Each friend should contribute $196.5 towards the party supplies.
To solve this problem, we need to follow these steps:
1. Calculate the total cost of all party supplies:
- 100 balloons cost $720
- 100 plates cost $475
- 100 cups cost $5.45 each
- 100 napkins cost $2.09 each
- 10 invitations cost $1.60 each
- We need to find the cost of the plastic punchbowl.
2. Find the cost of the plastic punchbowl:
- To find the cost of the plastic punchbowl, we subtract the total cost of the known items from the total cost of all party supplies.
3. Calculate the total cost of all party supplies:
- Calculate the cost of 100 cups: [tex]\(100 \times \$5.45\)[/tex]
- Calculate the cost of 100 napkins: [tex]\(100 \times \$2.09\)[/tex]
- Sum up the costs of all known items.
4. Find the cost per friend:
- Once we have the total cost of all party supplies, we divide this total by the number of friends (10) to find out how much each friend should contribute equally.
Let's calculate step by step:
1. Calculate the total cost of all party supplies:
- Cost of 100 balloons: $720
- Cost of 100 plates: $475
- Cost of 100 cups: [tex]\(100 \times \$5.45\)[/tex]
- Cost of 100 napkins: [tex]\(100 \times \$2.09\)[/tex]
- Cost of 10 invitations: [tex]\(10 \times \$1.60\)[/tex]
- Total cost of known items [tex]= \(720 + 475 + (100 \times 5.45) + (100 \times 2.09) + (10 \times 1.60)\)[/tex]
2. Find the cost of the plastic punchbowl:
- Total cost of all party supplies - Total cost of known items = Cost of plastic punchbowl
3. Calculate the total cost of all party supplies:
- [tex]\(100 \times \$5.45 = \$545\)[/tex]
- [tex]\(100 \times \$2.09 = \$209\)[/tex]
- [tex]\(10 \times \$1.60 = \$16\[/tex]
- Total cost of known items = [tex]\(720 + 475 + 545 + 209 + 16\)[/tex]
4. Find the cost per friend:
- Total cost of all party supplies / Number of friends = Cost per friend
Let's compute these steps to find the solution.
Let's calculate step by step:
1. Calculate the total cost of all party supplies:
- Cost of 100 balloons: $720
- Cost of 100 plates: $475
- Cost of 100 cups: [tex]\(100 \times \$5.45 = \$545\)[/tex]
- Cost of 100 napkins: [tex]\(100 \times \$2.09 = \$209\)[/tex]
- Cost of 10 invitations: [tex]\(10 \times \$1.60 = \$16\)[/tex]
- Total cost of known items = [tex]\(720 + 475 + 545 + 209 + 16 = \$1965\)[/tex]
2. Find the cost of the plastic punchbowl:
- Total cost of all party supplies - Total cost of known items = Cost of plastic punchbowl
- Total cost of all party supplies - $1965 = Cost of plastic punchbowl
3. Calculate the total cost of all party supplies:
- Total cost of all party supplies = [tex]720 + 475 + (100 \times 5.45) + (100 \times 2.09) + (10 \times 1.60)[/tex] = 720 + 475 + 545 + 209 + 16 = $1965
4. Find the cost per friend:
- Total cost of all party supplies / Number of friends = Cost per friend
- [tex]\( \frac{\$1965}{10} = \$196.5 \)[/tex]
So, each friend should contribute $196.5 towards the party supplies.
the complete Question is given below:
For a party, 10 friends are buying 100 cups, 100 plates, a punchbowl, and 200 balloons. If the friends share the cost equally, how much should each friend contribute? Party Supplies 100 balloons $720 100 plates $475 100 cups $5.45 100 napkins $2.09 What steps do you need 10 invitations $1.60 to solve to find the plastic punchbowl
Select the correct answer from each drop-down menu.
In the figure, AC and BD bisect each other. Complete the statements to prove that quadrilateral ABCD is a parallelogram.
