Hello there, there are multiple ways of solving this problem, let me show you.
[tex]{\huge{\boxed{\mathbb{QUESTION}}}}}[/tex]
A Freight Train Travels 144 miles in 6 hours. How Far will it travel in 15 hours?
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For this problem I will show you 2 methods.
[tex]{\huge{\boxed{\mathbb{METHOD\:ONE}}[/tex]
Cross multiplication, cross multiplication involves algebra to use.
Let x be our answer for this problem. Here is our it would look like
[tex]\frac{6}{144}=\frac{15}{x}[/tex], now we will cross multiply, here is what it'd look like now.
[tex]6x=2160[/tex], then do simple algebra and divide both sides by 6. and then we get [tex]x=360[/tex] miles in 15 hours.
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[tex]{\huge{\boxed{\mathbb{METHOD\:TWO}}[/tex]
For method two we can look for the unit rate. Also known as our rate for one.
divide 144 by 6 and we get 24, then multiply it by 15 and we get 360.
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[tex]{\huge{\boxed{\mathbb{EXACT\:ANSWER}}[/tex]
360 miles in 15 hours.
Have a good day :) !The figure shows triangle DEF and line segment BC, which is parallel to EF:
Triangle DEF has a point B on side DE and point C on side DF. The line BC is parallel to the line EF.
Part A: Is triangle DEF similar to triangle DBC? Explain using what you know about triangle similarity. (5 points)
Part B: Which line segment on triangle DBC corresponds to line segment EF? Explain your answer. (3 points)
Part C: Which angle on triangle DBC corresponds to angle F? Explain your answer. (2 point
Part A: Yes, Triangle DEF and DBC are the same triangle, but DBC is smaller than DEF because it is just a cut off of DEF.
Part B: I am pretty sure it is angle C.
Part C: I am pretty sure it is angle D.
Answer:
Step-by-step explanation:
Part A.
m < B = m < E (corresponding angles, (BC parallel to EF))
m < C = m < F ( as above)
So triangles DBC and DEF are similar ( by 2 equal angles).
Part B.
Line segment BC ( as they are both opposite < D)
Part C.
< C as its in same relative position to < F.
How is solving −7x = −10.5 different from solving − 1 7 x = −10.5? How are the solutions related? Complete the explanation.
The function a(1) =1/2I^2 describes the area of an isosceles right triangle with leg I. Make a table of values for I=1,2,3 and 4. Enter your outputs as decimals
Functions can be represented using equations, graphs and tables.
The function is given as:
[tex]a(l) = \frac 12 l^2[/tex]
When l = 1, we have:
[tex]a(1) = \frac 12 \times 1^2[/tex]
[tex]a(1) = 0.5[/tex]
When l = 2, we have:
[tex]a(2) = \frac 12 \times 2^2[/tex]
[tex]a(2) = 2.0[/tex]
When l = 3, we have:
[tex]a(3) = \frac 12 \times 3^2[/tex]
[tex]a(3) = 4.5[/tex]
When l = 4, we have:
[tex]a(4) = \frac 12 \times 4^2[/tex]
[tex]a(4) = 8.0[/tex]
Represent the above results as a table, we have:
l a(l)
1 0.5
2 2.0
3 4.5
4 8.0
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A gardener has a flower pot that he wants to fill with dirt. The flower pot has a radius of 8 cm at its opening and a radius of 7 cm at its base. The flower pot has a height of 10 cm.
Part A:
Provide an estimate for the amount of dirt, in cubic centimeters, that the gardener will need to completely fill the flower pot.
Part B:
Explain how you determined your answer.
Part A: The approximate volume of the frustum is [tex]1769cm^3[/tex].
Part B: How the answer was determined was to view the flower pot as a frustum of a cone, and apply the formula in calculating the volume of the flower-pot.
The flower pot has the shape of a conical frustum (See the attached image). The volume of the frustum is given by
[tex]F = \frac{\pi y}{3}(R^2+Rr+r^2)[/tex]
where
[tex]y=\text{height of the frustum}=H-h=10cm\\R=\text{radius of larger cone}=8cm\\r=\text{radius of smaller cone}=7cm[/tex]
substituting the values of [tex]y[/tex], [tex]R[/tex] and [tex]r[/tex] into the frustum formula and using [tex]\pi\approx 3.14[/tex]
[tex]F = \frac{\pi y}{3}(R^2+Rr+r^2)\\\\=\frac{\pi\times 10 }{3}(8^2+8\times 7+7^2)\\\\=\frac{10\pi}{3}(64+56+49)\\\\=\frac{1690\pi}{3}\\\\\approx 1769cm^3[/tex]
the approximate volume of the frustum is [tex]1769cm^3[/tex]
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a number cube is rolled.what is the probability of rolling a number greater than 4
Answer: 2/6
Step-by-step explanation:
There’s only 2 numbers greater than 4 on a die, so two would be the numerator and the denominator would be the number of possibilities you could roll, which is 1-6.
