Answer:
990 ft
Step-by-step explanation:
1 yard = 3 feet, using this we can multiply 140 by 3 to convert it from yards to feet.
140 yd * 3 = 420 ft.
Next, to find the perimeter we need to follow this formula:
l + l + w + w.
420 ft + 420 ft + 75 ft + 75 ft = 990 ft
The total distance that needs to be fenced in feet is;
990 ft.
Please solve this question, i have exams tommorow :(
Answer:
2xy/ ( ab)
Step-by-step explanation:
xy/ ( 3ab) + 5xy/(3ab)
Since the denominator is the same, we can add the numerators
xy+5xy = 6xy
6xy/ (3ab)
We can simplify 6/3 = 2
2xy/ ( ab)
Mathematics and body temperature? Please answer the questions in 3.
Answer:
keep the model answer photo
Aaden wants to get a subscription to an online library. There are two subscription options, one of which charges a fixed 96 dollar annual fee and the other which charges 3 dollars per book he borrows.
Here's a graph that shows a system of equations for this scenario where xxx is the number of books Aaden borrows and y is the total cost of the subscription.
What does point R represent in this context?
Choose 1 answer:
(Choice C, Checked, Correct)
CORRECT (SELECTED)
A number of books and their cost where both subscriptions cost the same
Using a system of equations, the meaning of point R is given as follows:
A number of books and their cost where both subscriptions cost the same.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable. In a graph, the solution to the system is the intersection point of the two equations.
In this problem, the point R is the point in which:
3y = 96.
That is, the point in which the prices are equal, hence:
A number of books and their cost where both subscriptions cost the same.
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fita operates her own lawn mowing business. A new customer will pay an initial start-up fee, plus a constant fee fro each time the customer would liek to have their lawn mowed. Customer A had his lawn mmowed 10 times and paid a total of $370. Customer B had her lawn mowed 7 times and paid a total of $265. What is the initial start-up fee for signing up with Rita's lawn mowing service?
The initial start-up fee for signing up with Rita's lawn mowing service is $20, using simultaneous equations.
What are simultaneous equations?Simultaneous equations are two or more algebraic equations that share variables like x and y and can be solved at the same time.
Data and Calculations:Let y = fixed cost (initial start-up cost)
Let x = variable cost per lawn mowing
Formation of Simultaneous Equations:Equation 1: Customer A = y + 10x = $370
Equation 2: Customer B = y + 7x = $265
Elimination Method:Subtract equation 2 from equation 1 to get:
3x = $105
x = $35
Substitute x in any of the two equations to find the value of y, thus:
Customer A:
y + 10($35) = $370
y + #350 = $370
y = $20 ($370 - $350)
Thus, the initial start-up fee for signing up with Rita's lawn mowing service is $20, using simultaneous equations.
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Find x and y, show steps
Answer:
(x, y) = (16/3, -1/9)
Step-by-step explanation:
A system of two linear equations can be solved a number of ways. One of the easiest is by graphing. Algebraic methods usually work better when the equations are in standard or general form.
GraphA graphing calculator can work with the given equations. The solution it shows in the first attachment is ...
(x, y) = (16/3, -1/9)
Algebraic methodAn algebraic method of solving a pair of linear equations can start with them in general form. We can obtain that form by subtracting one side of the equation from both sides. Here, we choose to do that so the coefficient of x is positive.
First equation
5(x -3y) -6 -(4x +1) = 0 . . . . . . . subtract (4x+1) from both sides
5x -15y -6 -4x -1 = 0 . . . . . . eliminate parentheses
x -15y -7 = 0 . . . . . . . . . . collect terms
Second equation
3(x +6y) +4 -(9y +19) = 0 . . . . . . subtract (9y+19) from both sides
3x +18y +4 -9y -19 = 0 . . . . . . eliminate parentheses
3x +9y -15 = 0 . . . . . . . . . . . collect terms
x +3y -5 = 0 . . . . . . . . . . . remove common factor of 3
We notice the coefficients of x and y are related by convenient factors, so we can use the "elimination method" to solve these equations. Subtracting the first from the second, we get ...
