Answers
The first five terms of the given sequence are a₁ = 50, a₂ = 25, a₃ = 12.5, a₄ = 6.25 and a₅ = 3.125.
What is a geometric sequence?In a geometric sequence the ratio of any two consecutive terms are equal. This ratio is known as the common ratio of the sequence.
Given that,
a₁ = 50 and aₙ = aₙ₋₁ ÷ 2
The first five terms are a₁, a₂, a₃, a₄ and a₅.
All the terms can be written using aₙ = aₙ₋₁ ÷ 2 as follows,
a₂ = a₁ ÷ 2
⇒ a₂ = 50 ÷ 2
⇒ a₂ = 25
a₃ = a₂ ÷ 2
⇒ a₃ = 25 ÷ 2
⇒ a₃ = 12.5
a₄ = a₃ ÷ 2
⇒ a₄ = 12.5 ÷ 2
⇒ a₄ = 6.25
a₅ = a₄ ÷ 2
⇒ a₅ = 6.25 ÷ 2
⇒ a₅ = 3.125
Hence, the first five terms are 50, 25, 12.5, 6.25 and 3.125 respectively.
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Related Questions
CARPENTRY A carpenter is building a podium. The side panel of the podium is cut from a rectangular piece of wood. The rectangle must be
sawed along the dashed line in the figure.
Answers
The measure of angle1 in the given rectangular figure is 64° .
In the question ,
it is given that ,
the one of the angle is 116° .
From the figure below ,
we can see that
the dashed line is a transversal to AB and CD ,
the angles on the line AB form a linear pair ,
So , angle2 + 116° = 180°
angle2 = 180° - 116°
angle2 = 64°
Since the side panel of the podium is cut from rectangular piece
the figure is representing two parallel lines , cut by the transversal .
By the property of transversal that alternate interior angles are equal in measure ,
angle 1 = angle 2
hence , angle 1 = 64° .
Therefore , The measure of angle1 in the given rectangular figure is 64° .
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Write the ratio as a fraction in simplest form, with whole numbers in the numerator and denominator.
32 kg to 56 kg
Answers
Answer:
4/7
Step-by-step explanation:
32:56
32÷2=16
56÷2=28
16:28
16÷2=8
28÷2=14
8:14
8÷2=4
14÷2=7
4:7
32:56 ~ 32/56
=4/7
please help me with this problem.
Answers
Answer:
(- 25, 5 )
Step-by-step explanation:
- 3x - 6y = 45 → (1)
- 5y = x → (2)
substitute x = - 5y into (1)
- 3(- 5y) - 6y = 45
15y - 6y = 45
9y = 45 ( divide both sides by 9 )
y = 5
substitute y = 5 into (2)
- 5(5) = x , then
x = - 25
solution is (- 25, 5 )
mr. bray prepares a list of 434343 us presidents, 888 of whom died in office. then 181818 of his students each select a president at random (there can be repeats) for their creative writing assignments. what is the probability that at least one of the students select a president who died in office? round your answer to the nearest hundredth.
Answers
There is a 0.97541 or 97.541% probability that at least one student will choose a president who passed away in office.
Take into account the details offered.
43 US presidents are listed by Mr. Bray, 8 of them passed away while in office.
Consequently, p= 8/43.
If 8 of the 43 presidents died while in office, then 43-8=35 presidents survived.
q= 35/43
Let X represent how many presidents have passed away while in office.
The probaility that at least one student will choose a president who passed away in office is:
P(X[tex]\geq[/tex]1 ) = 1 -P(X=0)
P(X[tex]\geq[/tex]1 ) = 1 -¹⁸c₀(8/43)⁰(35/43)¹⁸
By using Combinations Formula,
By solving we get,
P(X[tex]\geq[/tex]1 ) = 0.97541
As a result, there is a 0.97541 or 97.541% chance that at least one student will choose a president who passed away in office.
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Determine if the given sequence is an arithmetic sequence. If it is, identify the common difference.
5, 4, 3, 2, ...
Is this an arithmetic sequence?
