The simplification by combining like terms of 4t-(t + 3t) is 0.
According to the given question.
We have an expression 4t - (t+3t).
As we know that, like terms are terms whose variables (and their exponents such as the 2 in x2) are the same. when we combine like terms, such as 2x and 3x, we add or subtract their coefficients.
Since, we have to combine the like terms of the given expression 4t-(t+3t).
Here 4t, t and 3t both are the like terms.
So, we add and subtract coeffcients of t to simplify the given expression.
Therefore, the simplification of 4t - (t + 3t) is given by
4t -( t+ 3t)
= 4t - t -3t
= 4t - 4t
= 0
Hence, the simplification by combining like terms of 4t - (t + 3t) is 0.
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in subscript 4 200 = what
Answer:
8
Step-by-step explanation:
200 ×4=800
OR
200+200+200+200=800
PLEASE HELP!!!
In the figure below, mWXZ=108*, and m1 is two times m2 Find m2.
Here mWXZ=108*and m1 is two times m2 so, The value of m2 is [tex]36[/tex]°.
The fundamental geometric shapes are lines and angles. Infinite points that stretch infinity in both directions make up lines, which are geometric objects. Straight lines with little depth or width are present. You will learn about a number of lines, including transversal, intersecting, and perpendicular lines. A figure called an angle is one in which two rays originate from the same point. In this area, you could also encounter contrasting and related viewpoints. The most useful area of mathematics is the study of geometric shapes and their characteristics. As we've already mentioned, the foundation of any geometric shape is made up of lines and angles. Without employing lines and angles, it is impossible to draw a two-dimensional to three-dimensional shape. Consequently, it is imperative to discover the meanings of the two terminologies. Here, the fundamental definitions and characteristics of lines as well as angles are provided. A line is a simple, one-dimensional shape that can go on forever in opposing directions. A line may be vertical or horizontal. It can be drawn either top to bottom or left to right. When the ends of two rays collide at a single location, an angle is a geometry that results. They are expressed as radians or degrees (°). A 360-degree angle is the same as a whole rotation.
Let the angle m2 be x
so, according to the question m1= 2m2=2x
so, m1+m2=[tex]108[/tex]°
⇒2x+x=[tex]108[/tex]°
⇒3x=[tex]108[/tex]°
⇒x=[tex]36[/tex]°
means angle m2=[tex]36[/tex]°
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Log x + log 6= log(2x+1)
In logarithm , value of function is 1/4.
How should log be defined?
The power to which a number must be increased in order to obtain another number is known as a logarithm (see Section 3 of this Math Review for more about exponents). For instance, the logarithm of 100 in base ten is 2, since ten multiplied by two equals 100: log 100 = 2, since 102 = 100.The distinction between log and ln is that log is expressed in terms of base 10, while ln is expressed in terms of base e.Log x + log 6= log(2x+1)
use log property log m + log n = log ( mn)
log ( 6x) = log (2x + 1)
6x = 2x + 1
4x = 1
x = 1/4
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If f(x)=x² + x + 2 and g(x) = 2x² - 7 then prove that: 2 fg(2) = f(2) g(2).
Answer:
See explanation
Step-by-step explanation:
f(x)=x² + x + 2 and g(x) = 2x² - 7
f(2) g(2)=
((2)² + (2) + 2)(2(2)² - 7)=
(4 + 2+ 2)(2(4) - 7)=
(8)(8 - 7)=
8*1=8
2 fg(2)=
2 f(g(2))=
2 f(2(2)² - 7)=
2 f(2(4)-7)=
2 f(8-7)=
2 f(1)=
2(1² + 1 + 2)=
2(1+3)=
2(4)=8
8=8
2 fg(2)=f(2) g(2) √
Add or subtract as indicated.
75.2 + 123.96 + 3.897
Answer: 203.057
Step-by-step explanation:
75.2+123.96+3.897
199.16+3.897
203.057
A= 7x^2-3x+10 B=-4x^2+6x-4
A-B=
Hello,
A - B = 7x² - 3x + 10 - (-4x² + 6x - 4)
A - B = 7x² -3x + 10 + 4x² -6x + 4
A - B = 11x² - 9x + 14
53(2x−6)+18=23(x+3)−4
Answer: X=365/83 OR x= 4.39
Step-by-step explanation:
Simplify by combining like terms. b-2(1+c-b)
The simplification by combining like terms of b -2(1 + c - b) is 3b -2c - 2.
