If L, M and N are the midpoints of the sides of the triangle PQR, PR= 46, PQ = 40, and LN = 17, find each measure.; LM, MN, QR and the perimeter of LMN
Answers
LM = 23; MN = 20 ; QR = 34 ; Perimeter of LMN is 60
Here, we want to find the measures
From what we have, triangle LMN is formed by joining the midpoints of the triangle PQR
From the midpoint theorem, the sides of PQR are parallel and exactly half the measure of the sides they face
For example, LM is half PR
a) LM
[tex]LM\text{ = }\frac{1}{2}\times PR\text{ = }\frac{1}{2}\times46\text{ = 23}[/tex]b) MN
[tex]MN\text{ = }\frac{1}{2}\times PQ\text{ = }\frac{1}{2}\times\text{ 40 = 20}[/tex]c) QR
Here, QR will be twice the measure of LN
[tex]QR\text{ = 2}\times LN\text{ = 2}\times17\text{ = 34}[/tex]d) To find the perimeter of LMN, we have to add up the measure of the side lengths
We have this as;
[tex]\text{LMN = LM + LN + MN = 23 + 17 + 20 = 60}[/tex]Related Questions
Find the four terms of the arithmetic sequence given the 13th term (a_{13}=-60) and the thirty third term (a_{33}=-160).Given terms: a_{13}=-60 and a_{33}= -160Find these terms:a_{14}= Answera_{15}= Answera_{16}= Answera_{17}= Answer
Answers
Given:
13th term = -60
33rd term = -160
Find:
14th, 15th, 16th, and 17th term
Solution:
For us to determine the 14 - 17th term, we need to identify the common difference in this arithmetic sequence. The formula is:
[tex]\frac{a_{33}-a_{13}}{33-13}[/tex]Let's plug in the values of a₃₃ and a₁₃ in the formula above.
[tex]\frac{-160-(-60)}{33-13}[/tex]Then, solve.
[tex]\frac{-100}{20}=-5[/tex]Hence, the common difference between the terms is -5.
So, the next 4 terms after a₁₃ are shown below:
[tex]\begin{gathered} a_{14}=-65 \\ a_{15}=-70 \\ a_{16}=-75 \\ a_{17}=-80 \end{gathered}[/tex]
Solve using substitution. y=103x + 4y = 19
Answers
We want to find the solutions for the following system
[tex]\begin{cases}y=10 \\ 3x+4y=19\end{cases}[/tex]We already know the value for the y variable, if we substitute this value on the second equation it is possible to find the x value.
[tex]\begin{gathered} 3x+4\cdot(10)=19 \\ 3x+40=19 \\ 3x=19-40 \\ 3x=-21 \\ x=\frac{-21}{3} \\ x=-7 \end{gathered}[/tex]And those are the results for our system
[tex]\begin{cases}x=-7 \\ y=10\end{cases}[/tex]Find a point N on the segment with endpoints K(-2, -3) and L(4,3) that partitions thesegment, starting at point K, 1/3 of the way to point L.
