Answers
Answers:
[tex]\displaystyle \lim_{x\to -3^{+}} h(x) = 1\\\\\displaystyle \lim_{x\to -3^{-}} h(x) = 1\\\\\displaystyle \lim_{x\to -3} h(x) = 1\\\\\displaystyle \lim_{x\to 0^{+}} h(x) = 0\\\\\displaystyle \lim_{x\to 0^{-}} h(x) = 3\\\\\displaystyle \lim_{x\to 2^{-}} h(x) = \infty\\\\\displaystyle \lim_{x\to 2^{+}} h(x) = \infty\\\\[/tex]
The limit exists at -3
The limit does not exist at 0
The limit exists at 2, assuming your teacher allows positive infinity to be an answer (otherwise, the limit doesn't exist).
============================================================
Explanation:
If we start on the left side of x = -3, and approach toward x = -3 itself, then we will approach y = 1. Imagine it's like a car on a roller coaster able to move along the curve. If the car is to the left of x = -3, then it goes uphill slowly approaching that limiting value.
If we start on the right side of x = -3, and approach -3 itself, then we approach the same y value as before
So that's how I'm getting
[tex]\displaystyle \lim_{x\to -3^{+}} h(x) = 1\\\\\displaystyle \lim_{x\to -3^{-}} h(x) = 1\\\\\displaystyle \lim_{x\to -3} h(x) = 1\\\\[/tex]
The third limit is basically the combination of the first two limits. If the LHL (left hand limit) and the RHL (right hand limit) are equal, then the limit exists.
--------------------------------------
We see that the LHL and RHL at x = 0 aren't the same. So the limit does not exist at x = 0
The LHL for x = 0 is 3 while the RHL for x = 0 is 0.
That explains why
[tex]\displaystyle \lim_{x\to 0^{+}} h(x) = 0\\\\\displaystyle \lim_{x\to 0^{-}} h(x) = 3\\\\\\\displaystyle \lim_{x\to 0} h(x) = \text{DNE}\\\\\\[/tex]
DNE means does not exist
-------------------------------------
Lastly, when we approach x = 2 from the left, we head upward toward positive infinity.
So [tex]\displaystyle \lim_{x\to 2^{-}} h(x) = \infty\\\\[/tex]
Also, [tex]\displaystyle \lim_{x\to 2^{+}} h(x) = \infty\\\\[/tex] because we're heading upward forever when approaching x = 2 from the right side.
We can then say [tex]\displaystyle \lim_{x\to 2} h(x) = \infty\\\\[/tex]
Related Questions
m.ng giúp mình về phần vector trong ma trận nha
Answers
Answer:
maybe if u translate it in English
Step-by-step explanation:
it wouldv been helpful if u mind?
Which of these statements is correct? The system of linear equations 6 x minus 5 y = 8 and 12 x minus 10 y = 16 has no solution. The system of linear equations 7 x + 2 y = 6 and 14 x + 4 y = 16 has an infinite number of solutions. The system of linear equations 8 x minus 3 y = 10 and 16 x minus 6 y = 22 has no solution. The system of linear equations 9 x + 6 y = 14 and 18 x + 12 y = 26 has an infinite number of solutions
Answers
Answer:
The only true statement is:
"The system of linear equations 8x - 3y = 10 and 16x - 6y = 22 has no solution."
Step-by-step explanation:
First, some definitions.
A system of linear equations has infinite solutions if both equations define the same line, has no solutions if we have two parallel lines, has one solution in all the other cases.
Where two lines are parallel if we can write them as:
a*x + b*y = c
a*x + b*y = d
where c and d are different numbers.
Now we can analyze the given statements:
a)
6x - 5y = 8
12x - 10y = 16
has no solution?
If we divide both sides of the second equation by 2, we get:
(12x - 10y)/2 = 16/2
6x - 5y = 8
We get the first equation, then both equations define the same line, thus the system has infinite solutions, then the statement is false.
b)
7x + 2y = 6
14x + 4y = 16
has infinite solutions?
Let's divide the second equation by 2, then we get:
(14x + 4y)/2 = 16/2
7x + 2y = 8
If we rewrite our system of equations, we get:
7x + 2y = 6
7x + 2y = 8
These are parallel lines, thus, this system has no solutions.
