The actual solution must be approximated to the tenth place.
How do you solve an equation to the nearest tenth?
To round the decimal number to its nearest tenth, look at the hundredth number. If that number is greater than 5, add 1 to the tenth value. If it is less than 5, leave the tenth place value as it is, and remove all the numbers present after the tenth place.
To estimate the tenth place, you have to determine the actual solution and the approximate.
Assume the solution to the system of equations is:
(x, y), (1.25, 1)
1.25 is to the hundredth place.
So, the next thing is to approximate 1.25 to 1.3 (the tenth place).
So, we have:
(x, y), (1.3, 1)
Hence, the actual solution must be approximated to the tenth place.
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Hurry please I’ll give you 20 points
The general rule is power of power. It can be represented by (x^m)^n = x^mn.
What is an exponent?
The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself.
Now complete the given table:
Problem to First repeated second repeated Power of
simplify multiplication multiplication the form of a^n
(2²)³ 2²×2²×2² 2×2×2×2×2×2 2⁶
(5³)⁴ 5³ × 5³ × 5³ × 5³ 5×5×5×5×5×5×5×5×5×5×5×5 5¹²
(7³)⁴ 7³ × 7³ × 7³ × 7³ 7×7×7×7×7×7×7×7×7×7×7×7 7¹²
((3x)²)³ (3x)²×(3x)²×(3x)² 3x×3x×3x×3x×3x×3x (3x)⁶
(4y²)³ (2y)²×(2y)²×(2y)² 2y×2y×2y×2y×2y×2y (2y)⁶
The general rule is (x^m)^n = x^mn. The name of the rule is power of power.
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Find the solutions to x² = 24.
OA. x= 16-√4
B. x = +2√6
O C.
x = +6√ √2
OD. x +4√6
Answer:
x = 2[tex]\sqrt{6}[/tex]
Step-by-step explanation:
[tex]\sqrt{24}[/tex] = [tex]\sqrt{(2)(2)(2)(3)}[/tex] We can pull out a pair of 2's
2[tex]\sqrt{(2)(3)\\}[/tex] = 2[tex]\sqrt{6}[/tex]
Nicole randomly selects a red card from a standard deck of cards. What outcome is the complement of drawing a red card?
Selecting an ace
Selecting a heart
Selecting a face card
Selecting a black card
The complement of the event: "drawing a red card" is the last option:
"Selecting a black card"
What outcome is the complement of drawing a red card?The complement of an event is the set of all the outcomes such that the original event is false.
For example, the complement of drawing a red card, would be "not drawing a red card"
We know that there are two types of coloes, black and red.
Then "drawing a black card" is equivalent to "not drawing a red card"
Thus, the complement is the last option:
"Selecting a black card"
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I need help please! In each case below, list the lettered measures for angles or sides in descending order (FROM GREATEST TO LEAST).
Answer:
β, α, γ
Step-by-step explanation:
The figure only shows us the side lengths of the triangle, but is asking for the angles.
Thus, we have to use the angle relationships of a triangle to answer the question.
⭐What are the angle relationships of a triangle?
the angle opposite of the largest side is the largest anglethe angle opposite of the smallest side is the smallest angleα° is opposite of the side length with 9 cm.
β° is opposite of the side length with 12 cm.
γ° is opposite of the side length with 5 cm.
∴ The angles from highest to the least are β, α, γ
IF THIS RESPONSE HELPED YOU, PLEASE MARK IT THE BRAINLIEST :-)
Answer:
Step-by-step explanation:
The answer should be BAY but if i check it don't work
Before sending track and field athletes to the Olympics, the U. S. Holds a qualifying meet. The upper box plot shows the top 12 men's long jumpers at the U. S. Qualifying meet. The lower box plot shows the distances (in meters) achieved in the men's long jump at the 2012 Olympic games. Which pieces of information can be gathered from these box plots?
We require median, interquartile range, outliers, minimum and maximum value.
What are statistics?
Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data.
