Answer and Step-by-step explanation: An equation represents proportional relationship when dividing the quantities of the equation results in a quotient that is always the same. For example, in general:
Equation: y = mx
[tex]\frac{y}{x}[/tex] = m
m is a constant value, which means is the same.
A. Equation: 120 - x = L
Equation from alternative A is NOT proportional since the division of the quantities doesn't result in a constant.
B. Equation: 1.08p = t
Dividing total cost per item's price, will always give the sales tax, which is constant. So, this equation IS proportional.
[tex]\frac{t}{p}=1.08[/tex]
C. Equation: [tex]x=\frac{m}{4}[/tex]
This equation is proportional because dividing marbles per how much each sister gets, always gives the number of sisters:
[tex]\frac{m}{x}=4[/tex]
D. Equation: [tex]V=12s^{2}[/tex]
This equation is NOT proportional because side length is squared, so it is not constant linearly.
Answer:
Step-by-step explanation:
A. Equation: 120 - x = L
Equation from alternative A is NOT proportional since the division of the quantities doesn't result in a constant.
B. Equation: 1.08p = t
Dividing total cost per item's price, will always give the sales tax, which is constant. So, this equation IS proportional.
C. Equation:
This equation is proportional because dividing marbles per how much each sister gets, always gives the number of sisters:
A chemist has three different acid solutions,
The first solution contains 20 % acid, the second contains 35 % acid, and the third contains 55%
acid.
She created 108 liters of a 40 % acid mixture, using all three solutions. The number of liters of
55 % solution used is 3 times the number of liters of 35 % solution used.
How many liters of each solution was used?
The chemist used
liters of 20% solution,
liters of 35 % solution, and
liters of 55 % solution.
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Answer:
36 liters of 20%18 liters of 35%54 liters of 55%Step-by-step explanation:
Let a, b, c represent the quantities of 20%, 35%, and 55% solutions, respectively. Then for the given mix, we have ...
a + b + c = 108 . . . . . total number of liters
.20a +.35b +.55c = 0.40·108 . . . . . liters of acid
0a - 3b + c = 0 . . . . . 55% solution was 3 times 35% solution
__
Solving these three equations by your favorite method gives ...
(a, b, c) = (36, 18, 54)
The chemist used 36 liters of 20%, 18 liters of 35%, and 54 liters of 55%.
_____
Comment on alternate approach
Since the ratio of 55% to 35% is 3 : 1, that mix will have an acid content of ...
(3(.55) +1(.35))/4 = 0.50 = 50%
So, the final mix is equivalent to some quantity of 50% mix being added to some quantity of 20% mix. The fraction that is 50% mix* will be (40-20)/(50-20) = 2/3 of the total, or (2/3)(108 L) = 72 L.
Now we know that (1/3)(108 L) = 36 L of 20% solution is needed and (1/4)(72 L) = 18 L of 35% solution is needed. 3 times that is 54 L of 55% solution.
__
* After you work a few mixture problems, you can see the pattern. If we start with an equation for x = fraction of 50% to use with 20% to make 40%, we get ...
x(50%) +(1 -x)(20%) = 40%
x(50% -20%) = 40% -20% . . . . . subtract 1(20%) and factor out x
x = (40% -20%)/(50% -20%)
The key here is to see where the numbers 20%, 40%, and 50% show up in the fraction.
In efforts of improving their orofit margins, a company is considering creating their own manufacturing plant for their product. It had a start-up cost of 25,000 to build the plant. This plant will drop the production cost down to $15 per item. If each item sells for $50, then how many items would it take to get an overall profit of $100,000 for the year?
Answer:
To get an overall profit of $100,000, then 3,571 items is needed to be produced
Step-by-step explanation:
Mathematically;
Profit = Revenue - Production cost
In the question, we are told that the profit we are expecting is $100,000
Let the number of items to be produced for sales be x items
Now let’s look at the production cost ;
The production cost will be number of items for sale * production cost = 15 * x = $15x
Now, we need to add the start-up cost to the production cost to get the total amount spent on production;
Mathematically the total amount would be = $25,000 + $15x
Let’s look at the revenue;
The revenue will be selling price of each item * price of each item;
Mathematically, that would be 50 * x = $50x
So therefore;
50x - (25,000 + 15x) = 100,000
50x -25,000 -15x = 100,000
35x = 100,000 + 25,000
35x = 125,000
x = 125,000/35 = 3571.42 which is approximately 3,571 items
7) Cameron wants to buy new lacrosse equipment that costs $55.25. She plans to save $4.25 each
week. Write and solve an equation to determine how many weeks it will take her to save enough
money to buy the equipment. Define your variable and label your answer!
Answer:
13 weeks
Step-by-step explanation:
Let's say the number of weeks she will take is x. This would mean that 4.25 times the number of weeks(x) is equal to 55.25
Equation:
4.25x = 55.25
x=13
I need help a-sap! Please and thank you!!
