Answers
The solution is: Piece-wise function
f(x)=x+6 , x≤1
f(x) = x^2 + 3 , x>1, the following functions is graphed below.
Option C is correct.
Explanation:
We are given a graph of piece-wise function which break at x=1
We need to choose correct option for graph.
Function is break at x=1.
We will get two function
For x≤1 and x>1
As we can see x≤1, graph is linear and x>1 graph is parabolic.
Equation of linear graph, x≤1
Take two point of graph (0,6) and (-6,0)
Equation of line:
y-y1/y2-y1 = x-x1/x2-x1
y = x+1
f(x)=x+6 , x≤1
Equation of parabolic graph, x>1
f(x) = x^2 + 3
Piece-wise function
f(x)=x+6 , x≤1
f(x) = x^2 + 3 , x>1
Please see the attached figure.
Hence, The option C is correct.
learn more on function:
https://brainly.com/question/2412552
#SPJ1
Related Questions
100 Points! Algebra question. Photo attached. Please show as much work as possible. Thank you!
Answers
Answer:
Refer to the step-by-step.
Step-by-step explanation:
Verify the given identity.
[tex]E_0\cos^4(\theta)=E_0(\frac{1}{2} +\frac{\cos(2\theta)}{2} )^2[/tex]
Pick the more complex side to manipulate, in this case it is the R.H.S.
(1) - Apply the following double-angle identity
[tex]\boxed{\left\begin{array}{ccc}\text{\underline{Double-Angle Identity:}}\\\\\cos(2A)=1-2\sin^2(A)\end{array}\right}[/tex]
[tex]E_0(\frac{1}{2} +\frac{\cos(2\theta)}{2} )^2\\\\\Longrightarrow \boxed{ E_0\Big(\frac{1}{2} +\frac{1-2\sin^2(\theta)}{2}\Big )^2}[/tex]
(2) - Split of the right fraction
[tex]E_0(\frac{1}{2} +\frac{1-2\sin^2(\theta)}{2} )^2\\\\\Longrightarrow E_0(\frac{1}{2} +\frac{1}{2} -\frac{2\sin^2(\theta)}{2})^2\\\\\Longrightarrow \boxed{E_0(1 -sin^2(\theta))^2}[/tex]
Apply the following Pythagorean identity
[tex]\boxed{\left\begin{array}{ccc}\text{\underline{Pythagorean Identity:}}\\\\1-\sin^2(A)=\cos^2(A)\end{array}\right}[/tex]
[tex]E_0(1 -sin^2(\theta))^2\\ \\\Longrightarrow E_0(\cos^2(\theta))^2\\\\\therefore \boxed{E_0\cos^4(\theta)=E_0\cos^4(\theta)}[/tex]
Thus, the identity is verified.
It has been proven and verified that [tex]E_0cos^4 \theta = E_0(\frac{1}{2} +\frac{cos2 \theta}{2} )^2[/tex] below.
How to verify the equality of the cosine function?In Mathematics and Geometry, the standard equation of a cosine function is represented or modeled by the following mathematical equation (formula):
y = Acos(Bx - C) + D
Where:
A represents the amplitude.B = 2π/P.P represents the period.C represents the phase shift.D represents the center line (midline).In this exercise, you are required to prove that the right-hand side of the cosine function is equal to left-hand side of the cosine function;
[tex]E_0cos^4 \theta = E_0(\frac{1}{2} +\frac{cos2 \theta}{2} )^2[/tex]
From the double-angle formulas, we have:
2sin²θ = 1 - cos2θ
cos2θ = 1 - 2sin²θ
Next, we would evaluate the right-hand side of the cosine function by substituting "1 - 2sin²θ" for cos2θ as follows;
[tex]E_0cos^4 \theta = E_0(\frac{1}{2} +\frac{1-2sin^2 \theta}{2} )^2\\\\E_0cos^4 \theta = E_0(\frac{1}{2} +\frac{1}{2} -\frac{2sin^2 \theta}{2})^2\\\\E_0cos^4 \theta = E_0(1 -\frac{2sin^2 \theta}{2})^2\\\\E_0cos^4 \theta = E_0(1 -sin^2 \theta)^2\\\\[/tex]
E₀cos⁴θ = E₀(1² - (sin²θ)²)
E₀cos⁴θ = E₀(1 - sin⁴θ) ⇒ (Verified).
