Let's call the smaller number "x" and the larger number "y." Since 7 is added to the larger number, y + 7 = 4x. Since 28 is added to the smaller number, x + 28 = 2y.
We can solve this system of equations by substituting the first equation into the second equation to eliminate one of the variables:
x + 28 = 2(y + 7)
x + 28 = 2y + 14
x - 2y = -14
Then, we can substitute the second equation into the first equation to eliminate the other variable:
y + 7 = 4(x + 28)
y + 7 = 4x + 112
y - 4x = -105
Now we have a system of two equations in two variables, which we can solve using methods such as substitution or elimination. Let's use substitution:
x - 2y = -14
y - 4x = -105
If we solve the second equation for y, we get y = 4x - 105. Substituting this expression into the first equation gives:
x - 2(4x - 105) = -14
x - 8x + 210 = -14
-7x = -224
x = 32
Substituting this value back into the expression for y gives us y = 4(32) - 105 = 107.
Therefore, the two numbers are x = 32 and y = 107. If 7 is added to the larger number, the value obtained is 107 + 7 = 114, which is four times the smaller number (32). If 28 is added to the smaller number, the value obtained is 32 + 28 = 60, which is twice the larger number (107).
Simplify.
21. 5t(2)(3)
24. 9(8n)
22. 7(a-b+5)
25. 3k+ 6k-12
23. 9y+ 15y-10y
26. 2t + 5m+7t-4m
The simplification of the following expression, are;
21. 5t(2)(3) = 30t
24. 9(8n)= 72n
22. 7(a-b+5)= 7a - 7b + 35
25. 3k+ 6k-12 = 9k - 12
23. 9y+ 15y-10y = 14y
26. 2t + 5m+7t-4m = m + 9t
What is simplification?The procedure in mathematics to utilize and analyze the function or expression to make the function or expression uncomplicated or more coherent is called simplifying and the process is called simplification.
We are given the following expression, we need to simplify all of them;
21. 5t(2)(3)
= 30 t
24. 9(8n)
= 72n
22. 7(a-b+5)
= 7a - 7b + 35
25. 3k+ 6k-12
= 9k - 12
23. 9y+ 15y-10y
= 14y
26. 2t + 5m+7t-4m
= m + 9t
Learn more about simplification;
https://brainly.com/question/17579585
#SPJ1
(100 POINTS) Need some help with this (Detailed Explanation appreciated)
The addition of equality states that "if you add on one side, you must add the same number to the other side."
How do you appreciate someone for great work?To be aware of something, or to understand that something is valuable: [ + that clause ] I appreciate that this is a difficult decision for you. To appreciate something also means to be grateful for something: I appreciated your help very much.Coworker appreciation quotes for being dedicated“Wow thanks for working overtime today, I wouldn't have finished this report without your help! "Your dedication at work doesn't go unnoticed."Thank you for going above and beyond what's required of your job."“Thank you for always representing us with pride!Your answer would be C because 3x-1=26 because -1 and you're solving a math problem -1 would change to positive to cancel out the -1 add 1 to 26 which would be 27 then you would get 3x=27 which would then lead to 3/27 which is 9.3x = 27 This is true, for you add 1 to each side (doing the opposite of PEMDAS to isolate the x)C is your answerWe are summing the 3rd 4th and 5th terms because k goes from 3 to 5
The third term is
-2(3) +5 = -6+5 = -1
The fourth term is
-2(4) + 5 = -8+5 = -3
The fifth term is
-2(5) +5 = -10 +5 = -5
Add these 3 terms together
-1+-3+-5 = -9
To learn more about appreciated refer to:
https://brainly.com/question/11251332
#SPJ1
Find the quotient of (−2/9)÷(−21/3÷1/9).
Answer:
176366843 / 50000000000
Answer:
[tex]\frac{-2}{567}[/tex]
Step-by-step explanation:
Which of the following constructions must you know how to do in order to construct a circumscribed circle for a given triangle?
angle bisector
inscribed quadrilateral
perpendicular bisector
duplicating a line segment
10000
The following constructions are crucial in drawing inscribed circles:
Construct an angle bisector
Construct perpendicular lines
What is the procedure to follow in drawing inscribed circles on an equilateral triangle?
An inscribed circle is a circle drawn in a triangle. An equilateral triangle is a triangle with three equal sides and angles.
The procedure to follow in drawing inscribed circles in such an equilateral triangle is as follows:
You need to construct an angle bisector at each angle of the triangle
Where they meet at the center, is the center of the inscribed circle.