Answer:
x = 80 degrees
Step-by-step explanation:
A straight line forms 180 degrees in total. It is given that the first angle is 100 degrees. 180 - 100 = 80, therefore x = 80 degrees
Help ASAP
Write the fraction [tex]\frac{45}{81}[/tex] in simplest form.
Answer:
[tex]\frac{5}{9}[/tex]
Step-by-step explanation:
Given
[tex]\frac{45}{81}[/tex] ( divide numerator and denominator by HCF of 9 )
= [tex]\frac{5}{9}[/tex] ← in simplest form
3 (4x - 2) - 30 = -6 (6 - 2x) - 20
A.Infinite Solutions/Identity
B.No Solution
C.x = 0
D.x = 1
show work please
Answer:
B.
Step-by-step explanation:
3(4x-2)-30=-6(6-2x)-20
12x-6-30=-36+12x-20
12x-36=12x-56
Which statement is false A the inequality sign alwats opens up to the largers number. B the greater number in the equality is always above the number on the vertical number line. C the smaller number is inequality is always located to the left of the other number on the horizontal number line. D inequality sign always open up to a smaller number
Answer:
D inequality sign always open up to a smaller number
Step-by-step explanation:
Yesenia swims laps at a pool. For every 10 laps she swims the backstroke, she swims 15 laps of freestyle. Which ratio shows the number of laps Yesenia swims the backstroke to the number of laps she swims freestyle?
Answer:
2 3
Step-by-step explanation:
Vance wants to determine if an old photo frame is still rectangular. The height of the frame is
8 inches, the base is 6 inches and the diagonal is 10 inches long. Is the old photo frame still
rectangular? How do you know?
Answer:
The old photo frame is still rectangular
Step-by-step explanation:
Rectangles
The rectangle shape can be identified because it has 4 internal angles of 90° each. The diagonal forms with two adjacent sides a right triangle where the Pythagora's Theorem must stand. Being a and b the length of the sides of the rectangle and d the diagonal, then:
[tex]d^2=a^2+b^2[/tex]
Vince's photo frame has dimensions of 8 inches and 6 inches, with a diagonal of 10 inches. If the above condition is met, then the frame is still rectangular.
Calculating:
[tex]10^2=6^2+8^2[/tex]
[tex]100=36+64[/tex]
[tex]100=100[/tex]
Since the condition is met, the old photo frame is still rectangular
Which ratio is NOT equivalent to 1:2
10:20
20:30
5:10
4:8
Answer:
The ratio 20:30 is not equivalent to 1:2.
Which expression represents the area of this figure in square feet
Answer: A im positive its A
Step-by-step explanation: 3 times 2 equals 6 and add that to 3 times 4 which is 12 and you get 18
Perform the indicated operation.
(-7) · (-5)
-12
-35
12
35
Answer:
35
Step-by-step explanation:
A negative number multiplied by a negative number is positive. Multiplication is repeditive addition.
(-7) * (-5) = -(-7 + -7 + -7 + -7 + -7) or -( -5 + -5 + -5 + -5 + -5 + -5 + -5 ) = 35.
Answer:
35 is the answer I remember my brother telling me that two negitives always makes a positive no matter the symbol
Step-by-step explanation: 7 x 5 = 35 that is really all you have to do. but this is a random tip always remember that two negitives equal a positve also when you add positve to negitive it goes right so say you have -5 + 5 that would equal zero. when you add negitive and negitve numbers it will have a negitive sum
Karen works at a car dealership. She makes only $5 an hour, but for every car she sells, she makes $1,000 in commission. If Karen worked 200 hours this month and made a total of $6,000, how many cars did Karen sell this month?
Answer:
4
Step-by-step explanation:
To quickly find the product of a whole number time 1000, add *Blank* Zeroes to the number
Answer:
Add three zeros to the end.
Step-by-step explanation:
When you add three zeros, the result is equivalent to when multiplying by 1000. For example, 20 times 1000 is 20,000.
Hi! I believe your answer is 3 zeros. For example, 7 × 1,000 = 7,000 (add 3 zeros). I hope this helps you! Good luck and have a great day/night. ❤️✨
2. Rena mixes i cup of blue paint for every cup of red paint to make purple paint.
Enter the number of cups of red paint Rena mixes with 1 cup of blue paint.
HELPS ME SOLVE THIS PROBLEM PLEASE
Answer:
The third answer, y = 4x + 1
Step-by-step explanation:
Let's take the pair x = 2, and y = 9.
We know what x is, and what the result, y, is now.
Let's plug x into the third equation, y = 4x + 1
y = 4 * 2 + 1
y = 8 + 1
y = 9
We already know that y = 9, so this equation is correct.
Hope this helps!
(Let me know if you want to know why it's not any of the others.)
CAN SOMEONE PLZ HELP ME:))))))))
Ms. Rivera's class hoped to raise $135. They missed heir goal by $8.62. How ip much money did Ms. Rivera's class raise?
