We label each equation
3x + 4y = 5 (1)
2x – 3y = 9 (2)
We now want to get rid of one of the variables (x or y). Lets get rid of x:
We need (1) and (2) to have the same number of x's so we multiple (1) by 2 and (2) by 3 so they both have 6 x's
6x + 8y = 10 (1)*2
6x - 9y = 27 (2)*3
Now to get rid of the x's we take one of the equations from the other. It is easier to do (2)*3 -(1)*2
6x - 9y = 27 (2)*3
6x + 8y = 10 (1)*2
-17y = 17
If we devide this equation by -17 we get
y = -1
We can plug this value of y into (1) to get
3x -4 = 5
add 4 to both sides of the equation
3x = 9
Divide by 3
x = 3
Now to check put x and y into (2)
6 - (-3) = 9
As this is true, we have the solution
x = 3, y = -1
Identify the terms coefficients and constants in the expression 20x+13
Constant: 13
Coefficient: 20
One number is 3 1/3 larger than the other. The tripled sum of these numbers is 133.What is the largest number?
Let denote the two numbers with X and Y. n represent one number
Y=X + 3 1/3
The sum of the two numbers is: X+Y=X + X + 3 1/3
The triple sum is: 3(X + X + 3 1/3)
3(X + X + 3 1/3) = 133
3X + 3X + 10 = 133
6X + 10 = 133
6X = 123
X = 12 1/2 , Y= X+ 3 1/3 = 12 1/2 = 3 1/3 is the largest number
Answer:
[tex]23\frac{5}{6}[/tex]
Step-by-step explanation:
Let x be the smaller number,
Thus, according to the question,
Second number or larger number = [tex]x+ 3\frac{1}{3}[/tex]
Now, sum of these number = [tex]x+x+ 3\frac{1}{3}=2x+\frac{10}{3}[/tex]
Again according to the question,
[tex]3\times ( 2x + \frac{10}{3})= 133[/tex]
[tex]6x + 10 = 133[/tex]
[tex]6x = 123[/tex]
[tex]\implies x = \frac{123}{6}[/tex]
Thus, the larger number = [tex]\frac{123}{6}+3\frac{1}{3}=\frac{123}{6}+\frac{10}{3}=\frac{123+20}{6}=\frac{143}{6}=23\frac{5}{6}[/tex]
if 1 is added to three times a number, the result is equal to 5 more than two times this number. find the number
The number is 4.
[tex]1 + 3*4 = 13\\2 * 4 + 5 = 13[/tex]
The problem is about solving a simple algebraic equation. The given condition can be put into an equation and solved step by step. The number that meets the condition is 4.
Explanation:The subject of this problem is algebra. We need to find a number that satisfies the given condition. If we define the unknown number as 'x', the given statement can be translated into the following algebraic equation: 1 + 3x = 2x + 5.
To find the number, we solve this equation step by step. First, we can rearrange the equation by subtracting 2x from both sides, which gives us: 1 + x = 5. Then, subtracting 1 from both sides, we have: x = 4.
So, the number that satisfies the given condition is 4.
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17x-3y=4 2x-4y=1 the solution to the system of equations is
ANSWER
[tex]x=\frac{13}{62}[/tex]
and
[tex]y= \frac{-9}{62}[/tex]e have
EXPLANATION
[tex]17x-3y=4---(1)[/tex]
[tex]2x-4y=1[/tex]
Let us make y the subject and call it equation (2)
[tex]2x=1+4y[/tex]
[tex]x=\frac{1}{2}+2y--(2)[/tex]
We put equation (2) in to equation (1)
[tex]17(\frac{1}{2}+2y)-3y=4[/tex]
[tex]\frac{17}{2}+34y-3y=4[/tex]
[tex]34y-3y=4- \frac{17}{2} [/tex]
Simplify to get,
[tex]31y= \frac{8-17}{2} [/tex]
[tex]31y= \frac{-9}{2} [/tex]
Divide both sides by 31,
[tex]y= \frac{-9}{2} \div 31[/tex]
[tex]y= \frac{-9}{2} \times \frac{1}{31}[/tex]
[tex]y= \frac{-9}{62}[/tex]
We put this value in to equation (2) to get,
[tex]x=\frac{1}{2}+2\times -\frac{9}{62}[/tex]
[tex]x=\frac{1}{2} -\frac{18}{62}[/tex]
We collect LCM to obtain,
[tex]x=\frac{31-18}{62}[/tex]
[tex]x=\frac{13}{62}[/tex]
how do i write 3y-9x=24 in function notation
To write an expression in function notation, you must solve it for the dependent variable.