So the statement is false.
c)
8x - 3y = 10
16x - 6y = 22
has no solution?
Again, let's divide the second equation by 2 to get:
(16x - 6y)/2 = 22/2
8x - 3y = 11
If we rewrite our system:
8x - 3y = 10
8x - 3y = 11
These are parallel lines, thus the system has no solutions, so this statement is correct.
d)
9x + 6y = 14
18x + 12y = 26
Has infinite solutions?
Dividing the second equation by 2 we get:
(18x + 12y)/2 = 26/2
9x + 6y = 13
So the equations are different (are parallel lines again) so this system has not infinite solutions.
Then the statement is false.
Answer:
The answer to your question is the third choice.
Step-by-step explanation:
a) 6x - 5y = 8
12x - 10y = 16
We observe that these lines are the same so they have infinite solutions.
b)
7x + 2y = 6
14x + 4y = 16
These lines are parallel because they have the same slope, so they do not cross, there is no solution.
c)
8x - 3y = 10
16x - 6y = 22
These lines are parallel because they have the same slope, so they do not cross, there is no solution.
d)
9x + 6y = 14
18x + 12y = 26
These lines are parallel because they have the same slope, so they do not cross, they do not have an infinite number of solutions.
Jai bought a helmet and a pair of skates.
The helmet cost £45.
He sold both items for £224.
Jai made a 120% profit on the cost of the helmet and a 40% profit on the total cost.
What was the percentage profit on the skates?
Give your answer to 1 decimal place.
Answers
Answer:
Profit % on skates = 8.7 %
Step-by-step explanation:
Step 1 : Find cost price of skates
Cost price of helmet = £45
Let cost price of skate be = x
Selling price = £224
Cost price = (x + 45)
Total profit % = 40%
[tex]Profit \% = \frac{Selling \ price - cost \ price }{Cost \ price} \times 100[/tex]
[tex]\frac{40}{100} = \frac{224 - (x + 45)}{(x + 45)}\\\\40(x+ 45) = 100(224 - (x +45))\\\\40(x + 45) = 22400 - 100(x + 45)\\\\40(x +45) + 100(x+ 45) = 22400\\\\140(x + 25) = 22400\\\\x + 45 = \frac{22400}{140}\\\\x = 160 - 45 = \£ \ 115[/tex]
Total cost price = 45 + 115 = £160
Step 2 : Selling price of Helmet
Cost price of Helmet = £45
Let selling price of helmet be = y
Profit % of helmet = 120 %
[tex]Profit \% = \frac{selling \ price - cost \ price}{cost \ price}[/tex]
[tex]\frac{120}{100} = \frac{y -45}{45}\\\\\frac{120 \times 45}{100} = y -45\\\\54 = y - 45\\\\99 = y[/tex]
Step 3 : Selling price of skates
Total selling = selling price of helmet + selling price of skates
224 = 99 + selling price of skates
224 - 99 = selling price of skates
125 = selling price of skates
Step 4 : Profit percentage on skates
Cost price of skate = £ 115
Selling price of skate = £ 125
[tex]Profit \% \ on \ skates = \frac{selling\ price- cost \ price }{cost \ price} \times 100[/tex]
[tex]= \frac{125-115}{115} \times 100\\\\=\frac{10}{115} \times 100\\\\= 8.7 \%[/tex]
A golfer hits a golf ball.
The function
d(t) = –2t2 + 7t + 4
most closely represents the height(h) of the golf ball in feet after t seconds. How
long is the golf ball in the air?
Answers
Answer:
The golf ball was in the air for 4 seconds.
Step-by-step explanation:
Solving a quadratic equation:
Given a second order polynomial expressed by the following equation:
[tex]ax^{2} + bx + c, a\neq0[/tex].
This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:
[tex]x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}[/tex]
[tex]x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}[/tex]
[tex]\Delta = b^{2} - 4ac[/tex]
In this question:
We have to find the amount of time it takes for the ball to hit the ground. We have that:
[tex]d(t) = -2t^2 + 7t + 4[/tex]
Which is a quadratic equation with [tex]a = -2, b = 7, c = 4[/tex].
