The equation solved in terms of a is 10x + 15/ 2x + 13
What is the subject of formula?The subject of a formula is defined as the variable that is expressed in terms of the other variables in an equation or given expression.
It is also described as the variable that is being worked out in a given equation.
Given the equation;
a(2x + 3) = 9x + 15 + x
collect like terms
a(2x + 3) = 10x + 15
To make 'a' the subject, divide both sides by the coefficient of a which is (2x + 3)
a = 10x + 15/ 2x + 13
Thus, the equation solved in terms of a is 10x + 15/ 2x + 13
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Solve each system by substitution. 3x+5y=13 , 2x + y = 4
The solution of the system of equations involving 3x + 5y = 13 and 2x + y = 4 is (1 , 2).
A system of linear equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy both equations.
There are three methods that can be used to solve system of linear equations.
1. Elimination
2. Substitution
3. Graphing
Using substitution method, given two linear equations in x and y,
3x + 5y = 13 (equation 1)
2x + y = 4 (equation 2)
Using the second equation, find the value of one variable, lets say y, in terms of the other.
2x + y = 4 (equation 2)
y = 4 - 2x
Substitute the equation of y to the first equation.
3x + 5y = 13 (equation 1)
3x + 5(4 - 2x) = 13
3x + 20 - 10x = 13
Combining all terms containing the variable x on one side and the constants on the other side of the equality, and solving for x.
3x + 20 - 10x = 13
3x - 10x = 13 - 20
-7x = -7
x = 1
Substitute the value of x in the equation of y.
y = 4 - 2x
y = 4 - 2(1)
y = 4 - 2
y = 2
Hence, the solution of the given system of equations is (1 , 2).
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CUANTO ES 4:5=16:20 ????? AYUDA PORFIS SE LOS VOY A AGRADESER MUCHISIMO
Chris buys an item for $6.43. He gives the cashier a $50 bill. How much money should Chris get back
Answer:
43.57
Step-by-step explanation:
subtract 6.43 from 50
Answer: 43.57
Step-by-step explanation: 50 dollars minus 6 dollars and 43 cents and it gives you 43.57
Melanie spent half of her allowance going to the movies. She washed the family
car and earned nine dollars. What is her weekly allowance if she ended with
seventeen dollars?
Answer:43
Step-by-step explanation:
(9+17)x2
A board must be cut so that its length is 40.50 cm. The tolerance is 0.25 cm . Which inequality describes the allowable lengths for the board?
(A) |x-0.25| ≤ 40.50
(C) |x-40.50| ≤ 0.25
(B) |x+0.25| ≤ 40.50
(D) |x-0.25| ≤ 40.75
The inequality that describes the allowable lengths for the board is |x - 40.50| ≤ 0.25
How to determine which inequality describes the allowable lengths for the board?The given parameters are
Length = 40.50 cm
Tolerance = 0.25 cm
The inequality that describes the allowable lengths for the board is represented as:
|x - Length| ≤ Tolerance
This gives
|x - 40.50| ≤ 0.25
Hence, the inequality that describes the allowable lengths for the board is |x - 40.50| ≤ 0.25
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The ratio of the measure of the angles of a triangle is 1: 2: 3 . The length of the shortest side is 8 . What is the perimeter of the triangle?
The perimeter of the triangle is 37.86
Given,
The ratio of the measure of the angles of triangle = 1:2:3
Let the angles be taken as x, 2x, 3x.
Total angle of a triangle is 180°.
We can now find x.
x + 2x + 3x = 180°
6x = 180°
x = 180°/6 = 30°
x = 30°
2x = 2 × 30° = 60°
3x = 3 × 30° = 90°
Let the sides of the triangle be a, b, c.
The length of the shortest side is given = 8
Lets take a as 8.
We can use Trignometric Formulas here:
Trignometric Formulas:
sin θ = [tex]\frac{opposite side}{hypotenuse}[/tex]
cos θ = [tex]\frac{adjacent side}{hypotenuse}[/tex]
tan θ = [tex]\frac{opposite side}{adjacent side}[/tex]
By using sin rule we can find other sides.
That is,
sin 30° = opposite side / hypotenuse
sin 30° = a/b
sin 30° = 8/b
b = 8 × sin 30°
b = 16
Next,
sin 60° = opposite side / hypotenuse
sin 60° = c/16
c = sin 60° × 16
c = 13.86
Now we can find the perimeter of the triangle = a + b + c
= 8 + 16 + 13.86
= 37.86
The perimeter of the triangle is 37.86
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A shipping container will be used to transport several 130-kilogram crates across the
country by rail. The greatest weight that can be loaded into the container is 26500
kilograms. Other shipments weighing 7700 kilograms have already been loaded into
the container. What is the greatest number of 130-kilogram crates that can be loaded
into the shipping container?