Answers
First find the length of the segment KL
Apply the formula for distance between two points as;
d = √{y2-y1}^2 + {x2-x1}^2 where
y1= -3 , y2 = 3 , x1 = -2 and x2 = 4
d= √ {3--3}^2 + { 4--2}^2
d= √ 9^2 + 6^2
d= √ 81 + 12
d= √93 = 9.6
So the length of the segment is 9.6
From point K {-2, -3} , find 1/3 of the length to locate point L
This will be : 1/3 * 9.6 =3.2
This means point L is 3.2 units from point K, now apply the distance formula to find x and y coordinates for L, where K is {-2,-3} and L {x,y}
d = √{y2-y1}^2 + {x2-x1}^2
3.2 = √{y--3}^2 + {x--2}^2
3.2 =√ {y+3}^2 +{x+2}^2
3.2^2 = {y+3}^2 + {x+2}^2
10.3 = y^2 + 6y + 9 + x^2 +4x +4
10.3 = y^2 + 6y +x^2 +4x +9+4
10.3 = y^2 + 6y +x^2 +4x +13
0=y^2 +6y +x^2 +4x +13-10.3
0= y^2 +6y +x^2 +4x +2.7
y^2 + 6y +x^2 +4x +2.7 = 0
{-0.9,-0.5)
Solve the equation for all complex and real solutions. Use potential zeros and synthetic division[tex]5x^4+7x^3+119x^2+175x-150=0[/tex]
Answers
Answer: the complex solutions are:
Step-by-step explanation: x = 5i , -5i , 3/5 ,-2
Larry and his brother wanted to put new carpet down in threerooms in his house. The three rooms measured 10' x 12, 13' x 15,and 12' x 12'. If the carpet Larry wants to use is $25.56 a sq. yd.and the roll of padding is $99 for a 30 sq.yd. roll, answer thefollowing questions. Remember that 1 square yard = 9 square feet.1. Total square footage to be covered with carpeting would besquare feet.2. How many square yards would that be?sq.yd.3. Based on the price of $25.56 a sq.yd., what would the total costbe for the carpeting? $4. To make sure Larry has enough padding, how many rolls wouldhe have to buy?What would that cost? $5. What would the total cost of the carpeting job be includingcarpet and padding? $
Answers
Find the area of each room and then add the three areas.
[tex]\begin{gathered} 10\times12=120 \\ 13\times15=195 \\ 12\times12=144 \\ \\ 120+195+144=459 \end{gathered}[/tex]The total square footage to be covered is 459.
Part 2)Since each square yard has 9 square feet, divide the square footage by 9 to find how many yards is that equal to:
[tex]\frac{459}{9}=51[/tex]Then, the area is equal to 51 square yards.
Part 3)The cost for each square yard is $25.56. Multiply that amount by 51 to find the total cost:
[tex]25.56\times51=1303.56[/tex]The total cost for the carpeting is $1303.56.
Part 4)Each roll of padding has 30 square yards. Since 51 yards must be covered, and two rolls would yield 60 square yards, then, the minimum amount of rolls needed is 2.
The cost for 2 rolls would be 2*$99 = $198.
Part 5)Add the cost of the two rolls of padding and the carpeting job to find the total cost:
[tex]\text{ \$}198+\text{ \$}1303.56=\text{ \$}1501.56[/tex]Then, the total cost of the carpeting job including the carpet and padding would be $1501.56.
Therefore, the answers are:
Part 1) 459 square feet.
Part 2) 51 square yards.
Part 3) $1303.56
Part 4) 2 rolls for $198
Part 5) $1501.56
Which graph correctly represents ? 1/5y - 1/2x > 2
Answers
A graph which represents the solution to this inequality is shown in the image attached below.
What is an inequality?An inequality can be defined as a mathematical relation that compares two (2) or more integers and variables in an equation based on any of the following arguments (symbols):
Greater than (>).Less than (<).Greater than or equal to (≥).Less than or equal to (≤).Next, we would evaluate and simplify the given inequality in order to determine the graph which represent its solution as follows:
1/5y - 1/2x > 2
Subtracting 2 both sides, we have:
1/5y - 1/2x - 2 > 2 - 2
1/5y - 1/2x - 2 > 0
(2y - 5x - 20)/10 > 0
2y - 5x - 20 > 0
2y > 5x + 20
Dividing both sides by 2, we have:
y > 5x/2 + 10
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pls help. this is so confusing on how to find the p=S(t)=r+i part of the word problem.
Answers
Using a linear function, it is found that:
a) Sales are increasing at a constant rate of 30 purchases/month.
b) The linear function is: p = S(t) = 30t + 3990.
c) The total purchases will be of 5130 in June 2010.
d) The sales will be of 5400 in March of 2011.