How long is the golf ball in the air?
We have to find t for which [tex]d(t) = 0[/tex]
So
[tex]-2t^2 + 7t + 4 = 0[/tex]
[tex]\Delta = b^{2} - 4ac = (7)^2 - 4(-2)(4) = 81[/tex]
[tex]t_{1} = \frac{-7 + \sqrt{81}}{2*(-2)} = -0.5[/tex]
[tex]t_{2} = \frac{-7 - \sqrt{81}}{2*(-2)} = 4[/tex]
Time is a positive measure, so t = 4.
The golf ball was in the air for 4 seconds.
What is the solution to this inequality?
14 + x ≤ 26
Answers
Answer:
[tex]14 + x \leqslant 26 \\ x \leqslant 26 - 14 \\ { \tt{x \leqslant 12}}[/tex]
A
2x+5
x² + 5x + 6
x² + 5x+6
B
2x+5
Answers
Answer:
what is the question?
Step-by-step explanation:
answer the question
Find the surface area of each solid figure
Answers
Answer:
First find the SA of the triangular figure
4 x 3 = 12 cm^2 (the triangles on the sides)
2 x 3 = 6 cm^2 (the back square)
2 x 5 = 10 cm^2 (the slanted square)
*I'm not sure if this question includes the bottom of the triangle but here it is anyways
4 x 2 = 8 cm^2
Including the bottom the SA of the triangular figure is:
12 + 6 + 10 + 8 = 36 cm^2
Find the SA of the rectangular shape
4 x 2 = 8 cm^2 (the bottom square)
2 x 6 = 12 x 2 = 24 cm^2 (the sides)
4 x 6 = 24 x 2 = 48 cm^2 (the front and back)
Add them up
8 + 24 + 48 = 80 cm^2
If you wanted to find the SA of the whole figure it would be:
12 + 6 + 10 + 8 + 24 + 48 = 108 cm^2
Hope this helps!
What is the mean of the data?
Answers
Answer:
The mean (average) of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set. The median is the middle value when a data set is ordered from least to greatest. The mode is the number that occurs most often in a data set.
Lori downloaded all the pictures she took at Rita’s wedding into a single computer folder. She took 86 of the 134 pictures with her camera and the remainder of them with her cell phone. Of the pictures Lori took with her cell phone, one out of every five was blurry.
Answers
Answer:
87
Step-by-step explanation:
Find the area of this circle. Use 3 for T.
Α = πη2
5 in
[?] in?
Answers
Hope this help!!!
Have a nice day!!!
Use the slope formula to find the slope of the line through the points (2,10) and (10,−8).
Answers
The slope formula is the changes of two y-values over/to the changes of two x-values.
[tex] \large \boxed{m = \frac{y_2 - y_1}{x_2 - x_1} }[/tex]
Substitute two given points in the formula to find the slope. The m-term represents the slope from y = mx+b.
[tex]\large{m = \frac{10 - ( - 8)}{2 - 10} } \\ \large{m = \frac{10 + 8}{ - 8} } \\ \large{ m = \frac{18} { - 8} \longrightarrow \frac{9}{ - 4} } \\ \large \boxed{m = - \frac{9}{4} }[/tex]
Answer
The slope is -9/4.Hope this helps and let me know if you have any doubts!
Answer:
m=-9/4
Step-by-step explanation:
Hi there!
The formula for the slope (m) calculated from two points is given as (y2-y1)/(x2-x1), where (x1,y1) and (x2,y2) are points
we are given the two points (2,10) and (10,-8)
to avoid any confusion, let's label the values of the points
x1=2
y1=10
x2=10
y2=-8
now substitute into the formula:
m=(-8-10)/(10-2)
subtract
m=(-18)/(8)
simplify (reduce to lowest terms)
m=-9/4
Hope this helps!
SOMEONE HELP ME PLEASE
find the real fifth root of -32
Answers
Answer: -2
This is because (-2)^5 = -32. Applying the fifth root to both sides lets us say [tex]-2 = \sqrt[5]{-32}[/tex]
There are four other roots but they are complex. Effectively, we are solving the equation [tex]x^5 + 32 = 0[/tex]
WHAT is the answer? Pls Time limit
Answers
Answer:
11 is the answer.....
