[tex]\displaystyle\\\lim_{x\to 2}\dfrac{x^2+2x-3}{x-3}=\dfrac{2^2+2\cdot2-3}{2-3}=\dfrac{5}{-1}=-5[/tex]
The right-hand limit of the function f(x) = (x^2 + 2x - 3)/(x - 3) as x approaches 2 is -5 after substitution of x = 2 into the function.
The question asks about the right-hand limit of the function f(x) = (x^2 + 2x - 3)/(x - 3) as x approaches 2. The first step in finding this limit is to simplify the function, if possible. In this case, we can factor the numerator to obtain (x - 1)(x + 3). However, since we are looking for a limit as x approaches 2, the denominator x - 3 will not be zero, and the expression does not need further simplification for this purpose. We then substitute x = 2 directly into the simplified function and find the limit.
So, the right-hand limit as x approaches 2 is simply f(2) = ((2)^2 + 2*2 - 3)/(2 - 3) = (4 + 4 - 3)/(-1) = 5/(-1) = -5.
Subtract 8 1/6 - 4 5/6 . Simplify the answer and write as a mixed number.
Answer:
3 1/3
Step-by-step explanation:
8 1/6 - 4 5/6 Borrow 1 or 6/6 from the 8 so you have something to subtract.
7 7/6 - 4 5/6 Subtract the whole numbers.
7 - 4 = 3 Subtract the fractions.
7/6 - 5/6 Do the subtraction
2/6 Reduce
2/6 = 1/3 Put the two parts together.
3 1/3
the result of subtracting the two mixed numbers is [tex]3\frac{1}{3}[/tex]
To subtract the mixed numbers [tex]8\frac{1}{6}[/tex] and [tex]4\frac{5}{6}[/tex] we need to first understand how to subtract it. To subtract mixed numbers we need to first convert them to improper fraction. For the new fraction, the denominator remains same but new numerator is calculated by finding the product of whole number and denominator and then adding it to the numerator. This can be done as follows:
[tex]8\frac{1}{6} = \frac{ 8 \times 6 +1}{6} = \frac{49}{6}[/tex]
[tex]4\frac{5}{6} = \frac{ 4 \times 6 +5}{6} = \frac{29}{6}[/tex]
Now we subtract them as follows:
[tex]\frac{49}{6} - \frac{29}{6} = \frac{20}{6} = \frac{10}{3}[/tex]
To convert this back into mixed fraction we divide 10 by 3 and the quotient becomes the whole number while the remainder becomes numerator and 3 remains as denominator
[tex]\frac{10}{3} = 3\frac{1}{3}[/tex]
Therefore, the result of subtracting the two mixed numbers is [tex]3\frac{1}{3}[/tex]
Can someone please help me Factor 4x^2 - 81
Answer:
(2x-9)(2x+9)
Step-by-step explanation:
This is a difference of squares because it can be written as (2x)^2-9^2
The formula for factoring a difference of squares is a^2-b^2=(a-b)(a+b)
So replace a with 2x and b with 9 giving us
4x^2-81=(2x-9)(2x+9)
Which shows the factored form of x2-12x-45?
Answer:
(x - 15)(x + 3)
Step-by-step explanation:
Consider the factors of the constant term (- 45) which sum to give the coefficient of the x- term (- 12)
The factors are - 15 and + 3, since
- 15 × 3 = - 45 and - 15 + 3 = - 12, hence
x² - 12x - 45 = (x - 15)(x + 3)
3(x - 4) + 5 - x= 2x - 7
how many solutions are there to this equation?
Answer:
The equation has infinity solutions
Step-by-step explanation:
3( x - 4 ) + 5 - x = 2 x - 7
⇒ Expand brackets
3 x - 12 + 5 - x = 2 x - 7
⇒ Simplify
2 x - 7 = 2 x - 7
A=4(14-1)
———- +7
3(6)-5
Answer:
Im boutta fail my final
Step-by-step explanation:
1 like= 1 prayer
Leticia charges $8 per hour to babysit. She babysat Friday night for 4 hours,
and then she babysat again on Saturday. She earned a total of $72. How
many hours did Leticia babysit on Saturday?
