Answer:
HEY THERE!
Step-by-step explanation:
the correct answer for your question is 90°
Answer:
The answer is c :)
Step-by-step explanation:
90 degrees
Find the area enclosed by y1 = (x - 1)3 and y2 = x -1.
I wanted to double check the answer. The professor got something completely different.
Find area between two curves
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Answer:
0.5
Step-by-step explanation:
The "enclosed area" can be taken to mean different things. Here, we consider it to mean the finite area bounded between the two curves, regardless of which curve is higher value than the other.
The area is bounded on the interval [0, 2]. On half that interval y1 > y2; on the other half, y2 > y1. This means the integral of the area between the curves will be different for one part of the interval than for the other. (The curves are symmetric about the point (1, 0).)
The area on the interval [0, 1] is given by the integral ...
[tex]\displaystyle\int_0^1{(y_1-y_2)}\,dx=\int_0^1{((x-1)^3-(x-1))}\,dx\\\\=\int^1_0{(x(x-1)(x -2))}\,dx=\left.(\frac{x^4}{4}-x^3+x^2)\right|^1_0=\boxed{\frac{1}{4}}[/tex]
The area on the interval [1, 2] is the integral of the opposite integrand, but has the same value.
The positive area over the whole interval from 0 to 2 is 1/4+1/4 = 1/2.
If you simply integrate y2-y1 or y1-y2 over that interval, the result is 0.
an amount of R3000, Is invested to three years at simple interest rate and it earned R905 interest. determine the simple interest rate at which the money was invested
Answer:
Step-by-step explanation:
P=R3000.00
T=3 years
SI=R905
SI=P\times R\times T\\R905=R3000\times \frac{r}{100}\times 3SI=P×R×T
R905=R3000×
100
r
×3
R905=\frac{R9000r}{100}R905=
100
R9000r
R905=\frac{R905}{R90}R905=
R90
R905
r=\frac{R905}{R90.}r=
R90.
R905
r=10.06\%r=10.06%
The diagram shows triangle ABC.
С
Work out the sizes of angles x, y and z.
40°
110°
х
Z
A
В
Answer:
x=70
y=30
z=20
Step-by-step explanation:
x=180-110 (angles on a straight line)
y=180-110-40 (angle sum of triangle)
z= 180-90-70 (angle sum of triangle)
Answer:
x=70°
y=30°
z=20°
Step-by-step explanation:
x=180°-110°(anlges on a straight line)
x=70°
y+110°+40°=180°(sum of angles of triangle)
y+150°=180°
y=180°-150°
y=30°
z+x+90°=180°(sum of angles of triangle)
z+70°+90°=180°
z+160°=180°
z=180°-160°
z=20°
Plz help. Last one today. 20 points. Thx!
Joyce paid $60.00 for an item at the store that was 50 percent off the original price. What was the original price?
$
Give your answer to the nearest cent.
2. Commission: A car saleswoman earns a
commission of 7% on each car she sells. How
much did she earn on the sale of a car for
$12,500?
Answer:
Step-by-step explanation:
commission = 0.7% of $12,500
= 0.007×$12,500
= $87.5
Help please. I'm stuck
Answer:
The numbers are 65, 67, and 69
Step-by-step explanation:
Hi there!
We need to find 3 consecutive odd integers.
Consecutive numbers are numbers that follow each other (ex. 1, 2, 3, 4)
We're given that 5 times the first number + 4 times the second + 3 times the third = 800
Let's make the first number x
Since the second number is consecutive to the first and odd, it will be x+2 (Why? Well, let's say x is 5. In that case, x+1=6, which is even. However, x+2=7)
Therefore, the third number is x+4 (once again, if x is 5, x+3=8, but x+4=9)
5 times the first number is 5x
4 times the second is 4(x+2)
3 times the third is 3(x+4)
And of course, that equals 800
As an equation, it'll be:
5x+4(x+2)+3(x+4)=800
open the parenthesis
5x+4x+8+3x+12=800
combine like terms
12x+20=800
Subtract 20 from both sides
12x=780
Divide by 12 on both sides
x=65
The first number is x, so the first number is 65
The second number is x+2, or 65+2=67
The third number is x+4, or 65+4=69
Hope this helps!