Step-by-step explanation:
6x-15+39+90 = 180
Use implicit differentiation to find an equation of the tangent line to the curve at the given point. y2(y2 − 4) = x2(x2 − 5) (0, −2) (devil's curve)
Answers
Answer:
Step-by-step explanation:
Given that:
[tex]y^2 (y^2-4) = x^2(x^2 -5)[/tex]
at point (0, -2)
[tex]\implies y^4 -4y^2 = x^4 -5x^2[/tex]
Taking the differential from the equation above with respect to x;
[tex]4y^3 \dfrac{dy}{dx}-8y \dfrac{dy}{dx}= 4x^3 -10x[/tex]
Collect like terms
[tex](4y^3 -8y)\dfrac{dy}{dx}= 4x^3 -10x[/tex]
[tex]\dfrac{dy}{dx}= \dfrac{4x^3 -10x}{4y^3-8y}[/tex]
Hence, the slope of the tangent line m can be said to be:
[tex]\dfrac{dy}{dx}= \dfrac{4x^3 -10x}{4y^3-8y}[/tex]
At point (0,-2)
[tex]\dfrac{dy}{dx}= \dfrac{4(0)^3 -10(0)}{4(-2)^3-8-(2)}[/tex]
[tex]\dfrac{dy}{dx}= \dfrac{0 -0}{4(-8)+16}[/tex]
[tex]\dfrac{dy}{dx}= 0[/tex]
m = 0
So, we now have the equation of the tangent line with slope m = 0 moving through the point (x, y) = (0, -2) to be:
(y - y₁ = m(x - x₁))
y + 2 = 0(x - 0)
y + 2 = 0
y = -2
Patel squeezed oranges so that his family could have fresh-squeezed juice for breakfast. He squeezed StartFraction 4 over 17 EndFraction cups from the first orange, StartFraction 3 over 10 EndFraction cups from the second orange, StartFraction 9 over 20 EndFraction cups from the third orange, StartFraction 3 over 11 EndFraction cups from the fourth orange, and StartFraction 7 over 15 EndFraction cups from the fifth orange. Patel estimates that he needs 3 cups of orange juice for his family. About how much more orange juice does he need to reach his estimate?
Answers
Answer:
A. 1/2 cups
Step-by-step explanation:
13/15 is close to 1
1/5 is a small amount
9/20 is just over 1/2
5/11 is just under 1/2
7/15 is just under 1/2
Estimate: 1 + 1/2 + 1/2 + 1/2 + a little = 2 1/2
He needs 3 cups, so he needs another 1/2 cup.
Answer: A. 1/2 cups
Answer:
it a 1/2
Step-by-step explanation:
Longhorn Pizza has the following number of topping options available: four vegetables, two meats, and two cheeses. A pizza is ordered with exactly four toppings. What is the probability that the pizza is ordered with exactly two vegetables, one meat, and one cheese
Answers
Answer:
The probability is [tex]\frac{24}{70}[/tex].
Step-by-step explanation:
topping options available: four vegetables, two meats, and two cheeses
Number of topping on one pizza = 4
Getting two vegetables = (4 C 2)
Getting one meat = (2 C 1)
Getting one cheese = (2 C 1)
Choosing 4 toppings out of 8 = (8 C 4)
probability that the pizza is ordered with exactly two vegetables, one meat, and one cheese
[tex]\frac{(4C2)\times (2C1)\times (2C1)}{(8C4)}\\\\\frac{6\times 2\times 2}{70}\\\\\frac{24}{70}[/tex]
3. Find the value of X (In the picture) (giving points to best answer/brainlest)
Answers
Answer:
101 =x
Step-by-step explanation:
The measure of the exterior angle is equal to the sum of the opposite interior angles
143 = 42+x
Subtract 42 from each side
143-42 = 42+x-42
101 =x
Answer:
x = 101 degrees
Step-by-step explanation:
The sum of the external angle and its adjacent is 180 degrees
143 + y = 180
y = 37 degrees
The sum of the inner angles of a triangle is 180 degrees
37 + 42 + x = 180
79 + x = 180
x = 101 degrees
Find the equation of a line with a slope of −1/2 that passes through the point −4, 10
Answers
Answer:
y - 10 = -1/2(x + 4)
General Formulas and Concepts:
Algebra I
Coordinates (x, y)
Point-Slope Form: y - y₁ = m(x - x₁)
x₁ - x coordinate y₁ - y coordinate m - slopeStep-by-step explanation:
Step 1: Define
Identify variables
m = -1/2
Point (-4, 10) → x₁ = -4, y₁ = 10
Step 2: Find
Substitute in variables [Point-Slope Form]: y - 10 = -1/2(x - -4)Simplify: y - 10 = -1/2(x + 4)Answer: [tex]y=-\frac{1}{2} x+8[/tex]
Step-by-step explanation:
An equation of a line can be in slope intercept form which is y=mx+b
m is the slope, b is the y intercept, x it the x coordinate, and y is the y coordinate. Since we know the slope is -1/2 and we know a x coordinate is -4 and a y coordinate is 10 we can sub them in and solve for the value of b.
