Answer:
Step-by-step explanation:
discriminant = 3² – 4·2(-10) = 89
discriminant > 0 ∴ two real solutions
Can someone please help me with continuity? I would like to check my work, I’m a bit confused on the differentiability part
For f to be continuous at some point x = c, you require that
• f(c) exists and is finite, and
• the limits of f as x approaches c from either side match, and their value must be f(c)
For f to be differentiable at x = c, you require that
• f is continuous at c (i.e. the above conditions are all met), and
• the derivative f ' is continuous at c
Without having the graph of f ', you can assess whether the last condition is met by some function by mentally tracing a tangent line to the graph as you get closer to c. If the slope of the tangent doesn't change, then the function is differentiable. This is usually accompanied by jumps or sharp corners in the graph.
Some examples:
• every polynomial is both continuous and differentiable
• the absolute value function |x| is continuous but not differentiable at x = 0
• 1/x is neither continuous nor differentiable at x = 0
(a) Neither continuous nor differentiable
Why? f has a vertical asymptote at x = -2 and f (-2) does not exist. f is not continuous, and therefore not differentiable.
(b) Neither continuous nor differentiable
Why? From the left, f is approaching 2.5, while from the right, it's approaching 5.
(c) Neither continuous nor differentiable
Why? The limits from either side of x = 2 match and are equal to 0.5, but f (2) itself does not exist (which is indicated by the point being a hollow circle).
If the circle was instead filled in, so that f (2) = 0.5, then f would be continuous there, but still not differentiable. Notice the sharp corner. Or, using the tangent-line analysis, the slope of the tangent to the left of x = 2 is negative, but to the right it would be positive.
(d) Both continuous and differentiable
Why? f doesn't have any special features at x = 3 that would suggest it's not continuous nor differentiable.
(e) Neither continuous nor differentiable
Why? Similar reasoning as in (a). There's another vertical asymptote, but the graph shows f (4) = 1. However, the limits from either side of x = 4 are positive infinity, not 1.
solve and receive brain list
Answer:
x = 19/22
Step-by-step explanation:
8x-12+36x = 26
44x - 12 = 26
44x = 38 (add 12 on both sides)
x = 19/22 (divide bot sides by 44 and simplify)
Derrick has 2 1/2 cups of sugar. He needs 1/8 of a cup of sugar for each recipe. How many recipes can be make
Answer:
20
Step-by-step explanation:
Julie drank 2/3 liter of water monday before going jogging she drank 5/7 liter of water after her jog how much water did julie drink altogether answer in mixed number
Answer:
1 8/21
Step-by-step explanation:
5/7 = 15/21
2/3 = 14/21
15/21+14/21=29/21
The Maine Public Health Department reported that there have been 90 flu cases requiring hospitalization in Portland, ME (population of 70,000) since the beginning of 2018 - today is July 4th, 2018. On February 1st, 2018, 43 of those cases were hospitalized. What was the prevalence rate of flu cases requiring hospitalization thus far in 2018?
Answer:
The prevalence rate of flu cases requiring hospitalization thus far in 2018 is:
= 0.13%
Step-by-step explanation:
a) Data and Calculations:
Population of Portland, ME = 70,000
Number of flu cases requiring hospitalization on February 1st, 2018 = 43
Number of flu cases requiring hospitalization on July 4th, 2018 = 90
The prevalence rate of flu cases requiring hospitalization thus far in 2018 = 90/70,000 * 100 = 0.13%
b) The prevalence rate represents the proportion of the population of Portland, ME, who have the flu at the time that the Maine Public Health Department reported the number of flu cases requiring hospitalization on July 4th, 2018.
Graph the linear function using slope intercept form
y=2x+6
Solve the following problems. Rajesh jogged 3/4 mile and then walked 1/6 mile to cool down . how far did he travel?
Answer: 11/12 or if you want to pit it in decimal
Use 0.90
Step-by-step explanation:
What is 5/10 = x/100
Answer:
= 50
Step-by-step explanation:
In triangle DEF, if the measures of angles D and E are equal, and the measure of
angle F is 26, what are the measure of angles D and E?
