Solve for the unknown variables
Answers
Answer:
This term is known as algebra.
Step-by-step explanation:
Algebra is all about solving for unknown values. Of course, in the primary phrase (question) it says, "Solve for the unknown variables," and the unknowns are unknown variables that have values that are unknown and must be found through algebraic processes.
What is an "algebra" in mathematics?Variables like as x, y, and z are coupled with mathematical operations such as addition, subtraction, multiplication, and division to generate a meaningful mathematical statement. An algebraic expression is as basic as 2x + 4 = 8. Algebra is concerned with symbols, and these symbols are connected to one another through operators. It is more than just a mathematical concept; it is a skill that we all have without even realizing it. Understanding algebra as a concept is more important than solving equations and achieving the proper solution since it applies to all other disciplines of mathematics that you will learn or have previously learned.
What is Algebra?Algebra is a field of mathematics that works with symbols and the mathematical operations that may be performed on them. These symbols, which have no set values, are referred to as variables. We frequently encounter values that change in our real-life issues. However, there is a continual requirement to represent these changing values. In algebra, these values are frequently represented by symbols such as x, y, z, p, or q, and these symbols are referred to as variables. Furthermore, these symbols are subjected to different mathematical operations such as addition, subtraction, multiplication, and division in order to determine the values. 3x + 4 = 28. Operators, variables, and constants are used in the algebraic formulas above. The integers 4, 28, and x are constants, and the arithmetic operation of addition is done. Algebra is a branch of mathematics concerned with symbols and the mathematical operations that may be applied to them. Variables are symbols that do not have predefined values. In our daily lives, we regularly face values that shift. However, there is a constant need to express these shifting values. These values are usually represented in algebra by symbols such as x, y, z, p, or q, and these symbols are known as variables. Furthermore, in order to ascertain the values, these symbols are subjected to various mathematical operations such as addition, subtraction, multiplication, and division. 3x + 4 = 28. The algebraic formulae above make use of operators, variables, and constants. The constants are the numbers 4, 28, and x, and the arithmetic operation of addition is done.
Branches of AlgebraThe use of many algebraic expressions lessens the algebraic complexity. Based on the usage and complexity of the expressions, algebra may be separated into many branches, which are listed below:
Pre-algebra: The basic methods for expressing unknown values as variables help in the formulation of mathematical assertions. It facilitates in the transition of real-world problems into mathematical algebraic expressions. Pre-algebra entails creating a mathematical expression for the given problem statement.
Primary algebra: Elementary algebra is concerned with resolving algebraic expressions in order to arrive at a viable solution. Simple variables such as x and y are expressed as equations in elementary algebra. Based on the degree of the variable, the equations are classed as linear, quadratic, or polynomial. The following formulae are examples of linear equations: axe + b = c, axe + by + c = 0, axe + by + cz + d = 0. Primary algebra can branch out into quadratic equations and polynomials depending on the degree of the variables.
Algebraic ExpressionsAn algebraic expression is made up of integer constants, variables, and the fundamental arithmetic operations of addition (+), subtraction (-), multiplication (x), and division (/). An algebraic expression would be 5x + 6. In this situation, 5 and 6 are constants, but x is not. Furthermore, the variables can be simple variables that use alphabets like x, y, and z, or complicated variables that use numbers like
\(x^2,x^3,x^n,xy,x^2y,\)
and so forth. Algebraic expressions are sometimes known as polynomials. A polynomial is a mathematical equation that consists of variables (also known as indeterminates), coefficients, and non-negative integer variable exponents. As an example,
\(5x^3+4x^2+7x+2=0\)
Any equation is a mathematical statement including the symbol 'equal to' between two algebraic expressions with equal values. The following are the many types of equations where we employ the algebra idea, based on the degree of the variable: Linear equations, which are stated in exponents of one degree, are used to explain the relationship between variables such as x, y, and z. Quadratic Formulas: A quadratic equation is usually written in the form
\(ax^2+bx+c=0,\)
Related Questions
A charity needs to report its typical donations received. The following is a list of the donations from one week. A histogram is provided to display the data.