Dada la función f(x)=1+6Sen(2x+π/3) . Halle: Período, amplitud y desfase (1.5 puntos) Dominio y rango de la función (1.5 puntos) Grafique la función trigonométrica (2 puntos)
Dada una ecuación de la forma
y = A sin(B(x + C)) + DTenemos que:
la amplitud es Ael periodo es 2π/Bel desfase es C (a la izquierda es positivo)el desplazamiento vertical es DSabemos que:
f(x)=1+6Sen(2x+π/3)
Y podemos reescribirla como:
f(x)=6Sen(2(x+π/6))+1
Siendo:
A = 6 → AmplitudT = 2π/B = 2π/2 = π → PeríodoC = π/6 → DesfaseEl dominio de un a función trigonométrica es todo el conjunto de los números reales (x ∈ R ).La imagen de una función trigonométrica de esta forma es:
y ∈ [-A+D,A+D]
y ∈ [-6+1, 6+1]
y ∈ [-5,7]
La gráfica se adjunta.
What is the sum of 4th squared number and the 2nd cube number
Answer:
mark me as brinalist if answers are correct
Consider the functions z = 4 e^x ln y, x = ln (u cos v), and y = u sin v.
Express dz/du and dz/dv as functions of u and y both by using the Chain Rule and by expressing z directly in terms of u and v before differentiating.
Answer:
remember the chain rule:
h(x) = f(g(x))
h'(x) = f'(g(x))*g'(x)
or:
dh/dx = (df/dg)*(dg/dx)
we know that:
z = 4*e^x*ln(y)
where:
y = u*sin(v)
x = ln(u*cos(v))
We want to find:
dz/du
because y and x are functions of u, we can write this as:
dz/du = (dz/dx)*(dx/du) + (dz/dy)*(dy/du)
where:
(dz/dx) = 4*e^x*ln(y)
(dz/dy) = 4*e^x*(1/y)
(dx/du) = 1/(u*cos(v))*cos(v) = 1/u
(dy/du) = sin(v)
Replacing all of these we get:
dz/du = (4*e^x*ln(y))*( 1/u) + 4*e^x*(1/y)*sin(v)
= 4*e^x*( ln(y)/u + sin(v)/y)
replacing x and y we get:
dz/du = 4*e^(ln (u cos v))*( ln(u sin v)/u + sin(v)/(u*sin(v))
dz/du = 4*(u*cos(v))*(ln(u*sin(v))/u + 1/u)
Now let's do the same for dz/dv
dz/dv = (dz/dx)*(dx/dv) + (dz/dy)*(dy/dv)
where:
(dz/dx) = 4*e^x*ln(y)
(dz/dy) = 4*e^x*(1/y)
(dx/dv) = 1/(cos(v))*-sin(v) = -tan(v)
(dy/dv) = u*cos(v)
then:
dz/dv = 4*e^x*[ -ln(y)*tan(v) + u*cos(v)/y]
replacing the values of x and y we get:
dz/dv = 4*e^(ln(u*cos(v)))*[ -ln(u*sin(v))*tan(v) + u*cos(v)/(u*sin(v))]
dz/dv = 4*(u*cos(v))*[ -ln(u*sin(v))*tan(v) + 1/tan(v)]
What is equal to 30- 6v - 13w
this is so confusing can anyone help?
Answer:
C.
Step-by-step explanation:
For an angle to be supplementary to another angle, they must be equal to 180. Angles 6, 10, 13, and 9 are all supplementary to angle 16. Although there are more choices in different answers it wouldn't work with question, so C is the right answer.