Your answer
Answer:
77 = m∠D = m∠E
Step-by-step explanation:
In a triangle the sum of the measures of the angles = 180. So m∠D + m∠E + m∠F = 180
Let m∠D = m∠E = x
Then x + x + 26 = 180
2x + 26 = 180
2x = 154
x = 77 = m∠D = m∠E
Use the coordinates of the labeled point to find the point-slope equation of
the line
812-18
O A. y + 1 = -2(x - 2)
O B. y-2-2(x+1)
O C. y- 1 = -2(x + 2)
O D. y-2 = 2(x + 1)
Answer: y+1 = -2(x-2) is the correct answer
Step-by-step explanation: I just took the exam :)
Ally and Beck went fishing and caught a total of 75 fish. At home,
Ally told Jair she caught twice as many fish as she actually caught.
Beck told Jair he caught three times as many fish as he actually
caught. If what they told Jair had been true, then Ally would have
caught 75 fewer fish than Beck. How many fish did Beck actually
catch?
Answer:
Beck actually caught 45 fish
Step-by-step explanation:
System of Equations
We call the following variables:
x = number of fish Ally caught
y = number of fish Beck caught
They caught a total of 75 fish, thus:
x + y = 75 [1]
If Ally had caught twice as much fish as she actually did, and Beck had caught three times as many fish as he actually did, then Ally would have caught 75 fewer fish than Beck, thus:
3y = 2x + 75 [2]
From [1]:
x = 75 - y [3]
Substituting in [2]:
3y = 2(75 - y) + 75
Operating:
3y = 150 - 2y + 75
Simplifying:
5y = 225
Dividing by 5:
y = 45
Beck actually caught 45 fish
Answer:
Beck caught 45 fish
Step-by-step explanation:
a = number of fish Ally caught
b = number of fish Beck caught
They caught a total of 75 fish, so we have:
b + a = 75
From the facts in our question we know Ally would have caught 75 fewer fish than Beck.
3b = 2a + 75
a = 75 - b
3b = 2(75 - b) + 75
3b = 150 - 2b + 75
5b = 225
5b ÷ 5 = 225 ÷ 5
b = 45
Beck caught 45 fish.
Which of these polygons is not a regular polygon?
B
С
D
А
B
A
Answer:
B. A regular polygon is a shape with sides that are all equal to each other.
We see that for shape B, the sides are not equal to each other, as some sides are longer than others.
Hope this helps!
What is the answer. I can’t figure out the formula
9514 1404 393
Answer:
Angles 4, 5, 6, 7, 8, 9 are 82°Angles 1, 2, 3, 10, 11, 12 are 98°Step-by-step explanation:
Angles are related in this geometry by being either congruent or supplementary. Corresponding and vertical angles are congruent; any linear pair of angles is supplementary.
The given angle 5 is on the southwest corner of the intersection of the parallel line with the transversal. All southwest and northeast angles are congruent to that. That is, angles 4, 5, 6, 7, 8, 9 will all have the same measure. The remaining angles will have the supplementary measure.
Angles 4, 5, 6, 7, 8, 9 are 82°
Angles 1, 2, 3, 10, 11, 12 are 98°
_____
As you know, supplementary angles total 180°, so each is found by subtracting the other from 180°: 180° -82° = 98°.
please help me find this out please
Answer:
can you zoom in on the questions?
Step-by-step explanation:
What is the value of x?
Ms. Hart paid $300 for 6 admission tickets and a $15 parking pass for an amusement park.
What is the cost of one admission ticket?
The cost of one admission ticket is $
Answer:
The cost of one admission ticket is 47.5
A small water bottle holds 75% as much as a larger water bottle, if the smallholds 36 units, how much does a large hold
Answer:
48 units
Step-by-step explanation:
36 is 75% of what number
36 = .75n
n = 36/.75
n = 48
Write the quadratic equation whose roots are 6 and -6, and whose leading coefficient is 2.
(Use the letter x to represent the variable.)
Answer:
y = 2x² - 72 = 0
Step-by-step explanation:
2(x - 6)(x + 6) = 0
2(x² - 36) = 0
2x² - 72 = 0
The quadratic equation with roots 6 and -6 and a leading coefficient of 2 is 2x² - 72 = 0 represents the quadratic equation.
A quadratic equation with roots at 6 and -6 can be written in factored form as:
(x - 6)(x + 6) = 0
To find the quadratic equation with the leading coefficient of 2, we multiply both sides of the equation by 2:
2(x - 6)(x + 6) = 0
Expanding the equation:
2(x² - 36) = 0
Distributing the 2:
2x² - 72 = 0
Therefore, the quadratic equation with roots 6 and -6 and a leading coefficient of 2 is:
2x² - 72 = 0
To know more about quadratic equation click here :
https://brainly.com/question/30111792
#SPJ2
WILL MARK BRAINLIST JUST ANSWER QUICKLY
A puddle originally contained 5 gallons of water. After a hot day, only 3.5 gallons of water remain.