Ο No
O Yes
Select the correct choice and fill in any answer boxes in your choice below.
O A. The common difference is
O B. There is no common difference.
Answers
Answer:
Is this an arithmetic sequence?
Yes.
Is there a common difference and if so, what is it?
Yes, there is a common difference : 1
The common difference is 1
How much of a radioactive kind of promethium will be left after 265 hours if the half-life is 53
hours and you start with 15,488 grams?
grams
Answers
265 hours and half life is 53 so 265/53=5, so you half 15488 5 times which gives you 484.
Ms. Galindo’s class has adopted two equal sections of a highway to keep clean. The combined length of the two sections is
6/8
of a mile. How long is each section?
Answers
Each section of a highway has length of 1.5 miles.
In this question, Ms. Galindo’s class has adopted two equal sections of a highway to keep clean.
We need to find the length of each section.
Let each section measures x mile.
The combined length of the two sections is 6/8 of a mile.
So, we get an equation x + x = 6/8
We solve above equation to find the value of x.
2x = 6/8
x = (6/8) / 2
x = 6/4
x = 1.5
Therefore, each section of a highway has length of 1.5 miles.
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the probability that jacie will eat cheese on any given day is 0.6 while the probability that robyn will eat cheese on any given day is 0.25. if these events are independent, what is the probability that jacie or robyn will eat cheese on a randomly selected day?
Answers
The probability for Jacie or Robyn would consume cheese on a random day is 0.15.
What is defined as the independent events?Two occurrences are considered independent if indeed the occurrence of one does not alter the likelihood of the occurrence of the other. The mathematical expression of event independence A and B is the chance of both A and B occurring being equal to the sum of both the probabilities of both B and A (i.e., P) (A and B).The likelihood of Jacie eating cheese on any particular day is 0.6.
The likelihood of Robyn eating cheese on any particular day is 0.25.
Both events are independent.
As a result, the probability for Jacie or Robyn would consume cheese on a random day is;
P(Jacie or Robyn) = P(Jacie). P(Robyn)
P(Jacie or Robyn) = 0.6 x 0.25
P(Jacie or Robyn) = 0.15
Thus, the probability for Jacie or Robyn would consume cheese on a random day is 0.15.
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A bakery sells 4 dozen cupcakes every 3 hours. If the bakery is open 8 hours each day, how many days does it take to sell 640 cupcakes?
Answers
5 days does it take to sell 640 cupcakes.
Given:
A bakery sells 4 dozen cupcakes every 3 hours.
If the bakery is open 8 hours each day.
4 dozen cupcakes = 4*12 cupcakes
= 48 cupcakes
48 cupcakes = 3 hours
divide by 3 on both sides
3hours/3 = 48/3 cupcakes
1 hour = 16 cupcakes
Number of cupcakes for 8 hours = 8 * 16 = 128 cupcakes.
128 cupcakes sells in one day.
To sell 640 cupcakes = 640/128
= 5 days.
Therefore 5 days does it take to sell 640 cupcakes.
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bruce bought two books.one book costs $4 more than three times than the other.they both equal 72$
Answers
Bruce paid $17 and $55 respectively for each of the books
How to determine the cost of each book?From the question, we have the following statements:
Number of books = 2One book = $4 more than three times the other.Both books = 72$Represent the books with the variables x and y
So, we have the following equations
x = 4 + 3y
x + y = 72
To start with;
We can substitute 4 + 3y for x in the equation x + y = 72
So, we have the following representation
4 + 3y + y = 72
Evaluate the like terms
4 + 4y = 72
Collect the like terms in the above equation
So, we have the following equation
4y = 72 - 4
Evaluate the like terms
4y = 68
Divide both sides by 4
So, we have
y = 17
Recall that x = 4 + 3y
Substitute 17 for y in the equation x = 4 + 3y
x = 4 + 3 * 17
Evaluate the products
x = 4 + 51
Evaluate the sum
This gives
x = 55
Hence, the cost of the books are $17 and $55
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Possible question
Bruce bought two books, one book costs $4 more than three times than the other. They both equal $72.