(x +3y -5) -(x -15y -7) = 0 -0
18y +2 = 0 . . . . . . collect terms
y +1/9 = 0 . . . . . . . divide by 18, reduce the fraction
y = -1/9
Using this in the second equation, we have ...
x +3(-1/9) -5 = 0
x = 5 1/3
The solution to the system of equations is (x, y) = (5 1/3, -1/9).
how to find z scores
The formula for calculating a z-score is is z = (x-μ)/σ, where x is the raw score, μ is the population mean, and σ is the population standard deviation
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There was 320 hamburgers and cheeseburgers sold combined there were three times the cheeseburgers sold as hamburgers how many hamburgers were sold
Answer:
240
Step-by-step explanation:
h+c=320
c=3h ( since 3 times the cheeseburger)
Now plug in 3h for C
h+3h=320 = 4h=320
Now divide 320 by 4 to get "h" alone
h=80
now plug 80 back t the eqation of c=3h
so now it is...
c=3 x 80
which is 240
so ur andswer is 240
The owner of Brookstone coffee has 13 regular full-time employees. 7 are female and 6 are male. As he plans the schedule, he likes to ensure exactly two employees on any given shift are male. If 5 work a shift, how many combinations can be created?
Using the combination formula, it is found that 525 combinations can be created.
The order in which the employees are chosen is not important, hence the combination formula is used to solve this question.
What is the combination formula?[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this problem:
3 female employees are chosen from a set of 7.2 male employees are chosen from a set of 6.Then the number of combinations is given by:
[tex]n = C_{7,3}C_{6,2} = \frac{7!}{3!4!} \times \frac{6!}{2!4!} = 525[/tex]
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A particle moves along line segments from the origin to the points (3, 0, 0), (3, 5, 1), (0, 5, 1), and back to the origin under the influence of the force field F(x, y, z) = z2i + 5xyj + 2y2k. Find the work done.
Parameterize each line segment from [tex](x_0,y_0,z_0)[/tex] to [tex](x_1,y_1,z_1)[/tex] by
[tex]\vec r(t) = (1-t) (x_0\,\vec\imath + y_0\,\vec\jmath + z_0\,\vec k) + t (x_1\,\vec\imath + y_1\,\vec\jmath + z_1\,\vec k[/tex]
with [tex]0\le t\le1[/tex]. The work done by [tex]\vec F[/tex] on the particle along each segment is given the line integral of [tex]\vec F[/tex] with respect to that segment,
[tex]\displaystyle \int_{C_i} \vec F \cdot d\vec r = \int_0^1 \vec F(\vec r_i(t)) \cdot \dfrac{d\vec r_i(t)}{dt} \, dt[/tex]
• (3, 0, 0) to (3, 5, 1)
[tex]\vec r_1(t) = 3\,\vec\imath + 5t\,\vec\jmath + t\,\vec k[/tex]
[tex]W_1 = \displaystyle \int_0^1 \left(t^2\,\vec\imath + 75t\,\vec\jmath + 50t^2\,\vec k\right) \cdot \left(5\,\vec\jmath + \vec k\right) \, dt \\\\ ~~~~~~~~ = \int_0^1 (375t + 50t^2) \, dt = \frac{1225}6[/tex]
• (3, 5, 1) to (0, 5, 1)
[tex]\vec r_2(t) = 3(1-t)\,\vec\imath + 5(1-t)\,\vec\jmath + \vec k[/tex]
[tex]W_2 = \displaystyle \int_0^1 \left(\vec\imath + 75(1-t)\,\vec\jmath + 50 \,\vec k\right) \cdot \left(-3\,\vec\imath - 5\,\vec\jmath\right) \, dt \\\\ ~~~~~~~~ = -3 \int_0^1 \,dt = -3[/tex]
• (0, 5, 1) to (0, 0, 0)
[tex]\vec r_3(t) = 5(1-t)\,\vec\jmath + (1-t)\,\vec k[/tex]
[tex]W_3 = \displaystyle \int_0^1 \left((1-t)^2\,\vec\imath + 50(1-t)^2\,\vec k\right) \cdot \left(-5\,\vec\jmath - \vec k\right) \, dt \\\\ ~~~~~~~~ = \int_0^1 (-50 + 100t - 50t^2) \, dt = -\frac{50}3[/tex]
Then the total work done by [tex]\vec F[/tex] on the particle is
[tex]W = W_1 + W_2 + W_3 = \boxed{\dfrac{369}2}[/tex]
how many solutions are there to the system 8x=12y-9 and 27y+18x=21?
