In a quadrilateral ABCD, AB ∥ DC and AD ∥ BC . Find the perimeter of ΔCOD if point O is the intersection of the diagonals and AC = 20 in, BD = 20 in, AB = 13 in.
Answer:
33
Step-by-step explanation:
As the opposite sides of a quadrilateral are parallel and equal in length so
(AB) = (CD) =13
And the diagonals of a quadrilateral bisect each other at their intersection point (O in this case), so length of side OC will be the half of diagonal AC.
(OC) = (AC) /2
(OC)=20/2
(OC) =10
Similarly,
(OD) =10
Now,
Perimeter of Triangle OCD = (OC) + (CD) + (OD)
=10+13+ 10
=33
Determine the unknown side length of the golden rectangle with the given side length. s = ____ l = 9 a. 5.56 c. 4.94 b. 4.85
The smaller of two numbers is 2 less than 3/4 the larger. The sum of the two numbers is 47. Find the value of the numbers.
Final answer:
The two numbers in question are found by setting up a system of linear equations. The larger number is 39.2, and the smaller number is 27.4, found through substitution and simplification of equations representing their relationship and their sum.
Explanation:
The question involves solving a system of linear equations. Given the smaller number is 2 less than 3/4 the larger number, and the sum of the two numbers is 47, we can set up the following equations where x represents the larger number and y represents the smaller number:
y = ¾ x - 2
x + y = 47
We can substitute equation (1) into equation (2) which gives us x + (¾ x - 2) = 47. Solving for x gives us the larger number, and then y can be determined using either equation (1) or (2).
Following these steps:
x + (¾ x - 2) = 47
1¾ x - 2 = 47
1¾ x = 49
x = 49 / (5/4)
x = 49 * (4/5)
x = 39.2 (larger number)
y = ¾ * 39.2 - 2
y = 29.4 - 2
y = 27.4 (smaller number)
Thus, the two numbers are 39.2 and 27.4.
If m BOC = 30°, then m CAB = degrees
Answer: It's 330
Step-by-step explanation:
Answer:
The answer is 330.
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a number tripled and tripled again is 729.what is the number
Which describes the inverse operations used after the distributive property
Answer:
subtraction then division on edge
Step-by-step explanation:
Josh wanted to buy a bike but didn't have enough money. Sam Slick said, "I can fix that. Each time you jump that fence, i'll triple your money. There's one small thing though. Each time I pay, you must give me $54 back for the priviledge of jumping." Josh agreed, jumped the fence, received his payment from sam slick, and paid sam $54. Repeating the routine 1 more time, josh was distressed to find that after sam had made his payment to josh, josh had only $54 with which to pay sam and so had nothing left. Sam, of course, went merrily on his way, leaving josh wishing that he had known a little more about mathematics.
We can see here that according to the agreement, each time Josh jumped the fence, his money would be tripled. Thus, Josh had to pay Sam $54 back for the privilege of jumping.
Josh jumped the fence for the first time. Sam Slick paid Josh the agreed-upon amount, which was triple the initial money Josh had. Then Josh paid Sam $54 back as per the agreement.
We see that Josh jumped the fence for the second time. Sam Slick paid Josh the agreed-upon amount, which was triple the money Josh had after paying Sam $54. After Josh received the payment, he had only $54 left, which was exactly the amount he needed to pay Sam.
Write a polynomial function with rational coefficients so that P(x) = 0 has the given roots. 4, 16, and 1 + 9i
Help on 37? Thank you!
a bag of 5 lemons costs £1
a bag of 4 oranges costs £1.80
How much more does one orange cost than one lemon?
the seven houses on Kent lane are numbered from 1 to 7 .the local newspaper choose two of the houses at random to receive a free Sunday paper. What is the probability that house 6 and 7 receive the free paper
Andrea’s backyard is 400 square feet. Her rectangular swimming pool is 10 feet long, and six feet wide. What is the area of Andrea’s backyard, not including the swimming pool?
Answer: The answer is 340
Step-by-step explanation:
You have to first find the area of the swimming pool 60 then you subtract it by the backyard 400 so you would get 340.
At a games tournament, 1,008 people are divided into teams of 6. How many terms will play in the first round?
I got for an answer 168. But I feel like that is wrong??? Can someone help me with this???
Final answer:
To find out how many teams will play in the first round, divide the total number of people by the number of people in each team. In this case, there will be 168 teams playing in the first round.
Explanation:
To find out how many teams will play in the first round, we need to divide the total number of people by the number of people in each team. In this case, we have 1,008 people divided into teams of 6.
To calculate the number of teams, we divide 1,008 by 6: 1,008 ÷ 6 = 168.
Therefore, there will be 168 teams playing in the first round.
Explain how you know that 21/30 is greater than 2/3?
Movies are on sale for 1414 the original price. If the original price is $20, which expression gives the sale price?
Answer:
I'm answering super late but I want to help others who don't know the answer
Step-by-step explanation:
The answer is in the picture.
Your welcome :D
8 pounds 4 ounces = how many ounces
Which expression would you use to find the number of outcomes for flipping 4 coins?
Answer:
[tex]2^4[/tex].
Step-by-step explanation:
If we flip a coin then we have two possibilities, i.e., head or tail. So,
Number of outcomes for flipping a coin = 2
If n coins are tossed, then the total number of outcomes is defined by the expression [tex]2^n[/tex].
It is given that the number of coins is 4.
