I have an ACT practice guide problem that I need answered and explainedIt has a list of answers to choose from I will list that belowA. 1B. -2C. 4D. The limit does not exist.
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SOLUTION
The limit of a function at a point aa in its domain (if it exists) is the value that the function approaches as its argument approaches a.
The limit of a function F exist if and only if
[tex]\begin{gathered} \lim _{x\rightarrow x^+}f(x)=\lim _{x\rightarrow x^-}f(x) \\ \\ \text{The left-hand limit =The Right-hand Limit} \end{gathered}[/tex]Considering the image given, the limit of the function from the left is from the first graph
[tex]\lim _{x\rightarrow1^-}f(x)=4\Rightarrow\text{ The left hand limit}[/tex]
Similarly, the limit of f(x) from the right-hand side is on the second graph
[tex]\lim _{x\rightarrow1^+}f(x)=-2\Rightarrow The\text{ Right -hand limit}[/tex]Since
[tex]\begin{gathered} \text{Left-hand limit}\ne Right\text{ hand imit} \\ 4\ne-2 \end{gathered}[/tex]Therefore
The Limit does not exist (D)
Related Questions
Jamal's deck is in the shape of a polygon and is shown on the grid below.(-8,6)(6,6)o[(-8, -4),(6,-4)What is the area of Jamal's deck?square units
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Let;
A(-8,6) B(6,6) C(6, -4) D(-8, -4)
Let's find the length AB
x₁= -8 y₁=6 x₂=6 y₂=6
We will use the distance formula;
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex][tex]=\sqrt[]{(6+8)^2+(6-6)^2}[/tex][tex]=\sqrt[]{14^2+0}[/tex][tex]=14[/tex]Next, we will find the width BC
B(6,6) C(6, -4)
x₁= 6 y₁=6 x₂=6 y₂=-4
substitute into the distance formula;
[tex]d=\sqrt[]{(6-6)^2+(-4-6)^2}[/tex][tex]=\sqrt[]{(-10)^2}[/tex][tex]=\sqrt[]{100}[/tex][tex]=10[/tex]Area = l x w
= 14 x 10
= 140 square units
7. How many prime factors does the number 124 have?
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It a popular math theorem, that any natural number can be factored out into prime numbers. For example the number 24 is factored as 2³*3, so its prime factors are 2 and 3.
In this case, we want to factor 124. We start by noticing that 124 is an even number, therefore, the first prime factor we try is 2. Next, we divide 124 by 2. We get
[tex]\frac{124}{2}=62[/tex]which is again an even number. This means that we can again divide by 2. We do so
[tex]\frac{62}{2}=31[/tex]Note that 31 is a prime number. So we can't continue dividing. Then
[tex]124=2\cdot2\cdot31=2^2\cdot31[/tex]So it has 2 different prime factors
solve the system using any method
-x^2-10x-y=30
3x^2+30x-y=-66
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Answer:
(-4,-6) (-6,-6)
Step-by-step explanation:
-y = x^2 + 10x + 30
y = -x^2 - 10x - 30
3x^2 + 30x -(-x^2-10x-30) = -66
3x^2 + 30x + x^2 + 10x + 30 = -66
4x^2 + 40x +30 + 66 = 0
4x^2 + 40x + 96 = 0
x^2 + 10x + 24 = 0
(x+6)(x+4) = 0
x = -6
x = -4
y = -x^2 - 10x - 30
y = -(-6)^2 - 10(-6) - 30
Y = -36+60 - 30
y= -6
y= -(-4)^2 - 10(-4) - 30
y = -16 + 40 - 30
y = -6
A.Ghamarvion earned $8.00 an hour and was given a 75% wage ge increase. How much does Ghamarvion earn per hour after his ae raise? B. A population increased from 328 569 people to 400,232 people. What was the percent of change in the population?
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Evaluate the integral of the product if x and quantity x squared plus 1 and x, dx.
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The integral is given
[tex]\int x(x^2+1)dx[/tex]ExplanationTo determine the solution to the integral.