The maximum number of 130 kg crates that can be loaded into the shipping container is 137 which is calculated using linear inequality.
A linear inequality in mathematics is an inequality involving a linear function. One of the symbols for inequality is found in a linear inequality. It displays non-equal data in graph style.
An example of linear inequality is : 2x+8>18
Linear inequality can be represented using several symbols such as:
<,>,≥ and ≤.
Let us consider there are x number 130 kg crates.
The shipping container can take a maximum weight of 26500 Kilogram.
There is already 7700 kilograms of shipment loaded
Therefore we can write an linear inequality in x such as:
130x+7700 ≤ 256500
Subtracting 7700 from both sides we get:
130x+7700-7700 ≤ 25600-7700
or,130x ≤ 17900
Dividing both sides by 130
or, x ≤ 137.69....
Now we can say as the crates must be whole therefore the maximum number of 130 kg crates that the shipping container can hold is 137.
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What do the meter, liter, and gram all have in common? they are all units of mass. they are all units of capacity. they are all basic units of measure in the customary system. they are all basic units of measure in the metric system.
Meter, liter, and gram are all basic units of measure in the metric system.
The U.S. customary system and the metric system are the two major systems of measurement. The system of measurement that uses the meter, liter, and gram as the base units of length (distance), capacity (volume), and weight (mass) is referred as Metric system.
Most of the countries use the metric system but in the United States, the US Customary system is used where the things are measured in feet, inches, and pounds. Meter, liter, and gram are all basic units of measure in the metric system.
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Answer:
It is D
Step-by-step explanation: I am verifying the persons answer. You're welcome.
One reason a sample may fail to represent the population of interest is _____.
a. population proportion
b. measurement error
c. statistical inference
One reason a sample may fail to represent the population of interest is sampling error.
A sample is often used in the place of a very large population to carry out studies. Also a sample can be selected in multiple ways. Some of the systems used for this process are random sampling and systematic samplings.
But if there is an error in the selection of the sample, it may not represent the population properly. This error is referred as sampling error. sampling error affects the credibility of the sample selected nd thus affects the population interest in studies.
Sampling error is occurs when a statistician fails to select the appropriate sample representing the whole population. So it is basically a statistical error.
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ASB is fundraising for their annual carnival to raise money for prom. They have Decided to sell lemonade for $2 per cup and orange drinks for $3 per cup.
Question 1: Suppose their goal is raise $240 and have sold 60 cups of lemonade, how many cups of orange drink would they need to sell to reach their goal?
Question 2: If the fundraising goal is to make $2500, what equation represents this scenario?
Question 3: Rewrite the equation form part d to express the number of orange drinks as a function of the number of lemonade drinks.
1. The number of cups of orange drink that ASB would need to sell to reach their goal of raising $240 after selling 60 cups of lemonade is 40 cups.
2. To raise $2,500, the equation representing the scenario is 2L + 3D = 2,500.
3. Rewriting the equation from part 2 above to express the number of orange drinks as a function of the number of lemonade drinks is F(D) = (2,500 - 2L)/3.
What is a mathematical function?A mathematical function is a mathematical expression, rule, or law, defining the value relationship between the independent variable and the dependent variable.
For instance, when we state that the number of orange drinks is a function of the number of lemonade drinks, it means that the number of orange drinks to be sold depends on the number of lemonade drinks sold.
Data and Calculations:Lemonade Orange Drink
Selling price per cup $2 $3
Expected total revenue = $240
Number of cups sold 60
Total revenue $120 ($2 x 60) $120 ($240 - $120)
Number of cups to be sold 40 ($120/$3)
2. The equation is:
2L + 3D = 2,500
Where:
L is the number of Lemonade
D is the number of Orange drinks sold.
3. The rewritten equation is:
F(D) = (2,500 - 2L)/3
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what are two different methods for solving a real-world problem that can be represented by an equation
Subtraction Property of Equality and Addition Property of Equality are two different approaches to resolving a real-world problem that can be depicted by an equation.
What is defined as the Addition Property of Equality?When the identical quantity is added to the both sides of an equation, it generates an equivalent equation, according to the addition property of equality.
2 = 1+1, for example, is an equation given that both the right and left sides of the equal sign symbolize the number 2. However, by adding the number 3 to both sides, this same new equation 2 +3 = 1 + 1 + 3 is founded. As a result of the Addition Property of Equality, if a = b, then a + c = b + c.What is defined as the Subtraction Property of Equality?To maintain equality, if we deduct a number from one side of the equality, we must subtract the very same number from the opposite side of the equality.
