The following equations are equivalent:
2 + x = 5
x + 1 = 4
Negative 5 + x = negative 2
This is because, in each equation, x is the same variable, and it has the same value on both sides of the equation.
In the first equation, x is equal to 3.
In the second equation, x is equal to 3
In the third equation, x is equal to -3
Note that the equation 9 + x = 6 and x + (negative 4) = 7 are not equivalent as these equations have different values for x.
Review the graph of function f(x), which is defined for -
6 ≤x≤ 8.
Which one-sided limit does not exist?
Olim f(x)
X-2*
O
O
lim f(x)
x-2"
lim f(x)
x--6*.
lim f(x)
x--6
The one-sided limit that does not exist is given as follows:
lim x -> -6^- f(x).
How to obtain the one sided limit that does not exist?A one sided limit will not exist when it is outside the domain of the function.
The domain of a function is composed by the set of all the input values of the function, hence on the graph it is given by the values of x.
For this problem, the domain is then given as follows:
-6 ≤ x ≤ 8.
To the left of -6, the function is not defined, hence the one-sided limit that does not exist is given as follows:
lim x -> -6^- f(x).
Meaning that the correct option is given by the last option.
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PLEASEEEEE HELP I NEEEED JUST ONE
the above question is an example with answer
Answer: Pretend the function g(x)=4x+1 is x and replace x in f(x) with it
Step-by-step explanation:
Graph the function f(x)=√x+3.
What are the minimum and maximum values on the interval [-11, 5)?
Write your answers in the boxes.
Minimum:
Maximum:
The values of maximum and minimum values are 11i + 3 and √5+ 3 .
What is Function?Function can be defined in which it relates an input to the output. Functions are relationships in mathematics where each input has a particular output. Functions are often used in science and mathematics. In this section, we will learn the definitions of functions, various kinds of functions, and properties, along with examples to help us understand.
Given,
The function is f(x) = √x+3.
We have to find the maximum and minimum values on the interval [-11,5]
So,
f'(x) = 1/2√x
As when,
f'(x) = 0
has no solution than,
f(-11) = √-11 + 3
= 11i + 3
f(5) = √5+ 3 .
Therefore, The values of maximum and minimum values are 11i + 3 and √5+ 3 .
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In economics, a service is
Answer:
providing goods
Step-by-step explanation:
i need 20 words so here, you can you go without the hard rock you can you go without it is not the first half way to you by the
12
R
T
37
35
Enter the ratio equivalent to tan(R).
>S
Answer:
[tex]\frac{35}{12}[/tex]
Step-by-step Explanation:
The tangent of an acute angle in a right triangle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.
Evaluate the following integral: ∫20(45t3−34t2+25t)dt
The integral[tex]∫20(45t^3-34t^2+25t)dt[/tex] can be evaluated by using the power rule of integration, which states that the derivative of x^n is [tex]nx^(n-1)[/tex]. This rule can be applied to each term of the integral separately.
The first step is to integrate [tex]∫20(45t^3-34t^2+25t)dt[/tex] with respect to t. By using the power rule, we can find the antiderivative of each term inside the parentheses:
[tex]∫45t^3 dt = (45/4)t^4 + C[/tex] (the antiderivative of 45t^3 is (45/4)t∧4)
[tex]∫34t^2 dt = (34/3)t^3 + C[/tex] (the antiderivative of 34t^2 is (34/3)t∧3)
[tex]∫25t dt = (25/2)t^2 + C[/tex] (the antiderivative of 25t is (25/2)t∧2)
Now, we can substitute these results back into the original integral:
[tex]20(∫45t^3 dt - ∫34t^2 dt + ∫25t dt) = 20((45/4)t^4 + (34/3)t^3 + (25/2)t^2) + C= 20(15t^4-11t^3+25t^2) + C[/tex]
So, the evaluated integral for [tex]∫20(45t^3-34t^2+25t)dt[/tex] is [tex]20(15t^4-11t^3+25t^2) + C.[/tex]
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The first and second terms of an exponential sequence (G.P.) are the first and third terms of a linear sequence (A.P.). The fourth term of the linear sequence is 10 and the sum of its first five terms is 60. Find the first four terms of the linear sequence.