Reason options for 3rd statement:
•Alternate Interior Angles Theorem
•Vertical Angles Theorem
•Alternate Exterior Angles Theorem
Reason options for 9th statement:
•Converse of Alternate Exterior Angles Theorem
•Converse of Alternate Interior Angles Theorem
•Converse of Corresponding Angles Theorem
•Converse of Exterior angle theorem
Answer:1Vertical angles theoram
Step-by-step explanation:2 coverse of alternate interior angles theoram
Answer:
1. Reason options for 3rd statement:
Alternate Interior Angles Theorem
2.Reason options for 9th statement:
Converse of Alternate Interior Angles Theorem
Step-by-step explanation:
4 friends evenly divided up a n-slice pizza. One of the friends,Harris, ate 1 fewer slice than he received. How many slices of pizza did Harrison eat? Write your answer as an expression
Answer:
Step-by-step explanation:
(n/4)-1
Divide total slices by 4 friends then subtract 1 to get Harrison’s amount
Higher Order Thinking Jamie says
that 19 - 10 is equal to 20 – 10
because both use subtraction. Is Jamie
correct? Explain why or why not.
**1st grade question**
Answer: Jamie is incorrect
Step-by-step explanation:
The same number 10 is subtracted from both numbers 19 and 20. There result will only be the same if both numbers are equal.
We compare both numbers;
19 and 20
On the number line 19 comes before 20, which means 20 is greater than 19. Hence the result of subtracting the same number 10 from both of them cannot be the same.
So Jamie is incorrect.
Answer:
she is wrong 19-10 equals to 9
Step-by-step explanation:
you subtract 19 from 10 and get 9:)
Giulia is playing a game with 6 cards: 4 kings, 1 queen, and 1 jack. She draws 1 card out of the stack of cards, replaces it, and then draws another card.
What is the probability that she will draw a king and then a jack, P(king, then jack)?
Answer: 1/9
Step-by-step explanation:
Total number of cards = 6
Probability = required outcome/ all possible outcome
number of kings=4
number of jack=1
Probability of drawing a king = 4/6
probability of drawing a jack = 1/6
Probability of drawing a king and then a jack is p(king and jack) = p(king) × p(jack) = 4/6 × 1/6 = 4/36
= 1/9
Answer:
1/9
thats all
Step-by-step explanation:
Jessica is a custodian at Oracle arena. She waxes 20 mi squared of the floor 3/5 of an hour. Jessica waxes the floor at a constant rate. At this rate how many square meters can she wax per hour.
The correct answer is:
Jessica can wax approximately 34,533,185 square meters per hour at her constant rate of waxing the floor.
To find out how many square meters Jessica can wax per hour, we first need to convert the square miles to square meters, then divide by the time taken.
1. Convert square miles to square meters:
Since 1 mile = 1609.34 meters, to convert square miles to square meters, we square this conversion factor:
[tex]\[ 1 \text{ mile}^2 = (1609.34)^2 \text{ meters}^2 \] \[ 1 \text{ mile}^2 = 2,589,988.36 \text{ meters}^2 \][/tex]
So, 20 square miles would be:
[tex]\[ 20 \text{ miles}^2 \times 2,589,988.36 \text{ meters}^2/\text{mile}^2 = 51,799,767.2 \text{ meters}^2 \][/tex]
2. Calculate the rate per hour:
Jessica waxes 20 square miles in [tex]\( \frac{3}{5} \)[/tex] of an hour.
So, her rate per hour is:
[tex]\[ \frac{20 \times 2,589,988.36}{\frac{3}{5}} \text{ meters}^2/\text{hour} \][/tex]
To simplify the calculation, we'll first find the reciprocal of [tex]\( \frac{3}{5} \): \[ \frac{1}{\frac{3}{5}} = \frac{5}{3} \][/tex]
Now, we multiply the reciprocal by 20 square miles:
[tex]\[ 20 \times 2,589,988.36 \times \frac{5}{3} \text{ meters}^2/\text{hour} \] \[ \text{meters}^2/\text{hour} = 34,533,184.8 \][/tex]
So, Jessica can wax approximately [tex]\( 34,533,184.8 \)[/tex] square meters per hour at her constant rate.
standard form Ax+By=C
x-3y=-6
Explanation:
The equation is already in standard form.
A is 1. The number 1 is often unwritten.
B is -3. The negative or positive sign is included with the equation.
C is -6. (If using this for the quadratic formula, c is actually 6 because the equation should equate to 0).
Peggy is thinking of a number such that when twice the number is added to three times one more than the number she gets the same result as when she multiplies four times one less than the number. What number is Peggy thinking of?
Answer:
-7
Step-by-step explanation:
Lets assume the number Peggy is thinking of be "x".
