Answers
a) The function is continuous in it's entire domain.
b) The increasing and decreasing intervals for the function are given as follows:
Increasing: (0,2).Decreasing: (2,10).What is the continuity concept?A function f(x) is continuous at x = a if it is defined at x = a, and the lateral limits are equal, that is:
[tex]\lim_{x \rightarrow a^-} f(x) = \lim_{x \rightarrow a^+} f(x) = f(a)[/tex]
In this problem, we have a piece-wise function which has the definition changing at x = 2, hence the continuity must be studied at x = 2.
The lateral limits for the function in this problem are defined as follows:
[tex]\lim_{x \rightarrow 2^-} A(x) = \lim_{x \rightarrow 2} x^2 + 2 = 2^2 + 2 = 6[/tex][tex]\lim_{x \rightarrow 2^+} A(x) = \lim_{x \rightarrow 2} \frac{-3x + 30}{4} = 0.25(-3(2) + 30) = 6[/tex]The second limit is also equals to the numeric value at x = 2, due to the equal sign in the definition, hence the function is continuous at x = 2 and for all other values in the domain.
The intervals of increase and decrease are given as follows:
Increasing: (0,2). -> y = x² increases for x > 0, the 2 changes just the range.Decreasing: (2,10). -> decreasing line, due to the negative slope.TranslationThe function for this problem is the piece-wise function A(x).
Item a asks if the function is continuous.
Item b asks when the function is increasing and when it is decreasing.
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Related Questions
50 POINTS !!
PLEASE HELP !! ILL GIVE BRAINLIEST TO THE RIGHT ANSWERS.
Answers
use the formula a^2 +b^2=c^2
Nina and Luca were told to draw a net for the three-dimensional figure shown below. Which statement
nets is true?
Three-dimensional Figure
Answers
Answer:
d
Step-by-step explanation:
The length of a rectangle is four times its width. If the area of the rectangle is 196 yd², finds its perimeter.
Answers
Answer:
perimeter = 70 yards
Step-by-step explanation:
⭐What is the area of a rectangle?
area = length * width⭐What is the perimeter of a rectangle?
perimeter = 2(length) + 2(width)Strategy1. Make the equation for the area of the given rectangle and solve for x
2. Substitute x into the expressions of the length and width and solve for the perimeter
Working1. Define the expressions of the length and width of the rectangle
width: x
length: 4x
2. Make the equation for the area of the rectangle
[tex]196yd^2 = 4x * x\\196yd^2 = 4x^2[/tex]
3. Solve for x
[tex]\frac{196}{4} = x^2[/tex] . . . . . . . . . . divide both sides by 4
[tex]49 = x^2[/tex]
[tex]\sqrt{49} = \sqrt{x^2}[/tex] . . . . . . . . square root both sides to isolate x
∴ [tex]7 = x[/tex]
4. Substitute x into the expressions of the length and the width
width: x
width = 7
height: 4x
height = 4(7) = 28
5. Solve for the perimeter
[tex]perimeter = 2(length) + 2(width)[/tex]
[tex]perimeter = 2(28) + 2(7)\\perimeter = 56 + 14\\perimeter = 70[/tex]
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Nico is trying to divide a 6 by 4 inches of rectangular cartoon sheet into pieces of squares. Given that he used up all of the materials and that all squares are of similar dimensions, what is the minimum number of squares he can produce?
Answers
Answer:
Minimum of 6 squares.
Step-by-step explanation:
The dimension of the rectangular carton = 6 by 4 inches.
The area of the carton = length x width
= 6 x 4
= 24 square inches
Assume that we have a square of side length 2 inches, then;
area of the square = length x length
= 2 x 2
= 4 square inches
So that since all materials is to be used,
the minimum number of squares that it can produce = [tex]\frac{24}{4}[/tex]
= 6
The minimum number of squares he can produce is 6.
What is a rectangle?
