In parallelogram ABCD point K belongs to diagonal BD so that BK:DK=1:4. If the extension of AK meets BC at point E, what is the ratio of BE:EC?
Answers
Answer:
BE : EC = 1 : 3
Step-by-step explanation:
Consider triangles AKD and EKB. In these triangles
∠AKD≅∠EKB as vertical angles;∠ADK≅∠EBK as alternate interior angles;∠KAD≅∠KEB as alternate interior angles.Then ΔAKD is similar to ΔEKB by AAA theorem.
Similar triangles have proportional corresponding sides:
[tex]\dfrac{AD}{EB}=\dfrac{AK}{EK}=\dfrac{DK}{KB}.[/tex]
Since [tex]\dfrac{DK}{KB}=\dfrac{4}{1},[/tex] then [tex]AD=4BE.[/tex]
Opposite sides in parallelogram have the same lengths, then [tex]BC=AD.[/tex]
Now
[tex]BC=BE+EC,\\ \\BC=\dfrac{1}{4}BC+EC,\\ \\EC=BC-\dfrac{1}{4}BC=\dfrac{3}{4}BC.[/tex]
Find the ratio
[tex]\dfrac{BE}{EC}=\dfrac{\frac{1}{4}BC}{\frac{3}{4}BC}=\dfrac{1}{3}.[/tex]
The ratio of BE:EC is 1:2.
How do we calculate?We have Parallelogram ABCD
Point K on diagonal BD such that BK:DK = 1:4
The extension of AK meets BC at point E
Since BK:DK = 1:4,
we know that BK = 1/5 * BD
and DK = 4/5 * BD.
AK extends to meet BC at point E means that AE is parallel to BD and BE is parallel to AK.
pair A,B,C,D,K,E;
A = (0,0);
B = (5,0);
C = (5,5);
D = (0,5);
K = (3.5,0);
E = (3.5,2.5);
Since AE is parallel to BD and BD is a diagonal of parallelogram ABCD, we know that AE bisects BD. This means that AE = BD/2 = 3/5 * BD.
Since BE is parallel to AK and AK is a diagonal of parallelogram ABCD, we know that BE bisects AK. This means that BE = AK/2 = 1/5 * BD.
Therefore, the ratio of BE:EC = 1/5 * BD
: 2/5 * BD
= 1:2.
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Related Questions
six more than seven times a number is less than three times the number decreased by fourteen. FInd the numbers that make this true
Answers
Answer:
find below
Step-by-step explanation:
7x-6 = 3x-14
4x = -8
x = -2
-2*7-6 = -14-6 = -20
-2*3-14 = -6-14 = -20
Find the value of x so that the line m is parallel to line I.
Answers
Here's why:
If these two lines are parallel, it means those 2 angles, (3x+11)° and (4x-21)°, are equal. So to find X, you need to set the equation
[tex]3x + 11 = 4x - 21 \\ x - 21 = 11 \\ x = 32[/tex]
If you want to check if it's the right answer, you can go back to those two angles, and if you put 32 instead of X, you'll get two identical numbers (that is 107°)
What is the answer to linear equation: 9t = -3
Answers
Answer:
-3
Step-by-step explanation:
Anything that is negative multiplied by a negative is a positive so knowing this, you can multiply -3*-3=9 or divide 9/-3=-3
Hope this helps
<> Anna <>
Answer:
The answer to linear equation 9t=-3 is t = - (1/3)
Step-by-step explanation:
9t=-3
Solving for t: Dividing both sides of the equation by 9:
9t/9=-3/9
t=-(3/9)
Simplifying the fraction on the right side of the equation dividing the numerator and denominator by 3:
t = - (3/3) / (9/3)
t = - (1/3)
Find the value of y when x = 4 in the equation 4x - 2 = y + 5 Show your work help
Answers
Then multiply 4 times 4
Subtract 2
Then subtract 5 from both sides
16-2=y+5
14=y+5
9=y
Write as a fraction in lowest terms:
0.126126125= a/b
Answers
Answer:
a= 14
b= 111
just took it
For the figures below, assume they are made of semicircles, quarter circles and squares. For each shape, find the area and perimeter. Give your answer as a completely simplified exact value in terms of π (no approximations).
