Carolyn made an error in her work because she did not correctly distribute the negative in Step 3.
System of EquationsA system of equations is the given term math for two or more equations with the same variables. The solution of these equations represents the point of the intersection.
You can solve a system of equations by the adding or substitution methods. In the addition method, you eliminate a variable, on the other hand, in the substitution method you replace a variable for the other.
The question gives:3x-2y=7 (1)y=x+2The question shows that Carolyn applies the substitution method because she replaces the variable y (equation 2) in equation 1. See the given step 2.
3x – 2y = 7
3x – 2(x + 2) = 7
3x – 2x - 4 = 7 - here it is the mistake. (Carolyn did not correctly distribute the negative).
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How do you split a sentence into two simple sentences?
To split a sentence into two simple sentences, first, highlight the clauses while dividing sentences. When necessary, add subjects or other words in place of subordinating liners to make sub-clauses autonomous.
In the given question we have to explain how we split a sentence into two simple sentences.
As we know that;
A basic sentence typically consists of a subject, a verb, and maybe an object and modifiers. It only has one independent clause, though. Here are a few illustrations: She composed.
First, highlight the clauses while dividing sentences. When necessary, add subjects or other words in place of subordinating liners to make sub-clauses autonomous.
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Which president proposed the creation of the Environmental Protection Agency ?
President Richard Nixon proposed the creation of The Environmental Protection Agency (EPA).
What is the Environmental Protection Agency?
The Environmental Protection Agency is an independent government agency of the United States, which was considered mandatory by the government for environmental issues.
The Agency followed a series of measures to improve air quality, decrease greenhouse gas emissions, forbid water pollution, and invest in oil spill control measures.
The EPA had many obligations in the United States, two of which were to set industry standards to reduce their impact on the environment and investigate air pollution.
How did the EPA launch?
The operation of the agency began on December 2, 1970, after President Nixon had signed an executive order. The order established by the EPA was made official by signing by the committee hearings in the House and Senate.
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Solve for ttt:
-18 = -3t−18=−3t
Answer: 4z
Step-by-step explanation:
the coefficient of x in the expansion of (a x)5 (1-2x)6, where a is positive, is 90. find the value of a.
In the given expansion ,the value of a = -4/3 .
Binomial Distribution:
The binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a series of n independent experiments. Each asks a yes-no question and each has its own Boolean outcome: success (probability p) or failure (probability p) (probability q = 1-p. A single success/failure experiment is also called a Bernoulli trial or Bernoulli experiment, and a series of results is called a Bernoulli process. For one trial, n = 1, binomial distribution is Bernoulli distribution. The binomial distribution is the basis for the common binomial test of statistical significance.
In general, (A + B)⁵ = A⁵ + 5A⁴ᵇ + 10A²ᵇ*³ + 10A³ᵇ*² + 5AB⁴ + B⁵
So,
(3–2x)⁵= 3⁵ + 5*3⁴*(-2x) + 10* 3^3 *(-2x)^2 + 10*3^2*(-2x)^3 + 5*3*(-2x)^4 + (-2x)^5.
Multiplying that by (1 + ax) gives:
3^5 + 5*3^4*(-2x) + 10* 3^3 *(-2x)^2 + 10*3^2*(-2x)^3 + 5*3*(-2x)^4 + (-2x)^5 + ax(3^5 + 5*3^4*(-2x) + 10* 3^3 *(-2x)^2 + 10*3^2*(-2x)^3 + 5*3*(-2x)^4 + (-2x)^5).
In bold, we find the terms of x^2, so the coefficient of x^2 is 10*3^3*(-2)^2+a*5*3^4*(-2) = 360 - 810a
We know that this must equal 1440, so 360–810a = 1440.
Therefore a= -4/3.
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How do you solve an equation with 2 answers?
The quadratic formula x = [-b (b2 - 4ac)] / 2a] provides the solutions to the quadratic equation ax2 + bx + c = 0. (2a).
Given,
Equation with two answers are quadratic equations.
Quadratic equation;
The polynomial equations of degree two in one variable of type f(x) = ax2 + bx + c = 0 and with a, b, c, and R R and a 0 are known as quadratic equations. It is a quadratic equation in its general form, where "a" stands for the leading coefficient and "c" for the absolute term of f. (x).
The solution for quadratic equation;
The quadratic formula x = [-b (b2 - 4ac)] / 2a]gives the solutions to the quadratic equation ax2 + bx + c = 0. (2a). Get the problem into standard form, ax2 + bx + c = 0, and then use the quadratic formula to solve the quadratic equation.
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a certain star is 3.6 x 10^2 light years from the earth. one light year is about 5.9 x 10^12 miles how far from the earth in miles is the star
The earth is 21.24 x 10¹⁴ miles far from the star.