2/6, 1/3, or approx. 33.3%
A number cube will have six sides and two out of six will be greater than four, therefore, there is around a 33.3% chance you will roll a number greater than 4. :)
Solve the division fact:
7 = 56 :
Answer:
the correct answer to the math problem is 8
Step-by-step explanation:
56÷8=7
Sal's total profit on lunch specials for the next month is $1,593. The profit amounts are the same: $2 for each sandwich and $3 for each wrap. In a paragraph of at least three complete sentences, explain how the graphs of the functions for the two months are similar and how they are different.
Both still have the same profit. $2 for sandwiches and $3 for wraps. The only reason why there is a difference in the total amount is the change in number of sandwich or wrap sold in a given month. Therefore, next month's total sale is higher than last month's total sale making it safe to assume that the sale of sandwich or wrap is higher than last month's sale.
{hope this helps}
What are the solutions to the equation (x-1)(x+2)=-2?
Method used:-
Completing the square method.
Steps :-
[tex]( x - 1 ) ( x + 2 ) = - 2\\x^{2}+x-2=-2 \\x^{2}+x=-2+2 \\x^{2}+x=0[/tex]
Now, make the left hand side of the equation by adding the square of ½ to both sides of the equation.
[tex]x^{2}+x+\left(\frac{1}{2}\right)^{2}=\left(\frac{1}{2}\right)^{2} \\x^{2}+x+\frac{1}{4}=\frac{1}{4} \\\left(x+\frac{1}{2}\right)^{2}=\frac{1}{4} \\\sqrt{\left(x+\frac{1}{2}\right)^{2}}=\sqrt{\frac{1}{4}} \\[/tex]
Simplify the equation. You'll get a +ve & -ve value.
[tex]x+\frac{1}{2}=\frac{1}{2} \\x+\frac{1}{2}=-\frac{1}{2}[/tex]
Simplify it further.
[tex]\boxed{\sf\:x=0}\\ \boxed{\sf\:x=-1 }[/tex]
The solutions are :-
x = 0 & x = -1
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Hope it helps ⚜
Solve 4 | x + 7 |= 24.
Answer
either 168 or 164thats all i can tell you
Step-by-step explanation:
lois made a dish with 6 1/3 cups of pasta . One serving of the pasta is 0.2 cups. How many servings of pasta were in the dish Lous made?
Answer:
33 2/3
Step-by-step explanation:
First you would change 0.2 to a fraction. This would be 1/5. You would then have to make these two have a common denominator. 6 1/3 would also become an improper fraction for visual sake.. The lowest common denominator they share is 15. I've drawn the process in the image above.
So now we have 95/15 and 3/15. From here, we would divide 95 by 3.
95 ÷ 3 = 31 10/15
This would give us 31 and 10/15 servings of pasta in the bowl. If we're talking about full servings, 31 would be the correct number, but if we're talking exact, then it is 31 2/3.
rachel got prepaid debit card with $30 on it. For her first purchase with the card, she bought some bulk ribbon at a craft store. The price of the ribbon was 22 cents per yard. If after that purchase there was $19.88 left on the car, how many yards of ribbon did rachel buy.
Answer:
46 yards.
Step-by-step explanation:
Subtract the new balance from the original balance:
30.00 - 19.88 = 10.12
Therefore, Rachel spent $10.12
Divide the result by the cost of ribbons per yard:
10.12 ÷ 0.22 = 46
Therefore, Racheal bought 46 yeards of ribbon.
If the Fed's reserve requirement is 5 percent, then what quantity of excess reserves does the Bank of Cheerton now hold?
The quantity of excess reserves that the Bank of Cheerton now hold is $210
From the attached table, the amount generated on the reserve is $4,200
If the Fed's reserve requirement is 5 percent, then the quantity of excess reserves that the Bank hold is given as:
Quantity of excess reserves = 5% of $4,200
Quantity of excess reserves = 0.05 * 4200
Quantity of excess reserves = $210
Hence the quantity of excess reserves that the Bank of Cheerton now holds is $210.
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Find the volume of a cylinder whose radius is 2 cm and whose height is 6 cm (use ╥=3.14 and give the answer to the nearest hundredth).
V = πr²h
V = 3.14 · 2² · 6
V = 3.14 · 24
V = 75.36
Hope this helps!
Answer: 75.36
Step-by-step explanation:
6x-36+120=180
what is the value of x, in degrees?
At a local amusement park, 70% of the rides are made for kids who are 48 inches and taller. If there are 80 rides in total, how many are made for kids who are 48 inches and taller?
Answer:
56
Step-by-step explanation:
Basically you want to find out what is 70% of 80.
first you have to set up your problem
[tex]\frac{n}{80}[/tex] = [tex]\frac{70}{100}[/tex]
the first fraction would be the percent (70) over 100. (you always use 100)
The fraction to the left would be n over 80. the denominator (the number on the bottom) would be the whole amount. n would be the unknown number
To solve you would use the butterfly method. 80 x 70 and 100 x n. 80 x 70 is 5600 and 100 x n is 100n.
