Answers
The piece-wise function is defined as follows:
[tex]f(x) = x^2, 0 \leq x < 3[/tex].[tex]f(x) = -\frac{5}{3}x + 14, 3 < x \leq 6[/tex].[tex]f(x) = \frac{3}{2}x - 5, 6 \leq x \leq 10[/tex].What is a piece-wise function?A piece-wise function is a function that has multiple definitions, depending on the input.
In this graph, for x at least 0 and less than 3, the parabolic curve passes through (0,0), (1,1), (2,4) and has an open interval at (3,9), hence the definition is:
[tex]f(x) = x^2, 0 \leq x < 3[/tex]
For x greater than 3 and at most 6, it is a line going through (3,9) and (6,4), hence:
[tex]m = \frac{9 - 4}{3 - 6} = -\frac{5}{3}[/tex]
[tex]f(x) = -\frac{5}{3}x + b[/tex]
Goes through (3,9), hence:
[tex]9 = -\frac{5}{3}(3) + b[/tex]
b = 14.
So
[tex]f(x) = -\frac{5}{3}x + 14, 3 < x \leq 6[/tex]
For x between 6 and 10, it is a line going through (6,4) and (10,10), hence:
[tex]m = \frac{10 - 4}{10 - 6} = \frac{6}{4} = \frac{3}{2}[/tex]
Then:
[tex]f(x) = \frac{3}{2}x + b[/tex]
When x = 10, f(x) = 10, hence:
[tex]10 = \frac{3}{2}(10) + b[/tex]
10 = 15 + b
b = -5.
Hence:
[tex]f(x) = \frac{3}{2}x - 5, 6 \leq x \leq 10[/tex]
More can be learned about piece-wise functions at https://brainly.com/question/24734454
#SPJ1
Related Questions
The following data shows the temperature of a city, in degrees Celsius, on consecutive days of a month:
8.5, 8.3, 8.2, 8.9, 8.4, 8.2, 8.7, 8.5, 8.3, 8.5, 8.4
Which box plot best represents the data? (1 point)
Answers
SECOND ONE
Step-by-step explanation:
Trust me
The second box plot represents the data 8.5, 8.3, 8.2, 8.9, 8.4, 8.2, 8.7, 8.5, 8.3, 8.5, 8.4 option second is correct.
What is the box and whisker plot?A box and whisker plot is a method of abstracting a set of data that is approximated using an interval scale. It's also known as a box plot. These are primarily used to interpret data.
We have a box plot shown in the picture.
The data:
8.5, 8.3, 8.2, 8.9, 8.4, 8.2, 8.7, 8.5, 8.3, 8.5, 8.4
From the data given:
The minimum value = 8.2
The maximum value = 8.9
Q1 = 8.3
Q2 = 8.4
Q3 = 8.5
As we can see in the second box plot this data is represented.
Thus, the second box plot represents the data 8.5, 8.3, 8.2, 8.9, 8.4, 8.2, 8.7, 8.5, 8.3, 8.5, 8.4 option second is correct.
Learn more about the box and whisker plot here:
brainly.com/question/3209282
#SPJ1
If x + y = 2 and x - y = 6, solve for x and y.
Answers
Answer:
Step-by-step explanation:
Givens
x + y = 2
x - y = 6
Solution
Just add the two equations together. The y's will drop out.
x + y = 2
x - y = 6 Add
2x = 8 Divide by 2
2x/2 = 8/2 Combine
x = 4 Substitute x = 4 into the top equation
x + y = 2
4 + y = 2 Subtract 4 from both sides
4-4+y=2-4 Combine
y = - 2
Answer
x = 4
y = -2
Linear equations in two variables
Graph y = -4 then explain why it is not a function, can somone ELI5
Answers
Answer:
y=-4 is a function
Step-by-step explanation:
It passes the vertical line test, and each x has only one y, so it is a function.
x = -4 is NOT a function because one x has multiple y values. It does not pass the vertical line test.
