Answers
By algebra properties we find the following relationships between each pair of algebraic expressions:
First equation: Case 4Second equation: Case 1Third equation: Case 2Fourth equation: Case 5Fifth equation: Case 3How to determine pairs of equivalent equations
In this we must determine the equivalent algebraic expression related to given expressions, this can be done by applying algebra properties on equations from the second column until equivalent expression is found. Now we proceed to find for each case:
First equation
(7 - 2 · x) + (3 · x - 11)
(7 - 11) + (- 2 · x + 3 · x)
- 4 + (- 2 + 3) · x
- 4 + (1) · x
- 4 + (5 - 4) · x
- 4 - 4 · x + 5 · x
- 4 · (x + 1) + 5 · x → Case 4
Second equation
- 7 + 6 · x - 4 · x + 3
(6 · x - 4 · x) + (- 7 + 3)
(6 - 4) · x - 4
2 · x - 4
2 · (x - 2) → Case 1
Third equation
9 · x - 2 · (3 · x - 3)
9 · x - 6 · x + 6
3 · x + 6
(2 + 1) · x + (14 - 8)
[1 - (- 2)] · x + (14 - 8)
(x + 14) - (8 - 2 · x) → Case 2
Fourth equation
- 3 · x + 6 + 4 · x
x + 6
(5 - 4) · x + (7 - 1)
(7 + 5 · x) + (- 4 · x - 1) → Case 5
Fifth equation
- 2 · x + 9 + 5 · x + 6
3 · x + 15
3 · (x + 5) → Case 3
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Related Questions
In 2017, a company's sales were about $9 million. Sales increased at an approximately constant rate and reached
about $14.5 million in 2020, Estimate the sales in 2026. Show your work.
Answers
Answer: To estimate the company's sales in 2026, we need to find the average increase in sales per year and then use that to predict the sales for 2026.
The total increase in sales from 2017 to 2020 was $14.5 million - $9 million = $<<14.5-9=5.5>>5.5 million.
The number of years from 2017 to 2020 is 2020 - 2017 = <<2020-2017=3>>3 years.
Therefore, the average increase in sales per year was $5.5 million / 3 years = $<<5.5/3=1.83>>1.83 million/year.
Since the average increase in sales per year was $1.83 million/year, we can estimate the sales in 2026 by adding that amount to the sales for each year from 2020 to 2026. For example, the estimated sales for 2021 would be $14.5 million + $1.83 million = $16.33 million. Similarly, the estimated sales for 2022 would be $16.33 million + $1.83 million = $18.16 million, and so on.
Using this method, we can estimate that the sales for 2026 will be $26.73 million.
doors for the small cabinets are 10.5 inches long. Doors for the large cabinets are 2.7 times as long as the doors for the small cabinets. How many large doors can be cut from a board that is 12 feet long?
Answers
Answer:
5 doors.
Step-by-step explanation:
10.5 times 2.7 is 28.35. 12 times 12 is 144. and 144 divided by 28.35 is 5.08 simplified to 5 doors
A city has 3 new houses for every 7 old houses. If there are 21 new houses in the city, how many old houses are there?
A.
52
B.
49
C.
51
D.
47
Answers
Answer:
B. 49
Step-by-step explanation:
21/3 = 7
7*7 = 49
Tritan walk 1/4 of mile in 1/10 of an hour. What i the unit rate of mile per hour?
Answers
Half a mile every hour is equal to 1/5 mile every 4/10th of an hour.
What is unitary method ?Area is the total amount of space that an object's shape or a flat (2-D) surface occupy.
Create a square on paper by using a pencil. Two dimensions make it up. A shape's area on paper is the space it takes up.
Imagine that your square is made up of smaller unit squares.
The area of a figure is equal to the number of unit squares required to completely cover the surface area of a particular 2-D shape. Square cms, square feet, square inches, square meters, etc. are a few common units for measuring area.
To get the area of the square figures presented below, draw unit squares with 1-centimeter sides. Therefore, the shape will be measured.
According to our question-
(1/5) / (4/10) = x / 1
Cross-multiplication yielding
1/5 * 1 = 4/10 * x
How to find x?