Answers
Answer:
Part a) The area of the figure is [tex]\frac{9}{2}(4+\pi )\ cm^{2}[/tex]
Part b) The perimeter of the figure is [tex]3(2+2\sqrt{2}+ \pi)\ cm[/tex]
Step-by-step explanation:
Step 1
Find the area of the figure
In this problem we have that
The figure ABC is the half of a square and the other figure is a semicircle
Find the area of the figure ABC
we have
[tex]AB=6\ cm, BC=6\ cm[/tex]
The area of the half square ABC is equal to find the area of triangle ABC
so
[tex]A1=\frac{1}{2}*6*6=18\ cm^{2}[/tex]
Find the area of the semicircle
The area of the semicircle is equal to
[tex]A2=\pi r^{2}/2[/tex]
we have that
[tex]r=6/2=3\ cm[/tex]
substitute
[tex]A2=\pi (3)^{2}/2[/tex]
[tex]A2=(9/2) \pi\ cm^{2}[/tex]
The area of the figure is equal to
[tex]18\ cm^{2}+(9/2) \pi\ cm^{2}= \frac{9}{2}(4+\pi )\ cm^{2}[/tex]
Step 2
Find the perimeter of the figure
The perimeter of the figure is equal to
[tex]P=AB+AC+length\ CB[/tex]
we have
[tex]AB=6\ cm[/tex]
Applying Pythagoras theorem
[tex]AC=\sqrt{6^{2}+6^{2}}\\AC=6\sqrt{2}\ cm[/tex]
Remember that
the circumference of a semicircle is equal to
[tex]C=\frac{1}{2}2\pi r=\pi r[/tex]
[tex]r=6/2=3\ cm[/tex]
[tex]C=\pi(3)[/tex]
[tex]C=3 \pi\ cm[/tex]
The perimeter of the figure is equal to
[tex]P=6\ cm+6\sqrt{2}\ cm+3 \pi\ cm[/tex]
Simplify
[tex]P=3(2+2\sqrt{2}+ \pi)\ cm[/tex]
Jamal claims that the graph of f(x)+2 is equivalent to the graph of f(x+k).For the case where Jamals claim is correct, what must be the value of k?
A.-4
B.-1
C.1
D.2
Answers
Answer:
[tex]k=2[/tex]
Step-by-step explanation:
1) Rewriting:
[tex]f(x+k)=f(x)+2[/tex]
2) Suppose f(x)= ax (Linear function with b=0)
[tex]a(x+k)=ax+2\\a(x+k)=x+2\\ax+ak=x+2 \Rightarrow a=1\\x+k=x+2\\k=2[/tex]
3) Check the graph below
The correct option is D) 2.
Step-by-step explanation:
Given :
f(x) +2 and f(x +k)
Solution :
let, [tex]f(x) = ax[/tex] (linear function with b = 0)
so, [tex]f(x+k)=a(x + k)\;\;\;at,\; x=x+k[/tex]
Rewriting,
[tex]f(x+k)=f(x) + 2[/tex]
[tex]a(x + k) = ax +2[/tex]
[tex]k = 2 \;\;\;(at,\;a=1)[/tex]
Therefore, the correct option is D) 2.
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pre algebra 25=12+r r =? please show your work
Answers
[tex]25=12+r\\r=25-12\\r=13[/tex]
12 + r = 25 subtract 12 from both sides
12 - 12 + r = 25 - 12
r = 13
A local amusement park charges $21.50 per daily adult ticket and $14.75 per daily child's ticket. A group of 12 people paid $204.00 for tickets. Which system of equations could be used to find x, the number of adult tickets purchased, and y, the number of children's tickets purchased
Answers
Answer:
[tex]x+y=12[/tex]
[tex]21.50x+14.75y=204[/tex]
Step-by-step explanation:
Let x be the number of adult tickets and y be the number of children's tickets.
