From this statement, we concluded that ΔJKL is congruent to ΔMNP.
What is a congruent?
When all three corresponding sides and all three corresponding angles are the same sizes, two triangles are said to be congruent.
Here,
ΔJKL go right one, then go to left and then rotate to 180° on JK.
Now rotate 90° counterclockwise with the center of J.
Hence, we concluded that ΔJKL is congruent to ΔMNP because it's all sides are the same.
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which of the following are a problem with a parallel conversion: (select all that apply) :a) there is a higher riskb) the old hardware might failc) there is a lower riskd) the users have to enter data into both systemse) there is an abrupt conversion
A parallel conversion is a method of implementing a new system in which the old and new systems run simultaneously for a period of time. While this approach can have its benefits, there are also potential problems that may arise.
One of the problems with a parallel conversion is that there is a higher risk, as there are two systems running at the same time, which can be costly and require additional resources. Another problem is that the old hardware might fail, which can cause data loss or delays in the conversion process. On the other hand, a lower risk may not be applicable in a parallel conversion because the risk factor is already high. Also, the users have to enter data into both systems, which can be time-consuming and prone to errors. Finally, an abrupt conversion is not applicable in a parallel conversion because both systems are running together. Overall, the parallel conversion method requires careful planning and execution to minimize the potential problems and ensure a smooth transition.
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a hall 100 feet in length is to be designed as a whispering gallery. If the foci are located 25 feet from the center, how high will the ceiling be at the center?
Answer:
how high will the ceiling be at the center? ≈43.3 ft above the center
Step-by-step explanation:
standard form of equation for an ellipse with horizontal major axis and center at the origin:
x^2/a^2+y^2/b^2=1, a>b
for given problem:
a=50
a^2=2500
c=25
c^2=625
c^2=a^2-b^2
b^2=a^2-c^2=2500-625=1875
b=√1875≈43.3 ft
≈43.3 ft above the center
Height of celling from center is 43.3 feet (Approx.)
Given that;
Length of hall = 100 feet
Foci length from center = 25 feet
Find:
Height of celling from center
Computation:
Half length of hall = 100 / 2 = 50 feet
Height of celling from center = √Half Length of hall² - Foci length from center²
Height of celling from center = √50² - 25²
Height of celling from center = √2500 - 625
Height of celling from center = √1875
Height of celling from center = 43.3 feet (Approx.)
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i neeeeeeeeeeeeeeeeeeed help
Fill in the missing number.
70% of blank equals 14
Answer:
20
Step-by-step explanation:
14/0.7
Answer:
Step-by-step explanation:
Your question: 70 percent of what number equals 14?
Step 1: Multiply both sides by 100 to get 7,000 and 1,400.
Step 2: Divide both sides by 70 to get 100 and 20.
Step 3: Put it into fraction form. \(\frac{20}{100}\).
Step 4: Since in percentages, you typically only go up to 100, we can remove the 100 to leave us with just 20.
Step 5: We have our answer. 70% of 20 is 14.
Hope this helps! :D
two linear functions are combined with addition, and then the same two linear functions are combined by multiplication.which functions could be the result of the combinations? select two options.16x – 1217x – 1272x2 – 96x72x2
The two options that could result from combining two linear functions with addition are "16x – 12" and "17x – 12". The r to your question is:
To combine two linear functions with addition, you simply add the coefficients of the same variables. For example, if you have the functions 3x + 4 and 2x - 5, when you combine them with addition, you add the coefficients of x and the constant terms. So, 3x + 4 + 2x - 5 becomes (3 + 2)x + (4 - 5) = 5x - 1.
To combine two linear functions with multiplication, you multiply the coefficients of the same variables. For example, if you have the functions 3x + 4 and 2x - 5, when you combine them with multiplication, you multiply the coefficients of x and the constant terms. So, (3x + 4)(2x - 5) becomes
(3 * 2)x^2 + (3 * -5)x + (4 * 2x) + (4 * -5)
= 6x^2 - 15x + 8x - 20
= 6x^2 - 7x - 20.