Consider the equation X = Y. If a real number 'b' is deducted from the LHS of X = Y, we should then subtract b from Y, so X - b = Y - b. As a result, the formula is as follows:X = Y : X - b = Y - bThus, Subtraction Property of Equality as well as Addition Property of Equality are two different ways of solving a real-world problem that may be represented by an equation.
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HELP ASAP
(−2x − 13) + (19 + 5x)
Answer:
3x+6
Step-by-step explanation:
Let's simplify step-by-step.
−2x−13+19+5x
=−2x+−13+19+5x
Combine Like Terms:
=−2x+−13+19+5x
=(−2x+5x)+(−13+19)
=3x+6
A surveyor needs to find the distance from point A to point B across a canyon. She places a stake at A, and a coworker places a stake at B on the other side of the canyon. The surveyor then locates C on the same side of the canyon as A such that CA ⊥ AB. A fourth stake is placed at E, the midpoint of CA. Finally, a stake is placed at D such that CD ⊥ CA and D,E, and B are sited as lying along the same line.
a. Explain how the surveyor can use the triangles formed to find AB.
The surveyor can find AB if he finds CD as CD = AB.
What actually means by a triangle's congruency?Two triangles are said to be congruent if their three corresponding sides are equal and their three corresponding angles are equal in size.These triangles can be moved, rotated, flipped, and turned to appear identical.If they are readjusted, they will coincide.Two triangles are congruent if they satisfy all five congruence conditions.They are side-side-side (SSS), side-angle-side (SAS), angle-side-angle (ASA), angle-angle-side (AAS), and right angle-hypotenuse-side (RHS).So,
First, connect B and D and make a square ACDB with BC as a diagonal.
In triangle ACB and DCB:So, ACB ≅ DCB under SAS condition.
Therefore, the surveyor can find AB if he finds CD as CD = AB.
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If 35% of a number is 63 and 60% of the same number is 108, find 25% of that number.
Given the following triangle, find c.
1. 12
2. 18/17
3. 6/17
4. 3√34
Answer:
Step-by-step explanation:
4.
do A squared plus B squared equal C squared, you should get [squared root[ of 306 then simplify it to 3 squared root 34 by using the family tree
The total entrance fee for a group of 4 adults and 3 children to a water park is $220.
The total fee for a group of 2 adults and 1 child is $98. Determine the entrance fee for
an adult and the entrance fee for a child.
What does the solution represent in terms of this situation?
The entrance fee in the water park for the adult $37 and for the child are $24.
What basically is a two-variable linear equation?The maximum power of a variable in a linear equation of two variables is one.
A linear equation with two variables raised the same power is a two-variable equation.It is written as ax + by + c = 0, where a, b, and c have all become real numbers, but a and b remain not equal to zero.3x + 9y = 5 and -x + 8y = 6 are both two-variable linear equations.Now, for the question's given condition;
Let the cost for the adult is 'x'.
Let the cost for the child is 'y'.
The total cost for entrance fee is $220.
The group of 4 adults and 3 children costs 220.
4x + 3y = 220 ........equation 1
The group of 2 adults and 1 child costs $98.
2x + y = 98 .........equation 2
Use elimination method to solve the equations;
x = 37 and y = 24.
Therefore, the entrance fee in the water park for the adults is $37 and for the child us $24.
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Ryker goes to the golf driving range every Saturday morning. The cost is a flat fee of $10, plus $2.50 per bucket of golf balls. One Saturday morning, Ryker spent $52.50. Write and solve an equation to find out how many buckets Ryker used.
A driving range charges $4 to rent a golf club plus $2.75 for every bucket of golf balls you hit. Write an equation that shows the total cost c of hitting b buckets of golf balls.
C - 2.75b + 4
sorry if i didn't answer it right
what is 5u+10u for math 8?
Answer:
(5+10)u
= 15u
is the solution
Write an algebraic expression.
7. Bobby ran 4 miles and will run 3 miles a day from now on. Jack ran 6 miles and will
run 5 miles a day from now on.
a. Create an algebraic expression that represents the amount of miles that Bobby & Jack
will run together. Simplify, if possible.
b. Determine how many miles they will run after 8 days.