10, 10, 10, 10, 15,15,15,19, 20, 20, 20, 25, 25, 25, 30, 30, 55, 55
A graph titled Donations to Charity in Dollars. The x-axis is labeled 10 to 19, 20 to 29, 30 to 39, 40 to 49, and 50 to 59. The y-axis is labeled Frequency. There is a shaded bar up to 8 above 10 to 19, up to 6 above 20 to 29, up to 2 above 30 to 39, and up to 2 above 50 to 59. There is no shaded bar above 40 to 49.
Which measure of center should the charity use to accurately represent the data? Explain your answer.
The median of 22.7 is the most accurate to use to show that they have plenty of money.
The mean of 20 is the most accurate to use to show that they need more money.
The median of 20 is the most accurate to use, since the data is skewed.
The mean of 22.7 is the most accurate to use, since the data is skewed.
Answers
Therefore, the correct answer is: The median of 20 is the most accurate to use, since the data is skewed.
What is histogram?A histogram is a graphical representation of the distribution of a dataset. It is a visual representation of the frequency distribution of continuous or discrete data. The x-axis represents the range of values of the data and is divided into equal intervals called bins or buckets. The y-axis represents the frequency or count of the data values that fall into each bin.
The data in the histogram is skewed to the right, meaning that there are some high values that are pulling the mean up towards them. In this case, the mean is not an accurate measure of center because it is being heavily influenced by the two values of 55.
Therefore, the best measure of center to use in this case is the median, which is less sensitive to extreme values and gives a better representation of the typical donation received by the charity. In this case, the median donation is $20, which is a more accurate representation of the center of the data than the mean.
Therefore, the correct answer is: The median of 20 is the most accurate to use, since the data is skewed.
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WILL BRAINLIEST IF ANSWERED UNDER 3 MINUTES!
A football team has an away game, and the bus breaks down. The coaches decide to drive the players to the game in cars and vans. Four players can ride in each car. Six players can ride in each van. There are 48 players on a team. The equation 4x + 6y = 48 models this situation, where x is the number of cars and y is the number of vans.
Find 4 possible solutions in the context of the problem.
Answers
Answers:
(0, 8)
(3, 6)
(6, 4)
(12, 0)
There are infinitely many answers to pick from. All that matters is that they are on the line 4x+6y = 48
=====================================================
Explanation:
Plug in x = 0 and solve for y to get y = 8. That means we can have 0 cars and 8 vans.
Plug in y = 0 and solve for x to get x = 12. So we could have 12 cars and 0 vans.
----------
That takes care of two possible solutions, but we need 2 more.
Here's how to get more solutions. Start at the point (0,8). Then we'll use the slope to help get to another point. The slope here is -4/6 = -2/3, so we go down 2 and over to the right 3.
Starting at (0,8) and going down 2 and to the right 3 has us land on (3,6) which is another solution. I'll let you confirm if (x,y) = (3,6) works in the equation or not. This solution tells us we could have 3 cars and 6 vans.
Then from (3,6) we do another "down 2, right 3" motion to land on (6,4) which is yet another solution. In this case, we have 6 cars and 4 vans.
We can stop here since we have four solutions now.
Businesses deposit large sums of money into bank accountsImagine an account with $10 million dollars in it.
A. How much would the account earn in one year of simple interest at a rate of 2.12%? Round to the nearest cent.
B.How much would the account earn in one year at 2.12% if the interest was compounded daily? Round to the nearest cent.
C.How much more interest is eamed by interest compounded daily compared to simple interest?
Answers
again, let's assume daily compounding means 365 days per year.