10 / 20 = x
x = 1 / 2
Half a mile every hour is equal to 1/5 mile every 4/10th of an hour.
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Lela is making peach pies. She uses 9 peaches for each pie. If she uses 18 peaches for 2 pies and 36 peaches for 4 pies, how many peaches will she need for 7 pies?
A.45
B.54
C.63
D.70
Answers
Lela is making peach pies. She uses 9 peaches for each pie. If she uses 18 peaches for 2 pies and 36 peaches for 4 pies, how many peaches will she need for 7 pies?
A. 45 B. 54C. 63D. 70Answer : C. 63Explanation :As, Lela is using 9 peaches for each pie.
Thus, she used 18 peaches for 2 pies, which is 2 times 9 and 36 peaches for 4 pies, which is 4 times 9. Therefore, to make 7 pies, she would need :
Peaches used for one pie = 9
=> Peaches used for 7 pies = 9 × 7
=> Peaches needed for 7 pies = 63
Hence, she will need 63 peaches to make 7 pies.
9x² + 31x+ 20 = ( ? ) ( ? )
2x² +7x-4 = ( ? )( ? )
2x² - 13x-5 = ( ? )( ? )
Answers
Answer: The square root of 169 is 13, so the two solutions for x are:
x = (13 + 13) / 4 = 3.25
x = (13 - 13) / 4 = -0.25
Since the quadratic expression 2x^2 - 13x - 5 equals 0 when x is either 3.25 or -0.25, the factors of this expression are (x - 3.25)(x + 0.25).
In summary, the factors of the first quadratic expression are (x + 1.056)(x + 5.937), the factors of the second expression are (x - 0.75)(x + 3.75), and the factors of the third expression are (x - 3.25)(x + 0.25).
Step-by-step explanation: To find the factors of a quadratic expression, we can use the quadratic formula. The quadratic formula states that for a quadratic expression of the form ax^2 + bx + c = 0, the solutions for x are given by the formula x = (-b ± sqrt(b^2 - 4ac)) / (2a).
In the first equation, a is 9, b is 31, and c is 20. Plugging these values into the quadratic formula, we get:
x = (-31 ± sqrt(31^2 - 4 * 9 * 20)) / (2 * 9)
This simplifies to:
x = (-31 ± sqrt(961 - 720)) / 18
This further simplifies to:
x = (-31 ± sqrt(241)) / 18
We can find the value of the square root by using a calculator or by remembering some common square roots. The square root of 241 is approximately 15.937, so the two solutions for x are:
x = (-31 + 15.937) / 18 = -1.056
x = (-31 - 15.937) / 18 = -5.937
Since the quadratic expression 9x^2 + 31x + 20 equals 0 when x is either -1.056 or -5.937, the factors of this expression are (x + 1.056)(x + 5.937).
We can use the same approach to find the factors of the other two quadratic expressions. For the second expression 2x^2 + 7x - 4, the values of a, b, and c are 2, 7, and -4, respectively. Plugging these values into the quadratic formula, we get:
x = (-7 ± sqrt(7^2 - 4 * 2 * -4)) / (2 * 2)
This simplifies to:
x = (-7 ± sqrt(49 + 32)) / 4
This further simplifies to:
x = (-7 ± sqrt(81)) / 4
The square root of 81 is 9, so the two solutions for x are:
x = (-7 + 9) / 4 = 0.75
x = (-7 - 9) / 4 = -3.75
Since the quadratic expression 2x^2 + 7x - 4 equals 0 when x is either 0.75 or -3.75, the factors of this expression are (x - 0.75)(x + 3.75).
For the third expression 2x^2 - 13x - 5, the values of a, b, and c are 2, -13, and -5, respectively. Plugging these values into the quadratic formula, we get:
x = (13 ± sqrt(13^2 - 4 * 2 * -5)) / (2 * 2)
This simplifies to:
x = (13 ± sqrt(169 + 40)) / 4
``
Which of the following is not a benefit of stressing
1. Poor circulation
2. Increased speed and power
3. Increased flexibility
4. Minimized chances of injuries
Which of the following is not in upper body stretch?