Now as given, when twice the number is added to three times one more than the number. We can write it as
∴ [tex]2x+3(x+1)[/tex]--- Equation 1
Again, it is given that Peggy gets the same result as when she multiplies four times one less than the number.
∴ [tex]4(x-1)[/tex]-- equation 2
Next, we can equate both the equation 1 and 2 as it is given that result is same.
[tex]2x+3(x+1)= 4(x-1)[/tex]
Let´s distribute 3 into [tex](x+1)[/tex] and 4 into [tex](x-1)[/tex]
⇒ [tex]2x+3x+3=4x-4[/tex]
⇒ [tex]5x+3=4x-4[/tex]
Subtract both side by 4x and 3
∴ [tex]x=-7[/tex]
∴ Peggy was thinking of -7
The total number of restaurant purchased meals that the average person will eat in a restaurant, and a car, or at home in a year is 171 . The total number of these meals eaten in a car or at home exceeds the number eaten in a restaurant by 11. Twenty more restaurant purchased meals will be eating in a restaurant than at home. Find the number of restaurant purchased meals eaten in a restaurant, the number eaten in a car, and the number eating at home.
Answer:
80 restaurant purchased meals are eaten in a restaurant31 meals are eaten in a car60 meals are eaten at homeStep-by-step explanation:
Let us suppose r be the total number of meals eaten in a restaurant
Let us suppose c be the total number of meals eaten in a car
Let us suppose h be the total number of meals eaten in a home
The total number of meals eaten in a restaurant, in a car or at home is given as 163. Hence, [tex]r + c + h = 171.....[A][/tex]The total number meals eaten in a car or at home exceeds the number eaten in a restaurant by 11. Hence, [tex]c + h = r + 11.....[B][/tex]Twenty more restaurant-purchased meals will be eaten in a restaurant than at home. Hence, [tex]r = h + 20.....[C][/tex]Substituting Equation [B] into [A],
[tex]r + c + h = 171.....[A][/tex]
[tex]r + r + 11 = 171[/tex]
[tex]2r + 11 = 171[/tex]
[tex]2r = 160[/tex]
[tex]r = 80[/tex]
Putting [tex]r = 80[/tex] in [tex]r = h + 20.....[C][/tex]
[tex]80 = h + 20[/tex]
[tex]h = 60[/tex]
Putting [tex]r = 80[/tex] and [tex]h = 60[/tex] in [tex]r + c + h = 171.....[A][/tex]
[tex]80 + c + 60 = 171[/tex]
[tex]c = 171 - 60 - 80[/tex]
[tex]c = 31[/tex]
Therefore,
80 restaurant purchased meals are eaten in a restaurant31 meals are eaten in a car60 meals are eaten at homeVerification:
[tex]r + c + h = 171[/tex]
Putting [tex]r = 80[/tex], [tex]c = 31[/tex] and [tex]h = 60[/tex] in [tex]r + c + h = 171[/tex]
[tex]80 + 31 + 60 = 171[/tex]
[tex]171 = 171[/tex]
Keywords: number, equation
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Maria finds a local gym that advertises 102 training sessions for $767. Find the cost of 117 training sessions.
Answer:
$986
I attempted to do the simple math. I feel brain dead right now.
Circles!!! NEED HELP!!!
Picture:
Answer: [tex]x=105\°[/tex]
Step-by-step explanation:
You can identify from the given figure that the angle that measures 70 degrees is formed by two intersecting Chords.
It is important to remembe that, by definition:
[tex]Angle\ Formed\ by\ Two\ Chords =\frac{1}{2}(Sum\ of\ Intercepted\ Arcs)[/tex]
Based on this, you know that:
[tex]70\°=\frac{35\°+x}{2}[/tex]
Having this equation, the final step is to solve for "x" in order to find its value. You get that this is:
[tex](70\°)(2)=35\°+x\\\\140\°=35\°+x\\\\140\°-35\°=x\\\\x=105\°[/tex]
Jennie's car gets 32.4 miles per gallon on the highway. If her car's fuel tank holds 12.7 gallons, how far can she drive on one tank of gas?
Multiply the miles per gallon by the total gallons:
32.4 x 12.7 = 411.48 total miles.
Answer:
411.48
Step-by-step explanation:
411.48
7w/4+3=9w/10+6
I really need help on this
Answer:
w=3 9\17
Step-by-step explanation:
What do you know about the slope when X2 - X1 = 0 ?