What are the light years?
A light-year is a significant length measure that is used to express astronomical distances. It is around 9.46 trillion kilometers, or 5.88 trillion miles, in length.
We have given,
1 light year = 5.9 x 10¹² miles
Distance of the star = 3.6 x 10² light years
To get this we just convert the distance of the star in light years into miles.
3.6 x 10² light years x( 5.9 x 10¹² miles/1 light years)
We cancel out the lightyears and then we are left with:
3.6 x 10² light years x 5.9 x 10¹² miles
In dealing with scientific notation, when we multiply them we can treat the coefficients and exponents of 10 separately.
Coefficients:
3.6 x 5.9 = 21.24
Exponents of 10:
10² x 10¹² = 10⁽²⁺¹²⁾ = 10¹⁴
Then we combine them again to form:
21.24 x 10¹⁴ miles
Hence, the earth is 21.24 x 10¹⁴ miles far from the star.
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Why is area in square units?
The number of unit squares needed to completely cover a shape is its area. As a result, it is expressed and measured in square units.
The word "area" refers to a free space. The area of a thing is the amount of space it occupies in two dimensions. A closed figure's surface area is calculated by counting how many unit squares completely encircle the surface. The square unit is frequently expressed as square inches, square feet, etc., and is the accepted unit of area.
Consider, there are several squares with sides that are 1 unit by 1 unit wide in the grid. The surface area of each square is one square unit. Each square is a unit square. As a result, the area is stated and measured in square units.
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to calculate the expected risk premium on a stock, one must subtract the ________ from the stock’s expected return.
To calculate the expected risk premium on a stock, one must subtract the Inflation rate from the stock’s expected return.
How to complete the blank in the statement?From the question, we have the following parameters that can be used in our computation:
Expected risk premiumStock's expected returnMathematically, the relationship between the expected risk premium and the stock's expected return is represented as follows
Expected risk premium = Stock's expected return - Inflation rate
This means that the Inflation rate must be subtracted from the stock’s expected return to calculate the expected risk premium
Hence, the statement that completes the blank is Inflation rate.
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How do you dilate an image with a scale factor?
To dilate an image with a scale factor, multiply the scale factor with the dimensions of the image
The dilation is the process of changing the size of the given shape or figure ,the shape of the figure will be always same. Therefore dilation is one form transformation of shapes
The scale factor is the ratio of the measurement of the new shape to the measurement of the original shape.
We can use the scale factor for the dilation
To get the dilate and image with scale factor, we have to multiply the scale factor with the measurement of the original shape
The equation will be
The dimension after dilation = scale factor × original dimensions
Therefore, to dilate an image, multiply the scale factor and the original dimensions
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Which graph represents y=^3square root x
You plug your phone in to charge. After 10 mins your phone is at 30%. If your phone is charging at a rate of 5% every 2 minutes, write an equation in point slope form representing the battery percent,y, after x minutes.
y-5=3(x-2) is the equation in point slope form representing the battery percent, y, after x minutes.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
After 10 mins your phone is at 30%.
If your phone is charging at a rate of 5% every 2 minutes,
4 minutes=10%
6 minutes=15%
8 minutes=20%
10 minutes=25 %
The equation of point slope form.
y-5=3(x-2)
Hence, y-5=3(x-2) is the equation in point slope form representing the battery percent, y, after x minutes.
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PLEASE HELP MEEEEEEE, GIVING 30 POINTS IF YOU SOLVE (MY THRID TIME REPOSTING THIS)
A rental car company charges $40.50 per day to rent a car and $0.15 for every mile driven. Elizabeth wants to rent a car, knowing that:
She plans to drive 125 miles.
She has at most $210 to spend.
Write and solve an inequality which can be used to determine x, the number of days Elizabeth can afford to rent while staying within her budget.
Answer: 4 days, more below
Step-by-step explanation:
40.50x + 0.15y < 210
(0.15)(125)=18.75
40.50x + 18.75 < 210
40.50x < 191.25
x < 4.7222222...
She can afford to rent the car for 4 days if she drives 125 miles and has 210$ to spend.
Pedro has a balance of $5810 on a credit card with an APR of 16.2%. Paying
off his balance in which of these lengths of time will result in him paying the
least amount of interest?
O 1 Month
2 Months
3 Months
4 Months
The least amount of interest, if Pedro has a balance of $5810 on a credit card with an APR of 16.2%, is $78.345 for one month, so option A is correct.
What is interest?When the loan is given to you, then some amount is charged to you for the principal amount and that is called interest.