From the upper box plot representing the top 12 men's long jumpers at the U.S. Qualifying meet, we can gather the following pieces of information:
The median (middle value) of the data is around 7.6 meters, as indicated by the line in the center of the box.
The interquartile range (IQR), which is the range between the first and third quartiles, is approximately 0.4 meters, as indicated by the height of the box.
There are some outliers or values that fall outside the range of the box, which is represented by the dots or asterisks outside the box.
The minimum and maximum values for the data are around 7.3 meters and 8.0 meters, respectively, as indicated by the lower and upper ends of the whiskers.
From the lower box plot representing the distances achieved in the men's long jump at the 2012 Olympic games, we can gather the following pieces of information:
The median (middle value) of the data is around 8.0 meters, as indicated by the line in the center of the box.
The interquartile range (IQR), which is the range between the first and third quartiles, is approximately 0.5 meters, as indicated by the height of the box.
There are some outliers or values that fall outside the range of the box, which is represented by the dots or asterisks outside the box.
The minimum and maximum values for the data are around 7.5 meters and 8.4 meters, respectively, as indicated by the lower and upper ends of the whiskers.
The main difference between the two box plots is the median value, which is 0.4 meters apart and the IQR for the Olympic games is slightly bigger than the Qualifying meet.
Hence, we require median, interquartile range, outliers, and minimum and maximum values.
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We require median, interquartile range, outliers, and minimum and maximum values.
What are statistics?
Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data.
From the upper box plot representing the top 12 men's long jumpers at the U.S. Qualifying meet, we can gather the following pieces of information:
The median (middle value) of the data is around 7.6 meters, as indicated by the line in the center of the box.
The interquartile range (IQR), which is the range between the first and third quartiles, is approximately 0.4 meters, as indicated by the height of the box.
There are some outliers or values that fall outside the range of the box, which is represented by the dots or asterisks outside the box.
The minimum and maximum values for the data are around 7.3 meters and 8.0 meters, respectively, as indicated by the lower and upper ends of the whiskers.
From the lower box plot representing the distances achieved in the men's long jump at the 2012 Olympic games, we can gather the following pieces of information:
The median (middle value) of the data is around 8.0 meters, as indicated by the line in the center of the box.
The interquartile range (IQR), which is the range between the first and third quartiles, is approximately 0.5 meters, as indicated by the height of the box.
There are some outliers or values that fall outside the range of the box, which is represented by the dots or asterisks outside the box.
The minimum and maximum values for the data are around 7.5 meters and 8.4 meters, respectively, as indicated by the lower and upper ends of the whiskers.
The main difference between the two box plots is the median value, which is 0.4 meters apart and the IQR for the Olympic games is slightly bigger than the Qualifying meet.
Hence, we require median, interquartile range, outliers, and minimum and maximum values.
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The graph of function f is shown. An exponential function with vertex at (1, 3) and passes through (minus 2, 10), (8, 2) also intercepts the y-axis at 4 units. Function g is represented by the equation. g ( x ) = 4 ( 1 4 ) x + 2 Which statement correctly compares the two functions? A. They have the same y-intercept but different end behavior. B. They have different y-intercepts and different end behavior. C. They have the same y-intercept and the same end behavior. D. They have different y-intercepts but the same end behavior.
Answer:
Without being able to see the graph, it is not possible for me to accurately compare the two functions. Is it possible for you to provide more information about the functions or the graph?
Answer:
Step-by-step explanation:
graph please
Cristiano is saving money to buy a bike that costs $189. He saved $99 so far. He plans on saving $10 each week. In how many week will he have enough money to the bike?Use the bar diagram to solve arithmetically. Then use an equatuio to slove algebraically.
Answer:
It will take him 9 weeks to be able to buy the bike.
Cristiano is saving money to buy a bike that costs $189. He saved $99 so far. He plans on saving $10 each week. The correct answer is 9 weeks.
What were the steps to lead us to this answer?So, we have:
- Cost of the bike = $189
- Money saved = $99
- Money saving each week = $10
We are trying to find how many weeks will he have enough money to the bike.