Answer:
Step-by-step explanation:
A typical geometric sequence can be represented as
c
0
a
,
c
0
a
2
,
⋯
,
c
0
a
k
and a typical arithmetic sequence as
c
0
a
,
c
0
a
+
Δ
,
c
0
a
+
2
Δ
,
⋯
,
c
0
a
+
k
Δ
Calling
c
0
a
as the first element for the geometric sequence we have
⎧
⎪
⎨
⎪
⎩
c
0
a
2
=
c
0
a
+
2
Δ
→
First and second of GS are the first and third of a LS
c
0
a
+
3
Δ
=
10
→
The fourth term of the linear sequence is 10
5
c
0
a
+
10
Δ
=
60
→
The sum of its first five term is 60
Solving for
c
0
,
a
,
Δ
we obtain
c
0
=
64
3
,
a
=
3
4
,
Δ
=
−
2
and the first five elements for the arithmetic sequence are
{
16
,
14
,
12
,
10A typical geometric sequence can be represented as
c
0
a
,
c
0
a
2
,
⋯
,
c
0
a
k
and a typical arithmetic sequence as
c
0
a
,
c
0
a
+
Δ
,
c
0
a
+
2
Δ
,
⋯
,
c
0
a
+
k
Δ
Calling
c
0
a
as the first element for the geometric sequence we have
⎧
⎪
⎨
⎪
⎩
c
0
a
2
=
c
0
a
+
2
Δ
→
First and second of GS are the first and third of a LS
c
0
a
+
3
Δ
=
10
→
The fourth term of the linear sequence is 10
5
c
0
a
+
10
Δ
=
60
→
The sum of its first five term is 60
Solving for
c
0
,
a
,
Δ
we obtain
c
0
=
64
3
,
a
=
3
4
,
Δ
=
−
2
and the first five elements for the arithmetic sequence are
{
16
,
14
,
12
,
10
Which compound inequality is represented by the graph?
Answer:
the third one
Step-by-step explanation:
an open circle means it does not include that number. therefore, it needs to be x is less than -2. a closed circle means it includes that number. therefore, x is greater than or equal to 4
Use the graph to write a linear function that relates y to x.
The required equation is y=x/3+3
What are linear equations?Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.
Given here the line passes through the points (3,4) and (0,3)
Thus the slope intercept form of the line passing through these points is
y=x/3+3 where m=4-3/3-0 is the slope of the line
Hence, The required equation is y=x/3+3
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What are the indices for the directions indicated by the two vectors in the following sketch?
The indices for the directions are indicated by the two vectors in the following sketch - [1 0 0] and [ 2 0 3].
Miller Indices of Direction Vector:
The Miller indices of direction are rationalized components of the direction vectors taken in all crystallographic directions. They are indicated by [[u v w ]]. They are always defined as the smallest integers, so if they occur in fractional or decimal form, we need to convert them into the smallest integral value by algebraic manipulation.
The indices of direction 1.
Let the length of direction 1 along the x-axis be X units. The length of the vectors along the y and z axes is 0.
[ X 0 0 ]
⇒ [tex]\left[\begin{array}{ccc}0&0&0\\X'&X'&X'\\\end{array}\right][/tex]
Divide each length by X to convert it into the smallest integer.
⇒ [1 0 0]
And, this is the Miller indices of the direction vector 1.
So, the Miller indices of the direction vector 1 are [ 1 0 0].
Direction 2
The indices of direction 2.
Let the length of direction 2 along the x-axis be X units. The length of the vector along the y and z axes are 0.
[ 0.2 0 0.3 ]
⇒[ 2 0 3 ]
Multiply each fractional length by 10 to convert it into the smallest integer.
So, the Miller indices of the direction vector 2 are [ 2 0 3].
Therefore, The indices for the directions are indicated by the two vectors in the following sketch - [1 0 0] and [ 2 0 3].
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Decrease 120% by 15%
By simply dividing the reduced value by 12, the value of 120 decreases by 12%, yielding a percentage drop of 102.
what is percentage ?In mathematics, a ratio or number expressed as a fraction of 100 is called a percentage. Also occasionally used are the acronyms "pct.," "pct," and "pc." However, the percentage symbol "%" is widely used to represent it. The % quantity is dimensionally empty. Basically, percentages are fractions when the denominator is 100. A percent symbol (%) should be placed next to a number to indicate that it is a percentage. For instance, you score a 75% on a test if you properly answer 75 out of 100 questions (75/100). When calculating percentages, multiply the result by 100 after dividing the amount by the total. By multiplying (value/total) by 100%, the percentage is determined.
given
The value of the percentage decrease
= · 120 - (15% × 120)
= 120 - 15% × 120
= 85 ÷ 100 × 120
= 85 × 120 ÷ 100 = 102
You may calculate the percentage drop by simply dividing the lowered value by the original value and multiplying the result by 100.