\(~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$10000000\\ r=rate\to 2.12\%\to \frac{2.12}{100}\dotfill &0.0212\\ t=years\dotfill &1 \end{cases} \\\\\\ I = (10000000)(0.0212)(1)\implies \boxed{I=212000}\)
\(~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$10000000\\ r=rate\to 2.12\%\to \frac{2.12}{100}\dotfill &0.0212\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{daily, thus 365} \end{array}\dotfill &365\\ t=years\dotfill &1 \end{cases}\)
\(A=10000000\left(1+\frac{0.0212}{365}\right)^{365\cdot 1}\implies A\approx 10214256.88 \\\\\\ \underset{\textit{earned interest amount}}{10214256.88~~ - ~~10000000 ~~ \approx ~~ \boxed{214256.88}}\)
what's their difference? well
\(\stackrel{\textit{compounded daily}}{\approx 214256.88}~~ - ~~\stackrel{\textit{simple interest}}{212000}\implies \boxed{2256.88}\)
Writing an Equation of a Perpendicular Line:
What is the answer for steps 1, step 2, and step 3?
Answers
The slope of the graph of the given equation is 1 / 3.
The opposite reciprocal of the slope is -3.
The equation of the perpendicular line in slope intercept form is y = -3x + 6.
How to find the equation of a line?
The line passes through (5, -9) and is perpendicular to the graph of y = 1 / 3 x - 1 .
The equation that represent the line in slope intercept form can be calculated as follows:
Using slope intercept form,
y = mx + b
where
m = slopeb = y-interceptTherefore, the slope of the given graph is 1 / 3.
The opposite reciprocal of the slope form is as follows:
m = - 3
Let's use the slope intercept form to write the equation of the perpendicular line.
Hence,
y = -3x + b
using (5, -9)
-9 = -3(5) + b
-9 + 15 = b
b = 6
Therefore, the equation in slope intercept form is y = -3x + 6
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The ratio of red marbles to blue marbles is 3:5. If there are 360 marbles total in the collection, how many of each color are there?
Answers
Answer:
135 red and 225 blue
Step-by-step explanation:
Skjsoakakakao
AMIGOS AND AMIGAS PLS HELP MY POOR BRAIN ILY FAM:
1) 8+ 9p = 9p - 7
2) 2(3x + 6) = 3(2x - 6)
Answers
1. 9p - 9p = -8 - 7
0 = - 15
2. 6x + 12 = 6x - 18
6x - 6x = - 18 - 12
0 = - 30
That's what I got
Clara needs to separate her pizza dough
into equal pieces by mass and roll out the
dough to be a certain thickness. Which
metric tools and units should Clara use to
check?
Answers
Answer:
Step-by-step explanation:
tg
Melanie is taking four classes this semester: American History, Algebra 2, English 2, and Environmental Science. How many ways can ther four classes be arranged into her schedule?
Answers
Answer:
24.
Step-by-step explanation:
That would be 4!
= 4*3*2
= 24 ways.
Melanie's classes can be arranged in 24 ways, found using the permutation 4P4.
What is Permutation?The act of organizing all the components of a set into some sequence or order is known as permutation. Permuting, in other words, is the act of reordering the components of a set that has previously been sorted.
A permutation is the selection of r items from a collection of n items without replacement, with the order of the items being significant.
nPr = (n!) / (n-r)!
What is a Combination?The combination is a method of picking elements from a collection in which the order of selection is irrelevant (unlike permutations).
A combination is a selection of r items from a collection of n items with no replacements and no regard for order.
nCr = (n!)/{(r!)((n-r)!)}
How do we solve the given question?We are informed that Melanie is taking four classes this semester: American History, Algebra 2, English 2, and Environmental Science.
We are asked to find out the number of ways in which Melanie's classes can be arranged.
To find the number of arrangements, we will use permutation here as the order of selection matters. Our sample size, n = 4, and the number of selections we need to make, r = 4.
We will use the formula: nPr = (n!) / (n-r)!
∴ 4P4 = (4!)/(4-4)! = 4!/0! = 4!/1 = 4! = 1*2*3*4 = 24. (∵ 0! = 1)
∴ Melanie's classes can be arranged in 24 ways, found using the permutation 4P4.
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Pls help
A box is in the shape of a trapezoidal prism. How many cubic centimeters of space are in the box?