Answer:
slope is undefined
Step-by-step explanation:
Using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
If x₂ - x₁ = 0
Since division by zero is undefined then the slope of the line is undefined
This applies to a vertical line parallel to the y- axis
Jamal bought 2 pounds of red apples and 3.2 pounds of green apples from a grocery store, where both kinds of apples are $1.65 a pound. How much did Jamal spend on apples? PLEASE HELP :(
In this question, we're trying to find out how much Jamal spent on apples.
We know that he bought 2 pounds of red apples and 3.2 pounds of green apples.
We also know that each pound of apples, no matter what kind it is, are $1.65 a pound.
In order to find the total cost of these apples, we would need to multiply the amount of pounds he has to the cost per pound.
Solve:
2 · 1.65 = 3.30
3.2 · 1.65 = 5.28
Add those numbers together:
5.28 + 3.30 = 8.58
This means that Jamal spent $8.58 on apples.
Answer:
$8.58
Answer:
$8.58
Step-by-step explanation: this ok?
Help meee!!!! In this diagram the area of the saller square is .....
Answer:
The area of the larger square is 20 [tex]cm^2[/tex]
Step-by-step explanation:
Given:
The area of the smaller square = [tex]10 cm^2[/tex]
To Find:
The are of the larger square = ?
Solution:
The diagonal of the smaller square = diameter of the circle = sides of the larger square
The diagonal of the smaller square is
=>[tex]\sqrt{2(10)}[/tex]
=>[tex]\sqrt{20}[/tex]
=>[tex]\sqrt{2\times 2 \times 5}[/tex]
=>[tex]2\sqrt{5}[/tex]
Now this diagonal is equal to the side of the larger square
so the are of the larger square is
=>[tex](2\sqrt{5})^2[/tex]
=>[tex](2\sqrt{5}) \times (2\sqrt{5}) [/tex]
=> 20 [tex]cm^2[/tex]
would some one please solve part A for me I have been try to solve it for a while thank you very much .
Step-by-step explanation:
4x + 10 = 32
4x = 32 - 10
4x = 22
x = 11/2
if we add 4 to both sides of the equation :
4x + 10 + 4 = 32 + 4 ➡ 4x + 14 = 36
4x = 36 - 14 ➡ 4x = 22 and x = 11/2
as you can see the value for x didn't change because when we add/subtract or multiple/divide same number from both sides of an equation the result won't change.
A person invests 3000 dollars in a bank. The bank pays 5.75% interest compounded annually. To the nearest tenth of a year, how long must the person leave the money in the bank until it reaches 7200 dollars?
Answer:
15.7 years
Step-by-step explanation:
Use the formula for compound interest. A = P(1 + i)ⁿ
A is the total amount of money. A = 7200
P is the principal, starting money. P = 3000
i is the interest per compounding period in decimal form. Since interest is compounded annually, i = 0.0575
n is the number of compounding periods. n = ?
Substitute the information into the formula and isolate n.
A = P(1 + i)ⁿ
7200 = 3000(1 + 0.0575)ⁿ Solve inside the brackets
7200 = 3000(1.0575)ⁿ
7200/3000 = 1.0575ⁿ Divide both sides by 3000
2.4 = 1.0575ⁿ
n = (㏒ ans) / (㏒ base)
n = (㏒ (2.4)) / (㏒ (1.0575))
n = 15.659..... Exact answer
n ≈ 15.7 Rounded to the nearest tenth of a year
Therefore the person must leave the money in the bank for 15.7 years until it reaches 7200 dollars.
Eli rode his dirtbike around a 400 meter track at a constant speed of 1000 meters per minute how many minutes does it take Eli to complete 6 laps of the track
It will take Eli 2.4 minutes to complete 6 laps
Step-by-step explanation:
Given
Speed = s = 1000 meters per minute
Length of one lap = 400 meters
We have to compute time for 6 laps,, so we have to find the length of 6 laps combined
[tex]Length\ of\ laps = Length\ of\ one\ lap * 6\\= 400 * 6\\= 2400\ meters[/tex]
So our total distance will be: 2400 meters
using the formula for speed
[tex]s = \frac{d}{t}\\1000 = \frac{2400}{t}\\t = \frac{2400}{1000}\\t = 2.4[/tex]
So
It will take Eli 2.4 minutes to complete 6 laps
Keywords: Speed, distance
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g(x) = (x + 2)2 what is its graph
Answer: The graph is a parabola facing up ,
Step-by-step explanation:
Since the coefficient of [tex]x^{2}[/tex] is positive , then the graph is a parabola facing up.