What is the cost of each book
Sandra Williams bought a home with a 10.25% adjustable rate mortgage for 25 years. She paid $9.27 monthly per thousand on her original loan. At the end of 3 years she owes the bank $50,000. Since then, interest rates have increased to 12.75%. The bank will renew the mortgage at this rate, or Sandra can pay the bank $50,000. She decides to renew and will now pay $11.10 monthly per thousand on her loan. (You can ignore the small amount of principal paid during the 3 years.)
The old monthly payment is $
.
The new monthly payment is $
.
The percent increase in her monthly payment (to the nearest tenth) is
%.
Answers
The old monthly payment was = 9.27 x 50 = 463.5
The new monthly payment is = 11.10 x 50 = 555
The percent increase in his monthly payment is 1.947%
Given,
Sandra Williams bought a home with a 10.25% adjustable rate mortgage for 25 years. She paid $9.27 monthly per thousand on his original loan
According to the question:
So, per thousand value of $65000 is 50000/1000 =50
Now, the old monthly payment was = 9.27 x 50 = 463.5
She decides to renew and will now pay $11.10 monthly per thousand on his loan.
So, the new monthly payment is = 11.10 x 50 = 555
The percent increase in his monthly payment is= 11.10 /9.27 - 1 x 100
19.7411 % and to nearest tenth it is 1.947%
Hence, the old monthly payment was = 9.27 x 50 = 463.5
the new monthly payment is = 11.10 x 50 = 555
The percent increase in his monthly payment is 1.947%
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line that passes through the point (8,−3) and has a slope of 1/4
Answers
The equation of line having a slope of 1/4 which passes through point (8,-3) is y = (1/4)x - 5.
What is the equation of line with the given point and slope?The equation of line is expressed as;
y = mx + b
Where m is slope and b is y-intercept.
Given the data in the question;
Point (8, -3 )
x = 8y = -3Slope m = 1/4Determine the y-intercept 'b'.
Substitute the point and slope into the equation of line formula and solve for b.
y = mx + b
-3 = (1/4)(8) + b
-3 = 8/4 + b
-3 = 2 + b
b = -3 - 2
b = -5
Now, substitute slope and y-intercept into y = mx + b to determine the equation of the line.
y = mx + b
y = (1/4)x + (-5)
y = (1/4)x - 5
Therefore, the equation of the line is y = (1/4)x - 5.
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Write the equation of a line in point slope form that has a slope of 2 and passes through the point (-2,5)
Answers
Answer:
y=2x+9
Step-by-step explanation:
Fill in the equation
5=2(-2)+b
Solve for b
5 = -4+b
9 = b
Put the original equation
y=2x+9
Explanation:
m=2
y=5
x=-2
y=mx+b
5=2(-2)+b
b=9
Eli is following this recipe to bake bread rolls.
He uses 900 g of flour.
How much of the other ingredients does he use?
Recipe: Makes 12 bread rolls
600 g flour
12 g salt
9 g yeast
45 ml oil
360 ml water
g salt
0
g yeast
0
ml oil
0
ml water
Answers
Answer:
1022
Step-by-step explanation:
360+600+12+45+9=1022
Graph the function f(x)=−14x−2.
Use the line tool and select two points to graph.
Answers
The slope is negative so the function is decreasing.
Let’s find the intersection points of the function:
0=-14x-2
14x=-2
X≈-0.142
(-0.142,0)
Y=-14*0-2
Y=2
(0,2)
Here is the answer:
Rich is attending a 4-year college. As a freshman, he was approved for a 10-year, federal unsubsidized student loan in the amount of $7,900 at 4.29%. He knows he
has the option of beginning repayment of the loan in 4.5 years. He also knows that during this non-payment time, interest will accrue at 4.29%.
If Rich decides to make no payments during the 4.5 years, the interest will be capitalized at the end of that period.
a. What will the new principal be when he begins making loan payments?
b. How much interest will he pay over the life of the loan?
Answers
a) The new principal (principal + capitalized interest) when Rich begins making loan payments will be $9,425.10.
b) The total interest that Rich will pay over the life of the loan is $4,914.20.
How is interest on student loans determined?The interest on student loans is based on simple interest.
The only interest capitalized is the interest during the non-payment period if the student does not pay the interest.
Some students elect to pay the interest during the non-payment period to reduce the capitalized interest and principal during the payment period.
Capitalization refers to the addition of interest to the principal amount.
Period of student loan = 10 years
The amount of the federal unsubsidized student loan = $7,900
Interest rate = 4.29%
Capitalized interest during the non-payment time = $1,525.10 ($7,900 x 4.29% x 4.5)
New principal when Rich begins making loan payments = $9,425.10 ($7,900 + $1,525.10)
Total interest for loan = $4,914.20 ($7,900 x 4.29% x 14.5)
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It cost $4.50 for zoo parking, plus an additional $6.25 for admission per person into the zoo. If Jay starts off with $55.00 and buys 3 admission tickets, how much money will he have left?
Answers
Answer: he will be left with 31.74 dollars
Step-by-step explanation:
i first put 55.00 - 4.50 = 50.5
then you subtract 50.5 with 6.25 3 times so the and is 31.74
hope this helped !!
How many inches are in 5 1/4 feet?
Answers
Answer: 63 inches
Step-by-step explanation:
Answer:
63 inches
Hope this helps :)
Use the diagram. What is measure angle 2 + measure angle 3?
Enter the correct value in the box.
measure angle 2 + measure angle 3 = ?
Answers
Answer:
The red symbol drawn over ∠2 and ∠3 indicates that the two angles total 90°. Therefore:
[tex]m\angle{2}+m\angle{3}=90^{\circ}[/tex]
help meeeeeeeeeeee pleaseeeeeeeeeee rn rnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeee pleaseeeeeeeeeee rn rnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
The quadratic function has only maximum value :
[tex]F(x)_{min}[/tex] = 30
x = 3
There is no minimum value of the quadratic function.
Given,
In the question:
The quadratic function is given as:
F(x) = [tex]-3x^2+18x +3[/tex]
Determine whether the following quadratic function has a maximum or a minimum value. Then find the maximum and minimum value of the function.
Now, According to the question:
The quadratic function is given as:
F(x) = [tex]-3x^2+18x +3[/tex]
Take out the leading coefficient
F(x) = -3[tex](x^2-6x)+3[/tex]
Complete the square:
F(x) = [tex]-3(x^2+(2(-3))x + (-3)^2)+(3-(-3)^2))[/tex]
Express the function in vertex form
F(x) = [tex]-3(x-3)^2+30[/tex]
To find the maximum value
[tex]F(x)_{min}[/tex] = 30
x = 3
For Minimum value:
F(x) = [tex]-3x^2 +18x +3[/tex]
Rewrite the function by completing the square
F(x) = [tex]-3(x-3)^2+30[/tex]
The graphs always open downwards
So, There is no minimum value of the quadratic function.
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A shelter has enough food to feed an average of 45 hungry people a day for 20 days. If an average of 18 peo
Answers
The number of days that the food will last when an average of 18 people are at the shelter everyday is 50 days.
How to calculate the number of people?From the information given, the shelter has enough food to feed an average of 45 hungry people a day for 20 days.
Let the number of days that the people can be fed when 18 people come be Illustrated as x.
Therefore, this will be illustrated as x. This will be:
x = (45 × 20) / 18
x = 900 / 18
x = 50
The number of days is 15 days.
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Complete question
A shelter has enough food to feed an average of 45 hungry people a day for 20 days. If an average of 18 people are at the shelter everyday, how long will the food last?
The price of products may increase due to inflation and decrease due to depreciation. Marco is studying the change in the price of two products, A and B, over time. The price f(x), in dollars, of product A after x years is represented by the function below: f(x) = 12500(0.82)x Part A: Is the price of product A increasing or decreasing and by what percentage per year? Justify your answer. (5 points) Part B: The table below shows the price f(t), in dollars, of product B after t years: t (number of years) 1 2 3 4 f(t) (price in dollars) 5600 3136 1756.16 983.45 Which product recorded a greater percentage change in price over the previous year? Justify your answer. (5 points)
Answers
Step-by-step explanation:
so, after clarification from your side, we know
f(x) = 12500 × (0.82)^x
so, with every new year we are multiplying the value of the previous year by 0.82.
in other words
f(n) = f(n-1) × 0.82
with f(0) = 12500
because anything to the power of 0 equals 1.
A
so, the price is decreasing every year, because any multiplication with a positive value smaller than 1 decreases the original number.
multiplying an amount by a decimal number like 0.82 creates exactly 82% of the original amount because 1 represents 100%.
that means the value decreases every year by 100 - 82 = 18% compared to the value of the previous year.
B
1 5600
2 3136
3 1756.16
4 983.45
remember, Part A showed always an 18% decrease over the previous year.
from 5600 to 3136, this was a change of
100% = 5600
1% = 100%/100 = 5600/100 = $56
the price difference was 5600 - 3136 = 2464
how many % was that decrease ?
as many as how often 1% fits into 2464 :
2464 / 56 = 44%
that was much more than Part A.
from 3136 to 1756.16, this was a change of
100% = 3136
1% = $31.36
the price difference was 3136 - 1756.16 = $1,379.84
how many %
1,379.84 / 31.36 = 44%
again.
from 1756.16 to 983.45, this was a change of
100% = 1756.16
1% = $17.5616
the price difference was 1756.16 - 983.45 = 772.71
hire many %
772.71 / 17.5616 = 43.99997722...%
and again 44% (just a little rounding uncertainty).
so, product B recorded a much greater percentage change in value over the previous year than product A :
44% to 18%
Use the number line to plot –3, 1, and 3. Which statements are true? Select all that apply. –3 > 1 –3 = 3 1 < 3 –3 < 1
Answers
Answer:
The answer is –3 < 1
Step-by-step explanation:
-3 is below zero. 1 is above zero. therefore, -3 less than 1
Warren has 40 coins (all nickels, dimes, and quarters) worth $4.05. He has 7 more nickels than dimes. How many quarters does Warren have?
Please provide a detailed explanation and steps on how to do
Answers
If he has 7 more nickels than dimes. The number of quarters that Warren have is 7.
How to determine the number of quarters?Let coins be:
n + d + q = 40
Where;
n = nickels
d =dimes
q = quarters
Hence,
.05n + .10d + .25q = 4.05
n = d + 7
Substitute (d+7) for n
(d+7) + d + q = 40
2d + q = 40 - 7
2d + q = 33
q = (33-2d)
So,
.05(d+7) + .10d + .25q = 4.05
.05d + .35 + .10d + .25q = 4.05
15d + .25q = 4.05 - .35
.15d + .25d = 3.70
Substitute (33-2d) for q
.15d + .25(33-2d) = 3.70
.15d + 8.25 - .5d = 3.70
.15d -.5d = 3.70 - 8.25
-.35d = -4.55
Divide both side by -/35d
d = -4.55 / -.35
d = 13 dimes
Nickels
n = d+7 where d is 13
n = 13 + 7
n = 20 nickels
Quarters
q = (33-2d)
q = 33 - 2(13)
q = 33 - 26
q = 7 quarters
Therefore 7 is the quarters.
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what is the most appropriate measure of central tendency to use in determining the average time it takes students to graduate from college, assuming that a few students take an extraordinary long time to finish their degree, and why it is the most appropriate?
Answers
As a result of using all values in the data set to calculate an average, the mean is the most widely used measure of central tendency.
Why is central tendency important?A measure of central tendency, also known as a measure of center or a measure of central placement, is a summary statistic that seeks to summarize an entire collection of data by using a single number that corresponds to the middle or center of the distribution.
Where can you locate the central tendency?You are probably most familiar with the central tendency measure known as the mean, which is the arithmetic average. It is fairly easy to determine the mean. Simply add up all the values then divide by the dataset's observation count.
What use do central tendency metrics serve in evaluating student learning?The teacher can get a mathematical breakdown of how well the children are doing through measures of central tendency.