[tex]y=mx+b\\10=(-\frac{1}{2})(-4)+b\\10=2+b\\10-2=2+b-2\\8=b[/tex]
The value of b is 8. We can now sub it in for our equation of the line. This time with x and y as variables.
y=-1/2x+8
You deposit $10,000 in an account earning 4% interest compounded monthly. a. How much will you have in the account in 25 years? b. How much interest will you earn?
Answers
Answer:
In 25 years I will have $ 27,137.65. Therefore, I will earn $17,137.65 interest.
Step-by-step explanation:
Given that I deposit $ 10,000 in an account earning 4% interest compounded monthly, to determine how much will you have in the account in 25 years and how much interest will I earn, the following calculation must be performed:
10,000 x (1 + 0.04 / 12) ^ 25x12 = X
10,000 x (1 + 0.00333) ^ 300 = X
10,000 x 2.7137 = X
27,137.65 = X
Therefore, in 25 years I will have $ 27,137.65. Therefore, I will earn $17,137.65 interest.
50 points!!
The first few steps in deriving the quadratic formula are
shown.
Which best explains why
62
is not added to the left
40?
-C-ax? +bx
side of the equation in the last step shown in the table?
Use the subtraction property of
equality
Factor out a
-ax² + x
O The term
b?
is added to the right side of the
40²
b?
b
2a
Find half of the b value and square
it to determine the constant of the
perfect square trinomial
4a?
equation, so it needs to be subtracted from the left
side of the equation to balance the sides of the
equation.
ba
-C-
4a
a
4a
The distributive property needs to be applied to
determine the value to add to the left side of the
equation to balance the sides of the equation.
O The term
b2
40²
needs to be converted so it has a
common denominator before adding it to the left side
of the equation to balance the equation.
© The square root of the term needs to be found before
Answers
Answer:
The distributive property needs to be applied to determine the value to add to the left side of the equation to balance the sides of the equation
Step-by-step explanation:
There is a factor of a outside of the parentheses on the right has side
We are really adding a( b^2/4a^2) to the right side
Simplifying we are adding b^2 /4a
This is what we need to add to the left side to be fair and equal.
We used the distributive property to determine what we were actually adding to the right side.
Question 4 of 10
Which of the following formulas would find the lateral area of a right cylinder
with height equal to hand r as the radius?
A. LA = 2012 + 2q rh
B. LA = 20
C. LA = 2 r rh
D. LA = 27.12
SUBMIT
Answers
Answer:
LA = 2πrh
Step-by-step explanation:
The lateral surface area is the area of all the sides of a 3-dimensional object excluding its base and top.
The lateral area of a cylinder is the area of its surfaces excluding the area of its base and top
LA = 2πrh
PLEASE WILL MARK IF YOU HELP!!
Answers
Answer:
22°
63°
m<H=22°
m<G=63°
Problem 1
Answer: 79--------------------------
Work Shown:
For any triangle, the three angles always add to 180
For any isosceles triangle, the base angles are congruent. The base angles are opposite the congruent sides. We see that angle O = angle H.
O+H+T = 180
H+H+T = 180
2H+T = 180
2H+22 = 180
2H = 180 - 22
2H = 158
H = 158/2
H = 79
=======================================================
Problem 2
Answer: 54--------------------------
Work Shown:
We'll use the same ideas as problem 1.