We are given that there are total 12 people. Therefore, we can set:
[tex]x+y=12[/tex]
Moreover, we are given that an adult ticket costs $21.50 and a child's ticket costs $14.75, therefore, cost of x adult tickets will be [tex]21.50x[/tex] and cost of y children's ticket will be [tex]14.75y[/tex]. We can form the second equation by setting the total cost of tickets as:
[tex]21.50x+14.75y=204[/tex]
Therefore, the required system of equations that could be used to find x and y will be:
[tex]x+y=12[/tex]
[tex]21.50x+14.75y=204[/tex]
Answer:
[tex]x+y = 12[/tex]
[tex]21.50x+14.75y=204.00[/tex]
Step-by-step explanation:
Given :
A local amusement park charges $21.50 per daily adult ticket and $14.75 per daily child's ticket.
Group of 12 people paid $204.00 for tickets.
To Find : System of equations could be used to find x, the number of adult tickets purchased, and y, the number of children's tickets purchased.
Solution :
Since group contains 12 people so no. of tickets are 12 .
Let out of 12 people no. of adults's tickets are x.
Let out of 12 people no. of children's ticket are y .
⇒[tex]x+y = 12[/tex]
Since charge of one adult ticket = $21.50
So, charge of x adult tickets = $21.50 x
Since charge of one child ticket = $14.75
So, charge of y children tickets =$14.75 y
And we are given that total amount paid by these 12 people = $204.00
Thus [tex]21.50x+14.75y=204.00[/tex]
Hence , System of equations could be used to find x, the number of adult tickets purchased, and y, the number of children's tickets purchased:
[tex]x+y = 12[/tex]
[tex]21.50x+14.75y=204.00[/tex]
find the unit rate 240 miles in 8 days
Answers
Answer:
30 miles per 1 day
Step-by-step explanation:
so 30 miles for each day and if you add 30 eight times which is the same as 30 times 8 you will get 240 miles hope it helps
Solve. Give your answer in scientific notation. (3.4x10^2)x(2x10^3)
A.1.4x10^-1
B.6.8x10^5
C.5.4x10^5
D.6.8x10^6
Answers
The solution in scientific notation si:
Option D: 6.8 * 10⁵
How to give the answer in scientific notation?
Scientific notation is a way of expressing very large or very small numbers. It involves writing a number as a product of a number between 1 and 10 and a power of 10.
For example, 800,000,000 can be written in scientific notation as 8 × 10⁸.
We are given the expression:
(3.4 * 10²) * (2 * 10³)
= (3.4 * 2) * 10² ⁺ ³
= 6.8 * 10⁵
A rescue helicopter is used to help victims who fell in a ditch. The helicopter begins at sea level, which is an elevation of 0 feet. It then travels down for 100 seconds at a speed of 10.5 feet per second. It then travels directly up for 150 seconds at a speed of 5.2 feet per second. After this 250 second period, how much time, in seconds, will it take for the rescue helicopter to travel back to sea level at the helicopter's maximum speed of 15.8 feet per second?
Answers
Answer:
17 seconds
Step-by-step explanation:
The rescue helicopter travels down for 100 seconds at a speed of 10.5 feet per second.
So, the distance it covered = 100(10.5) = 1050 feet.
It then travels directly up for 150 seconds at a speed 5.2 feet per second.
So, the distance = 150(5.2) = 780 feet
Now, the distance from sea level = 1050 - 780 = 270 feet.
It will reach this distance with a maximum speed of 15.8 feet per second.
Hence, the time required to reach this distance = [tex]\frac{distance}{speed}[/tex]
= [tex]\frac{270}{15.8}[/tex]
≈ 17 seconds
Solve the system by the elimination method. 2x + y - 4 = 0 2x - y - 4 = 0 When you eliminate y, what is the resulting equation? x = 0 4x = -8 4x = 8
Answers
This is because when you add the two expression together 2x+2x=4x the y values cancel and -4+-4=-8
4x-8=0 is equivalent to 4x=8
Answer:
Option C.
