Answers
Answer:
Step-by-step explanation:
To find the length of LK, we can use the triangle similarity concept. First, let's compare triangles LJK and LMK. We can see that they share angle L, and we know that LJ = 10 and KM = 7. By comparing the corresponding sides, we can set up the proportion: LK / LJ = KM / KJ Substituting the given values, we have: LK / 10 = 7 / 11 To solve for LK, we can cross multiply and then divide: LK * 11 = 10 * 7 LK * 11 = 70 LK = 70 / 11 So, LK = 6.36 (rounded to two decimal places). Therefore, the answer is not provided in the answer choices.
From the answer choices, we can conclude that LK = d. 70/11.
What is the value?From the figure we are given, we can use the property of corresponding angles to determine the probable value of LK. From the corresponding sides, LK/LJ is equal to KM/KJ. Now, we substitute the given values to have the following:
LK / 10 = 7 / 11
To get the exact value of LK, we cross-multiply as follows:
LK * 11 = 10 * 7
LK * 11 = 70
LK = 70 / 11
So, the value of LK = 70/11.
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Related Questions
GRADE 8 UNIT 5 LESSON 5 OPEN UP RESOURCES
#3 A car is traveling on a small highway and is either going 55mph or 35mph, depending on the speed limits, until it reaches its destination 200 miles away. Letting x represent the amount of time in hours that the car is going 55mph, and y being the time in hours that the car is going 35mph, an equation describing the relationship is:
55x + 35y = 200
a. If the car spends 2.5 hours going 35mph on the trip, how long does it spend going 55mph?
b. If the car spends 3 hours going 55mph on the trip, how long does it spend going 35mph?
c. If the car spends no time going 35mph, how long would the trip take?
Answers
a. It spends 2.04 hours going 55 mph.
b. It will spend 1 hour going 35 mph.
c. The trip will take 3.64 hours.
Step-by-step explanation:
Given equation is;
55x + 35y = 200
Where
x represent the time when speed is 55 mph
y represent the time when speed is 35 mph
a. If the car spends 2.5 hours going 35mph on the trip, how long does it spend going 55mph?
Putting y=2.5 in given equation
[tex]55x+35(2.5)=200\\55x+87.5=200\\55x=200-87.5\\55x=112.5\\[/tex]
Dividing both sides by 55
[tex]\frac{55x}{55}=\frac{112.5}{55}\\x=2.04\ hours[/tex]
It spends 2.04 hours going 55 mph.
b. If the car spends 3 hours going 55mph on the trip, how long does it spend going 35mph?
Putting x=3 in given equation
[tex]55(3)+35y=200\\165+35y=200\\35y=200-165\\35y=35[/tex]
Dividing both sides by 35
[tex]\frac{35y}{35}=\frac{35}{35}\\y=1[/tex]
It will spend 1 hour going 35 mph.
c. If the car spends no time going 35mph, how long would the trip take?
Putting y=0 in given equation
[tex]55x+35(0) = 200 \\55x+0=200\\55x=200[/tex]
Dividing both sides by 55
[tex]\frac{55x}{55}=\frac{200}{55}\\x=3.636[/tex]
Rounding off
x = 3.64
The trip will take 3.64 hours
Keywords: linear equation, division
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A water pipe floods 50 square feet every 1/5 minute.what is the flooded area after 6 minutes
Answers
Final answer:
To find the flooded area after 6 minutes, calculate the number of 1/5-minute intervals in 6 minutes, which is 30. Then, multiply by the area flooded in each interval. The flooded area after 6 minutes would be 1500 square feet.
Explanation:
The question is asking to calculate the area that would be flooded by a water pipe after 6 minutes, given that the pipe floods 50 square feet every 1/5 of a minute. To find the answer, we need to determine how many 1/5-minute intervals are in 6 minutes, and then multiply that number by the area flooded in each interval.
First, calculate the number of intervals: 6 minutes × (5 intervals/minute) = 30 intervals.
Next, multiply the number of intervals by the area flooded per interval: 30 intervals × 50 square feet/interval = 1500 square feet.
Therefore, after 6 minutes, the flooded area would be 1500 square feet.
List 3 rational numbers between 3 and 3.9
Answers
The number are "3.4, 3.7, and 3.8"
Rational numbers:List of number 3 rational numbers in 3 and 3.9.