Construct a straight perpendicular line, from the center to one side of the triangles
Set the compass just on the center point, you can change the length to where the perpendicular intersects the triangle to fit in, and construct your inscribed circle.
Learn more about drawing inscribed circles in an equilateral triangle here:
brainly.com/question/10132966
#SPJ1
what is the slope of the line?
The slope of the graph of the line is 40.
What is slope?The slope of a line is the ratio of the amount that y increases as x increases some amount. Slope tells you how steep a line is, or how much y increases as x increases. The slope is constant (the same) anywhere on the line.
Taking any to points on the line point (5, 200) and (10, 400)
Slope = change in y-coordinates / change in x-coordinates
change in y-coordinate = 400 - 200 which is 200
change in x-coordinate = 10 - 5 = 5
slope = 200/5 which is 40
In conclusion the slope of the straight line graph is 40
Learn more about slope: https://brainly.com/question/1884491
#SPJ1
What is the length of sides of the square shown below?
45
90⁰
A
B. 4-2
C. 1
D. 2.2
E 2
OF. 4
Answer:
45
Step-by-step explanation:
it's very easy to do if u know
25 POINTS!
Which of the following is an equation of a line PARALELL to the equation y=-4x+5
A. Y=4x+1
B. Y=-4x+1
C. Y=1/4x+1
D. Y=-1/4x+1
Which of the following is an equation of a line PERPENDICULAR to the equation y=-4x+5
A. Y=4x+1
B. Y=-4x+1
C. Y=1/4x+1
D. Y=-1/4x+1
describe one situation where parametric equations can describe a physical situation where a standard relationship between two variables will not suffice
Consider presenting a particle moving through three dimensions as an illustration. Several x, y, and z-based equations could be used to describe its path.
Explain the term parametric equations?There are two kinds of parametric equations which are frequently encountered in practical applications.
The concept problem described the first as circular motion.Projectile motion is the second type.Circular Motion:
In parametric equations that model circular motion, sine and cosine have periodic functions for x and y.
Either x is a sine function and y is a cosine function, or vice versa.Thus, Consider presenting a particle moving through three dimensions as an illustration. Several x, y, and z-based equations could be used to describe its path.Projectile Motion:
The vertical component of projectile motion is quadratic, and the horizontal component is linear.
This is due to the fact that starting height, starting velocity, and gravitational force are the three variables that have the most impact on an object's location throughout flight. The vertical component has no bearing on the horizontal component.To know more about the parametric equations, here
https://brainly.com/question/28498229
#SPJ4
GIVING BRAINLIEST PLS HELP!! Which of the following absolute value expressions are equal to 10. (More than 1)
-8 + |-17 - 1|
120 ➗ |-2 • 3|
|-15 ➗ 5| • (-5)
|20 - 25| • 2
33 - |6 + 17|
Answer:
The First One and the last one
martin is considering the expressions 1/2(7x+48) and -(1/2x-3). he wants to know if one expression is greater than the other for all values of x. which statement about the relationship between the expressions is true
Part B how did u found your answer to part A
Answer:
2
Step-by-step explanation:
Someone please help me
Answer: You are correct
Step-by-step explanation: You are correct with both answers because 9x + 7 and 7 + 9x will equal the same thing. Here's an example
X=3
9(3) + 7
27+ 7
34
7 + 9(3)
7+27
34
34=34
It only equals 34, no matter the order. So, it has one solution.
I hope this helps!
Answer:
Equivalent
Step-by-step explanation:
The expressions 9x+7 and 7+9x are equivalent .The equation has infinite many solutions
Vladas believes that an equation with a squared term is never a function of x. Which equation can be used to show vladas that his hypothesis is incorrect?.
The equation that shows that his hypothesis is wrong is:-
x²+ y²= 25
What is an equation in math?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are separated by the 'equal' sign.
How do we solve equations?Remove parentheses from each side of the equation and combine similar terms to make it simpler.
To separate the variable term on one side of the equation, use addition or subtraction.
To find the variable, use division or multiplication.
Vladas said that the equation with a squared term is never a function of x.
According to the Pythagorean Theorem, the square of two natural numbers is the third number. When these numbers are used to create a triangle, a right-angled triangle is formed, with a 90° angle between the two smaller sides.
Among the four provided hypotheses:
Option (C) is true since x2+y2=25.
To learn more about equations click the following link:-
https://brainly.com/question/4675274
#SPJ4
Can some one show me what is 8.92×1.7 please
Answer: 15.164
Step-by-step explanation:
An equation is shown.