Number of outcomes = [tex]2^4=2\times 2\times 2\times 2=16[/tex]
Hence, he required expression is [tex]2^4[/tex].
solve the equation, justify each step with an algebraic property 62= 5 + x
The solution to the equation 62 = 5 + x is x = 57. This is found by subtracting 5 from both sides of the equation and checking the solution by substitution.
Explanation:To solve the equation 62 = 5 + x, we will follow algebraic properties to isolate the variable x.
Start with the equation 62 = 5 + x.Apply the Subtraction Property of Equality by subtracting 5 from both sides of the equation to eliminate terms: 62 - 5 = 5 - 5 + x, which simplifies to 57 = x.Thus, x = 57.To check the answer, substitute x = 57 back into the original equation: 5 + 57 = 62, which is true.Therefore, the solution to the equation is x = 57, and after checking, it is reasonable.
a science museum has a scale model of a ladybug in the model 50 cm represents 9 mm the length of the model is 1 m how long is the actual ladybug
ABCD is a parallelogram.Find the measure of ABC
Answer:
(C)50°.
Step-by-step explanation:
It is given that ABCD is a parallelogram and m∠ADB=38° and m∠BDC=12°.
Now, [tex]m{\angle}ADC={\angle}ADB+{\angle}BDC[/tex]
[tex]m{\angle}ADC=38^{\circ}+12^{\circ}[/tex]
[tex]m{\angle}ADC=50^{\circ}[/tex]
Also, opposite angles of parallelogram are equal, therefore m∠ADC=m∠ABC=50°.
Hence, option C is correct.
Todd would like to purchase a bicycle that costs $246. This is $48 more than twice the cost of his last bicycle. How much did his last bicycle cost?
A rowing team is practicing on a river. When the boat travels downstream, the current increases the speed of the boat. But when the boat travels upstream, the current decreases the speed of the boat. The team wrote a system letting s represent the speed in calm water and c represent the speed of the current. They found the solution for the system (s, c) to be (14, 6). How fast was the team traveling upstream and downstream?
A. The team traveled at 6 km per hour upstream and 14 km per hour downstream.
B. The team traveled at 14 km per hour upstream and 6 km per hour downstream.
C. The team traveled at 8 km per hour upstream and 20 km per hour downstream.
D. The team traveled at 20 km per hour upstream and 8 km per hour downstream.
Final answer:
The team traveled at 8 km per hour upstream and 20 km per hour downstream. Downstream speed is calculated by adding the speed of the boat in calm water to the speed of the current (s + c), and upstream speed by subtracting the current speed from the boat's speed (s - c).
Explanation:
The student is asking about the speeds a rowing team would travel when going upstream and downstream in a river. The system of equations they've solved has given a solution for the speed in calm water, represented by s, and the speed of the current, represented by c, as (14, 6). To find the speed of the team traveling upstream and downstream, we use these values in conjunction with the direction of the current.
When traveling downstream, the current adds to the speed of the boat in calm water, so you would add the speed of the boat and the speed of the current: s + c. This equates to 14 km/h (speed in calm water) + 6 km/h (speed of current) = 20 km/h downstream.
Conversely, when traveling upstream, the current subtracts from the speed of the boat in calm water, so you would subtract the speed of the current from the speed of the boat: s - c. This is 14 km/h (speed in calm water) - 6 km/h (speed of current) = 8 km/h upstream.
Therefore, the correct answer is: C. The team traveled at 8 km per hour upstream and 20 km per hour downstream.
A fruit salad consists of blueberries, raspberries, grapes, and cherries. The fruit salad has a total of 280 pieces of fruit. There are twice as many raspberries as blueberries, three times as many grapes as cherries, and four times as many cherries as raspberries. How many cherries are there in the fruit salad?
Final answer:
The given ratios indicate there should be 17.5 cherries in the fruit salad, but the number must be a whole number. There appears to be an error in the problem statement, as the conditions cannot be met with the total number of fruits given.
Explanation:
Solving the Fruit Salad Problem
Let's define the number of cherries in the fruit salad as x. According to the problem, there are four times as many cherries as raspberries, so the raspberries would be 4x. Since there are twice as many raspberries as blueberries, the blueberries would be 2(4x) = 8x. Lastly, there are three times as many grapes as cherries, meaning there are 3x grapes. To find out how many cherries are in the fruit salad, we can set up the following equation representing the total pieces of fruit:
x + 4x + 8x + 3x = 280
Adding all terms on the left side of the equation gives:
16x = 280
Dividing both sides by 16 to find the value of x gives:
x = 280 / 16
x = 17.5
Since we cannot have half a cherry in the fruit salad, the correct number of cherries must be a whole number. Therefore, it seems there's a mistake in the original statement regarding the relationship between the number of cherries and other fruits. Without the correct ratios or total pieces of fruit, a precise answer cannot be determined.
I don’t think this is correct but I got an area of 21.Can anyone help me or correct me on my error??
Simplify 24/2^2+6 plz
Julian wants to spend NO MORE than $1,250 on his trip. The airfare is $358. Write & solve an inequality to find the maximum amount he can spend on the rest of his trip.
Amount of money Julian can spend on trip= $1250
Amount spent on airfare = $358
Money left for trip = Total money - money spent on airfare= 1250 - 358= $892
So writing an inquality ,
[tex] x\leq 1250-358 [/tex]
where x is amount he can spend on trip.
Solving the inequality,
[tex] x\leq 892 [/tex]
So he can spend less than or equal to $892 on the trip.
Brian has 3 basketball cards and 5 basketball card what faction of Brian card are baseball cards
solve 12x - 14 = 16x
Help with this please!
The sum of two numbers is 24 and their difference is 2. What are the numbers?