Step-by-step explanation:
System of the equation consists of two equations
2x + y - 4 = 0
2x + y - 4 + 4 = 0 + 4
2x + y = 4--------(1)
and 2x - y - 4 = 0
2x - y + 4 - 4 = 0 + 4
2x - y = 4------(2)
Now we will add these equations to eliminate y.
(2x + y) + (2x - y) = (4 + 4)
(2x + 2x) + (y - y) = 8
4x = 8
Therefore, resulting equation will be 4x = 8
Option C. will be the answer.
The candy machine in the bookstore has five rows to choose from with six items in each row. Currently, there are seven items that are sold out. If Ari randomly pushed a button, what is the probability he will select an item that is already sold out?
Answers
Answer:
23.3%
Step-by-step explanation:
so 5 by 6 is 30
so to find the fraction or desimal or persent u need to put 7/30
and that would be .23 reapeating then time it by 100 to get
23.3% ps the 3 is reapeating
Final answer:
The probability that Ari will select a sold-out item is 7/30 or approximately 23.33%.
Explanation:
The question asks about the probability that Ari will select an item that is already sold out from a candy machine with a certain configuration and number of sold-out items. To calculate this probability, we need to know the total number of items in the machine and how many are sold out.
There are five rows with six items each, giving a total of 30 items. With seven items sold out, there are 30 - 7 = 23 items available for purchase. The probability of selecting a sold-out item is the number of sold-out items divided by the total number of items. In this case, it's 7/30, which simplifies to 7/30.
So, if Ari randomly pushes a button on the candy machine, the probability that he will select an item that is already sold out is 7/30, or approximately 23.33%.
Which inequality is true? A. |-15| > |-19| B. |-16| < |13| C. |-15| > |12| D. |12| < |-8| E. |-19| > |-20|
Answers
The modulus or absolute value function of a real number x is the non-negative value of x without regard to its sign.
The only correct option is C. because 15 is indeed greater than 12.
Options A., B., D. and E. are wrong.
Answer: C
Step-by-step explanation: |-15| is 15. |12| is 12. 15 is greater then 12.
Which is an example of dealer incentives? A. Sun car dealers pay $18,000 to Galaxy car manufacturers for a car worth $20,000. B. Sun car dealers pay $21,000 to Galaxy car manufacturers for a car worth $20,000. C. Sun car dealers pay $20,000 to Galaxy car manufacturers for a car worth $20,000.
Answers
Answer: A. Sun car dealers pay $18,000 to Galaxy car manufacturers for a car worth $20,000.
Step-by-step explanation:
Hi, "dealer incentives" for this case mean that a car dealer pays a reduced price for a car. This incentive allows the car dealer to make a profit.
To be an example of dealer incentive the option must state that the car dealer makes a profit.
So, with this information analyzed the correct option is A."Sun car dealers pay $18,000 to Galaxy car manufacturers for a car worth $20,000" because this option states that the Sun car dealers make a profit of $2000.
Feel free to ask for more if it´s necessary or if you did not understand something.
Saheel has $20,000 property damage insurance and $5,000 comprehensive and collision insurance with a $500 deductible. One evening he slides on a patch of ice and hits a parked car, causing $4,500 worth of damage. The accident causes $1,750 of damage to his own car. How much will the insurance pay to fix both cars?
Answers
Answer:
$5750
Step-by-step explanation:
Property damage insurance = $20,000
Comprehensive insurance = $5,000
Deductible = $500
Amount of Property damage caused by him by hitting a parked car = $4,500
Amount of Damage caused to his own car = $1,750
Since, the property damage of $4500 is within the property damage insurance limit of $20,000 and own damage of $1,750 is also within the comprehensive insurance limit of $5000, he'll be paid the entire amount excluding the compulsory deductible of $500.