The number sequence has the form a/b, where a and b are integers, and b is not equivalent to 0.As there were numerous quantities or measures that numerals alone could not effectively explain, rational numbers were required. The most typical application of rationals is the measurement, either of length, mass, time, or whatever.Therefore the number are "3.4, 3.7, and 3.8".
Learn more about the numbers here:
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Final answer:
Three rational numbers between 3 and 3.9 are 3.2, 3.3, and 3.6.
Explanation:
To list 3 rational numbers between 3 and 3.9, we can consider the numbers that lie between these two values.
We can start by looking for numbers with a tenths place greater than 3 but less than 9.
To find three rational numbers between 3 and 3.9, we simply need to choose numbers that have a finite number of digits after the decimal point.
Some examples of rational numbers in this range are 3.2, 3.3, and 3.6.
These satisfy the condition of being between 3 and 3.9.
What is the distance between the coordinates (5,5) and (7,2)? Round your
answer to the nearest tenth.
Answers
Answer:
4
Step-by-step explanation:
when you write them down and draw a diaganal line from 7,2 to 5,5 it passes 4 intersections, so it would be 4 units. When you round if it is 4 or less it stays the same and if it is 5 or more then it changes so it would still be 4.
Stay Safe
The box plots below show the ages of college students in different math courses.
A box-and-whisker plot labeled Math 1 is shown. The number line goes from 16 to 22. The whiskers range from 17 to 21, and the box ranges from 18-20. A line divides the box at 19. A box-and-whisker plot labeled Math 2 is shown. The number line goes from 16 to 24. The whiskers range from 17 to 23, and the box ranges from 18-20. A line divides the box at 19.
Math 1 Math 2
Which statement is true?
The median age of the students in Math 1 is greater than the median age of the students in Math 2.
The median age of the students is Math 1 is less than the median age of the students in Math 2.
The mean and median age are most likely the same for both sets of data.
The mean and median age are more likely to be the same for the students in Math 1.
Answers
Answer:
The correct option for this is C.) The mean and median age are more likely to be the same for the students in Math 1.
Step-by-step explanation:
i) The median age of the students is Math 1 is less than the median age of the students in Math 2.
This statement is NOT TRUE as the median age of students in Math 1 = median age of students in Math 2 = 19
ii) The mean and median age are most likely the same for both sets of data.
This statement is NOT TRUE. The mean age of students in Math 2 should be greater than mean age of students in Math 1.
iii) The mean and median age are more likely to be the same for the students in Math 1.
This statement is TRUE.
Answer:
The mean and median age are more likely to be the same for the students in Math 1.
Step-by-step explanation:
The median age of the students for the student is Math 1 is less than the median age of the students in Math 2.
The statement is not true as the median age of students in Math 1 is equal to the median age of the students in Math 2 = 19.
Also, the mean and median age are the most likely to be the same for both sets of data.
The above statement is also not true as the mean age of students in Math 2 should be greater than the mean age of students in Math 1.
What is the difference of (Negative 3.4 x + 4.7) minus (3 + 2.9 x)?
Negative 0.5 x + 1.7
Negative 6.3 x minus 1.7
Negative 0.5 x minus 1.7
Negative 6.3 x + 1.7
Answers
Answer:
A.-0.5x+1.7
Step-by-step explanation:
-3.4x+4.7-3+2.9x
-0.5x+1.7
Answer:
-0.5x+1.7
Step-by-step explanation:
Warm up your day with a easy math problem! Which quantity is proportional to 35⁄80?
Comment all that are true.
A. 3⁄5
B. 14⁄36
C.26⁄52
D.21⁄48
E. 7⁄16
Answers
D and E are the only ones true.
Answer:
E
Step-by-step explanation:
You simplify the fraction by dividing both top and bottom by 5
35÷5=7
80÷5=16
A oth grade student can complete 20 multiplication facts in 1 minute. If he works at the same rate, how long should it
take him to complete 35 multiplication facts? (Type your answer as a decimal number]
minutes
Answers
1.3 minutes = 30 facts
1.45 minutes =35 facts
Answer is 35
It should take the student 1.75 minutes to complete 35 multiplication facts.
