Both x² and mx + b are differentiable functions of x (they are both polynomials), so if f(x) is also differentiable, we need to pay special attention at x = 2 where the two pieces of f meet.
Continuity means that the limit
[tex]\displaystyle \lim_{x\to2} f(x)[/tex]
must exist.
From the left side, we have x < 2 and f(x) = x², so
[tex]\displaystyle \lim_{x\to2^-} f(x) = \lim_{x\to2} x^2 = 4[/tex]
From the right, we have x > 2 and f(x) = mx + b, so
[tex]\displaystyle \lim_{x\to2^+} f(x) = \lim_{x\to2} (mx+b) = 4m+b[/tex]
It follows that 4m + b = 4.
Differentiability means that the limit
[tex]\displaystyle \lim_{x\to2} \frac{f(x) - f(2)}{x - 2}[/tex]
must exist.
From the left side, we again have x < 2 and f(x) = x². Then
[tex]\displaystyle \lim_{x\to2^-}\frac{f(x)-f(2)}{x-2} = \lim_{x\to2} \frac{x^2-4}{x-2} = \lim_{x\to2} (x+2) = 4[/tex]
From the right side side, we have x > 2 so f(x) = mx + b. Then
[tex]\displaystyle \lim_{x\to2^+}\frac{f(x)-f(2)}{x-2} = \lim_{x\to2} \frac{(mx+b)-(2m+b)}{x-2} = \lim_{x\to2} \frac{mx-2m}{x-2} = \lim_{x\to2}m = m[/tex]
The one-sided limits must be equal, so m = 4, and from the other constraint it follows that 16 + b = 4, or b = -12.
Nine lollies cost less than $10, while ten lollies cost more than $11 how much does each lollipop cost?
$21 it will cost for lollipop
Answer:
$1.10
Step-by-step explanation:
1.10 times 10
Vector u has a magnitude of 5 units and a direction angle of 30°. Vector v has a magnitude of 7 units and a direction angle of 120°. What is the direction angle of their vector sum?
A. 82.21°
B. 84.46°
C. 85.11°
D. 86.13°
Answer:
B. 84.46°
Step-by-step explanation:
Since the vectors are at right angles to one another, even a crude diagram will quickly show you that the direction of the sum is ...
30° + arctan(7/5) ≈ 84.4623° ≈ 84.46°
What is the y-coordinate of the point of intersection for the two lines given below?
A: 4
B: -14
C: -3
D: -2
Answer:
B. -14
Step-by-step explanation:
If you solve the system using the method of elimination, the y terms will automatically cancel each other out without any manipulation at all. So go with it and solve for x first. If the y terms cancel out, you're left with x = -3.
If x = -3, sub that value in for x in eitheer one of the original equations and solve for y:
[tex]3x-y=5[/tex] becomes
[tex]3(-3)-y=5[/tex] and
[tex]-9-y=5[/tex] so
[tex]y=-14[/tex]
What is the probability of randomly selecting an odd number from the numbers 1-15
Answer:
7/15
Step-by-step explanation:
odd numbers are those that do not have divides ie1,2,3,5,7,11,13
The probability of randomly selecting an odd number from the numbers 1-15 is 8/15.
What is the probability?
Probability is used to know the odds that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
Probability that a randomly selected number would be odd = number of odd numbers / total numbers
Odd numbers between 1 and 15 = 1 , 3, 5, 7, 9, 11, 13, 15
Probability that a randomly selected number would be odd = 8/15
To learn more about probability, please check: https://brainly.com/question/13234031
#SPJ2
Joanne divided 14 of a pastry into 3 equal pieces. Which fraction of the original pastry represents each of the 3 pieces Joanne cut?
Answer:
[tex]\frac{1}{12}[/tex]
Step-by-step explanation:
Note Is a 1/4 of a pastry instead of 14 of a pastry
we know that
To find the fraction of the original pastry that represents each of the 3 pieces cut by Joanne, divide 1/4 by 3
so
[tex](1/4)/3=\frac{1}{12}[/tex]
Answer:
1/12
Step-by-step explanation:
Match the type of graph with its description.
1. bar graph
2. line graph
3. scatter plot
4. histogram
5. box-and-whisker plot
a. Compares data that is in categories.
b. Used to see trends in data.
c. Organizes data into 4 groups of equal size, and is often used to compare two sets of data.
d. Shows change over time.
e. Shows frequency of data, using equal intervals with no space between the bars.
1. bar graph - Compares data that is in categories.
2. line graph - Shows change over time.
3. scatter plot - Used to see trends in data.