The minimum point is at x = -2 ( using the formula for calculate vertex , x = [tex]\frac{-b}{2a}[/tex] )
And the y - intercept = 4
Harita must memorize 90 measures of music for her cello solo at a concert. She plans on memorizing 18 new measures for
every 3 days of practice. Which equation can be used to determine m, the number of measures Harita still needs to
memorize, as a function of d, the number of days of practice since she began learning the piece?
Om = 72 - 150
Om= 90 - 60
Om = 101 - 210
Om= 108 - 3d
What is d?
m = 90 - 6d is the equation to determine m, the number of measures Harita still needs to memorize, as a function of d, the number of days of practice since she began learning the piece
Solution:
Given that Harita must memorize 90 measures of music for her cello solo at a concert
To find: equation to determine m, the number of measures Harita still needs to memorize, as a function of d, the number of days of practice since she began learning the piece
Let "m" be the number of measures Harita still needs to memorize
Let "d" be the number of days of practice since she began learning the piece
Given that She plans on memorizing 18 new measures for every 3 days of practice
Rate per day is given as:
[tex]\frac{18}{3} = 6[/tex]
Therefore she memorises 6 per day
Therefore, the equation that relates 'm' to 'd' is:
m = total measures of music she must memorise - (number of measures she memorises per day x d)
m = 90 - 6(d)
m = 90 - 6d
Thus the required equation is found
Answer:
m = 90 - 6d is the equation to determine m, the number of measures Harita still needs to memorize, as a function of d, the number of days of practice since she began learning the piece
Step-by-step explanation:
Ribbon a is 1/3. M long. It is 2/5 M shorter than ribbon B. How long is Ribbon B?
Ribbon B is [tex]\frac{11}{15}[/tex] meters long
Solution:
Given that,
Ribbon A is 1/3 meter long. It is 2/5 meter shorter than ribbon B
To find: length of Ribbon B
From given information in question,
Length of Ribbon A = [tex]\frac{1}{3} \text{ meter }[/tex]
Length of Ribbon A is 2/5 meter shorter than ribbon B
Therefore we can say,
Length of Ribbon A = length of ribbon B - [tex]\frac{2}{5}[/tex]
[tex]\frac{1}{3} = \text{ length of ribbon B } -\frac{2}{5}\\\\\text{length of ribbon B } = \frac{1}{3} + \frac{2}{5}\\\\\text{length of ribbon B } = \frac{ 5 + 6}{15} = \frac{11}{15}[/tex]
Therefore ribbon B is [tex]\frac{11}{15}[/tex] meters long
I don’t understand this help please
Answer:
9
Step-by-step explanation:
The first simplification we can make is to replace 6^0 with 1.
The first rules of exponents we can apply are ...
(a·b)^c = a^c·b^c . . . . . . similar to the distributive property
(a^b)^c = a^(b·c)
This reduces your expression to ...
[tex](2^8\cdot 3^{-5})^{-2}\cdot\left(\dfrac{3^{-2}}{2^3}\right)^4\cdot 2^{28}=2^{8(-2)}\cdot 3^{-5(-2)}\cdot\dfrac{3^{-2(4)}}{2^{3(4)}}\cdot 2^{28}\\\\=2^{-16}\cdot 3^{10}\cdot\dfrac{3^{-8}}{2^{12}}\cdot 2^{28}[/tex]
Now we can apply another two rules of exponents:
(a^b)(a^c) = a^(b+c)
1/a^b = a^-b
Using these, we have ...
[tex]=2^{-16-12+28}\cdot 3^{10-8}\\\\=2^0\cdot 3^2\\\\=1\cdot 9=9[/tex]
The value of the expression is 9.