8 + x = 32
What value of x makes the equation true?
4
24
40
256
The value of x which will make the equation 8 + x = 32 true will be 24 thus, option (B) is correct.
What is the equation?There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.
The equation must be constrained with some constraints.
As per the given equation,
8 + x = 32
Put x = 4
8 + 4 = 12 ≠ 32
Put x = 24
24 + 4 = 32 (so it will be the solution)
Hence "The value of x which will make the equation 8 + x = 32 true will be 24".
For more about the equation,
brainly.com/question/10413253
#SPJ1
What is the slope of a line perpendicular to the line whose equation is 6x+y=-5.Fully simplify your answer.
Answer:
The slope is 1/6.
Step-by-step explanation:
The slope of the given equation is -6. Perpendicular lines have negative reciprocal slopes.
In a division question, when would you find the restrictions – before or after finding the
reciprocal? Explain your reasoning.
we find the restrictions after finding the reciprocal
What is Division?A division is a process of splitting a specific amount into equal parts.
The values that give a value of 0 in the denominator are the restrictions.
To divide rational expressions, multiply by the reciprocal of the divisor.
The restrictions to the domain of a product consist of the restrictions to the domain of each factor.
To solve this we changes to reciprocal
The reciprocal rule of division method is “Multiply the dividend by the reciprocal of the divisor”.
Hence, we find the restrictions after finding the reciprocal
To learn more on Division click:
https://brainly.com/question/21416852
#SPJ1
two angles that are located between two coplanar lines on the same side of the transversal are called
When two angles that are located between two co-planar lines on the same side of the transversal are called Alternate external angles.
Alternate External Angles
The pairs of angles outside the two lines and on either side of a transversal that cuts two lines are referred to as the alternate external angles.
In the given diagram below, the alternate exterior angles are:
∠2 and ∠8
∠1 and ∠7
Hence, when two angles that are located between two co-planar lines on the same side of the transversal are called Alternate external angles.
To read more about Alternate External Angles.
https://brainly.com/question/26111088
#SPJ4
The table and scatter plot show the revenue of a small convenience store from 2012 to 2020. The line of fit represents the predicted revenue y, in thousands of dollars, x years after 2012. Complete the statements to analyze the residuals.
Year Revenue (thousands of dollars)
2012 365
2013 338
2014 367
2015 379
2016 371
2017 380
2018 384
2019 381
2020 390
The number of positive residuals is
The number of negative residuals is
The smallest residual is
The largest residual is in the year .
Does the largest residual correspond to an outlier in the data?
Enter yes or no.
Revenue is a calculation or estimation of periodic profits primarily based totally on a particular popular accounting practice or the policies mounted via way of means of a central authority or authorities agency.
The required details for revenue in given paragraph.
What is revenue?
Revenue is simply the profit you earn from your business
Solution;
The number of positive revenues were generated is 6 years
The number of negative revenues were generated in 3 years
smallest revenues were in 2013
Largest revenue was generated in 2020
Actually we are just comparing the data from all previous years and we are also comparing the revenues from them so that we can analyze them and do accounting further
accordingly to multiply the revenues
To learn more about revenues:
https://brainly.com/question/8645356
#SPJ1
2. The graph shows the number of feet a remote
control car travels every second.
How far does the remote control car travel per second?
A 1 foot
B 2 feet
C 3 feet
14 feet
Q#2:
E 6 feet
3. The graph of a linear function is shown.
The following points lie on the line: (0, 80) and (8, 60).
What is the equation of the function?
Remote Control Car Distance
y
Distance (in feet)
654321
-
0 1 2 3 456
Time (in seconds)
y
100
Sook 80
60
40
20
X
atsenil s to rigang
Holla
0 2 4 6 8 10
2. The distance traveled by the remote control car each second is given as follows: C. 3 feet.
3. The equation of the linear function is given as follows: y = -2.5x + 80.
How to obtain the distance traveled by the car each second?This distance is the rate of change of the output variable relative to the input variable of the linear function, hence it is the slope of the linear function.
Two points on the graph are given as follows:
(0,0) and (1,3).
Then the slope is calculated as the change in the output divided by the change in the input, as follows:
m = (3 - 0)/(1 - 0) = 3.
Meaning that option C is correct.
How to obtain the equation of the linear function?The linear function in this problem is defined in slope-intercept format, as follows:
y = mx + b.