Assuming that you want the expression to be written in the form [tex] y = f(x) [/tex] (i.e., assuming that x is the independent variable), we have to solve the expression for y, which means that we want y to remain alone on the left hand side, and move everything else to the right hand side.
So, first of all, we can add 9x to both sides to get
[tex] 3y = 9x+24 [/tex]
Finally, we divide both sides by 3:
[tex] y = 3x + 8 [/tex]
Leticia earns $8 each time she rakes the yard. she has earned $24 so far. Write and solve an equation to show how many more times Leticia needs to take the yard to earn enough to buy a music player that costs $45. Show your work.
Leticia needs to take the 21/8 yards to earn enough to buy a music player that costs $45 and this can be determined by forming the linear equation.
Given :
Leticia earns $8 each time she rakes the yard.She has earned $24 so far.The following steps can be used to determine the equation that shows how many more times Leticia needs to take the yard to earn enough to buy a music player that costs $45:
Step 1 - Let the number of yards she takes after she earns $24 be 'x'.
Step 2 - The amount she needs to earn to buy a music player is:
= 8x
Step 3 - The linear equation according to the given data is given by:
24 + 8x = 45
Step 4 - Simplify the above equation.
8x = 21
[tex]\rm x = \dfrac{21}{8}[/tex]
Leticia needs to take the 21/8 yards to earn enough to buy a music player that costs $45.
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A department store sold 34 shirts one day. All short-sleeved shirts cost $11.00 each and all long-sleeved shirts cost $21.00 each. Total receipts for the day were $514.00. How many of each kind of shirt were sold?
The department store sold 20 short-sleeved shirts and 14 long-sleeved shirts. Calculations were made by setting up a system of equations and solving for the variables representing the number of shirts sold.
To solve how many short-sleeved and long-sleeved shirts were sold given the total sales and price per shirt, we can set up a system of equations. Let x represent the number of short-sleeved shirts and y represent the number of long-sleeved shirts. We have two equations: x + y = 34 (since a total of 34 shirts were sold) and 11x + 21y = 514 (representing the total sales from the shirts).
First, we can solve for x in terms of y from the first equation: x = 34 - y. Substituting this expression for x into the second equation gives us 11(34 - y) + 21y = 514. Simplifying this, we get 374 + 10y = 514, which simplifies down to y = 14.
Substituting y = 14 back into the original first equation x = 34 - y, we find that x = 34 - 14, so x = 20. Therefore, the store sold 20 short-sleeved shirts and 14 long-sleeved shirts.
In a recent year , the world production of wheat was about 5.2x10^8 metric tons. Canada produced 1/25 of this wheat. About how much wheat did Canada produce?
A 20.8x10^8
B 2.08x10^7
C 2.08x10^6
D 20.8x10^7
you have 5/8 if a pepproni pizza. you divide the remaining pizza into 3 equal slices. what portion of the original pizza is each slice?
You have 5/8 remaining of a pizza. You want to divide it into 3 equal slices.
To find the answer, Divide 5/8 with 3, or multiply 5/8 x 1/3
5/8 x 1/3 = 5/24
Each portion is 5/24 of the original slice.
hope this helps
the density of pure gold 1,204 pounds per cubic foot? how many cubic feet is 481.6lbs of pure gold?
Answer:
Volume of Gold = 0.4 cubic feet.
Step-by-step explanation:
First we have to make sure the units are same as the units the answer is required in.
Answer should be given in cubic feet.
Density is given in pounds per cubic foot. And Mass is given in pounds. So units are in order. Therefore, we can go ahead with the calculation.
