Joseph used the problem-solving strategy Work Backward to solve the inequality 2n+5<13. Shawnee solved the inequality using the algebraic method. Compare the two methods
Answer:
1. Using Backwards Method, we get,
We have the inequality 2n+5<13.
So, we subtract both the sides by 5,
i.e. 2n+5-5<13-5
i.e. 2n < 8
Now, divide both sides by 2, we get,
[tex]\frac{2n}{2} <\frac{8}{2}[/tex]
i.e. n < 4.
So, using the Backwards method, we get the solution is n<4.
2. Now, we use the Algebraic method,
We have, 2n+5<13
Take 5 to the right side of the inequality,
i.e. 2n<13-5
i.e. 2n < 8
Now, take the 2 on the right side of the inequality.
i.e. [tex]n<\frac{8}{2}[/tex]
i.e. n < 4.
So, again using the Algebraic Method, we get that the solution is n<4.
I don't get how to do this. Please Explain step-by-step please.
(-8x³y²)² × 2x²y⁶
--------------------------
32x⁸y³
Cual es el resultado de la suma de polínomios (5a + a2 - 14) (10a + a2 + 39)
There are 46 legs in a zoo exhibit. The number of 2 legged animals is 2 more then the number of 4 legged animals. How many of each is in the exhibit?
Lee has a jar of 100 pennies. She adds groups of 10 pennies to the jar. She adds 5 groups. What numbers does she say?
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Four friends at a party popped 3/4 of a bag of popcorn. They ate half of what was popped what fraction of the popcorn bag did they eat
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A small business earns a profit of $6500 in January and $17,500 in May. What is the rate of change in profit for this time period?
Mary having her living room and bedroom painted. Interior Designs USA charges $60.00 to evaluate the space plus $35.00 per hour of labor. Splash of Color charges $55.00 per hour with no initial fee. Which of the following are true? Select all that apply.
The true statement are as follows:
If it takes more than 5 hours to paint the rooms, Splash of Color will be more cost effective.If it takes 3 hours to paint the rooms, both companies will charge the same amount.Here's a breakdown of why each statement is true or false:
True:
If it takes more than 5 hours to paint the rooms, Splash of Color will be more cost effective. As the painting time increases, the hourly rate becomes a bigger factor, and Splash of Color's lower rate outweighs Interior Designs USA's initial fee advantage.
If it takes 3 hours to paint the rooms, both companies will charge the same amount. Both companies will charge 3 hours of labor at their respective rates: $35/hour * 3 = $105 for Interior Designs USA and $55/hour * 3 = $165 for Splash of Color.
False:
If it takes 7 hours to paint the two rooms, Interior Designs USA will charge the least. Interior Designs USA will cost $60 + $35/hour * 7 = $315, while Splash of Color will cost $55/hour * 7 = $385.
Splash of Color will always charge the least. This is not true because Interior Designs USA can be cheaper for smaller jobs due to their lack of an initial fee (e.g., 1 hour painting time).
If it takes 10 hours to paint the rooms, Splash of Color will charge $200 more than Interior Designs USA. Splash of Color will cost $55/hour * 10 = $550, while Interior Designs USA will cost $60 + $35/hour * 10 = $410. The difference is actually $140, not $200.
Complete question:
Mary having her living room and bedroom painted. Interior Designs USA charges $60.00 to evaluate the space plus $35.00 per hour of labor. Splash of Color charges $55.00 per hour with no initial fee. Which of the following are true? Select all that apply.
If it takes 7 hours to paint the two rooms, Interior Designs USA will charge the least.Splash of Color will always charge the least.If it takes more than 5 hours to paint the rooms, Splash of Color will be more cost effective.If it takes 10 hours to paint the rooms, Splash of Color will charge $200 more than Interior Designs USA.If it takes 3 hours to paint the rooms, both companies will charge the same amount.if a fish swims 7/8 of the depth of 32 foot deep lake, how many feet down did the fish swim?