In which the coefficients are given as follows:
m is the slope.b is the y-intercept.When x = 0, y = 80, hence the intercept is given as follows:
b = 80.
When x increases by 8, y decayed by 20, hence the slope is calculated as follows:
m = -20/8 = -2.5.
This means that the equation is given as follows:
y = -2.5x + 80.
More can be learned about linear functions at https://brainly.com/question/24808124
#SPJ1
Find the 23rd term 20,-2,-24 and find explicit formula
-464 is the 23rd term of sequence 20,-2,-24
What is Sequence?Sequence is an enumerated collection of objects in which repetitions are allowed and order matters.
The sequence is 20,-2,-24...
An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is always the same.
In the sequence first term is 20
and common difference is -2-20 is -22
The general term of arithmetic sequence is aₙ=a+(n-1)d
We need to find 23rd term
a₂₃=20+(23-1)(-22)
=20+22(-22)
=20-484
=-464
Hence, -464 is the 23rd term of sequence 20,-2,-24
To learn more on Sequence click:
https://brainly.com/question/21961097
#SPJ1
Can you find the perimeter of each triangle and type the correct code? Please remember to type in ALL CAPS with no spaces.
Perimeter of triangles is 6x + 12, 18x + 12, 12x - 9 and 14x - 4.
What is perimeter of a triangle?
The perimeter of any two-dimensional figure is defined as the distance around the figure. Therefore, perimeter of a triangle is sum of three sides of a triangle.
According to the given question:
Perimeter of given triangles is
1) Sum of all sides of triangle 1
= (x + 6) + (3x + 2) + (2x + 4)
= 6x + 12
2) Sum of all sides of triangle 2
= (6x + 4) + (7x + 1) + (5x + 7)
= 18x + 12
3) Sum of all sides of triangle 3
= (4x - 3) + (3x) + (5x - 6)
= 12x - 9
4) Sum of all sides of triangle 4
= (6x - 8) + (3x + 7) + (5x - 3)
= 14x - 4
To know more about perimeter of triangle visit
https://brainly.com/question/29472908
#SPJ1
−1/3(x+1 1/2)=−3 1/4
Responses
x=5 1/4
x equals 5 and 1 over 4
x=8 1/4
x equals 8 and 1 over 4
x=11 1/4
x equals 11 and 1 over 4
x=14 1/4
The value of x will be;
⇒ x = 8 1/4
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ - 1/3 (x + 1 1/2) = - 3 1/4
Now,
Since, The expression is,
⇒ - 1/3 (x + 1 1/2) = - 3 1/4
Solve for x as;
⇒ - 1/3 (x + 3/2) = - 13/4
⇒ x + 3/2 = 13/4 × 3/1
⇒ x + 3/2 = 39/4
⇒ x = 39/4 - 3/2
⇒ x = 39/4 - 6/4
⇒ x = 33/4
⇒ x = 8 1/4
Thus, The value of x will be;
⇒ x = 8 1/4
Learn more about the mathematical expression visit:
brainly.com/question/1859113
#SPJ1
all this for brainiest and a lot of points
1.) how do you get from 10^8 to 10^4
2.) how do you get from 10^0 to 10^-1
3.) what is 10^-4 equivalent to
4.) what is 1/1000000 equivalent to
5.) look at the attached picture
I NEED THIS ASAP!!
f(x)=x^2. what is g(x)?
Answer:
A
Step-by-step explanation:
Joe is responsible for reserving hotel rooms for a company trip. His company changes plans and increases how many people are going on the trip, so they need at least 505050 total rooms. Joe had already reserved and paid for 161616 rooms, so he needs to reserve additional rooms. He can only reserve rooms in blocks, and each block contains 888 rooms and costs \$900$900dollar sign, 900. Let bbb represent the number of additional blocks that joe reserves. 1) which inequality describes this scenario? choose 1 answer:.
The inequality expression is :16 + 8B ≥ 50
Least amount that could be spent = $4500
What is inequality expression?
An algebraic inequality is a mathematical statement that uses the inequality sign to relate an expression to a value, a variable, or another expression. "Greater than" and "greater than or equal to" are two verbs that can be translated as inequalities.
need at least 50 total rooms.
Room already booked = 16
Number of Blocks booked = B
Each Block = 8
8B - Addition room Booked
Total room booked = 8B + 16
Total room booked ≥ need at least 50 total rooms
8B + 16 ≥ 50
=> 16 + 8B ≥ 50 , option B is correct
=> 8B ≥ 34
=> 4B ≥ 17
minimum B = 5
Cost = 900 * 5 = 4500 $
least amount of additional money Joe can spend to get the rooms they need in dollars = 4500
To learn more about inequality expression visit:https://brainly.com/question/29506182
#SPJ4
Find nd the 10th term of the series attached.