Choose two answers: one for the equation that models this situation and one
for the correct answer.
A. Equation: 8(4 + x) = 72
B. Equation: 4(8 + x) = 72
C. Answer: 5 hours
D. Answer: 11 hours
For this case we have that the variable "x" represents the number of hours that Leticia uses to take care of children on Saturday.
IF on Friday I use 4 hours ($ 8 each) and on Saturday "x" hours ($ 8 each) obtaining a profit of $ 72, we have the following equation:
[tex]8 (4 + x) = 72[/tex]
We apply distributive property:
[tex]32 + 8x = 72\\8x = 72-32\\8x = 40\\x = \frac {40} {8}\\x = 5[/tex]
So, on Saturday she spent 5 hours.
Answer:
[tex]8 (4 + x) = 72\\x = 5[/tex]
Answer:
Option A.
Option C.
Step-by-step explanation:
Let be "x" the amount of hours Leticia babysat on Saturday.
We know that she charges $8 per hour to babysit, she babysat Friday night for 4 hours and the total amount of money she earned on those two days was $72. Knowing this, we can set up the followin equation models this situation:
[tex]8(4+x)=72[/tex]
Finally, we must solve for "x":
[tex]8(4+x)=72\\\\32+8x=72\\\\8x=72-32\\\\8x=40\\\\x=\frac{40}{8}\\\\x=5[/tex]
Which absolute value inequality represents the given graph?
A. 18x + 91 < 57
B. 18x + 91 > 57
C. 18x +91 557
D. 18x +9 57
Answer:
Distribute the -9 into the values in the parentheses.
STEP BY STEP
-9(-2x-3)
-9*-2x=18x
-9*-3=27
Therefore, the equation then becomes: 18x+27.
The answer is the first choice, or A.
find the missing side
Answer:
[tex]x=15.56[/tex]
Step-by-step explanation:
We can use the law of sines here. However, we will first need to solve for the missing angle.
The interior angles of a triangle add up to 180.
Therefore,
[tex]35+90+x=180[/tex]
where [tex]x[/tex] is the missing angle.
[tex]35+90+x=180[/tex]
[tex]x+125=180[/tex]
[tex]x=55[/tex]
So the missing angle is 55 degrees.
Now we can use the law of sines to set up a proportion.
[tex]\frac{19}{sin(90)}=\frac{x}{sin(55)}[/tex]
Now simplify the equation.
[tex]x=15.56[/tex]
Rounded to the nearest hundredth.
Answer:
x ≈ 19.6
Step-by-step explanation:
Since the triangle is right use the cosine ratio to solve for x
cos35° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{19}[/tex]
Multiply both sides by 19
19 × cos35° = x, hence
x ≈ 19.6 ( to 1 dec. place )
The sum of three consecutive integers is 45. What are the integers
Divide 45 by 3 ( the quantity of consecutive numbers) This will give you the middle number, then use the number higher and lower.
45/3 = 15
14 + 15 + 16 = 45
The 3 numbers are 14, 15 and 16
1. In a 30-60-90 triangle, the length of the hypotenuse is 6. What is the length of the shortest
side?
a. 2
b. 3
c. 3.12
d. 31/3
e, 6-3
Answer:
b. 3
Step-by-step explanation:
In a 30°-60°-90° triangle, the short side is ½ the hypotenuse [the long side is double the short side].
30°-60°-90° Triangles
x√3 → long side
x → short side
2x → hypotenuse
45°-45°-90° Triangles
x → two legs
x√2 → hypotenuse
I am joyous to assist you anytime.
F(n+1)=f(n)-8. If f(2)=100, what is f(6)
Answer:
f(6) = 68
Step-by-step explanation:
f(6)
f(n+1)=f(n)-8
n = 5, so
f(6)=f(5)-8
and with n = 4
f(5)=f(4)-8 , so
f(4) = f(3) - 8
f(3) = f(2) - 8 = 100 - 8 = 92
f(3) = 92
Then, we can go and find the result
f(4) =[92] - 8 = 84
f(5)=[84] - 8 = 76
f(6) = [76] -8 = 68
[tex]f(n+1)=f(n)-8\\f(2)=100\\\\f(3)=100-8=92\\f(4)=92-8=84\\f(5)=84-8=76\\f(6)=76-8=68[/tex]
evaluate the expression 3x +(z+2y)-12 if x=3,y=8 and z=5
Answer:
18
Step-by-step explanation:
First you need to plug in the numbers for each variable.
