Answer: [tex]y=6-0.5x[/tex]
Step-by-step explanation:
Given : The initial height of candle = 6 inches
Amount of candle burn each hour = one half an inch per hour.
[tex]=\dfrac{1}{2}\text{ inch per hour}[/tex]
Now , the height of candle = ( initial height ) -( Rate of burning) (Numb er of hours)
Let y be the height of the candle after x hours.
Then, the equation to represent the situation will be :
[tex]y=6-\dfrac{1}{2}x\\\\\Rightarrow\ y=6-0.5x[/tex]
The equation to represent the situation will be, [tex]y=6-\frac{1}{2} \times x[/tex].
Given A candle is 6 inches tall.
The candle burns at a rate of one half an inch per hour.
Let [tex]x[/tex] be the number of hours candle burn and [tex]y[/tex] be the height of the candle after [tex]x[/tex] hours.
Now , the height of candle = ( initial height ) -( Rate of burning) (Number of hours)
So, the equation to represent the situation will be, [tex]y=6-\frac{1}{2} \times x[/tex].
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4. The sail of a boat is in the shape of a right triangle. If the area of the sail is 42 square feet and its base is 12 feet, what is the height of the sail?
To find the height of a sail shaped as a right triangle, utilize the area formula A = (base x height) / 2, rearranged to solve for height, leading to the solution of 7 feet for the given area of 42 square feet and base of 12 feet.
To find the height of a sail that is shaped as a right triangle with an area of 42 square feet and a base of 12 feet, we can use the formula for the area of a triangle, which is A = (base x height) / 2. Therefore, we can rearrange the formula to solve for the height:
Height = (2 x Area) / base
By plugging in the values we have:
Height = (2 x 42) / 12 = 84 / 12 = 7 feet
The height of the sail is therefore 7 feet.
What is the value of x? Enter your answer in the box. x =
charles leaves the marina and sails his boat 10° west of north for 1.5h at 18km/h. he then makes a right turn to a heading of 60° east of north and sails for 1 2h at 20km/h a) at the end of time how far is charles from his starting point to his nearest km
The total distance from Charles' starting point at the marina to his destination is calculated by adding the vectors representing each leg of his journey and using the Pythagorean theorem to find the length of the resultant vector. This comes out to be approximately 40 km.
Explanation:This problem can be solved using vector addition and the Pythagorean theorem. Charles’ first leg of the journey is 10° west of north, therefore we could consider it as a vector directed north-west. Charles travels 1.5h at 18 km/h, therefore the lenght of this vector is 27km. Charles’ second leg of the voyage heads 60° east of north, that could be considered as a vector heading north-east. He sails for 1.5h at 20 km/h resulting in a vector of 30 km.
Now, if we place these two vector head to tail keeping their direction intact, we form a right triangle. Using Pythagorean theorem, the hypotenuse of the triangle will give us the distance from initial to final point. Therefore, the formula becomes √(27² + 30²) = √(729 + 900) = √1629 ≈ 40.36 km which is approximately 40 km to the nearest kilometer.
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An investment is currently worth 1.2 x 10^7 dollars. Twenty years ago, the investment was worth 9.6 x 10^5 dollars.
How many times greater is the value of the investment today than the value of the investment twenty years ago?
Answer:
12.5
Step-by-step explanation:
Hope this helps!
3. A test has 20 questions worth 100 points total. The test consists of True/False questions worth 4 points each and multiple choice questions worth 8 points each
C. Solve the system to determine how many questions of each type there are on the test. You may use any method, but you must show your work.
Answer:
x+y=20
4x+8y=100
x=-2y+25
x=-y+20
-2y+25=-y+20
-y=-5
y=5
x=15
There are 15 true/false questions and 5 multiple choice questions
Tom and his friend Edward are seeking to join the gym. Tom saw on television that platinum Jim was having a grand opening in a few months. Tom is considering a membership at platinum gym. Platinum Jim tried it one time registration fee of $60, and membership is $20 a month. Tom’s best friend Edward says he plans to join super fit because if it only charges $10 a month but has a one time registration fee of $150
On a map of Illinois, the distance between Chicago and Algonquin is 3.2 centimeters. If 2 centimeters = 40 kilometers, what is the approximate distance between the two cities?