So,
The amount paid by the insurance company to fix both cars = 4500+1750 - 500
= 6250 - 500
= $5750
The insurance will cover a total of $5,750 for the damages caused by Saheel's accident. It will completely cover the $4,500 worth of damage to the parked car that he hit, and will cover $1,250 of the $1,750 damage to his own car after the deductible.
Explanation:In this case, Saheel has coverage for both property damage ($20,000) and comprehensive and collision insurance ($5,000 with a $500 deductible). When he slid on ice and hit a parked car, causing $4,500 worth of damage, his property damage insurance will cover this cost since it is under the $20,000 limit.
As for the $1,750 damage to his own car, his comprehensive and collision insurance can cover this after he pays the $500 deductible. So, his insurance will pay $1,250 ($1,750 - $500 deductible) towards the repair of his own car.
Therefore, the total money that the insurance company will pay to fix both cars would be $5,750 ($4,500 for the parked car's damages and $1,250 for Saheel's car damages after deductible).
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Is 3x+12-2x equivalent to x+12. Use two properties of operations to justify your answer
Answers
Answer:
Step-by-step explanation:
Commutative property: 3x+12-2x = 3x-2x+12
Substitution property: 3x-2x+12 = x+12
x+12 = x+12
Subtraction property: x-x+12 = x-x+12
Substitution property: 12 = 12
Order least to greatest
Answers
Answer:
2 6/15, 2 4/9, 2 3/5, 2 2/3
Step-by-step explanation:
Make all the fractions improper fractions. So 2 2/3= 8/3, 2 6/15= 13/15, etc.
Then make all the denominators 45 and then order them from there.
Match the products of complex numbers with their standard forms (need help :( )
Answers
2.(4+i)(2-5i)
3.(5-2i)(4-i)
4.(1-4i)(5-2i)
Jake sold 36 tickets at the school fair, and Jeanne sold 15 tickets. What is the ratio in simpilest form, of the number of tickets Jeanne sold to the number of tickets Jake sold.
Answers
Answer:
12:5
Step-by-step explanation:
We want to find the ratio of Jeanne's tickets to Jake's tickets
Jeanne's tickets: Jake's tickets
15:36
We can simplify this ratio by dividing each side by 3
15/3:36/3
5:12
Answer:
Step-by-step explanation:
15:36
simplifies to
5:12
Jeanne: Jake
Which of the following phrases are inequalities?
Answers
Answer:
B, C D
Step-by-step explanation:
Inequalities are the "alligators" < or > or the "alligators" with lines ≤ or ≥
< less than
>greater than
≤ less than or equal to
≥ greater than or equal to
ANSWERS:
B) 11 > (w - 4)^2 & C) y < 3^4 & D) 5 + 9 < 5 x 9
About this > inequality sign:
Greater thanMore thanAboveExceedsAbout this < inequality sign:
Less thanFewer thanBelowAbout this > inequality sign:
Greater than/Equal toNo less thanAt leastMinimum ofAbout this < inequality sign:
Less than/Equal toNo more thanAt mostMaximum Ofrefurbished phone 30% off now only 78£ how much was the phone before
Answers
Answer:
120 pounds
-hope this helps
Answer:
£111.43
Step-by-step explanation:
100% represents the original cost of the phone
30% off is then (100 - 30) = 70% of the original cost
divide the cost by 70 to find 1% then multiply by 100 for original cost
original cost = [tex]\frac{78}{70}[/tex] × 100 = £111.43
If x=9 and y=−2, evaluate the following expression : 6x−8y
Answers
6(9)-8(-2)
6*9=54
8*(-2)=-16
54-16=38
38<-----
Answer:
70
Step-by-step explanation:
x=9 and y=−2, evaluate the following expression : 6x−8y
plug in
6(9) - 8(-2)
= 54 + 16
= 70
x+1/3=5 6/9
A. 1/3
B. 1 8/9
C. 4 1/3
D. 5 1/3
Answers
x=
D) 5 1/3
Simplify 5 6/9 to 5 2/3. Subtract 1/3 from both sides and you are left with x=5 1/3
1/8 of pizza costs 2 dollars. In an hour, 6 1/4 pizzas were sold. How much money was made at the food booth in that hour
Answers
Answer:
$12.50
Step-by-step explanation:
1) Mutliply 6 with 2
6*2= 12
2) multiply 1/4 with 2
1/4 * 2 =1/2
3) add 12 and 1/2
12+1/2 = 12.50
By converting the mixed number of pizzas sold to an improper fraction and multiplying by the price per whole pizza, we find the food booth made $100 in one hour from selling pizzas.