According to the given question.
We have an expression b -2(1 + c - b).
As we know that, like terms are terms whose variables (and their exponents such as the 2 in x2) are the same. when we combine like terms, such as 2x and 3x, we add or subtract their coefficients.
Since, we have to combine the like terms of the given expression b -2(1 + c - b).
Here b and 2b both are the like terms.
So, we add and subtract coeffcients of b to simplify the given expression.
Therefore, the simplification of the expression b -2( 1 + c - b) is given by
b - 2( 1+ c - b)
= b - 2 -2c + 2b
= 3b -2c - 2
Hence, the simplification by combining like terms of b -2(1 + c -b) is 3b -2c - 2.
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You can find many different proofs to prove that (0.999 . . . =1 . How can you use the formula for the sum of a geometric series to show that 0.999 . . . . . =1 ?
We can use the formula for the sum of a geometric series as Summation.
What is Geometric Series:
A geometric series is the sum of finite or infinite terms of a geometric sequence. For the geometric sequence a, ar, ar2, ..., arn-1, ..., the corresponding geometric series is a + ar + ar2 + ..., arn-1 + .... We know that "series" means "sum". In particular, the geometric series means the sum of the terms that have a common ratio between every adjacent two of them. There can be two types of geometric series: finite and infinite.
Now, Solution of the given problem
We can write
0.999...=9/10+9/100+9/1000+⋯
=9/10+9/10(1/10)+9/10(1/10)2+⋯
=∞∑n=0 9/10(1/10)n,
which is a geometric series
with a=9/10and r=1/10
.So, the sum is a/1−r=9/10 / 1−1/10 = 1.
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The exchange rate of Japanese Yen on a certain day was Rs 10.25 . On the same day, if $3 was exchanged for Rs 345, how many Yens could be exchanged for $123?
The amount of $123 will be equal to 1380 yens.
What is currency exchange?The rate at which one currency will be exchanged for another is known as the exchange rate in the world of finance. The most frequent types of currencies are national currencies.
Given that the exchange rate of the Japanese Yen on a certain day was Rs 10.25. On the same day, if $3 was exchanged for Rs 345.
The amount of $123 in the yens will be calculated by forming the equations below:-
1 yen = 10.25 rs
1 rs = ( 1 / 10.25 ) yens ........................(1)
$3 = 345 rs
1 rs = $3 / 345 .........................(2)
From both the equations:-
( 1 / 10.25 ) yens = $ ( 3 / 345 )
$ 1 = ( 345 / ( 10.25 x 3 ) yen
$ 123 = ( 345 x 123 / ( 10.25 x 3 ) yen
$ 123 = 1380 yen
Therefore, the amount of $123 will be equal to 1380 yens.
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Mariah thinks that the following equation is always true (that it's an identity). Is it always true? Find evidence
for or against the following equivalency rule by substituting various values in for a and b.
(a+b)² = a² + b²
Answer: It is not always true, so it's not an identity
========================================================
Explanation:
Let's try replacing each 'a' with 1, and each b with 2. Feel free to pick two of your favorite nonzero numbers.
So we'll plug in a = 1 and b = 2
[tex](a+b)^2 = a^2+b^2\\\\(1+2)^2 = 1^2+2^2\\\\(3)^2 = 1^2+2^2\\\\9 = 1+4\\\\9 = 5\\\\[/tex]
The last equation is a false statement. This means the first equation is also false for a = 1 and b = 2.
This is one counter-example to disprove that (a+b)² = a² + b² is true in general.
Therefore, the equation is not an identity.
--------------
What is an identity however is this
(a+b)² = a² + 2ab + b²
If you were to plug in a = 1 and b = 2, then you'd get 9 on each side. This is one example to help partially confirm it's an identity.
More rigorous proof is in the form of using the FOIL method, the distributive property, or the box method.