Answers
To determine the number of cubic centimeters of space in the trapezoidal prism box, we need to use the formula V = (1/2)h(a+b)l, where V represents the volume of the box, h represents the height of the trapezoidal base, a and b represent the lengths of the top and bottom bases of the trapezoid, and l represents the length of the box. Once we have these measurements, we can substitute them into the formula to get the volume of the box in cubic centimeters.
The formula for the volume of a trapezoidal prism is V = (1/2)h(a+b)l. This formula combines the height of the trapezoid with the length of the prism to find the total volume of the box. By finding the measurements of the trapezoid's height, top base, bottom base, and the length of the prism, we can substitute them into the formula and solve for the box's volume in cubic centimeters.
In conclusion, to find the number of cubic centimeters of space in a trapezoidal prism box, we need to use the formula V = (1/2)h(a+b)l, where V represents the volume of the box, h represents the height of the trapezoidal base, a and b represent the lengths of the top and bottom bases of the trapezoid, and l represents the length of the box. Once we have these measurements, we can substitute them into the formula and solve for the box's volume in cubic centimeters.
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please helpppppppppppppppppppppppppppppppppppppppp
Convert the following fractions into percent and decimals.
1/4, 1/25 , 1/6 , 1/3
Answers
Answer:
1/4 is 0.25
1/25 is .04
1/6 is 0.16
1/3 is 0.3
9. For which equation is the solution 6? (1 point)
Ox+6=10
04x=24
Ox-6=12
04=24
Answers
Answer:
04x=24
Step-by-step explanation:
04x=24
divide both sides by 4 to let x stand alone
04x÷4=24÷4
x=6
is my answer correct?
Answers
Answer: B. Graph on the top right
The correct answer is B, which is the graph on the top right.
Step-by-step explanation:
Hope this helps =)
The cost of a daily rental car is as follows: The initial fee is $69.99 for the car, and it costs $0.30 per mile. If John initially pays $200.00 before taxes and does not want to exceed that amount, how many miles can he drive?
x ≥ 433 miles
x = 450 miles
x ≥ 450 miles
x ≤ 433 miles
Answers
x \(\geq\) 433
explanation:
let m equal miles
0.30m + 69.99 = 200
-69.99 -69.99
0.30m = 130. 01
130.01 / 0.30 = 433. 36...
but we're gonna round it to 433
so 433 miles
If y varies directly as x, and y is 48 when x is 6, which expression can be used to find the value of y when x is 2? y = StartFraction 48 Over 6 EndFraction (2)
Answers
Answer:
The expression that can be used to find the value of \(y\) when \(x\) is 2 is \(y = 8\cdot x\)
(\(x = 2\))
\(y = 8\cdot (2)\)
\(y = 16\)
Step-by-step explanation:
As we know that \(y\) varies directly as \(x\). The following expression is done:
\(y \propto x\)
\(y = k\cdot x\)
Where \(k\) is the proportionality constant.
If we know that \(x = 6\) and \(y = 48\), the proportionality constant is:
\(k = \frac{y}{x}\)
\(k = \frac{48}{6}\)
\(k = 8\)
The expression that can be used to find the value of \(y\) when \(x\) is 2 is \(y = 8\cdot x\)
(\(x = 2\))
\(y = 8\cdot (2)\)
\(y = 16\)
in the figure below X is best described as a
Answers
Answer:
Idk
Step-by-step explanation:
Idk
Create the smallest cylinder possible with the tool and record the values of the radius, height, and volume (in terms of pi). Scale the original cylinder by the given scale factors, and then record the resulting volumes (in terms of pi) to verify that the formula V=VxK^3 holds true for a cylinder
Answers
The resulting volume of the scaled cylinder is k³π. Hence, the formula V = VxK^3 holds true for a cylinder.
Given: We need to create the smallest cylinder possible with the tool and record the values of the radius, height, and volume (in terms of pi). Then scale the original cylinder by the given scale factors, and record the resulting volumes (in terms of pi) to verify that the formula V=VxK^3 holds true for a cylinder.