There is one solution in the system of equation
How to determine the number of solutions?The system of equations is given as:
8x=12y-9 and 27y+18x=21
Divide 8x=12y-9 by 8
x = 1/8(12y-9)
Substitute x=1/8(12y-9) in 27y+18x=21
27y + 18 * 1/8(12y-9) =21
Expand
27y + 27y - 20.25 =21
Evaluate the like terms
54y = 41.25
Divide by 54
y = 0.7639
Hence, there is one solution in the system of equation
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You go to the shops on Monday and buy 1 apple, 1 banana, and 1 carrot; the whole transaction totals €15. On Tuesday you buy 3 apples, 2 bananas, 1 carrot, all for €28. Then on Wednesday 2 apples, 1 banana, 2 carrots, for €23.
Your question is incomplete. Please find the missing content below
You go to the shops on Monday and buy 1 apple, 1 banana, and 1 carrot; the whole transaction totals €15. On Tuesday you buy 3 apples, 2 bananas, 1 carrot, all for €28. Then on Wednesday 2 apples, 1 banana, 2 carrots, for €23.
Construct a matrix and vector for this linear algebra system.
Matrix is A = [ [ A₁₁ , A₁₂ , A₁₃]
[ A₂₁ , A₂₂ , A₂₃]
[ A₃₁ , A₃₂ , A₃₃] ]
Vector S = [sMon , sTue , sWed]
(i) consider A as fruits
A₁₁ = 1
A₁₂ = 1
A₁₃ = 1
A₂₁ = 3
A₂₂ = 2
A₂₃ = 1
A₃₁ = 2
A₃₂ = 1
A₃₃ = 2
(ii) Consider s as days
sMon = 15
sTue = 28
sWed = 23
Hence the matrix and vector is: A = [ [ A₁₁ , A₁₂ , A₁₃]
[ A₂₁ , A₂₂ , A₂₃]
[ A₃₁ , A₃₂ , A₃₃] ]
Vector S = [sMon , sTue , sWed]
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Marcelina uses a blend of white corn and yellow corn to make tortilla chips at her restaurant. She needs to buy 50\,\text{kg}50kg50, start text, k, g, end text of corn in total for her next order. White corn costs \$0.30$0.30dollar sign, 0, point, 30 per kilogram, yellow corn costs \$0.15$0.15dollar sign, 0, point, 15 per kilogram, and she wants to spend \$12$12dollar sign, 12 total.
What does point EEE represent in this context?
Answer:
CORRECT (SELECTED)
Marcelina spends the intended amount of money and buys the intended amount of corn.
Point EEE is on line aaa, so it represents a scenario where she spends \$12$12dollar sign, 12. Also, point EEE is on line bbb, so it represents a scenario where she buys 50\,\text{kg}50kg50, start text, k, g, end text of corn.
The point EEE represent option b is correct: Marcelina spends the intended amount of money but she bought more than she did intended amount of corn.
What is the case about?She buy 50kg of corn in total
White corn costs = $0.30 per kilogram,
Yellow corn costs = $0.15 per kilogram,
She wants to spend $12 total.
So the equation will be:
C= (20, 50) = 20 white, 50 yellow
But 30 while and 20 yellow is needed.
Since C = 20 +50
= 70 corns
While: 30 + 20
= 50 corns.
This therefore tells that Marcelina spends the intended amount of money but she bought more than she did intended amount of corn and therefore, option b is correct.
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Answer:
Marcelina spends less than the intended amount of money and buys less than enough corn.
Step-by-step explanation:
The equation of line
Khan
Please help, multiple choice question
Select the correct inequality for the graph below:
y > −2x + 2
y ≥ −2x + 2
y < −2x + 2
y ≤ −2x + 2
The correct answer is option D which is y ≤ −2x + 2.
What is inequality?The relation between two expressions that are not equal, employing a sign such as ≠ ‘not equal to’, > ‘greater than, or < ‘less than.
When we draw the graphs we will see that the inequality y ≤ −2x + 2 is showing the same graph. It is cutting the y-axis at (0,2) and the x-axis at (2,0).
Therefore the correct answer is option D which is y ≤ −2x + 2.
The graph is attached with the answer below.
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A cannonball is shot horizontally off a
10.5 m high castle wall at 47.4 m/s. How
far from the base of the wall does the
cannonball land?