[tex]\int x(x^2+1)dx=\int x^3+x\text{ dx}[/tex][tex]\int(x^3+x)dx=\frac{x^4}{4}+\frac{x^2}{2}+C[/tex]AnswerHence the correct option is C.
[tex]\frac{x^4}{4}+\frac{x^2}{2}+C[/tex]A company discovers that to produce x=700 new electronic parts, it will cost y=$61100. To produce 620 new electronic parts, it will cost $54460
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Answer:
The cost increases at a rate of $83 per item.
Step-by-step explanation:
Given two points, use the following to determine the equation:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Given the points (700,61100) and (620, 54460), substitute and compute for the slope:
[tex]\begin{gathered} m=\frac{61100-54460}{700-620} \\ m=\frac{}{}83 \end{gathered}[/tex]The cost increases at a rate of $83 per item.
A new auditorium is being built for a college. The balcony has 60 seats. Thefloor has 15 rows with x seats in each row. The number of people in theauditorium must be under 315 to meet safety regulations.What is the solution of this inequality, and what is its meaning?
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x < 17
This means the new auditorium must have less than 17 seats 1n each row on the floor to meet the safety regulations.
Explanation:Number seats in the balcony = 60
Number of seats on the floor = number of rows × number of seats on each row
Number of seats on the floor = 15× x = 15x
The number of people in the auditorium must be under 315:
This means the number of people can be less than 315 but not above it.
We represent less than 315 as < 315
The inequality equation:
Number seats in the balcony + Number of seats on the floor < 315
60 + 15x < 315
Rewritting the inequality equation:
15x + 60 < 315
Solving the inequality:
15x + 60 < 315
collect like terms by subtracting 60 from both sides:
15x + 60 - 60 < 315 -60
15x < 255
Divide both sides by 15:
15x/15 < 255/15
x < 17
This means the new auditorium must have less than 17 seats in each row on the floor to meet the safety regulations.
Solve for the values of x and y for the regular hexagon.a. x = 120, y = 60b. x = 110, y = 70c. x = 105, y = 75d. x = 60, y = 120e. X = 115, y = 65
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Remember that the sum of the interior angles of an hexagon is equal to 720°
Because this is a regular hexagon,
[tex]\begin{gathered} 6x=720\rightarrow x=\frac{720}{6} \\ \rightarrow x=120 \end{gathered}[/tex]Notice angles x and y lay in the same straight line.
Thereby,
[tex]\begin{gathered} x+y=180 \\ \rightarrow120+y=180 \\ \rightarrow y=180-120 \\ y=60 \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} x=120 \\ y=60 \end{gathered}[/tex](The correct answer is option A)
Thor was selling candy at a softball game and recorded the number of candy he sold each day in the line graph above. Which histogram below represents the data shown in the line graph?.
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Day 1 = 70, Day 2 = 74, Day 3 = 78, Day 4 = 80
How to Graph 2x-3y=6 in a coordinate plane.
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Explanation:
To graph the equation 2x - 3y = 6, we need to find two points in the line.
So, first let's make y = 0 and solve for x
2x - 3y = 6
2x - 3(0) = 6
2x = 6
2x/2 = 6/2
x = 3
Then, if x = 0, we get:
2x - 3y = 6
2(0) - 3y = 6
-3y = 6
-3y/(-3) = 6/(-3)
y = -2
Therefore, the points that we will use to graph the equation are (3, 0) and (0, -2).