Formula used:Volume of Cylinder = πr²h Where r = radius of the cylinderh = height of the cylinder K = Scale factor V = Volume of cylinder
1. Smallest Cylinder: Let's take radius, r = 1 and height, h = 1, then the volume of the cylinder is,
Volume of Cylinder = πr²h= π1² × 1= π
Therefore, the volume of the smallest cylinder is π.
2. Scaled Cylinder: Let's take radius, r = 1 and height, h = 1, then the volume of the cylinder is,
Volume of Cylinder = πr²h= π1² × 1= π
Therefore, the volume of the cylinder is π.Let's scale the cylinder by the given scale factor "k" to get a new cylinder with the same shape, but with different dimensions. Then the new radius and height are kr and kh, respectively.
And the new volume of the cylinder is given by the formula V = π(kr)²(kh)= πk²r²h= k³π
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A company makes steel rods shaped like cylinders. Each rod has a radius of 3 centimeters and a height of 20 centimeters. How much steel will the company need to make 297 rods?
Use 3. 14 for \pi , and do not round your answer
Answers
Answer:
I'm not sure though
Step-by-step explanation:
but this is what I got . volume of a cylinder = pi r square h
so 3.14 ×3×3×20=565.2
pls help asap!!! Find the value of z
Answers
HALP PLS NO LINKS OR FILES PLS
SCREENSHOT BELOW!!!
Answers
Answer:
12 and 13
Step-by-step explanation:
How many square inches of cloth are cut from the square (n = 3.14) if it’s 38inches
Answers
The number of square inches of cloth cut from the square will be 1,017.36 square inches. Then the correct option is A.
What is the area of the circle?It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.
Let r be the radius of the circle. Then the area of the circle will be
A = πr² square units
The radius is given as,
r = 36 / 2
r = 18 inches
The area of the circle is given as,
A = π x (18)²
A = 3.14 x 324
A = 1,017.36 square inches
The number of square inches of cloth cut from the square will be 1,017.36 square inches. Then the correct option is A.
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The complete question is given below.
A circle is cut from a square piece of cloth, as shown:
A square, one side labeled as 36 inches, has a circle inside it. The circle touches all the sides of the square. The portion of the square outside the circle is shaded.
How many square inches of cloth is cut from the square?
(π = 3.14)
1,017.36 in2
1,489.24 in2
1,182.96 in2
1,276.00 in2
workers are loading boxes onto a truck . So far, they have loaded 48 boxes onto the truck. According to their inventory, they still need to load 96% of boxes on the truck. What is the total number of boxes the workers are loading on the truck? Explain.
Answers
Answer:
1,200
Steps down below
Step-by-step explanation:
Steps
1: 48=4% loaded on truck and they have 96% left to load
2: so set up a proportion and it should look like this
3: 48 over x = 4 over 100
4: 48/x=4/100
6: do cross multiplication 100×48= 4,800÷ 4 = 1,200 total on truck
Answer: 1,200 total on truck
Hope this helps.
5 5/9 - 2 4/9?? Help!
Answers
Answer:
The answer would be 3 1/9
Step-by-step explanation:
5-2= 3 5/9-4/9 = 1/9
Answer:
3 1/9
Step-by-step explanation:
(5 x 9 + 5)/9 - 2 4/9
(45 + 5)/9 - 2 4/9
50/9 - 2 4/9
50/9 - (2 x 9 + 4)/9
50/9 - (18 + 4)/9
50/9 - 22/9
(50 - 22)/9
28/9
3 1/9
Find the value of z and z + 45
z = ?
z + 45 = ?
Answers
Answer:
ligma
Step-by-step explanation:
Please help I need the answers ASAP!
Answers
Part A:
Find m∠2,
Since ∠1 and ∠2 are alternate interior angles, they are equal. So, m∠2=60°
Part B:
Find m∠3,
Since ∠2 and∠3 are supplementary, the sum of their measures is 180°. So, m∠3=180°-60° which is 120°.