4. histogram - Shows frequency of data, using equal intervals with no space between the bars.
5. box-and-whisker plot - Organizes data into 4 groups of equal size, and is often used to compare two sets of data.
School is almost over, good luck!!
Write the rule for the translation
Answer:
(x, y)-->(x-7, y+4)
Step-by-step explanation:
To get from T to T', you have to move the image 7 units to the left of the preimage. From that point, you have to move up 4.
You deposit 350 in an account that pays 3% annual intrest. Find the balance afer 2 years if the intrest is compounded
[tex]\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$350\\ r=rate\to 3\%\to \frac{3}{100}\dotfill &0.03\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &2 \end{cases} \\\\\\ A=350\left(1+\frac{0.03}{1}\right)^{1\cdot 2}\implies A=350(1.03)^2\implies A=371.315[/tex]
What is the volume of a sphere whose radius is 6 ft
Answer:
Option C. [tex]288\pi\ ft^{3}[/tex]
Step-by-step explanation:
we know that
The volume of a sphere is equal to
[tex]V=\frac{4}{3} \pi r^{3}[/tex]
we have
[tex]r=6\ ft[/tex]
substitute
[tex]V=\frac{4}{3} \pi (6)^{3}[/tex]
[tex]V=288\pi\ ft^{3}[/tex]
The volume of the sphere with a radius of 6 ft is 904.78 ft³.
Explanation:The volume of a sphere can be calculated using the formula: V = (4/3)πR³. Given a radius of 6 ft, we can substitute this value into the formula to find the volume:
V = (4/3)π(6 ft)³
V = (4/3)π(216 ft³)
V = 904.78 ft³
Learn more about volume of a sphere here:https://brainly.com/question/21623450
#SPJ3
Given that f(x) is the original function, what is true about the transformation, g(x)? g(x) is reflected about the y-axis. g(x) is reflected about the y-axis and shifted up by 4 units. g(x) is reflected about the x-axis. g(x) is reflected about the x-axis and shifted up by 4 units.
Answer:
C
GX is reflected across the X-axis
g(x) is reflected across the X-axis if f(x) is the original function.
What is function?function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.
here we have f(x) is the original function, the true value of g(x) is that g(x) is reflected across the X-axis.
To know more about function follow
https://brainly.com/question/25638609
#SPJ2
Last week at best bargain, 75% of the computers sold were laptops. If 340 computers were sold last week, how many laptops were sold?
Answer:
255
Step-by-step explanation:
1. 75% is actually 0.75, and you want to find 75% of 340.
2. Multiply 0.75 and 340. 0.75 x 340 = 255
3. Answer = 255
A company launches 4 new products. The market price, in dollars, of the 4 products after a different number of years, x, is shown in the following table:
Product Function Year 1
(dollars) Year 2
(dollars) Year 3
(dollars)
Product 1 f(x) = 4x + 8 12 16 20
Product 2 g(x) = 2^x 2 4 8
Product 3 h(x) = x^2 + 12 13 16 21
Product 4 j(x) = x^3 1 8 27
Based on the data in the table, for which product does the price eventually exceed all others?
Product 1
Product 2
Product 3
Product 4
It’s product two right???
Product 4 after the third year is 27 which is higher than the rest after 3 years.
And because x is raised to the third, the amount would Increase by being raised to the 3rd every year.
The answer is Product 4.
prove that 5^31–5^29 is divisible by 100.
5^31-5^29
=5^29(5^2-1)
=5^29(25-1)
=5^29(24) ...a
100=5^2x4 ...b
Divide a by b
5^29(24) / 5^2 x 4
=5^27 x 6
This, 5^31-5^29 is divisible by 100.
An investment advisor believes that there is a 30% chance of making money by investing in a specific stock. If the stock makes money, then there is a 52% chance that among those making money, they would also get a dividend. Find the probability that the investor makes money but does not receive a dividend.
First, you have to find the 52% of the 30%(chance that he gets a dividend) .Then you simply have to subtract the result (15.6%) from the 30%. Your result is 14.4% chance that he wont get a divident.
Answer:
14.4%
Step-by-step explanation:
An investment advisor believes that there is a 30% chance of making money by investing in a specific stock. If the stock makes money, then there is a 52% chance that among those making money, they would also get a dividend. Find the probability that the investor makes money but does not receive a dividend.