Final answer:
The approximate distance between Chicago and Algonquin is 64 kilometers.
Explanation:
To find the approximate distance between Chicago and Algonquin, we can use the given scale of 2 centimeters = 40 kilometers. Since the distance on the map is 3.2 centimeters, we can set up a proportion to find the actual distance:
2 cm / 40 km = 3.2 cm / x km
Cross multiplying, we get 2x = 40 x 3.2, which simplifies to 2x = 128. Dividing by 2, we find that x is equal to 64. Therefore, the approximate distance between Chicago and Algonquin is 64 kilometers.
ST=x+3 and TU=4x-6 what is the value of ST and SU
I know ST=6 and SU=12, but I'm not sure how to do the problem, can someone explain?
(S, T, and U are all on the same line)
Answer:
ST= 6 unit and SU = 12 unit
Step-by-step explanation:
Here, S, T, and U are all on the same line,
Also, T is between S and U,
Such that ST = TU
Here, ST = x+3 and TU = 4x-6,
⇒ x + 3 = 4x - 6
Subtracting 3 on both sides,
⇒ x = 4x - 9
Subtracting 4x on both sides,
⇒ -3x = -9
Divide both sides by -3,
⇒ x = 3
Hence, ST = 3 + 3 = 6,
And, SU = ST + TU = ST + ST = 2 ST = 2(6) = 12
This situation is described by the image below, where we can see that:
Points S, T, and U are colinear points.
Point T is the midpoint of the segment SU.
This means that:
ST = TU
We also know that:
ST = x + 3
TU = 4x - 6
Then we can write:
ST = x + 3 = 4x - 6 = TU
x + 3 = 4x - 6
3 + 6 = 4x - x
9 = 3x
9/3 = x = 3
Now that we know the value of x we can replace it in the equations of ST and TU
ST = x + 3 = 3 + 3 = 6
TU = 4x - 6 = 4×3 - 6 = 6
And T is a point between S and U, this means that:
SU = ST + TU = 6 + 6 = 12
SU = 12
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A book has a front and a back and 400 pages. The front and back cover are each 0.9mm thick measured to 1 decimal place. Each page is 0.13 mm thick measured to 2 decimal places. Calculate the minimum thickness of the book.
Answer:
Step-by-step explanation:
0.9 UB=0.95
0.9 LB=0.85
0.13 UB= 0.135
0.13 LB= 0.125
0.85x2=1.7
0.125x400=50
1.7+50=51.7
Minimum thickness=51.7mm
To calculate the minimum thickness of the book, add up the thickness of the front cover, the back cover, and all the pages. The minimum thickness of the book is 54.8mm.
Explanation:To calculate the minimum thickness of the book, we need to add up the thickness of the front cover, the back cover, and all the pages. The front cover has a thickness of 0.9mm, the back cover has a thickness of 0.9mm, and each page has a thickness of 0.13mm. There are 400 pages in the book. So, the minimum thickness of the book can be calculated as:
Front cover thickness + Back cover thickness + (Number of pages x Page thickness)
0.9mm + 0.9mm + (400 x 0.13mm) = 0.9mm + 0.9mm + 52.0mm = 54.8mm
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Karita had $138.72 in her checking account. She wrote checks for $45.23 and $18.00. Then she made a deposit of $75.85 into her account
a band made 8,000 copies of an album they sold 6,280 copies how many copies are left
Big sale at the mall this weekend! Tank tops are on clearance for 70% off. T-shirts that regularly cost $20.00 are on sale for $12.00 each if you buy 3 or more. All jeans are half off. Write an equation to calculate the total cost of 2 tank tops, 3 T-shirts, and 1 pair of jeans. Use t to represent the original price of a tank top and j to represent the original price of a pair of jeans.
The equation to calculate the total cost of 2 tank tops, 3 T-shirts, and 1 pair of jeans is Total price = 1.6t + 36 + j/2.
What is an Equation?An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.
Given that,
Tank tops are on clearance for 70% off.
Let t be the original price.
Sale price of tank top = t - 20% of t = t - 0.2t = 0.8t
Sales price for 2 tank tops = 1.6t
Sale price for a T shirt = 12 if you buy 3 or more T shirts.