Read more on cosine function here: https://brainly.com/question/26993851
#SPJ1
Can someone help me with thisss plssss it’s due today
Answers
Part A: The equation of the circle in standard form is x² + (y - 7)² = 2².
Part B: Center: (h, k) = (0, 7), Radius: 2
Part C: Please check the attachment.
How to analyze and graph the equation of a circle
In this problem we find the definition of the equation of a circle in general form, whose standard form must be found:
(x - h)² + (y - k)² = r²
Where:
(h, k) - Coordinates of the center.r - RadiusThis can be done by completing the square. First, write the equation of the circle:
x² + y² = 14 · y - 45
Second, complete the square by algebra properties:
x² + y² - 14 · y + 45 = 0
x² + (y² - 14 · y + 49) = 4
x² + (y - 7)² = 2² (PART A)
Third, write the coordinates of the center and the radius of the circle:
Center: (h, k) = (0, 7), Radius: 2 (PART B)
Finally, we proceed to graph the resulting expression.
To learn more on equations of circles: https://brainly.com/question/29288238
#SPJ1
In a certain Integrated Math II class of 29 students, 6 of them play golf and 14 of them play soccer. There are 9 students who play neither. Create a table to find probabilities.
5. What is the probability that a student chosen randomly from the class plays golf or
soccer?
6. What is the probability that a student chosen randomly from the class plays golf and soccer?
I rlly need the help!
Answers
The solution is:
20/29 is the probability that a student chosen randomly from the class plays golf or soccer.
0 is the probability that a student chosen randomly from the class plays golf and soccer.
Here, we have,
given that,
In a certain Integrated Math II class of 29 students, 6 of them play golf and 14 of them play soccer.
There are 9 students who play neither.
Number of students that play = 20
let, students play golf = A
students play soccer = B
so, given that,
n ( A) = 6 and, n ( B) = 14
so, total sample space = 29
now, P(A) = 6/29
P(B) = 14/29
and, P(students who play neither) = 9/29
we get, 6/29 + 14/ 29 + 9/29 = 29/29 = 1
i.e. there are no students who play both golf and soccer = 0
all the events are independent.
so, we have,
the probability that a student chosen randomly from the class plays golf or soccer = P(A) + P(B)
= 6/29 + 14/ 29
= 20/29
and, the probability that a student chosen randomly from the class plays golf and soccer = 0.
Find out more on probability at
brainly.com/question/29347656
#SPJ1
The heights of a certain group of adult parrots was found to be normally distributed. The mean height is 34cm with a standard deviation of 8cm. IN a group of 400 of these birds, how many would be more than 18cm tall?
Answers
The required number of parrots out of 400 birds which are more than 18 cm tall is 391 parrots.
Given that the heights of adult parrots are normally distributed with a mean height of 34 cm and standard deviation of 8 cm.
The formula used to calculate the z-score for the height of 18 cm is
z = (x - mean) / standard deviation
By substituting the value of mean and standard deviation gives,
z = (18 - 34) / 8.
On simplification of numerator gives,
z= -16 / 8 = -2.
To find the proportion of parrots more than 18 cm tall by calculating the area under the standard normal curve to the right of z = -2 by the standard normal distribution table.
That implies, proportion = area to right of z = -2 is approximately equal to 0.9772.
The formula used to calculate the number of parrots that is more than 18 cm tall is proportion × total number of parrots.
That implies, the number of parrots out of 400 birds which are more than 18 cm tall is 0.9772 × 400 = 390.88 ≈ 391.
Therefore, the required number of parrots out of 400 birds which are more than 18 cm tall is 391 parrots.
Learn more about standard normal deviation table click here:
https://brainly.com/question/31329054
#SPJ1
QUESTION 8 1 POINT
.