Please help with the following:
1. For what value(s) of "r" is 3r-6=7+3r
A) all real numbers
B)all negative numbers
C)0
D) no values of r
2. What is the range of f(x)=[[x-1]]?
A)all reals
B)all integers
C)all real > or = 1
D)all integers > or = 1
What is the volume of the box pictured below?
A 8/9 cubic foot
B 9/10 cubic foot
C 1 1/15 cubic feet
D 1/3 cubic feet
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An alloy consists of nickel, zinc, and copper in the ratio 2:7:9. How much of each metal is needed to make 3.6 kg of this alloy?
Answer
Find out the how much of each metal is needed to make 3.6 kg of this alloy .
To proof
As given
An alloy consists of nickel, zinc, and copper in the ratio 2:7:9 .
This shows that an alloy contains 18 parts and assume one part of alloy be u .
Thus
An alloy consists of nickel = 2u
An alloy consists of zinc = 7u
An alloy consists of copper = 9u
As given
Total weight of alloy = 3.6 kg
Thus equation becomes
2u + 7u + 9u = 3.6
18u = 3.6
[tex]u = \frac{3.6}{18}[/tex]
u = 0.2 kg
An alloy consists of nickel = 2 × 0.2
= 0.4 kg
An alloy consists of zinc = 7 × 0.2
= 1.4 kg
An alloy consists of copper = 9 × 0.2
= 1.8 kg
Hence proved
To make 3.6 kg of alloy in the given ratio, 400 grams of nickel, 1400 grams of zinc and 1800 grams of copper are required.
Explanation:The question is asking how much of each metal, namely nickel, zinc, and copper, is needed to make 3.6 kg of an alloy with a ratio 2:7:9. To solve this, first, we have to understand that the ratio represents relative amounts of each metal, not their exact weights. The entire alloy is made up of 2 parts nickel, 7 parts zinc, and 9 parts copper - a total of 18 parts. We can find the weight equivalent to one part by dividing the total weight of the alloy - 3.6 kg or 3600 grams - by 18. This gives us 200 grams as the weight of one part. To find the weight of each metal needed, we multiply the weight of one part by the number of parts in the ratio: nickel is 2 * 200 = 400 grams, zinc is 7 * 200 = 1400 grams, and copper is 9 * 200 = 1800 grams.
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Kelly Ann took 15 minutes to walk from her home to the library. Her average speed was 3 miles in 45 minutes. how far was it from Kelly Ann's house to the library? (PLEASE SHOW STEPS!!)
Ron walk 0.5 mile on the track in 10 minutes Stevie walk 0.25 miles on the track in six minutes find the unit rate for each walker in miles per hour who is a fast walker
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Geneva wants to put fencing around her rectangular flower bed. The width of her flower bed is the length. The perimeter of the flower bed is 20 feet.
What are the dimensions of her flower bed?
A. length = 7 feet; width = 3 feet
B. length = 6 feet; width = 4 feet
C. length = 3 feet; width = 7 feet
D. length = 4 feet; width = 6 feet
solve each equation 2n-5=21
Determine if each function is linear or nonlinear.
Select each function and put it in the correct column its suppose to go in. Ex: A is linear or non.
Linear:
Non-Linear:
A) y = x/2 - 19
B) 2y = x to the 2nd power
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D) y = x + √25
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In the function y = 10.00x + 35, y represents the cost of cabin lodging per occupant and x represents the number of occupants. How much does the cost increase for every occupant?
Answer:
$10.
Step-by-step explanation:
We have been given a function [tex]y=10.00x+35[/tex], where y represents the cost of cabin lodging per occupant and x represents the number of occupants.
Since slope of a line is also known as unit rate, so the cost increase for every occupant will be equal to the slope of line.
We can see from our given expression that 10.00x represents the slope of line, so the cost increase for every occupant is $10.
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Which of the following best defines 3 to the power of 2 over 3?
Square root of 9
Cube root of 9
Cube root of 3
Square root of 3
Answer:
The cube root of 9
Step-by-step explanation:
what does a and b equal in this equation.
a − 3b = 16