Sales price for 3 T shirts = 3 × 12 = 36
Let j be the original price of a jean.
Sale price = j/2
Equation to find the total price is,
Total price = 1.6t + 36 + j/2
Hence the required equation is Total price = 1.6t + 36 + j/2
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Final answer:
To calculate the total cost of 2 tank tops, 3 T-shirts, and 1 pair of jeans with given discounts, use the equation C = 0.60t + 36.00 + 0.5j, where t is the original price of a tank top and j is the original price of jeans.
Explanation:
The question involves calculating the total cost of purchasing 2 tank tops, 3 T-shirts, and 1 pair of jeans, with specified discounts, using the original prices of a tank top (t) and a pair of jeans (j) as variables. To compute this, we will establish an equation based on the given discounts.
For tank tops at 70% off, each tank top costs 0.30t since they are 30% of the original price. Buying 2 means spending 2(0.30t) = 0.60t.
For T-shirts, the sale offers them at $12.00 each when buying 3 or more. Thus, the total for 3 T-shirts is 3($12.00) = $36.00.
For jeans at half off, the cost of 1 pair is 0.5j, representing 50% of the original price.
Combining these, the equation for the total cost (C) is: C = 0.60t + 36.00 + 0.5j.
The price of a mountain bike is decreased from $250 to $220 by what percent is the price decreased?
A scuba diver is swimming 30 feet below sea level. A hang glider passes over the position of the scuba diver. The hang glider is 215 feet above sea level. What is the distance between the scuba diver and the hang glider? A) 185 feet B) 245 feet C) -185 feet D) -245 feet
Forty nine people are waiting in line to see the dinosaur movie seventeen are in front of Jackie how many are behind her the dinosaur movie lasts 97 minutes it starts at 4:30 pm what time will it end
A family's vacation destination is 850 miles from their home. They travel by car 6 hours on the first day of their trip. Their average speed is 45 mph. The next day they travel 7 hours, averaging the same speed. How many miles are left for the family to travel?
A) 225 miles
B) 265 miles
C) 285 miles
D) 345 miles
the cost of the fabric is $1.31. what would you expect to pay for a similar piece of fabric that is 18 inches by 42 inches?
Approximately $991.56 for a similar piece of fabric that is 18 inches by 42 inches, assuming the cost per square inch remains the same.
To calculate the cost of a similar piece of fabric that is 18 inches by 42 inches, you need to first determine the area of the fabric in square inches and then multiply it by the cost per square inch.
The area of the fabric is given by the formula:
Area = Length × Width
In this case, the length is 18 inches, and the width is 42 inches. So,
Area = 18 inches × 42 inches = 756 square inches
Now that you have the area of the fabric, you can calculate the cost. If the cost of the fabric is $1.31 for 1 square inch, then you can simply multiply the cost per square inch by the total area:
Cost = Cost per square inch × Area
Cost = $1.31 × 756 square inches
Now, calculate the cost:
Cost = $991.56
So, you would expect to pay approximately $991.56 for a similar piece of fabric that is 18 inches by 42 inches, assuming the cost per square inch remains the same.
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Given: ΔXYZ
XY = 28 cm; XZ = 30 cm; YZ = 32
AB is a midsegment parallel to XY
What is the length of AB?
Answer:
I think the answer is
7cm
Answer:
The correct answer should be 7cm if not 14cm
What are two partial products you could add to find 990x37
To find the product of 990 and 37 using partial products, break down each number into its place value components and multiply accordingly.
Explanation:To find the product of 990 and 37 using partial products, we can break down each number into its place value components. First, we multiply the ones place of 990 by the ones place of 37, which gives us 0. Next, we multiply the tens place of 990 by the ones place of 37, which gives us 370. Finally, we multiply the hundreds place of 990 by the ones place of 37, which gives us 3330. Adding all these partial products together, we get 3700 + 3330 + 0 = 7030.
Sheila is going to divide a 36 inch piece of ribbon into 5 equal pieces she says each piece will be 7 inches long what is Sheila’s error
Harriet counts 15 big boxes and 12 small boxes of notebooks. Each large box contains 189 notebooks, and each small box contains 79 notebooks. Estimate the total number of notebooks. Is your estimate an overestimate or an underestimate? Explain why it is better to have an overestimate than an underestimate.