The first three steps in writing f(x) = 40x + 5x2 in vertex form are shown.
Write the function in standard form.
f(x) = 5x2 + 40x
Factor a out of the first two terms.
1(x) = 5(x2 + 8x)
Form a perfect square trinomial.
(%) =16
1(x) = 5(x2 + 8x + 16) -5(16)
What is the function written in vertex form?
® f(x) = 5(x + 4) -80
® f(x) = 5(x + 8) - 80
O f(x) = 5(x + 4)2 - 80
• f(x) = 5(x + 8) - 80
Answers
Answer: Choice C [tex]f(x) = 5(x+4)^2 - 80[/tex]
======================================================
Reason:
The expression [tex]x^2+8x+16[/tex] factors to [tex](x+4)^2[/tex] using the perfect square trinomial formula [tex](a+b)^2 = a^2 + 2ab + b^2[/tex]. In this case, a = x and b = 4.
The -5(16) simplifies to -80
Therefore, [tex]5(x^2+8x+16) - 5(16)[/tex] turns into [tex]5(x+4)^2 - 80[/tex]
Compare this to [tex]a(x-h)^2 + k[/tex] to see that h = -4 and k = -80. The vertex is located at (h,k) = (-4, -80)
Answer:
c) 5(x+4)² - 80
Step-by-step explanation:
You have already gotten the third (second-last) step for finding the vertex as follows:
f(x) = 5(x² + 8x + 16) -5(16)
= 5(x+4)² - 80
Additional remarks: to find the vertex, you can just use find the value of x when x+4 = 0, meaning x = -4 and y = -80. Hence, the vertex is (-4, -80).
Hope this helps and feel free to mark this as brainliest! :)
How many cubic feet of dirt are there in a hole that is 3’ deep x 3’ wide x 3’ long?.
Answers
Answer:
27
depth ×breadth×width=3×3×3
= 27
Fully simply 15x^4y^4(−5x^3y^5)
Answers
Answer:
[tex]-75x^{7}y^{9}[/tex]
Step-by-step explanation:
Quayleen wants to decorate her Christmas tree. She wants to place the tree on a wooden block covered with coloured paper with picture of Santa Claus on it. She must know the exact quantity of paper to buy for this purpose. If the box has length, breadth and height as 80 cm, 40 cm and 20 cm respectively. How many square sheets of paper of side 40 cm would she require?
Answers
[tex]\bullet\:{\boxed{\tt{\red{{Given :}}}}}[/tex]
• Length of the wooden box [tex](l)[/tex] = 80cm.
• Breadth of the wooden box [tex](b)[/tex] = 40cm.
• Height of the wooden box [tex](h)[/tex] = 20cm.
• Side of the square sheet paper = 40cm.
[tex]\bullet\:{\boxed{\tt{\red{{To : Find :}}}}}[/tex]
The number of sheets required.
[tex] \bullet\:{\boxed{\tt{\red{{Formula \: \: used :}}}}}[/tex]
[tex] \star{\underline{\boxed{{\sf{{{TSA}} = \underline{\underline{{\purple\sf 2(lb+bh+hl)}}}}}}}} \star[/tex]
[tex]\star{\underline{\boxed{{\sf{{{Area \: of \: square}} = \underline{\underline{{\purple{\sf side \times side }}}}}}}}}\star[/tex]
[tex]\star{\underline{\boxed{{\sf{{{Number \: of \: sheets \: required} = {{{\purple{\sf \dfrac{TSA}{area \: of \: one \: sheet}}}}}}}}}}} \star[/tex]
[tex] \bullet\:{\boxed{\tt{\red{{Concept :}}}}}[/tex]
As Quayleen wants to place the tree on a wooden block covered with coloured paper with picture of Santa Claus on it. So for knowing the number of sheets required, we need two things one the TSA and Area of one sheet. Once, we will get the values we will divide them to get the answer. Let's Start !!