To determine how long it will take the 5th grade student to complete 35 multiplication facts at the same rate as 20 facts in 1 minute, we can set up a proportion or use unit rates. Since the student can complete 20 facts in 1 minute, we find the time per fact by dividing the total time by the number of facts:
1 minute / 20 facts = 0.05 minutes per fact
Then, we multiply the rate by the number of new facts:
0.05 minutes per fact * 35 facts = 1.75 minutes
Therefore, it should take the student 1.75 minutes to complete 35 multiplication facts.
What is 5(z+4) + 5(2-z) simplified?
Answers
Answer: 30
Step-by-step explanation:5(Z+4) + 5(2-Z).
Open the brackets by multiplying true by the number out of the bracket.
5Z + 20 + 10 - 5Z
Now, collect like terms, we have.
5Z - 5Z + 20 + 10. Now we have
0 + 30 = 30//
What is the slope of the line that contains these points?
x -4, 1, 6, 11
y -3,-2,-1,0
Answers
Answer:
slope = 1/5
Step-by-step explanation:
[tex]\frac{0-(-3)}{11-(-4)} =\frac{3}{15} =1/5[/tex]
Shira has 20 books on her bookshelf. Of those 15 are about horses, the rest are nature books. What fraction of Shiras books are about nature.
Answers
Answer:
1/4
Step-by-step explanation:
15 out of the 20 books are horses. 5 of those are nature. 5/20 is the fraction, but can be simplified to 1/4
Shira has 5 out of 20 books about nature on her bookshelf, which simplifies to a fraction of 1/4 of her books being about nature.
Explanation:Shira has 20 books in total on her bookshelf. Out of these, she has 15 books about horses, meaning the remaining books are about nature.
To find the fraction that represents the nature books, we need to subtract the number of horse books from the total number of books.
So, the number of nature books is 20 total books - 15 horse books = 5 nature books. The fraction of books about nature would therefore be the number of nature books divided by the total number of books, which is 5/20.
This fraction can be simplified by dividing both the numerator and the denominator by 5, resulting in 1/4. Therefore, 1/4 of Shira's books are about nature.
Classify the following triangle. Check all that apply.
A. Right
B. Scalene
C. Acute
D. Equilateral
E. Obtuse
F Isosceles
Answers
Answer:
A, E
Step-by-step explanation:
I think it is obtuse and scalene, but I don't think that is the only answer. Hope that can help a little.
The triangle is an isosceles and an obtuse triangle.
A triangle with two sides of equal length is an isosceles triangle. The isosceles triangle has three acute angles, meaning that the angles are less than 90°. The sum of three angles of an isosceles triangle is always 180°.
In an isosceles triangle, the two equal sides are called legs, and the remaining side is called the base. The angle opposite the base is called the vertex angle
The three types of Isosceles Triangles are :
Isosceles acute triangle
Isosceles right triangle
Isosceles obtuse triangle
Given data ,
Let the triangle be represented as ΔABC
Now , the measure of ∠ABC = 120°
So , it is an obtuse triangle with angle > 90°
Now , the measure of sides AB = measure of BC
So , an isosceles triangle, the two equal sides are called legs, and the remaining side is called the base
Therefore , it is an Isosceles obtuse triangle
Hence , the triangle is isosceles
A pitcher struck out 11 out of 40 batters. Write an equivalent decimal.
Answers
Answer:
0.275
Step-by-step explanation:
We want to write 11 out of 40 batters as a decimal.
We can write 11 out of 40 as a fraction to get:
[tex] \frac{11}{40} [/tex]
Note that:
[tex] \frac{11}{40} = \frac{1}{4} \times \frac{11}{10} [/tex]
This implies that:
[tex] \frac{11}{40} = 0.25 \times 1.1[/tex]
This gives us
[tex] \frac{11}{40 } = 0.275[/tex]
pls help me for part A and B if correct I will mark brainslit :)) !!
