The value of the multiplication of the given fractions [tex](\frac{1}{2} - \frac{2}{5}) * (- \frac{5}{7} + \frac{1}{14} )[/tex] is -9/ 140.
What are fractions?In mathematics, a fraction is used to denote a portion or component of the whole. It stands for the proportionate pieces of the whole. Numerator and denominator are the two components that make up a fraction.
What is multiplication of factors?A fraction multiplied by another fraction, an integer, or a set of variables is referred to as a fraction. The steps for multiplying fractions are as follows:
Add the numerator to the numerator to multiply. Add the denominator to the denominator and multiply. If necessary, simplify the fractions.
The multiplication of the given numbers is:
[tex](\frac{1}{2} - \frac{2}{5}) * (- \frac{5}{7} + \frac{1}{14} ) \\\\(\frac{5-4}{10} ) * (\frac{-10 + 1}{14} )\\\\\frac{1}{10} * \frac{- 9}{14} \\\\\frac{-9}{140}[/tex]
Hence, value of the multiplication of the given fractions [tex](\frac{1}{2} - \frac{2}{5}) * (- \frac{5}{7} + \frac{1}{14} )[/tex] is -9/ 140.
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LOTS OF POINTS PLEASE HELP
Three Algebra 1 students are comparing how fast their social media posts have spread. Their results are shown in the following table:
Student Amber Ben Carter
Description Amber shared her photo with 3 people. They continued to share it, so the number of shares increases every day, as shown by the function. Ben shared his post with 2 friends. Each of those friends shares with 3 more every day, so the number of shares triples every day. Carter shared his post with 10 friends, who each share with only 2 people each day.
Social Media Post Shares f(x) = 3(4)x
Day Number of Shares
0 2
1 6
2 18 Carter shared his post with 10 friends, who each share with only 2 people each day.
Graph each function using at least three points for each curve. All graphs should be placed together on the same coordinate plane, so be sure to label each curve. You may graph your equation by hand on a piece of paper and scan your work, or you may use graphing technology.
A graph of each of the exponential equation is shown in the image attached below.
What is an exponential function?In Mathematics, an exponential function can be modeled by using this mathematical expression:
f(x) = ab^x
Where:
a represents the initial value or y-intercept.x represents time.b represents the rate of change.Since Amber shared her photo with 3 people who continued to share it, an exponential function that models the situation is given by:
f(x) = 3(4)^x
Similarly, Ben's post was shared with 2 friends and each of them shared it with 3 more every day, tripling the number of shares every day, an exponential function that models the situation is given by:
g(x) = 2(3)^x
Lastly, an exponential function that represents the spread of Carter's social media post is given by:
h(x) = 10(2)^x
In this scenario, we would use an online graphing calculator to graph each function as shown in the image attached below.
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They continued to share it, so the number of shares increases every day, as shown by the function.
Social Media Post Shares f(x) = 3(4)x
Day Number of Shares
0 2
1 6
2 18 Carter shared his post with 10 friends, who each share with only 2 people each day.
1. The population of a town was 5655 in 2010. The population grows at a rate of 1.4% annually. (a) Use the exponential growth model to write an equation that estimates the population t years after 2010. (a) Estimate the population of the town in 2022. Show your work.
(a) The exponential growth model is P = 5655 e^(0.014t)
(b) Population of the town in 2022 is 6689.5065.
What is Population Growth?Population growth is defined as the number of people increasing over years in a specific region calculated using annual growth rate.
(a) The formula to calculate population growth is,
P = P₀ e^(r t)
Given,
Initial population in 2010, P₀ = 5655
Annual growth rate, r = 1.4% = 0.014
Substituting,
P = 5655 e^(0.014t)
(b) To estimate the population of town in 2022,
t = 2022 - 2010 = 12 years
Substituting value of t in the formula in (a),
P = 5655 e^(0.014 × 12)
= 5655 e^(0.168)
= 5655 × 1.1829
= 6689.5065
Hence the population is 6689.5065 in 2022.