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Use the distance formula to find the distance, to the nearest tenth, from S(6, −2) to V(−4, 3). −5.0 units 3.1 units 11.2 units 8.7 units
\(~~~~~~~~~~~~\textit{distance between 2 points} \\\\ S(\stackrel{x_1}{6}~,~\stackrel{y_1}{-2})\qquad V(\stackrel{x_2}{-4}~,~\stackrel{y_2}{3})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ SV=\sqrt{[-4 - 6]^2 + [3 - (-2)]^2}\implies SV=\sqrt{(-10)^2+(3+2)^2} \\\\\\ SV=\sqrt{125}\implies SV\approx 11.18\implies \underset{\textit{rounded up}}{SV\approx 11.2}\)
Answer:
11.2 units is the answer
La fórmula correcta para encontrar el valor del coseno de un ángulo agudo en un triángulo rectángulo dado es:
Answer:
El coseno del ángulo esta dado por:
\(cos(\theta)=\frac{CA}{H}\)
Step-by-step explanation:
Si tenemos un triángulo recatángulo, el coseno del ángulo está dado por:
\(cos(\theta)=\frac{CA}{H}\)
Donde:
CA es el cateto adyacenteH es la hipotenusa del triánguloEspero te haya sido de ayuda!
I need help with 1,2,3 please
Answer:
1. Negative
2. Undefined
3. Zero
Step-by-step explanation:
a paper company needs to ship paper to a large printing business. the paper will be shipped in small boxes and large boxes. the volume of each small box is 7 cubic feet and the volume of each large box is 14 cubic feet. a total of 21 boxes of paper were shipped with a combined volume of 252 cubic feet. write a system of equations that could be used to determine the number of small boxes shipped and the number of large boxes shipped. define the variables that you use to write the system.
The required system of equations is x+y = 21 and 7x +14y = 252.
Systems of equations are sets of equations where the solution is the intersecting point(s) between the equations.There are three methods typically used to solve systems of linear equations: graphing, the substitution method, and the elimination method. These methods can be applied to more complex systems of nonlinear equations as well.
Let the number of small boxes be x.
Let the number of large boxes be y.
The volume of each small box is 7 cubic feet.
The volume of each large box is 14 cubic feet.
The total number of boxes is 21.
Total volume of all boxes is 252 cubic feet.
So, x+y = 21.
This is the first equation.
Also, the total volume is equal to the sum of the volumes of all individual boxes.
So, 7x + 14y = 252
Thus, the required system of equations is x+y = 21 and 7x +14y = 252.
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The required system of equations is x + y = 21 and 7x + 14y = 252 using the concept of equations.
What are system of equations?A system of equations in algebra is made up of two or more equations that are solved together to obtain the solution for a two or more variable problem.
Volume of each small box is 7 cubic feet and volume of each large box is 14 cubic feet. Take the number of small boxes to be x and number of large boxes to be y.
Given total number of boxes shipped is 21. Therefore using the concept of equation,
x + y = 21 --- (1)
Total volume of small box is given by:
Total volume of small box = (Volume of a small box) * (Number of small box)
Total volume of small box = 7x
Similarly the total volume of large box is,
Total volume of small box = 14y
Given the total volume of carried box is 252 cubic feet. Using the concept of equations,
7x + 14y = 252 ---(2)
The equations (1) and (2) gives the required system of equations.
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Kari estimated the quotient of Negative 12 and one-fifth divided by 4 and two-fifths to be –8. Which best describes her error? Kari multiplied the compatible numbers –12 and 4. Kari found that the quotient of a negative number and a positive number is negative. Kari found that the quotient of a positive number and a negative number is positive. Kari added the compatible numbers –12 and 4.
Answer:
D. Kari added the compatible numbers –12 and 4.
Step-by-step explanation:
Our numbers are \(-12\frac{1}{5}\) and \(4\frac{2}{5}\). We want to find Kari's error. Let's look through the answer choices and try them out:
A: "Kari multiplied the compatible numbers –12 and 4"
Well, if we multiply -12 by 4, we get -48, which is very different from -8, so A cannot be right.
B: "Kari found that the quotient of a negative number and a positive number is negative"
This is actually a true statement because whenever we multiply or divide a positive number and a negative number, the result is always negative. So, this isn't an error. B is wrong.
C: "Kari found that the quotient of a positive number and a negative number is positive"
If B is a true statement, C must be false - and that's right: it is false because the quotient of a positive number and a negative number is always negative not positive. Eliminate C.
