The area of mathematics known as algebra aids in the representation of circumstances or problems as mathematical expressions.
What is meant by algebra?Mathematical expressions can be used to depict situations or issues, and algebra is the field of mathematics that does this. For a mathematical expression to have meaning, it needs to include variables like x, y, and z as well as mathematical operations like addition, subtraction, multiplication, and division.Algebra is a common thread that runs through practically all of mathematics. It involves the study of variables and the rules for manipulating them in formulas. Since all mathematical applications involve manipulating variables as though they were numbers, elementary algebra is a prerequisite.The order in which you perform operations in arithmetic and algebra is governed by a number of laws. The Commutative, Associative, and Distributive Laws are the three that receive the most attention.Given data :
1. We split it into the following:
[tex]\sqrt{4*6}[/tex]
Now, we use the radical rule which states that,
[tex]\sqrt{ab} = \sqrt{a} *\sqrt{b}[/tex] a,b > 0
So, we get,
[tex]\sqrt{4}[/tex] [tex]\sqrt{6}[/tex]
= 2[tex]\sqrt{6}[/tex]
2. We split it into the following:
[tex]\sqrt{12*9}[/tex]
Now, we use the radical rule which states that,
[tex]\sqrt{ab} = \sqrt{a} *\sqrt{b}[/tex] a,b > 0
So, we get,
[tex]\sqrt{12}[/tex] [tex]\sqrt{9}[/tex]
= 6 [tex]\sqrt{3}[/tex]
3. √7 . √14 =
= √7 . √7 .√2
= 7.√2
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The number of loaves of bread purchased and the total cost of the bread in dollars can be modeled by the equation c = 3.5b. Which table of values matches the equation and includes only viable solutions?
A 2-column table with 4 rows. The first column is labeled loaves (b) with entries negative 2, 0, 2, 4. The second column is labeled cost (c) with entries negative 7, 0, 7, 14.
A 2-column table with 4 rows. The first column is labeled loaves (b) with entries 0, 0.5, 1, 1.5. The second column is labeled cost (c) with entries 0, 1.75, 3.5, 5.25.
A 2-column table with 4 rows. The first column is labeled loaves (b) with entries 0, 3, 6, 9. The second column is labeled cost (c) with entries 0, 10.5, 21, 31.5.
The table for the function c{b} is -
{b} : 1 2 3 4
c{b} : 3.5 7.0 10.5 14
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that the number of loaves of bread purchased and the total cost of the bread in dollars can be modeled by the equation c = 3.5b.
We can write the table for the function c{b} as -
b c{b}
1 3.5
2 7.0
3 10.5
4 14
Therefore, the table for the function c{b} is -
{b} : 1 2 3 4
c{b} : 3.5 7.0 10.5 14
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3. Solve this system by elimination
-5x - 10y = 20
-5x - 8y = 14
6. Solve this system by substitution
x = 4
-4x - 5y = 4
Answer:
3. (-4/5, -3) 6. (4, 12/-5)
Step-by-step explanation:
3. so first we have
-5x - 10y = 20
-5x - 8y = 14
so first we have to have the x's be opposite so we multiply the top one by -1 which gets us
5x + 10y = -20
-5x - 8y = 14
then we cancel out the x's and subtract 10 by 8 and -20 by 14 so it's now
2y = -6
then we divide by 2 on both sides so it's
y = -3
but now we have to solve for x so we substitute y in on the bottom equation so now it is
-5x - 8(-3) = 20
now we multiply
-5x + 24 = 20
subtract 24 from both sides
-5x = -4
divide by -5
x = -4/5
then put it in coordinates
(-4/5, -3)
6. so we have
x = 4
-4x - 5y = 4
so first we have to substitute the top in for the bottom so now we have
-4(4) - 5y = 4
distribute
-8 - 5y = 4
add 8 to both sides
-5y = 12
divide
y = 12/-5
coordinates
(4, 12/-5)
There are two bags A and B.