A rectangle is a 2-dimensional quadrilateral with four right angles that add up to 360 degrees. It has two diagonals which bisect each other. The diagonals are equal in length
Area of a rectangle = length x width
6 x 4 = 24 square inches.
What is a square?
A square is a quadrilateral that has four sides of equal lengths.
Possible areas of the square = 1 inches square, 4 inches square, 9 inches square, 16 inches square.
Minimum number of square = 24 / 4 = 6 squares
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Rewrite without parentheses and simplify.
(V+2)^2
Answers
Answer:
V^2 + 4V + 4
Step-by-step explanation:
PLS HELP ME!!!
COSINE RULE I THINK!!
please explain in some detail and will mark brainliest
Answers
Answer:
Step-by-step explanation:
if there is any triangle ABC and a,b,c are sides opposite angles A,B,C respectively , then
[tex]cos~A=\frac{b^2+c^2-a^2}{2bc} \\cos~B=\frac{c^2+a^2-b^2}{2ca} \\cos~C=\frac{a^2+b^2-c^2}{2ab}[/tex]
B=101
a= 3 cm
b=y
c=1 cm
use formula for cos B
cos 101=cos(90+11)=sin 11
[tex]-sin~11=\frac{1^2+3^2-y^2}{2 \times 3 \times 1} \\-6 \times sin~11=1+9-y^2\\y^2=10+6~sin~11\\y^2\approx 10+6\times 0.1908\\y^2 \approx11.1448\\y\approx3.338[/tex]
Answer:
2.16
Step-by-step explanation:
To find the length y:
Since we have an angle with two sides next to it, it is 'cosy', so we can use the cosine rule to find y. Let's make y = a for the formula.
Using the cosine formula:
a^2 = b^2 + c^2 - 2bc cos(A)
where b=1, c=3 and A=101
substitute these values in the formula:
a ^2 = 1^2 + 3^2 - 2(1)(3) × cos(101)
a ^2 = 4.647970...
Square root to find a:
a = √4.647970...
a = 2.16
thus, y = 2.16 to 3sf
2x +3=5 so what is the value of x
Answers
Answer:
x = 1
Step-by-step explanation:
2x + 3 = 5
=> 2x = 5-3
=> 2x = 2
=> x = 2/2
=> x = 1
Therefore, the value of x is 1
Hope it helps :)
Answer:
x=1
Step-by-step explanation:
Hi there!
2x+3=5
Our goal is to isolate x on one side of the equal sign, and we can do this using inverse operations. For example, the inverse operation of addition is subtraction. Subtract both sides of the equation by 3 to isolate 2x:
2x+3-3=5-3
2x=2
The inverse of multiplication is division. Divide both sides by 2:
2x÷2=2÷2
x=1
I hope this helps!
What is 3x?
I’m confused because I know x is the variable. So let’s say x=30. Do I multiply it like 3 • 30 = 90?
3x=90
Answers
Answer: 3 · 30= 90
Step-by-step explanation:
yes you are correct
please answer in full process
questions
Given L || M find the value of unknown angles in each of the following figures
Answers
Answer:
Angle x = 120 degrees
Angle y = 60 degrees
Step-by-step explanation: Angle x has to be equivalent to the 120 degree angle that is already given since lines l and m are parallel as well as lines p and q. To find angle y, you must realize that angles x and y are supplementary angles, so their sum is 180 degrees. Since we now know that angle x is 120 degrees, you must subtract 120 from 180 in order to find the value of angle y: 180 - 120 = 60 degrees. I'm sure that there are other methods to figuring this question out, but this is how I did it.
please answer the following question, AND NO LINKS OR YOU WILL GET REPORTED.
Answers
Answer:
Mode
Step-by-step explanation:
I believe mode because 8 is the number that appears most often in this set of numbers.
note: Mode is the number that appears most often in any set of numbers.
50 POINTS !!
PLEASE HELP !! ILL GIVE BRAINLIEST TO THE RIGHT ANSWERS.