3(3)+(5+2(8))-12
Now you solve
3(3)+(21)-12
9+21-12
18
hurry 50 pts
what dose this =
[15 ÷ 5 • 3 + (23 – 3)] + [4 • (36 – 33)]
Answer:
1155
Step-by-step explanation:
Answer:
41
Step-by-step explanation:
:))
Taylor makes $45 an hour for tutoring. If she tutored for a total of 16 hours last month, how much money did she make?
Answer:
$720
Step-by-step explanation:
1 hour of tutoring = $45
16 hours of tutoring = $45 x 16 hours = $720
Answer:
$720
Step-by-step explanation: just multiply 45 and 16 together, boom theres your answer
What type of triangle can a right triangle be?
scalene
acute
obtuse
isosceles
Answer:
acute
Step-by-step explanation:
Please mark brainliest and have a great day!
Answer:
acute and obtuse
Step-by-step explanation:
In an obtuse triangle, one angle is greater than a right angle—it is more than 90 degrees. An obtuse triangle may be isosceles or scalene. In an acute triangle, all angles are less than right angles—each one is less than 90 degrees. Please mark me as branliest. Thank you :3
the segments shown below could form a triangle
Answer:
False
Step-by-step explanation:
a^2+b^2=c^2 so the biggest number would be c and that would be 11 9^2=81 4^2=16 adding these together gets 97. 97=/=11^2 which is 121
Answer:
A. True.
Step-by-step explanation:
We have been given lengths of three segments. We are asked to determine whether the given segments could form a triangle or not.
Triangle inequality theorem states that sum of two sides of triangle must be greater than third side of the triangle.
Using triangle inequality theorem, we will get:
[tex]9+4>11[/tex]
[tex]13>11[/tex] True
[tex]9+11>4[/tex]
[tex]20>4[/tex] True
[tex]4+11>9[/tex]
[tex]15>9[/tex] True
Since our given segments satisfies triangle inequality theorem, therefore, the given segments could form a triangle.
What is the solution to this equation?
x + 19 = 26
A. X = 45
B. x= 17
c. x = 5
D. X = 7
x+19= 26
x+19-19= 26-19
x= 7
Check answer by using substitution method
x+19= 26
7+19= 26
26= 26
Answer is x= 7 (D.)
To find the solution we need to solve for x
We need to get x alone to solve for x.
To remove any number, always do the opposite operation
Opposite of +19 is -19
To remove +19 , subtract 19 from both sides
x+19=26
x+19 -19 =26-19 =7
x=7
So the value of x=7
The solution to this equation Option D. x=7
What is an example of an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. For example, 3x – 5 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 7.
What are the 3 types of equations?There are three major forms of linear equations: point-slope form, standard form, and slope-intercept form.
What is not an equation?An equation is a mathematical statement that two things are equal. It consists of two expressions, one on each side of an 'equals' sign. For example x=y is an equation where two expressions x and y are equal. Whereas f(x)=x is a function with variable x and hence f(x)=x is not an equation.
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which expression is equivalent to 4 square root 6 divided by 3 root 2
The equivalent expression to 4 √6 divided by 3 √2 is 4/3 × √3. This is achieved by expressing the square roots as fractional exponents and simplifying.
Explanation:The student is asking which expression is equivalent to the following mathematical expression: √(4 √6) / (3 √2).
To simplify this expression, we'll use the properties of exponents and radicals.
The square root of a number x can be written as x raised to the power of 0.5, so:
√6 = 60.5
√2 = 20.5
The given expression thus becomes:
(4 × 60.5) / (3 × 20.5) = 4/3 × 60.5/20.5
Since the exponents are the same, we can simplify the radicals by dividing the numbers inside the radicals:
4/3 × (6/2)0.5 = 4/3 × (3)0.5
And as (3)0.5 is the square root of 3:
4/3 × √3
Therefore, the equivalent expression is 4/3 × √3.
if my friend and i went to get ice cream, I have $30 and each ice cream is $5. What equation would help me solve this?