Answers
Answer:
answer choice b is the correct answer
Step-by-step explanation:
5/8 times 2 1/2
1 3/4
1 3/4 > 1 1/4
Solve the following by using mathematical Induction. For >/ 1
1^2+2^2+3^3+......+ n^2 = 1/6 n(n+1)(2n+[)
Answers
Answer:
See explanation
Step-by-step explanation:
Prove that
[tex]1^2+2^2+3^3+...+n^2=\dfrac{1}{6}n(n+1)(2n+1)[/tex]
1. When [tex]n=1,[/tex] we have
in left part [tex]1^2=1;[/tex] in right part [tex]\dfrac{1}{6}\cdot 1\cdot (1+1)\cdot (2\cdot 1+1)=\dfrac{1}{6}\cdot 1\cdot 2\cdot 3=1.[/tex]2. Assume that for all [tex]k[/tex] following equality is true
[tex]1^2+2^2+3^3+...+k^2=\dfrac{1}{6}k(k+1)(2k+1)[/tex]
3. Prove that for [tex]k+1[/tex] the following equality is true too.
[tex]1^2+2^2+3^3+...+(k+1)^2=\dfrac{1}{6}(k+1)((k+1)+1)(2(k+1)+1)[/tex]
Consider left part:
[tex]1^2+2^2+3^2+...+(k+1)^2=\\ \\=(1^2+2^2+3^3+...+k^2)+(k+1)^2=\\ \\=\dfrac{1}{6}k(k+1)(2k+1)+(k+1)^2=\\ \\=(k+1)\left(\dfrac{1}{6}k(2k+1)+k+1\right)=\\ \\=(k+1)\dfrac{2k^2+k+6k+6}{6}=\\ \\=(k+1)\dfrac{2k^2+7k+6}{6}=\\ \\=(k+1)\dfrac{2k^2+4k+3k+6}{6}=\\ \\=(k+1)\dfrac{2k(k+2)+3(k+2)}{6}=\\ \\=(k+1)\dfrac{(k+2)(2k+3)}{6}[/tex]
Consider right part:
[tex]\dfrac{1}{6}(k+1)((k+1)+1)(2(k+1)+1)=\\ \\\dfrac{1}{6}(k+1)(k+2)(2k+3)[/tex]
We get the same left and right parts, so the equality is true for [tex]k+1.[/tex]
By mathematical induction, this equality is true for all n.
find the radius of a discus woth a circumference 8.6 pi inches
Answers
Answer:
4.3π or 13.51 = r
Step-by-step explanation:
C=2πr To find the circumference of a circle, you must have the formula
8.6π = 2πr Substitute the C for 8.6π
4.3π = r Divide both sides by 2π
13.51 = r Simplify 4.3π if needed
what is 738 divided by 13 in fraction form
Answers
Answer:
56.76923076...
Step-by-step explanation:
738 divided by 13 should be [tex]\frac{738}{13}[/tex] as an improper fraction.
As a mixed fraction, it is: [tex]56\frac{10}{13}[/tex]
And as a decimal it is approximately 56.769
I did this problem on a calculator after doing some written work on it.
146+8 1/5
How do I solve this
Answers
Step-by-step explanation:
[tex]146 + 8 \frac{1}{5} \\ \\ = 146 + \frac{8 \times 5 + 1}{5} \\ \\ = \frac{146 \times 5 + 40 + 1}{5} \\ \\ = \frac{730 + 41}{5} \\ \\ = \frac{771}{5} \\ \\ = 154 \frac{1}{5} \\ \\ thus \\ \\ \huge \orange{ \boxed{146 + 8 \frac{1}{5} = 154 \frac{1}{5}}}[/tex]
Evaluate
Evaluate -(-7)7
Answers
Answer:
The answer is 49 because -(-7)×7 =7×7 = 49
Yo sup??
-(-7)7
=(-1)*(-1)*7*7
=1*49
=49
Hope this helps.
What is diversification?
A. investing in volatile stocks
B. investing in various types of investments
C. investing in low-risk investments
(20 points!!!!!! )
Answers
Answer:
b. investing in various types of investments
Step-by-step explanation:
i hope this helps!
brainliest is appreciated... :}
Answer:
1. diversification is the process of allocating capital in a way that reduces the exposure to any one particular asset or risk.
A. Stock market volatility is arguably one of the most misunderstood concepts in investing.
(B i) Stocks.
(ii) Bounds
(III) mutual funds
(iv) index funds
(C). Bank Savings.
Certificates of Deposit (CDs) ...
Treasury Securities. ...