In this case, angle O = angle D = 63 since they are the base angles opposite the congruent sides.
D+G+O = 180
63+G+63 = 180
G+126 = 180
G = 180-126
G = 54
A triangle has three vertices at the points A = (0, -2), B = (3, 4), and C = (-1.5, 2.5). Prove that this triangle is a right-angle triangle, using algebra. (Note: a right angle triangle has one 90 degree angle).
Answers
Answer:eraf
Step-by-step explanation:
Help! I will give brainliest!
Answers
Answer:
B 24
Step-by-step explanation:
3/5 is 54°
1/3 is 30°
54-30 = 24
Find the value of x 720
Answers
9514 1404 393
Answer:
x = 63
Step-by-step explanation:
The base angles of each isosceles triangle are equal, so we can write the sum of the four angles in the quadrilateral as ...
72° +(72° +x°) +x° +90° = 360° . . . . . clockwise from upper left
2x = 126 . . . . . . . . . divide by °, subtract 234
x = 63 . . . . . . . . . . . divide by 2
I need the answer. Please help me
Answers
C = 25 deg
a ≈ 10.72 ft
b ≈ 11.83 ft
Answer:
C = 25
a = 10.72
b = 11.83
Step-by-step explanation:
C:
Solve; 180 - (90 + 65)
a:
Tan(65) = a/5
Tan(65) * 5 = a
10.72 = a
b:
Cos(65) = 5/b
Cos(65) * b = 5
b = 5 / Cos(65)
b = 11.83
Hope this helps!
PLEASE HELP!!!
WILL MARK BRAINLIEST!!!
If the diameter of the circle shown below is 6ft and 0 is a right angle, what is the length of segment AB to the nearest foot?
Multiple choice!
Thank you!
Answers
Answer:
how old are you gghhjjzetstu9u
Answer:
4 ft
Step-by-step explanation:
let's find radius first
radius=diameter/2
=6/2
=3 ft
radii=3 ft
Now by using pythagoras theorem
a^2 + b^2 = c^2
3^2 + 3^2 =AB^2
9+9=AB^2
18=AB^2
[tex]\sqrt{18}[/tex] AB
4.24 =AB
4 ft =AB (after converting to nearest foot)
PLEASE HELP ME I HAVE TO PASS THIS TEST
30 POINTS
Answers
Answer:
Hi, there the answer is
These are the equations with exactly one solution
-5x + 12 = –12x – 12
-5x + 12 = 5x + 12
-5x + 12 = 5x – 5
Hope This Helps :)
Step-by-step explanation:
First degree equations
A first degree equation has the form
ax + b = 0
There are some special cases where the equation can have one, infinitely many or no solution
If , the equation has exactly one solution
If a=0 and b=0 the equation has infinitely many solutions, because it doesn't matter the value of x, it will always be true that 0=0
If a=0 and the equation has no solution, because it will be equivalent to b=0 and we are saying it's not true. No matter what x is, it's a false statement.
We have been given some equations, we only need to put them in standard form
-5x + 12 = –12x – 12
Rearranging
7x + 24 = 0
It has exactly one solution because a is not zero
.......................
-5x + 12 = 5x + 12
Rearranging
-10x + 0 = 0
It has exactly one solution because a is not zero
.......................
-5x + 12 = 5x – 5
Rearranging
-10x + 17 = 0
It has exactly one solution because a is not zero
.......................
-5x + 12 = -5x – 12
Rearranging
0x + 24 = 0
It has no solution, no matter what the value of x is, it's impossible that 24=0
Answer: These are the equations with exactly one solution
-5x + 12 = –12x – 12
-5x + 12 = 5x + 12
-5x + 12 = 5x – 5
What is the zero of the function represented by this graph?
Answers
explanation: the x-intercept is (-5,0), the x value of the x intercept is the zero.
Find all real zeros of the function y = -7x + 8
Answers
9514 1404 393
Answer:
x = 8/7
Step-by-step explanation:
The only real zero of this linear function is the value of x that makes y=0:
0 = -7x +8
7x = 8 . . . . . . add 7x
x = 8/7 . . . . . .divide by 7