Use the values of a₁ and Sn to find the value of a n a₁=4 and S₄₀=6080 ; a₄₀
Using the values of the first term and the sum of the first 40 terms of the given series, a(40) = 300
Suppose we are given a series:
a(1) + a(2) + a(3) + ....+ a(n)
Then, the sum of the first n terms is given by:
S(n) = n/2 [a(1) + a(n)]
Parameters given in the problem:
a(1) = 4
S(40) = 6080
To find a(40), substitute n = 40, a(1) = 4, and S(40) = 6080 into the formula:
S(n) = n/2 [a(1) + a(n)]
S(40) = 40/2 [4 + a(40)]
6080 = 20 . [4 + a(40)]
Divide both sides by 20
304 = 4 + a(40)
Subtract 4 from both sides:
304 - 4 = 4 + a(40) - 4
a(40) = 300
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bir basamaklı en küçük pozitif tam sayı
Answer:
Step-by-step explanation:
jjjjjjjj
Write an equation for each line. m = 5/6 and the y -intercept is (0,12) .
The equation of line for m = 5/6 and the y -intercept is (0,12) is y = 5/6x + 12.
What is the equation of line?The formula for a straight line is y = mx + c where c is the height at which the line intersects the y-axis, often known as the y-intercept, and m is the gradient.
The equation for line is y = mx + c
Given, m = 5/6, y-intercept = (0,12)
now putting the values in the equation,
y = 5/6x + 12
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Solve each equation. 12-3(2 w+1)=7 w-3(7+w)
The solution of the given linear equation in one variable 12 -3(2w + 1) = 7w -3(7 + w) is at w = 3.
According to the given question.
We have a linear equation in one variable.
12 -3(2w + 1) = 7w -3(7 + w)
As we know that, the linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution.
Thereofre, the solution of the linear equation in one variable 12 -3(2w + 1) = 7w -3(7 + w) is given by
12 - 3(2w + 1) = 7w - 3(7 + w)
⇒ 12 - 6w -3 = 7w - 21 -3w (by distributive rule)
⇒ 9 - 6w = 4w - 21 (subtracting the like terms)
⇒ 9 + 21 = 4w + 6w
⇒ 30 = 10w
⇒ 30/10 = w
⇒ w = 3
Hence, the solution of the given linear equation in one variable 12 -3(2w + 1) = 7w -3(7 + w) is at w = 3.
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The arithmetic mean of the monthly salaries of two employees is $ 3210 . One employee earns $ 3470 per month. What is the monthly salary of the other employee?
a. What is the given information and what is the unknown?
$2950 is the monthly salary of the other employee.
a. the given information = mean of two salaries = 3210
= salary of 1st employee =3470
the unknown information = salary of 2nd employee = 2950
How to solve an equation?
To solve linear equations, utilize the steps that are provided below.
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.The common denominator can be multiplied by each side of the equation to eliminate fractions.Lets take an example of solve z for 7z – (3z – 4) = 12
Here is no multiplication or division, so this will be easy to solve
⇒ 7z – (3z – 4) = 12
⇒ 7z – 3z + 4 = 12
⇒ 4z = 12 – 4
⇒ 4z = 8
⇒ z = 8/4
⇒ z = 2
See, that was so simple, using the mentioned methods, every linear equation can be solved easily.
We know that mean, [tex]m = \frac{\text{sum of the terms}}{\text{number of terms}}[/tex]
Here is given the
mean = 3210
term₁ = 3470 (salary of one of the employees)
term₂ = ? (salary of the 2nd employee)
So, if we simplify
⇒ [tex]m = \frac{\text{sum of the terms}}{\text{number of terms}}[/tex]
⇒ [tex]3210 = \frac{3470 + term_2}{2}[/tex]
⇒ [tex]3210[/tex] × [tex]2 = 3470 + term_2[/tex]
⇒ [tex]6420[/tex] = [tex]3470 + term_2[/tex]
⇒ [tex]term_2 = 6420 - 3470[/tex]
⇒ [tex]term_2 = 2950[/tex]
So, the salary of the other employs is $ 2950
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What is ±/324 ?
Nesecito ayar la respuesta
Answer:
+18 or -18
Step-by-step explanation:
30% squares units percent of increase 70%
133.3333333333% (increase) is percent of increase 70%.