[tex] \bullet\:{\boxed{\tt{\red{{Solution :}}}}}[/tex]
As we know that ::
Total surface area of cuboid [tex]\large[ \sf 2(lb+bh + hl)][/tex]
Here,
✧ Length [tex](l)[/tex] = 80cm
✧ Breadth [tex](b)[/tex] = 40cm
✧ Height [tex](h)[/tex] = 20cm
Now, by putting the values we get :
[tex] \longrightarrow 2 \bigg[ (80 \times 40) + (40 \times 20) + (20 \times 80) \bigg]\sf {cm}^{2}[/tex]
[tex]\longrightarrow 2 \bigg[ (3200) + (800) + (1600) \bigg] \sf {cm}^{2} [/tex]
[tex] \longrightarrow 2 \bigg[ 5600 \bigg] \sf {cm}^{2} [/tex]
[tex] \longrightarrow 11200 \: \sf {cm}^{2}[/tex]
Hence, the total surface area of the wooden box is 11200 cm²
Now,
The area of each sheet of paper will be :
[tex] \sf \longrightarrow side \times side[/tex]
[tex]\sf \longrightarrow (40 \times 40) \: {cm}^{2} [/tex]
[tex]\longrightarrow \sf (1600) \: {cm}^{2} [/tex]
Hence, the area of each sheet of paper is 1600 cm²
Now,
For finding the number of sheets required
[tex] \longrightarrow \tt \dfrac{total \: surface \: area \: of \: box}{ area \: of \: one \: sheet} [/tex]
[tex]\longrightarrow \sf\dfrac{ \cancel{11200}_{7}}{\cancel{1600}_{1}}[/tex]
[tex] \longrightarrow \purple{ \sf 7}[/tex]
Therefore, Quayleen requires 7 sheets.
[tex]\rule{280pt}{2pt}[/tex]
Given that the sum to infinity of a G.P. is 10. If the first term of the series is given as 5, determine the 3rd term.
Answers
Answer:
a₃ = 1.25
Step-by-step explanation:
the sum to infinity is calculated as
S ∞ = [tex]\frac{a_{1} }{1-r}[/tex]
a₁ is the first term and r the common ratio
given a₁ = 5 and S∞ = 10 , then
10 = [tex]\frac{5}{1-r}[/tex] ( multiply both sides by (1 - r)
10(1 - r) = 5
10 - 10r = 5 ( subtract 10 from both sides )
- 10r = - 5 ( divide both sides by - 10 )
r = 0.5
then
a₂ = a₁ × r = 5 × 0.5 = 2.5
a₃ = a₂ × r = 2.5 × 0.5 = 1.25
Is 40% of 90 closer to 10 or 30?
Answers
Answer:
Closer to 30.
Step-by-step explanation:
To answer this first find 40% of 90.
90*0.4=36
0.4 is the same as 40%
Hope this helps!
If not, I am sorry.
I need a written answer for all three questions please.
Answers
The values of the trigonometry ratios are:
cos α = - 5/13 and cot α = 5/12cot α = -5/12 and sec α = 13/5How to solve the trigonometry ratios?1: sin α = -12/13 and tan α > 0, find cos α and cot α
Because tan α > 0, then it means that cos α and sin α are negative
So, we have:
sin²α + cos²α = 1
Substitute sin α = -12/13
(-12/13)² + cos²α = 1
This gives
cos²α = 1 - (-12/13)²
Evaluate the squares
cos²α = 1 - 144/169
Evaluate the difference
cos²α = 25/169
Take the square root of both sides
cos α = - 5/13
The cotangent ratio is represented as:
cot α = cos α/sin α
This gives
cot α = (-5/13)/(-12/13)
Evaluate
cot α = 5/12
Hence, cos α = - 5/13 and cot α = 5/12
2: tan α = -12/5 for α in quadrant IV, find sec α and cot α
Because α is in quadrant IV, then it means that sec α is positive
cot α = 1/tan α
This gives
cot α = 1/(-12/5)
Evaluate
cot α = -5/12
Also, we have:
sec²α = 1 + tan²α
Substitute tan α = -12/5
sec²α = 1 + (-12/5)²
Evaluate the squares
sec²α = 1 + 144/25
Evaluate the sum
sec²α = 169/25
Take the square root of both sides
sec α = 13/5
Hence, cot α = -5/12 and sec α = 13/5
Read more about trigonometry ratios at:
https://brainly.com/question/11967894
#SPJ1
How do I solve this?