Given:
Pedro has a balance of $5810 on a credit card with an APR of 16.2%,
Calculate the simple interest for one month as shown below,
[tex]SI = P \times r \times t / 100[/tex]
SI = 5810 × 16. 2 × 1 / (12 ×100) [time in year = 1 / 12]
SI = $78.345
SI = 5810 × 16. 2 × 2 / (12 ×100) [For 2 months]
SI = $156.87
Therefore, the least amount of interest, if Pedro has a balance of $5810 on a credit card with an APR of 16.2%, is $78.345 for one month.
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c(1) = -20
c(n) = c(n − 1) + 10
Find the 2nd term in the sequence.
Answer:
-10
Step-by-step explanation:
So we are going to find c(2)
c(2)=c(1)+10
c(2)=-20+10
c(2)=-10
a school show had ticket sales of $1345 the first night and $935 the second night. 180 student tickets were sold and 110 adult tickets were sold on the first night. 100 student tickets were sold and 90 adult tickets were sold. find the price of a student ticket.: * a) $5.75 b) $8.75 c) $6.50 d) $3.50 e) $7.50
A school show had sold the ticket sales of first and second nights. The price of a student ticket is $3.54, a So, the correct answer is option (d).
Total sale on tickets at the first night = $1345
Total sale on tickets at the second night = $935
Let the price of student ticket and adult ticket in school show be "$x" and "$y" respectively. According to problem,
On first night total sale,
180x + 110y = $1345 --(1)
On Second night total sale,
100x + 90y = $935 --(2)
we have to determine the price of student ticket i.e x and price of adult ticket i.e y .. We have a system of linear equation which consists two equations (1) and (2) . Now, we solve these equations using Substitution method,
From equation (2), 100x = 935 - 90y
=> x = (935 - 90y )/100 --(*)
Substitute the value of x in equation (1) 180x + 110y = $1345
=> 180(935 - 90y )/100 + 110y = 1345
Simplify ..
=> 168120 - 16200y + 11000y = 134500
=> 168120 - 134500 = 16200y - 11000y
=> 33620 = 5200y
=> y = 33620/5200
=> y = 6.46
put the value of y in equation (*) we get,
x = (935 - 90× 6.46)/100 = 3.536
Hence, the value of x is $3.536 and value of y is $6.46..
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I need help with question number 10 the question says Ash has 61 toothpicks but do I keep increasing by 1 until I get 61?
The largest figure that Ash can built with 61 toothpicks is of:
A composition of 12 hexagons.
How to obtain the largest figure?The number of toothpicks needed is modeled with a linear function, defined as follows:
y = mx + b.
The coefficients of the function are given as follows:
m is the slope, representing the number of toothpicks per new figure.b is the y-intercept, representing the number of toothpicks of the first figure.The number of toothpicks in each figure is represented by the following sequence:
(6, 11, 16, ...).
Hence the parameters are given as follows:
m = 5, b = 6.
Thus the definition of the function is of:
T(n) = 5(n - 1) + 6. (as the first figure is with n = 1).
T(n) = 5n + 1.
Then the number of hexagons with 61 toothpicks is obtained as follows:
5n + 1 = 61
5n = 60
n = 60/5
n = 12 hexagons.
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Help needed was not thought this
Answer:
Yes what is the question
Answer:
what is the question
Step-by-step explanation:
I need help pleaseee
Answer: 1/10th
Step-by-step explanation:
20 different lengths, 2 are 21.5 = 2/20 reduce to 1/10 so 10%
Write an equation in slope-intercept form of the line.
(Use integers or fractions for any numbers in the equation.)
Answer:
[tex]y=-\frac{1}{2} x+5[/tex]
What is the measure of one of the central angles in the regular Pentagon What is the measure of one of the congruent base angles in triangle ABC?
The measure of one of the central angles of a regular pentagon is 72° .
In the question ,
a regular pentagon is given ,
we have to find the measure of one of central angle ,
we know that a pentagon has 5 equal sides .
and the sum of the central angles is 360° .
it is given that the pentagon is regular , So , all the central angles are equal in measure .
The central angle can be calculated using the formula ,
central angle = 360°/n , where n is number of sides .
substituting the value of number of sides as = 5 ,
we get ,
central angle = 360°/5 = 72° .
Therefore , the central angle is = 72° .
The given question is incomplete , the complete question is
What is the measure of one of the central angles in the regular Pentagon ?
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9(-2)
Help I don't get it :'(
So, let's think about what it's asking
it next to the parentheses means to distribute, or multiply into.
Multiply 9 * -2
A negative times a positive is a negative.
9 * 2 = 9 + 9 = 18
Make the final answer negative because its a positive and a negative multiplied. A positive and a positive multiplied gives you a positive. A negative and a negative multiplied gives you a positive too.
-18
1) x-2y=15
2) x-3=4y
A) rearrange equation (2) to make x the ubject
B) uing your anwer to part a) olve the imultaneou equation uing ubtitution
x= -9 and y= -3
What is equation?