Money Market Accounts. ...
Stable Value Funds. ...
Fixed Annuities. ...
Immediate Annuities
8904 divided by 21 long dividion
Answers
Answer:424
Step-by-step explanation:
One side of a triangle is 2 times the second side. The third side is 5 feet longer than the second side. The perimeter of a triangle is 81 feet. Find the length of each side.
Answers
Answer:
The length of the side of the triangles are;
First side = 38 ft
Second side = 19 ft
Third side =24 ft
Step-by-step explanation:
To solve the question we are going to take;
Second side is x ft
Since, the first side is 2 times the second side then;
First side of the triangle is 2x ft
Since the third side is 5 ft less than the second side, then;
The third side is (x+5) ft
But, the perimeter of the triangle is 81 ft
Perimeter of a triangle is given by the sum of sides;
Therefore;
x + 2x +(x +5) = 81 ft
4x + 5 = 81
4x = 76
x = 19 ft
Therefore;
Second side = 19 ft
First side = 38 ft
Third side = 24 ft
A cylinder has a height of h meters, and the base has a radius of 7 meters. If the volume of the cylinder is 539π find the height
Answers
Answer:
Therefore,
The Height of Cylinder is 11 meters.
Step-by-step explanation:
Given:
Cylindrical Shape
Radius = r = 7 meter
Volume of Pipe = 539π
To Find:
Height = ?
Solution:
Formula for Volume of Cylinder is given by
[tex]\textrm{Volume of Cylinder}=\pi (Radius)^{2} \times Height[/tex]
Substituting the given values we get
[tex]539\pi=\pi(7)^{2}\times Height\\\\Height=\dfrac{539}{49}=11\ meter[/tex]
Therefore,
The Height of Cylinder is 11 meters.
If a triangle has side lengths 27, 79, and 84 is it a right triangle
Answers
Answer:
Nope
Step-by-step explanation:
A right triangle must have a 90 degree angle.
for every $50 of candy you sell, you get to keep 7% of it. how much commission do you make if you sell $200 worth of candy?
Answers
You'll make 14 dollars.
7% of 50 is 3.5.
If you add 3.5 four times you'll get 14.
200 - 7% is 186.
200 - 14 is 186.
Answer:
$14
Step-by-step explanation:
Well, first find 7% of 50. To do this you need to make the percent a decimal by moving the decimal that is already(7 is the whole number, if there were any fractions it would be 7.00%) there two space to the left, adding zeros as needed.
0.07 x 50 = x
3.5 = x
Now you can multiply it by whatever you want. In this case it would be 4 since 50 time 4 is 200.
3.5 x 4 = 14
So the amount of money that you would make would be $14.
Hope this helped you out.
A factory is shipping 9 bicycles to a store. Each bicycle has a mass of 11.6 kg and is packed in a box with a mass of 3.41kg. What is the total mass of all the bicycles and their packing boxes?
Answers
Answer:
135.09 kg
Step-by-step explanation:
First, we must determine the total weight of each bicycle including their boxes. To do this, we must add 3.41 kg and 11.6 kg. 3.41 + 11.6 = 15.01.
Next, multiply the weight of one bike and its box to the total amount of bicycles there are. There are 9 bikes, so 15.01*9 = 135.09 kg.
To find the total mass of all bicycles and their boxes, add the mass of one bicycle (11.6 kg) and its box (3.41 kg) to get the total mass for one unit (15.01 kg), and then multiply by the total number of bicycles (9), resulting in a total mass of 135.09 kg.
The total mass of all the bicycles and their packing boxes can be calculated by first determining the mass of one bicycle with its box, and then multiplying that by the total number of bicycles being shipped. The mass of one bicycle is 11.6 kg and the mass of its packing box is 3.41 kg. Adding these together gives us the total mass for one bicycle and its box.
Mass of one bicycle: 11.6 kg
Mass of one box: 3.41 kg
Total mass for one bicycle and its box: 11.6 kg + 3.41 kg = 15.01 kg
This total mass for one bicycle and its box must then be multiplied by the number of bicycles to obtain the total mass for all bicycles and their boxes.
Number of bicycles: 9
Total mass for all bicycles and boxes: 9 * 15.01 kg = 135.09 kg
Therefore, the total mass of all the bicycles and their packing boxes is 135.09 kg.