1. Arms circles
2. Trunk twist
3. Straddle stretch
4. Triceps stretch
Answers
The option that is not a benefit of stretching is 1. Poor circulation
The option that is not in upper body stretch is 3. Straddle stretch
What are the Advantages of Stretching?The benefits include:
Increase your physical activity performance.Reduce your risk of injury.Assist your joints in moving through their entire range of motion.Increase blood flow to the muscles.Allow your muscles to work as efficiently as possible.Improve your ability to perform daily tasks.The straddle stretch is one that is not considered an upper body stretch. Straddle stretch, also known as the middle split, requires a lot of leg flexibility. In conclusion, the correct option is C.
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Create an equivalent expression for 18^-7. 18^5. -18² 18² 1/18^-2 1/18²
Answers
The equivalence of the expression 18⁺⁷ * 18⁵ is
D. 1/18²How to write the equivalence of the expressionPower or exponents as used in mathematics are number written on top of a base number. The power says how many times the base number multiplies itself.
The given expression 18⁺⁷ * 18⁵ is solved using the power rule, the power rule used is equation of bases> In equation of bases the base are kept constant and the mathematical operators act on the powers
This method is used as in this case as shown below
= 18⁺⁷ * 18⁵
= 18⁺⁷⁺⁵
= 18⁻²
= 1/18²
Therefore the equivalence of the expression is 1/18²
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how do we do this I just forgot please help!
I will pray for you If you do it
Thanks
Answers
Answer:
Step-by-step explanation:
=(37 * 45 ) + (63 * 45 )
=1665 + 2835
=4500
Answer:
4720275Step-by-step explanation:
[tex]\tt 37\times 45\times63\times45[/tex]
[tex]\tt 1665\times63\times45[/tex]
[tex]\tt 104895\times 45[/tex]
[tex]\tt 4720275[/tex]
____________________
Hope this helps you!
Have a great day! :)
What is the range of this table?
Answers
Answer: B
Step-by-step explanation:
Range will always be Y
Domain will always be X
A relation contains the points (1, 2), (2, −1), (3, 0), (4, 1), and (5, −1). Which statement accurately describes this relation?
Answers
The relation represents y as a function of x as for each value of x there is a unique value of y.
What is a function?A function y = f(x) is defined as a one to one relation between sets X and Y. The set X is called the domain while Y is called the range of f(x).
The given data is as follows,
A relation contains the points (1,2),(2,-1),(3,0),(4,1), and (5,-1).
Here x is the element of domain and y is of the range of the given relation.
Here, the values of y are distinct for different values of x.
Hence, the given relation represents y as a function of x because for each value of x there is a single value of y.
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Penny has 14 coins, all nickels, dimes, and quarters, totaling $2. 50. She has twice as many dimes as nickels, and twice as many quarters as dimes. How many dimes does she have?.
Answers
Out of the 14 coins she has, she will have 4 dimes, totaling $2.5.
What is expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression in mathematics is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) You can think of expressions as being comparable to phrases. A phrase in language may contain an action on its own, but it does not constitute a whole sentence.
Here,
Let n be the nickels, d be the dimes, q be the quarters.
Total coins=14
Total amount=$2.5
n=2d
d=2q
q=d/2
d+q+n=14
d+2d+d/2=14
2d+4d+d=28
7d=28
d=4
She will have 4 dimes out of 14 coins that she owns with an amount of $2.5.
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For a project in his Geometry class, Feng uses a mirror on the ground to measure the height of his school’s flagpole. He walks a distance of 8.65 meters from the flagpole, then places a mirror on flat on the ground, marked with an X at the center. He then steps 1.1 meters to the other side of the mirror, until he can see the top of the flagpole clearly marked in the X. His partner measures the distance from his eyes to the ground to be 1.65 meters. How tall is the flagpole? Round your answer to the nearest hundredth of a meter.
Answers
The height of the flagpole, found using the ratio of the sides of similar triangles is 12.975 meters
What are similar triangles?Similar triangles are triangles in which two angles of one triangle are congruent to two angles in the other triangle, such that they have the same shape.