What is a linear function?A linear function, in slope-intercept format, is modeled according to the following rule:
y = mx + b
In which:
The coefficient m is the slope of the function, which is the rate of change of the function, that is, the change in y divided by the change in x.The coefficient b is the y-intercept of the function, which is the the value of y when the function crosses the x-axis(x = 0).For this problem, we have that:
The reference month is of April 2007, hence the intercept is of b = 3990.In 16 months, from April of 2007 to August of 2008, sales increased to 4470, hence the slope is given by: m = (4470 - 3990)/16 = 30.The slope of 30 is the constant rate of purchases per month, and the linear function is given by:
p = S(t) = 30t + 3990.
June 2010 is 3 x 12 + 2 = 38 months after April 2007, hence the purchases will be of:
S(38) = 30 x 38 + 3990 = 5130.
The sales will be of 5400 in t months after April 2007, for which:
S(t) = 5400
Hence:
30t + 3990 = 5400
t = (5400 - 3990)/30
t = 47 months.
One month shy of four year, hence in March of 2011.
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please answer this using the foil method[tex] {9x}^{2} + 60x + 100[/tex]
Answers
Answer
Given expression
[tex]9x^2+60x+100[/tex]By factorization, we have
[tex]\begin{gathered} 9x^2+30x+30x+100 \\ 3x(3x+10)+10(3x+10) \\ (3x+10)(3x+10) \end{gathered}[/tex]Now to check, using FOIL method, we have
F = First, i.e 3x(3x) = 9x²
O = Outer = 3x(+10) = +30x
I = Inner = +10(3x) = +30x
L = Last = +10(+10) = +100
Select the correct inequality and graph for the statement. Samuel gets 25 or more for mowing the lawn. PLSSS HELP!!
Answers
The statement "Samuel will get 25 or more for mowing the lawn" can be represented using the inequality → x ≥ 25 and the graph number [2] represents the correct graph.
What is an inequality?In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. There are two types of inequalities namely strict and slack inequalities.
Given is the following statement - "Samuel will get 25 or more for mowing the lawn".
The given statement is -
Samuel will get $25 or more for mowing the lawn.
Assume that Samuel gets $x for mowing the lawn.
Then according to the question, we can write the inequality as -
x ≥ 25
" ≥ " sign to represent either 25 or more.
So, the inequality can be written as x ≥ 25 and the graph number [2] represents the correct graph.
Therefore, the statement "Samuel will get 25 or more for mowing the lawn" can be represented using the inequality → x ≥ 25 and the graph number [2] represents the correct graph.
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[Refer to image attached for complete question]
A cylinder shaped jelly jar has a radius of 2 cm and a height of 6 cm. How much jelly can the jar hold?
Answers
Question: A cylinder-shaped jelly jar has a radius of 2 cm and a height of 6 cm. How much jelly can the jar hold?