Answer:
[tex]C) \ -2(2/3)^8[/tex]--------------------------
The nth term is visible in the sum:
[tex]t_n=3(-2/3)^{n-1}[/tex]Apply n = 10 to find the 10th term:
[tex]t_{10}=3(-2/3)^{10-1}[/tex][tex]t_{10}=3(-2/3)^9[/tex][tex]t_{10}=3(-2/3)^{8+1}[/tex][tex]t_{10}=3(-2/3)^8*(-2/3)[/tex][tex]t_{10}=-2(-2/3)^8[/tex][tex]t_{10}=-2(2/3)^8,\ since\ the\ power\ is\ even\ number[/tex]The matching choice is C.
In a company, 80% of the workers are women. If 760 people work for the company who aren't women, how many workers are there in all? Use pencil and paper. Show two different ways that you can solve this problem.
Using mathematical operations, we know that the total number of workers in the company is 3,800.
What are mathematical operations?A mathematical "operation" is the process of calculating a value utilizing operands and a math operator.
There are predefined rules associated with the math operator's symbol that must be applied to the supplied operands or numbers.
Parentheses, Exponents, Multiplication, Division, and Addition Subtraction are also known as PEMDAS (from left to right).
So, we know that 80% of all workers are women.
760 people who work for the company are not women.
Which means:
80% = x
20% = 760
Now, calculate the total workers as follows:
80/x = 20/760
20x = 80 * 760
x = 80 * 760/20
x = 3,040 (Women workers)
Total workers: 3040 + 760 = 3,800 workers
Therefore, using mathematical operations, we know that the total number of workers in the company is 3,800.
Know more about mathematical operations here:
brainly.com/question/28937023
#SPJ1
There were 35 bunche of roe and tulip. Each bunch had 12 of the ame flower. There 7 more bunche of tulip than roe. How many tulip were there?
As per the unitary method, the number of tulip were 21.
Unitary method:
In algebra, unitary method defines how to find the value of a unit from the value of a multiple and the value of a multiple from the value of a unit.
Given,
Here we have There were 35 bunches of rose and tulip. Each bunch had 12 of the roe flower. There 7 more bunches of tulip than rose.
Now we need to find how many tulip were there.
Let number of bunches of roses be x.
And then the number of bunches of tulips will be x + 7
The total number of bunches of flowers = 35
So, it can be written as,
=> x + x + 7 = 35
When we simplify this one then we get,
=> 2x + 7 = 35
Now, we have to subtracting both sides by 7
=> 2x = 28
Then dividing both sides by 2
=> x = 14
So, the number of bunches of roses = 14
Then the number of bunches of tulips = 14 + 7 = 21
To know more about Unitary method here.
https://brainly.com/question/28276953
#SPJ4
what happens if there are 36 members and you use more then 6 members per row
Answer:
6
Step-by-step explanation:
Review the following derivation of the tangent double angle identity. The steps are not listed in the correct order
After reviewing the derivative of the tangent double , the correct order of the derivative is (a) .
In the question ,
the derivative of the double tangent is given ,
we have to select the correct order of the derivative .
the function is tan(2x) .
Step 4: tan(2x) = Sin(2x)/cos(2x)
Step 3 :
expanding sin(2x) and cos(2x) using identity ,
we get ,
= 2sinxcosx/(cos²x - sin²x)
Step 5 :
dividing the numerator and denominator by cos²x .
= [2sinxcosx/cos²x]/[cos²x/cos²x - sin²x/cos²x]
Step 1 : simplifying further,
we get ,
= [2sinx/cosx]/[1 - sin²x/cos²x]
Step 2 : writing sinx/cosx = tanx
we get ,
tan2x = 2tanx/(1 - tanx)
Therefore , the correct order for the given derivative is (a) 4, 3, 5, 1, 2 .
The given question is incomplete , the complete question is
Review the following derivation of the tangent double angle identity. The steps are not listed in the correct order
(a) 4, 3, 5, 1, 2
(b) 4, 5, 3, 1, 2
(c) 3, 4, 5, 1, 2
(d) 3, 4, 1, 5, 2
Learn more about Derivative here
https://brainly.com/question/28381632
#SPJ4