Probability is the chance/likelihood that an event will occur or not
The chances that one makes money from a stock is 30%
Chances that one will not=70%
Chances that there will dividend among those who made money is =52%
chances that there wont be dividend is =100%-52%=48%
the probability that One will make money and not receive a dividend
is 30%*(100%-52%)
14.4%
Expand logb square root of 41/97
Answer:
A
Step-by-step explanation:
logb √(41/97)
Square root can be written in exponent form:
logb (41/97)^½
Using log exponent rule:
½ logb (41/97)
Using log quotient rule:
½ (logb 41 - logb 97)
Find an explicit rule for the nth term of the sequence.
-4, -8, -16, -32, ...
Select one:
a. an = -4 • 2n - 1
b. an = 2 • -4n + 1
c. an = 2 • -4n
d. an = -4 • 2n
Answer: -4 . 2ⁿ⁻¹
Step-by-step explanation: This is a geometric progression
the nth term is given by arⁿ⁻¹
a = the first term of the sequence
r = common ratio
n= number of terms
for this sequence
a = -4
r = -8/-4 = 2
nth term, an = -4 . 2ⁿ⁻¹
Answer:
an = 2 ● (-4)n-1
Step-by-step explanation:
Just got it right
PLEASE HELP ASAP 50 Pts + BRAINLIEST TO RIGHT/BEST ANSWER
Answer:
[tex]f(x)=(x+2)(x-5)(x-6)[/tex]
Step-by-step explanation:
we know that
If the zeros of the function are
x=-2, x=5 and x=6
then
The factors are
(x+2), (x-5) and (x-6)
therefore
The polynomial function in factored form is equal to
[tex]f(x)=(x+2)(x-5)(x-6)[/tex]
NEED HELP ASAP ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
what is the value of x assume that the line is tangent to the circle
Answer:
70
Step-by-step explanation:
An angle on the circle is half of the intercepted arc. Since the circle is 360, you can subtract 220 from 360 and find the intercepted arc which is 140. Divide that by 2 and you get 70.
Identify m∠EOF. HELP PLEASE!! I don't understand!
Answer: 119°
Step-by-step explanation:
A circle equals 360° degress. If you subtract the two angles shown in the picture you'll get 238°.
Now vertical angles are congurent thus if we divide 238 into 2 we get 119°.
Answer:
it's 119
step explanation:
i guessed and got it rt, lol.
HELP DO NOT UNDERSTAND THIS QUESTION AT ALL THE BEST ONE WILL BE MARKED AS BRAINLIEST
Step-by-step answer:
A line with slope (or gradient) m, passing through a point (x0,y0) can be represented by the equation:
(y-y0) = m(x-x0) ......................(1)
Here,
(x0,y0) = (1,7), and
slope/gradient = -2
Substitute values into (1) above gives
(y-7)=2(x-1)
Expand and simplify
y-7 = 2x-2
y =2x -2 + 7
y=2x+5
is the final answer.
What is the monthly payment of a financed amount of $14,452 with an APR of 8.9 percent? The term is for 5 years and the monthly payment per $100 is $2.41. $332.80 $348.29 $100.00 $241.00
Answer:
$348.29
Step-by-step explanation:
The payment is calculated by multiplying the rate per hundred times the number of hundreds. The latter is found by dividing the loan amount by $100.
$2.41 × $14,452/$100 ≈ $348.29
Answer:$299.16
Step-by-step explanation:
Financed amount = $14452
APR = 8.9%
Period / time = 5 years
monthly payment = $100 for every $2.07
To calculate the monthly payment of a financed amount we multiply the financed amount by the ratio of the given amount paid per $100
The monthly payment would be = 14452 * 2.07/100 = 14452 * 0.0207
= $299.16 approximately
therefore the monthly payment of a financed amount of $14452 is equal to $299.16
40 Points Please Help I'm not sure if they are correct.
Distance Formula:
D=(x2 −x1 )^2 +(y2 −y1 )^2
1. Find the distance between (0,0) and (6,8)?
2. Find the distance between (-3,2) and (3,5)?
3. Find the distance between (-1,-1) and (4,-5)?
Replace the x and y values in the given equation.
1. d = √((6-0)^2 + (8-0)^2
= √(6^2 + 8^2)
= √(36 + 64)
= √100
= 10
2. d = √((3-(-3))^2 + (5-2)^2
=√((3+3)^2 + 3^2)
=√(6^2 + 3^2)
= √(36 + 9)
= √45
=3√5 ( exact ) or as a decimal 6.7082 (round as needed)
3. d = √((4-(-1))^2 + (-5-(-1))^2
= √((4+1)^2 + (-5+1)^2)
= √(5^2 + -4^2)
=√(25 + 16)
= √41 (exact) or as a decimal 6.4031 (round as needed)
The equation yˆ=24.387x + 328.182 models Math SAT scores, y, where x is the number of hours spent studying.
