An equation may have more than one solution.
What is an equation?
A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.
Calculating the value of the unknown variable while keeping the equation balanced on both sides is the process of solving equations. A condition on a variable is an equation when it ensures that two expressions in the variable have the same value. The variable's value for which the equation holds true is referred to as the equation's solution. If the LHS and RHS are switched, an equation doesn't change. The solution is discovered after isolating the variable for which the value must be determined. Depending on the kind of equation we are dealing with, we can solve it. There are various types of equations, including linear, quadratic, rational, and radical ones.
Steps to solve a linear equation:
1. If necessary, remove the parentheses and use the distributive property.
2. By merging like terms, make both sides of the equation simpler.
3. The LCD (least common denominator) of all the fractions should be multiplied by both sides of the equation if there are any fractions.
4. If the equation contains decimals, multiply both sides by the lowest power of 10 to make the result a whole number.
5. Using the addition and subtraction properties of equality, move the constant terms to the other side of the equation and the variable terms to the other.
6. Using the equality properties of multiplication or division, set the variable's coefficient to 1.
7. Get the answer by isolating the variable.
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For what values of k are the graphs of 8y=4x+3 and 4y=k(x+5) parallel? perpendicular?
parallel k= __
perpendicular k= __
The values of k for parallel and perpendicular in the equations 8y=4x+3 and 4y=k(x+5) are 7/12 and 1/21, respectively.
what is slope ?A line's slope determines how steep it is. A mathematical expression for the gradient is called "gradient overflow" (the change in y divided by the change in x). The slope is the ratio of the vertical change (rise) between two points to the horizontal change (run) between those same two points. When a straight line's equation is written as y = mx + b, the slope-intercept form of an equation is used to represent it. The y-intercept is located at a point where the line's slope is m, b is b, and (0, b). For instance, the slope of the equation y = 3x - 7 and the y-intercept (0, 7).
given
for parallel their slope will be equal
y1= 1x/2 + 3/8 .... eq1
y2= kx/4 + 5k/4 ..... eq2
y1 = y2
1x/2 + 3/8 = kx/4 + 5k/4
1/2 + 3/8 = k/4 + 5k/4
7/8 = 6k/4
k = 7/12
for perpendicular product of their slope is 1
y1 * y2 = 1
1x/2 + 3/8 * kx/4 + 5k/4 = 1
1/2 + 3/8 * k/4 + 5k/4 = 1
k = 1/21
so The values of k for parallel and perpendicular in the equations 8y=4x+3 and 4y=k(x+5) are 7/12 and 1/21, respectively.
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HELLPPPP ASAP PLEASE I NEED HELP WHOEVER GETS FIRST GETS BRAINLIEST AND 100 coinss
This is a simple cross multiplication problem! Any time you're given a ratio and then the actual quantity of something, you can use cross multiplication to figure out the quantity of the other thing!
We know that the ratio of toads to frogmen is 7 : 2. We also know there were 98 actual toads. Therefore we can set up our equations!
[tex]ratio_{toads}=ratio_{frogmen}\\actual_{toads}=actual_{frogmen}\\\\7=2\\98 = x\\\\7x=196\\x=28[/tex]
The first two equations above everything is how you would have everything set up! The second equations under them are the numbers plugged in, and the rest is just simplification.
So, your final answer should be 28 frogmen!
What are the exact values of a and b ?
CORRECT ANSWER
PROVIDE EXPLANATION
Answer:
b
Step-by-step explanation:
i think i say c because a is 30 degrees and c is 90 the whole triange needs to be 180 so b would be 60 also you see one side is 10 the other side also known as b is also 10 they have to be the same length and a is five because half of 10 is 5
lil help here please
Answer:
j=30
Step-by-step explanation:
reduce the fraction 3×15×24 /16×20×6 no links or files
Answer:
1 38888888889/50000000000
Step-by-step explanation:
The answer to the first part equation is 1080 ( 3*15*24). The answer to the second question ( 16*20*6) is 1920. Then you divide 1920/ 1080= 1 38888888889/50000000000
27. If A=7-4w + 5v + 10wv and B = 7w + 3wv-12, find A + B, A-B and B-A.
Answer:
A+B = 7-4w+5v +10wv + 7w +3wv - 12
=3w +5v +13wv-5
A-B= 7 - 4w +5v +10wv - (7w +3wv - 12)
=7 - 4w +5v +10wv - 7w - 3wv + 12
=19 - 11w +5v +7wv
B-A =7w +3wv - 12-(7 - 4w +5v +10wv)
=7w +3wv - 12 - 7 + 4w - 5v - 10wv
=11w - 7wv - 19 - 5v
what is the domain of y=2(x+1)-(3x-2)
Answer:
Domain is all real numbers (basically any number)
Step-by-step explanation:
Step 1: Simplify the expression first
y = 2(x+1)-(3x-2)
y = 2x + 2 -3x + 2
y = -x + 4
Step 2: Observe the graph
y = -x + 4 is simply a linear graph with a negative fixed gradient of -1, with a y-intercept of 4.