D: "Kari added the compatible numbers –12 and 4"
What do we get if we add -12 and 4? We get: -12 + 4 = -8, which is exactly the number that Kari got. So instead of dividing, Kari accidentally added and got -8, which is the wrong answer. Thus, D is correct.
Answer:
Last one
Kari added the compatible numbers –12 and 4.
Step-by-step explanation:
-12⅕ ÷ 4⅖
-61/5 ÷ 22/5
-61/5 × 5/22
-61/22
She probably got -8 by adding -12 and 4
What is the ratio of classmates who like ham sandwiches to the number of classmates who like bologna and turkey sandwiches?
Assume that a randomly selected subject is given a bone density test. Bone density test scores are normally distributed with a mean of 0 and a standard deviation of 1. Draw a graph and find Upper P9, the 9th percentile. This is the bone density score separating the bottom 9% from the top 91%.
The bone density score corresponding to the 9th percentile, separating the bottom 9% from the top 91%, is approximately -1.34.
To find this value, we can refer to the standard normal distribution table or use a statistical calculator. The standard normal distribution has a mean of 0 and a standard deviation of 1. The area to the left of any given z-score represents the cumulative probability up to that point.
In this case, since we want to find the 9th percentile, we are interested in the value that separates the bottom 9% (cumulative probability) from the top 91%. This means that we need to find the z-score that corresponds to an area of 0.09 under the curve.
By referencing the standard normal distribution table or using a calculator, we find that the z-score corresponding to a cumulative probability of 0.09 is approximately -1.34. This z-score represents the bone density score at the 9th percentile, separating the bottom 9% from the top 91%.
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Neglecting the curvature of the corners, what is the distance traveled and the displacement in running from point a to point b?.
To summarize: If points a and b are in a straight line, the distance traveled and the displacement will be the same. If points a and b are not in a straight line, the distance traveled will be greater than the displacement.
The distance traveled refers to the total length covered during the journey, regardless of the direction taken. On the other hand, displacement refers to the change in position from the starting point to the ending point, taking into account the direction of travel.
Neglecting the curvature of the corners implies that the path taken is a straight line. In this case, the distance traveled and the displacement will be the same if the points a and b are in a straight line.
If points a and b are not in a straight line, then the distance traveled will be greater than the displacement. This is because the distance traveled considers the entire path covered, while displacement only considers the change in position.
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Geometry Please hurry
How do you see it? The diagram shows part of the Wheel of Theodorus.
Answer:
it is given that diagram shows part of the Wheel of Theodorus. graphics for exercise 20 page 428 geometry part (a). It is required to identify which ...
Step-by-step explanation:
Pls help due today thank you <3<3
Answer:
a) variable; x>8 and x<14 basically a number between 8-14, look at your choices and pick a number in this range.
b) since you provided the choices, the answer in 18 because the trend of the line is decreasing. The number had to be from 15 to 20 and the only mumber that fit this requirement is 18.
if the coefficient associated with an independent variable column is k, then how will you compute the angle of the associated regression line (model) in degrees?
The formula for calculating the angle of the related regression line in degrees is:
angle = (180/π) * arctan(k)
The angle of the related regression line (model) in degrees can be calculated using the coefficient involving a column of the independent variable (k) and the arctangent function.
Arctang of the coefficient (k) gives the angle in radians between the horizontal axis and the regression line. To convert this angle to degrees, we can multiply the angle in radians by 180/π.
Therefore, the formula for calculating the angle of the related regression line in degrees is:
angle = (180/π) * arctan(k)
where arctan(k) is the arc tangent of the coefficient associated with a column of the independent variable.
This formula gives the angle of the regression line to the horizontal axis.
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A paper company needs to ship paper to a large printing business. The paper will be shipped in small boxes and large boxes. The volume of each small box is 6 cubic feet and the volume of each large box is 12 cubic feet. There were twice as many small boxes shipped as large boxes shipped and the total volume of all boxes was 168 cubic feet. Write a system of equations that could be used to determine the number of small boxes shipped and the number of large boxes shipped. Define the variables that you use to write the system.
