between two amounts that shows the number of times one value contains within the other.
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help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Using the exponential function given y = 7.1(1.03)ˣ, the amount produced in 2006 was 7.8 billion pounds and the estimated amount in 2014 is 9.8 billion pounds
Exponential FunctionAn exponential function is a function of form f (x) = ax, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.
In the function given;
y = 7.1(1.03)ˣ
x = number of years after 2003a) What is the estimated number in 2006
We can find the value of x in 2006 as
2006 - 2003 = 3
x = 3
Let's substitute the values into the formula above;
y = 7.1(1.03)³
y = 7.76 ≅ 7.8 billion pounds
b)
The cheese produced in 2014
x = 2014 - 2003 = 11
Plug in the value
y = 7.1(1.03)¹¹
y = 9.83 ≅ 9.8 billion pounds
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The estimate of the total cheese production in 2006 is 7.8 billions of pounds.
The estimate of the total cheese production in 2014 is 9.8 billions of pounds.
How to solve exponential equation?[tex]y =7 .1( {1.03})^{x} [/tex]
Where,
The amount of cheese produced in billions of pounds = yThe number of years after 2003 = xCheese production is between 2003 and 2009The total cheese production in 2006;
x = 3 years
[tex]y =7 .1( {1.03})^{x} [/tex]
[tex]y =7 .1( {1.03})^{3} [/tex]
[tex]y =7 .1(1.092727)[/tex]
y = 7.7583617 billions of pounds
Approximately,
y = 7.8 billions of pounds
The total amount of cheese produced in 2014;
x = 11
[tex]y =7 .1( {1.03})^{x} [/tex]
[tex]y =7 .1( {1.03})^{11} [/tex]
[tex]y =7 .1(1.3842338707244)[/tex]
y = 9.8280604821435
y = 9.8 billions of pounds
In conclusion, the estimated production of cheese in 2006 and 2014 are 7.8 and 9.8 billions of pounds respectively.
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a rectangular sheet of metal with a perimeter of 4 meters will be rolled and formed into the lateral side of a cylindrical container. find the dimensions of the container with the maximum volume.
The container's dimensions and maximum volume are 4/3 and 2/3 when the lateral side of a cylindrical container will be formed from a rectangular sheet of metal with a perimeter of 4 meters.
Given that,
The lateral side of a cylindrical container will be formed from a rectangular sheet of metal with a perimeter of 4 meters.
We have to find identify the container's dimensions and maximum volume.
We know that,
2(x+y)=4
x+y=2
Now,
Volume is π(x/2)²y
=π(x²/4)(2-x)
=π(f(x))
Now, volume will be maximum when f(x) will be max,
f(x)=x²/4(2-x)
f'(x)=2x(2-x)-x²
f'(x)=4x-3x²
We get,
f'(x)=0
4x-3x²=0
x(4-3x)=0
x=0, 4-3x=0
x=4/3
y value is 2-4/3=6-4/3=2/3
Therefore, The container's dimensions and maximum volume are 4/3 and 2/3 when the lateral side of a cylindrical container will be formed from a rectangular sheet of metal with a perimeter of 4 meters.
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Please help me I am really not good with proofs and reasons.
It is proven that m∠LKG = 120°, and the corrected statement 6 is In a parallelogram opposite angles are equal i.e m∠JKG = m∠GHJ = 60°.
Parallelogram:A quadrilateral that has two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles that are additional to the transversal on the same side. 360 degrees is the sum of all interior angles.
Here we have proof of Parallelogram
To get correct statement 6 let's rewrite the whole process from the start
Given that GHIK is a parallelogram, m ∠GHJ = 60° and JKL is a line
Here we need to prove m∠LKG = 120°
Statement - Reason
1. GHIK is a parallelogram - Given
2. m ∠GHJ = 60° - Given
3. JKL is a line - Given
4. m ∠JKL = m∠LKG + m∠JKG - On line-segment, ∠JKL is equal to the
the sum of Non-overlapping parts
m∠LKG and m∠JKG
5. m ∠JKL = 180° - Angle formed by a straight line is 180°
6. 180°= m∠LKG + 60° - In a parallelogram opposite angles are
equal i.e m∠JKG = m∠GHJ = 60°
7. m∠JKG = m∠GHJ - Transitive/ Substitution
9. m∠LKG = 180° - 60°
10. m∠LKG = 120° - from statement 6
Therefore,
It is proven that m∠LKG = 120°, and the corrected statement 6 is In a parallelogram opposite angles are equal i.e m∠JKG = m∠GHJ = 60°.