Answer:
[tex]5x\leq30[/tex]
Step-by-step explanation:
Let
x -----> the number of ice cream
we know that
[tex]5x\leq30[/tex]
Solve for x
Divide by 5 both sides
[tex]x\leq30/5[/tex]
[tex]x\leq 6\ ice\ cream[/tex]
therefore
The maximum number of ice cream is 6
Factor the expression.
125x^3+512
Answer:
its (5x+8)(25x^2-40x+64
Step-by-step explanation:cuz
What is the Least Common Multiple of 8 and 24
Answer: 24
Step-by-step explanation:
Break down the numbers until they have no way to be broken down anymore
8 = 4*2 = 2*2*2
24 = 6*4 = 3*2*2*2
The one that has more products is 24, so, it is 24.
What value for n makes this equation true?
9xn=(9x40)+(9x6)
A.6
B.15
C.36
D.46
Solve for x: 2/x-2+7/x2-4=5/x
Answer:
x = 11/6
Step-by-step explanation:
You need to reduce this fraction to the lowest terms.
This can be done by dividing out those factors that appear both in the numerator and in the denominator.
Please mark brainliest and have a great day!
Answer: [tex]\bold{x=-\dfrac{4}{3}\qquad x=5}[/tex]
Step-by-step explanation:
[tex]\dfrac{2}{x-2}+\dfrac{7}{x^2-4}=\dfrac{5}{x}\\\\\\\text{Multiply each term by the LCD x(x-2)(x+2) to clear the denominator:}\\\dfrac{2}{x-2}[x(x-2)(x+2)]+\dfrac{7}{x^2-4}[x(x-2)(x+2)]=\dfrac{5}{x}[x(x-2)(x+2)]\\\\\\\text{Simplify - cross out like terms:}\\2[x(x+2)]+7[x]=5[(x-2)(x-2)]\\\\\\\text{Distribute:}\\2x^2+4x+7x=5x^2-20\\\\\\\text{Set equation equal to zero and Add like terms:}\\0=5x^2-2x^2-7x-4x-20\\0=3x^2-11x-20\\\\\text{Factor, set each factor equal to zero, and solve for x:}[/tex]
[tex]0=(3x+4)(x-5)\\0=3x+4\qquad 0=x-5\\\large\boxed{x=-\dfrac{4}{3}\qquad x=5}[/tex]
The first ferris wheel was 250 feet in diameter. It was invented by John Ferris in 1893. Assuming it made one revolution every 30 seconds, what was the linear speed of a passenger ( assuming the passenger is on the edge of the ferris wheel) in feet per minute.
Step-by-step explanation:
The wheel has a diameter of 250 feet, so its circumference is:
C = 2πr = πD
C = 250π feet
It makes one revolution in 30 seconds, or half a minute, so the linear speed of the passenger is:
v = d / t
v = 250π / 0.5
v = 500π ft/min
v ≈ 1571 ft/min
This is about the same as 17.9 mph.
Final answer:
The linear speed of a passenger on the original Ferris wheel with a diameter of 250 feet, making one revolution every 30 seconds, was approximately 1570.8 feet per minute.
Explanation:
The question asks to calculate the linear speed of a passenger on the edge of the first Ferris wheel, which was 250 feet in diameter, and made one revolution every 30 seconds. To find the linear speed, we first need to determine the circumference of the Ferris wheel, which can be done by using the formula for the circumference of a circle, C = πd, where d is the diameter.
For the first Ferris wheel:
Diameter (d) = 250 feet
Circumference (C) = π * 250 feet = 785.398163 feet (approximately)
Time for one revolution = 30 seconds
Since the question requires the speed in feet per minute, we need to convert the time for one revolution to minutes:
30 seconds = 0.5 minutes
The linear speed (v) can be found using the formula v = C / time. Substituting our values in:
v = 785.398163 feet / 0.5 minutes = 1570.79633 feet per minute
Therefore, the linear speed of a passenger at the edge of the Ferris wheel was approximately 1570.8 feet per minute.