In this case, Reduced Value equals Original Value - New Value.
By simply dividing the reduced value by 12, the value of 120 decreases by 12%, yielding a percentage drop of 102.
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Will this question be independent or dependent.
There are 8 boys and 6 girls on soccer team. The coach will select a captain and then select a co captain. What is the probability of selecting a boy then a girl
The probability of selecting a boy then a girl is 24/91
What is probability?Probability is defined as the chance of occurrence of an event
E. It is the ratio of the number of required outcome over the total of all possible outcomes in an even.
the given parameters that will help us to determine the probabilities are
There are 8 boysThere are 6 girls on soccer teamTotal number of Students in the soccer = 8+6 = 14The probability of the event is
P(E) = Pr(B) Then Pr(G)
Pr(E) = 8/14 *6/13
Simplify the fractions to have 48/182
= 24/91
Conclusively the selection is 24/91
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Xavier’s car used 1 1/3 gallons to travel 59 miles. How many miles can the car go on one gallon of gas
The car can go 44.25 miles on one gallon of gas
How to calculate the number of miles the car can travel on one gallon?Xavier's car used 1 1/3 gallons to travel for 59 miles
The number of miles travelled on one gallon of gas can be calculated as follows
1 1/3 gallons= 59 miles
1 gallon= x
Cross multiply both sides
4/3x= 59
4x= 177
x= 177/4
x= 44.25
Hence Xavier's car can travel 44.25 miles on one gallon of gas
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Fish tank cost $12.50 each fish cost $0.20 what is m and b and equation representing relationship
Answer:
y = 0.20x + 12.5
Q)Lets set the cost of the cost as the y-axis and the amount of fish as the x-axis. 12.50, a constant and the y-intercept, is the price when you don't have any fish.
0.2 is the slope and in this case, the amount of 1 fish.
0.2x + 12.5 is the total amount as every fish added adds 20 cents. 12.5 is the fishtank which you need to get before getting any fish.
Can someone help me with this 8 exercises ?, thanks a lot!
Answer:
.........,..........,.
Step-by-step explanation:
.................. .....
The undergraduate
grade point
averages (UGPA) of students taking
an admissions test in a recent year
can be approximated by a normal
distribution, as shown in the figure.
(a) What is the minimum UGPA that
would still place a student in the top
10% of UGPAS?
(b) Between what two values does the
middle 50% of the UGPAS lie?
Mean=3.24
Std.=0.17
a) The Corresponding minimum UGPA = 3.70
b) The range of middle 50% values will be: (3.28, 3.52).
What is the z-score?
A z-score (also known as a standard score) is a measure of how many standard deviations an individual data point is from the mean of a distribution. A z-score is calculated by subtracting the population mean from an individual data point, and then dividing that number by the population standard deviation.
a) z score corresponding to top 5% area = 1.645
Hence,
Corresponding minimum UGPA = 3.40 + 1.645*0.18 = 3.70
b) z score corresponding to middle 50% area = -0.67, 0.67
Hence,
The range of middle 50% values will be:
(3.40 - 0.67*0.18, 3.40 + 0.67*0.18)
(3.28, 3.52)
Hence,
a) The Corresponding minimum UGPA = 3.70
b) The range of middle 50% values will be: (3.28, 3.52).
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What are the measurement’s of questions 1,2 and 3
Angles in parallel lines are formed when two parallel lines intersect with another line known as a transversal. So here ∠y is 40° and ∠z is 140°.
What are the angles over parallel lines?Parallel lines form a pair of angles when cut by a transversal. As a result, corresponding angles are equal, as are alternate interior angles, alternate exterior angles, vertical angles, and the sum of interior angles on the same side of the transversal.We know that sum of angles over a straight line is 180°
So here ∠x + 140° = 180°
So ∠x = 180 - 140
Therefore ∠x = 40°
So in this figure ∠x = ∠y , Since they are corresponding angles are equal.
Therefore ∠y = 40°
So ∠z will be 140° . Since ∠y = 40° its opposite angle will also be 40°.
So ∠z + 40° = 180°
Therefore ∠z = 140°
So the angles ∠y = 40° and ∠z = 140°.
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George is 48 inches tall and growing at a rate of 2 inches a year his sister is 42 inches tall and growing at a rate of 3 inches in a year if their growth rate continues how long will it be before Georgia sister is taller than he is
Answer: It will take 7 more years for George’s sister to be taller than him.