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(05.02 MC)
The average ACT score follows a Normal distribution, with a mean of u = 21.1 and a standard deviation of a = 5.1. What is the probability that the mean ACT score of
50 randomly selected people will be more than 23?
A. 0
B. 0.9958
C. 0.3547
D. 0.0042
E. 1
Answer:
Step-by-step explanation:
The answer is D
The depth of a rain puddle D(t) is given in inches, and t is given in minutes. If the depth is changing with respect to time, which expression gives the rate of change at which the depth is changing at 5 minutes?
D(6) − D(4)
D′(5)
D″(6) − D″(4)
D″(5)
D'(5) is the expression that gives the rate of change at which the depth is changing at 5 minutes
How to determine which expression gives the rate of change at which the depth is changing at 5 minutes?A rate of change describes the rate at which one quantity changes in relation to another quantity.
Also, the derivative of a function can be found by determining the average rate of change of the function. Thus, these two terms are used interchangeably.
Given: The depth of a rain puddle D(t) is given in inches, and t is given in minutes.
The rate of change of D(t) is the derivative of D(t) which is written as D'(t).
Therefore, the expression that gives the rate of change at which the depth is changing at 5 minutes will be D'(5)
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Jason aldeen bought a house for $275,000. He made a down payment of 15%. The interest rate is 4. 2% for 15 years. Use the loan payment calculator to answer the following questions. (do not use commas or dollar signs in your answer) how much was jason's down payment?.
Jason's down payment is calculated to be 41250 if he bought the house for 275,000
Down payment is a term used to describe an initial payment made when something is bought on credit.
The original price of the house that Jason Aldeen bought is 275,000. Jason made a down payment of 15%. This means Jason Aldeen paid 15% of the original cost of the house. Therefore,
Jason's down payment is 15% of $275000
Down payment = 15% × 275,000
Down payment = 15/100 × 275000
Down payment = 0.15×275000
Down payment = 41250
Therefore; the down payment on the house bought by Jason Aldeen is calculated to be 41250
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(Pythagorean Theorem and the Coordinate Plane MC)
PLS HELP
Determine the length of the line segment shown.
graph of line segment from negative 6 comma negative 5 to 0 comma 3
100 units
25 units
10 units
8 units
10 units is the length of the line segment
How to determine the length of the line segment?
Given that: the graph of the line segment from negative 6 comma negative 5 to 0 comma 3. Thus:
point 1 (-6, -5) => x1 = -6, y1 = -5
point 2 (0, 3) => x2 = 0, y2 = 3
Length of x-axis (x): x2 -x1 = 0-(-6) = 6
Length of y-axis (y): y2 -y1 = 3-(-5) = 8
Let the length of the line segment be L
Using Pythagorean Theorem:
L² = x² + y²
L² = 6² + 8²
L² = 36 + 64
L² = 100
L = √100 = 10 units
Therefore, the length of the line segment is 10 units. The 3rd option is the answer
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If the given graphs are isomorphic, then identify the correct mapping (an isomorphism) between the sets of vertices of the two graphs.
a) f(u1) = v1, f(u2) = v2, f(u3) = v4, f(u4) = v5, and f(u5) = v3
b) f(u1) = v1, f(u2) = v2, f(u3) = v3, f(u4) = v4, and f(u5) = v5
c) The two graphs are not isomorphic.
d) f(u1) = v2, f(u2) = v4, f(u3) = v1, f(u4) = v5, and f(u5) = v3
The correct mapping (an isomorphism) between the sets of vertices of the two graphs is f(u1) = v1, f(u2) = v2, f(u3) = v4, f(u4) = v5, and f(u5) = v3
The two given graphs are isomorphic in nature
In the firsts graph, the serial order is u1, u2, u3, u4, u5
wherease in the second graph the order is v1, v2, v4, v5, v3
Upon analysis, it can be seen that the correct mapping (an isomorphism) between the sets of vertices of the two graphs is
f(u1) = v1, f(u2) = v2, f(u3) = v4, f(u4) = v5, and f(u5) = v3
Then the correct mapping (an isomorphism) between the sets of vertices of the two graphs is f(u1) = v1, f(u2) = v2, f(u3) = v4, f(u4) = v5, and f(u5) = v3.