Roots of -2x^2 -6x+5=0
For this case we have the following quadratic equation:
[tex]-2x ^ 2 -6x + 5 = 0[/tex]
Where:
[tex]a = -2\\b = -6\\c = 5[/tex]
The roots will be given by the following formula:
[tex]x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2a}[/tex]
Substituting the values we have:
[tex]x = \frac {- (- 6) \pm \sqrt {(- 6) ^ 2-4 (-2) (5)}} {2 (-2)}\\x = \frac {6 \pm \sqrt {36 + 40}} {- 4}\\x = \frac {6 \pm \sqrt {76}} {- 4}\\x = \frac {6 \pm \sqrt {2 ^ 2 * 19}} {- 4}\\x = \frac {6 \pm2 \sqrt {19}} {- 4}\\x = \frac {3 \pm \sqrt {19}} {- 2}[/tex]
We have two roots:
[tex]x_ {1} = \frac {-3- \sqrt {19}} {-2}\\x_ {2} = \frac {-3+ \sqrt {19}} {2}[/tex]
Answer:
[tex]x_ {1} = \frac {-3- \sqrt {19}} {2}\\x_ {2} = \frac {-3+ \sqrt {19}} {2}[/tex]
Amanda decided to save the money that she earned babysitting to buy school clothes. Amanda wants to buy two pairs of jeans that cost $32 each, three shirts that cost $18 each, and a jacket that costs $54. How much money does Amanda need to buy all of the clothes that she wants?
Answer:
Step-by-step explanation:
Two pairs of jeans cost $32 dollars so multiply 32 x 2 and get $64.
Three shirts cost $18, multiply 18 x 3 to get $54.
One jacket costs $54 so just do 1 x 54 and you will get $54.
54 + 54 + 64 = $172.
I hope this helped!
Amanda needs $172 to buy all the clothes she wants.
Explanation:To calculate the total cost of the clothes Amanda wants to buy, we need to add up the cost of each item.
Cost of two pairs of jeans: 2 x $32 = $64Cost of three shirts: 3 x $18 = $54Cost of one jacket: $54To find the total cost, we add up these amounts:
= $64 + $54 + $54
= $172.
Therefore, Amanda needs $172 to buy all the clothes she wants.
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The diagram below shows twelve 30-60-90 triangles placed in a circle so that the hypotenuse of each triangle coincides with the longer leg of the next triangle. The fourth and last triangle in this diagram are shaded. The ratio of the perimeters of these two triangles can be written as m/n where m and n are relatively prime positive integers. Find m + n
Answer:
m+n = 337
Step-by-step explanation:
Lets start from the first triangle, It is given to be as 30-60-90.
The hypotenous of first rectangle be 2x, then other sides are by default x and
[tex]\sqrt{3}(x)[/tex] , using laws of trigonometry.
(sin(30) = 0.5 and cos(30) = [tex]\frac{\sqrt{3}}{2}[/tex])
The perimeter of first triangle is ,
= [tex]2x + x + \sqrt{3}(x) = x(3+\sqrt{3}) = \sqrt{3}x(1+\sqrt{3})[/tex]
Now, for second triangle, the longer leg is 2x, and similarly again,
other 2 sides are [tex]\frac{2x}{\sqrt{3}} and \frac{4x}{\sqrt{3}}[/tex].
Again the perimeter of triangle comes out as,
= [tex]\sqrt{3}(x)(1+\sqrt{3})(\frac{2}{\sqrt{3}})[/tex]
Thus, the repeating pattern is identified. The consecutive perimeters differ by, multiplying by factor [tex]\frac{2}{\sqrt{3}}[/tex]
Thus, we can say that perimeter of 4th triangle is,
= [tex](\frac{2}{\sqrt{3}})^{3}(X)[/tex], where X is the repeating constant.
And of 12th triangle is,
= [tex](\frac{2}{\sqrt{3}})^{11}(X)[/tex],
Evaluating the above ratio, we get,
= [tex]\frac{81}{256}[/tex]
Thus, m =256 and n=81.
Thus, m+n = 256+81 = 337.
The hexagon is made from a rectangle and two identical triangles.
13 cm
5 cm
12 cm
Work out the area of the hexagon.
Answer:
The area of the hexagon is 108 cm².
Step-by-step explanation:
Consider the below figure attached with this question.
From the below figure we get
Length of rectangle = 12 cm
width of rectangle = 5 cm
It is given both triangles are identical.
Base of each triangle = 12cm
Height of each triangle = (13-5)/2 = 4 cm
Area of rectangle is
[tex]Area=length\times width=12\times 5=60[/tex]
Area of rectangle is
[tex]Area=\frac{1}{2}\times base\times height[/tex]
[tex]Area=\frac{1}{2}\times 12\times 4=24[/tex]
Area of one triangle 24 cm². So, area of both triangle is
[tex]2\times 24=48[/tex]
Area of hexagon = Area of rectangle + Area of both triangles
= [tex]60+48[/tex]
= [tex]108[/tex]
Therefore, the area of the hexagon is 108 cm².