Bag A has 6 red counters and 4 green counters. Bag B has 3 red counters and 7 green counters.
A counter is removed from Bag a and placed into Bag B. A counter is then removed from Bag B.
Work out the probability the counter removed is red.
The probability that the counter removed is red is given as follows:
18/55.
How to obtain the probability?A probability is obtained as the division of the number of desired outcomes by the number of total outcomes.
The probabilities of a red counter being removed from Bag B is obtained considering these following scenarios:
Red from A: 4/11 of 6/10.Green from A: 3/11 of 4/10.Hence the probability that the counter removed is red is calculated as follows:
p = 4/11 x 6/10 + 3/11 x 4/10 = 36/110 = 18/55.
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What does represent? index of refraction index of reflection angle of incidence angle of refraction.
The figure represents the angle of refraction
The angle of refraction is represented by the angle θ2
Light rays that are refracted change their direction as they travel through different media. Light changes direction when it travels from one medium to another.
The refracted beam will bend toward the normal if the incident light is moving from a less dense to a denser material. Here, the angle of refraction (hence, "r") is always smaller than the angle of incidence. (In line with the diagram)
Similar to this, the refracted ray will bend away from the normal if the incident light is moving from a denser medium to a less dense material. In this situation, the angle of incidence is never greater than the angle of refraction, or "r."
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You are placing a fountain in a triangular koi pond. You want the
fountain to be the same distance from each edge of the
pond. Where should you place the fountain? Explain
your reasoning. Use a sketch to support your answer.
As the person wanted the fountain to be the same distance from each edge of the pond and the incenter of the triangle is equidistant
How to illustrate the distance?From the information, the person is placing a fountain in a triangular koi pond and want the fountain to be the same distance from each edge of the
pond.
The intersection of all three of the triangle's interior angle bisectors is where a triangle's incenter is located. It can be thought of as the intersection of the triangle's internal angle bisectors. The fountain is equally spaced from each edge of the pond because the person wanted it to be, and the triangle's incenter is also evenly spaced.
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Find 4½ x 2½ write the product as a mixed number
Answer: 11 1/4
Step-by-step explanation:
4 1/2 * 2 1/2
= 9/2 * 5/2
= 45 / 4
= 11 1/4
16
d
out of
What is the solution set to the following
equation?
4m² - 8m +9=0
Select one:
O a. m = 1 + 4i√√/5
2+i√/5
O b. m =
2
O c. m = -1 ± 4i√√5
O d. m =
-2+i√/5
2
The solutions of the quadratic equation are:
m = 1 ± i*√(5)/2
The correct option is b.
How to find the solutions of the quadratic equation?Here we want to solve the quadratic equation:
4m² - 8m +9 = 0
Replacing the coefficients on the quadratic formula, we will see that the solutions are:
[tex]m = \frac{8 \pm \sqrt{(-8)^2 - 4*4*9} }{2*4} \\\\m = \frac{8 \pm \sqrt{-80} }{8}\\\\m = 1 \pm\sqrt{-80/64} \\\\m = 1 \pm\sqrt{-5/4} \\\\m = 1 \pm\sqrt{-5}/2\\\\m = 1 \pm\sqrt{5}i/2[/tex]
These are the solutions.
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3. Triangle DEF with vertices D(0, 6), E(3, 5), and F(1, 1):
90° counterclockwise about the point (5,2)
The vertices of the triangle DEF after the 90º counterclockwise rotation about the point (5,2) are given as follows:
D'(-11, -2), E'(-10, 1) and F'(-6, -3).
What are the rotation rules?The five more known rotation rules are given as follows:
90° clockwise rotation: (x,y) -> (y,-x)90° counterclockwise rotation: (x,y) -> (-y,x)180° clockwise and counterclockwise rotation: (x, y) -> (-x,-y)270° clockwise rotation: (x,y) -> (-y,x)270° counterclockwise rotation: (x,y) -> (y,-x)Considering the 90º counterclockwise rotation about the point (5,2), the rule is given as follows:
(x,y) -> (-y - 5, x - 2).