The final step is dividing. 5600 divided by 100 giving you 56
question y+5/y+6=5/4
pleas answere this question it is really hard for me I will be thankfull
Refer to the attachment.
=》y = -10
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Hope it helps ⚜
find.
number y if 2/5of y is 22
[tex]\sf -(6-4x)[/tex]
Answer:
[tex] - (6 - 4x) = - 6 + 4x[/tex]
Answer:
[tex]-6+4x[/tex]
Step-by-step explanation:
[tex]-(6-4x)[/tex]
[tex]\mathrm{Distribute\:parentheses}[/tex]
[tex]=-\left(6\right)-\left(-4x\right)[/tex]
[tex]\mathrm{Apply\:minus-plus\:rules}[/tex]
[tex]-\left(-a\right)=a,\:\:\:-\left(a\right)=-a[/tex]
[tex]=-6+4x[/tex]
Will give brainliest i rlly need help
Answer:
1/6
Step-by-step explanation:
-3/4 - (-1/2) = - 1/4
-2/3 - 5/6 = - 3/2
-1/4 ÷ -3/2
Jake fills a tank that can hold 200 gallons of water. The tank already has 50 gallons of water in it when Jake starts filling it at the rate of 10 gallons per minute. Karla fills a tank that can hold 300 gallons of water. That tank already has 100 gallons of water in it when Karla starts filling it at the rate of 5 gallons per minute. Jake and Karla start filling the tanks at the same time. How long after they start filling the tanks do the tanks have the same volume of water? What is that volume of water? I
Answer:
Let m represent the number of minutes.
Amount of water in Karla's tank: 100 + 5m
Amount of water in Jake's tank: 50 + 10m
Same amount of water: 100 + 5m = 50 + 10 m
---> 100 = 50 + 5m
---> 50 = 5m
---> 10 = m
In ten minutes, Karla's tank will have 100 + 5(10) = 100 + 50 = 150 gallons.
In ten minutes, Jake's tank will have 50 + 10(10) = 50 + 100 = 150 gallons.
Step-by-step explanation:
hope this helped!
This is a plan view of a garden. The grass (shaded) has an area of 64 square metres. What is the length of the sides labelled x?
A. 5.5m
B. 6.0m
C. 6.8m
D. 9.0m
Please answer
The length of the sides of the square labelled x is b. 6.0 m.
Recall:
The formula for the area of a square with equal side, s, is given as s².Given that the grass area is 64 sq. meters, to find the length of the sides labelled x, first find the area tat has sides labelled x.
Area = Total area of the garden - 64 sq. m
Area = (10 × 10) - 64
Area = 36 sq. m.
Area of square = s²
Lex x = s
Therefore:x² = 36
Take the square root of both sidesx = 6 m
Therefore, the length of the sides of the square labelled x is b. 6.0 m.
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Plz help me give me answer
Answer:
C
Step-by-step explanation:
Answer:
C. 3, because |-3| = 3
Hope you could get an idea from here.
Doubt clarification - use comment section.
NPM = __?__
Less than BAC
Less than CAB
Less than BCA
Less than ABC
A container holds 4 gallons of lemonade. A large lemonade contains 16 ounces. How many large lemonades could a restaurant sell before they run out of lemonade?
Answer:
32 large lemonades
Step-by-step explanation:
4 gallons = 512 ounces
512 ounces / 16 ounces
= 32 large lemonades.
CAN SOMEONE HELP ME PLEASE ASAP!?
Answer: 20 ft.
Step-by-step explanation:
Simply multiply 5 x 4.
Answer:
20 ft`
Step by step explanation:
N/A
The average rate of population decline between 2004 and 2014 is 1.45 thousand deer per year. If the population continued to decline at this rate, in which year would the population have reached 225 thousand deer? Explain your reasoning.
Answer:
in 155 years it would reach 225 thousand deer
Step-by-step explanation:
The sum of six times a number and six more than the number is the same as the difference between -30 and twice the number what is the number
Answer:
-4
Step-by-step explanation:
let the number be x
6x+(x+6)=-30-2x
7x+6=-30-2x
9x=-36
x=-4
Jamal finds some dimes and quarters in his change purse. How much money (in dollars) does he have if he has 9 dimes and 4 quarters? How much money (in dollars) does he have if he has xx dimes and yy quarters? Total value, 9 dimes and 4 quarters (dollars): Total value, xx dimes and yy quarters (dollars):
Answer:
$1 dollar and $0.90cents
Step-by-step explanation:
HELP !!! HI PLEASE HELP PLEASE I NEED MATH HELP LOL
Answer:
(-1, 0.5)
Step-by-step explanation:
please mark brainliest
Don’t understand this one, hoping for help