The computation shows that the distance from the base of the wall that the cannonball land will be 132.2m
How to calculate the value?The peak height equation will be illustrated as:
v²sinx = 2h
(47.4)²x = 2(9.81)(10.5)
Divide to get the value of x
x = 17.63°
Therefore, the distance will be:
d ° (47.4)² × 2(17.63) / 9.81
= 132.2m
Therefore the distance is 132.2m.
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Answer:
its 69.8
Step-by-step explanation:
How many characteristics of a population does a random variable represent?
1. As many as you wish
2. Single
3. Less than one
4. Two or more
The characteristics of a population that a random variable represents are 1. As many as you wish and 4. Two or more.
What is a random variable?A random variable is a variable with unknown outcomes.
A random variable can have either discrete or continuous values.
It is discrete when it has specific values. It is continuous when it assumes some continuous values.
Thus, the characteristics of a population that a random variable represents are 1. As many as you wish and 4. Two or more.
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A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 50 and 52 minutes. Find the probability that a given class period runs between 51.5and 51.75 minutes.
The required probability of giving class period run between 51.5 and 51.75 is 0.125.
The lengths of her classes are uniformly distributed between 50 and 52 minutes.
What is the probability?
Probability, can be define as the ratio of favorable events to the n number of total events.
since,
[tex]p(r) = \frac{51.75-51.5}{52-50}[/tex]
p(r) = 0.125
Thus, the required probability of class period runs between 51.5 and 51.75 is given by 0.125
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Find x. please pleaseeeee help
Answer: [tex]35^{\circ}[/tex]
Step-by-step explanation:
The labeled angle is [tex]100^{\circ}[/tex] by the alternate interior angles theorem.
Thus, as angles in a triangle add to [tex]180^{\circ}[/tex], [tex]x=35^{\circ}[/tex]
117 Mr. Turtle, Mrs. Squirrel and Ms. Pigeon work at the Magic Forest's post office. Mr. Turtle can
deliver a package from the Southern Glade to the Northern Glade in 3 days, while Ms. Pigeon can
deliver it in 30 minutes. How much time will the same job take Mrs. Squirrel, if the ratio of Mr.
Turtle's time to the Mrs. Squirrel's time is the same as the ratio of Mrs. Squirrel's time to Ms.
Pigeon's time?
Using proportions, it is found that the same job will take Mrs. Squirrel 6 hours.
What is a proportion?
A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The times are given as follows:
Mrs. Squirrel: x.Mr. Turtle: 3 days.Mr. Pigeon: 30 minutes = Half an hour = 1/48 day.The ratios are as follows:
Turtle/Squirrel = Squirrel/Pigeon.
Hence:
[tex]\frac{3}{x} = \frac{x}{\frac{1}{48}}[/tex]
[tex]x^2 = \frac{3}{48}[/tex]
[tex]x^2 = \frac{1}{16}[/tex]
[tex]x = \sqrt{\frac{1}{16}}[/tex]
x = 1/4.
It takes 1/4 of a day for Mrs. Squirrel to do the job, hence 1/4 x 24 hours = 6 hours.
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Rewrite 32/35 and 9/10
The question was incorrect. Please find the correct content below.
Compare 32/35 and 9/10.
Comparing 32/35 and 9/10 we have 32/35 is greater than 9/10, that is 32/35 > 9/10.
Fraction is the ratio of two numbers. The upper number is called Numerator and the Lower number is called the Denominator.
We know that if the denominators are the same for two fractions then which has the greatest numerator is a greater fraction than the other.
Given the fractions are 32/35, 9/10
To compare this two fractions we have to make denominators equal first.
LCM of 10,35 = 70
Calculating the fractions,
32/35 = (32*2)/(35*2) = 64/70
9/10 = (9*7)/(10*7) = 63/70
Since 64 > 63
So 64/70 > 63/70
Therefore, 32/35 > 9/10
Hence fraction 32/35 is greater than the other fraction 9/10.
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Question 1. Chose the quadrilaterals that have the following property! * 1 point This geometry shape has 4 sides. Quadrilateral Square Rhombus Triangle Kite Circle
Answer:
quadrilateral
Step-by-step explanation:
A 4-sided polygon is a quadrilateral.
Use any convenient method to solve the following system of equations. If the system is dependent, express the solution set in terms of one of the variables. Leave all fractional answers in fraction form.
2x−2y+6z=163x+3y−4z=−5x−y+3z=9
For a solution to be the solution to a system, it must satisfy all the equations of that system. There exists no solution for the system of equations.