Step 3: Identify the domain
For linear graphs, domain is all real numbers.
(No restrictions on the graph according to question)
Find the volume of a cone with a base radius of 3in and a height of 11in. Use the value 3.14 for π, and do not do anu rounding. Be Sure to include the correct unit in your answer.
So the formula to find the volume of a cone is,
[tex]V = \pi r^{2} \frac{h}{3}[/tex]
Given,
Base of the cone is 3 inchesHeight of the cone is given as 11 inchesTo Find : The Volume of the cone
Applying the values we get,
[tex]V = 3.14X(3)^{2} X \frac{11}{3}[/tex]
[tex]V = 28.26X\frac{11}{3}[/tex]
[tex]V = 103.62in^{3}[/tex]
Hence , the volume of the cone is 103.62in³
A farmer has 240 acres to plant. He needs to decide how many acres of corn to plant and how many of oats. He can make $40 per acre profit for corn and $30 per acre for oats. However, the corn takes 2 hours of labor per acre to harvest and the oats only take 1 hour per acre. He only has 320 hours of labor he can invest. To maximize his profit, how many acres of each should he plan
Answer:
The acres of each the farmer must plant to obtain the maximum profit is:
160 acres of oat.80 acres of corn.Step-by-step explanation:
First, we're gonna take the data of the exercise:
Area: 240 acres.Profit of the corn: $40/acreProfit of the oat: $30/acreTime spent by corn: 2 hour per acre.Time spent by oat: 1 hour per acre.Total working time available: 320 hours.Now, we're gonna suppose that all the area could be planted with corn (the most profitable), in this form, we obtain the highest profit to take this how reference:
Total profit with corn = area * profit of the cornTotal profit with corn = 240 acres * $40/acreTotal profit with corn = $9600How you can see, $9600 is the highest profit that the farmer can obtain, but, as each acre of corn needs 2 hours, the farmer would need 480 hours of labor to plant all the area with corn, with the 320 hours availables, the farmer just could plant 160 acres of corn, therefore, the real profit would be:
Total profit with corn = 160 * $40Total profit with corn = $6400Now, we're gonna make the same exercise but with the oats, to obtain the total profit with this:
Total profit with oat = area * profit of the oatTotal profit with oat = 240 acres * $30/acreTotal profit with oat = $7200Taking into account the hours of labor availables, the oat gives $800 more profit than the corn, but in that case we'd lose 80 hours of labor that could be used to make a better profit, but, as the oat per hour of labor is more profitable, we're gonna use 2/3 of the area to plant oat and 1/3 to plant corn:
Area used for oat = 240 acres * 2/3Area used for oat = 160 acresArea used for corn = 240 acres * 1/3Area used for corn = 80 acresHow you can see, with 160 acres of oat, the farmer would need 160 hours of labor and, with 80 acres of corn, the farmer would need 160 hours of labor too, by this, we know all the available time will be used, now, we're gonna calculate the profit in each case:
Real profit with oat = used area * profit of the oatReal profit with oat = 160 acres * $30/acreReal profit with oat = $4800Real profit with corn = 80 acres * $40/acreReal profit with corn = $3200The total profit to the farmer with this plan is:
Total profit = Corn profit + Oat profitTotal profit = $3200 + $4800Total profit = $8000The profit with the given plan is $8000, that is better than the profit only with oat or corn separately and, this is the maximum profit the farmer can make.
GOOD MORNING PEOPLE :) CAN SOMEONE PLEASE HELP ME WITH THIS MATH QUESTION PLEASE ASAP:)
NO LINKS!!!!!
Answer:
B
Step-by-step explanation:
The owner-manager of Good Guys Enterprises obtains utility from income (profit) and from having the firm behave in a socially conscious manner, such as making charitable contributions or civic expenditures. Can you set up the problem and derive the optimization conditions if the owner-manager wishes to obtain a specific level of utility at the lowest possible cost? Do these conditions differ from the utility maximizing conditions?