The Density of Gold = [Mass of Gold/Volume of Gold]
By substituting values,
[tex]1204[/tex] ponds per cubic foot = [[tex]481.6[/tex] pounds / Volume of gold]
Making Volume of God the subject of the equation,
Volume of Gold = [[tex]481.6[/tex] pounds / tex]1204[/tex] ponds per cubic foot ]
Volume of Gold = 0.4 cubic feet.
8.0 ÷ 10 A) Sixty thousand
B) Six thousand
C) Six hundred
D) sixdy
You and a friend buy two fruit smoothies and leave a tip. You split the total and your half cokes to 3.60. What percent tip (in decimal form) did you and your friend leave if the fruit smoothies cost $3 each?
If you bought a $3 smoothie and your total (with tip) is $3.60, you have to divide 3.6/3. You get 1.2, which means you left a 20% tip, which would be .2 in decimal form.
To find the percent tip, divide the tip amount by the total cost and multiply by 100.
Explanation:To find the percent tip, we need to first calculate the total cost of the smoothies and the tip. Since the smoothies cost $3 each, the total cost of the smoothies is $3 * 2 = $6. Let's assume the tip amount is x dollars. The split total (including the tip) is $3.60, which is equal to half of the total cost plus the tip: $3 + $3 + x = $6 + x. Solving this equation, we can find the value of x:
$6 + x = $3.60 * 2$6 + x = $7.20x = $7.20 - $6 = $1.20The tip amount is $1.20. To find the percent tip in decimal form, we divide the tip amount by the total cost and multiply by 100: $1.20 / $6 * 100 = 20%. Therefore, you and your friend left a 20% tip.
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[tex]12(m + 3x) = 18(x - 3m)[/tex]
To solve the equation 12(m + 3x) = 18(x - 3m), we can start by distributing the coefficients and collecting like terms. Finally, m = -3x/11.
Explanation:The given equation is 12(m + 3x) = 18(x - 3m).
To solve this equation, we need to distribute the 12 and 18 coefficients to the terms inside the parentheses. This gives us 12m + 36x = 18x - 54m. Next, we collect like terms on each side of the equation. Combining the 'm' terms, we get 12m + 54m = 18x - 36x. Simplifying both sides further, we have 66m = -18x.To isolate 'm', we divide both sides of the equation by 66, resulting in m = -18x/66. This can be simplified to m = -3x/11.Therefore, the solution to the equation is m = -3x/11.
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Fill in the Blank, 1.) 2t+8>-4(t+1). t>_____
Hey there!!
Given equation :
... 2t + 8 > -4 ( t + 1 )
Using the distributive property :
... 2t + 8 > -4t - 4
Adding 4t on both sides :
... 6t + 8 > - 4
Subtracting 8 on both sides :
... 6t > - 12
Dividing by 6 on both sides :
... t > -2
Hence, the number in the blank is -2.
Hope my answer helps!!
How many weeks of flea treatment would Jim’s dog get from one package if each treatment only lasted 3 weeks In a normal year when a flea treatment last 4 weeks how many more weeks of treatment would Jim’s dog get from one package. Each flea treatment usually last for about 4 weeks but one year the fleas were especially bad Jim’s dog needed to be treated for fleas every 3 weeks until the weather cooled off
Solution
Number of weeks in a year = 52 weeks
If in a normal year when each package of flea treatment lasts for 4 weeks, then in a year there Jim's dog will have to be treated for
[tex]\frac{52}{4} =13 times[/tex]
Where as, when the fleas are bad in a year, the treatment lasts for only 3 weeks.
Then in a year Jim's dog would get
[tex]\frac{52}{3} =17 times[/tex]
So Jim's dog will get 17- 13 =4 treatments more.
4 treatments that are made in 3 weeks each will be 4×3 =12 weeks more treatment
The Number treatments is the ratio of the number of weeks in a year and the number weeks per treatment. Hence, Jim's dog would get 4 more treatments due to the bad weather.