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hello can someone help me pls
Answers
The size of the angle x = 54 degrees
The regular pentagon is given
Number of sides of the pentagon = 5
O is the center of the pentagon
The sum of all the angle around a point is 360 degrees
From the figure we can see that the it equally divided by 5 parts
The measure of each angle = 360/5
= 72 degrees
Consider the corresponding triangle
Sum of all the interior angles of the triangle is 180 degrees and the two sides of the triangle is equal, therefore it is an isosceles triangle
Then,
x + x+ 72 = 180
2x + 72 = 180
2x = 180- 72
2x = 108
x = 108/2
x = 54 degrees
Hence, the size of the angle x = 54 degrees
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You win 50 tickets, 12 tickets, and 16 tickets at
an arcade. You are able to buy 3 of the same item with 3 tickets left over.
How many tickets does 1 item cost?
Answers
Answer:
25
Step-by-step explanation:
First, we add 50, 12, and 16, which gives us 78. Then, we remove 3 from the answer, giving us 75. Then, divide 75 by 3.
Answer = 25.
(ps: sorry for any spelling mistakes, i dont really type answers alot)
If you are able to buy 3 of the same item with 3 tickets left over. As a result, 1 item cost 26 tickets.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.
It is given that, You win 50 tickets, 12 tickets, and 16 tickets at an arcade. You are able to buy 3 of the same item with 3 tickets left over.
Number of tickets won,
= 50 + 12 + 16
= 78 tickets
Number of items bought = 3 items
Let the cost of 1 item be 'x' tickets.
The cost of 3 items = 3x
By the amount, we can buy 78 tickets as,
3x = 78
x = 26
Thus, if you are able to buy 3 of the same item with 3 tickets left over. As a result, 1 item cost 26 tickets.
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Karla drank a 15-fluid-ounce bottle of water before tennis practice. After practice, she drank 4 cups of water. What is the total amount of water Karla drank?
a 7 c and 9 fl oz
b 7 c and 7 fl oz
c 5 c and 9 fl oz
d 5 c and 7 fl oz
Answers
The total amount of water Karla drank before and after the tennis practice is 5 cups and 9 fluid ounces.
The correct answer option is option C.
What is the total amount of water Karla drank?Volume of water Karla drank before tennis practice = 15-fluid-ounceVolume of water Karla drank after tennis practice = 4 cupsConvert fluid ounces to cups:
1 fluid ounces = 0.125 cups
15 fluid ounces = 1.875 cups
Total volume of water Kayla drank = Volume of water Karla drank before tennis practice + Volume of water Karla drank after tennis practice
= 1.875 cups + 4 cups
= 5.875 cups
Approximately,
5 cups and 9 fluid ounces
Therefore, the total volume of water Karla drank is approximately 5 cups and 9 fluid ounce
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Use point-slope form to write the equation of a line that passes through the point
(1,-5) with slope-1.
Answers
The equation of a line that passes through the point (1,-5) with slope -1 is y = -x - 4.
Given:
(1,-5) with slope m = -1
The standard slope intercept form is y = mx + c.
substitute m = -1 and (1,-5)
-5 = -1(1) + c
-5 = -1 + c
c = -4.
y = mx + c
y = -1(x) + (-4)
y = -x - 4.
Therefore the equation of a line that passes through the point (1,-5) with slope -1 is y = -x - 4.
Therefore equation of a line that passes through the point (1,-5) with slope -1 is y = -x - 4.
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The length of KL¯¯¯¯¯¯¯¯ is 8x−17 units. The length of ST¯¯¯¯¯¯¯ is −2x+18 units. For what value of x are the segments congruent?
NO LINKS OR FILE
Answers
Answer:
x = 3.5units
Step-by-step explanation:
Congruent means the same length, so set the given lengths equal to each other.
8x - 17 = -2x + 18
Add 2x to both sides.
10x -17 = 18
Add 17 to both sides.
10x = 35
Divide by 10
x = 3.5
When x is 3.5, KL and ST are the same length. Check.
8(3.5) - 17 = 11
and
-2(3.5) + 18 = 11