So, we are going to multiply and add the numbers to find are answer:
→ (n × $ 10) + $ 99 = $ 189
→ n × $ 10 = $ 90 n = $ 90 $ 10 n=9 weeks.
Therefore, Cristiano is saving money to buy a bike that costs $189. He saved $99 so far. He plans on saving $10 each week. The correct answer is 9 weeks.
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A guy wire is attached to an upright pole 6 meters above the ground. If the wire is anchored to the ground 5 meters from the
base of the pole how long is the wire? Give your answer to two decimals.
A guy wire is attached to an upright pole 6 meters above the ground. If the wire is anchored to the ground 5 meters from the base of the pole 7.81 m long is the wire. This can be solved by using the concept of Pythagoras theorem.
What is Pythagoras theorem?The widely accepted geometric principle known as the Pythagorean Theorem states that the square on the hypotenuse of a right triangle equals the sum of the squares on its legs (the side opposite the right angle).
The hypotenuse side of a right-angled triangle's square is equal to the sum of its other two sides, according to Pythagoras' Theorem. The perpendicular, base, and hypotenuse of this triangle are its three designated sides.
Let, assume ΔABC is a right-angled triangle
where, AC = 6m be the pole.
AB = 5m is the length of a guy wire and is attached to stake B
By Pythagoras theorem,
BC² = AB² + AC²
or, BC² = (5)² + (6)²
or, BC² = 36 + 25
or, BC = √61 m
or, BC = 7.81 m
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If $3x 7\equiv 2\pmod{16}$, then $2x 11$ is congruent $\pmod{16}$ to what integer between $0$ and $15$, inclusive
2x 11 is congruent to 13 mod 16, if 3x 7 is congruent to 2 mod 16.
If 3x 7 is congruent to 2 mod 16, then 2x 11 is congruent mod 16 to what integer between 0 and 15, is inclusive.
To find the solution of 2x 11 congruent mod 16, given 3x 7 congruent to 2 mod 16, we can first use the given equation to find the value of x and then substitute it into the second equation.
First, we can solve for x in the given equation:
3x 7 is congruent to 2 mod 16
3x is congruent to 2 mod 16
x is congruent to 6 mod 16
Now that we know that x is congruent to 6 mod 16, we can substitute it into the second equation:
2x 11 is congruent to 2(6) 11 which is congruent to 13 mod 16
So the solution is that 2x 11 is congruent to 13 mod 16.
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PLEASE HELP ASAP. I WILL GIVE BRAINLIEST!!!
Which of the following is not an expression
A. 7 - 5x
B. 2 + 3x = 8
C. x/2 + 1
D. 2x + 6
Answer:
B) 2 + 3x = 8
Step-by-step explanation:
Option B is not an expression as expressions do not have equal signs.
Alex is planning to surround his pool ABCD with a single line of tiles. How many units of tile will he need to surround his pool
The number of units that tile will he need to surround his pool is 19.82units.
this question is of quadratic equation ,
The number of units of tile simply refers to the perimeter.
So, we need to find all the sides of the rectangle.
Now, we have,
AB = 4.24 units
BD = 7.07 units.
So, we can find AD using pythagoras theorem.
So,
(AD)² + 4.24² = 7.07²
(AD)² + 17.978 = 49.985
(AD)² = 49.985 - 17.978
AD = √32.007
AD = 5.66 units
AD = BC = 5.66 units
Likewise, AB = DC = 4.24 units
Thus,
perimeter = 2(5.66) + 2(4.24) = 19.8 units.
The number of units that tile will he need to surround his pool is 19.82units.
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A person loans his friend $500. They agree to an annual interest rate of 5%.
Write an expression for computing the amount owed on the loan, in dollars, after 1 years If no payments are made.
If no payments are made then the then after 1 year the interest will go by 5% , therefore the amount to be paid will become , P + 25 = 525 $.
Principle + 5% of 500
Therefore, the equation becomes ,
Amount = P + 25
To calculate the interest ,
interest = principal × interest rate × term
= 500 x 5 x 1
= 2500.