The parameters that can be used to find the height of the flagpole are;
Distance of the mirror from the flagpole = 8.65 meters
Distance of Feng on the other side of the flagpole = 1.1 meters
The height from Feng's eyes to the ground = 1.65 meters
According to the law of reflection, the angle of incident and the angle of reflection are the same
The angle made by Feng and the ground = Angle made by the flagpole and the ground = 90°
The triangle formed by the Feng and the flagpole are therefore similar by AA similarity postulate
The ratio of corresponding sides of similar triangles are the same, therefore;
[tex]\dfrac{1.65}{Height\, of \, the \, flagpole} = \dfrac{1.1}{8.65}[/tex]
[tex]Height\, of \, the \, flagpole = \dfrac{1.65}{1.1} \times 8.65 = 12.975[/tex]
Height of the flagpole = 12.975 meters
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Solve the system of equations.
4x - 9y - 2 = 0
12x - 5y + 38 = 0
x =
y =
Answers
2.(x,y)=(-4,-2)
From a normally distributed population, a simple random sample of size 30 is taken. The mean of the sample is 144 and the standard deviation of the sample is 12. Which interval is a 99% confidence interval for the population mean?.
Answers
On solving the provided question, we got that The 90% confidence interval for the population mean mu is (140.4, 147.6)
The meaning of the standard deviationA measure of how far the data are from the mean is called standard deviation (or). Data that have a low standard deviation are more likely to be centered around the mean than those that have a high standard deviation.
xbar = 144 (sample mean)
s = 12 (sample standard deviation)
n = 30 (sample size)
z = 1.645 (critical value at 90% confidence; use a calculator or table to compute this value)
[tex]The lower limit of the confidence interval is L, which is found by\\\\L = xbar - z(s/sqrt(n))\\L = 144 - 1.645(12/sqrt(30))\\L = 140.395985571616\\L = 140.4\\[/tex]
Similarly the upper limit U is
U = xbar + z(s/sqrt(n))
U = 144 + 1.645(12/sqrt(30))
U = 147.604014428384
U = 147.6
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State the domain and range of the following function {(2,3),(7,9),(4,-7),(6,2)(3,-5)
Answers
Domain: {2,7,4,6,3}
Range: {3,9,-7,2,-5}
I NEED HELPPP!! PLEASE ANSWER ASAP I WILL GIVE BRAINLIEST AFTER 2 PEOPL ANSWER THISSSSS
Answers
Answer:
x = 4
Step-by-step explanation:
5 x .8 = 4
Answer: the value of x is 4
Step-by-step explanation:
x=5*0.8=4
Sandra has 10 books. She divides them into groups of 2 each. How many groups can she make?
Answers
Answer:
5 groups
Step-by-step explanation:
10/2=5
let f be a function by f(x)= -5x-3, D is its graph. Determine the coordinates of the point of intersections of D with the x-axis and the y-axis
Answers
Indirectly we are asked for x and y intercepts because
The point at which a line crosses x axis is called its x intercept and there y coordinate is 0.Similarly the point at which a line crosses y axis is called its y intercept and there x coordinate is 0Let us find out
f(x)=-5x-3Y intercept:-
put x=0
y=-5(0)-3y=-3(0,-3)
X intercept
put y=0
-5x-3=0-5x=3x=-3/5(-3/5,0)
Which table of values represents a linear function?
Answers
Therefore the table values of which represents a linear function are table 2 and table 3
What is linear equation?A linear equation is a first-order (linear) term and a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. A "linear equation of two variables" is what is sometimes referred to here, where y and x are the variables.
Here,
The values shown in table 2 have same constant rate of change of 3 units.
where as,
The values shown in table 3 have same constant rate of change of 5 units.
Therefore the table values of which represents a linear function are table 2 and table 3
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Write the expression in simplest radical form. Please help !!
Answers
Answer:
[tex]7\sqrt5[/tex]
Step-by-step explanation:
245 ÷ 5 = 49
49 is a square number (7)
So you put 7 on the outside and 5 on the inside.
Use the values In 3≈ 1.1 and In 47≈ 3.85 to find the approximate value of log3 47.
O log, 47
4.95
O log3 47
4.235
O log3 47
0.286
O log3 47≈ 3.5
Answers
The value of the equation log(3 47) is about 4.235.