Find the GCF of the following three monomials:
21x³y5
63x5y²
45x¹y³
Answers
The greatest common factor (GCF) of the three monomial, 21x³y⁵, 63x⁵y² and 45x¹y³ is 3xy²
How do i determine the greatest common factor (GCF)?The greatest common factor (GCF) of the three monomials, 21x³y5, 63x5y² and 45x¹y³ can be obtained as follow:
First, we shall determine the factors of each monomials. This is illustrated below:
21x³y⁵ = 3 × 7 × x × x × x × y × y × y × y × y
63x⁵y² = 3 × 3 × 7 × x × x × x × x × x × y × y
45x¹y³ = 3 × 3 × 5 × x × y × y × y
Finally, we shall determine the greatest common factor (GCF) from the factors listed above. This is shown below:
3 × x × y × y = 3xy²
Thus, we can conlude that the greatest common factor (GCF) of the three monomials is 3xy²
Learn more about greatest common factors (GCF):
https://brainly.com/question/20587582
#SPJ1
Solve for x. Round to the nearest tenth of a degree, if necessary.
Answers
Answer: 29.9986-----30.0 degrees
Step-by-step explanation:
x = [tex]tan^-^1(5.6/9.7)\\\\toa[/tex]
[tex]\tan(x )=\cfrac{\stackrel{opposite}{5.6}}{\underset{adjacent}{9.7}} \implies \tan^{-1}(~~\tan( x )~~) \approx \tan^{-1}\left( 0.58 \right) \\\\\\ x \approx\tan^{-1}\left( 0.58 \right)\implies x \approx 30.0^o[/tex]
John collected data to determine how many minutes his teammates spend practicing basketball each night. Identify the outlier in his data.
Question 1 options:
10 minutes
40 minutes
30 minutes
5 minutes
Answers
Answer:
Step-by-step explanation:
5 minutes is the outlier. It sticks out from the rest.
Please help!! I don’t understand trigonometric functions
Answers
The horizontal transformations are defined as follows:
cos(ax).
They are classified as follows:
Stretch if |a| < 1.Compression if |a| > 1.The vertical transformations are defined as follows:
acos(x).
They are classified as follows:
Stretch if |a| > 1.Compression if |a| < 1.More can be learned about transformations at brainly.com/question/29209050
#SPJ1
r (c) (x-3) cm The diagram below shows 2 rectangles, M and N, with their dimensions expressed in terms of x. M (3x+4) cm N ( Page 8 (x-3) cm (x+2) cm Given that the difference between the areas of the two rectangles is 64 cm², show that x²-2x-35 = 0.
Answers
Since the difference between the areas of the two rectangles is 64 cm², it has been proven that it is equal to x² - 2x - 35 = 0.
How to calculate the area of a rectangle?In Mathematics and Geometry, the area of a rectangle can be calculated by using the following mathematical equation:
A = LB
Where:
A represent the area of a rectangle.B represent the breadth of a rectangle.L represent the length of a rectangle.Area of rectangle M = L × B
Area of rectangle M = (x - 3) × (3x + 4)
Area of rectangle M = 3x² - 5x - 12
Area of rectangle N = L × B
Area of rectangle N = (x + 2) × (x - 3)
Area of rectangle N = x² - x - 6
Difference = Area of rectangle M - Area of rectangle N
Difference = 3x² - 5x - 12 - (x² - x - 6)
Difference = 3x² - 5x - 12 - x² + x + 6
64 = 2x² - 4x - 6
0 = 2x² - 4x - 6 - 64
0 = 2x² - 4x - 70
By dividing all through by 2, we have:
0 = x² - 2x - 35
x² - 2x - 35 = 0 (Proven).
Read more on area of a rectangle here: brainly.com/question/29604954
#SPJ1
Missing information:
The question is incomplete and the complete question is shown in the attached picture.
If a town's population doubles every 4 years, how
many people will be in the down 12 years later if the
current population is 28,100? y = ab*
Answers
The population of the town 12 years later will be 224,800 if the current population is 28,100 and the population doubles every 4 years.
Since the population doubles every 4 years, we can use the formula:
P = P0 x [tex]2^{t/4}[/tex]
where P0 is the initial population, t is the time elapsed in years, and P is the population after time t.
In this case, the initial population P0 is 28,100, and we want to know the population after 12 years, so t = 12. Substituting these values into the formula, we get:
P = 28,100 2^(12/4)
= 28,100 x 2³
= 28,100 * 8 = 224,800
To learn more about the exponential growth;
https://brainly.com/question/12490064
#SPJ1
Which of the following statements are true regarding the reflection of A(1 1/2,-2)? Select all that apply..
Answers
The correct statements are:
A) When this point is reflected across the x-axis, the x-coordinate stays the same and the y-coordinates are opposites.C) When this point is reflected across the y-axis, the x-coordinates are opposites and the y-coordinate stays the same.D) When this point is reflected across the x-axis, the x-coordinates are opposites and the y-coordinate stays the same.How to explain the statementsWhen a point is reflected across the x-axis, the x-coordinate remains the same, but the y-coordinate changes sign. Therefore, statement A) is true.
When a point is reflected across the y-axis, the y-coordinate remains the same, but the x-coordinate changes sign. Therefore, statement C) is true.
It should be noted that to represent the reflection of point A (1,-2) across the y-axis, we flip the sign of the x-coordinate to obtain the image point A' (-1,-2). Therefore, statement D) is true.
Learn more about coordinate on
https://brainly.com/question/17206319
#SPJ1
A certain car has a fuel efficiency of 28.1 miles per gallon (mi/gal). Express this efficiency in kilometers per liter (km/L).
Answers
Answer:
the answer is 10.63km/L.
Find the sum of -17x,-15x,-2x
Answers
i really need the answer to this, can anyone help me please?
Answers
The value of total area of the shape is,
⇒ 82 cm²
We have to given that;
Figure of shape is shown.
Since, Figure is made by three rectangles.
And, Area of rectangle is,
A = length x width
Hence, The area of upper rectangle is,
A = 3 x 8
A = 24 cm²
Area of middle rectangle is,
A = (11 - (3 + 5)) x (8 - 2)
A = 3 × 6
A = 18 cm²
Area of lower rectangle is,
A = 5 x 8
A = 40 cm²
Thus, The value of total area of the shape is,
⇒ 24 + 18 + 40 cm²
⇒ 82 cm²
Learn more about the rectangle visit:
https://brainly.com/question/2607596
#SPJ1
In Exercises
frequencies.
9.
Gender
9 and 10, find and interpret the marginal
(See Example 1.)
Male
Female
Set Academic Goals
No
168
142
Yes
64
54
suport
no sas8
Answers
09. The total sample, 118 individuals set academic goals (regardless of gender), while 310 individuals did not set academic goals.
10. The total sample, 290 individuals have cats, while 306 individuals do not have cats. Furthermore, 312 individuals have dogs, while 284 individuals do not have dogs.
In order to find the marginal frequencies, we need to calculate the totals for each category separately.
For question 9:
The marginal frequency for "Set Academic Goals - yes" is 64 + 54 = 118. This represents the total number of individuals who answered "yes" to setting academic goals.
The marginal frequency for "Set Academic Goals - no" is 168 + 142 = 310. This represents the total number of individuals who answered "no" to setting academic goals.
The marginal frequency for "Male" is 64 + 168 = 232. This represents the total number of males.
The marginal frequency for "Female" is 54 + 142 = 196. This represents the total number of females.
Interpretation:
The marginal frequencies provide us with the total counts for each category in a contingency table. In this case, we can see that out of the total sample, 118 individuals set academic goals (regardless of gender), while 310 individuals did not set academic goals. Additionally, there were 232 males and 196 females in the sample.
For question 10:
The marginal frequency for "Cat - yes" is 104 + 186 = 290. This represents the total number of individuals who have cats.
The marginal frequency for "Cat - no" is 208 + 98 = 306. This represents the total number of individuals who do not have cats.
The marginal frequency for "Dog - yes" is 104 + 208 = 312. This represents the total number of individuals who have dogs.
The marginal frequency for "Dog - no" is 186 + 98 = 284. This represents the total number of individuals who do not have dogs.
Interpretation:
The marginal frequencies reveal the total counts for each category in the contingency table. In this case, we can observe that out of the total sample, 290 individuals have cats, while 306 individuals do not have cats. Furthermore, 312 individuals have dogs, while 284 individuals do not have dogs.
To learn more about the relative frequency;
https://brainly.com/question/29739263
#SPJ1
What is the range of the function y=−7x−5?
Answers
Step-by-step explanation:
"Range'' is the values of 'y' that a graph can have....there are no limits on this one
(-∞,+∞)
convert 500 cm to m?
Answers
Hello!
m dm cm mm
5 , 0 0
500cm = 5m
The equilateral triangle shown has a perimeter of 30 inches and a height of a inches.
What is the value of a?
O 5 in
O 5√3 in
O10 in
•10√3 in
Answers
The height of the equilateral triangle is a = 5√3 inches
Given data ,
Since the triangle is equilateral, all sides are of equal length.
Let's call the length of one side x.
Therefore, the perimeter of the triangle is 3x, which is given to be 30 inches.
On simplifying , we get
3x = 30
x = 10
Now, we know that the height of an equilateral triangle is given by the formula:
height = √3/2 x
Substituting the value of x, we get:
height = √3/2 x 10
height = 5√3 inches
Hence , the height of triangle is 5√3 inches
To learn more about equilateral triangle click :
https://brainly.com/question/17824549
#SPJ1
If p(x)=0.5(x-5)^2+14, what is the value of p(3)
Answers
Answer:
p(3) = 16
Step-by-step explanation:
to evaluate p(3) substitute x = 3 into p(x)
p(3) = 0.5(3 - 5)² + 14
= 0.5(- 2)² + 14
= 0.5(4) + 14
= 2 + 14
= 16
Bir saat 4:15 saat ve dört yarım saat kaç şey kaç saat eder
Answers
Answer:
dört yarım saat 2 saattir
Step-by-step explanation:
The equation a(s) = 37.5s - 1.5s2 models the function
represented in the table. Fill in the blank to complete the
restricted domain of the function. D = {0 ≤s ≤
Answers
The restricted domain of the function is 0≤s≤25
The equation is a(s) = 37.5s - 1.5s² models the function represented in the table
a(s) = s(37.5 - 1.5s)
The critical points are s=0 or
37.5 - 1.5s
37.5 = 1.5s
s=25
As area can not be negative, the area should be positive
s< 0 and s>25
Therefore, restricted domain is 0≤s≤25
To learn more on Equation:
https://brainly.com/question/10413253
#SPJ1
The equation y=195(1.10)x can be used to represent growth in the number of Salad Supreme restaurants since 2005. Which is the most reasonable conclusion based on this information? A. Salad Supreme had 110 restaurants in 2005. B. Salad Supreme is increasing the number of restaurants by 10% each year. C. Salad Supreme is increasing the number of restaurants by 195 each year. D. Salad Supreme is increasing the number of restaurants by 110% each year.
Answers
The most reasonable conclusion based on the given information is: Salad Supreme is increasing the number of restaurants by 10% each year. Option B
How to determine the most reasonable conclusionBased on the given equation y = 195(1.10)^x, where x represents the number of years since 2005 and y represents the number of Salad Supreme restaurants, we can draw the following conclusions:
A. Salad Supreme had 110 restaurants in 2005: This conclusion is not supported by the given equation.
B. Salad Supreme is increasing the number of restaurants by 10% each year: This conclusion is supported by the equation.
C. Salad Supreme is increasing the number of restaurants by 195 each year: This conclusion is not supported by the equation.
D. Salad Supreme is increasing the number of restaurants by 110% each year: This conclusion is not supported by the equation. The growth factor of 1.10 (or 10%) indicates a 10% increase each year, not 110%.
Therefore, the most reasonable conclusion based on the given information is: Salad Supreme is increasing the number of restaurants by 10% each year.
Learn more about equation at https://brainly.com/question/29174899
#SPJ1
If the Coach chooses the Three-Year Plan, what is the total amount he will spend after 12 months? ANSWER QUICK ILL GIVE BRAINLIST!
Answers
Answer:
$17,320 after 12 months.
Step-by-step explanation:
f the Coach chooses the Three-Year Plan, the total amount he will spend after 12 months can be calculated as follows:
First, we need to calculate the total amount of monthly payments made in 12 months:
12 months x $610 per month = $7,320
Then, we need to add the down payment made at the time of purchase:
$7,320 + $10,000 = $17,320
Therefore, if the Coach chooses the Three-Year Plan, he will spend a total of $17,320 after 12 months.
Select the graph of the solution. Click until the correct graph appears. |x| + 1 < 3
Answers
The graph of the modulus function is plotted
Given data ,
Let the modulus function be represented as A
Now , the value of A is
| x | + 1 < 3
On simplifying the inequality , we get
Subtracting 1 on both sides , we get
| x | < 2
When x is positive or zero: In this case, the absolute value of x is equal to x itself. Therefore, we have x < 2
When x is negative: In this case, the absolute value of x is equal to -x. Therefore, we have -x < 2
Hence , the graph of function is plotted
To learn more about modulus functions click :
https://brainly.com/question/13682596
#SPJ1
1,3,5,7,9…. What is the next number
Answers
Answer: 11
Step-by-step explanation:
this is a sequence of odd numbers.
it goes;
1,3,5,7,9,11,13,15,17,19,21,23....
Please help really urgent
Answers
Answer:
0.0909
Step-by-step explanation:
4 blue + 5 red + 3 black = 12 chips in total.
p=probability
1st draw:
p (blue) = 4/12
there are now 11 chips in the bag, 4-1 =3 are blue.
2nd draw?
p (blue) = 3/11
probability of pulling one blue chip followed by another blue chip is:
(4/12) X (3/11) = (4X3)/12X11)
= (12)/(132)
= 1/11
0.0909
Question
Evaluate |—15u| + |3v| + 3 when u
=
3 and v = 3.
Answers
The value of given expression is 57.
We are given that;
|—15u| + |3v| + 3
u=3, v = 3
Now,
To evaluate the expression, you need to substitute the values of u and v and simplify. The absolute value of a number is the distance from zero on the number line, so it is always positive or zero. You can write your solution as:
|—15u| + |3v| + 3 = |—15(3)| + |3(3)| + 3 = |—45| + |9| + 3 = 45 + 9 + 3 = 57
Therefore, by the given expression the answer will be 57.
To know more about an expression follow;
brainly.com/question/19876186
#SPJ1
Which segments are congruent?
JN and LN
JN and NM
LN and NK
NK and NM
Answers
Answer:
LN and NK
Step-by-step explanation:
A perpendicular bisector of a line segment divides the line segment into 2 equal halves.
Here, line JM is a perpendicular bisector of line segment LK at point N. So, line JM divides the line segment LK into 2 equal halves.
The two equal halves are segment LN and segment NK.
Therefore, segment LN is congruent to segment NK.
Enter the number that belongs in the green box
Answers
Answer:
Set your calculator to Degree mode.
10² = 6.78² + 4² - 2(6.78)(4)(cos x)
100 = 61.9684 - 54.24(cos x)
38.0316 = -54.24(cos x)
cos x = -.701173
[tex]x = {cos}^{ - 1} ( - .701173)[/tex]
x = 134.52°
y intercepts of f((x)=x^{2}+2x-3
Answers
Answer:
The y-intercept is -3
Written as a point it is (0, -3)
Step-by-step explanation:
To find the y-intercept, let x = 0
(and to find x-intercepts, let y = 0)
So let's let x = 0
f(x) = x^2 + 2x - 3
y = x^2 + 2x - 3
y = 0^2 + 2(0) - 3
y = -3
This means the y-intercept is -3. The graph crosses the y-axis at -3. This is the point (0, -3).