Solving Equations With Variables
4 - x = 12
Answers
Answer:
take the 4
-4 -x = -4 12
-x = 8
Step-by-step explanation:
Answer:
4=8
Step-by-step explanation:
because you have to minus - 4 and then to the other side to get 8 so your final answer will be x=8
a surveyor determined the value of an area of land over a period of several years since 1950. the land was worth $31,000 in 1954 and $35,000 in 1955. use the data to determine an exponential model that describes the value of the land. a
Answers
\(y=19.08(1.129)^{-1}\) is the exponential model that describes the value of the land.
What is exponential model?Exponential growth is a process by which quantity increases over time. When the instantaneous rate of change (that is, the derivative) of a quantity with respect to time is proportional to the quantity itself, it is said to be proportional to the quantity itself. A quantity experiencing exponential growth is an exponential function of time, which means that the variable representing time is the exponent (in contrast to other types of growth, such as quadratic growth).
\($$Use the exponential model:$$y=a \cdot b^x$$Let $y$ be the value of the area of land in thousand dollars and $x$ be the number of years since 1950.Given two consecutive $x$-values $x=4$ (year 1954) and $x=5$ (year 1955), the growth factor $b$ is the ratio of their $y$ -values:$$b=\frac{35}{31} \approx 1.129$$Use the value of $b$ and one of the data points to find the initial value, $a$. Here, I used $(4,31)$ :\)
\($$\begin{gathered}31=a(1.129)^4 \\\frac{31}{(1.129)^4}=a \\19.08 \approx a\end{gathered}\\\\\\So, the function describing the value of the land is:$$y=19.08(1.129)^{-1}$$\)
Thus, \(y=19.08(1.129)^{-1}\) is the exponential model that describes the value of the land.
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if y - 1/y =8 then find the value of y^2-1/y^3
Answers
Step-by-step explanation:
\( {y}^{2} - \frac{1}{ {y}^{3} } \)
factorise out y² ;
\( = {y}^{2} (1 - \frac{1}{y} ) \\ \\ = 8 {y}^{2} \)
I need help on this one too please
Answers
Answer: 6x^3 I hope this helps! :D
Step-by-step explanation: The GCF of 18^3 and 30x^5 is 6x^3.
I need help with these
Answers
The 15 and 9 units side lengths of the parallelogram ABCD, and the 36° measure of the acute interior angle, A indicates the values of the ratios are;
1. AB:BC = 5:3
2. AB:CD = 1:1
3. m∠A : m∠C= 1 : 4
4. m∠B:m∠C = 4:1
5. AD: Perimeter ABCD = 3:16
What is a ratio?A ratio is a representation of the number of times one quantity is contained in another quantity.
The shape of the quadrilateral ABCD in the question = A parallelogram
Length of AB = 15
Length of BC = 9
Measure of angle m∠A = 36°
Therefore;
1. AB:BC = 15:9 = 5:3
2. AB ≅ CD (Opposite sides of a parallelogram are congruent)
AB = CD (Definition of congruency)
AB = 15, therefore, CD = 15 transitive property
AB:CD = 15:15 = 1:1
3. ∠A ≅ ∠C (Opposite interior angles of a parallelogram are congruent)
Therefore; m∠A = m∠C = 36°
∠A and ∠D are supplementary angles (Same side interior angles formed between parallel lines)
Therefore; ∠A + ∠D = 180°
36° + ∠D = 180°
∠D = 180° - 36° = 144°
∠D = 144°
m∠A : m∠C = 36°:144° =1:4
m∠A : m∠C = 1:4
4. ∠B = ∠D = 144° (properties of a parallelogram)
m∠B : m∠C = 144° : 36° = 4:1
5. AD ≅ BC (opposite sides of a parallelogram)
AD = BC = 9 (definition of congruency)
The perimeter of the parallelogram ABCD = AB + BC + CD + DA
Therefore;
Perimeter of parallelogram ABCD = 15 + 9 + 15 + 9 = 48
AD:Perimeter of the ABCD = 9 : 48 = 3 : 16
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I GIVE BRAINLIEST FOR CORRECT ANS
Answers
True
7/19 = 0.36
5/19 = 0.26