Explanation:
The cylinder-shaped jelly has a volume of gelatin equal to its cylindrical volume. Therefore, we must find the volume of the given cylinder. The volume V of the cylinder with radius r and height h is given by the following formula:
[tex]V=h\pi r^2[/tex]Applying the data of the problem, we obtain:
[tex]V=h\pi r^2=6\text{ * }\pi\text{ * \lparen2}^\text{\rparen}^2\text{ = 24}\pi\text{ =75.398}[/tex]Answer: we can conclude that the correct answer is:
[tex]\text{ 24}\pi\text{ =75.398}[/tex]counselor at a summer camp are assigned beds to the campers Jackson is assign a bed and then Eva is assigned one are these two events dependent or independent
Answers
Solution;
The events are independent
if you could give me the answer without explantion i would be happy to leave a good review
Answers
The coordinates of the fourth side are (6, -8)
Explanation:Let the coordinate of the fourth side be (x, y)
The diagonals of a parallelogram bisect eachother, so the midpoint of (-3, -2) and (x, y) is equal to the midpoint of (4, -4) and (-1, -6)
[tex]\begin{gathered} (\frac{x-3}{2},\frac{y-2}{2})=(\frac{4-1}{2},\frac{-6-4}{2}) \\ \\ (\frac{x-3}{2},\frac{y-2}{2})=(\frac{3}{2},-5) \\ \\ \frac{x-3}{2}=\frac{3}{2}\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\text{.}(1) \\ \\ \frac{y-2}{2}=-5\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots.(2) \end{gathered}[/tex]Solving these equations:
x - 3 = 3
x = 3 + 3 = 6
and
y - 2 = -10
y = -10 + 2 = -8
The coordinates are (6, -8)
parallel linessolve for x
Answers
We have two parralel lines with angles 32x + 4 and 34x - 2
From the figure, the angles are corresponding angles
Corresponding angles are equal
That is,
34x - 2 = 32x + 4
Collect the like terms
34x - 32x = 4 + 2
2x = 6
Divide both sides by 2
2x / 2 = 6 / 2
x = 3
The answer is 3
how much bags of fertilizer will brett need to cover the entire garden.
Answers
Area A = ?
Bag area covers = 54 ft2
Square Area S = 18ft X 18 ft
. = 324 ft2
Then now divide S/B
S/B = 324/54
. = 36/6
. = 6
Then answer is
Brett will need 6 bags of fertilizer
You pick a card at random. Without putting the first card back, you pick a second card at random.4567What is the probability of picking an even number and then picking an even number?Simplify your answer and write it as a fraction or whole number.
Answers
Given:
4 5 6 7
Given that you picked a card at random, without replacement, you then pick a second card at random.
Let's find the probability of picking an even number and then picking an even number.
Number of possible events = 4
Number of even numbers = 4, 6, ==> 2 even numbers.
Hence, to find the probability, we have:
[tex]\begin{gathered} P=\frac{2}{4}*\frac{1}{3} \\ \\ P=\frac{2*1}{4*3} \\ \\ P=\frac{2}{12}=\frac{1}{6} \end{gathered}[/tex]Therefore, the probability of picking an even number and then picking an even number is 1/6.
ANSWER:
[tex]\frac{1}{6}[/tex]- Lana had a fixed budget for a party. She spent one third of the
budget on decorations. Of the money that remained, she spent
on refreshments and the rest on door prizes for the guests.
If she spent $60 on door prizes, what was her budget?
Answers
Lana's fixed budget for a party is $180.
How to find Lana's fixed budget for a party?Let x be Lana's fixed budget for a party.
Lana spent one-third of the budget on decorations.
x - 1/3x = 2x/3
Remaining money,
2x/3 -x + (2x/3-x)-x =0
Since she spent $60 on door prizes
-x/3 + 60 = 0
-x/3 = -60
x = 180
Lana's fixed budget for a party is $180.
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Can anyone answer this
Answers
Answer:
add the number of sides then divide the number by the number of sides
Here is a vertical algorithm that we can use to find 60.19 – 47.52.Which place value column(s) will require regrouping?Please see image below.
Answers
Regrouping happens when we need to "borrow" value from the higher order digits to perform a subtraction properly. This happens on the tenths, because we need to subtract 5 from 1, which we can't do normally. So we need to regroup from the ones and tens, in order to solve the problem. The correct answer is B.
I will show you the pic
Answers
The general form of a linear equation is given by:
y = kx
where k is a constant.
From the given options you can notice that the only equation similar to the previous one is:
y = 1/6 x
Then, the previous equation is the linear equation.
Liam is setting up folding chairs for a meeting. If he arranges the chairs in 8 rows of the same length, he
has 3 chairs left over. If he arranges the chairs in 6 rows of that same length, he has 13 left over. How many
chairs does Liam have?
Liam has
chairs.
Answers
The most appropriate choice for linear equation will be given by-
Liam have 43 chairs
What is linear equation?