A loan is defined as a thing or money which is borrowed, especially a sum of money that is expected to be paid back with an interest rate which is fixed by both the parties.
Loans are typically taken or granted by by corporations, financial institutions, and governments. They allow for growth in the overall money supply in an economy and open up competition by lending to new businesses.
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Find the length of the third side. If necessary round to the nearest tenth
The side lengths of a right-angle triangle can be calculated using the Pythagorean Theorem. Which states that the square of the hypotenuse is equal to the sum of squares of the other sides in the triangle.
[tex]a^2+b^2=c^2[/tex]
the hypotenuse is always the longest side of a triangle and is always the opposite side length to the right anglerearranging the equation can help calculate the third side:
[tex]c^2-a^2=b^2[/tex]
[tex](5)^2-(4)^2=b^2[/tex]
[tex]25-16=b^2[/tex]
[tex]9=b^2[/tex]
[tex]\sqrt{9}=\sqrt{b^2}[/tex]
[tex]{ {{b_1=+3} \atop {b_2=-3}} \right.[/tex]
note: a length can never be negative so never take into account a negative answer
b = 3
Is horizontal the Y?
Yes, if the value of y = 0 then it makes the horizontal line.
The term horizontal line is defined as one that goes from left to right.
And here we also know that they are parallel to the x –axis in the coordinate plane.
And the horizontal line has a slope of zero.
While we looking into the move along the right of the line, then it does not rise or fall at all.
Here we have to the that the following factors are also included in feature:
In as the horizontal line is parallel to the x-axis and it is parallel to the horizon.
Where as the horizontal line is a sleeping line and it is also defined as can be a sleeping, standing, or a slanting line.
Where the horizontal line is perpendicular to the y-axis.
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Elizabeth has 214 gallons of milk in her refrigerator, and she drinks 23 of the quantity. How much milk does Elizabeth drink?
Answer:
9 days
Step-by-step explanation:
We know
Elizabeth has 214 gallons of milk; she drinks 23 of the quantity each day.
We take
214 / 23 = 9 days
So, she can drink in 9 days
What is the surface area
of the square pyramid?
9 in
6 in
Answer:The Surface Area of Pyramid is 105 cm².
Step-by-step explanation:
What is Surface Area of Pyramid?
If “P” is the base perimeter, “l” is the slant height, and “B” is the base area, then the total surface area of the regular pyramid formula is given by (½)Pl + B Square units.
Given:
slant height, l= 8 cm
So, the base Perimeter = 4 x 5
= 20 cm
Now, area of the base = 5 cm x 5 cm
= 25 cm²
Then, surface area of a square pyramid
= 1/2 x slant height x base perimeter + area of base
= 1/2 x 8 x 20 + 25
= 80 + 25
= 105 cm²
BROO PLS SOMEONE HELP IM SO CONFUSED
The start of an arithmetic sequence is shown below.
Work out the nth term
Work out the 30th term in this sequence.
4 - 13 - 22 - 31
The 30th term of the arithmetic sequence is 265
What is an arithmetic sequence in math?
Arithmetic sequences are those in which each term is increased by the addition or subtraction of a constant k. In contrast to a geometric sequence, where each term rises by being multiplied by or divided by a constant k,A series of numbers is considered to be an arithmetic progression or sequence if there is a constant difference between the terms. Consider the mathematical progression with a common difference of 2 in the numbers 5, 7, 9, 11, 13, and so on.An is equal to a1 + d(n - 1), where d is the common difference across terms in the series, and a1 is the first term in the sequence.This is an arithmetic sequence since there is a common difference between each term. In this case, adding 9 to the previous term in the sequence gives the next term. In other words, [tex]a_{n}[/tex]= [tex]a_{1}[/tex]+ d ( n - 1 )
Arithmetic Sequence: d = 9
This is the formula of an arithmetic sequence.