Step-by-step explanation:
Answer:
Step-by-step explanation:
7 years
7. Choose all the expressions that are equal
to 1.25 10.
0 12.5-
12.5 ÷ 10²
0.125 100
O 1,250 104
0 12.5 ÷ 1
125 - 1,000
Upon solving the decimals, The expression which is equivalent to 0.125 are -12.5 ÷ 10²⇒ 0.125 and 1,250 ÷ 10⁴ ⇒ 0.125.
A decimal is a number that is divided into two parts: a whole and a fraction. Between integers, decimal numbers are used to express the numerical value of complete and partially whole quantities.
Decimal fractions and recurring (repeating or non-terminating, like) decimals are the three different sorts of decimals (a.k.a. converting a decimal into a fraction whose denominator is a power of ten).
1.25 ÷ 10 ⇒ 0.125
Upon solving the decimals,
12.5 ÷ 10² ⇒ 0.125
0.125 ÷ 100 ⇒ 0.00125
1,250 ÷ 10⁴ ⇒ 0.125
12.5 ÷ 1 ⇒ 12.5
125 ÷ 1,000 ⇒ 0.0125
The expression which is equivalent to 0.125 are -
12.5 ÷ 10² ⇒ 0.125
1,250 ÷ 10⁴ ⇒ 0.125
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3y-5x=-9 use technology to find points and graph
The points to be graphed are (0, -3) and (1.8, 0). The graph of the equation is shown in the attached image
How to find the points and graph?
In order to graph the equation of the line 3y-5x=-9:
First, find the value of x when y = 0:
3y-5x=-9, when y = 0:
3(0) - 5x=-9
- 5x = -9
x = 9/5
x = 1.8
Also, find the value of y when x = 0:
3y-5x=-9, when x = 0:
3y - 5(0) = -9
3y = -9
y = -9/3
y = -3
Therefore, the values to be plotted on our graph are (0, -3) and (1.8, 0). The image of the graph is attached
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Selkirk Company obtained a $15,000 note receivable from a customer on January 1, 2021. The note, along with interest at 9%, is due on July 1, 2021. On February 28, 2021, Selkirk discounted the note at Unionville Bank. The bank’s discount rate is 12%.
Required:
Prepare the journal entries required on February 28, 2021, to accrue interest and to record the discounting for Selkirk. Assume that the discounting is accounted for as a sale. (Do not round intermediate calculations. If no entry is required for a transaction/event, select "No journal entry required" in the first account field.)
The journal entries required on February 28, 2021, for Selkirk Company to accrue interest and to record the discounting are as follows:
Journal Entries:Debit Interest Receivable $225
Credit Interest Revenue $225
Debit Cash $15,048
Debit Interest Expense $177
Credit Note Receivable $15,000
Credit Interest Receivable $225
What are the steps in recording a discounted note receivable?When a note receivable is discounted, the following steps are followed:
Compute the maturity valueCompute the discount (discount rate times maturity value)Compute the proceeds (maturity value less discount)Compute the net interest income or expense (proceeds less carrying value)Prepare the journal entries.Transaction Analysis:February 28, 2021
Interest Receivable $225 Interest Revenue $225
Cash $15,048 Interest Expense $177 Note Receivable $15,000 Interest Receivable $225
Note receivable = $15,000
Interest = 9%
Maturity period = 6 months (Jan 1, 2021, to July 1, 2021) or 180 days
Discount date = February 28, 2021
Maturity value = $15,675 ($15,000 + $15,000 x 9% x 6/12)
Discount = $627 ($15,675 x 12% x 120/360)
Proceeds = $15,048 ($15,675 - $627)
Accrued interest = $225 ($15,000 x 9% x 60/360)
Note's carrying value on February 28, 2021, = $15,225 ($15,000 + $225)
Interest expense = $177 ($15,048 - $15,225)
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Question 1 (1 point)
Simplify-9(x + 3) + 15x
06x-27
33x
06x + 27
24 + 27 I will give 100 points pls hurry
Answer:
A) 6x - 27
Step-by-step explanation:
Given expression:
[tex]-9(x + 3) + 15x[/tex]
Apply the distributive property:
[tex]\implies -9 \cdot x -9 \cdot 3+15x[/tex]
[tex]\implies -9x -27+15x[/tex]
Collect like terms:
[tex]\implies -9x+15x -27[/tex]
Combine like terms:
[tex]\implies 6x -27[/tex]
Answer:
[tex] \sf \: a) \: 6x - 27[/tex]
Step-by-step explanation:
Now we have to,
→ simplify the given expression.
The expression is,
→ -9(x + 3) + 15x
Let's simplify the expression,
→ -9(x + 3) + 15x
→ -9x - 27 + 15x
→ (-9x + 15x) - 27
→ (6x) - 27
→ 6x - 27
Hence, the answer is 6x - 27.
Seven less than the product of 9 and a number equals 8. Use the variable b for the unknown number
The equation formed by the sentence is 9b - 7 = 8.
What is equation ?
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 equations 3x + 5 and 14, which are separated by the 'equal' sign.
A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.
A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is used.
Let the variable be b
By the given sentence we get the equation
9b - 7 = 8
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Marcella has a red, square tablecloth with a diagonal of ^6 feet. She also has a white, square tablecloth with a diagonal of ^12 feet. Jordan says that the length of the diagonal of the white tablecloth is twice the length of the diagonal of the red tablecloth. Is he correct.
Answer:
Out of all possible choices you've shown, I'd say the best answer would be C
Step-by-step explanation:
Find the two missing numbers in the following sequence: 1, 8, ?, 16, 17, 24, 25, 32, 33, ?
Answer:
7 and 40
Step-by-step explanation:
for you to get the next number you have to add 7 to that number...then add 1 to the number you have gotten then continue like that
eg: to get 8 you had to add 7 to 1 now to get the next number add 1 to 8 to get 9 then add 7 to 9 to get 16 then continue like that
How many terms each expression has in 5 - g
The expression 5 - g has two terms in it, "5" and "g" where 5 is a constant and g is a variable.
How can the terms of an algebraic expressions be found?To find the number of terms in an algebraic expression, you find out the number of signs that separate the terms and these signs only include the plus and minus signs. In this case 5 - g has two terms, 5 and g.
A term can be a number, a variable, a product of two or more variables, or a number and a variable product. An algebraic expression can be made up of a single term or a group of terms. For example, the two terms in the expression 4x + y are 4x and y. It should be noted that the terms combine to form the expression.
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Please help me on this asap
The new points of the trapezoid are P'(4, -8), Q'(8, -8), R'(8, 4) and S'(-8, 4)
What is an equation?An equation is an expression relating two or more numbers and variables.
Dilation is the increase or decrease in size of a figure by a scale factor. The rule for dilation is:
(x, y) ⇒ (kx, ky)
The vertices of the trapezoid is P(1, -2), Q(2, -2), R(2, 1) and S(-2, 1)
If the trapezoid is dilated by a scale factor of 4 about the origin, the new points are:
P'(4, -8), Q'(8, -8), R'(8, 4) and S'(-8, 4)
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If sum of 5 numbers in AP is 40 then find the middle term
Answer:
8
Step-by-step explanation:
Let the AP numbers be: ( a - 3d ), ( a - d ), a, ( a + d ), ( a + 3d )
We are given that sum of all these numbers is 40.
⇒ a - 3d + a - d + a + a + d + a + 3d = 40
⇒ 5a + 4d - 4d = 40
⇒ 5a = 40
⇒ a = 40 / 5 = 8
We know that the middle term of the five numbers given is 'a'.
As a result, the given AP's middle term is 8.
Good luck <3
For this item, a non- integer answer should be entered as fraction using / as the fraction bar . Simplify the numeral expression. 2/3 devised 2/4 + ( 3/4 + 1/6) divided by 1/3
Answer:67/24
Step-by-step explanation:
i did it
Last Wednesday, students could choose ham or turkey sandwiches for lunch. The cafeteria made 400 sandwiches in all, 288 of which were turkey. What percentage of the sandwiches were turkey sandwiches?
47 percent of the sandwiches had turkey.
How the Percentage is calculated?Find the whole amount of what you're looking for to get a percentage of.
To calculate the percentage, divide the number.
Add 100 to the value.
A % is a quantity or ratio that, in mathematics, represents a portion of one hundred. It's frequently represented by the sign "%" or just "percent" or "pct." For instance, 35% is equal to the fraction 0.35 or the decimal 0.35.
The value of the number out of 100 is the proportion of the number. For instance, there are 26 females and 24 boys in a class. As a result, 52 out of 100 students in the class are females, or 52% of the class.
The Latin word "per centum," which meaning "by the hundred," was the source of the English word "percentage." Percentages.
According to our question
47+53= 100%,
So 1= 1%
= 47x1= 47, So it equals 47%.
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