Answers
Answer:
6.7 km
Step-by-step explanation:
c² = 4.9²+4.5²
= 24.01 + 20.25
= 44.26
c = √44.26 = 6.7
6+3(13 – 2) - 52
Help me
Answers
Answer:
the answer is 14
Step-by-step explanation:
Determine whether the function is periodic. If it is, find the period.
3.
(1 point)
y
-2:
2
periodic: about 3
not periodic
periodic; about 2
periodic; about 12
Answers
9514 1404 393
Answer:
not periodic
Step-by-step explanation:
There is no value p such that f(x) = f(x+p) for all x. Hence. the function is NOT PERIODIC.
_____
It seems possible that subtracting the linear increase would result in a periodic function. Because of the linear increase, there is no left- or right-shift of the function that will map it to itself.
Help with both questions (8 and 9) please.
No link answers thx
Answers
Step-by-step explanation:
8.
Let the number is x. A number minus 7 is (x-7). It is doubled to get 86. So,
[tex](x-7)^2=86\\\\x-7=\sqrt{86}\\\\x-7=\pm 9.27\\\\x-7=9.27\ and\ x-7=-9.27\\\\x=16.27\ or\ x=-2.27[/tex]
The number can be 16.27 or -2.27.
9.
The diameter of the cylindrical tank, d = 20 ft
Radius, r = 10 ft
It is filled with oil to a depth of h feet.
The volume of a cylindrical shaped object is given by :
[tex]V=\pi r^2 h[/tex]
Put the given values,
[tex]V=\pi (10)^2h\\\\V=3.14\times 100\times h\\\\V=314h\ ft^3[/tex]
So, the volume of the tank is equal to [tex]314h\ ft^3[/tex].
Two cars leave towns 360 kilometers apart at the same time and travel toward each other. One car’s rate is 10 kilometers per hour less than the others. If they meet in 2 hours what is the rate of the slower car
Answers
9514 1404 393
Answer:
85 km/h
Step-by-step explanation:
Let s represent the speed of the slower car. Then the travel time is ...
time = distance/speed
2 = 360/(s +(s+10))
4s +20 = 360 . . . . . multiply by 2s+10
4s = 340 . . . . . . . . . subtract 20
s = 85 . . . . . . . . . . . divide by 4
__
The rate of the slower car is 85 km/h.
Solve the inequality -5<5y<15
Answers
Answer:
−1 < y < 3
Step-by-step explanation:
A quadratic function and an exponential function are graphed below. Which graph most likely represents the quadratic function? (5 points)
graph of function g of x is a curve which joins the ordered pair 0, 1 and 1, 2 and 3, 8 and 5, 32 and 6, 64. Graph of function f of x is a curve which joins the ordered pair 0, 1 and 1, 2 and 3, 10 and 5, 26 and 6, 37
f(x), because an increasing exponential function will eventually exceed an increasing quadratic function
g(x), because an increasing quadratic function will eventually exceed an increasing exponential function
g(x), because an increasing exponential function will always exceed an increasing quadratic function until their graphs intersect
f(x), because an increasing quadratic function will always exceed an increasing exponential function until their graphs intersect
Answers
Answer:
It's A
Step-by-step explanation:
I just did the test and it is A
Any help pls. Question is : Find the equation of line B, which is perpendicular toy-2x=-8(x-8)and passes through the point (6,-6). Find the midpoint of the line segment AB in the following figure
Answers
Answer:
Perpendicular line ⇒ 2x + 9y + 42 = 0
midpoint: (-1,1)
Step-by-step explanation:
Let's find the coordinates of midpoint of AB
Here, from figure, A = (-3,-2), B = (1,4)
So midpoint:
[tex]P = (\frac{-3+1}{2},\frac{-2+4}{2})[/tex]
∴ P = (-1, 1)
Now, given straight line is x - 2y = -8(x-8)
⇒x - 2y = -8x+64
⇒9x - 2y - 64 = 0
Perpendicular line to 9x - 2y - 64 = 0 is 2x + 9y + k = 0
Perpendicular line passes though (6,-6)
Putting the values, we get
2(6) + 9(-6) + k = 0
⇒12 - 54 + k = 0
⇒k = 42
∴ Perpendicular line ⇒ 2x + 9y + 42 = 0
Please help giving brainliest
Answers
Answer:
look at the picture I sent
helpp pleasee! Actual help not fake people, you will be reported
Answers
Answer:
side AB
Step-by-step explanation:
Find the length of side xx in simplest radical form with a rational denominator. 3
Answers
The length of x is 6 in simplest radical form.
What is a right-angled triangle?'A triangle in which one of the interior angles is 90° is called a right-angled triangle. The longest side of the right triangle, which is also the side opposite the right angle, is the hypotenuse and the two arms of the right angle are the perpendicular and the base.'
According to the given ,
Perpendicular = 3
Hypotenuse = x
We know,
sin∅ = 3/x
∅ = 30°
⇒ sin30 = 3/x
⇒ 1/2 = 3/x [ sin30 = /2 ]
⇒ x = 3 * 2
⇒ x= 6
Hypotenuse = 6
Applying Pythagoras theorem:
Hypotenuse² = Perpendicular² + Base²
6² = 3² + Base²
6² - 3² = Base²
Base² = 25
Base = √25
Base = 5
We can conclude the value of x to be 6.
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The dimensions of a picture frame can be represented as (x+4) inches and (x+3) inches. The value of the area, in square inches, of the picture frame is equal to the value of the perimeter, in inches
Answers
The wrist circumference in relation to height tells us how big our body frames are.
How is frame size calculated?The wrist circumference in relation to height tells us how big our body frames are. A man who is above 5' 5" tall and with a wrist measurement of 6" would be considered to have tiny bones.
The following chart can be used to establish whether a person has tiny, medium, or large bones by measuring their wrist with a measuring tape and comparing the results.
Women:
under 5'2" in height"
Medium wrist size is between5.5" and5.75" Small wrist size is less than5.5" "
Large is defined as a wrist size of 5.75 or greater."
between 5'2" and 5'5" tall
smaller than 6 inches around the wrist"
Bracelet size 6 is medium "Medium = wrist size between 6.25" and 6.5" Large
Over 5' 5" in height"
Small wrists measure less than 6.25", Medium wrists measure 6.25" to 6.5," and Large wrists measure over 6.5."
Example :
2(x + 3 ) + 2 (x + 4 ) = (x + 3 )( x + 4)
x² + 7x + 12 = 4x + 14
x² + 3x - 2 = 0
(x + 3 / 2 )² = 17 / 4.
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anyone know this click to see links will get reported
Answers
Answer:
exponents, exponents, parenthesis, parenthesis/exponents, parenthesis.
Step-by-step explanation:
Geometry need help asap
Answers
On solving the provided question, we can say that - here in quadrilateral we have x + 146 + 47 + y = 360 => [tex]x= 83.5[/tex]
what is quadrilateral?A quadrilateral is a four-sided polygon in geometry that has four edges and four corners. The word is a derivative of the Latin words quadri and latus (meaning "side"). Having four sides, four vertices, and four corners, a rectangle is a two-dimensional form. Concave and convex come in primarily two varieties. Additionally, there are several subclasses of convex quadrilaterals, including trapezoids, parallelograms, rectangles, rhombuses, and squares. Four straight sides make up a rectangle, which is a two-dimensional form. There are several different types of quadrilaterals, including parallelograms, trapezoids, rectangles, kites, squares, and rhombuses.
here,
x + 146 + 47 + y = 360
2x + 193 = 360
2x = 167
[tex]x= 83.5[/tex]
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How many fourths are equivalent to 2\8
Answers
Answer:
1/4
Step-by-step explanation:
8/8=1
6/8=3/4
4/8=2/4
2/8=1/4
Write an equation of the line that passes through (-3,3) and is perpendicular to the line 2y = 8x - 6
Answers
The equation of line that passes through (-3,3) and is perpendicular to 2y = 8x - 6 is y = (-1/4)x + 9/4.
What is the equation of line that passes through (-3,3) and is perpendicular to 2y = 8x - 6?The slope-intercept form is expressed as;
y = mx + b
Where m is slope and b is the y-intercept.
Given the equation of the original line.
Write in slope intercept form
2y = 8x - 6
y = 8x/2 - 6/2
y = 4x - 3
Using the slope intercept, slope m is 3.
The equation of a perpendicular line to 2y = 8x - 6 must have a slope that is the negative reciprocal of the original slope.
Slope of perpendicular line = -1 / ( 4 )
Slope of perpendicular line = -1/4
Plug the slope m = -1/4 and point (-3,3) into point-slope formula and simplify.
( y - y₁ ) = m( x - x₁ )
( y - 3 ) = (-1/4)( x - (-3) )
( y - 3 ) = (-1/4)( x + 3 )
y - 3 = (-1/4)x - 3/4
y = (-1/4)x - 3/4 + 3
y = (-1/4)x + 9/4
Therefore, the equation of the perpendicular line is y = (-1/4)x + 9/4.
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The scatter plot shows the ages of drivers who attended a car show and the ages of their cars.
What is the age range of drivers who own an 8-year-old car?
Answers
The required range of drivers who own 8 years car is 23years.
Given that,
The scatter plot shows the ages of drivers who attended a car show and the ages of their cars.
We have to determine,
The age range of drivers who own an 8-year-old car.
According to the question,
The Range is the difference between the lowest and highest values.
Therefore,
The age range of drivers who own 8 years old car is 17,25 and 40 years.
Then,
Range of drivers who own 8 years car = highest value of range - lowest value of age.
Range of age of drivers who own 8 years car = 40 - 17 = 23years
Hence, The required range of drivers who own 8 years car is 23years.
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The equation of a circle is (x+10)2+(y−4)2=100.
What is the center and radius of the circle?
Responses
center: (10, −4); radius: 10,000
center: , begin ordered pair 10 comma negative 4 end ordered pair, ; radius: 10,000
center: (−10, 4); radius: 10,000
center: , begin ordered pair negative 10 comma 4 end ordered pair, ; radius: 10,000
center: (10, −4); radius: 10
center: , begin ordered pair 10 comma negative 4 end ordered pair, ; radius: 10
center: (−10, 4); radius: 10
Answers
The center of the circle is (-10,4) and the radius is 10.
What is a circle?The circle is defined as the locus of the point traces around a fixed point called as the center and is equidistant from the outer trace.
All points in a plane that are at a specific distance from a specific point, the center, form a circle. In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.
The equation of the circle is,
( x - h )² + ( y - k )² = r²
(x+10)² + (y−4)² = 100
(x+10)² + (y−4)² = 10²
Compare the equations and find the center and radius,
Center = ( h,k) = ( -10,4)
Radius = r = 10
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Find the length of the missing side. It’s a written response
Answers
Answer:
the missing side is [tex]\sqrt{89}[/tex]
Step-by-step explanation:
We use Pythagoras theorem
[tex]8^{2} +5^{2} =x^{2} \\64 + 25 = x^{2} \\89=x^{2} \\\sqrt{89} =x[/tex]
please tell me how to solve!!
Answers
the equation in the form of slope interpretation is y = 1/3x -4.
What is a Linear equation?An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation has the conventional form y = mx + c.
Given data in a table such as it makes a linear equation slope-intercept form of the given equation is y = mx +c
Where m is the slope
c is constant
The slope for the given data
m = (y₂ - y₁) / (x₂ - x₁)
m = (-5 + 6 )/ (-3 + 6)
m = 1/3
Hence, the equation would be
y = 1/3x + c
for constant we would satisfy the equation with other coordinates of the line.
Substituting ( 0, -4) in the above equation
-4 = 0 + c
c = -4
thus, the equation of the line is y = 1/3x -4
therefore, the linear equation of the given data is y = 1/3x -4.
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