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Work out the area of a rectangle with base, b = 30mm and perimeter, p = 70mm
one-way anova uses which statistic to test the hypothesis of equality of means across treatment groups or population for a completely randomized design? f-statistic z-statistic t-statistic
With a one-way ANOVA, you are comparing the T Statistic with the T critical value.
What is Z-test?
The Z test is a parametric procedure that is used on data that is dispersed in a normal fashion. For testing hypotheses, the z-test can be used on one sample, two samples, or proportions. When the population variance is known, it analyzes if the means of two big groups are dissimilar.
The critical value should be compared to the test statistic. The alternative hypothesis should be accepted in place of the null hypothesis if the test statistic is more extreme in the alternative's favor than the critical value. The null hypothesis should not be rejected if the test statistic is less extreme than the critical value.
Thus, with a one-way ANOVA, you are comparing the T Statistic with the T critical value.
The question is incomplete, the complete question is"
With a one-way ANOVA, you are comparing the _____ with the _____.
A. T Statistic with the T critical value
B. F Statistic with the F critical value
C. Correlation coefficient with the confidence interval
D. Outlier with the 4th quartile outer-most limit
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Use completing the square to solve for x in the equation (x minus 12) (x 4) = 9. x = –1 or 15 x = 1 or 7 x = 4 plus-or-minus startroot 41 endroot
By using completing the square method, the value of x in the given equation (x - 12)(x + 4) = 9 is: D. x - 4 = ±√73
The standard form of a quadratic equation.In Mathematics, the standard form of a quadratic equation is given by:
ax² + bx + c = 0.
In this exercise, you're required to determine the value of x in the given equation by using completing the square method. Therefore, we would expand the equation as follows:
(x - 12)(x + 4) = 9
x² - 8x - 48 = 9
Adding 48 to both sides of the equation, we have:
x² - 8x - 48 + 48 = 9 + 48
x² - 8x = 57
In order to complete the square, we would have to add (half the coefficient of the x-term)² to both sides of the quadratic equation as follows:
x² - 8x + (8/2)² = 19 + (8/2)²
x² - 8x + 16 = 57 + 16
x² - 8x + 16 = 73
Factorizing the quadratic equation, we have:
(x - 4)² = 73
Taking the square root of both sides of the quadratic equation, we have:
x - 4 = ±√73
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Complete Question:
Use completing the square to solve for x in the equation (x - 12)(x + 4) = 9.
A. x = -1 or 15
B. x = 1 or 7
C. x - 4 = ±√41.
D. x - 4 = ±√73
a radioactive substance has a decay rate of 1.7% per year. what is its half life? give your answer correct to 2 decimal places.
The half life for this radioactive substance is 40.76 years
As we know that radioactive decay is a first order reaction
For first order reaction, we can write
N = [tex]N^{0}[/tex][tex]e^{-kt}[/tex]
Where N = Amount of substance at time ‘t’
N0 = Initial amount of substance
K = rate constant for first order reaction
t = time in years
Now, as per the question,
This substance is decaying at a rate of 1.7% that means 98.3% will remain after decaying.
For time t = 1 years , N/[tex]N^{0}[/tex] = 0.983
Therefore, we have
N/[tex]N^{0}[/tex] = [tex]e^{-kt}[/tex]
0.983 = [tex]e^{-k }[/tex]
-k = ln(0.983)
-k = -0.017
K = 0.017 [tex]year^{-1}[/tex]
Now for half life, We can write N/[tex]N^{0}[/tex] = 0.5
Therefore, N/[tex]N^{0}[/tex] = [tex]e^{-kt}[/tex]
0.5 = [tex]e^{-0.017t}[/tex]
ln(0.5) = -0.017t
-0.693 = -0.017t
t = 0.693/0.017 = 40.76 years
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are the following statements true or false? and are matrices. ? 1. is diagonalizable if for some diagonal matrix and some invertible matrix . ? 2. is diagonalizable if and only if has eigenvalues, counting multiplicities. ? 3. if is diagonalizable, then is invertible. ? 4. if there exists a basis for consisting entirely of eigenvectors of , then is diagonalizable.