Hence the vertices are given as follows:
D'(-11, -2), E'(-10, 1) and F'(-6, -3).
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Set up a proportion to solve for x in the following similar triangles.
Answer:
9/6=12/x-4
Step-by-step explanation:
Sooo yeah umm..... I need help.
Answer:
[tex]\mathrm{Slope } = \dfrac{2}{3}[/tex]
Step-by-step explanation:
To find the slope take any two convenient x, y value combo.
Find the difference between the two y-values(we call it rise).
Find the difference in the corresponding x-values (we call this the run)
[tex]\dfrac{rise}{run} = slope[/tex]
Take points (3, 1) and (6,3). I could choose any two points but working with positive numbers makes it easier
Rise = 3- 1 = 2
Run = 6 - 3 = 3
[tex]\mathrm{Slope } = \dfrac{2}{3}[/tex]
Just for the heck of it let's take two other points to make sure we haven't goofed
Take points (-1, - 5/3) and (1, -1/3)
rise = -1/3 - (-5/3) = -1/3 + 5/3 = 4/3
run = 1 - (-1) = 2
rise over run = 4/3 ÷ 2 = 4/3 x 1/2 = 2/3
pendiente y ángulos A(-8,6) B(11,2)
The slope of the line containing the points A(-8,6) and B(11,2) is given as follows:
m = -0.2105.
The angle of the line is given as follows:
θ = -11.89º.
How to obtain the slope and the angle?The two points on the line are given as follows:
A(-8,6) and B(11,2).
Given two points, the slope is obtained by the division of the change in y by the change in x, hence:
m = (2 - 6)/(11 + 8)
m = -0.2105.
The slope represents the tangent of the angle, hence the angle is the arc tangent of the slope, thus:
θ = arctan(-0.2105)
θ = -11.89º.
TranslationThe problem asks for the slope and for the angle of the line containing points A and B.
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I need help with this question please and thank you
Answer:
See below
Step-by-step explanation:
Late one night a burglar got into one of the vault in Fort Knox and he tole a big ack of gold coin. On hi way out, he wa topped by one of the guard who aw him tealing the bag. Fortunately for him, the burglar wa able to negotiate a deal with the guard and offered him half the money he had taken, plu an extra $2,000 thrown in. Jut a he wa walking away, thinking he had gotten away he wa topped by a econd guard who took the ame bribe: Half the money with an extra $2000 thrown in. Jut a he wa about to leave , he wa topped by a third guard who let him go only after receiving half of all the burglar had left with $ 2,000 extra thrown in. By the time he left he had mixed emotion. After all he did leave with $9,000 more than he had when he arrived and he wa able to ecape. But he thought of all the money he left behind. How much did he teal in the firt place?
Therefore, the burglar's initial theft was $12,000.
To begin, we may express the data in the problem using algebra.
Let x represent the original sum that the burglary victim took.
The thief was left with x/2 + 2000 after giving the first guard the other half of the money plus $2,000, according to the issue.
He had (x/2 + 2000)/2 + 2000 when he gave the same sum to the second guard.
He also handed the third guard the same amount, leaving him with
((x/2 + 2000)/2 + 2000)/2 + 2000.
However, because we are certain that he left with $9,000 more than when he came, we may state:
((x/2 + 2000)/2 + 2000)/2 + 2000 = x + 9000
We can now determine x:
x = (900022*2 - 6000)/3
x = 36000/3
x = 12000
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K is the midpoint of GJ and I is the midpoint of HJ
IF GH=t+47 and IK=-5t+84 what is the value of t?
By using the fact that the triangles are similar, we can write and solve an equation to find that t = 11.
How to find the value of t?Here we know that K is the midpoint of GJ and I is the midpoint of HJ, this means that triangle JKI is similar to JHG, but dilated by a factor 1/2.
That means that we can write:
(1/2)HG = IK
We know that:
GH = t + 47
IK = -5t + 84
Replacing these in the equation above, we will get:
(1/2)*(t + 47) = -5t + 84
t + 47 = 2*(-5t + 84)
t + 47 = -10*t + 168
t + 10t = 168 - 47
11t = 121
t = 121/11 = 11
The value of t is 11.
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Lexie's younger brother helped pick up all the paper clips in
Lexie's room. He was able to collect 8,100 paper clips. If he wants
to distribute the paper clips in 90 boxes, write an equation
showing how many paper clips each box will contain?
This equation divides the total number of paper clips (8100) by the number of boxes (90)
What is equation?An equation is a mathematical statement that asserts the equality of two expressions. It is usually expressed using an equals sign (=), with the expressions on either side of the sign separated by the equation symbol. Equations are used to describe relationships between different variables, or to solve for unknown values. Equations are also used to explain physical phenomena, such as Newton's second law of motion, which states that force equals mass times acceleration (F = ma).
The equation that would be used to determine how many paper clips each box will contain is 8100 ÷ 90 = 90.
This equation divides the total number of paper clips (8100) by the number of boxes (90) in order to determine that each box will contain 90 paper clips.
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How do you find the mean value of a Class 10?.
The mean is dividing the sum of all values in a data set by the number of values.
Average is another word for "mean." For instance, if we say that the average height of the 9th grade class is 150 cm, it signifies that this is the mean of all of the kids' heights. The statistical notion of mean, which is employed in a variety of financial areas and corporate appraisal, has significant financial implications. The three statistical measurements of a data set's central tendency are mean, median, and mode.
The mean, which measures the central tendency of the data, is the average or computed central value of a set of numbers. The statistical metric known as central tendency identifies the complete collection of data or distribution by a single value. It offers a precise description of the entire set of facts. The ratio of the sum of all observations to the total number of observations is another way to define the mean in statistics.
Given a data set, X = {x₁,x₂, . . . ,xₙ}, the mean (or arithmetic mean, or average), denoted X, is the mean of the n values x₁,x₂, . . . ,xₙ.
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A parallelogram is shown on this coordinate plane.
What is the perimeter, in units, of the parallelogram?
A) 24
B) 36
C) 48
D) 64
The perimeter, in units, of the parallelogram exists 48.
What is meant by coordinate plane?Two number lines combine to produce the coordinate plane, a two-dimensional surface. The x-axis is the name given to one horizontal number line. The y-axis is the name given to the other number line, which is vertical. At a place known as the origin, the two axes collide. The coordinate plane allows us to graph points, lines, and more.
A coordinate plane is a framework for describing and graphing points and lines. The coordinate plane is composed of two axes, one vertical (y) and one horizontal (x). The coordinate plane has four quadrants. The origin is the location where these lines converge (0, 0).
Therefore, the correct answer is option C) 48.
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A newpaper advertiement offer a $10 000 ued car for nothing down and 36 monthly payment of $450. What i the interet rate ued? How much interet will you have to pay if you purchae thi car?
If you purchase the car with this loan, you will have to pay a total of $5,400 in interest.
To calculate the interest rate used for this loan, we can use the formula:
Interest rate = (Monthly payment x 12) / Principal
Plugging in the given values, we get:
Interest rate = ($450 x 12) / $10,000 = 0.54 or 54%
To calculate the total interest paid on the loan, we can use the formula:
Total interest = Principal x Interest rate
Plugging in the given values, we get:
Total interest = $10,000 x 0.54 = $5,400
So if you purchase the car with this loan, you will have to pay a total of $5,400 in interest.
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Find the Maximum on the interval {3,5} for the line y= 2x+1
The maximum value of the linear equation on the given interval is:
y = 11
How to find the maximum on the given interval?We want to find the maximum of the linear function:
y = 2x + 1
On the interval [3, 5]
Notice that we have a line with a positive slope, thus, this is an increasing line.