What does the y-intercept of the equation represent in the context of the situation?
The average number of hours studied is about 328.
Without any studying, the score would be about 328.
Without any studying, the score would be about 24.
The average number of hours studied is about 24.
Answer:
Without any studying, the score would be about 328
Step-by-step explanation:
The y-intercept of an equation represents the point where its graph crosses the y-axis. At this point the value of x is always equal to 0.
The y-intercept of the equation in this context would represent the Math SAT score of a student who did not do any studying, that is the number of hours spent studying, x = 0.
Substitute x = 0 in the given equation and solve for y;
y = 24.387(0) + 328.182
y = 328.182
Therefore, Without any studying, the score would be about 328
Evaluate d^2y/dx^2 for 2x^2+2y=17
Answer:
d^2y/dx^2 = 2
Step-by-step explanation:
We take the derivative with respect to x twice here. Find the first derivative, simplify the results and then differentiate that result again with respect to x.
(d/dx)(2x^2+2y=17+ → 4x + 2(dy/dx) = 0. Simplifying, we get:
dy/dx = -2x
Now take the derivative of this new equation, obtaining:
d^2y/dx^2 = 2
Alexandria, a car dealer, earns 40% commission of her luxury vehicles sales. Last year, her sales were $480,000. What was the total dollar amount of her commission last year?
Answer:
192,000
Step-by-step explanation:
480,000x.40 = 192,000 commission.
Answer:
480000 * 0.40 = $192,000
The total dollar amount of her commission last year is $192,000
Step-by-step explanation:
Three Friends are starting a food truck and a contributing a total of 140,000 to begin operations. Their investments are in the ratio of 2:5:7. What is the difference in investment betweenThe smallest investor and the largest Al smallest investor and the largest inverstor
Answer:
Step-by-step explanation:
The sum of those numbers is 14. Let's divide 14000 by 14 to get the number of parts (each part will be an investment in dollars) and we get 10,000. So if a person invests 2 parts, he invests 2(10,000). A person that invests 5 parts invests 5(10,000), and likewise for the person investing 7 parts: 7(10,000). That gives us 20,000 + 50,000 + 70,000 = ?
(140,000)
The difference in investment between the largest and the smallest is 50,000
Final answer:
To find out the investments of three friends in a ratio of 2:5:7, one part is calculated as $10,000. The smallest investor contributes $20,000 and the largest investor contributes $70,000. Hence, the difference in their investments is $50,000.
Explanation:
The question is asking to determine the individual investments of three friends in a food truck business based on their total contributions amounting to $140,000 and the ratio of their investments being 2:5:7. First, we find the total number of parts in the ratio (2+5+7=14 parts). To find the value of one part, we divide the total investment by the number of parts ($140,000 \/ 14 = $10,000 per part).
Now, we can calculate each friend's investment:
The difference in investment between the smallest and the largest investor is $70,000 - $20,000 = $50,000.
sketch the graph of y = sin(x) over the interval [-π /2 , π /2 ]
Is it just the regular graph within those numbers?
Correct. It is only interested in the portion of the graph confined to this interval
So far, Greg has driven 5.1 miles. He needs to drive a total of 25 miles. How many more miles must Greg drive?
Answer: 19.9
Step-by-step explanation:
25 - 5.1 = 19.9
Answer:
19.9
Step-by-step explanation:
25-5.1
= 19.9
To make sure:
19.9+5.1
=25
I hope this help you.
What is the value of x?
sin49° = cosx
Enter your answer in the box.
x = ? °
Answer:
x =41°Step-by-step explanation:
⇒ sin (49°) = cos (90° - 49°) = cos (41°)
Sinus is a periodic trigonometric function, defined in the context of a right triangle as the ratio of the opposite leg to the hypotenuse.
Cosinus is a periodic trigonometric function, defined in the context of a right triangle as the ratio of the adjacent leg to the hypotenuse.
Final answer:
To find the value of x where sin49° equals cosx, we utilize the identity sin(90° - x) = cos x, which yields the answer x equals 41°.
Explanation:
To find the value of x where sin49° = cosx, we use the trigonometric identity sin(90° - x) = cos x. Since sin49° is given, we can set up our equation as:
sin(90° - x) = sin49°.
This reveals that 90° - x = 49°
Solving for x, we get:
x = 90° - 49°
x = 41°
Therefore, the value of x is 41°.
Analiza la sigientes preguntas y subraya la respuesta correcta segun corresponda a al resolver el sistema
Como? No entiendo perdón