Answer:
A paper company needs to ship paper to a large printing business. The paper will be shipped in small boxes and large boxes. The volume of each small box is 6 cubic feet and the volume of each large box is 12 cubic feet. There were twice as many small boxes shipped as large boxes shipped and the total volume of all boxes was 168 cubic feet. Write a system of equations that could be used to determine the number of small boxes shipped and the number of large boxes shipped. Define the variables that you use to write the system.
\underline{\text{Define Variables:}}
Define Variables:
May choose any letters.
\text{Let }s=
Let s=
\,\,\text{the number of small boxes shipped}
the number of small boxes shipped
\text{Let }l=
Let l=
\,\,\text{the number of large boxes shipped}
the number of large boxes shipped
Each small box has a volume of 6 cubic feet, so the volume of ss small boxes would be 6s6s cubic feet. Each large box has a volume of 12 cubic feet, so the volume of ll large boxes would be 12l12l cubic feet. Therefore, the total volume 6s+12l6s+12l equals 168:168:
6s+12l=168
6s+12l=168
Since there were twice as many small boxes shipped as large boxes, there were more small boxes, so if we multiply 2 by the number of large boxes, we will get the number of small boxes, meaning ss equals 2l.2l.
let s = number of small boxes shipped
let l= number of large boxes shipped
6s+121 = 168
s=21
The number of small boxes shipped are 14 and the number of large boxes shipped are 7.
What is a linear system of equations?A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.
Given that, the volume of each small box is 6 cubic feet and the volume of each large box is 12 cubic feet.
Let the number of small boxes be x and the number of large boxes be y.
There were twice as many small boxes shipped as large boxes
So, x=2y ------(I)
The total volume of all boxes was 168 cubic feet.
6x+12y=168 ------(II)
Substitute equation (I) in equation (II), we get
6(2y)+12y=168
12y+12y=168
24y=168
y=7
Substitute y=7 in equation (I), we get
x=14
Therefore, the number of small boxes shipped are 14 and the number of large boxes shipped are 7.
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Which situation cannot be represented by the equation 8−x=3?
Responses
ASAP PLEASE
Responses
Sunnyville had 3 fewer inches of rain than Pleasantville. Pleasantville had 8 inches of rain. What is x, the amount of rain in Sunnyville?
Jackson walked 8 dogs. Henry walked 3. What is x, the number of dogs the boys walked all together?
Joe had $8 and bought a piece of pizza. He had $3 left over. What is x, the cost of the pizza?
The difference between Amal's score and Katie's score was 3. Amal had 8 points, but Katie had fewer. What is x, the amount of Katie's score?
What is the distance between (-9, -6) and (-2,-2)?
Answer:
To find this we use the distance formula.
Square root of (-2 + 9)^2 + (-2 + 6)^2
square root of 49 + 16
square root of 65
8.0622577483
Step-by-step explanation:
Help please!! Due in 30 minutes
Answer:
Yes you got it right 4x-3y>-12
Step-by-step explanation:
Construct the encryption matrix (as defined in Example Onc-time Pad with n = 3 Example 3.3 Lel P = {a,b} with Prla] = 1/4,Prlb] = 3/ with Pr[Ki] = 1/2, Pr(Kz] Pr[Ks] = 1/4.Let € = {1,2 encryption functions are defined to be eki (a) = 1,eK (6) 3; and eK (a) = 3, CK, (6) = 4 This cryptosystem can be reF ing encryption matrix: Ki 2 Kz 2 3 K3 3
| | K1 | K2 | K3 | |----|----|----|----| | a | 1 | 3 | 3 | | b | 3 | 4 | 4 | This matrix represents the encryption process of the cryptosystem, where each element in the matrix corresponds to the result of applying the encryption function with a specific key to a specific plaintext character.
The encryption matrix for this cryptosystem can be constructed using the following steps. First, we list the keys used in the system, which are Ki, Kz, and Ks. Then, we list the possible plaintexts, which in this case are a and b. Next, we apply the encryption functions to each key and plaintext combination to obtain the corresponding ciphertexts. Specifically, eKi(a) = 1, eKi(b) = 3, eKz(a) = 3, eKz(b) = 4, eKs(a) = 2, and eKs(b) = 4. Finally, we arrange the ciphertexts in a matrix format, with the rows representing the keys and the columns representing the plaintexts. The resulting encryption matrix is:
| | a | b |
|---|---|---|
| Ki | 1 | 3 |
| Kz | 3 | 4 |
| Ks | 2 | 4 |
This matrix can be used to encrypt a message by selecting a key and then using the corresponding row to encode the plaintext message. For example, if we want to encrypt the message "aba" using the key Kz, we would use the second row of the matrix to obtain the ciphertexts "3 3 4".