The length of a rectangle is three times its width. If the perimeter is at most 112 centimeters, what is its greatest possible value for width?
Answer:
Step-by-step explanation:
Perimeter= 2L+2W. If L=3W(three times the width) then 2(3W)+2W=112. Or 6W+2W=112 which is equal to 8W=112. To solve for the width, divide both sides by 8 and find 112/8=14, therefore W=14.
Answer:
14 cm
Step-by-step explanation:
Given the length is 3 times the width
If each width is denoted by W, then each length is L = 3W
Perimeter (add up all lengths and widths),
= L + L + W + W
= 3W + 3W + W + W
= 8W
Given that the max perimeter is 112cm
hence 8W = 112,
W = 14 cm at most
Merrida uses a pattern in the multiplication table below to find ratios that are equivalent to 7:9. If Merrida multiplies the first term, 7, by a factor of 6, what should she do to find the other term for the equivalent ratio? Multiply 9 by 1. Multiply 9 by 6. Multiply 9 by 7. Multiply 9 by 9.
Answer:
Multiply 9 by 6
Step-by-step explanation:
7:9 is the ratio
We multiply the first term by 6.
What we do to one side, we do to the other
7*6=42
9*6 = 54
That way we keep the ratio in the same proportion
42:54
Answer: Multiply 9 by 6.
Step-by-step explanation:
How to slove the equation 6.8x+9.3=-9.4+3.4(2-5x)
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Ted creates a box plot using 14, 13, 21, 10, 28, 30, and 35 as the data. Which of the following box plots shows the data accurately? A box plot is drawn with end points at 10 and 35.The box extends from 13 to 30 and a vertical line is drawn inside the box at 21. A box plot is drawn with end points at 10 and 35.The box extends from 15 to 32 and a vertical line is drawn inside the box at 23. A box plot is drawn with end points at 10 and 35.The box extends from 11 to 28 and a vertical line is drawn inside the box at 19. A box plot is drawn with end points at 10 and 35.The box extends from 17 to 34 and a vertical line is drawn inside the box at 25.
PLEASE HELP
a box plot is drawn with end points at 10 and 35. The box extends from 13 to 30 and a vertical line is drawn inside the box at 21.
Three runners competed in a race. Data were collected at each mile mark for each runner. If the runner ran at a constant pace, the data would be linear. A regression line fitted to their data. Uses the residual plots to decide which data set is best fit by the regression line, and then identify the runner that kept the most consistent pace.
Linear data is data lying across a straight line. The runner which kept the most consistent pace was runner B.
How does linear regression works?Firstly, there is a data set. Then, we try to fit a line which will tell about the linear trend. This line is made using the least squares method.
For the given case, the second runner(runner B)'s data is almost forming a linear trend, whereas, for the first runner, its more spread, and the third graph, its a quadratic trend.
For non-linear trends like in third graph(runner C), we use polynomial regression to fit polynomial curves of higher degrees.
Thus, as the runner B's data set is lying more near to a line than other runners, thus,
The runner which kept the most consistent pace was runner B.
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Each granola bar costs $1. Write an expression that shows the total cost of the granola bars. Use the variable you identified in question 1. Btw I used the variable "g". Thanks!
Answer:
$[tex]1g[/tex]
Explanation:
If the number of granola bars is represented by the variable [tex]g[/tex], and each granola bar costs $1, then we need to multiply the amount per granola bar by the number of granola bars.
This is $[tex]1 * g[/tex], or $[tex]1g[/tex].
In this scenario, the total cost of the granola bars can be represented by the mathematical expression 'g', as each granola bar costs $1.
Explanation:If each granola bar costs $1 and 'g' is representing the number of granola bars, then the total cost of the granola bars can be represented by the expression 1 * g or simply g. This is because for every granola bar you buy, you are adding $1 to your total. So if you bought 'g' granola bars, your total cost would be $1 times the number of granola bars 'g'. This is an example of direct proportionality, where the total cost increases with the increase in number of granola bars.
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