What is 70% of 38, please show work
Answers
Answer: 26.6
Step-by-step explanation: To solve this problem, let's ignore the first 2 words which are "what is."
So, we can really change the problem to say 70% of 38.
To find 70% of 38, first write 70% as a decimal by moving the decimal point 2 places to the left to get .70.
Next, the word "of" means multiply, so we have (.70)(38) which is 26.6.
So 70% of 38 is 26.6.
how do you solve 23.61 divided by 3
Answers
Answer:
7.87
Step-by-step explanation
Divide
in an arithmetic series a1= -14 and a5=30 find the sum of the first 5 terms
Answers
The sum of the 5 terms in the arithmetic series is 40.
Step-by-step explanation:
Step 1; First we need to determine the three values between a1= -14 and a5=30. The difference between the first and fifth value = 30 - (-14) = 30 + 14 = 44.
Since there are 4 values after a1 we divide the difference by the number of terms, the difference between each term = 44 / 4 = 11. So the difference between each term is 11.
Step 2; To find out the terms we just add the difference to the previous number.
a1 = -14.
a2 = -14 + 11 = -3.
a3 = -3 + 11 = 8.
a4 = 8 + 11 = 19.
a5 = 19 + 11 = 30.
So a1 + a2 + a3 + a4 + a5 = -14 -3 + 8 + 19 + 30 = 40.
The sum of the first 5 terms in this arithmetic series is 40, calculated based on the formulas for an arithmetic series involving the first term, the fifth term, and the common difference.
Explanation:In an arithmetic sequence or series, the difference between each term (the common difference) is constant. We can represent this as: an = a1 + (n - 1) * d, where d is the common difference. Given in this problem that a1 = -14, a5 = 30, and n = 5.
First, we can find the common difference d using the formula: d = (a5 - a1) / (5 - 1) . So, d = (30 - (-14)) / (5 - 1) = 44 / 4 = 11.
Then, we can find the sum of the first 5 terms using the formula: Sn = n / 2 * (2a1 + (n - 1) * d). That gives us: S5 = 5 / 2 * (2(-14) + (5 - 1) * 11) = 5 / 2 * (-28 + 44) = 5 / 2 * 16 = 40.
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The length of a rectangle is five times its width. If the area of the rectangle is 320m, find the perimeter
Answers
Answer: The perimeter is 96 m
Step-by-step explanation:
If we tag the length of the rectangle as [tex]l[/tex] and the width as [tex]w[/tex], and if in addition we are told [tex]l=5 w[/tex],the dimensions of the rectangle are as shown in the figure.
Now, the area of a rectangle is given by:
[tex]A=(l)(w)=320 m^{2}[/tex]
Since [tex]l=5 w[/tex]:
[tex]A=(5w)(w)=320 m^{2}[/tex]
Isolating [tex]w[/tex]:
[tex]5w^{2}=320 m^{2}[/tex]
[tex]w=\sqrt{\frac{320 m^{2}}{5}}[/tex]
[tex]w=8 m[/tex]
On the other hand, the perimeter of a triangle is given by the addition of each of its sides. Then, if the rectangle has two sides that measure [tex]w[/tex] and two sides that measure [tex]5 w[/tex], the perimeter is:
[tex]P=2(5)(w)+2w[/tex]
Substituting the value of [tex]w[/tex] in the last equation:
[tex]P=2(5)(8 m)+2(8 m)[/tex]
Finally the perimeter is:
[tex]P=96 m[/tex]
Final answer:
The perimeter of the rectangle is determined by first finding the width using the area given, then calculating the length as five times the width and using the formula P = 2l + 2w. The perimeter is 96 meters.
Explanation:
To solve for the perimeter of the rectangle when we know the area is 320m² and the length is five times the width, we first let w represent the width of the rectangle. Therefore, the length is 5w. Given that the area A is equal to the length times the width, we have the equation w × 5w = 320. Solving for w, we get w² = 64 so w = 8 meters.
Since the length is five times the width, it is 5 × 8 = 40 meters. The perimeter P of a rectangle is given by P = 2l + 2w, where l is the length and w is the width. Substituting the values we have, P = 2(40) + 2(8) = 96 meters.