At first, we need to know the meaning of algebraic expressions.
Algebraic expressions consists of numbers and variables connected with addition,subtraction, multiplication and division sign.
Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions with an equal to sign
A one degree equation is known as linear equation.
Let the number of chairs in one row be x
Number of chairs in 8 rows = 8x
3 chairs are left
Total number of chairs = 8x + 3
Number of chairs in 6 rows = 6x
13 chairs are left
Total number of chairs = 6x + 13
By the problem,
[tex]8x+3=6x+13\\8x-6x=13=3\\2x=10\\x=\frac{10}{2}\\x=5[/tex]
Number of chairs Liam has =
[tex]6\times 5 + 13\\30+13\\43[/tex]
Liam has 43 chairs
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x f(x) −5 1 −4 0 −3 1 −2 2 −1 3 0 4 1 5 2 6 3 7 What are the vertex and range of the function?
Answers
The vertex is the turning point of a function while the range is the interval of the value of the function thus vertex of the given function is at (-4,0) while the range is [0,6].
What is the range and domain of a function?A function's range is the set of all values that the function accepts, and its domain is the set of all values for which the function is defined.
The domain is for the independent variable while the range is for the dependent variable.
As per the given function,
x f(x) −5 1 −4 0 −3 1 −2 2 −1 3 0 4 1 5 2 6
The graph of this function has been plotted below,
The vertex is the point where the function is changing its sign of slope or turning point.
It is clear that at (-4,0) it is changing its slope of sign therefore (-4,0) will be the vertex.
The range is the interval where the function exists since the given function goes from y = 0 to y = 6 so [0,6] will be the range of the function.
Hence "The vertex is the turning point of a function while the range is the interval of the value of the function thus vertex of the given function is at (-4,0) while the range is [0,6]".
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Solve for n in the proportion 7/3 = n/21.
Answers
7/3 = n/21
We need to find the value of n,
Cross multiplying,we get
3n = 21 x 7
=> 3n = 147
=> n = 147/3
=> n = 49 is the required answer
Round 0.4275 to the nearest thousand
Answers
we have
0.4275
if we round to the nearest thousand, we look at the third digit of our number
0.4275
do you know the answer now?
0.42 is not correct
and only 2 decimals will be rounded to the nearest hundreth
becuase we have a 5 after 7, the number will be rounded up
0.428
this is the answer
if we would have for example
0.3521
the rounded to the nearest thousand would be 0.352
Graph the line y= 3x - 5 using the slope and y-intercept.
Step-by-Step Solution
Step 1: Identify the slope and y-intercept of the line.
y = 3x-5
The slope is m = 1.
(Type an integer or a fraction.)
Answers
The required slope m is 3 and the y-intercept is - 5.
What is a y-intercept?On a graph, the y-intercept can be found by finding the value of y when x=0. This is the point at which the graph crosses through the y-axis.
· The y-coordinate of a point where a line, curve, or surface intersects the y-axis.
Given : The line y = 3x - 5
This is of the form y = mx + c which is the equation of the line.
On comparing these two equations
Thus the slope is 3 .
And y intercept is :
y = 3x - 5 and when x = 0
y =- 5.
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identify the set of numbers that best describes each situation explain your choice. 9. the amount of money in a bank account
Answers
The sets of the real numbers are
Whole numbers
Integers
Rational numbers
Irrational numbers
The whole numbers mean positive integers with zero
The integers mean positive , negative whole numbers, and zero
Rational numbers mean
Printer A prints 36 pages every 1.5 minutes. Printer B prints 114 pages every 3 minutes.
Printer C prints 115 pages every 5 minutes. Which printer prints the fastest?
Answers
Printer B= 114 pages per 3 minutes. Printer B is the fastest printer. I did scratchwork on paper but I still sent it to you. Sorry my handwriting is sloppy. ; ) I hope it helps.