Angle 16 is supplementary to angle 9 by the Same Side Interior Angles Theorem, which makes it supplementary to angle 10 by the Alternate Exterior Angles Theorem, which is also congruent to angle 13 by the Vertical Angles Theorem, which is also supplementary to angle 6 by the Alternate Exterior Angles Theorem.
Jose bought a piece of fabric that was 5.6 meters long. From that, he cut 0.4
meter. How much fabric is left?
Answer:
Jose has 5.2 meters of fabric left.
Step-by-step explanation:
5.6 - 0.4 = 5.2
What is the least possible degree of a polynomial that has roots -5,1 + 4i, and -4i?
3
2
5
4
Without any extra conditions, the answer could be 3, and the simplest polynomial with the given roots would be
(x + 5) (x - (1 + 4i )) (x + 4i )
= x ³ + 4x ² + (11 - 4i ) x + 80 - 2i
If the polynomial is supposed to have only real coefficients, then any complex roots must occur along with their complex conjugates:
(x + 5) (x - (1 + 4i )) (x - (1 - 4i )) (x + 4i ) (x - 4i )
= x ⁵ + 3x ⁴ + 23x ³ + 133x ² + 112x + 1360
and then the degree would be 5.
class 7th chapter: Simple Equation
The solution of the equation p-1 =20 is -------- *
a) 19
b) 20
c) 21
Answer:
C
Step-by-step explanation:
p=20+1
238.64 yards.what is the diameter of the field?use 3.14 for pie and do not round your answer
Answer:
It should be 8.6 yards, as 238.64÷3.14 = 74.
√74 = 8.60, or 8.6 :)
A bacteria culture initially contains 100 cells and grows at a rate proportional to its size. After an hour the population has increased to 310.
(a) Find an expression for the number of bacteria after
hours.
(b) Find the number of bacteria after 3 hours.
(c) Find the rate of growth after 3 hours.
(d) When will the population reach 10,000?
Answer:
a) The expression for the number of bacteria is [tex]P(t) = 100\cdot e^{1.131\cdot t}[/tex].
b) There are 2975 bacteria after 3 hours.
c) The rate of growth after 3 hours is about 3365.3 bacteria per hour.
d) A population of 10,000 will be reached after 4.072 hours.
Step-by-step explanation:
a) The population growth of the bacteria culture is described by this ordinary differential equation:
[tex]\frac{dP}{dt} = k\cdot P[/tex] (1)
Where:
[tex]k[/tex] - Rate of proportionality, in [tex]\frac{1}{h}[/tex].
[tex]P[/tex] - Population of the bacteria culture, no unit.
[tex]t[/tex] - Time, in hours.
The solution of this differential equation is:
[tex]P(t) = P_{o}\cdot e^{k\cdot t}[/tex] (2)
Where:
[tex]P_{o}[/tex] - Initial population, no unit.
[tex]P(t)[/tex] - Current population, no unit.
If we know that [tex]P_{o} = 100[/tex], [tex]t = 1\,h[/tex] and [tex]P(t) = 310[/tex], then the rate of proportionality is:
[tex]P(t) = P_{o}\cdot e^{k\cdot t}[/tex]
[tex]\frac{P(t)}{P_{o}} = e^{k\cdot t}[/tex]
[tex]k\cdot t = \ln \frac{P(t)}{P_{o}}[/tex]
[tex]k = \frac{1}{t}\cdot \ln \frac{P(t)}{P_{o}}[/tex]
[tex]k = \frac{1}{1}\cdot \ln \frac{310}{100}[/tex]
[tex]k\approx 1.131\,\frac{1}{h}[/tex]
Hence, the expression for the number of bacteria is [tex]P(t) = 100\cdot e^{1.131\cdot t}[/tex].
b) If we know that [tex]t = 3\,h[/tex], then the number of bacteria is:
[tex]P(t) = 100\cdot e^{1.131\cdot t}[/tex]
[tex]P(3) = 100\cdot e^{1.131\cdot (3)}[/tex]
[tex]P(3) \approx 2975.508[/tex]
There are 2975 bacteria after 3 hours.
c) The rate of growth of the population is represented by (1):
[tex]\frac{dP}{dt} = k\cdot P[/tex]
If we know that [tex]k\approx 1.131\,\frac{1}{h}[/tex] and [tex]P \approx 2975.508[/tex], then the rate of growth after 3 hours:
[tex]\frac{dP}{dt} = \left(1.131\,\frac{1}{h} \right)\cdot (2975.508)[/tex]
[tex]\frac{dP}{dt} = 3365.3\,\frac{1}{h}[/tex]
The rate of growth after 3 hours is about 3365.3 bacteria per hour.
d) If we know that [tex]P(t) = 10000[/tex], then the time associated with the size of the bacteria culture is:
[tex]P(t) = 100\cdot e^{1.131\cdot t}[/tex]
[tex]10000 = 100\cdot e^{1.131\cdot t}[/tex]
[tex]100 = e^{1.131\cdot t}[/tex]
[tex]\ln 100 = 1.131\cdot t[/tex]
[tex]t = \frac{\ln 100}{1.131}[/tex]
[tex]t \approx 4.072\,h[/tex]
A population of 10,000 will be reached after 4.072 hours.
3. A)Find the next number in the sequence.
$1,27, 9, 3, _1_
B) Is the sequence arithmetic, geometric, or neither?
Help me find this answer please
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Answer:
1/3; geometric
Step-by-step explanation:
Apparently, your sequence is ...
81, 27, 9, 3, 1, ...
The differences between these numbers vary, but the ratio of each to the one before is a constant:
27/81 = 9/27 = 3/9 = 1/3
The sequence is geometric with a common ratio of 1/3. The next number in the sequence is (1)(1/3) = 1/3.
What is the value of x in the diagram below? If necessary, round your answer
to the nearest tenth of a unit.
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Answer:
A. 7.2
Step-by-step explanation:
In this geometry, all of the right triangles are similar. This means corresponding sides have the same ratio.
short side/hypotenuse = x/12 = 12/20
Multiplying by 12 gives ...
x = 12(12/20) = 144/20
x = 7.2
The function f is defined by f(x)=2x+5/x+4 find f (3x)
Answer:
[tex]\displaystyle f(3x) = \frac{6x + 5}{3x + 4}[/tex]
General Formulas and Concepts:
Algebra I
FunctionsFunction NotationStep-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle f(x) = \frac{2x + 5}{x + 4}[/tex]
Step 2: Find
Substitute in x [Function f(x)]: [tex]\displaystyle f(3x) = \frac{2(3x) + 5}{3x + 4}[/tex]Simplify: [tex]\displaystyle f(3x) = \frac{6x + 5}{3x + 4}[/tex]A charter school did a local beach cleanup. They collected a total of 55 pounds of plastic bottles and aluminum cans. The California refund value for plastic is $1.60 per pound and $1.28 per pound for aluminum. The school recycled a total of $77.60 worth of plastic and aluminum. How many pounds of each, plastic and aluminum, did the class collect?
Answer:
Plastic is 22.5 pounds and aluminum is 32.5 pounds.
Step-by-step explanation:
total junk = 55 pounds
Value of plastic = $ 1.60 per pound
Value of aluminum = $ 1.28 per pound
Total value= $ 77.60
Let the plastic is p and the aluminum is 55 - p.
Total cost
77.60 = 1.6 p + (55 - p) x 1.28
77.60 = 1.6 p + 70.4 - 1.28 p
7.2 = 0.32 p
p = 22.5 pounds
So, plastic is 22.5 pounds and aluminum is 32.5 pounds.
With the information that you gather from the summary tables, test the following (you can use excel when appropriate): Determine if there is sufficient evidence to conclude the average amount of births is over 5000 in the United States and territories at the 0.05 level of significance. Determine if there is sufficient evidence to conclude the average amount of deaths is equal to 6000 in the United States and territories at the 0.10 level of significance. Determine if there is sufficient evidence to conclude the average amount of marriages is greater or equal to 2500 in the United States and territories at the .05 level of significance. Determine if there is sufficient evidence to conclude the average amount of divorces is less than or equal to 4000 in the United States and territories at the 0.10 level of significance.
Answer:
Kindly check explanation
Step-by-step explanation:
A.)
H0 : μ = 5000
H0 : μ > 5000
xbar = 6671 ; s = 8185.21 ; n = 52 ; α = 0.05
The test statistic :
T = (xbar - μ) ÷ (s/√(n))
T = (6671 - 5000) ÷ (8185.21/√52)
T = 3.814
Pvalue from Test statistic : ; df = n - 1 = 52-1= 51
Pvalue at 3.814; 51 = 0.000185
Pvalue < α ; Reject H0 and conclude that average birth is greater than 5000
B)
H0 : μ = 6000
H0 : μ < 6000
xbar = 4187 ; s = 4386 ; n = 52 ; α = 0.01
The test statistic :
T = (xbar - μ) ÷ (s/√(n))
T = (4187 - 6000) ÷ (4386/√52)
T = - 2.981
Pvalue from Test statistic : ; df = n - 1 = 52-1= 51
Pvalue at - 2.981; 51 = 0.0022
Pvalue < α ; Reject H0 and conclude that average death is less than 6000
C.)
H0 : μ < 2500
H0 : μ ≥ 2500
xbar = 2744 ; s = 3134.41 ; n = 52 ; α = 0.05
The test statistic :
T = (xbar - μ) ÷ (s/√(n))
T = (2744 - 2500) ÷ (3134.41/√52)
T = 0.561
Pvalue from Test statistic : ; df = n - 1 = 52-1= 51
Pvalue at 0.561; 51 = 0.289
Pvalue > α ; Fail to Reject H0 and conclude that average marriage is not greater Tha or equal to 2500
D.)
H0 : μ = 4000
H0 : μ ≤ 4000
xbar = 1451 ; s = 1217 ; n = 52 ; α = 0.01
The test statistic :
T = (xbar - μ) ÷ (s/√(n))
T = (1451 - 4000) ÷ (1217/√52)
T = - 15.10
Pvalue from Test statistic : ; df = n - 1 = 52-1= 51
Pvalue at - 15.10; 51 = 0.000001
Pvalue < α ; Reject H0 and conclude that average divorce is less eqaul to 4000
Two systems of equations are given below. For each system, choose the best description of its solution.
x - 5y = 5
-x + 5y = -5
a. The system has no solution.
b. The system has a unique solution:
(x,y) = _______
c. The system has infinitely many solutions. They must satisfy the following equation:
y = ________
Answer:
Infinitely many solutions.
They must satisfy [tex]y = \frac{1}{5}(x - 5)[/tex]
Step-by-step explanation:
Given
[tex]x - 5y = 5[/tex]
[tex]-x + 5y = -5[/tex]
Required
The best description
Add both equations
[tex]x - x - 5y + 5y = 5 - 5[/tex]
[tex]0+0 =0[/tex]
[tex]0 = 0[/tex] ---- this means that the system has infinitely many solutions.
Make y the subject in: [tex]-x + 5y = -5[/tex]
Add x to both sides
[tex]5y = x - 5[/tex]
Divide through by 5
[tex]y = \frac{1}{5}(x - 5)[/tex]
Hence, they must satisfy: [tex]y = \frac{1}{5}(x - 5)[/tex]
Find out the quotient
-72 ÷ (-2) = ?
-72 ÷ 2 = ?
72 ÷ (-2) = ?
(Thank you to whoever helps me out )
Answer/Step-by-step explanation:
✔️-72 ÷ (-2)
The division of two negative numbers will give us a positive number. i.e. - ÷ - = +
Therefore:
-72 ÷ (-2) = 36
✔️-72 ÷ 2
The division of a negative number and a positive number will give us a negative number. i.e. - ÷ + = -
Therefore:
-72 ÷ 2 = -36
✔️72 ÷ (-2)
The division of a positive number and a negative number will give us a negative number. i.e. + ÷ - = -
Therefore:
72 ÷ (-2) = -36
* Insert a digit to make numbers that are divisible by 6 if it is possible:
234_6
Answer:
i put in 3 to make 23436 because 36 is divisible by 6
7r - 3s =26
2r - 6s =8
Answer:
r = 3 2/3
s = -0.444333
Step-by-step explanation:
Multiply the top equation by 2
14r - 6s = 52
2r - 6s = 8 Subtract the two equations
12r = 44 Divide by 12
r = 44/12
r = 3 8/12
r = 3 2/3
2r - 6s = 8
2*(2 2/3) - 6s = 8
2*2.6667 - 6s = 8
5.3334 - 6s = 8 Subtract 5.3334 from both sides.
- 6s = 2 2/3 Divide by - 6
s = - 0.4443333
William invested $12,000 in a bank account that pays 9 percent simple interest. His friend invested the same amount at another bank that pays 8 percent interest compounded quarterly. These two functions, where t is time in years, represent the value of the investments: f(t) = 12(1.02)4t g(t) = 12(1.09)t The functions are graphed, and the point of intersection lies between 0.5 and 1.2. Based on the table, approximately how long will it be until both investments have the same value? Value of t f(t) = 12(1.02)4t g(t) = 12(1.09)t 0.5 12.48 6.54 0.6 12.58 7.84 0.7 12.68 9.16 0.8 12.79 10.46 0.9 12.89 11.87 1.0 12.99 13.08 1.1 13.09 14.39 1.2 13.20 15.70 A. 0.9 year B. 1.0 year C. 1.1 years D. 1.2 years
===========================================================
Explanation:
We have these two functions
f(t) = 12(1.02)^(4t)g(t) = 12(1.09)twhich represent the amounts for his friend and William in that order. Strangely your teacher mentions William first, but then swaps the order when listing the exponential function as the first. This might be slightly confusing.
The table of values is shown below. We have t represent the number of years and t starts at 0.5. It increments by 0.1
The f(t) and g(t) columns represent the outputs for those mentioned values of t. For example, if t = 0.5 years (aka 6 months) then f(t) = 12.48 and that indicates his friend has 12,480 dollars in the account.
I've added a fourth column labeled |f - g| which represents the absolute value of the difference of the f and g columns. If f = g, then f-g = 0. The goal is to see if we get 0 in this column or try to get as close as possible. This occurs when we get 0.09 when t = 1.0
So we don't exactly get f(t) and g(t) perfectly equal, but they get very close when t = 1.0
It turns out that the more accurate solution is roughly t = 0.9925 which is close enough. I used a graphing calculator to find this approximate solution.
It takes about a year for the two accounts to have the same approximate amount of money.
Answer:
B
Step-by-step explanation:
the volume of pyramid a is the volume of pyramid b. if the heigh of pyramid b increases to twice that of pyramid a the new volume of pyramid b the volume of pyramid a
Answer:
12.259-12.25 890654321
Help pls with answer!!!Rewrite the function in the given form.
Answer:
[tex]g(x) = \frac{-2}{x-1}+5\\\\[/tex]
The graph is shown below.
=========================================================
Explanation:
Notice that if we multiplied the denominator (x-1) by 5, then we get 5(x-1) = 5x-5.
This is close to 5x-7, except we're off by 2 units.
In other words,
5x-7 = (5x-5)-2
since -7 = -5-2
Based on that, we can then say,
[tex]g(x) = \frac{5x-7}{x-1}\\\\g(x) = \frac{5x-5-2}{x-1}\\\\g(x) = \frac{(5x-5)-2}{x-1}\\\\g(x) = \frac{5(x-1)-2}{x-1}\\\\g(x) = \frac{5(x-1)}{x-1}+\frac{-2}{x-1}\\\\g(x) = 5+\frac{-2}{x-1}\\\\g(x) = \frac{-2}{x-1}+5[/tex]
This answer can be reached through alternative methods of polynomial long division or synthetic division (two related yet slightly different methods).
-------------------------
Compare the equation [tex]g(x) = \frac{-2}{x-1}+5\\\\[/tex] to the form [tex]g(x) = \frac{a}{x-h}+k\\\\[/tex]
We can see that
a = -2h = 1k = 5The vertical asymptote is x = 1, which is directly from the h = 1 value. If we tried plugging x = 1 into g(x), then we'll get a division by zero error. So this is why the vertical asymptote is located here.
The horizontal asymptote is y = 5, which is directly tied to the k = 5 value. As x gets infinitely large, then y = g(x) slowly approaches y = 5. We never actually arrive to this exact y value. Try plugging in g(x) = 5 and solving for x. You'll find that no solution for x exists.
The point (h,k) is the intersection of the horizontal and vertical asymptote. It's effectively the "center" of the hyperbola, so to speak.
The graph is shown below. Some points of interest on the hyperbola are
(-1,6)(0,7) .... y intercept(1.4, 0) .... x intercept(2, 3)(3, 4)Another thing to notice is that this function is always increasing. This means as we move from left to right, the function curve goes uphill.
Select the correct answer. Which function is continuous across Its domain
Answer:
D is the answer
Step-by-step explanation:
plug the -2's in line 1 & 2 then 4 in 2 and 3
the 1&2 , and the 2 and 3 numbers have to match
Using the conditions for continuity, we find that the function D.) is continuous.
How to check if a function is continuous?A function f(x) is said to be continuous at a point x = a, in its domain if the following three conditions are satisfied:
f(a) exists (i.e. the value of f(a) is finite)the right-hand limit = left-hand limit, and both are finite.right-hand limit = left-hand limit = f(a)Since for -4 <= x < -2, -2 <= x < 4 and 4 <= x <= 8, the function f(x) is defined by straight lines , the function will be continuous for all x ≠ -2 and 4. Now for x = -2, 4, let us check all the three conditions:
A.
f(-2) = 0.5 * (-2)² = 2
left hand limit = -2 + 6 = 4
right hand limit = 0.5 * (-2)² = 2
Since, left hand limit is not equal to right hand limit, the function is not continuous at x = -2. No need to check further.
B.
f(-2) = 0.5 * (-2)² = 2
left hand limit = -2 -2 = -4
right hand limit = 0.5 * (-2)² = 2
Since, left hand limit is not equal to right hand limit, the function is not continuous at x = -2. No need to check further.
C.
f(-2) = 0.5 * (-2)² = 2
left hand limit = -2 + 4 = 2
right hand limit = 0.5 * (-2)² = 2
Since, left hand limit is not equal to right hand limit is equal to f(-2), the function is continuous at x = -2.
f(4) = 25 - 3*4 = 13
left hand limit = 0.5 * (4)² = 8
right hand limit = 25 - 3*4 = 13
Since, left hand limit is not equal to right hand limit, the function is not continuous at x = 4.
D.
f(-2) = 0.5 * (-2)² = 2
left hand limit = -2 + 4 = 2
right hand limit = 0.5 * (-2)² = 2
Since, left hand limit is not equal to right hand limit is equal to f(-2), the function is continuous at x = -2.
f(4) = 20 - 3*4 = 8
left hand limit = 0.5 * (4)² = 8
right hand limit = 20 - 3*4 = 8
Since, left hand limit is not equal to right hand limit is equal to f(-2), the function is continuous at x = 4.
Thus, the function is continuous.
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