From the situation described, it is found that:
a) The linear function that represents the amount of miles that Bobby & Jack will run together is T(x) = 2(4x + 5).
b) They will have run 74 miles after 8 days.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.For both Bobby's and Jack's function, we have that:
The amount that they have ran is the intercept.The daily amount that they will run is the slope.Hence the functions for the number of miles they will have run after x days are given by:
B(x) = 4 + 3x.J(x) = 6 + 5x.The total amount is:
T(x) = B(x) + J(x)
T(x) = 4 + 3x + 6 + 5x
T(x) = 8x + 10.
T(x) = 2(4x + 5).
After 8 days, the number of miles they will have run is:
T(8) = 2(4 x 8 + 5) = 2 x 37 = 74.
They will have run 74 miles after 8 days.
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What is the algebraic expression for "the sum of a number and 4"?
A. 4-z
B. 4/z
C. z+4
Answer:
C. z + 4
Hope this helps :)
Step-by-step explanation:
When it says "sum," it means the answer to 2 number that you add. The first number will be unknow which z will stand for, and the second number is 4 since it was stated in the statement, "the sum of a number and 4."
Find the missing terms in the sequence.
4, 6, 10, 16, 24, 34, __, 60, 76, __, 114
Answer:46 and 94
Step-by-step explanation:
Simplify each sum or difference. State any restrictions on the variables.
x / 3x + 9 - 8/x² + 3x
Simplification of the equation [tex]\frac{x}{3x+9}- \frac{8}{x^{2} +3x}[/tex] is equal to (x² -24)/ 3x(x+3), restriction on the variables are x ≠0 , x≠ -3.
As given in the question,
Given equation [tex]\frac{x}{3x+9}- \frac{8}{x^{2} +3x}[/tex]
Simplify the given equation,
x/ 3(x+3) - 8/x(x+3)
= (x² - 24) / 3x(x+3)
Restriction on the variables for the above equation is,
x≠ 0 , x≠ -3
Therefore, simplification of the equation [tex]\frac{x}{3x+9}- \frac{8}{x^{2} +3x}[/tex] is equal to (x² -24)/ 3x(x+3), restriction on the variables are x ≠0 , x≠ -3.
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This line graph shows the United States population from 1800 to 2000. A graph titled U S population has year on the x-axis, and millions of people on the y-axis. A line increases from 0 in 1800 to 300 in 2000. What was the population in the year 2000? about 50 million about 100 million about 200 million about 300 million
In the line graph it represents us to infer that the U.S. population in 2000 was about 300 million.
What is graph?A graph contains data of which input maps to which output.
Analysis of this leads to the relations which were used to make it.
For example, if the graph of a function is rising upwards after a certain value of x, then the function must be having increasingly output for inputs greater than that value of x.
WE have been given graph that titled U S population has year on the x-axis, and millions of people on the y-axis. A line increases from 0 in 1800 to 300 in 2000.
The line graph showed that:
The U.S. population was under 50 million in 1800
It increased exponentially after 1880
It reached around 300 million in 2000
The U.S. has seen its population rise exponentially over the last century such that; over 300 million and it was around the year 2000 that this milestone was reached.
Therefore U.S. population in 2000 was around 300 million.
In the line graph it represents us to infer that the U.S. population in 2000 was about 300 million.
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Answer:
300 million is ur answer:)
Step-by-step explanation:
How do I Evaluate 16 2/3?
Answer:
6.34960 correct to 5 decimal places.
Step-by-step explanation
16 ^ 2/3
= cube root of 16^2
∛(16^2)
= ∛(256)
= 6.349604208.
The 2 in the 2/3 means the square of 16, and the 3 in 2/3 mean 16^1/3
which is the same as the cube root.
The evaluation of mixed fractions [tex]16\dfrac{2}{3}[/tex] in improper fractions using the simplification rule is [tex]\dfrac{50}{3}[/tex].
The combination of a proper fraction and a whole number is called a mixed fraction.
When the numerator is greater than the denominator, such type of fraction is called an improper fraction.
To evaluate [tex]16 \dfrac{2}{3}[/tex] , convert the mixed number to an improper fraction and then simplify it.
Multiply the whole number [tex](16)[/tex] by the denominator [tex](3)[/tex] and add the numerator [tex](2)[/tex].
[tex](16 \times 3 )+ 2 \\= 48 + 2\\ = 50[/tex]
The sum is written with the denominator [tex]3[/tex] as [tex]\dfrac{50}{3}[/tex] .
The evaluation of mixed fractions [tex]16\dfrac{2}{3}[/tex] in improper fractions is [tex]\dfrac{50}{3}[/tex].
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Simplify: (3^2x4^2)^5
Hey there!