Describe log.The power to which a number must be increased in order to obtain another number is known as a logarithm. For instance, since ten raised to the power of two equals 100, the base ten logarithm of 100 is 2: log 100 = 2.
Given that the approximate values of log(3) and log(47) are 1.1 and 3.85, respectively,
we must determine the approximate value of log(347).
log(a × b) = log(a) × log(b)
we get ,
log(3 × 47) = log(3) × log(47)
substituting , the values of log(3) and log(47) ,
we get ,
log(3 × 47) = 1.1 × 3.85
≈ 4.235
Therefore , The approximate value of log(3 × 47) is 4.235 .
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work out the value of (4^0 x 6^0)
Answers
Answer: 1
Step-by-step explanation:
A class is planning a trip to the local City Museum of Art. There are 22 people going on this trip.
There are four drivers and two types of vehicles, cars and trucks. The cars set four people,
including the driver and the truck seats six people again including driver. How many trucks and
cars doe the class need for this trip? Write a system of equations to solve.
12/24
Answers
The number of trucks and cars need by the class for the trip will be 3 and 2 respectively
How to find the number of trucks and cars the class need for this tripInformation from the question is used as follows
There are 22 people going on this trip.
total number = 22
There are four drivers and two types of vehicles, cars and trucks
drivers = 4
vehicle types = 2
The cars set four people, including the driver and the truck seats six people again including drive
cars = 4 people
truck = 6 people
Total number of people + drivers = 26
let the number of people in the truck be t and the number of people in the car be c
6t + 4c = 26
assuming the trucks were 3
6 * 3 + 4c = 26
4c = 26 - 18
4c = 8
c = 2
The class will need 3 trucks and 2 cars
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god is good everyday and all time
Answers
The LORD is faithful to all generations, and His loving kindness endures forever.
Explain about the god is good everyday and all time?God Is Love, Therefore God Is Good God is light, and He is also love. God "is love." Because God loved the world so much that he gave his one and only Son, he ensured that everyone who trusted in him would not perish but have eternal life.
In the church, the adage "God is good, all the time, all the time" gained popularity a number of years ago. It is still in use today and was once used as a welcome and a response, frequently in a call-and-response pattern.
The Oxford English Dictionary describes omnibenevolence as unlimited or infinite compassion.
The complete question is,
Why is God so merciful all the time?
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this is the question
Answers
Answer:
1. no solution
2. one solution
3. infinitely many solutions
4. one solution
Step-by-step explanation:
1. same slope, different intercepts, parallel lines, no solution
2. different slopes, lines intersect at 1 point, one solution
3. same equation, infinitely many solutions
4. different slopes, lines intersect at 1 point, one solution
2. one solution
3. infinity many solutions
4. one solution
The perimeter of a rectangular pool i 110 feet. If the pool i 17 feet wide, find the length of the pool
Answers
It will be 38 feet long
What is perimeter?The perimeter is the space surrounding a shape's edge.
The sum of the lengths of all the sides in a rectangular shape is its perimeter. P = 2( L+B)
Given that a rectangle's width is 17 feet and its perimeter is 110 feet, the length will be P = 2 (L + B)
110 = 2 (L + 17)
55 - 17 = L.
The pool is therefore 38 feet long.
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The graph shows the relationship between the time and the distance a train traveled. Distance Traveled Distance (kilometers) 80- 70- 60- 50+ 40+ 30- 20+ 10+ 0 10 (40, 50) 20 30 40 50 60 Time (minutes) What does the point (40, 50) represent on the graph? Enter the answers in the boxes to complete the sentence. The point (40, 50) shows that in ✓ minutes, the train traveled kilometers.
Answers
Answer:
in 40 minutes ... travelled 50km
Step-by-step explanation:
Write the equation in slope-intercept form of the line that is parallel to the graph of each equation and passes through the given point. y=1/2x+5;(4,-5)
Answers
Find the greatest common factor (GCF) of 10 and 6 =. use the GCF to factor 10+6.
Answers
Answer: It would be 2.
Step-by-step explanation: The GCF of 10 and 6 would be 2 because that is the greatest number that 10 and 6 can be divided into. If we added them both to get 16. It would still be 2. I hope this helps!