The solutions are,
1. True
2. False
3. True
4. False
For all the given statements the true or false are,
A, X and D are n X n matrices.
1. A is diagonalizable if A XDX⁻¹ for some diagonal matrix D and some invertible matrix X.
→ True
2. A is diagonalizable if and only if A has n eigenvalues, counting multiplicities.
→ False, It always has n eigenvalues, counting multiplicity.
3. If A is diagonalizable, then A is invertible.
→ True, In this case, we can construct a P which will be invertible. And a D.
4. If there exists a basis for R" consisting entirely of eigenvectors of A, then is diagonalizable.
→ False, It's invertible if it doesn't have zero an eigenvector but this doesn't affect diagonalizability.
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1/4 m + 9 = -16
pls help me find this !! appreciated
The value of m from the above expression is - 100
1/4 m + 9 = - 16 m/4 + 9 = - 16m/4 + 9/1 = 16/1finding LCM = 44(m/4) + 4(9/1) = 4(-16/1)m + 36 = - 64 subtract 36 m + 36 -36 = - 64 - 36m + 0 = - 64 - 36m = - 100
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In the given expression 1/4 m + 9 = -16, the m is equal to -100.
What is an algebraic expression?An algebraic expression is consists of variables, numbers with various mathematical operations,
The given expression is,
1/4 m + 9 = -16,
Simplify the expression to find the value of m,
1/4 m = -16 - 9
1/4 m = -25
m = -100
The value of m for the given expression 1/4 m + 9 = -16, is -100.
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Complete the quare to make a perfect quare trinomial. Then, write the reult a a binomial quared. Q^25/6q
We get the flawless quarte trinomial, finish the quadrilateral is (q+5/12)² we can say as a quadratic equation is q²+ 5/6q+---.
Given that,
The equation is q²+ 5/6q+---
We have to find to create a flawless quarte trinomial, finish the quadrilateral.
We know that,
Take the equation
q²+ 5/6q+---
By adding some thing we get the quadratic equation.
The missing term we add is 5/2×6
We get
q²+ 5/6q+(5/6×2)²
q²+ 5/6q+(5/12)²
We can write as
(q+5/12)²
Therefore, we get the flawless quarte trinomial, finish the quadrilateral is (q+5/12)² we can say as a quadratic equation is q²+ 5/6q+---.
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subtract the difference of 9 and 2 from f
Answer:
f-(9-2)
f-7
Step-by-step explanation:
What are the solutions to the equation W 2w 3 4?.
By using the cross multiplication, we can determine the solutions to the equation w=2 , w=6.
How is cross multiplication defined?By multiplying the numerator of one side by the denominator of other side and equating the resulting two products, cross multiplying can be used to solve a fractional equation when each side has a fraction with a single denominator.
Given the expression [tex]\frac{w}{2w-4} = \frac{4}{w}[/tex]
By using cross multiplication, we have
[tex]w^{2} = 4(2w-3)\\ w^{2} = 8w-12\\w^{2}-8w+12=0\\(w-2)(w-6)=0\\w=2 and w=6[/tex]
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If angle 1 = (2x+5) and angle 7 = (4x-17), find x
The value of x is 11
What is supplementary angle ?
Two angles are said to be supplementary if their sums total 180 degrees. A linear pair's two angles, like angles 1 and 2 in the illustration below, are always supplementary. But two angles don't have to be close to one another to be supplementary. In the following image, 3 and 4 are supplementary since their sums equal 180 degrees.
Angles ∠1 and ∠7 are alternate exterior angles where a transversal crosses parallel lines, so are congruent.
∠ 1 = ∠ 7
∴2x + 5 = 4x - 17
4x - 2x =17+5
2x = 22
x = [tex]\frac{22}{2}[/tex]
x = 11
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