Answers
Answer:
x = 4
Step-by-step explanation:
The figure in the picture is a parallelogram. In parallelograms diagonals bisect each other. That means that they divide each other in half. That means that 6x + 1 is the same as 4x + 9.
6x + 1 = 4x + 9
2x + 1 = 9
2x = 8
x = 4
Two rigid transformations are used to map TriangleJKL to TriangleMNQ. The first is a translation of vertex L to vertex Q. What is the second transformation?
a reflection across the line containing LK
a reflection across the line containing JK
a rotation about point L
a rotation about point K
Answers
Triangle JKL is mapped to Triangle MNQ by two rigid transformations. Vertex L to vertex Q translation is the first. a rotation about point L is the second transformation. Option A is correct.
What is the triangle?A triangle is a three-sided polygon. It is one of the most fundamental geometric forms.
Two rigid transformations are used to map Triangle JKL to Triangle MNQ. The first is a translation of vertex L to vertex Q.
The second transformation is a rotation about point L.
Hence option A is correct.
To learn more about the triangle, refer to:
https://brainly.com/question/2773823
#SPJ1
Answer: Option 3 or C. a rotation about point L
Step-by-step explanation:
I took the quiz and got 100% correct on Edge 2022. Trust me if you are working on Edge the answer is correct. The proof is down below. I hope someone finds this helpful. Good luck everyone! :)
What is the approximate area of the circle shown below?
60 cm C
A. 11,310 cm²
B. 94 cm²
C. 2827 cm²
D. 188 cm²
Answers
The image of ABC is A'B'C. What transformations would result in this image?
ABC is rotated 180° around the origin, then T: ( x, y) → ( x - 1, y - 1).
ABC is reflected over the line x = 1, then is reflected over the line y = -1.
ABC is rotated -90° around the point, then T: ( x, y) → ( x + 5, y + 3).
ABC is rotated -90° around the origin, then T: ( x, y) → ( x + 5, y - 1).
(multi choice)
Answers
Triangle ABC was rotated 90° around the point, then translated using the rule (x, y) → ( x + 5, y + 3) to form triangle A'B'C'.
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are translation, reflection, rotation and translation.
Triangle ABC was rotated 90° around the point B, then translated using the rule (x, y) → ( x + 5, y + 3) to form triangle A'B'C'.
Find out more on transformation at: brainly.com/question/4289712
#SPJ1
please help mee, (20 points will give brainliest!!!)
Answers
Answer:
A) 48
B) -30
Step-by-step explanation:
Hello!
Part ATo compute f(-1) and f(5), we simply replace x with -1 and -5.
Calculate[tex]f(-1) + f(5)[/tex][tex]((-1)^2 - 1 + 9)+ (5^2 +5 + 9)[/tex][tex](9)+(39)[/tex][tex]48[/tex]The answer to A is 48
Part BWe have the values for f(-1) and f(5), so we just switch the operation
[tex](9) - (39)[/tex][tex]-30[/tex]The answer to B is -30
Find x, y, and z. Help me please :)
Answers
Answer:
x = 58°
z = 60°
y = 29( 58°)
Step-by-step explanation:
The arrows on the lines are trying to tell you that these lines are parallel to each other, whenever you see parallel lines think of *FUN* method
2y = 58° (alternate angles)
y = 29
x = 58° (alternate angles)
62° + 58° + z = 180° (sum of angles on a triangle)
120° + z = 180°
z = 60°
Which of the following represents the synthetic division form of the long division problem below? (2x ^ 3 - 6x ^ 2 + 4x + 7)/(x + 3)
Answers
Angle AMO is 50 degrees. If ray MB bisects angle AMO, what would be the measure of angle AMB?