What is a solution to a system of equations?For a solution to be the solution to a system, it must satisfy all the equations of that system, and as all points satisfying an equation are in their graphs, so solution to a system is the intersection of all its equation at a single point(as we need a common point, which is going to be the intersection of course)(this can be one or many, or sometimes none)
For the three equations,
2x−2y+6z=16
3x+3y−4z=−5
x−y+3z=9
Solve the first equation for x,
2x−2y+6z=16
x = 8 + y - 3z
Now substitute the value of x in both the equations, if the two equations are satisfied, then the equation will have a solution, if it's not then no solution exists.
[tex]3\left(8+y-3z\right)+3y-4z=-5\\6y-13z+24=-5\\\\\\ 8+y-3z-y+3z=9\\ 8=9[/tex]
Hence, There exists no solution for the system of equations.
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Find a degree 3 polynomial having zeros -4, 3 and 8 and the coefficient of x 3 equal 1.
The required polynomial is [tex]x^{3}-7x^{2} -20x+96[/tex]
Polynomial : If in an expression all of variables, constants and exponents are present with mathematical operations like addition, multiplication, subtraction & division, then it is called polynomial.
If a polynomial has degree 3 as a highest degree, then the polynomial is called degree 3 polynomial or cubic polynomial.
A degree 3 polynomial having zeros α, β, γ and the coefficient of x³ equal a is, a(x- α)(x- β)(x- γ)
Given, Zeros of the polynomial are -4, 3, 8 & coefficient of x³ equal 1.
Hence, the required polynomial is,
[tex]1(x-(-4))(x-3)(x-8)[/tex]
[tex](x+4)(x-3)(x-8)[/tex]
[tex]=(x+4)(x^{2} -11x+24)[/tex]
[tex]=x^{3}-11x^{2} +24x+4x^{2} -44x+96[/tex]
[tex]=x^{3}-7x^{2} -20x+96[/tex]
This is a degree 3 polynomial.
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PLEASE HELP ME WITH THIS MATH PROBLEM
m∠ A = 60°, m∠ A = 60°, m∠ A = 60° and the sum of the angles in the triangle is 180°
How to determine the angles
It is important to note that the sum of angles in a triangle equals 180°
The given structure is a triangle, thus, the angles sum up to 180°
m ∠ A + m ∠ B + m ∠ C = 180°
m∠ A = 60°
m ∠ B = 60°
m ∠ C = 60°
The sum of the angle in the triangle = 60° + 60° + 60° = 180°
Thus, m∠ A = 60°, m∠ A = 60°, m∠ A = 60° and the sum of the angles in the triangle is 180°
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the equation that models the problem is 3.95m+8.95b=47.65, where m is the number of magazines and b is the number of books
Based on the calculations, the number of books that were bought by Hugh are 4 books.
How to calculate the number of books?In order to determine the number of books that were bought by Hugh, we would substitute the value of the number of magazines into the given equation and then evaluate as follows:
3.95m + 8.95b = 47.65
3.95(3) + 8.95b = 47.65
11.85 + 8.95b = 47.65
8.95b = 47.65 - 11.85
8.95b = 35.8
b = 35.8/8.95
b = 4.
In conclusion, the number of books that were bought by Hugh are 4 books.
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Complete Question:
Hugh bought some magazines that cost $3.95 each and some books that cost $8.95 each. He spent a total of $47.65. If Hugh bought 3 magazines, how many books did he buy? The equation that models the problem is 3.95m + 8.95b = 47.65, where m is the number of magazines and b is the number of books.
20-26 JIT production, relevant benefits, relevant costs. The Knot manufactures men's neckware at its Spartanburg plant. The Knot is considering implementing a JIT production system. The following are estimated costs and benefits of JIT production: a. Annual additional tooling costs $250,000 annually. b. Average inventory would decline by 80% from the current level of $1,000,000. c. Insurance, space, materials-handling, and setup costs, which currently total $400,000 annually, would decline by 20%. d. The emphasis on quality inherent in JIT production would reduce rework costs by 25%. The Knot currently incurs $160,000 in annual rework costs. e. Improved product quality under JIT would enable The Knot to raise the price of its product by $2 per unit. The Knot sells 100,000 units per year. The Knot's required rate of return on inventory investment is 15% per year. 1. Calculate the net benefit or cost to The Knot if it adopts JIT production at the Spartanburg plant. 2. What nonfinancial and qualatative factors should The Knot consifer when making the decision to adopt JIT production? 3. Suppose The Knot implements JIT production at its Spartanburg plant. Give examples of performance measure The Knot could use to evaluate and control JIT production. What would the benefit of The Knot implementing an enterprise resource planning (ERP) system?