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Plot the x-intercept of the function f(x) = (x + 4)².
y
-6 -4 -2
10
Intro
8
6
4
2
2 4
Click or tap the graph to plot a point.
6
x
x
y
By graphing a plot point using the x-intercept form, the function (x + 4)2 is shown to be x2 + 16 + 8x.
what is function?The subject of mathematics includes quantities and their variations, equations and related structures, forms and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A relationship between inputs and outputs in which each input leads to a single, distinct result is known as a function. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, within functions, and on functions.
given
(x + 4)²
= x2 + 16 + 8x
By graphing a plot point using the x-intercept form, the function (x + 4)2 is shown to be x2 + 16 + 8x.
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How do you write a polynomial function with factors?
So on provided question we cans ay that Take the common binomial into account. Note that when we multiply our response by itself, the original polynomial results.
what are polynomials?A mathematical expression made up of coefficients and uncertainty that only makes use of additions, subtractions, multiplications, and positive integer powers of variables is known as a polynomial. The formula x2 4x + 7 denotes a single indeterminate x polynomial. An expression in mathematics known as a polynomial is made up of variables (also known as indeterminates) and coefficients that may be added, subtracted, multiplied, and raised to negative integer powers of non-variables. An algebraic statement with variables and coefficients is called a polynomial. An expression can only contain the operations addition, subtraction, multiplication, and non-negative integer exponents. Polynomials are the name for these expressions.
here,
Group the first two terms first, followed by the last two terms. Remove a GCF from each each binomial. Take the common binomial into account. Note that when we multiply our response by itself, the original polynomial results.
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Heila either walk or cycle to chool
the probability he walk to chool i 0. 65
if he walk to chool, the probability he i late i 0. 4
If he cycle to chool, the probability he i late i 0. 1
work out the probability that on any one day heila will not be late for chool
The probability that on any one day, Heila will not be late for school is 0.69 or 69%.
We can use conditional probability to find the probability that Heila will not be late for school on any one day.
Let W be the event that Heila walks to school, and L be the event that Heila is late for school.
We know that:
P(W) = 0.65 (the probability that Heila walks to school)
P(L | W) = 0.4 (the probability that Heila is late for school given that he walks to school)
P(L | W') = 0.1 (the probability that Heila is late for school given that he cycles to school)
The probability that Heila is not late for school is the complement of the event that he is late for school. So:
P(L') = 1 - P(L)
We can use the formula for conditional probability to find the probability that Heila is not late for school:
P(L' | W) = 1 - P(L | W) = 1 - 0.4 = 0.6
P(L' | W') = 1 - P(L | W') = 1 - 0.1 = 0.9
We also know that the total probability of the outcomes must be equal to 1. Therefore, we can find the probability that Heila walks to school, P(W) by using the following equation:
P(W) + P(W') = 1
We know that P(W) = 0.65, so we can find P(W') by subtracting P(W) from 1:
P(W') = 1 - P(W) = 1 - 0.65 = 0.35
Now, we can use the formula of Total Probability to find the probability that Heila will not be late for school:
P(L') = P(L' | W) * P(W) + P(L' | W') * P(W')
P(L') = 0.6 * 0.65 + 0.9 * 0.35 = 0.69
Therefore, the probability that on any one day, Heila will not be late for school is 0.69 or 69%.
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Angela wants to know how many of the 380 7th graders earned an A on the last Science test. She decides to sample 15% of the 7th graders in order to predict how many earned an A. What is her sample size?
Angela's sample size for the study on predicting how many 7th graders earned an A, is 57 students
How to find the sample size ?The number of observations used to calculate estimates for a certain population is known as the sample size. The sample size was determined by drawing from the population. Sampling is the practice of choosing a portion of the population from which to draw conclusions about the characteristics of the entire population.
In engaging in sampling, Angela wanted to sample 15 % of the 7th graders which means that her sample size would be :
= Percentage to be sampled x Number of 7th graders
= 15 % x 380
= 57 students
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What is the formula for finding the sides of a triangle?
Therefore , the solution of the given problem of trigonometry comes out to be we can find the sides of triangle by trigonometry ratios.
What does trigonometry mean?The area of mathematics known as trigonometry explores the correlation between square side length and As a result of the combination of astronomy and geometry studies, the field initially emerged inside the Nineteenth century, most likely there in third century BC. Precise methods of mathematics cover a number of geometric equations and possible applications to calculations.
Here,
To find the all sides of a triangle
By using trigonometry ,
We can:
Apply the law of sines or trigonometry to find the right triangle side lengths: a = c × sin(α) or
a = c × cos(β)
b = c × sin(β) or
b = c × cos(α)
Therefore , the solution of the given problem of trigonometry comes out to be we can find the sides of triangle by trigonometry ratios.
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the average person's heart beats about 4,200 times in 1 hour. Write and solve an equation to find about how many times that is per minute
Give an example of a quartic trinomial.
Give an example of a quintic polynomial.
Answer:
quartic trinomial : 3x4 – 2x3 + x2 + 8, a4 + 1, and m3n + m2n2 + mn.
quintic polynomial: x5 – x3 + x, y5 + y4 + y3 + y2 + y + 1, and 42a3b2.
Step-by-step explanation:
Quartic Polynomial
A polynomial of degree 4.
Examples: 3x4 – 2x3 + x2 + 8, a4 + 1, and m3n + m2n2 + mn.
a quintic function is defined by a polynomial of degree five.
Because they have an odd degree, normal quintic functions appear similar to normal cubic functions when graphed, except they may possess one additional local maximum and one additional local minimum.
The quartic trinomial having a degree of 4 and the quintic polynomial having a degree of 5.
Quartic Trinomial:
A quartic trinomial is a polynomial expression of degree four that consists of three terms.
The general form of a quartic trinomial is:
[tex]ax^4 + bx^2 + c[/tex]
Example:
Let's consider the quartic trinomial:
[tex]2x^4 - 5x^2 + 3[/tex]
In this example, the term "[tex]2x^4[/tex]" is the highest degree term (degree 4), the term "-[tex]5x^2[/tex]" is the second highest degree term (degree 2), and the constant term "3" has no variable.
So, the quartic trinomial has three terms.
Quintic Polynomial:
A quintic polynomial is a polynomial expression of degree five that may contain multiple terms.
The general form of a quintic polynomial is:
[tex]ax^5 + bx^4 + cx^3 + dx^2 + ex + f[/tex]
Example:
Let's consider the quintic polynomial:
[tex]3x^5 - 2x^4 + 4x^3 + x^2 - 7x + 2[/tex]
In this example, the term "[tex]3x^5[/tex]" is the highest degree term (degree 5), the term "-[tex]2x^4[/tex]" is the second highest degree term (degree 4), and so on. The quintic polynomial has six terms, including the constant term "2".
Hence the quartic trinomial having a degree of 4 and the quintic polynomial having a degree of 5.
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Triangle ABC is translated by the rule (x, y) → (x - 1, y + 6) then reflected across the y- axis. What are the coordinates of A”,B”, and C”?
The coordinates of A'', B'' and C'' are (-1, 4), (-4, 3) and (-1, 2) respectively.
What is Geometric Transformation?Transformation of geometrical figures or points is the manipulation of a given figure to some other way.
Different types of transformations are Rotation, Reflection, Glide reflection, Translation and Dilation.
Given triangle has coordinates,
A(2, -2), B(5, -3) and C(2, -4).
First the triangle is translated by the rule (x, y) → (x - 1, y + 6)
A(2, -2) becomes A'(2 - 1, -2 + 6) = A'(1, 4).
B(5, -3) becomes B'(5 - 1, -3 + 6) = B'(4, 3)
C(2, -4) becomes C'(2 - 1, -4 + 6) = C'(1, 2)
Then the translated triangle is reflected across the Y axis.
When reflected a point (x, y) across the Y axis, y coordinate remains same and x coordinate flips.
A'(1, 4) becomes A''(-1, 4)
B'(4, 3) becomes B''(-4, 3)
C'(1, 2) becomes C''(-1, 2)
Hence the vertices of the triangle after undergoes translation and reflection becomes A''(-1, 4), B''(-4, 3) and C''(-1, 2).
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In ΔTUV, u = 750 cm, mm∠T=105° and mm∠U=42°. Find the length of t, to the nearest centimeter.
The length of t to the nearest centimeter is 1083 cm.
What are Angles?Angles are the figure formed by the intersection of two lines or rays by sharing a common point. This point is called the vertex of the angle.
Given that,
u = 750 cm
m ∠U = 42°
m ∠T = 105°
We have the sine rule to find missing length as,
[tex]\frac{u}{sin U}[/tex] = [tex]\frac{t}{sin T}[/tex]
Substituting the measures given,
[750 / sin (42°)] = [t / sin (105°)]
Cross multiplying,
t = [ 750 × sin (105°)] / sin (42°)
t = 1082.59 ≈ 1083 cm
Hence the length of the missing side is 1083 cm.
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Hilda went hiking and used the app on her phone to track her progress. When she looked back, she discovered she had hiked down 230 feet, up 602 feet, down 183 feet, and up 762 feet to get to the lake. What is her elevation in relation to where she started?
Answer: 951 ft
Step-by-step explanation:
-230 + 602 - 183 + 762
= 951 ft
What is the solution to the equation 1 h 5 2 h 5 16 h 2 25?
The solution to the equation 1/h-5+2/h+5=16/h^2-25 is H=7 .
What is the answer to the equation?An equation’s solution is an array of all values that, when substituted for unknowns, make the equation true. To solve equations with one unknown raised to a power of one, two basic algebra methods using the additive and multiplicative properties are needed. The set of linear equations has three alternative solutions.
They are as follows:
One-of-a-kind solution.
There is no solution.
There are an infinite number of solutions.
False solutions are ones that do not fundamentally address the problem at hand but fool others into believing they do, while also causing additional major problems.
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What are the formula in coordinate geometry for Class 9?
The formula in coordinate geometry for Class 9 include distance formula, midpoint formula, section formula, equation of a line, slope of a line, equation of a circle, equation of a parabola, equation of an ellipse, equation of a hyperbola, area of a triangle, and area of a circle.
The distance formula is used to determine the distance between two points in a coordinate plane. The midpoint formula is used to find the midpoint between two points. The section formula is used to calculate the area of a triangle formed by three points. The equation of a line is used to define the line in terms of its slope and intercept. The slope of a line is used to calculate the angle of the line in relation to the x-axis. The equation of a circle is used to determine the equation of a circle with a given center and radius. The equation of a parabola is used to determine the equation of a parabola with a given focus and directrix. The equation of an ellipse is used to determine the equation of an ellipse with a given center and major and minor axes. In coordinate geometry the equation of a hyperbola is used to determine the equation of a hyperbola with a given center and asymptotes. The area of a triangle is used to find the area of a triangle given the three vertices. The area of a circle is used to find the area of a circle given the radius.
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What is the equation of this line in slope intercept form?
Answer:
y=-2x+3
Step-by-step explanation:
y=mx+b
What is the coefficient of y² in the expression 3y² 4x *?
So, on solving the provided question, we can say that coefficient of y² in the expression 3y² - 4x is 3
What is the coefficient?A coefficient in mathematics is a polynomial, a series, or the multiplicative coefficient of a particular term in an expression. Typically numeric, however any expression is permitted. The term "parameter" can also refer to the coefficients themselves if they are variables. A number times a variable equals a coefficient. Coefficient examples include: The coefficient is 14 in phrase 14c 14c 14c. The coefficient is 1 for word g. multiplies the variable by this amount. example Given that "z" is a variable and that 6z is the definition of the term, the coefficient is 6. One is the coefficient of the square of x.
here,
coefficient of y² in the expression 3y² - 4x is 3
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A triangle has two sides measuring 8. 5 cm and 15 cm. What are the least and greatest whole number possibilities for the third side? enter your answers in the boxes.
The least whole number possibility for the third side is 8 cm. The greatest whole number possibility for the third side is 22 cm.
A triangle is a three-sided polygon. It is a geometric shape that has three edges and three vertices. Triangles can be classified based on their side lengths (such as equilateral, isosceles, or scalene) or based on the angles between their sides (such as acute, right, or obtuse). Triangles are a fundamental shape in geometry and are used in many branches of mathematics and physics. To form a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
Using this rule, we can find the possible range of values for the third side of the triangle.
The least possible length of the third side would be:
8.5cm + 15cm - 15cm = 8.5cm
The greatest possible length of the third side would be:
(8.5cm + 15cm) - 1cm = 22.5cm
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Solve the equation, and check your solution.
8.4+
8.4 = 1.4x
8.4+
—
= 1.4x +
= X
Complete the solution using inverse relationships.
8.4 = 1.4x
= 1.4x +
= X
-
(Type whole numbers or decimals.)
The solution to the equation 8.4 = 1.4x for the unknown variable x is 6.
How to solve equation?8.4 = 1.4x
divide both sides by the variable of x
x = 8.4 / 1.4
x = 6
Check:
8.4 = 1.4x
8.4 = 1.4(6)
8.4 = 8.4
Using inverse relationship
8.4 = k / 1.4
cross product
8.4 × 1.4 = k
11.76 = k
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What is 3 to the 2 exponent?
Answer:
It would be 6 because the exponent is 2 so you multiply 3 twice which equals 6
Step-by-step explanation:
3 to the 2nd exponent is 3^2 = 9.
The weights and heights of six mathematics students are given in the following table: Weight (in pounds)
165 123 212 175 165 147
Height (in centimeters)
172 157 183 178 163 167
State whether weight is a function of height for the six students and explain.
a. Yes, height is a function of weight because two students weigh 165 pounds but have different heights.
b. No, height is not a function of weight because two students weigh 165 pounds but have different heights.
c. Yes, weight is a function of height because for each value of height there is one corresponding value of weight.
d. No, weight is not a function of height because there is not enough data to determine a function.
The input variable is "Height," while the output variable is "Weight."
Explain about the independent variable?A variable that is independent is precisely what it sounds like. It is a stand-alone variable that is unaffected by the other variables you are attempting to assess. Age, for instance, could be an independent variable.
The cause is the independent variable. Its value is unaffected by the other study variables. Effect is the dependent variable. Changes in the independent variable affect its value.
When doing an experiment, the independent variable is what you alter, and the dependent variable is what changes as a result of that change. This is an easy way to conceive of independent and dependent variables. The independent variable can alternatively be viewed as the cause, and the dependent variable as the result.
The input and output variables are "Height" and "Weight," respectively.
Detailed explanation:
"Weight and height are related"
As we all know, the independent variable in a function of the form y=f(x) is x, and the dependent variable is y.
In other words, after substituting the values of "x," we are getting the values of the quantity "y."
As a result, we can infer from the assertion that,
We are getting the values of "Weight" after substituting the values of "Height."
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Lilyan took out a 72-month car loan for $17,595. If he had paid a total of $22,556. 79 at the end of the loan, find the interet rate
Lilyan took out a 72-month car loan for $17,595. If he had paid a total of $22,556. 79 at the end of the loan, then the interet rate is 6.7%
What is principal amount?
The loan amount that the lender gives to the borrower is referred to as the primary amount. Additionally, it is the factor the lender uses to calculate interest.
What is simple interest?
Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time. The formula to calculate simple interest is I=P.r.t
Where P=principal amount, r=rate, t=time.
Lilyan took out a 72-month car loan for $17,595.
If he had paid a total of $22,556. 79 at the end of the loan,
find the interet rate
72 months = 6 years
principal = 17595
amount = 22556.79
we have to calculate interest
A = P ( 1+ r/100) ^ n
= 17595 ( 1+r/100)^6
22556.79/17595 ^ 1/6= 1+0.00r
r= 6.7%
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Can I simplify a function?
The following actions must be taken in order to simplify the rational function f (x) = p (x) q (x): Where q (x) = 0, identify the values of x.
what is functions ?The study of mathematics include the study of numbers, formulas and related structures, forms and the environments in which they exist, quantities and their variations, and the environments in which they exist. A function is an association between a number of inputs, each of which has an output. Simply described, a function is a relationship between inputs and outputs in which each input leads to a single, distinct result. Usually, the letter f is used to denote functions (x). input consists of x. There are four different types of functions. based on the following elements: one-to-one functions, many-to-one functions, on functions, one-to-one functions, and within functions.
given
The following actions must be taken in order to simplify the rational function f (x) = p (x) q (x): Where q (x) = 0, identify the values of x.
If so, all real values, with the exception of these roots, are in the domain of f (x).
It may be necessary to factor by grouping or by applying the factor theorem in order to fully factor both p (x) and q (x).
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A repair person charges a travel fee to visit a home and an hourly fee for the time spent fixing a leak.
A repair that takes 2 h costs $100. A repair that takes 6 h costs $260.
Write an equation to represent the total cost of a repair, y, as a function of the
number of hours spent fixing a leak.
So on solving the provided question, we can say that y = a + xb is the necessary equation for the total fee the repairman charged, y = 260 + 6x
What is equation?A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.
Here,
Let the total amount charged by the repairman be y and the total number of hours worked be x,
[tex]y = a + xb[/tex]
a is as travel fee
b is as hourly rate
Therefore, y = a + xb is the necessary equation for the total fee the repairman charged.
y = 260 + 6x
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A boat travels downstream at an average speed of 30 mph. The boat makes the same trip back upstream at an average speed of 18 mph. What is the speed of the boat? What is the speed of the water current?
Therefore , the solution to the given problem of equation comes out to be is 19 mph for a boat in calm water.
What does equation mean?An equation must always include two equal members and one or more unknown members (the unknown variables). When multiplied by itself, what number, for example, results in 16. To express this maths equation mathematically, use the equation or expression.
Here,
The determining formula is
30/u-4 = 46/u+4
(time equation, where u represents the boat's speed in still water)
Cross-multiply:
30*(u+4) = 46(u-4) (u-4),
30u + 120 = 46u - 184,
120 + 184 = 46u - 30u,
Thus,
304 = 16u
=> 304/16
=> 19.
The answer is 19 mph for a boat in calm water.
Therefore , the solution to the given problem of equation comes out to be is 19 mph for a boat in calm water.
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Shannon babysits and charges a flat fee of $10 plus $2 for very hour she babysits. She needs to make $72 this week. How many hours can Shannon babysit
Answer:
72 divided by 12 is 6 so 6 hours she needs to babysit
The workers at a bakery must make 12 batches of bagel dough an hour to meet the customers needs. The number of batches of dough, y, that each worker needs to mix in one hour is inversely proportional to the number of workers, x.
The value for constant of proportionality and inverse proportionality is k=12 and x=12/y respectively.
What is constant of proportionality and inverse proportionality?
The ratio between two proportional quantities' constant values is known as the constant of proportionality. When either their ratio or their product gives a constant, two changing values are said to be in a proportionate relationship.
When the value of one item rises in relation to a fall in the other or vice versa, two values are said to be inversely proportionate. This indicates that the natural behaviour of these two quantities is contrary
In a bakery workers must make 12 batches of bagel dough an hour.
The number of batches of dough, y, that each worker needs to mix in one hour is inversely proportional to the number of workers, x.
Lets find the constant of proportionality first.
According to the graph -
The point given in the graph is (6,2).
x=6 and y=2
(where 'x' denotes no of workers and 'y' denote no. of bagel dough batches).
Equation for constant of proportionality is -
x×y=k
6×2=k
k=12 is the constant of proportionality.
Now find the equation for inverse proportionality.
No. of workers (along x-axis) = x
No. of the bagel dough batches (along y-axis) = y
The algebraic equation relating both = x×y=k
The constant of proportionality is k=12.
x×y=12
xy=12
x=12/y
Therefore, the equation of inverse proportionality is x=12/y.
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A school is paving a new rectangular area to create an additional, flat parking lot for teachers. Which units should the principal use to estimate the number of parking spaces created, and why?
The principal should use Square meters because the average length and width of the parking spaces will determine the number of parking spaces created in the rectangular parking lot.
Parallel parking, perpendicular parking, and angle parking are the three most frequently used parking configurations for the majority of motorized vehicles. These are self-park setups, meaning the driver of the car can go to the parking on their own.The length is typically 16 feet to 18 feet for perpendicular or angled parking spaces. The typical breadth is between 7.9 feet and 9 feet. The standard length and breadth for parallel parking spaces are 20 feet and 7.9 feet, respectively.The required number of stalls times the projected land area per stall will give you the paved area needed for parking. For instance, a 200-spot parking lot will need a paved surface of 65,000 square feet, or approximately, with each stall requiring an estimated 325 square feet of space.To know more about rectangular area here
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how could you use a 1/4 cup measuring cup to to measure
the water
Answer:
Step-by-step explanation:
1 you would pour the water in the cup and see what dash it lands on
let's say you pour the water and it lands on the 1/8 mark it would be one 1/8
Hope this help if not sorry
Ben solves this equation
14 + 12x - 6 = 18 - 4x + 4
His work is shown:
Step 1: 8 + 12x = 22 - 4x
Step 2: 8x = 14
Step 3: x = 4
Step 2 is Incorrect.
Enter the correct equation for step 2.
The correct equation of step 2 is 16x = 14
How to determine the correct equation of step 2?from the question, we have the following parameters that can be used in our computation:
14 + 12x - 6 = 18 - 4x + 4
When the like terms on each side are Evaluated, we have
Step 1: 8 + 12x = 22 - 4x
When the like terms on all sides are Evaluated, we have
Step 2: 16x = 14
Hence, the correct equation is 16x = 14
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use pascal’s triangle to expand (z+1)^6
The expansion of (z+1)⁶ = z⁶ + 6z⁵+ 15z⁴ + 20z³+ 15z² + 6z + 1
Pascal's Triangle:A type of number pattern is Pascal's Triangle. The triangle-shaped arrangement of integers known as Pascal's Triangle provides the coefficients for the expansion of any binomial statement.
The arrangement of the numerals creates a triangle when they are reflected. The number 1 is first placed at the top, and then the numbers are arranged in a triangle design.
The expansion of (x + y)ⁿ is is given by
(x + y)ⁿ = a₀xⁿ + a₁xⁿ⁻¹y + a₂xⁿ⁻²y² + … + a[tex]_{n -1}[/tex] xyⁿ⁻¹ + a[tex]_{n}[/tex]yⁿ
Here we have (z+1)⁶
Write out Pascal's triangle starting from 1 and up to 6 rows
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 20 15 6 1
So coefficients of expansion are 1, 6, 15, 20, 15, 6, and 1
(z+1)⁶ = (1)z⁶ + (6)z⁵(1)+ (15)z⁴(1)² + 20z³(1)³ + 15z²(1)⁴ + 6z¹(1)⁵ + (1)z⁰(1)⁶
=> (z+1)⁶ = z⁶ + 6z⁵+ 15z⁴ + 20z³+ 15z² + 6z¹ + 1
Therefore,
The expansion of (z+1)⁶ = z⁶ + 6z⁵+ 15z⁴ + 20z³+ 15z² + 6z + 1
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