Consider the equation .(-22+3x/3x+7)=2
How do you begin isolating the variable x to one side of the equation? Multiply both sides by 3x + 7. Divide both sides by 3x + 7. Multiply both sides by -22 + 3x. Divide both sides by -22 + 3x. _______
The solution of the equation is______
Answer: The solution of the above equation would be -12.
and First option is correct " Multiply both sides by 3x + 7."
Step-by-step explanation:
Since we have given that
[tex]\dfrac{-22+3x}{3x+7}=2[/tex]
First we multiply (3x+7) on both sides , we get
[tex]-22+3x=2(3x+7)[/tex]
And then we will solve it for the value of 'x'.
[tex]-22+3x=6x+14\\\\-22-14=6x-3x\\\\-36=3x\\\\\dfrac{-36}{3}=x\\\\-12=x[/tex]
Hence, the solution of the above equation would be -12.
and First option is correct " Multiply both sides by 3x + 7."
Answer:
Multiply both sides by 3x + 7. Divide both sides by 3x + 7. Multiply both sides by -22 + 3x. Divide both sides by -22 + 3x
Step-by-step explanation:
12 tickets for $4.68 or 10 tickets for $4.50
Betsy participates in a scavenger hunt that requires her to retrieve items from 4 locations. The locations are on a map with the coordinates as given:
Location 1 is at (−4, −1) .
Location 2 is at (−4, 4) .
Location 3 is at (3, 4) .
Location 4 is at (3, −1) .
The paths from one location to another are straight lines. One unit on the coordinate grid equals 10 yd. Betsy starts at location 1 and goes to location 2, then location 3, and then location 4, and then returns back to location 1.
What is the total distance Betsy has traveled?
Answer:
240 yd
Step-by-step explanation:
Let A, B, C, and D represent location 1, location 2, location 3, and location 4 respectively.
Consider the figure in the attached file.
We need to find the total distance traveled by Betsy.
The distance covered by Betsy is
length of segment AB[tex]+[/tex] length of segment BC[tex]+[/tex] length of segment CD[tex]+[/tex] length of segment DA.
To find the distance AB, we need to find the distance from A to B on y-axis.
So, length of segment AB [tex]=5 [/tex] units
To find the distance BC, we need to find the distance from B to C on x-axis.
So, length of segment BC [tex]=7 [/tex] units
To find the distance CD, we need to find the distance from C to D on y-axis.
So, length of segment CD [tex]=5 [/tex] units
To find the distance DA, we need to find the distance from D to A on x-axis.
So, length of segment DA [tex]=7 [/tex] units
Hence, the total distance covered is [tex]5+7+5+7=24[/tex] units
It is given that 1 unit equals 10 yd, so distance traveled by Besty is [tex]10\times 24=240[/tex] yd
(Please help!) Solve the following system by substitution:
Y=x^2+4x+6
Y= -x+2
Thank you!
what fraction is a equivalent to 0.1. repeating
Graces turkey weighs six pounds and fourteen ounces. Christians turkey weighs eighteen pounds and three ounces. How much more does Christians turkey weigh than Graces?
To find out how much more Christians turkey weighs than Graces, convert the weights to the same unit and subtract Graces turkey weight from Christians turkey weight. The difference is 11.125 pounds.
Explanation:To find out how much more Christians turkey weighs than Graces, first convert the weights of the turkeys to the same unit. Then subtract Graces' turkey's weight from Christians' turkey's weight.
To convert 6 pounds and 14 ounces to pounds, divide the 14 ounces by 16 and add the result to 6. This equals 6.875 pounds.
Now subtract Graces' turkey weight from Christians' turkey weight: 18 pounds and 3 ounces - 6.875 pounds = 11.125 pounds. Therefore, Christians' turkey weighs 11.125 pounds more than Graces' turkey.
Albert thought of a number, added 5, multiplied the result by 2, took away 6 and then divided by 2 to give an answer of 8
Tom Quig traveled 260 miles east of St. Louis. For most of the trip he averaged 60 mph, but for
3)
one period of time he was slowed to 20 mph due to a major accident. If the total time of travel was
7 hours, how many miles did he drive at the reduced speed?
3y+11 plus 7x-30 plus 5x+14 find x and the y