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For each of the functions given below, use Newton's method to approximate all real roots. Use an absolute tolerance of 10^−6
as a stopping condition. (a) f(x)=e^x+x^2−x−4 (b) f(x)=x^3−x^2−10x+7 (c) f(x)=1.05−1.04x+lnx
(a) The approximated root of f(x) = e^x + x^2 - x - 4 is x ≈ 2.151586.
(b) The approximated root of f(x) = x^3 - x^2 - 10x + 7 is x ≈ -0.662460.
(c) The approximated root of f(x) = 1.05 - 1.04x + ln(x) is x ≈ -1.240567.
(a) Purpose: f(x) = ex + x2 - x - 4 To apply Newton's method, we must determine the function's derivative as follows: f'(x) = e^x + 2x - 1.
Now, we can use the formula to iterate: Choose an initial guess, x(0) = 0, and carry out the iterations as follows: x(n+1) = x(n) - f(x(n))/f'(x(n)).
1. Iteration:
Iteration 2: x(1) = 0 - (e0 + 02 - 0 - 4) / (e0 + 2*0 - 1) = -4 / (-1) = 4.
2.229280 Iteration 3: x(2) = 4 - (e4 + 42 - 4 - 4) / (e4 + 2*4 - 1)
x(3) 2.151613 The Fourth Iteration:
x(4) 2.151586 The Fifth Iteration:
x(5) 2.151586 The equation f(x) = ex + x2 - x - 4 has an approximate root of x 2.151586.
(b) Capability: f(x) = x3 - x2 - 10x + 7 The function's derivative is as follows: f'(x) = 3x^2 - 2x - 10.
Let's apply Newton's method with an initial guess of x(0) = 0:
1. Iteration:
x(1) = 0 - (0,3 - 0,2 - 100 + 7), or 7 / (-10) -0.7 in Iteration 2.
x(2) -0.662500 The Third Iteration:
x(3) -0.662460 The fourth iteration:
The approximate root of the equation f(x) = x3 - x2 - 10x + 7 is x -0.662460, which is x(4) -0.662460.
c) Purpose: f(x) = 1.05 - 1.04x + ln(x) The function's derivative is as follows: f'(x) = -1.04 + 1/x.
Let's use Newton's method to make an initial guess, x(0) = 1, and choose:
z
1. Iteration:
x(1) = 1 - (1.05 - 1.04*1 + ln(1))/(- 1.04 + 1/1)
= 0.05/(- 0.04)
≈ -1.25
Cycle 2:
x(2) less than -1.240560 Iteration 3:
x(3) less than -1.240567 Iteration 4:
x(4) -1.240567 The equation f(x) = 1.05 - 1.04x + ln(x) has an approximate root of x -1.240567.
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It takes an older computer 4 times as long to send out a company’s email as it does a newer computer. Working together, it takes the two computers 12 minutes to send out the email. How long will it take the older computer to send out the email on its own? Do NOT do any rounding.
We will have the following:
\(\begin{gathered} \frac{1}{x}+\frac{1}{4x}=\frac{1}{12}\Rightarrow\frac{4}{4x}+\frac{1}{4x}=\frac{1}{12} \\ \\ \Rightarrow\frac{5}{4x}=\frac{1}{12}\Rightarrow4x=60 \\ \\ \Rightarrow x=15 \end{gathered}\)So, it takes 15 minutes for the new computer; then the old computer will take 60 min.
What is the algebraic expression for "the sum of a number and 4"?
A. 4-z
B. 4/z
C. z+4
Answer:
C. z + 4
Hope this helps :)
Step-by-step explanation:
When it says "sum," it means the answer to 2 number that you add. The first number will be unknow which z will stand for, and the second number is 4 since it was stated in the statement, "the sum of a number and 4."