What is the percentage formula?
By dividing the value by the entire value and multiplying the result by 100, one may determine the percentage. The percentage calculation formula is (value/total value)100%.The word percentage comes from the Latin term per centum, which means "by the hundred." In the 16th century, the Latin phrase made its way into English. Later, it was shortened to percent and ended with a period.Use the formula percent change
Percent change = [tex]\frac{New - old}{old} * 100[/tex]
= 70- 30/30 * 100
= 40/30 * 100
= 133.3333333333% (increase)
Where: 30 is the old value and 70 is the new value.
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I need help please solving …
It takes the object about 26/49 minutes to travel 5 1/5 miles.
How long would it take the object to travel 5 1/5 miles?A mixed fraction is a non-integer that consists of a whole number and a proper fraction. An example of a mixed fraction is 1 1/2.
Speed measures how fast an object is moving with respect to time. Speed is the total distance travelled per time.
Speed = total distance / total time
In order to determine the total time it would take the object to travel the distance, divide the distance travelled by the speed.
Time = distance / speed
5 1/5 ÷ 9 4/5
26/5 ÷ 49 / 5
26/5 x 5/49 = 26 / 49 minutes
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which function is increasing? a. f(x) = (0.5)^x b. f(x) = (1/5)^x c. f(x) = 5^x d. f(x) = (1/15)^x
The function is increasing is f(x) = [tex]5^x[/tex]
For exponential functions: f(x) = [tex]a^{x}[/tex] (a>0 and a[tex]\neq 0[/tex] ), when A is greater than the function is increased.
0.5 <1, [tex]\frac{1}{15}[/tex]<1 , [tex]\frac{1}{5}[/tex]<1 , 5>1
so C is correct.
The exponential is a mathematical function denoted by the argument x is written as an exponent. Unless otherwise specified, the term generally refers to the positive-valued function of a true variable, although it are often extended to the complex numbers or generalized to other mathematical objects like matrices or Lie algebras. The exponential originated from the notion of exponentiation (repeated multiplication), but modern definitions (there are several equivalent characterizations) allow it to be rigorously extended to all or any real arguments, including irrational numbers. Its ubiquitous occurrence in pure and applied math led mathematician Walter to opine that the exponential function is "the most important function in mathematics".
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help pls pls pls pls pls pls
Answer:
It the square with 3/4 shaded. the point shows 0.75 and the square shows 75% which is 3/4.
The tape diagram shows that Elizabeth spent 919191 minutes, which was 70\%70%70, percent of her study time for her language exam, on conversation practice.
The total time needed for Elizabeth on the practice is 130 minutes.
What will the time be?It should be noted that Elizabeth spent 91 minutes, which was 70 percent of her study time for her language exam,
Let the total time be represented by x.
Therefore, 70% × x = 91
0.7 × x = 91
0.7x = 91
Divide
x = 91/0.7
x = 130
The total time needed is 130 minutes.
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The tape diagram shows that Elizabeth spent 91 minutes, which was 70 percent of her study time for her language exam, on conversation practice. What was the total time needed?
2 points
Donna Preski works 8 hours a day, 5 days a week. So far this year she
has worked 680 hours. How many weeks has she worked?
17 weeks
Step-by-step explanation:
you multiply the number of hours by the number of weeks, giving you 40, then divide the amount of total hours worked by 40, giving you 17
5 x 8 = 40
680/40 = 17
17 weeks.
hello people! if you have trouble in math in 8th grade pls dm me ill help
Step-by-step explanation:
Tell me the problem and I may help u
ASSIGN #1: Object A is moving 12 feet per second (ft/sec). Object B is moving 5 miles per
R.A. hour (mila/hr). Which object is moving faster
According to the given statement;
object A is moving faster by 8.184-5= 3.184
3.184 mph faster.
What is speed?The distance traveled in relation to the time it took to travel that distance is how speed is defined. Since speed only has a direction and no magnitude, it is a scalar quantity.
The most crucial scientific concept is measurement. Base or physical fundamental units are used to measure a wide range of measurable quantities. One such measurable quantity is speed, which calculates the ratio between the distance an object travels and the time needed to cover that distance. Let's explore speed in-depth in this session.