Answer:
So, the graph of 2x - 3y = 6 is
a hotel claims that 95% of its customers are very satisfied with its service. there is a sample size of seven customers. A. what is the probability that exactly six customers are very satisfied?B what is the probability that more than six customers are very satisfied?C. what is the probability that less than five customers are very satisfied?D. suppose that of seven customer selected, three responded that they are very satisfied. what conclusions can be drawn about the sample? the probability that three out of seven customers are very satisfied is__, assuming that 95% of customers are very satisfied. therefore, it is__that randomly selecting seven customers would result in three responding that they were very satisfied.(round all answers to four decimal places please)
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Let X be the number of customers satisfied
Given:
Sample size (n) = 7
The probability that a customer is very satisfied = 0.95
The probability distribution function for a binomial distribution is:
[tex]P(X=x)=(^n_x)p^x(1-p)^{n-x}_{}[/tex](a) Probability that exactly 6 customers are satisfied
[tex]\begin{gathered} P(X=6)=(^7_6)(0.95)^6(1-0.95)^{7-6} \\ =\text{ 7}\times\text{ 0.7351}\times0.05 \\ =\text{ 0.25728} \\ \approx\text{ 0.2573} \end{gathered}[/tex]The probability that exactly six customers are very satisfied is 0.2
(b) Probability that more than 6 customers are very satisfied
Which pairs of figures are congruent? Which pairs are similar?The first question.
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Given the two circles shown in the exercise, you need to remember that, by definition, two figures are congruent when they have the same size and they have the same shape.
In this case, you can identify that the circles have the same diameters (remember that a diameter of a circle is the length that passes through the center of the circle and touch two points on the circumference):
[tex]\begin{gathered} d_1=2units \\ d_2=2units \end{gathered}[/tex]Therefore, these circles have the same shape and size.
By definition, two figures are similar when their corresponding angles are congruent and the ratios of the corresponding sides are proportional.
In this case, since the figures are circles, you know that they both measure 360 degrees. Knowing that they also have the same diameter, you can determine that they are similar too.
Hence, the answer is: They congruent and similar.
all you need is in the photo please answer fast only give the answer don't put step by step pleaseeeeeeeeeeeeeeeeeeeeee
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The value of x1 = 7 and x2 = -2
From the question, we have
a=1
b=-5
c=-14
x= [-b ± √(b2 – 4ac)]/2a
substituting the value, we get
x= [5 ± √(-5² – 4*1*-14)]/2*1
=[5 ± √(25+56)]/2
=[5 ± √81]/2
=[5 ± 9]/2
x1 =[5 +9]/2=7
x2 =[5 -9]/2=-2
Quadratic Equation:
The polynomial equations of degree two in one variable of type f(x) = ax^2 + bx + c = 0 and with a, b, c, and R R and a 0 are known as quadratic equations. It is a quadratic equation in its general form, where "a" stands for the leading coefficient and "c" for the absolute term of f. (x).It is a given that the quadratic equation has two roots. Roots might have either a true or made-up nature.
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a cone has a height of 8 cm and a slant height of 10cm. Calculate the radius of the cone.
HALP PLEASE
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The radius of the cone is= 3.14*160 cm^2.
What is equations?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 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. Mathematical algebraic equations typically have one or more variables.A linear equation may have more than one variable. A linear equation is an equation in which the highest power of the variable is always 1.This is a second-order equation. In quadratic equations, at least one of the variables should be raised to exponent 2.According to our question-
Total SA of a cone = πr^2+πrl = πr(r+l)
Here r = 8 cm , slant height l=12 cm.
SA of cone =3.14 * 8 * ( 8+12) cm^2
=> 3.14*160 cm^2
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Hayden has read 3/5 of a book she has read 75 pages so far how many pages are in the whole book?
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Let there are x number of pages in whole book. So 3/5 of a book is equal to 3/5x.
Determine the value of x.
[tex]\begin{gathered} \frac{3}{5}x=75 \\ x=75\cdot\frac{5}{3} \\ =125 \end{gathered}[/tex]So there are 125 pages in the whole book.
Hello, Im trying to help my 9th grade daughter who is autistic with her test corrections. Its been over 20 years since I last took Algebra 1 and Im a bit rusty. She gets agitated easily and so Im trying to do some of the prep work now so I can help her when she gets home. I appreciate your assistance in advance
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The original graph is given below
a. If the starting number of players is 600 instead of 400 then
The y-intercept will be 600
The new graph will be a vertical stretch of the original graph by a scale factor of 600/400
[tex]\frac{600}{400}=1.5[/tex]Therefore,
The y-intercept will be 600. The new graph will be a vertical stretch of the original graph by a scale factor of 1.5
b. If the starting number of players is 800 instead of 400 then
The y-intercept will be 800
The new graph will be a vertical stretch of the original graph by a scale factor of 800/400
[tex]\frac{800}{400}=2[/tex]Therefore,
The y-intercept will be 800. The new graph will be a vertical stretch of the original graph by a scale factor of 2
what is the value of x in this equation ?
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Solution
We have the following equation given:
4(2x+1)= 27 + 3(2x-5)
And we can solve for x on this case:
8x +4 = 27 + 6x -15
8x -6x = 27-15 -4
2x = 8
x= 8/2= 4
Find the missing value in theequivalent ratio 12:18 = 16:ChooseA.20B.24C.28
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we have that
12:18 is the same that 12/18
simplify
12/18=6/9=2/3
Multiply by 8/8
(2/3)*(8/8)=16/24 ------> 16:24
therefore
the answer is the option BProblem N 2
we have that
each earbud costs 0.94
so
Multiply by 22
0.94*22=$20.68
the answer is $20.68(06.02)
Solve the system 2x + 2y = -6 and 3x - 2y = 11 by using graph paper or graphing
technology. What is the solution to the system?
O (1,-4)
O (-1,-7)
O (3,-2)
O (2,-1)
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Answer:
(1-4)
Step-by-step explanation:
Solve for the first variable(x or y) in one of the equations(you choose which equation) and then after finding the first variable(x or y) you plug it in into the equation u didnt use and solve
in point slope form: passes through (1, -3), slope = -1?
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Explanation
Step 1
Let
P1(1,-3)
slope=-1
Step 2
use the formula
[tex]y-y_1=m(x-x_1)[/tex]replacing
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-(-3)=-1(x-1) \\ y+3=-x+1 \\ \text{subtract 3 in both sides} \\ y+3-3=-x+1-3 \\ y=-x-2 \end{gathered}[/tex]I hope this helps you
Option for the first box: 25, 54, 50, 4Options for the second box:0.5, 2, -0.5, 1Options for the third box:0, 1, 0.5, -0.5 Options for the fourth box:4, 25, 29, 54
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Answer:
First box: 25
Second box: 1
Third box: -0.5
Fourth box: 29
First, we will find the amplitude of the sine function.
Sam gave the mother the child a bottle medication and told her a day . the following conversion laclors : 1 - 30 . 1lb(s) = 15mLHow many tablespoon is one dose?How many mL will the child take in one day?How many fl oz is this?How many days will the bottle and medication last?
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Given:
The doctor gave the mother of the sick baby 16 fl oz bottle of liquid medicine.
Dosage instructed to give the baby = 30 ml twice a day
a) How many tablespoon is one dose?
Using standard measurements, 1 tablespoon = 15 ml
Since 1 dose is 30 ml, the dose in tablespoon is:
[tex]\frac{30\text{ ml}}{15\text{ ml}}=\text{ 2 tablespoons}[/tex]1 dose is 2 tablespoons
b) Since, 30 ml is to be given 2 times daily, the ml the child will take a day is:
[tex]30\text{ mL }\ast\text{ 2 = 60 mL}[/tex]The child will take 60 mL a day
c) fl oz means fluid ounce
Also 1 fluid ounce is equivalent to 28.41 ml
Given:
28.41ml = 1 fl oz
60 ml =
[tex]\frac{60}{28.41}=2.11\text{ fl oz}[/tex]Therefore, 60 ml = 2.11 fl oz
d) How many days will the bottle and medication last?
To find the number of days the medication will last, we have:
[tex]\frac{16\text{ fl oz}}{2.11\text{ fl oz}}=\text{ 7.6}[/tex]Therefore, the bottle will last for approximately 8 days.
ANSWER:
a) 2 tbs
b) 60 ml
c) 2.11 fl oz
d) Approximately 8 days
Set up a proportion for each word problem and solve the problem
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Explanation
We are given that Meagan earned $550 at her job in 4 weeks.
We are required to find how many weeks it would take her to make $5000.
First, we need to find the rate at which she works per week as follows:
[tex]\begin{gathered} Since\text{ }4\text{ weeks = \$550} \\ 1\text{ }week=\frac{550}{4} \end{gathered}[/tex]To determine how many weeks it would take her to earn $5000, we need to divide the amount earned after x weeks by the rate as follows:
[tex]\begin{gathered} 1\text{ }week=\frac{550}{4} \\ x\text{ }weeks=5000\div\frac{550}{4}=5000\times\frac{4}{550} \\ =36.36363636\text{ weeks} \end{gathered}[/tex]Hence, the answer is 36.36363636 weeks.
The measurement of three angles of a triangle are (2x)degrees ,(3x)degrees and (x+30) degrees. What is the value of x?
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We have that the measurement of three angles of a triangle is:
1. Angle 1: 2x degrees.
2. Angle 2: 3x degrees.
3. Angle 3: (x+30) degrees.
We know that the sum of the internal angles of a triangle is equal to 180.
Therefore, to find the value of x, we can proceed as follows:
[tex]\begin{gathered} m\angle1+m\angle2+m\angle3=180^{\circ} \\ \\ 2x+3x+(x+30)=180^{\circ} \end{gathered}[/tex]Now, we can add the like terms as follows:
[tex]\begin{gathered} 2x+3x+x+30^{\circ}=180^{\circ} \\ \\ 5x+x+30^{\circ}=180^{\circ} \\ \\ 6x+30^^{\circ}=180^{\circ} \end{gathered}[/tex]We can subtract 30 degrees to both sides of the equation, and then we have to divide both sides by 6:
[tex]\begin{gathered} 6x+30^{\circ}-30^{\circ}=180^{\circ}-30^{\circ} \\ \\ 6x=150^^{\circ} \\ \\ \frac{6x}{6}=\frac{150}{6} \\ \\ x=25 \end{gathered}[/tex]Therefore, in summary, the value for x is equal to 25.
Can you find the correct answers to all parts of question 1 and 2. Could you also tell me why I got my answers wrong originally?
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1.
Part a) G(x) is still a function because it's the inverse function of f(x).
part b)
f(g(4)).
FIrst step for this is to find g(4) which is:
[tex]\begin{gathered} g(4)=f^{\text{ -1}}(4) \\ \\ g(4)=f^{\text{ -1}}(4)=g(4)=3 \end{gathered}[/tex]Part c)
Now, to find the equation of the tangent line we have to find the slope, which is the derivative, because the derivative is the slope of the tangent line at a given x-value
But they ask for the g function, in this case:
[tex]\begin{gathered} f^{\text{ -1}}(\text{ -2\rparen} \\ then,\text{ g\lparen-2\rparen=7} \end{gathered}[/tex]So, the derivative in f(x)= 7 is -4.5
So, the equation is:
[tex]\begin{gathered} y\text{ - g\lparen-2\rparen=m\lparen x - \lparen-2\rparen} \\ y\text{ - 7= -4.5\lparen x+2\rparen} \\ \\ y\text{ - }7=\text{ -}4.5(x+2) \end{gathered}[/tex]3.2 radians=________degrees
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SOLUTION
To convert from radians to degrees, we have the conversion rate
[tex]\begin{gathered} \pi radians=180^0 \\ 2\pi radians=360^0=180\times2 \end{gathered}[/tex]Then 3.2 radians will be
[tex]3.2\pi radians=180\times3.2=576^0[/tex]Therefore 3.2 radians =576°
The graph shows a relationship between temperature and time.504030Temperature (°F)2010h246810Number of HoursWhich best represents the equation that shows the temperature, t, after h hours?tu-n +45t = -45ht = -5h + 45t= -3h + 45
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as we can see in the graph we know that the equation that represents a line is the equation of the line
in this case
y=t
x=h
we need two points in order to calculate the slope
(0,45)=(x1,y1)
(5,30)=(x2,y2)
[tex]m=\frac{y2-y1}{x2-x1}=\frac{30-45}{5-0}=\frac{-15}{5}=-3[/tex]the y-intercept is 45
the form of the equation of the line is
[tex]y=mx+b[/tex]where
m=slope
b=y-intercept
in this case
m=-3
b=45
[tex]y=-3x+45[/tex]using the variables of the problem the equation that represents the problem is
[tex]t=-3h+45[/tex]the correct answer is the last one
The cost in dollars of making x items is given by the function C(x)=10x+700.The fixed cost is determined when zero items are produced. Find the fixed cost for this item.fixed cost=What is the cost of making 25 items?C(25)=Suppose the maximum cost allowed is $2700. What are the domain and range of the cost function, C(x)?When you enter a number in your answer, do not enter any commas in that number. In other words if you want to enter one thousand, then type in 1000 and not 1,000. It's not possible to understand what the interval (1,000,2,000) means, so you should write that as (1000,2000).domain=range=
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According to the situation, the domain of this function will contain all values that x can take. Since x is the number of items, it only can take values from 0 to a certain value.
To find this certain value, use the maximum cost allowed (2700) as C(x) and find x using the equation:
[tex]\begin{gathered} C(x)=10x+700 \\ 2700=10x+700 \\ 2700-700=10x \\ 2000=10x \\ x=\frac{2000}{10} \\ x=200 \end{gathered}[/tex]It means that the domain of the function is [0,200]
The range contains all the values that cost can take. We know that the fixed cost (which is the minimum cost) is 700 and the maximum cost is 2700.
It means that the range of the function is [700,2700]
Answer:
it is not clear
Step-by-step explanation:
• Which ratios have a unit rate of 37 Choose ALL that apply. 15 1 1 1 cup : cup cups: 25 cups 3 ) 3 3- cups : 2 cups 4 2 2 () 2 cups : cup 3 21 / 1 5 cups : cup 6 cup : 1 cup 3
Answers
Explanation:
The ratios are like fractions, they can be simplified. And since fractions are divisions in some occasions we can do the division in order to get a simpler number:
• 1 cup: 1/4 cup _ we can do the division with the KCF method: keep the first fraction, change division sign into multiplication sign and flip the second fraction:
[tex]1\colon\frac{1}{4}=1\times4=4[/tex]• 2 cups : 2/3 cup
[tex]2\colon\frac{2}{3}=2\times\frac{3}{2}=3_{}[/tex]• 15/2 cups : 2 1/2 cups
[tex]\frac{15}{2}\colon2\frac{1}{2}=\frac{15}{2}\colon\frac{5}{2}=\frac{15}{2}\times\frac{2}{5}=3[/tex]• 2 1/2 cups : 5/6 cup
[tex]2\frac{1}{2}\colon\frac{5}{6}=\frac{5}{2}\colon\frac{5}{6}=\frac{5}{2}\times\frac{6}{5}=\frac{6}{2}=3[/tex]• 3 3/4 cups : 2 cups
[tex]3\frac{3}{4}\colon2=\frac{15}{4}\colon2=\frac{15}{4}\times\frac{1}{2}=\frac{15}{8}[/tex]• 2/3 cup : 1 cup
[tex]\frac{2}{3}\colon1=\frac{2}{3}\times1=\frac{2}{3}[/tex]Answers:
The answers are the ones in a red rectangle:
Translate the sentence into an equation.Seven less than the product of 6 and a number is 2.Use the variable x for the unknown number
Answers
Seven less than the product of 6 and a number is 2.
→ The product of 6 and a number can be expressed as 6x
→ "Seven less than the product of 6 and a number", indicates that you have to subtract 7 to 6x, so that: 6x-7
→ According to the sentence, the result of this calculation is seven, so the complete expression is:
[tex]6x-7=2[/tex]