To determine how much money was made at the food booth in the given hour, we need to calculate the total sale of pizzas. Since 1/8 of a pizza costs $2, an entire pizza would cost 8 times that amount, which is $16 per pizza. It was stated that 6 1/4 pizzas were sold in that hour. To find the total, we multiply the price per pizza by the number of pizzas sold.
First, convert the mixed number 6 1/4 to an improper fraction to simplify the calculation: 6 1/4 is the same as (6 × 4 + 1) / 4, which is 25/4. Then, multiply the cost per pizza, which is $16, by the number of pizzas sold, which is represented by the fraction 25/4.
The equation for total money made is then $16 × {25}/ {4} = $100.
So, the food booth made $100 in that hour from selling pizzas.
the function c=1.50(n-2)+5.50
Answers
Answer:
c =1.50n +2.50
Step-by-step explanation:
c=1.50(n-2)+5.50
The first step is to distribute the 1.5
c= 1.50*n -1.50*2 + 5.50
c = 1.50n - 3.0 +5.50
Now we need to combine like terms
c =1.50n +2.50
Michael and Imani go out to eat for lunch. If their food and beverages cost $25.30 and there is an 8% meals tax, how much is the bill?
Answers
Answer:
The bill total is $27.32
Step-by-step explanation:
how to figure out tax amount: 25.30 x .08 = $2.024
add tax to cost of meal : 25.30 + 2.024 = $27.32
To calculate the total cost of the meal including an 8% tax, multiply the cost of the meal by the tax rate and add this to the original meal cost. The tax comes to $2.02. So, the total cost of the meal, including tax, is $27.32.
Explanation:The question asks how much the total bill is for Michael and Imani when they go out to eat for lunch. The food and beverages cost $25.30 and there is an 8% meal tax. To calculate the total cost of the meal including the tax, we can multiply the cost of the meal ($25.30) by the tax rate (8%) and add this to the original cost for the meal.
First, let's convert the tax rate from a percentage to a decimal. 8% is equivalent to 0.08 as a decimal. Then, we multiply $25.30 by 0.08:
$25.30 * 0.08 = $2.02
This amount ($2.02) is the tax on the meal. To get the total cost, add this tax amount to the cost of the meal:
$25.30 + $2.02 = $27.32
So, Michael and Imani's bill, including the 8% meals tax, will be $27.32.
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On a map, the distance between Jacksonville, FL and Tallahassee, FL is about 8 inches. According to the scale, 1 inch represents 20 miles. About how far apart are the two cities?
Answers
Answer: 160 miles
Step-by-step explanation:
Because if each inch is 20 miles then you multiply 20 times 8. You multiply by 8 because that how far they live from each other in inch but you want to know miles so you multiply the I with 20 and get 160 miles
Keiko makes 8 dollars for each hour of work. Write an equation to represent her total pay p after working h hours.
Answers
Answer:
8h = pStep-by-step explanation:
So if p is the total amount paid, and h is the amount of time spent working, it'll be worked out something like this.
The amount of money she makes per hour x the amount of time spent working = the amount she is paid.
Thus making it...
8 x h = p
but in algebra expressions, we don't normally use arithmetic symbols. So if we get rid of that, we get the answer of 8h = p.
:)