A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation. as in 3x + 5 Equals 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others. In this tutorial, let's study more about math equations.
A) rearranging equation (2) to make x the subject
[tex]x-3=4y\\x-4y=3[/tex]
Also,
[tex]4y=x-3\\y=(x-3)/4[/tex]
by subtitution method
putting this value of y in equation 1)
[tex]x-2((x-3)/4)=15\\\\x-2x+6=15\\x=-9\\y=(-9-3)/4\\y=-3[/tex]
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Which function is used to calculate maximum value?
Derivatives is used to calculate the maximum value of a function.
We will set the first derivative of the function to zero and solve for x to get the critical point. If we take the second derivative or f''(x), then we can find out whether this point will be a maximum or minimum. If the second derivative is positive, it will be a minimum value.
Derivatives
The rate of change of a function with respect to a variable. Derivatives are fundamental to the solution of problems in calculus and differential equations.
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Consider the following table. Is the relationship proportional? Explain your answer.
y
-27
12
57
147
-2
1
4
10
Answer:
The relationship shown in the table is not proportional. A proportional relationship is one in which the ratio of two quantities is always constant. In the table, we can see that the ratio of the values in the y column to the corresponding values in the x column is not constant. For example, the first two values in the y column are -27 and 12, which have a ratio of -27/1 and 12/2, respectively. These ratios are not equal, which indicates that the relationship is not proportional.
Furthermore, if the relationship were proportional, we would expect the values in the y column to increase at a consistent rate as the values in the x column increase. However, this is not the case in the table. For example, the first two values in the x column are 1 and 2, and the corresponding values in the y column are -27 and 12. The difference between these values is -27 - 12 = -39, which is a large negative value. However, the difference between the next two values in the y column is 57 - 147 = -90, which is a much larger negative value. This indicates that the relationship is not proportional, because the differences between the y values do not increase at a consistent rate as the x values increase.
Step-by-step explanation:
There are about 2.54 centimeters in 1 inch. if a segment is 2.7 centimeters long, how many inches is it, rounded to the nearest hundredth?
The number of inches made by a segment of 2.7 centimeters long, where 1 inch is 2.54 centimeters is 236 inches.
What is the symbol for an inch?Please also notice that the sign for inches is the double prime ("), not the double quotation mark, the straight quotation mark, or even (gasp!) the two consecutive single quotation marks (").
What exactly is 1 inch?The inch was defined as "three dry, spherical grains of barley set end to end lengthwise" during the early 14th century under King Edward II. The lengths of 12 poppy seeds together have also been used at various periods to define one inch. Since 1959, 2.54 cm has been the official definition of an inch.
From the above definition, we get that
The number of inches made by a segment of 2.7 centimeters long, where 1 inch is 2.54 centimeters is 236 inches.
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H(t)= 50- t/5
H(35)=
Please explain it
The value of the function H(t) = 50 - t / 5 at t = 35 will be 43.
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
The function is given below.
H(t) = 50 - t / 5
At t = 35, the value of the function will be given as,
H(35) = 50 - 35 / 5
H(35) = 50 - 7
H(35) = 43
The value of the function H(t) = 50 - t / 5 at t = 35 will be 43.
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What is the slope of the line that passes through the points (2, -4) and (5, 2)? Write
your answer in simplest form.
Answer:
used formula
Step-by-step explanation:
y-y1=m(x-x1)
30.9 divided by 100
PLEASE I NEED HELP ASAP
Answer:
0.309
Step-by-step explanation:
Help with question 3
Answer:
3.75
Step-by-step explanation:
I BELIVE YOUR ANSWER IS 3.75
Answer:
3.75
Step-by-step explanation:
Which equation repreent the line that pae through the point (2, -8) and (-3, 2)?
The Equation represent the line that passes through the points (2, -8) and (-3, 2) is 2x + y + 4 = 0
Two point form is one of the important forms used to represent a straight line algebraically. The equation of a line represents each and every point on the line, i.e., it is satisfied by each point on the line.
The two point formula is used to represent a line algebraically using the coordinates of two points that lie on that line. The formula for two point form can be given as:
(y - y1) = m(x-x1) -----------(1)
where , m is slope of line given by => y2-y1/ x2 - x1
(x, y) is an arbitrary point on the line.
(x1, y1) and (x2 , y2) are coordinates of points lying on the line.
According to the question,
The required line passes through (2,-8) and (-3,2)
Slope : m = 2 - (-8) / -3 -2
=> m = 2+8/-5
=> m = 10/-5
=> m = -2
Substituting the values in equation (1)
(y - (-8)) = -2(x-2)
Solving,
=> y + 8 = -2x + 4
=> 2x + y + 4 = 0 is required equation of line
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