Then the maximum is just what we get when we evaluate the function on the maximum value of the interval:
y = 2*5 + 1
y = 10 + 1
y = 11
The maximum value is 11.
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3. Ura Snob has three times as many dimes as quarters. If he has $2.75, how many quarters
does he have?
Answer:
75x = 300
x = 4
So he has
4 quarters
3x = 3*4 = 12 dimes
4x = 4*4 = 16 nickels
Step-by-step explanation:
Please look at photo!
The correct option A: The solution cannot include x = 3 and x = (-1/2) as it will make the equation as indeterminate form, whose solution is not possible.
Explain the indeterminate form of the equation?If an undefined statement containing an operations between two quantities evaluates to something like a single number meaning or infinity, it is referred to as having a determinate form. If an undefined expression doesn't quite evaluate to just a single numerical value or infinity but instead involves an operation between two numbers, it is referred to as having an indeterminate form.When establishing the limit of a ratio between two functions, including x/x3, x/x, and x2/x, the ratios go to, ∞, 1, and 0 accordingly when x approaches zero.For the stated equation.
6 / (2x + 1) - 1 / (x - 3) = 0.
When putting x = x = 3 and x = (-1/2), the denominator part will become zero.
This makes the whole equation as indeterminate form,whose solution is not possible.
Thus, the solution cannot include x = 3 and x = (-1/2) as it will make the equation as indeterminate form, whose solution is not possible.
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How do you graph y =- 7?.
Graph y=-7 by plotting y-intercept (0,-7) and all points have y=-7, it is a horizontal line.
What is graph ?
A graph is a mathematical structure used to represent relationships between objects. In a graph, objects are represented by vertices (or nodes) and relationships are represented by edges (or arcs). Graphs can be used to model a wide variety of real-world systems, including networks of roads, social networks, and the internet.
To graph y = -7, you can start by plotting the y-intercept, which is the point at which the line crosses the y-axis. In this case, the y-intercept is (0, -7) because when x = 0, y = -7.
To graph the line, you can then pick any other x-value, substitute it into the equation, and find the corresponding y-value. For example, if you pick x = 1, then y = -7. So, you can plot the point (1,-7) on the graph.
You can repeat this process with different x-values and plot more points on the graph.
Graph y=-7 by plotting y-intercept (0,-7) and all points have y=-7, it is a horizontal line.
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A chocolatier made 16 batches of salted caramel chocolate
bars. Each batch consisted of 42 chocolate bars. The
chocolatier sent an equal number of bars to each of its
6 stores. How many bars did each store receive?
Answer:
112 chocolate bars
Step-by-step explanation:
Given that the chocolatier made 16 batches of salted caramel chocolate bars, each batch consisted of 42 bars and he sent an equal number of bars to each of its 6 stores,
What is asked: To determine how many bars did each store receive.
Method of solving: Using elementary operations as multiplication and division.
Start considering each batch as the following box:
So it suggests that to find the total number of chocolates produced is equal to the product
Before multiplying, now see that the chocolatier is equally dividing them to its 6 stores, which means that he will take this quantity and divide equally into 6 boxes.
Therefore, this process is the same as dividing by 6, therefore
Is the expression that gives the result desired.
Simplifying the fraction and multiplying the terms gives
112 chocolate barsThis is the amount of chocolate bars each store received.
Your buine ha decided to tart recycling paper product. In exchange, the recycling company will donate 20 boxe of new paper each year to your buine. You currently order 150 boxe of paper per year, at $50 per box. If you tart recycling with the company, how much money will you ave each year?
You will save as much as $1000 each year if you start recycling with the company.
If your current order of 150 boxes of paper per year costs $50 per box, and in exchange of starting recycling with the company, the recycling company will donate 20 boxes of new paper each year to your business, then you will save as much as $1000 each year.
Determine how much you will save by multiplying the amount of boxes of paper the recycling company will give to your business with the cost of each box of paper.
20 boxes of new paper x $50 per box = $1000
Therefore, the amount you will save if you start recycling with the company will be as much as $1000 each year .
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Amrita had to travel 20 km to attend a function. She had covered 17km 50 m when her car broken down. How much ditance remained to be covered
The distance remained to be covered by amrita to attend a function is 2950 meters or 2.95 kilometers.
Given,
Total distance to be covered by Amrita = 20 KM = 20000 m
Distance covered by her car before broken = 17 Km 50 meter = 17050m
We know that,
1 Kilometer = 1000 meter
Remaining Distance = (20000 - 17050)m
= 2950 m
= 2.95 KM
Therefore, the distance remaining to be covered by amrita is 2950 meters or 2.95 Kilometers.
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A piece of artwork appreciate by 1. 28% in value every year. It wa purchaed for $1500. State the equation that can be ued to determine the value of the artwork in ""x"" year
the equation that can be used to determine the value of the artwork in "x" year is A = 1500(1 + 0.0128)^x.
An equation that can be used to determine the value of the artwork in "x" years is a compound interest equation. This type of equation is used to calculate the value of an investment over time, taking into account the initial investment amount and the interest rate.
Compound interest is the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from previous periods. It can be contrasted with simple interest, which is calculated only on the principal amount.
Compound interest is considered to be more beneficial for savers and investors, as it allows for interest to be earned on previously earned interest, leading to faster growth of the principal.
In this case, the artwork appreciates by 1.28% in value every year and was purchased for $1500. The formula for compound interest is:
A = P(1 + r)^n
Where:
A = the future value of the artwork
P = the initial investment (the purchase price of $1500)
r = the interest rate (1.28% per year)
n = the number of years
To use this equation, we need to convert the interest rate from a percentage to a decimal. We do this by dividing the interest rate by 100. So, 1.28% as a decimal is 0.0128.
Now we can substitute the values into the equation:
A = 1500(1 + 0.0128)^x
Therefore, the equation that can be used to determine the value of the artwork in "x" year is A = 1500(1 + 0.0128)^x.
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Please help, I already did the rest I just need help with the last one.
What is a sum of 4 and 5?.
The sum of 4 and 5 is 9
We know that the sum or also called a summation, is nothing but the result of arithmetically adding numbers.
In simple way we can say that the sum is a way of putting all things together.
The sum is nothing but the whole number which is obtained when two or more numbers have been added together.
and the numbers that are added are known as the addends.
When we add the numbers a plus symbol '+' is used.
Let us assume that we need to find the sum of numbers p and q then we write it as p + q, where p, q are addends.
Here, we need to find the sum of numbers 4 and 5.
4 + 5 = 9
so, the sum is 9
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number 6 please help
Answer: x = 26
Step-by-step explanation: All you need to do is to add up given two unknown angles. Then, you can solve the equation for 180 degree. Because in this case, these angles are complementary to 180 degrees.
If you add them up:
[tex]8x - 28 = 180\\x = 26[/tex]
So, the answer is 26.
19. Sketch the graph of x² + y² + 4x - 2y - 31 = 0.
Write the center and radius under the graph. (show all work)
For given equation of circle radius is 6 unit and center is at (-2,1).
What is a circle?
A circle is a special kind of ellipse in which the eccentricity is zero and the two foci are coincident. A circle is also termed as the locus of the points drawn at an equidistant from the center. The distance from the center of the circle to the outer line is its radius. Diameter is the line which divides the circle into two equal parts and is also equal to twice of the radius.
The equation of circle in the plane is given as:
(x-h)^2 + (y-k)^2 = r^2
where (x, y) are the coordinate points
(h, k) is the coordinate of the center of a circle
and r is the radius of a circle.
Now,
As shown in graph the graph by taking two points on graph
(-2,7) and (-2,-5)
Center will be at (-2-2)/2, (7-5)/2
i.e. (-2,1)
And for radius take magnitude of points from y-coordinate
(7+5)/2=6 unit
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