[tex]a_{n}[/tex] = [tex]a_{1}[/tex] + d ( n - 1 )
Substitute in the values of [tex]a_{1}[/tex] = 4 and d = 9
[tex]a_{n}[/tex]= 4 + 9 ( n - 1 )
[tex]a_{n}[/tex]= 4 + 9n - 9
[tex]a_{n}[/tex] = 9n - 5
.30th term = [tex]a_{n}[/tex] = [tex]a_{1}[/tex]+ d ( n - 1 )
= [tex]a_{30}[/tex]= 4 + 9 ( 30 -1 )
[tex]a_{30}[/tex]= 4 + 9 x 29
[tex]a_{30}[/tex]= 265
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Please help
Dean collected data on the favorite sports of the students of two grades. The table shows the relative frequencies of rows for the data collected:
Favorite Sport
Swimming Running Volleyball Row totals
Grade 8 0.17 0.24 0.05 0.46
Grade 9 0.14 0.18 0.22 0.54
Column totals 0.31 0.42 0.27 1
Based on the data, which statement is most likely correct?
In Grade 8, 17 students liked swimming.
In Grade 9, 27% of students liked volleyball.
In Grade 9, 14 students liked running.
In Grade 9, 18% of students liked running.
Based on the data, the statement that is most likely correct is D. In Grade 9, 18% of students liked running.
How to illustrate the information?The ratio (fraction or proportion) of the number of times a data value appears in the set of all outcomes to the total number of outcomes is known as the relative frequency.
From the information, the Dean collected data on the favorite sports of the students of two grades.
Here, the table shows the relative frequencies of rows for the data collected:
Swimming Running Volleyball Row totals
Grade 8 0.17 0.24 0.05 0.46
Grade 9 0.14 0.18 0.22 0.54
Column totals 0.31 0.42 0.27 1
In the table, Grade 9, 18% of students liked running. This is Illustrated above. The correct option is D.
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A lawyer charges $500 to be put on retainer for a client. The lawyer also charges an hourly rate of $75 for work done. a.Identify the fixed cost (the constant).b. Identify the independent variable (x). c. Identify the dependent variable (y). d.Write an equation that describes the situation above.
The answer will start with 500 USD. For every hour, 75 USD is charged. We can multiply 'x' to 75 USD which will represent the amount of hours. The equation will now become, 'y = 75x + 500'. In most cases, like this one, y will represent the total cost. Here are the answers.
a. 75USD
b. x (amount of hours)
c. y (total cost)
d. y = 75x + 500
Hope I understood what you were asking and if not I'm really sorry <3
what is the answer of 0.08 divided by 48.86
Answer:
610.75
Step-by-step explanation:
48.86 divided by 0.08
What is the value of the expression 4x 3 x )+ 5x x 2 for x 3?
The value of the given expression 4x(3-x)+5x(x-2) when x = -3 is 3.
What are expressions?A phrase is considered a mathematical expression if it contains at least two numbers or variables and one or more mathematical operations.
A number is 6 more than half of the other number, which is x.
This statement is represented by the mathematical equation x/2 + 6.
So, we have the expression:
4x(3-x)+5x(x-2)
Now, the value of the expression when x = -3.
Insert values and calculate as follows:
4x(3-x)+5x(x-2)
4(-3)(3-(-3))+5(-3)((-3)-2)
-12(6)-15(-5)
-72 + 75
3
Therefore, the value of the given expression 4x(3-x)+5x(x-2) when x = -3 is 3.
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Correct question:
What is the value of the expression 4x(3-x)+5x(x-2) for x=(-3)?
nter (A,B,C,D)in order below if $A$, $B$, $C$, and $D$ are the coefficients of the partial fractions expansion of $$12\cdot\frac{x^3 4}{(x^2-1)(x^2 3x 2)}
The partial fraction expansion of (x³ + 4)/ ((x² - 1)(x² + 3x + 2)) is -3/ 4(x + 1) + 5/12(x - 1) + 4/3(x + 2) - 3/ 2(x + 1)². So the coefficients A = -3/4, B = 5/ 12, C = 4/3 and D = -3/2.