Number of weeks in a year = 52
Period of flea treatment due to weather = 3 weeks Normal duration of flea treatment = 4 weeksThe number of flea treatment he'll get in a year can be calculated thus :
Normal weather = 52 / 3 = 17. 333 = 17 treatments
Bad weather = 52 / 4 = 13 treatments
Difference in treatment = 17 - 13 = 4
Therefore, as a result of the bad weather, Jim's dog would get 4 more treatments than during normal weather.
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What is four more than the number of weeks in a group of days
The sentence 'four more than the number of weeks in a group of days' is converted into the equation is W = D/7 + 4.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
Convert the sentence into an equation or expression.
The sentence is four more than the number of weeks in a group of days.
We know that in a week, there are 7 days. Then the equation will be
Week = (Days / 7) + 4
Simplify the equation, then the equation will be
W = D/7 + 4
The sentence 'four more than the number of weeks in a group of days' is converted into the equation is W = D/7 + 4.
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if i take a fourth of a number away from half the number, i get 10. what is the number?
I think the answer is 40.
Which choice is the closest estimate for the product? (5.4)⋅(3.8) A:18 B:15 C:24 D:20
Which equation represents the following graph?
A.) Y = 2/3 x + 2
B.) Y = 3/2 x + 2
C.) Y = 2/3 x – 2
D.) Y = -2/3 x + 2
Y intercept (0, 2) so b = 2
Slope = (2 - 0) / (0 + 3) = 2/3
Equation y = mx + b
In this case slope m = 2/3 and y intercept = b = 2
So equation y = 2/3 x + 2
Answer
A.) Y = 2/3 x + 2
47% as a fraction or a mixed number
If f(x)=x^2 and g(x)=6x+4, which value of x does (f+g)(x)=0
The answer is x = −2
open the attachment to get the show the explaining.
your aunt's age a minus 25 in algebraic expression
Answer : The expression for the given statement is [tex]a-25[/tex]
Step-by-step explanation :
We are given a statement :
"your aunt's age a minus 25"
Let the age of aunt be considered as 'a'
From the given statement, we conclude that
'Minus' in the above statement means subtract (-) operation.
Thus, the expression for the given statement is [tex]a-25[/tex]
4 1/2 divide by 1 5/6
The time it takes an excursion boat to travel 36 miles downstream is the same as the time it takes the boat to travel 12 miles upstream. If the stream is 4 miles per hour, which of the following is the speed of the boat in still water.
The speed of the boat in still water is 8 miles per hour.
Explanation:To find the speed of the boat in still water, we can use the formula:
Speed of the boat in still water = (speed downstream + speed upstream) / 2
Given that it takes the same amount of time for the boat to travel 36 miles downstream and 12 miles upstream, we can set up the following equation:
36 / (v + 4) = 12 / (v - 4)
Where v is the speed of the boat in still water. Cross multiplying and solving the equation, we get:
36(v - 4) = 12(v + 4)
36v - 144 = 12v + 48
24v = 192
v = 8
Therefore, the speed of the boat in still water is 8 miles per hour.
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in each bouquet of flowers there are 4 roses
If a number is raised to a power of 2, it is
(a) cubed
(b) powered
(c) squared
When a number is raised to the power of 2, it is squared. This means the number is multiplied by itself once.
Explanation:When a number is raised to the power of 2, it is squared. Squaring a number means multiplying it by itself. For example, if you have the number 4 and you square it (raise it to the power of 2), you would multiply 4 by 4, which equals 16. Therefore, 4 squared (or 4 to the power of 2) equals 16.
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Four times the difference of a number and five is 24.
Translate the sentence into an equation.
4x19=76 tada there ya go pally!
Meridith picked 4 times as many green peppers as red peppers how many green peppers did she pick.
what is the answer to 3(4g+6)=2(6g+9)
Answer:
Solution: All real numbers.
Step-by-step explanation:
[tex]3(4g+6)=2(6g+9)\qquad|\text{use distributive property}\\\\(3)(4g)+(3)(6)=(2)(6g)+(2)(9)\\\\12g+18=12g+18\qquad|\text{subtract 12g from both sides}\\\\18=18\qquad TRUE[/tex]
It's an identity equation.
They have 9 tents and 72 people. The same number of campers will be in each tent. How many campers will be in each tent
8 camper in each tent