Answers
What is the inverse of the fraction FX = 1/4 x = -12
Answers
The inverse function of the function f(x) will be f⁻¹(x) = 4x + 48. Then the correct option is D.
The complete question is attached below.
What is inverse of a function?Suppose that the given function is
f: X → Y
Then, if function 'f' is one-to-one and onto function (a needed condition for inverses to exist), then, the inverse of the considered function is
f⁻¹: Y → X
It simply means, inverse of 'f' is an undo operator, that takes back the effect of 'f'
The function is given below.
f(x) = (1/4)x – 12
Then the inverse function of the function f(x) will be
(1/4)f⁻¹(x) - 12 = x
f⁻¹(x) = 4x + 48
Then the correct option is D.
Learn more about inverse function here:
https://brainly.com/question/19425567
#SPJ1
A car manufacturer is reducing the number of incidents with the transmission by issuing a voluntary recall. During week 2 of the recall, the manufacturer fixed 192 cars. In week 4, manufacturer fixed 184 cars. Assume that the reduction in the number of cars each week is linear. Write an equation in function form to show the number of cars seen each week at the mechanic.
f(x) = 4x + 200
f(x) = 2x + 192
f(x) = −4x + 200
f(x) = −2x + 192
Answers
Answer:
the answer is f(x)=2x+192
Answer:
The answer is F(x)=2x+192
a motorcyclist riding North along a straight road at 50 km per hour observes that the wind appeared to have a velocity of 50 km per hour from the direction North 60 degrees West what is the velocity of the wind.
Answers
The velocity of the wind will be 50 km per hour.
What is a vector?The quantity which has magnitude, direction and follows the law of vector addition is called a vector.
A motorcyclist riding North along a straight road at 50 km per hour observes that the wind appeared to have a velocity of 50 km per hour from the direction North 60 degrees West.
Then the velocity of the wind will be
Let x be the speed of the wind. Then we have
x² = 50² + 50² - 2 x 50 x 50 x cos 60°
x² = 2500 + 2500 - 2500
x² = 2500
x = 50 km per hour
More about the vector link is given below.
https://brainly.com/question/13188123
#SPJ1
What is the solution to –2(8x – 4) < 2x + 5?
x > x is greater than StartFraction 1 Over 6 EndFraction.
x < x is less than StartFraction 1 Over 6 EndFraction.
x > 6
x < 6
Answers
The solution to the inequality, -2(8x – 4) < 2x + 5, is: B. x > 1/6.
How to Find the Solution of an Inequality?To find the solution to an inequality, solve the inequality to isolate the variable.
Given the inequality, -2(8x – 4) < 2x + 5, open the bracket:
-16x + 8 < 2x + 5
Combine like terms
-16x - 2x < -8 + 5
-18x < -3
Divide both sides by -18 then reverse < to >
-18x/-18 > -3/-18
x > 1/6
The solution is: B. x > 1/6
Learn more about inequalities on:
https://brainly.com/question/11613554
#SPJ1
In triangle QRS, angle Q measures 33.7°, angle R measures 52.3°, and angle S measures 94°. Based on the information that is provided, which could be a correct set of sides for this set of angles?
side QR = 7 cm , side RS = 10 cm , side QS = 12.6 cm
side QR = 10 cm, side RS = 7 cm, side QS = 12.6 cm
side QR = 12.6 cm, side RS = 10 cm, side QS = 7 cm
side QR = 12.6 cm, side RS = 7 cm, side QS = 10 cm
Answers
Answer:
side QR = 12.6 cm, side RS = 7 cm, side QS = 10 cm
Step-by-step explanation:
The side opposite to biggest angle is the longest side
In ΔQRS,
∠S > ∠R > ∠Q
∠S is the biggest and ∠ Q is the smallest angle.
So, the side opposite to ∠S, QR is the longest side and the side opposite o ∠Q , RS is the smallest side.
QR > QS > RS
QR = 12.6 cm ; QS = 10 cm and RS = 7 cm
PLEASE HELP I WILL GIVE 20 POINTS
Function g can be thought of as translated (shifted) version of f(x)=x^2
Answers
Can someone pls help me with this fast thank you
Answers
Answer: Yes
Step-by-step explanation:
[tex]\frac{123}{2}=\frac{246}{4}=\frac{369}{6}=\frac{492}{8}=61.5[/tex].
Since the ratio of distance in miles and the time in hours is constant, the relationship is proportional.
Using the basic identities, find the value of cosΘ if cotΘ = -12/5.
Answers
Step-by-step explanation:
please mark me as brainlest
Find the value of x. Then find the measure of each labeled angle.
Answers
Answer:
x = 70 and the labeled angles are 110 and 70
Step-by-step explanation:
This is a trapezoid, the bases are parallel.
Since the bases are parallel, given two angles are supplementary and their sum is equal to 180:
x + 40 + x = 180 add like terms
2x + 40 = 180 subtract 40 from both sides
2x = 140 divide both sides by 2
x = 70 and the labeled angles are 110 and 70
a man bought a motor at 400,000 Kenyan shillings in January 1999 it depreciated at a rate of 16% per annum if he value it six months determines its value in January 2003
Answers
The value of the car is January 2003 is $199,148.54.
What is the value of the car?Depreciation is the rate of decline in the value of an asset with the passage of time.
The exponential equation that can be used to determine the value of the car is:
Value of the car = purchase value(1 - rate of decline)^time
400,000 x (1 - 0.16)^(2003 - 1999)
400,000 x (0.84^4) = $199,148.54
To learn more about depreciation, please check: https://brainly.com/question/15085226
#SPJ1
Can someone explain to me #2 I only need #2
Answers
Answer:
in a rectangle, opposite sides are equal in length
Step-by-step explanation:
now in this question, Pythagoras theorem is being used to find the length
we know both sides by using Pythagoras theorem find third side and get the sum to find ac+bd
Step-by-step explanation:
So it tells you that AB = 21 and AD = 28
and you to find what BD + AC is and since BD is the same length as AC
you only need to find one of them, then double it
There is a formula you use called the Pythagorean theorem
The Pythagorean theorem is A²+B²=C²
In this problem A = 21 B = 28 and C = the length of BD
so it'll look like 21²+28²=Length of BD² or BD²=21²+28² now you find BD
first do 21²+28² --> 441+784 --> 1225 Now you know that 21²+28²=1225
so BD²=1225 Then to find BD, you find √1225(square root of 1225)
Which is 35 So BD=35 and you want to know what BD+AC is
so 35+35=70
Question 9 of 10
A fellow classmate tosses 3 coins and finds that 2 of them come up tails.
Which of the following is the best conclusion for her to come to?
OA. She needs to keep flipping the coins until she gets 50% heads in
order to determine if they are fair.
OB. If she flips the coins once more, they will all come up heads.
OC. The coins are unfair.
OD. This could easily happen with a fair coin after only 3 flips.
Answers
The best conclusion for her to come to: D. this could easily happen with a fair coin after only 3 flips.
What is a fair coin?A fair coin can be defined as an idealized type of coin that has an equal probability of revealing both heads and tails when randomly tossed.
This ultimately implies that, the best conclusion for her to come to is that this could easily happen with a fair coin after only 3 flips considering 2 of the three coins come up tails.
Read more on fair coin here: https://brainly.com/question/10837034
#SPJ1