A partial fraction expansion is a way of expressing a rational function (a function that can be written as the ratio of two polynomials) as the sum of simpler fractions, each with a numerator that is a constant or a simple polynomial. The process of finding the partial fraction expansion of a rational function is also known as partial fraction decomposition.
The denominator is
(x² - 1)(x² + 3x + 2) = (x² - 1)(x² + x + 2x + 2)
(x² - 1)(x² + 3x + 2) = (x + 1)(x - 1)(x + 1)(x + 2)
So by partial fraction expansion
(x³ + 4)/ ((x² - 1)(x² + 3x + 2)) = (x³ + 4)/ ((x + 1)(x - 1)(x + 1)(x + 2))
(x³ + 4)/ ((x + 1)(x - 1)(x + 1)(x + 2)) = A/ (x + 1) + B/(x - 1) + C/(x + 2) + D/ (x + 1)²
A(x - 1)(x + 1)(x + 2) + B(x + 1)²(x + 2) + C(x + 1)²(x - 1) + D(x - 1)(x + 2) = x³ + 4
(A + B + C)x³ + (2A + 4B + C + D)x² + (-A + 5B - C + D)x + (-2A + 2B - C - 2D) = x³ + 4
Thus from coefficients of x³, x², x and 1,
A + B + C = 1
2A + 4B + C + D = 0
-A + 5B - C + D = 0
-2A + 2B - C - 2D = 4
Solving
A = -3/4, B = 5/ 12, C = 4/3 and D = -3/2
--The question is not clear, the question is given below--
"Enter (A,B,C,D) in order below if A, B, C, and D are the coefficients of the partial fractions expansion of
[tex]$$12\cdot\frac{x^3 + 4}{(x^2-1)(x^2 +3x+ 2)}[/tex] "
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I don’t know this question
help me
The number of groups of like terms is 3
What is an algebraic expression?An algebraic expression is defined as an expression made up of terms, variables, coefficients, constants, and factors.
These algebraic expressions are also composed of mathematical operations, such as;
AdditionSubtractionDivisionBracketParenthesesMultiplication, etcA term can be described a single variable, number or numbers and variables that are multiplied together.
From the information given, we have the terms;
3x¹³, 9x¹⁰, -1x¹³, -16x¹³, 3x¹⁰, 3¹³, 10x¹⁰, 13x¹⁰
The similar terms are;
3x¹³, 3x¹⁰, 3¹³
Hence, the number is 3
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Camille thinks that -(-4) has a positive value and Laura thinks -(-4) has a negative value. Who is correct?
b.94 inches?
2. At a hardware store, a tool set normally costs $80. During a sale this week, the toc
set costs $12 less than usual. What percentage of the usual price is the savings?
Explain or show your reasoning.
Answer:
12%
Step-by-step explanation:
Find m/R.
P
(3x + 5)°
2
(8.x-12)
S
8x-12+3x+5=180(sum of straight angles)
8x+3x-12+5=180
11x-19=180
11x=180-19
11x=161
x=161÷11
Step-by-step explanation:
sum of straight angles are 180
A. What must the side length of each square represent for the rectangle to correctly represent (0. 3). (0. 5)?
The side length of each square represent for the rectangle to correctly represent (0, 3) · (0, 5) is 1 units.
A rectangle represented by (0, 3) · (0, 5) has length 3 units and breadth 5 units. To represent that rectangles with minimum number of squares of same size, we calculate the highest common factor.
Highest Common Factor is a mathematical concept used to find the greatest number that divides two or more numbers without leaving a remainder. It is also known as the greatest common divisor (GCD) or the greatest common factor (GCF).
Highest common factor of 3 and 5 is 1 as both are prime numbers. So squares with side length 1 unit best represent the rectangle to correctly represent (0, 3) · (0, 5).
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Tyrell is traveling to Chicago, Illinois. He takes a cab service from the airport to his hotel. The table shows the linear relationship between the number of miles the cab travels, x, and the total fee, y.