Answer:
Step-by-step explanation:
Certainly! To set up the problem, we can consider the owner-manager's utility as a function of two variables: income (profit) and charitable contributions or civic expenditures. Let's call these variables x and y, respectively.
The owner-manager utility is given by the function U(x,y), where x is the income (profit) and y is the charitable contributions or civic expenditures.
The cost of obtaining this utility is given by the function C(x,y), where x is the income (profit) and y is the charitable contributions or civic expenditures.
To find the lowest possible cost at which the owner-manager can obtain a specific level of utility, we can use the following optimization conditions:
The cost function C(x,y) should be minimized subject to the constraint U(x,y) = k, where k is the specific level of utility that the owner-manager wishes to achieve.
The first-order necessary conditions for a minimum are:
∂C/∂x = λ ∂U/∂x
∂C/∂y = λ ∂U/∂y
where λ is a Lagrange multiplier.
These conditions are known as the Karush-Kuhn-Tucker (KKT) conditions.
These optimization conditions differ from the utility-maximizing conditions in that we are minimizing the cost function instead of maximizing the utility function. In addition, we have the constraint U(x,y) = k, which means that we are trying to achieve a specific level of utility rather than trying to maximize it.
help it’s due today and i haven’t done it since wensday
Answer:
135
Step-by-step explanation:
:)
Answer:
When you convert them both you get 135
A raffle for 4 prizes is taking place. each person had to purchase a ticket to enter the raffle. If Lebron bought 4 tickets, Kobe 6 tickets, Jordan 7 and Diana Taurasi 7.
Round answer to the nearest thousandths (3 decimal places)
A). If the ticket gets put back into the raffle after each selections, what is the probability that Kobe wins the first prize and Dianna wins the second?
B) If each ticket can only be used once what is the probability that Kenton win first two prizes
C) What is the probability that Oberon wins first prize, Kobe the second, Jordan the 3rd and Diana the 4th, without replacement?
Raffles are chance-based contests in which participants compete to win exciting prizes.
How does a raffle work?To participate, all you need is a ticket with a number on it. Following the sale of all tickets, a drawing is conducted during which a random selection of tickets is made. If you chance to have the winning ticket, congratulations! a lot of engagement.
Raffles elicit a great deal of interest and support because people enjoy playing games of chance, especially when they have the possibility to win a significant prize.
high income. Your organisation has a strong possibility of making some big money from ticket sales if engagement is high!
low price. A virtual free raffle can be found online! A virtual raffle is the most cost-effective type of fundraising because you won't need to print actual tickets, reserve a location for the drawing, or buy refreshments.
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Find the length of the model in the picture!!!Then find the scale factor.The length of an actual bird is shown on the picture.
We calculated length of model bird in the picture = 2 ¹⁵₁₆ inch and scale factor =1/2
what is scale factor?
It is expressed as the ratio of the dimension of a model object and dimension of an actual object.
A scale factor is a number which is multiplied by an object in order to form a proportional enlarged or reduced object.
What is the length of the model in the picture?Given, the length of an actual bird = 5⁷₈ inch = 47/8 inch
also given, 1 inch = 0.5 inch
1 inch = 1/2 inch
we need to determine the length of model bird by multiplying the above factor.
now, length of model bird = 47/8 × 0.5 inch = 47/16 inch = 2¹⁵₁₆ inch
scale factor = length of model bird/ length of actual bird = 47/16 /47/8
scale factor = 1/2
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3. At practice the team wants to know how fast Ryan can skate. He skates 10 laps around the
rink in 3 minutes and, later on in practice he skates 5 laps in 1 minute. What was his
average speed in laps per minute?
The average speed in laps per minute of Ryan is 2.5 laps per minute
How to determine the average speed in laps per minute?From the question, we have the following parameters that can be used in our computation:
He skates 10 laps around the rink in 3 minutes In practice he skates 5 laps in 1 minuteThe above can be expressed as
(x, y) = (1, 5) and (3, 10)
The average speed in laps per minute can be calculated using the following slope equation
Slope = (y₂ - y₁)/(x₂ - x₁)
Rewrite as
Average speed = (y₂ - y₁)/(x₂ - x₁)
Where
(x, y) = (1, 5) and (3, 10)
Substitute the known values in the above equation
So, we have the following equation
Average speed = (10 - 5)/(3 - 1)
Evaluate
Average speed = 2.5
Hence, the average speed is 2.5
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Evaluate x−25 when x=35.