By finding the areas of the rectangle and the two triangles separately and adding them together, we determine that the area of the hexagon is 125 cm².
Explanation:To find out the area of the hexagon, you would need to find the areas of the rectangle and the triangles separately, and then add them together. The rectangle's area can be calculated easily using the formula for the area of a rectangle: Length x Breadth.
Assuming the rectangular part length to be 13cm and breadth to be 5cm, area of rectangle = 13cm x 5cm = 65cm².
The two triangles appear to be right triangles. You can use the formula for the area of a right triangle: 0.5 x Base x Height.
Assuming the base and height of the triangles to be 12cm and 5 cm, therefore the area of one triangle is 0.5 x 12cm x 5cm = 30cm². Since there are two of these triangles, their combined area = 2 x 30cm² = 60cm².
Finally, combining the areas of the rectangle and triangles equals the area of the hexagon: 65cm² + 60 cm² = 125 cm².
The area of the hexagon is
125 cm²
.
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type the outputs of these ordered pairs from greatest to least:(-1,2),(-3,-1),(6,0),(-1,4)
Answer:
4,2,0,-1
Step-by-step explanation:
Let
x ----> the independent variable or input value
y ----> the dependent variable or output value
we have the ordered pairs
(-1,2),(-3,-1),(6,0),(-1,4)
The input values are -1,-3,6,-1
The output values are 2,-1,0,4
Orders the output values from greatest to least
4>2>0>-1
therefore
4,2,0,-1
Answer:
4,2,0,-1
hope this helps
An amusement park charges admission plus a fee for each ride. Admission plus four ride cost $22. Admission plus seven ride cost $31. What is the charge for admission and the cost for each ride
Answer:
Admission fee charged = $3
Cost of each ride = $10
Step-by-step explanation:
Let admission fee charged by amusement park in dollars be =[tex]x[/tex]
Let cost of each ride in dollars be =[tex]y[/tex]
Given:
Admission plus four rides cost $22
If each ride cost in dollars = [tex]y[/tex]
Cost of 4 rides in dollars will be = [tex]4y[/tex]
So, the total cost in dollars will be given as =[tex]x+4y[/tex]
So, we have
[tex]x+4y=22[/tex]
Admission plus seven ride cost $31.
If each ride cost in dollars = [tex]y[/tex]
Cost of 7 rides in dollars will be = [tex]7y[/tex]
So, the total cost in dollars will be given as =[tex]x+7y[/tex]
So, we have
[tex]x+7y=31[/tex]
So, we have the system of equation as:
A) [tex]x+4y=22[/tex]
B) [tex]x+7y=31[/tex]
Solving the system by elimination method.
Eliminating [tex]x[/tex] by subtracting equation A from B.
[tex]x+7y=31[/tex]
- [tex]x+4y=22[/tex]
- - - [Sign of each term of subtract-ant gets reversed]
-----------------------------
[tex]3y=9[/tex]
Dividing both sides by 3.
[tex]\frac{3y}{3}=\frac{9}{3}[/tex]
∴ [tex]y=3[/tex]
Plugging in [tex]y=3[/tex] in equation A.
[tex]x+4(3)=22[/tex]
[tex]x+12=22[/tex]
Subtracting both sides by 12.
[tex]x+12-12=22-12[/tex]
∴ [tex]x=10[/tex]
Thus, admission fee charged = $3
Cost of each ride = $10
1. Determine if the set of ordered pairs is a relation or a function.
{(0,0), (0, 2), (0, 3), (0,4)}
Answer:
This is just a relation.
Step-by-step explanation:
It is easy to see if a set of ordered pairs is a relation or a relation that is a function.
If all the points are distinct, then you just have to look at the [tex]x[/tex]-coordinates.
If all the [tex]x[/tex]-coordinates are different, then it is a function. Otherwise, it is a just a relation.
So this cannot be a function because there is at least two different points that have [tex]x=0[/tex].
The perimeter of a rectangle with a length of 10 cm is 32 cm.
What is the width of the rectangle?
A. 6 cm
B. 10 cm
C. 12 cm
Answer:
32=2(10+x)
32=20+2x
2x=12
x=6
therefore breadth is 6 cm
area=l×b
10×6=60
Step-by-step explanation: