Answers
For the given graph , piecewise function for the given graph is as follow:
f(x) = 1 , if x < -2
2x , if -2 < x ≤ 0
(- x / 2) + 2 if x > 0
As given in the question,
Given is the graph of the function f( x )
Now to find the piecewise function for the given graph is as follow:
For x < -2 it is given that f ( x) = 1
Now consider two points for -2 < x ≤ 0
( x₁ , y₁ ) = ( 0 , 0 )
( x₂ , y₂ ) = ( -2 , -4 )
Equation of f(x) is given by :
( y - 0 )/ ( x -0 ) = ( -4 - 0)/ (-2 - 0 )
⇒ y = 2x
Now consider two points for x > 0
( x₁ , y₁ ) = ( 0 , 2 )
( x₂ , y₂ ) = ( 2 , 1 )
Equation of f(x) is given by :
( y - 2 )/ ( x -0 ) = ( 1 - 2)/ ( 2 - 0 )
⇒ y - 2 = -x / 2
⇒ y = ( -x / 2 ) + 2
Therefore, for the given graph , piecewise function for the given graph is as follow:
f(x) = 1 , if x < -2
2x , if -2 < x ≤ 0
(- x / 2) + 2 if x > 0
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Related Questions
which of the following present for their transformation is equivalent to reflection across the x axis .Arotation 90 degrees about the origin of reflection across the x-axis B rotation 90 degrees about the origin reflection across the y-axisC rotation across degrees about the origin and reflection across the x axis D rotation 180 degrees about the origin reflection across the y axis
Answers
for transformation equivalent to reflection across the x axis
rotate 180 degree about the origin and reflection about the x axis.
option C is correct.
A forty-foot piece of wire was cut into two pieces. The length of one-
piece is 9 times the length of the other. What is the length of the
longer piece? System of equations
Answers
The length of the longer piece is 39.4 ft.
Given, a forty-foot piece of wire was cut into two pieces.
The length of one-piece is 9 times the length of the other.
Let the length of one piece be x,
and the length of the other piece be 9x
Now, according to the question
x + 9x = 44
10x = 44
x = 4.4
then, the length of the longer piece be 9×4.4 = 39.4
Hence, the length of the longer piece is 39.4 ft.
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A stationary store sells large and small packages of greeting cards. Each large package contains h greeting cards. Each small package contains kgreeting cards, which is 4 less than the larger package. Express h in termsof k. *
Answers
In this case the answer is very simple. .
Step 01:
Data
large package = h cards
small package = k cards
Step 02:
large package - 4 = small package
h - 4 = k
h = k + 4
The answer is:
h = k + 4
PLEASE HELP AND HURRY!!!!!! Simplify: 7/8+3/4
Answers
Answer: 1.625
Step-by-step explanation:
13/8 = 1 5/8 = 1.625
0.6 times 2.2 with 2 diffrent models
Answers
Answer:
0.6 x 2.2 = 1.32
2.2 x 0.6 = 1.32
Step-by-step explanation:
You just have to do 0.6 x 2.2 and flip it to get your second model.
Answer:
0.6 x 2.2 = 1.32
2.2 x 0.6 = 1.32
Step-by-step explanation:
the commutative property allows this to happen; flip the order in which the numbers fall
yw have a great day
z ÷ 12 = 9
PLS NEED HELP FAST
STEP BY STEP
Answers
Answer:
z = 108
z/12 = 9
12 x z/12 = 12 x 9
12 x z/12 = 12 x 9
z = 12 x 9
= 108
Answer:
z = 108
Step-by-step explanation:
z / 12 = 9
Multiply 12 and 9
z = 12 * 9
12 * 9 = 108
z = 108
Hope I helped <3
If an object is dropped, the distance it fails during t seconds is given by d(t)=1/2gt^2, where g is about 32ft/sec^2. Find the distance an object would fall in 8 seconds.
Answers
Since the distanc function is given by
[tex]d(t)=\frac{1}{2}gt^2[/tex]in order to find the distance at 8 seconds, we need to substitute t=8 into this function, that is,
[tex]d(8)=\frac{1}{2}g(8)^2[/tex]By taking into account that g=32 ft/sec^2, we have
[tex]d(8)=\frac{1}{2}(32)(64)[/tex]which gives
[tex]\begin{gathered} d(8)=16\times64 \\ d(8)=1024 \end{gathered}[/tex]Therefore, the answer is 1024 ft, which corresponds to the last option.
lin is mixing orange paint for a play. the color takes 3 parts red to 2 parts yellow. if lin has 18 cups of yellow paint how many cups of red does he need?
Answers
the number of cups of red Lin needs is 27 cups
Explanation:number of parts of red = 3
number of parts of yellow = 2
the ratio of red to yellow = 3:2
when lin's number of cups of yellow = 18
let the number of cups of red = x
3 red = 2 yellow
x red = 18 yellow
cross multiply:
3(18) = 2(x)
54 = 2x
divide both sides by 2:
54/2 = 2x/2
x = 27
Hence, the number of cups of red Lin needs is 27 cups
Gabrielle is 15 years older than Milkhail. The sum of there ages is 95 what is Milhails age
Answers
The age of Milkhail is 40 years .
In the question ,
it is given that
the the sum of ages of Gabrielle and Milkhail is = 95
let the age of Milkhail be "m" .
given that Gabrielle is 15 years older than Milkhail
So, the age of Gabrielle is = m + 15
the equation representing the sum of ages is given by
total age = age of Milkhail + age of Gabrielle
95 = m + m + 15
adding the like terms ,
we get
95 = 2m + 15
subtracting 15 from both the sides
2m = 95 - 15
2m = 80
dividing both sides by 2
m = 80/2
m = 40
Therefore , the age of Milkhail is 40 years .
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if p=3x+4 and v=x+5, find pv-2p+v
Answers
Use substitution to simplify the expression.
pv - 2p + v
(3x + 4)(x + 5) - 2(3x + 4) + x + 5
3x² + 15x + 4x + 20 - 6x - 8 + x + 5
3x² + 15x + 4x + x - 6x + 20 + 5 - 8
3x² + 14x + 17
2 gallons = 9 litres
16
to convert 17 gallons into liters
Answers
Answer:
Step-by-step explanation:
17/2=8.5
8.5 x 9=76.5
2d a researcher wanted to know if there was a significant difference in cyber security breaches between cities on two different continents. what test should he conduct to determine if there is a significant difference in cyber security breaches between the continents? write up the results and determine what do the results mean? here is the data set: asia europe 40 25 52 35 63 20 70 18 25 19 19 14 11 9
Answers
There is no significant difference between the cyber security breaches of the two destinations and the values are t-value is 0.16221, the p-value is .874721.
We use two sample t-test to check for the significance.
We take the sample of Asia as treatment 1 and that of Europe as treatment 2
Treatment 1
[tex]N_{1}[/tex]: 5
[tex]df_{1}[/tex] = N - 1 = 5 - 1 = 4
[tex]M_{1}[/tex]: 24.6
[tex]SS_{1}[/tex]: 77.2
[tex]S^{2} _{1}[/tex] = [tex]SS_{1}[/tex]/(N - 1) = 77.2/(5-1) = 19.3
Treatment 2
[tex]N_{2}[/tex]: 6
[tex]df_{2}[/tex] = N - 1 = 6 - 1 = 5
[tex]M_{2}[/tex]: 23.5
[tex]SS_{2}[/tex]: 1051.5
[tex]S^{2} _{2}[/tex] = [tex]SS_{2}[/tex]/(N - 1) = 1051.5/(6-1) = 210.3
T-value Calculation
[tex]S^{2} p_{}[/tex] = (( df1/(df1 + df2)) * s21) + ((df2/(df2 + df2)) * s22) = ((4/9) * 19.3) + ((5/9) * 210.3) = 125.41
s2M1 = s2p/N1 = 125.41/5 = 25.08
s2M2 = s2p/N2 = 125.41/6 = 20.9
t = (M1 - M2)/√(s2M1 + s2M2) = 1.1/√45.98 = 0.16
The t-value is 0.16221. The p-value is .874721. The result is not significant at p < .05
Hence the answer is there is no significant difference between the cyber security breaches of the two destinations and the values are t-value is 0.16221, the p-value is .874721.
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PLEASE HELP If each side has a scale factor of 1 in. to 5 ft., the actualperimeter is and the actual area isO 60 ft, 80 ftO 300 ft, 80 ft?80 ft, 60 ft280 ft, 300 ft
Answers
The perimeter is determine as the add of the sides of the figure. In this case:
[tex]P=(5+2+2+2+1+1+1+2)(5ft)[/tex][tex]P=16(1in5tf)=80ft[/tex]For the area we will divide the figure as follow:
The total area will be:
[tex]A=A_a+A_b[/tex]We find the are of a rectangle by:
[tex]A=h\cdot b[/tex]Where h is height and b is base
Then:
[tex]A_a=5\cdot2=10[/tex][tex]A_b=2\cdot1=2[/tex]Then the total area is:
[tex]A=10+2=12^{\doubleprime}[/tex]In feets:
[tex]12(5ft)=60ft^2[/tex]What are the coordinates of point A? ES 2 (8,6) (-6, 8) (-5.7) Save and Exit
Answers
To write the coordinates of a point in a x - y plane you:
1. Find the distance in x-axis:
The given point A is 7 units distance in x-axis
2. Find the distance in y- axis
The given point A is -5 units distance in y-axis
You write the coordinates in form (x,y)
As x=7 and y=-5
Point A is (7, -5)Answer: -5,7
Step-by-step explanation:
Which is the graph of f (x ) = x^3 + 2x^2 – 4x– 1?-(Notice the increments on the graph are by 2.)
Answers
We must identify which graph corresponds to the function:
[tex]f(x)=x^3+2x^2-4x-1.[/tex]1) The function f(x) is a polynomial of degree 3, so it has 3 roots, i.e. it must cross the x-axis in 3 places. Taking into account this fact, we know that the 1st and 3rd graphs cannot represent the function f(x).
2) Now, when x takes a very big value, the cubic term of the polynomial dominates, and f(x) > 0 for x → ∞. From the remaining options, we see that the 2nd takes f(x) < 0 for x → ∞, so we can discard that option. The remaining option is the 4th graph, so we conclude that that is the correct option.
Answer: 4th graph.
x 31 36 41 46y 10 8 6 4I need to find the slope with these points
Answers
x 31 36 41 46
y 10 8 6 4
I need to find the slope with these points
we know that
To find out the slope, we need two points
take the points (31,10) and (36,8)
so
m=(8-10)/(36-31)
m=-2/5
m=-2/5
m=-0.40
therefore
the answer is -0.40Part 2)
we have
x -7 -4 -1 2
y -7 14 35 56
take the points (7,-7) and (-4,14)
m=(14+7)/(-4-7)
m=21/-11
m=-21/11
the answer is -21/11What is the regression equation for the given data?
Answers
The regression equation for the given data is y = -35.575 + 24.774 x.
Let x be the guests and y be the cost.
From the given table:
mean of x = ∑x / n
= 3+4+4+6+6+7+8+8 / 8
= 46/8
= 5.75
∑[tex]x^{2}[/tex] = 290
mean of y = ∑y/n
= 30+60+88+90+115+160+150+162 / 8
= 106.875
a = mean of y - mean of x * b
[tex]b = \frac{s_{xy} }{s_{xx} }[/tex]
[tex]s_{xx} \\[/tex] = ∑[tex]x^{2}[/tex] - (∑[tex]x)^{2}[/tex]/n
= 290 - 46*46/8
= 25.5
[tex]s_{xy} =[/tex] ∑xy - ∑x∑y / n
= 5548 - 46*855/8
= 631.75
a = 106.875 - 5.75*b
b = 631.75/25.5
b = 24.774
a = -35.575
Therefore the regression equation y = -35.575 + 24.774 x.
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Find the number of different ways that an instructor can choose 4 students from a class of 23 students for a field trip.
Answers
We have to find how many ways we can group 23 students in groups of 4.
This can be calculated as a combination of 23 in 4, as order does not matter and there is no repetition.
We can calculate it as:
[tex]\begin{gathered} C(n,r)=\frac{n!}{r!(n-r)!} \\ C(23,4)=\frac{23!}{4!(23-4)!} \\ C(23,4)=\frac{23!}{4!19!} \\ C(23,4)=\frac{23\cdot22\cdot21\cdot20}{4\cdot3\cdot2\cdot1} \\ C(23,4)=\frac{212520}{24} \\ C(23,4)=8855 \end{gathered}[/tex]Answer: there are 8855 ways.
Determine whether a relation is a function.
Answers
Romano pays 312.50 for a television set. The markup price of the television set is 25%. What equation could you use to find the amount of money that the ...
Answers
The equation used to find the amount of money the store bought the television sets is 1.25a = 312.50
How to find the equation that depict the amount of money paid for the television sets?Romano pays 312.50 dollars for a television set. The mark up price of the television set is 25%.
The equation that can be used to find the amount of money the store paid for the television sets can be calculated as follows;
Therefore,
25% of a + a = 312.50
where
a = cost of the television0.25a + a = 312.50
Therefore, the equation is 1.25a = 312.50
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From the graph , determine the value of x when F(x) = 4
Answers
for this we locate the point where y = 4, and find its ordered pair on the x-axis, and from the graph, x = - 3
answer: x = - 3
A dozen muffins is 12 muffins. A recipe calls for 3/4 cup of almonds to make half a dozen muffins. Use a complex fraction to find how many cups of almonds are needed to make a dozen muffins.
Answers
1) Firstly, let's set a proportion to find out how mny cups of almonds are needed.
muffins cups of almonds
6 3/4
12 x
2)
Cross multiplying it:
6x = 12 * 3/4
6x = 9
x= 9/6
3
In a right triangle, the length of one leg is 20 units. The length of the other leg is 12 units. What is the length of the hypotenuse?
Answers
The of the hypotenuse of the right triangle having a length of 20 units for one leg and 12 units for the other is √( 544 ) units.
What is the length of the hypotenuse?Pythagorean theorem states that the "square on the hypotenuse of a right-angled triangle is equal in area to the sum of the squares on the other two sides.
This is expressed as;
(Hypotenuse)² = (Leg 1 )² + (Leg 2)²
Given the data in the question;
Length of leg 1 = 20 unitsLength of leg 2 = 12 unitsLength of hypotenuse = ?Plug the given values into the formula above and solve for hypotenuse.
(Hypotenuse)² = (Leg 1 )² + (Leg 2)²
Hypotenuse = √( (Leg 1 )² + (Leg 2)² )
Hypotenuse = √( (20 )² + (12)² )
Hypotenuse = √( 400 + 144 )
Hypotenuse = √( 544 ) units
Therefore, √( 544 ) units is the length of the hypotenuse.
Option D) is the correct answer.
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The volume of a cube is 614.125 cubic inches. What is the length of each side of the cube?
Answers
The length of the side of cube is 8.5 inches.
What is volume of a cube?
A cube is a solid object that is three dimensional and has six square faces, facets, or sides, three of which meet at each vertex. One of the five Platonic solids, and the only regular hexahedron, is the cube. It consists of 8 vertices, 12 edges, and 6 faces.
The volume of a cube is a^3 cubic inches where a is the length of side of cube.
Give volume of a cube is 614.125 cubic inches.
Let the length of a side of cube is x inches.
Then volume of cube = x^3 cubic inches.
Now,
x^3 = 614.125
Finding cube root and we get
=> x^3 = 8.5 * 8.5 * 8.5
=> x = 8.5 inches
Therefore, the length of the side of cube is 8.5 inches.
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Using the function F(x)= 3x-1 solve for the following values F(-2)=
Answers
For the function F(x)=3x-1, the value for F(-2) will be (-7).
How to tackle this type of question of function?
Put value of variable in the given function.
Here,
x=-2
then, F(-2) = 3(-2) - 1
F(-2) = -6 - 1
F(-2) = -7
Hence, F(-2) = (-7)
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he graph of a function is shown.
5
4
3
2
-
y
--5-3-2-1₁ 1 2 3 4 5 x
-2-
-3+
7 9
Which function is represented by the graph?
O f(x) =
O
f(x) = {3
O f(x):
x-3, x<0
3,
x20
11
x + 3, x < 0
x 20
-x+ 3, x ≤ 0
3,
x>0
○ f(x) = { 3*
O
-x-3, x ≤0
x > 0
Answers
The function f(x) = {x + 3, x < 0, 3 x ≥ 0} represents the graph.
What is graph?
In mathematics, the set of ordered pairings where f(x)=y exists is the graph of a function f. These pairs are Cartesian coordinates of points in two-dimensional space and so form a subset of this plane in the typical situation when x and f(x) are real integers.
As show in the graph we can see that the function has a graph of x + 3 on left side of the y - axis for x < 0.
And the function has the constant graph y = 3 for x ≥ 0.
Therefore, the given graph is the graph of the function,
f(x) = {x + 3, x < 0, 3 x ≥ 0}.
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Complete the table below to find solutions to the linear equation y = 5x + 35
Answers
y = 5x + 35
When x = 0, we substitute x = 0 into the equation above and then solve for y
y = 5(0) + 35
y = 0+ 35
y = 35
when x =3, substitute into the equation and then solve for y
y = 5(3) + 35
y = 15 + 35
y = 50
when x=-7, substitute x=-7 into the equation above and then solve for y
y = 5(-7) + 35
y = -35+ 35
y=0
x y (x,y)
0 35 (0, 35)
3 50 (3, 50)
-7 0 (-7, 0)
On the prior screen, you sketched `ΔMJN` on the graph with vertices `M(16,-8)`, `J(16,2)`, and `N(4,0)`. What is the area of `ΔMJN`?
Answers
The triangle has an area of 60 square units.
How to determine the area of the triangle based on the location of its vertices
Herein we find the case of a triangle whose vertices are set on a Cartesian plane and whose area can be determined by means of the Heron's formula:
A = √[s · (s - MJ) · (s - JN) · (s - MN)]
s = (MJ + JN + MN) / 2
Where MJ, JN and MN are the side lengths of the triangle and s is the semiperimeter of the triangle.
First, determine the side lengths:
MJ = √[(16 - 16)² + [2 - (- 8)]²]
MJ = 10
JN = √[(4 - 16)² + (0 - 2)²]
JN = √[(- 12)² + (- 2)²]
JN = 2√37
MN = √[(4 - 16)² + [0 - (- 8)]²]
MN = √[(- 12)² + 8²]
MN = 4√13
Second, determine the semiperimeter:
s = (1 / 2) · (10 + 2√37 + 4√13)
s ≈ 18.294
Third, calculate the area of the circle:
A = √[18.294 · (18.294 - 10) · (18.294 - 2√37) · (18.294 - 4√13)]
A ≈ 60.002
The area of the triangle is approximately equal to 60 square units.
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What is the equation of the line that passes
through the point (-8, -8) and has a slope
of o?
Answers
Answer: y+8=m(x+8)
Step-by-step explanation: because you follow the form y-y1=m(x-x1)
Find the scale factor.
Answers
Answer:
scale factor k = [tex]\frac{4}{3}[/tex]
Step-by-step explanation:
the scale factor of Δ QRS to Δ LMN is the ratio of corresponding sides , image to original.
scale factor = [tex]\frac{QS}{LN}[/tex] = [tex]\frac{4}{3}[/tex]