Answer: 5
Step-by-step explanation:
1. Since you are told x=35. Plug it into x.
35-25
2. Simplify
35-25=5
Answer: 10
Step-by-step explanation:
x-25
substitute 35 for x
35-25 = 10
What is XZ to the nearest tenth?
7
51°
77
Round the number to the given place value.
In a town in California, the average consumption of soft drinks per day per elementary school
student is 15.766 ounces. Round this value to the nearest tenth.
Find the volume.
Pls NO links
There are two ways of finding the volume of a pyramid.
1. [tex]\large\tt V =\frac{lwh}{3}[/tex]
[tex]\tt V=\frac{lwh}{3}[/tex][tex]\tt V=\frac{(4in)(2in)(5in)}{3}[/tex][tex]\tt V=\frac{40in}{3}[/tex][tex]\tt V={13.33^3}[/tex]Therefore, the volume of a pyramid is 13.33in³
2. [tex]\large\tt V = \frac{Bh}{3}[/tex]
Where [tex]\longrightarrow\tt B = l \times w[/tex]
[tex]\longrightarrow\tt B = 4in \times 2in[/tex]
[tex]\longrightarrow\tt B = {8in^2}[/tex]
[tex]\tt V = \frac{Bh}{3}[/tex][tex]\tt V = \frac{4in^2 \times 5in}{3}[/tex][tex]\tt V = \frac{40in}{3}[/tex][tex]\tt V = {13.33^3}[/tex]Therefore, the volume of a pyramid is 13.33in³
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Fjfjdjfjdjdjdjdjjfjfjfhfjd
Answer:
A. 69°
Step-by-step explanation:
Given:
m<FED = 179°
m<NED = 19x - 4
m<FEN = 12x - 3
Required:
m<FEN
Solution:
m<NED + m<FEN = m<FED (angle addition postulate)
19x - 4 + 12x - 3 = 179 (substitution)
Add like terms
31x - 7 = 179
31x - 7 + 7 = 179 + 7
31x = 186
31x/31 = 186/31
x = 6
✔️m<FEN = 12x - 3
Plug in the value of x
m<FEN = 12(6) - 3 = 72 - 3
m<FEN = 69°
Could somebody please help it’s due in a couple of minutes, and please no links
Answer:
no solution
Step-by-step explanation:
Please help me!
Please!
Answer:
27
Step-by-step explanation:
9/1/3=9*3=27
Answer:
D. 27
Step-by-step explanation:
This is a simple division
[tex]9[/tex] ÷ [tex]\frac{1}{3}[/tex] =
[tex]\frac{9}{1}[/tex] ÷ [tex]\frac{1}{3}[/tex] =
Cross multiply
[tex]1[/tex] × [tex]1 = 1[/tex]
[tex]9[/tex] × [tex]3 = 27[/tex]
Set it up
[tex]\frac{27}{1}[/tex]
Then, the model represents 27
Can you please help me What is 2/3 x 1/2
Answer:
2/6 lol
Step-by-step explanation:
hope this helps :3
can somebody help me with this one question i’m stuck on?? ;^(
Answer:
The answer is 2.27mm
Step-by-step explanation:
One fifth of the animals at the shelter are stray cats. If there are 13 stray cats at the shelter, how many animals are there in total?
Answer:
1/5 x X = 13
x5 x5
x = 65 in total
The two-way table shows the number of students in a class who play basketball and/or football.
What is the missing number in the table?
A) 2
B) 10
C) 34
D) 46
will mark BRAINLIEST*
how to horizontally stretch a cubic fucnction
Answer:
Steps for How to Transform the Graph of a Cubic Function
Step 1: The standard form of a cubic function is y=a(x−h)3+k y = a ( x − h ) 3 + k , where a indicates a stretch or a shrink, h indicates a vertical shift, and k indicates a horizontal shift.
Step-by-step explanation:
PLS HELP ASAP!!!!! WILL GIVE 30 POINTS TO WHOEVER ANSWERS CORRECTLY
Describe a sequence of transformations that maps Figure A to Figure B.
Answer:
Reflection across the Y axis and you would have to translate figure a down by some units. I dont know the units because i cant see the grid/graph so this is the farthest I can tell you
Step-by-step explanation:
Hope this helps :)
40 pupils in class 4A scored 380 points in a contest. Each girl scored
10 points and each boy scored 8 points. How many girls are there in
class 4A?
There are 30 girls and 10 boys
HELP PLS
I’m rly confused
bro use a photo math...................