Assuming:
(3^2 * 4^2)^5
If so,
(3^2 * 4^2)^5
= (3 * 3 * 4 * 4)^5
= (9 * 16)^5
= (144)^5
= 144^5
= 144 * 144 * 144 * 144 * 144
= 20,736 * 20,736 * 144
= 429,981,696 * 144
= 61,917,364,224
Therefore, your answer should be:
61,917,364,224
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
The table shows the number of Calories José and Natalie burned after 1, 2, and 3 minutes of running. Graph the relationship between the number of minutes running and the number of Calories burned for each person. By which ordered pair is a unit rate represented?
Time (min) 0 1 2 3
Calories Burned
José 0 8 15 23
Natalie 0 5 10 15
A unit rate is represented by the second pair. The graph is also displayed.
A pair made consisting of two sections written inside parantheses and separated by commas is referred to as an ordered pair. For instance, an ordered pair with "x" as the first component and "y" as the second element is shown by the symbol (x, y). These items have unique names and, depending on the situation, can either be variables or constants.
The element order in an ordered pair has some bearing. It suggests that (x, y) could not always equal (y, x).
A coordinate geometry ordered pair is used to specify where a point is on the coordinate plane in relation to the origin.
Therefore, the graph is attached and the second pair represents the unit rate.
Graph is attached at end.
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Complete question -The table shows the number of Calories José and Natalie
burned after 1, 2, and 3 minutes of running. Graph the
relationship between the number of minutes running and
the number of Calories burned for each person. By which
ordered pair is a unit rate represented?
Calories Burned
X
Time (min) 0 1 2 3
Calories Burned
José 0 8 15 23
Natalie 0 5 10 15
Number of Calories
40 30 20 10 0 Calories Burned
In Colorado Springs, the fine for illegally parking in a zone reserved for people with disabilities is $350
This is $200 higher than the fine in Denver.
How much is the fine in Denver? Use x as your variable.
The cost of the fine in Denver is $100.
How much is the fine in Denver?The mathematical operation that would be used to determine the cost of the fine in Denver is subtraction. Subtraction is the mathematical operation that is used to determine the difference between two or more numbers. The sign used to denote subtraction is - . Other mathematical operations are addition, division and multiplication.
In order to determine the cost of the fine in Denver, subtract $200 from the cost of the fine in Colorado Springs.
The equation that represents the cost of the fine in Denver is:
Cost of the fine in Colorado Springs = $200 + cost of the fine in Denver
$350 = $200 + x
In order to determine the value of x, subtract $200 from both sides of the equation.
$350 - $200 = x
x = $100
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Let S = {3, {1, 4}, 2}. The number of elements in power set of S will be:
A) 6
C) 12
B) 8
D) 16
S has 3 elements - 3, {1, 4}, and 2 - so its power set will contain 2³ = 8 elements. (B)
What is the graph solution of 1 + k ≥ 4 or 9 + k < 2? ( I don't understand in how to solve this, if possible please do a step by step or at least explain how you got your answer.
Using the concept of the or operation, the solution of the given inequality in the number line is given at the graph in the end of the answer.
What is the result of the or operation between sets?The or operation between sets has as a result all the elements that belong to at least one of the sets.
For this problem, we have two inequalities:
1 + k ≥ 49 + k < 2.Then we solve the inequality then apply the or operation between them.
The solutions to the inequalities are given as follows:
1 + k ≥ 4 -> k ≥ 3 (numbers to the right of k = 3, with a closed interval).9 + k < 2 -> k < 2- 9 -> k < -7(numbers to the left of k = -7, with an open interval).The or operation will involve both the numbers to the left of k = -7 and the numbers to the right of k = 3 being plotted on the number line, as shown in the graph at the end of the answer.
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Write the equation of the circle that passes through the given point and has a center at the origin. (Hint: You can use the distance formula to find the radius.) (√3, 0)
The equation of the circle that passes through the point (√3 , 0) and has a center at the origin is x^2 + y^2 = 3.
Using the distance formula, get the radius of the circle by solving for the distance between the center and the point (√3 , 0).
radius = distance = √(x2 - x1)^2 + (y2 - y1)^2
radius = √(√3 - 0)^2 + (0 - 0)^2
radius= √3
The standard form of the equation of the circle is given by (x - h)^2 + (y - k)^2 = r^2, where (h , k) is the location of the center and r is the radius of the circle.
Given the radius and center of the circle, substitute these values to the standard form of the equation of the circle.
(x - h)^2 + (y - k)^2 = r^2
where (h , k) = (0 , 0)
r = √3
(x - 0)^2 + (y - 0)^2 = (√3)^2
x^2 + y^2 = 3
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