Cab Fare
Number of Miles Total Fee
2 $17.00
5 $21.50
7 $24.50
10 $29.00
15 $36.50
What does the y-intercept mean in this situation?
When the cab travels 0 miles, the total fee will be $14.00.
When the cab travels 0 miles, the total fee will be $1.50.
For every additional mile the cab travels, the total fee increases by $14.00.
For every additional mile the cab travels, the total fee increases by $1.50.
The y-intercept in this situation means A. When the cab travels 0 miles, the total fee will be $14.00.
What is the y-intercept?The formula to find the y-intercept is y = f(x), where x = 0, and then solve for y.
The equation for a linear relationship is y = mx + b, where x is the independent variable, y is the dependent variable, m is the slope of the line, and b is the y-intercept.
Cab Fare
Number of Miles Total Fee
2 $17.00
5 $21.50
7 $24.50
10 $29.00
15 $36.50
Difference between 7 and 5 = 2
Difference between $24.50 and $21.50 = $3
Variable cost per mile (Slope) = Rise/Run
= $1.50 ($3/2)
y = mx + b
y-intercept, b = 24.50 - 7(1.5)
= 14
= $14.00
Thus, the y-intercept in this situation means Option A while the slope shows that for every additional mile, the total fee increases by $1.50.
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Answer:
The y-intercept in this situation means A. When the cab travels 0 miles, the total fee will be $14.00.
Step-by-step explanation:
The nth term of a sequence is 3n squared -1. The nth term of a different sequence is 30 - n squared. Find the only number that is in both of these sequences
The number that belongs to both sequences is 26.
The formula known as the nth term allows us to locate any term in a series. The letter "n" stands for "number."
By changing the term number's value, we can create a series that uses the nth term (n).
To find the 10th term we would follow the formula for the sequence but substitute 10 instead of ‘n‘; to find the 50th term we would substitute 50 instead of n.
We have two sequences, let's call one as A and the other as B.
The n-th term of sequence A is written as:
aₙ = 3*n^2 - 1
the nth term of sequence B is written as:
bₙ = 30 - n^2
We want to find a term that belongs to both sequences, (it can be for different integers, we can use n for sequence A and x for sequence B)
Then we want to find:
aₙ = bₓ
where n and x are integer numbers.
Then we will heave:
3*n^2 - 1 = 30 - x^2
To find the pair, we could isolate one of the variables, then input different integers in the other variable and see if the outcome is also an integer.
Let's isolate n.
3*n^2 = 30 - x^2 + 1
3*n^2 = 31 - x^2
n^2 = (31 - x^2)/3
n = √( (31 - x^2)/3)
Now let's input different values for x, and see if the outcome is also an integer, notice that x is in a negative term inside a square root, then we have only a few values of x such that the equation can be true.
Then let's start with x = 1.
n(1) = √( (31 - 1^2)/3) = √(30/3) = √10
We know that √10 is not an integer.
now with x = 2,
n(2) = √( (31 - 2^2)/3) = √( (31 - 4)/3) = √(27/3) = √9 = 3
then if x = 2, we have n = 3.
Both of them are integers, then we get:
a₂ = 3*(3)^2 - 1 = 27 - 1 = 26
b₃ = 30 - 2^2 = 30 - 4 = 26
Therefore, The number that belongs to both sequences is 26.
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What kind of angle is ∠ABC Why?
Angle sum of three angles of ABC triangle must be equal to 180 degrees.
What is angle and triangle?Angle is the space between two intersecting lines or surface or at close to the point where there ends point meet.
A triangle is a polygon that has three straight sides and three angles.
What kind of angle is a ABC why?Let, ABC is a triangle. The angles in this triangle can be different types.
All angles in ABC can be lies between 90 degrees and that time triangle is called acute triangle. If ABC has one right angle, then this is termed as right-angled triangle.
If one of the angles is measured greater than 90 degrees, the triangle is called obtuse triangle.
if we find all angles in ABC triangle is equal to 60 degrees, this is termed as equilateral triangle.
But for each triangle, the sum of three angles must be equal to 180 degrees.
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