Hello, I need some assistance with this homework question please for precalculusHW Q30
Answers
EXPLANATION
Since the degree is 6, the polynomial has 6 zeros:
Then, using the Complex Root Theorem, since the polynomial has 2 complex roots, thus the conjugate of 5 + i is 5 - i, and the conjugate of 7 - i is 7 + i:
In conclusion, the remaining zeros are: 5 - i, 7 + i
A triangle is placed in a semicircle with a radius of , as shown below. Find the area of the shaded region.Use the value for , and do not round your answer. Be sure to include the correct unit in your answer.
Answers
Solution:
Given the figure below:
The area of the shaded region is expressed as
[tex]area\text{ of shaded region = area of semicircle - area of triangle}[/tex]step 1: Evaluate the area of the semicircle.
The area of the semicircle is expressed as
[tex]\begin{gathered} area\text{ of semicircle=}\frac{1}{2}\times\pi r^2 \\ where\text{ r is the radius of the circle} \end{gathered}[/tex]Thus, we have
[tex]\begin{gathered} area\text{ of semicircle = }\frac{1}{2}\times3.14\times4cm\times4cm \\ \Rightarrow area\text{ of semicircle =25.12 cm}^2 \end{gathered}[/tex]step 2: Evaluate the area of the triangle.
The area of the triangle is expressed as
[tex]\begin{gathered} area\text{ of triangle =}\frac{1}{2}\times base\times height \\ thus,\text{ we have} \\ area\text{ of triangle =}\frac{1}{2}\times8cm\times4cm \\ =16\text{ cm}^2 \end{gathered}[/tex]step 3: Evaluate the area of the shaded region.
Recall that
[tex]\begin{gathered} area\text{ of shaded reg}\imaginaryI\text{on = area of sem}\imaginaryI\text{c}\imaginaryI\text{rcle- area of tr}\imaginaryI\text{angle} \\ \end{gathered}[/tex]Thus, we have
[tex]\begin{gathered} area\text{ of shaded region = \lparen25.12 -16\rparen cm}^2 \\ =9.12\text{ cm}^2 \end{gathered}[/tex]Hence, the area of the shaded region is
[tex]9.12\text{ cm}^2[/tex]S
SOLUTION
Mr. McClary writes the equation 3(3x - 10) = 5(x + 10). The equation shows
the relationship between the perimeter of an equilateral triangle and the
perimeter of a regular pentagon. What is the perimeter of the pentagon?
A 20
B 50
C 100
D 150
Nikia chose A as the correct answer. How might she have gotten that answer?
Answers
The perimeter of pentagon is 150 so option D is correct.
Given:
Mr. McClary writes the equation 3(3x - 10) = 5(x + 10). The equation shows the relationship between the perimeter of an equilateral triangle and the perimeter of a regular pentagon.
3(3x-10) = 5(x+10)
9x - 30 = 5x + 50
9x - 5x = 30 + 50
4x = 80
divide by 4 on both sides
4x/4 = 80/4
x = 80/4
x = 20.
perimeter of pentagon = 5(x+10)
= 5(20+10)
= 5*30
= 150.
Therefore the perimeter of pentagon is 150 so option D is correct.
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If g(x)=5x, h(x)=√x, find the composition.
(g . h)(0)
( g . h ) ( 0 ) = _____
Answers
The value of the composition (g . h)(0) is 0
What is a function?A function can be defined as a mathematical law, expression of rule that explains the relationship between two variables in an equation.
These variables are;
The independent variableThe dependent variableThe functions are;
g(x) = 5xh(x) = √xThe composite function is gotten by substituting the value of x of the independent variable in the function.
The composite function (g . h)(0) is determined by substituting the value of x as h(x) in the function g(x), we get;
(g . h) = 5√x
Now, substitute the value of x as 0, we have;
(g . h)(0) = 5√0
Find the square root
(g . h)(0) = 5(0)
Find the product
(g . h)(0) = 0
Hence, the value is 0
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