1. 144.42
2. 135
3. 126.38
4 127.28
Answer:
126.38
Step-by-step explanation:
$135.00-$8.62=$126.38
Any help and this please ??
Which graph below shows the solution set for the inequality b ≥ 5?
pls help meeeeeeeee
Answer: we can’t see graphs but I can help you if you show me them
Step-by-step explanation:
PLEEEEEEEEEEEEASE HELP ME WITH THIS! IT IS DUE TOMORROW!!!
Emma jogs 2 miles along the beach in 1/3
of an hour. If she travels at a constant rate, how far will she jog in an hour?
1. Use the known information to write a rate.
Emma’s rate:
2 miles 1/3 hours
2. Write an equivalent rate with a denominator of 1.
2(3) miles / 1/3 (3) hours = ? /1 hour
Answer:
Step-by-step explanation:
6 miles
2 times 3 = 6
or
2 x 3/3 = 6
How to solve 3(x + 1) − (3x + 2)
Answer:
Step-by-step explanation:
3(x + 1) − (3x + 2)
we will expand the first bracket:
3x+3-3x-2
3x and -3x cancels
3-2=1
Answer:
1
Step-by-step explanation:
3x+3+−3x+−2
=(3x+−3x)+(3+−2)
=1
Review the incomplete derivation of the cosine sum identity.
A 2-column table with 5 rows. Column 1 has entries step 1, step 2, step 3, step 4, step 5. Column 2 has entries cosine (x + y), sine (StartFraction pi Over 2 EndFraction minus (x + y) ), blank, sine (StartFraction pi Over 2 EndFraction minus x) cosine (negative y) + cosine (StartFraction pi Over 2 EndFraction minus x) sine (negative y), blank.
Which expressions for Step 3 and Step 5 complete the derivation?
Step 3: Sine ( (StartFraction pi over 2 EndFraction minus x) + y )
Step 5: cos(x)cos(y) + sin(x)sin(y)
Step 3: Sine ( (StartFraction pi over 2 EndFraction minus x) + y )
Step 5: cos(x)cos(y) – sin(x)sin(y)
Step 3: Sine ( (StartFraction pi over 2 EndFraction minus x) minus y )
Step 5: cos(x)cos(y) + sin(x)sin(y)
Step 3: Sine ( (StartFraction pi over 2 EndFraction minus x) minus y )
Step 5: cos(x)cos(y) – sin(x)sin(y)
Answer:
Option (4)
Step-by-step explanation:
STEP - 1
cos(x + y)
STEP - 2
[tex]\text{sin}[\frac{\pi}{2}-(x+y)][/tex]
STEP - 3
[tex]\text{sin}[(\frac{\pi}{2}-x)-y][/tex]
STEP - 4
[tex]\text{sin}(\frac{\pi}{2}-x)\text{cos}(-y)+\text{cos}(\frac{\pi}{2}-x)\text{sin}(-y)[/tex]
STEP - 5
cos(x)cos(y) - sin(x)sin(y)
[Since, [tex]\text{sin}(\frac{\pi}{2}-x)=cos(x)[/tex] and [tex]\text{cos}(\frac{\pi}{2}-x)=\text{sin}(x)[/tex]]
[Since, cos(-x) = cos(x) and sin(-x) = -sin(x)]
Therefore, Option (4) will be the correct option.
Answer:
D
Step-by-step explanation:
Top Answer was right, don't know why it was rated poorly
Solve for h: A = (1/2)*b*h*
O h = 2*A*b
O h = A *(b/2)
O h = (2*A)/b
0 h = (2+b)/A
Step-by-step explanation:
The answer is the third option
someone please help me ASAP
Answer:
Step-by-step explanation:
1. 9.6x10^4
2. 7.2x10^8
3. 1.19x10^-7
4. 9.48x10^-3
5. 2.04x10^8
8x=-1/2 Whats the answer
whats the capitol of Florida miaaaaaaa
Answer:
Tallahassee
Step-by-step explanation:
Which number line shows the solution to -6 -(-2)
Answer:
2nd one
Step-by-step explanation:
Answer:
the first option
Step-by-step explanation:
-6 -(-2) can also mean -6+2 because the (-) in that equation can also mean -1, so a negative time a negative is a positive.
so, there is -6 and ur adding 2 to it, which is -4
four times a number p is more than 22
Answer:
[tex]4p\: > 22[/tex]
[tex]four \: times \: a \: number \: p \: is \: \\ more \: than \: 22[/tex]
The expression of inequality four times a number p is more than 22 is
4p > 22.
What is inequality?Inequality compares two non-equal terms of both sides of the inequality sign. There are four types of inequality.
Given statement four times a number p is more than 22.
As it is stated more than we have to form an inequality strictly greater than 22 which is,
4p > 22.
p > 22/4.
p > 5.5.
This number p can also be represented on a real number line with an open circle at 5.5 and extended to infinity.
learn more about inequality here :
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