The net benefit to The Knot if it adopts JIT production at the Spartanburg plant is $200000.
How to illustrate the information?Based on the information given, the net benefit will be:
= $1,000,000 × (1 - 80%)
= $1,000,000 × 0.2
= $200,000
The nonfinancial and qualatative factors that The Knot should consider when making the decision to adopt JIT production are:
Development of a detailed system.Willingness of suppliers to deliver smaller and more frequent orders. Skill level of workers should be enhanced.The benefit of The Knot implementing an enterprise resource planning (ERP) system is that it gives access to operating information in response to the supply.
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6:
Dana's phone has zero battery. After charging her phone for 1 minute, it has
2% battery. After 2 minutes, her phone has 6% battery. Based on this, predict
the number of minutes it will take for Dana to charge her phone's battery so
that it has 50% power and 90%power
Step-by-step explanation:
charging the phone for 1 minute ,it has 2%
i.e,1----->2
After 2 minutes from that time ,i.e total 3 minutes
it has 6% charge
i.e,3--------->6
from the both the above cases ,1 minute provide 2%=6/3
=2
Hence,
for getting 50%charge=50/2
=25 min
and,for 90 %charge=90\2
=45 min
Find the component of the set given
Answer:
{-3, 3, 4, 5, 6}
Step-by-step explanation:
The complement of a set is the set of all elements in the universe that are not in the given set.
Universal setThe set U is defined as ...
U = { x | x ∈ and -3 ≤ x ≤ 6 }
In roster form, this is ...
U = {-3, -2, -1, 0, 1, 2, 3, 4, 5, 6}
Given setThe given set is defined as ...
S = { x | x ∈ and -2 ≤ x < 3 }
In roster form, this set is ...
S = {-2, -1, 0, 1, 2} . . . . . note that 3 is not in set S
ComplementIf we remove the elements of set S from set U, we have ...
S' = {-3, 3, 4, 5, 6}
calculate the number of ways that the coach can assign the 4 positions to his 16 players.
The number of ways that the coach can assign the 4 positions to his 16 players would be 43, 680 ways
How to calculate the permutation
The formula for permutation is given as;
Permutation = [tex]\frac{n!}{(n - r)!}[/tex]
n = 16
r =4
Permutation = [tex]\frac{16!}{12!}[/tex]
Permutation = [tex]\frac{16 *15*14*13*12*11*10*9*8*7*6*5*4*3*2*1}{12*11*10*9*8*7*6*5*4*3*2*1}[/tex]
Permutation = 43, 680 ways
Thus, the number of ways that the coach can assign the 4 positions to his 16 players would be 43, 680 ways
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z-4/4+8= z + 9, z - 3, z - 7, z + 7
The values of the expressions are -17/3, -29/3 and 13/3
How to solve the expressions?The equation is given as:
z-4/4+8= z + 9
Rewrite properly as
[tex]\frac{z-4}{4}+8= z + 9[/tex]
Subtract 8 from both sides
[tex]\frac{z-4}{4}= z + 1[/tex]
Multiply through by 4
z - 4 = 4z + 4
Evaluate the like terms
3z = -8
Divide by 3
z = -8/3
Substitute z = -8/3 in z - 3, z - 7 and z + 7
z - 3 = -8/3 - 3 = -17/3
z - 7 = -8/3 - 7 = -29/3
z + 7 = -8/3 + 7 = 13/3
Hence, the values of the expressions are -17/3, -29/3 and 13/3
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Determine the length of CD. Show your work.
The length of line CD is 20. 9
How to determine the lengthNote that triangle CDY is an isosceles triangle
Using the Pythagoras theorem
Hypotenuse square = opposite square + adjacent square
Hypotenuse = line CD
opposite = 20
Adjacent = 6
Substitute into equation
[tex]Line CD^2 = 20^2 + 6^2[/tex]
[tex]Line CD^2 = 400 + 36[/tex]
[tex]Line CD^2 = 436[/tex]
Make line CD^2 subject by find the square root of the other side
[tex]Line CD = \sqrt{436}[/tex]
[tex]Line CD = 20.9[/tex]
Therefore, the length of line CD is 20. 9
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