According to the given valus;
Speed of object A = 12 ft per sec
I foot per second = 0.682 mph
12 ft per sec = 0.682x 12
= 8.184 mph
object В speed = 5 mph
object A is moving faster than B.
object A is moving faster by 8.184-5= 3.184
3.184 mph faster.
Hence,object A is moving faster than B by 3.184 mph.
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What is the equation of the line in slope-intercept form that is perpendicular to the line y = x – 2 and passes through the point (–12, 10)?
y = x – 6
y = x + 6
y = x + 26
y = x + 10
The equation of the line that is perpendicular to given line is y = -x -2
Equation of a lineFrom the question, we are to determine the equation of the line
From the given information,
We have that the two lines are perpendicular
If two lines are perpendicular, the product of their slopes is -1
That is,
m₁m₂ = -1
Where m₁ is the slope of the first equation
and m₂ is the slope of the second equation
In the given equation,
y = x - 2
Compare to the general form of the equation of a line
y = mx + b
Where m is the slope
and b is the y-intercept
Thus,
In the equation, y = x - 2
Slope = 1
Therefore,
The slope of the equation we are to determine is -1
Also, from the given information,
The line passes through the point (-12, 10)
Using the point-slope form of a line
y - y₁ = m(x - x₁)
x₁ = -12
y₁ = 10
Thus,
y - y₁ = m(x - x₁)
y - 10 = -1(x - -12)
y - 10 = -1(x + 12)
y - 10 = -x -12
y = -x -12 + 10
y = -x -2
Hence, the equation of the line that is perpendicular to given line is y = -x -2
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Back in 1997, Sally paid $11,448 for a new automobile. This amount included
the 6% sales tax. What was the price of the automobile without the tax? (Please show step by step)
Answer:
$10800
Step-by-step explanation:
$11,448 = 100% + 6%
= 100%
$11,448 = 106%
= 100%
Cross-multiply it :
$11,448 × 100% = × 106%
$11,448 × 100/100 = 106/100
$11,448 × 100/106 =
= $10800
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Take figure Q to figure R
1 unit left,2 units down and 90° clockwise rotation is the transformation of figure Q to make figure R.
What is the transformation of a graph?Transformation is rearranging a graph by a given rule it could be either increment,decrement, reflection, or rotation.
Reflection is a mirror image of a graph about any axis.
It seems that figure R is the rotation of Q clockwise by 90°.
In figure Q,
The Coordinate of the bottom left point of it is (3,1) if we rotate by 90° then it will remain at (3,1).
The coordinate of the same point in figure R is (2,-1)
So,
3 + x = 2 → x = -1 (1 unit left)
1 + y = -1 → y = -2 (2 units down)
Hence "1 unit left,2 units down and 90° clockwise rotation is the transformation of figure Q to make figure R".
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Evaluate the given expression when x = 3.
2
x + x² +2:
Answer:
3.2 + 3.2squared + 2 = 15.44
Step-by-step explanation:
Answer:
Step-by-step explanation:
x + x^2 + 2
3.2 + 3.2^2 + 2
3.2 + 10.24 + 2 = 15.44
When designing a simulation where darts are thrown at targets, what assumptions need to be made and why are they needed?
The assumptions need to be made in the dart simulation is that the object lands within the target area, and that it is equally likely that the object will land anywhere in the region. These are needed because in the real world it will not be equally likely to land anywhere in the region.
Dart game:
Basically, the dart game board consists of sisal fibers or boar bristles and cork. An 18 inch diameter board is divided into 20 sections.
Thin metal structures are used to design the dividing lines and with the same materials the numbers are designed.
Sometimes the manufactures opt for printing number formats. The board should be positioned on the wall in such a manner that the bull’s eye should be 5ft 8 inch above the floor.
Given,
Here we need to find When designing a simulation where darts are thrown at targets, what assumptions need to be made and why are they needed.
While looking at the definition of the dart game board,
We know that, we have to do the following,
We assume that the object lands within the target area, and that it is equally likely that the object will land anywhere in the region. These are needed because in the real world it will not be equally likely to land anywhere in the region.
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