What is the percent decrease?
Enter your answer in the box.
Answer:
The answer is 30%
Step-by-step explanation:
((5-3.5)/5) × 100%
Answer:
30%
Step-by-step explanation:
the other guy is right
Your friend has one week to pay the $26 fine for a parking ticket. After that, the fine Increases $7 each week.
A student council sells 44 bouquets for $176. Which equation represents the
relationship of x bouquets to y dollars?
Answer:
[tex]y = 4x[/tex]
Step-by-step explanation:
Given
[tex]x = 44[/tex]
[tex]y = 176[/tex]
Required
Determine the relationship between x and y
First, we calculate the unit rate, using:
[tex]y = kx[/tex]
Where k is the unit rate.
Substitute 176 for y and 44 for y
[tex]176 = k * 44[/tex]
Divide both sides by 44
[tex]\frac{176}{44} = \frac{44*k}{44}[/tex]
[tex]\frac{176}{44} = k[/tex]
[tex]4 = k[/tex]
[tex]k = 4[/tex]
Substitute 4 for k in [tex]y = kx[/tex]
[tex]y = 4x[/tex]
Hence, the relationship between x and y is: [tex]y = 4x[/tex]
evaluate the following algebraic expression for the given value of x.
4x-5 where x=5
Answer:
15 is answers
x=5
Step-by-step explanation:
4x-5
4×5-5
20-5
15
Solve the equation and show all your work. 7x = 4x + 15
Answer:
x=5
Step-by-step explanation:
subtract 4x from both sides
7x-4x=4x-4x+15
3x=15
divide by 3 on both sides
3x/3=15/3
x=5
if x is subtracted from 5 and the result is greater than 15. Find the range of values of x
Answer:
x<-10
Step-by-step explanation:
You can write this inequality:
5-x>15
Solving it:
5-x>15
-x>10
x<-10
Please show work so i know how you got your answer
Answer:
24
Step-by-step explanation:
7 5/6 x3 =23.5
In detail and with multiple examples, describe how you can use math in your daily life. it needs 15 to 16 sentence i will give you brainest help me plzzz
Hi, can someone help me?
Answer:
No, no puedo ayudarte aunque te deseo buena suerte
Answer:
the price !!
Step-by-step explanation:
the price of donut holes depends on the number of them!! you cant tell the price without the donuts !!
a way to think of it could be "the price can't exist without the product (the donuts) so, the price dependent on the donuts. its the dependent!"
i really hope this helps!
A bakery sold 36 brownies in a day, which was 30% of the total items sold that day. What was the total number of items the bakery sold that day?
Answer:
120
Step-by-step explanation:
We know that 36 is 30% of total items
So our equation would be 36/? = 30/100
From there we cross multiply so 36x100 = 3600
From there, we divide 3600 by 100
Therefore, your answer is 120
determine whether a triangle with these side lengths would be acute, right, or obtuse: 5, 7, and 10;
Answer:
obtuse
Step-by-step explanation:
Let 5 = a, 7 = b, 10 = c
if a^2 + b^2 = c^2, then the triangle is a right triangle by the converse of the Pythagorean Theorem
If a^2 + b^2 > c^2, then the triangle is an acute triangle by Theorem 8-4
if a^2 + b^2 < c^2, then the triangle is an obtuse triangle by Theorem 8-3
a^2 = 25
b^2 = 49
c^2 = 100
25 + 49 < 100, therefore the triangle is an obtuse
Write the equation for the graphed function
Answer:
4x² + 16x + 15 = 0
Step-by-step explanation:
We'll begin by determining the solutions to the graph.
The solutions to the graph is obtained by taking the values where the graph cut through the x–axis. This is illustrated below:
The solutions to the graph are:
x = –1.5 or –2.5
Finally, we shall determine the equation for the graph as follow:
x = –1.5 or x = –2.5
x = –3/2 or x = –5/2
Cross multiply
2x = –3 or 2x = –5
Rearrange
2x + 3 = 0 or 2x + 5 = 0
Combine
(2x + 3)(2x + 5) = 0
Expand
2x(2x + 5) + 3(2x + 5) = 0
4x² + 10x + 6x + 15 = 0
4x² + 16x + 15 = 0
Thus, the equation for the graph is:
4x² + 16x + 15 = 0