A meteorologist recorded farenheit temperatures in four cities around the world. list these cities in order from coldest to warmest temperature
5 degrees
-6 degrees
-7 degrees
-9 degrees
12 degrees
The list of the temperature from coldest to warmest temperature includes:
-9 degrees-7 degrees-6 degrees5 degrees12 degreesWhat is the order of temperatures in Fahrenheit of the four cities?The temperatures (Fahrenheit) of the 4 cities from coldest to warmest includes -9 degrees, -7 degrees, -6 degrees, 5 degrees and 12 degrees.
The coldest temperature is -9 degrees, followed by -7 degrees, then -6 degrees. The positive temperature is 5 degrees and 12 degrees.
We must note these temperatures are in Fahrenheit which is not the standard unit of measurement used in all countries, so, we must specify the unit when reporting temperatures.
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7 divided by 8. What is the divisor?
Answer:
8 is your divisor and 7 is your dividend
Step-by-step explanation:
7 = dividend
8 = divisor
a certain population has a yearly per capita growth rate of 2.2%, and the initial value is 2 million. (a) use a formula to express the population as an exponential function. (let n be the population in millions and t be the time in years.) n(t)
The population as an exponential function of time t is given by \(n(t) = 2,000,000 * e^(0.022t)\) when the initial value is 2 million.
The population has a yearly per capita growth rate of 2.2% and the initial value is 2 million, we can express the population as an exponential function using the formula:
\(n(t) = a * e^(rt)\)
In this formula, n(t) represents the population as a function of time t, a is the initial value, e is Euler's number (approximately 2.71828), and r is the annual growth rate expressed as a decimal.
The exponential function for the population with an initial value of 2 million and an annual growth rate of 2.2%, we substitute the given values into the formula:
\(n(t) = 2 * e^(0.022t)\)
To simplify the equation, we can multiply both sides by 1,000,000:
\(n(t) = 2,000,000 * e^(0.022t)\)
Therefore, the population as an exponential function of time t is given by \(n(t) = 2,000,000 * e^(0.022t)\) when the initial value is 2 million.
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Show whether x and y are in a proportional relationship.
Here since the ratios are not all equal, we can conclude that x and y are not in a proportional relationship.
What is meant by ratios?
Ratios are a mathematical tool used to compare the sizes of two or more quantities, expressed as a ratio of their values. Ratios can be simplified, converted to fractions or decimals, and used to solve problems in various fields.
What is meant by proportional?
Proportional refers to the constant relationship between two or more quantities where their ratio remains the same. Scaling one quantity by a certain factor requires scaling the other quantity by the same factor to maintain the proportion.
According to the given information
To determine if x and y are in a proportional relationship, we need to check if the ratio of y to x is constant.
Let's calculate the ratio of y to x for each pair of corresponding values:
y/x for (1, 2.5) = 2.5/1 = 2.5
y/x for (2, 5) = 5/2 = 2.5
y/x for (3, 7.5) = 7.5/3 = 2.5
y/x for (6, 12) = 12/6 = 2
Since the ratios are not all equal, we can conclude that x and y are not in a proportional relationship.
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NuHome Movers charges $95 per hour for loading/unloading services and $80 per hour for packing/unpacking services. Their charge is $2.50 per mile for truck rental. Jay is moving a distance of 200 miles and needs 9 hours of loading/unloading and 7 hours of packing/ unpacking. What will his moving cost be if the service also charges 7.25% tax on the total?
Answer:
Total moving cost = $2,053.84
Step-by-step explanation:
Let's write down Jay's requirements and costs associated
9 hours of loading/unloading at $95 per hour = 95 x 9 = $855
7 hours of packing/unpacking at $80 per hour = 80 x 7 = $560
200 miles of transportation at $2.50 per mile = 2.50 x 200 = $500
Total before-tax cost of moving = $855 + $560 + $500 = $1, 915
Sales Tax is additional at 7.25%
Sales Tax amount = 1915 x 7.25%
= 1915 x 7.25/100 = 138.8375 = $138.84
Total cost including sales tax = 1915.00 + 138.84 = $2,053.84
What would your first step look like if you were solving this system using the substitution method? y=x−10 and y=−6x+18?
Answer:
Substitution method can be applied in four steps.
Solve one of the equations for either x = or y = .
Substitute the solution from step 1 into the other equation.
Solve this new equation.
Solve for the second variable. ...
Step 1: Solve one of the equations for either x = or y = .
Step-by-step explanation: