Answers
The answer is:
The second piecewise function,
[tex]f(x)=\left \{ {{-x-2,x<0} \atop {-\frac{x}{2} }\geq 0} \right.[/tex]
Why?To answer the question, we need to find which piecewise function contains the graphs shown in the picture, we have that first line shown, is decreasing and exists from the negative numbers to 0, and the line cuts the x-axis and the y-axis at "-2", for the second line shown, we have that is decreasing but exists from 0 (including it) to the the positive numbers.
So, finding which piecewise satisfies the function shown, we have:
- First piecewise function:
[tex]f(x)=\left \{ {{-x-2,x<0} \atop {\frac{x}{2} }\geq 0} \right.[/tex]
First line,
We have the first line,
[tex]-x-2<0\\[/tex]
The variable has a negative coefficient (-1), meaning that the function (line) is decreasing, also we can see that the function does exists from all the numbers less than 0, to 0, and it cuts the x-axis at -2 and the y-axis at -2.
Second line,
[tex]\frac{x}{2}\geq 0[/tex]
The variable has positive coefficient, meaning that the function (line) is increasing.
Hence, since the second line is not decreasing, the piecewise function is not the piecewise function shown in the picture.
- Second piecewise function,
[tex]f(x)=\left \{ {{-x-2,x<0} \atop {-\frac{x}{2} }\geq 0} \right.[/tex]
First line,
We have the first line,
[tex]-x-2<0\\[/tex]
The variable has a negative coefficient (-1), meaning that the function (line) is decreasing, also we can see that the function does exist from all the numbers less than 0, to 0.
Second line,
[tex]-\frac{x}{2}\geq 0[/tex]
The variable has a negative coefficient ([tex](-\frac{1}{2})[/tex], meaning the the unction (line) is decreasing, also we can see that the function does exists from 0 (including it) to the positive numbers.
Hence, we have that the correct option is the second piecewise function,
[tex]f(x)=\left \{ {{-x-2,x<0} \atop {-\frac{x}{2} }\geq 0} \right.[/tex]
Note: I have attached a picture for better understanding.
Have a nice day!
Related Questions
For which triangle is the length of the hypotenuse an INTEGER?
Answers
B.
5 squared + 12 squared = x squared
5 squared = 25
12 squared = 144
144+25 = 169
Square root of 169 = 13
Hope this helps you!! ❤️❤️
Answer: B.
Step-by-step explanation:
In B, opp=5 adj = 12 hyp=x
Using pythagoras theorem
hyp² = opp² + adj²
x² = 5² +12²
x² = 25 + 144
x² = 169
x=√(69)
x=13
B is the only triangle with a hypotenuse whose length is interger.
Looking at A,
x² = 4² +2²
x= √(20) =4.47
x is not an interger
lets take c and see,
x² = 2² +5²
x = √(29) = 5.385, its also not an interger.
Now, we will take the last one and check
x² = 8² +14²
x=√260 = 16.12, it is not an interger
There B is the only triangle with an integer hypotenuse.
what is the next step in the construction of an angle bisector of angle ABC?
Answers
Answer:
A. Use straightedge to connect vertex B to right-most vertex of the equilateral triangle.
Step-by-step explanation:
The process is to create a bisector of angle ABC... so it means cutting angle at vertex/summit B in half.
Drawing a line from the vertex B to the right-most vertex of the equilateral triangle will deliver you the bisector.
The only answer choice that includes vertex B is the answer A, all other answers are dealing with vertex A and C... which will not help you to draw the bisector or angle ABC.
Answer:
Option A is right
Step-by-step explanation:
Given in the picture is an angle B formed by line segments AB and BC
To construct bisector of angle B
First with centre at B a circle is drawn which meets AB and BC at D and E respectively. With same radius equal to DE and centres of D and E two circles are drawn which intersect at the right most point.
The next step is join B to the rightmost vertex of equilateral triangles
This will be the angle bisector of angle ABC
Hence option A is right
A distance of 30 miles on a map is represented by a 2-inch line. If the map is enlarged to 3 times its size, what will be the scale of the enlarged map?
PLEASE HELP!
Answers
Answer:
[tex]\frac{1}{5}\frac{in}{miles}[/tex]
Step-by-step explanation:
we know that
The original scale of the map is
[tex]\frac{2}{30}\frac{in}{miles}=\frac{1}{15}\frac{in}{miles}[/tex]
If the map is enlarged to 3 times its size
then
the new scale will be
[tex]\frac{2*3}{30}\frac{in}{miles}=\frac{6}{30}=\frac{1}{5}\frac{in}{miles}[/tex]
The scale of the original map is 2 inches to 30 miles. After enlarging the map 3 times, the new scale will be 1 inch to 15 miles, as 6 inches on the enlarged map would represent 90 miles.
Explanation:The question is asking to determine the scale of a map after it has been enlarged. The original map scale is such that 2 inches represent 30 miles. If the map is enlarged 3 times its original size, each inch on the original map would now be represented by 3 inches on the enlarged map. Therefore, the 2 inches that originally represented 30 miles would now be stretched out to 6 inches on the enlarged map.
We can determine the new scale setting up a proportion:
Original scale: 2 inches / 30 miles
Enlarged scale: 6 inches / x miles
We know the distances must remain consistent, so we set up the proportion:
2 inches / 30 miles = 6 inches / x miles
By cross-multiplication, we find that:
2x = 180
x = 90
The scale of the enlarged map will therefore be 1 inch representing 15 miles, as we can conclude from 6 inches representing 90 miles.
Find the height of the cylinder below whose volume is approximately 1000 cubic inches use 3.14 for pi rounder you're answer to the nearest hundredth show your work pls help this is. Big test I got 3 more questions to ask
Answers
Answer:
[tex]h=15.73\ in[/tex]
Step-by-step explanation:
we know that
The volume of a cylinder is equal to
[tex]V=\pi r^{2} h[/tex]
we have
[tex]V=1,000\ in^{3}[/tex]
[tex]r=9/2=4.5\ in[/tex] ----> the radius is half the diameter
substitute and solve for h
[tex]1,000=(3.14)(4.5)^{2} h[/tex]
[tex]h=1,000/[(3.14)(4.5)^{2}][/tex]
[tex]h=15.73\ in[/tex]
Answer:
r = 11 in V =968 pi in3
Step-by-step explanation:
got it right on edge
If Johnny has twice more bottles of dish soap than Carolyn, and Carolyn has 20 more bottles of dish soap than Mr. White, how many bottles of dish soap does Johnny have if Mr. White has 35 bottles of dish soap?
Answers
Answer:
110
Step-by-step explanation:
Answer:
Jesus
Step-by-step explanation:
Why all this dish soap. Sounds like that vine.
ASAP!! The coordinates g(7,3), h(9,0), I(5,-1) form what type of polygon
Answers
Answer:
Triangle (scalene)
Step-by-step explanation:
Polygon is a closed figure.
The names of polygons depends on the number of sides. Some common polygons are:
3 sides - triangle
4 sides - quadrilateral
5 sides - pentagon
6 sides - hexagon
Triangle and Quadrilaterals have their own types as well.
The points G, H , and I are shown in the attached image. As you can see, it creates a 3-sided figure, which is a triangle.
Note: Since all 3 sides have different length, we call it a "scalene triangle"
Help please, thank you!
Answers
ANSWER
9 nickels 8 dimes
EXPLANATION
The simultaneous equations are:
1st equation: n+d=17
2nd equation: 0.05n+0.10d=1.25
Multiply through the second equation by 100.
This the equation:
3rd equation: 5n+10d=125
Make n the subject in equation (1).
n=17-d
Substitute this into equation (3)
5(17-d)+10d=125
85-5d+10d=125
-5d+10d=125-85
5d=40
Divide both sides by 5.
d=8
Put d=8 into n=17-d
This gives:
n=17-8
n=9
Answer:
8 dimes and 9 nickels
Step-by-step explanation:
In this exercise, we got a system of linear equations. We can solve this system by using several methods: substitution, reduction and equalization, and other advanced method call "Cramer's rule".
So, for this exercise we will use the substitution method.
1. Clear n for the first equation.
n + d = 17
n = 17 - d
2. Replace n in the second equation.
0.05n + 0.10d = 1.25
0.05(17 - d) + 0.10d = 1.25
0.85 - 0.05d + 0.10d = 1.25
0.85 + 0.05d = 1.25
3. We solve the obtained equation for d.
0.05d = 1.25 - 0.85
d = (1.25 - 0.85)/0.05
d = 0.40/0.05 = 8
dimes (d) = 8
4. we obtain the value of n using any of the two equations and with d = 8
Using the first equation
n + d = 17
n = 17 - d with d = 8
n = 17 - 8
n = 9
nickels (n) = 9
.
Using the properties of exponents and logarithms, find the value of x in 19+2 in x=25
Answers
Answer:
x = e³
Step-by-step explanation:
Using the property of logarithms
• [tex]log_{b}[/tex] x = n ⇔ x = [tex]b^{n}[/tex]
Given
19 + 2lnx = 25 ( subtract 19 from both sides )
2lnx = 6 ( divide both sides by 2 )
lnx = 3 [ note lnx = [tex]log_{e}[/tex] x ]
x = e³
Answer:
The correct answer is D 20.09
Step-by-step explanation:
State the x-intercept and the y-intercept of the line
Answers
[tex]x=-10, y=5\Longrightarrow\boxed{-10, 5}[/tex]
20 points EZ question plz help urgent
What should be the height of the bar for 11-15 text messages?
A) 1
B) 2
C) 4
D) 5
Answers
Answer:
Its C
hope this helps!!
The correct answer is A .)1
Find the area given figure. A) 44 B)60 C) 84 D) 72
Answers
Answer:
D) 72
Step-by-step explanation:
The way to find the area of this figure easily is to break it down in regular shapes we know. You can then see it as two horizontal rectangles on top and bottom, measuring 6 x 4 each, then a vertical rectangle in the middle measuring 4 x 6.
So, overall, we have 3 similar rectangles measuring 4x6 or 6x4... which are equivalent.
The area of each of those 3 rectangles is 24 units (6x4).
Since we have 3 of those: 3 * 24 = 72.
Jim earns 3% commission every month on his total sales. This month, his total sales were $620,000. How much commission did Jim earn? Plz show work:)
A. $18,600
B.$20,600
C. $186,000
D. $206,000
Answers
The answer is A. $18,600 because $620,000 × 3% = $18,600
plz help 5 star reating and a thanks if someone help
Answers
Answer:
B - +4.
Step-by-step explanation:
The person does not get 4.5 yards.
1/4, -1/4, and -4 do not work as well because negative numbers express loss, and not gain, and the person does not get any fractions.
Answer:
I believe the answer is B. +4
Step-by-step explanation:
suppose that one student is randomly selected during lunch time. what is the experimental probability if students the brought lunch from house is 55 and students that order school lunch is 45
Answers
Answer:
p(A) = 0.55
p(b) = 0.45
Step-by-step explanation:
Experimental probability = [tex]\frac{Number of favorable outcomes}{Total number of outcomes}[/tex]
total students = 55 + 45 ⇒ 100
let A be the probability that students brought lunch from house = [tex]\frac{55}{100}[/tex] ⇒ 0.55
let B be the probability that students order school lunch = [tex]\frac{45}{100}[/tex] ⇒ 0.45
When you use the distance Formula you are building a right triangle whose ____ connects two given points....
Answers
It’s C) , I believe..
Answer:
option C
Step-by-step explanation:
When we use the distance formula for two points ( x, y ) and ( x', y¹ )
Then formula is (distance)² = (x - x¹)² + (y - y¹)²
This is quite similar to the formula used in a right angle triangle to determine hypotenuse
(Hypotenuse)² = (base)²+(height)²
Therefore, option C is the answer.
What is the area of this figure?
Select from the drop-down menu to correctly complete the statement.
Answers
Answer:
146cm^2
Step-by-step explanation:
Area of trapezoid:
(4+14)/2*10=90
Area of triangle:
(14*8)/2=56
90+56=146
For this case we have a figure composed of a trapezoid and a triangle.
By definition we have that the area of a trapezoid is given by:
[tex]A = \frac {(B + b) * h} {2}[/tex]
Where:
B: It's the biggest side
b: It is the minor side
h: It's the height.
So:
[tex]A = \frac {(14 + 4) * 10} {2}\\A = 90 \ cm ^ 2[/tex]
For its part, the area of a triangle is:
[tex]A = \frac {b * h} {2}[/tex]
Where:
b: It's the base
h: It's the height
[tex]A = \frac {14 * (18-10)} {2}\\A = \frac {14 * 8} {2}\\A = \frac {14 * 8} {2}\\A = 56 \ cm ^ 2[/tex]
Thus, the total area is the sum of the two areas:
[tex]146 \ cm ^ 2[/tex]
ANswer:
[tex]146 \ cm ^ 2[/tex]
!!!!?!?!?!!!?!!?!!!!!?!!?!?!?!?!!?!?!?!
Answers
Answer:
it's A
Step-by-step explanation:
2x-y=6+2x-2y=4 start moving the numbers
Answer:
( 4 , 2 )
Hope this helps :)
Have a great day !
5INGH
Step-by-step explanation:
2 x - y = 6
2 x - 2 y = 4
x = 4 and y = 2
(2 × 4 )- (2 × 2) = 8 - 4 = 4
( 2 × 4 ) - 2 = 8 - 2 = 6
HELP PLEASE!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
x=6
Step-by-step explanation:
x-2 = sqrt(28-2x)
Square each side
(x-2)^2 = (sqrt(28-2x))^2
(x-2)^2 = 28-2x
FOIL
x^2 -4x+4 = 28-2x
Subtract 28 from each side
x^2 -4x+4-28 = 28-2x-28
x^2 -4x-24=-2x
Add 2x to each side
x^2 -2x-24=-2x
x^2 -2x+2x-24=-2x+2x
x^2-2x-24 =0
Factor
(x-6)(x+4)=0
Using the zero product property
x=6 x=-4
Check for extraneous solutions
x=6
x-2 = sqrt(28-2x)
6-2 =sqrt(28-12)
4 = sqrt(16)
4=4
Solution
x=-4
x-2 = sqrt(28-2x)
-4-2 =sqrt(28+8)
-6 = sqrt(36)
-6=6
Not a solution
what type of checking account requires a certain amount of money to be kept in it at all times in order to avoid fees
Answers
Answer:
Minimum balance account requires an amount of money to left in it all times in order to avoid fees.
Step-by-step explanation:
We have "many types of account" available in the banking sectors. As per the convenience of the customer, they opt from them. The minimum balance account is the type of account in which the customer has to maintain a standard amount prescribed by the bank in his account, failing to maintain it will lead to the gathering of fine or fee.
Answer:
Minimum Balance account.
Step-by-step explanation:
A minimum balance account is an account type that requires a minimum balance as set by the bank, at all times, in order to waive maintenance fees.
Failing this, certain amount is charged when money is deposited in that account. It can range from few dollars to 500 dollars in some banks.
Centennial park is evaluating
Answers
Answer:
270,000
Step-by-step explanation:
So, you have a number of people (15) that can stand comfortably within a certain area (5x8 ft = 40 sq feet). And you need to find out how many people can fit in the whole park area.
First step is to find out how big the park is, in square feet, so we can then evaluate the number of people that we can fit in.
You had the right number for calculating the area of the park:
A = 400 yards x 200 yards = 1,200 feet x 600 feet = 720,000 sq feet
Now, how many people can we fit in there? Let's use a simple cross-multiplication (x being the number of people fitting in the whole park, what we are looking for):
[tex]\frac{x}{720 000} = \frac{15}{40}[/tex]
By isolating x, we have x = (720,000 * 15) / 40 = 10,800,000 / 40 = 270,000
So, the park could accommodate 270,000 people.
That is of course if there are no trees, no benches, no kids playground or any other infrastructure in the park.
a large pizza has a diameter of 14 inches and is cut into 6 equal pieces. Find the area of 2 pieces, round to the nearest hundredth
Answers
Answer:
The area of two pieces is [tex]51.28\ in^{2}[/tex]
Step-by-step explanation:
step 1
Find the area of the circle (large pizza)
The area is equal to
[tex]A=\pi r^{2}[/tex]
we have
[tex]r=14/2=7\ in[/tex] ----> the radius is half the diameter
assume
[tex]\pi =3.14[/tex]
substitute
[tex]A=(3.14)(7)^{2}[/tex]
[tex]A=153.86\ in^{2}[/tex]
step 2
Divide the area into 6 pieces
[tex]153.86/6=25.64\ in^{2}[/tex]
step 3
Find the area of two pieces
[tex]25.64*2=51.28\ in^{2}[/tex]
Which of the following would not round to 1.2 when rounded to the nearest tenth?
A.1.149
B.1.209
C.1.22
D.1.18
Answers
Answer:
Step-by-step explanation:
A is correct answer
which equation shows the quadratic function used to solve 7x^2=9+x for x?
Answers
Answer:
Step-by-step explanation:
For this case we have the following equation of the second degree:
[tex]7x ^ 2 = 9 + x[/tex]
Rewriting:
[tex]7x ^ 2-x-9 = 0[/tex]
The solutions will be given by the following equation:
[tex]x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2a}[/tex]
We have to:
[tex]a = 7\\b = -1\\c = -9[/tex]
Substituting the values:
[tex]x = \frac {- (- 1) \pm \sqrt {(- 1) ^ 2-4 (7) (- 9)}} {2 (7)}\\x = \frac {1 \pm \sqrt {(- 1) ^ 2 + 4 (7) (9)}} {2 (7)}[/tex]
Answer:
Option D
Help!!!!!!
complete the problem involving the linear equation.
Answers
Answer:
8. slope = 29. y-intercept = -310. in the attachmentStep-by-step explanation:
The slope-intercept form y = mx + b
m - slope
b - y-intercept → (0, b)
We have the equation
y - 2x = -3 add 2x to both sides
y = 2x - 3
slope m = 2
y-intercept b = -3
We need two points to draw a graph of this linear function.
One is y-intercept (0, -3). The second one is calculated by choosing any value of x and put it to the equation:
for x = 2 → y = 2(2) - 3 = 4 - 3 = 1 → (2, 1).
if dy/dt=-10e^-t/2 and y(0)=20 what is the value of y(6)
Answers
ANSWER
[tex]y (6)= \frac{20}{ {e}^{3} } [/tex]
EXPLANATION
The given equation is:
[tex] \frac{dy}{dt} = - 10 {e}^{ - \frac{t}{2} } [/tex]
We integrate with respect to t to get,
[tex]y = 20 {e}^{ - \frac{t}{2} } + k[/tex]
The initial condition is y(0)=20
We apply the initial condition to get,
[tex]20= 20 {e}^{ - \frac{0}{2} } + k[/tex]
[tex]k = 0[/tex]
This implies that;
[tex]y = 20 {e}^{ - \frac{t}{2} } [/tex]
[tex]y (6)= 20 {e}^{ - \frac{6}{2} } [/tex]
[tex]y (6)= 20 {e}^{-3} [/tex]
Or
[tex]y (6)= \frac{20}{ {e}^{3} } [/tex]
The required solution is [tex]y(6) = 20e^{-3}[/tex]
IntegrationGiven the following differential equation [tex]dy/dt=-10e^{-t/2}[/tex]
To get the value of y, we will integrate the equation to have:
[tex]y=-20e^{-t/2} + k[/tex]
Given that y(0) = 20, hence;
[tex]20=-20e^{-0/2} + k\\ 20 = 20 + k\\ k = 0[/tex]
Hence the solution to the given integral is [tex]y=-20e^{-t/2} [/tex]
Next is to get y(6)
[tex]y(6)=-20e^{-6/2} \\ y(6) =20e^{-3}}[/tex]
Hence the required solution is [tex]y(6) = 20e^{-3}[/tex]
Learn more on differentiation here: https://brainly.com/question/25081524
Jane entered her artworks in a state competition. Her art scores from 7 judges are listed. 9,9,8,7,9,6,8 what is Jane’s mean score? A.6 B.7 C. 8 D.9
Answers
Answer:
C!
Step-by-step explanation:
To find the the mean add all the numbers and divde by the number of numbers. The sum of all the numbers is 56. There are 7 numbers.
56/7 is 8.
B
Because I like the letter b so ha
Use the information given in the table on the right to complete each of the following statements.
Brenda is 50 inches tall. Her z-score is
.
Answers
Answer:
0.5
Step-by-step explanation:
Given that height of 7 year old children are normally distributed with mean =49 inches and std deviation = 2inches
Brenda is 50 inches tall
This means her X score is 50
To convert this X score to Z score we use the formula given below
[tex]z=\frac{x-\mu}{\sigma}[/tex]
Here we know all the values of x, mu and sigma
Just substitute
Z score
=[tex]\frac{50-49}{2} =\frac{1}{2} \\=0.5[/tex]
Thus Z score of Brenda is 0.5
Answer:
0.5
Step-by-step explanation:
Which function is a linear function?
Answers
Answer:
y = f(x) = a + bx
Step-by-step explanation:
independent variable = x
dependent variable =y
Answer:A linear function is a straight line which is just a linear function with the equation y=mx+b
Step-by-step explanation:
Which expression is equivalent to 7^3 • 7-^5
I need help !
Answers
Anwer:
1/7^2
explantion:
The expression equivalent to 7^3 • 7-^5 is 1 / 7^2.
What is an expression?An expression is a number, or a variable, or a combination of numbers and variables and operation symbols.
Now the given expression is,
7^3 • 7-^5
Now using the exponential property,
n^a . n^b = n^(a+b)
Therefore, we can write as,
7^3 • 7-^5 = 7^(3-5)
Solving we get,
7^3 • 7-^5 = 7^-2
Since, n^-a = 1/n^a
⇒7^-2 = 1 / 7^2
Therefore, we can write
7^3 • 7-^5 = 1 / 7²
this is the required equivalent expression.
Thus, the expression equivalent to 7^3 • 7-^5 is 1 / 7^2.
To learn more about equivalent expression :
brainly.com/question/10188283
#SPJ2
What is equal to 5 - 1 3/10
Answers
Answer:
3 and 7/10
Step-by-step explanation: