Answer:
f(x) = {x-3 for x ≤ -1; -3x+14 for x > 5}
Step-by-step explanation:
To write the piecewise function, we can consider the pieces one at a time. For each, we need to define the domain, and the functional relation.
__
Left PieceThe domain is the horizontal extent. It is shown as -∞ to -1, with -1 included.
The relation has a slope (rise/run) of +1, and would intersect the y-axis at -3 if it were extended.
The first piece can be written ...
f(x) = x-3 for x ≤ -1
__
Right PieceThe domain is shown as 5 to ∞, with 5 not included.
The relation is shown as having a slope (rise/run) of (-3)/(1) = -3. If extended, it would intersect the point (5, -1), so we can write the point-slope equation as ...
y -(-1) = -3(x -5)
y = -3x +15 -1 = -3x +14
The second piece can be written ...
f(x) = -3x +14 for x > 5
__
Whole functionPutting these pieces together, we have ...
[tex]\boxed{f(x)=\begin{cases}x-3&\text{for }x\le-1\\-3x+14&\text{for }5 < x\end{cases}}[/tex]
_____
Additional comment
Sometimes it is convenient to write inequalities in number-line order (using < or ≤ symbols). This gives a visual indication of where the variable stands in relation to the limit(s). Perhaps a more conventional way to write the domain for the second piece is, x > 5.
(4x^2+9x-7)-(-7x^2+5x-1)
(4x
2
+9x−7)−(−7x
2
+5x−1)
Step-by-step explanation:
I think the expression is
(4x² + 9x - 7) - (-7x² + 5x - 1)
and that is the same as
4x² + 9x - 7 + 7x² - 5x + 1 =
= 11x² + 4x - 6
remember that the combination of two '-' signs turns this into one '+' sign.
to subtract a negative number is indeed the same as adding a positive number with the same absolute value.
Find the volume of the figure. If necessary, round your answer to the nearest tenth.
Answer choices
A: 441.6 cm^3
B: 883.2 cm^3
C: 147.2 cm^3
Answer:
A
Step-by-step explanation
math
HELP PLEASEE!!!
A prism is filled with 25 cubes with 1/2-unit side lengths. What is the volume of the prism in cubic units?
Answer:
3.125 cubic unit i guess
Answer:
3.125 unit cube is the answer i hope i helped u
What is the volume of this cone? use 3.14 for π and round your answer to the nearest tenth. in your answer, give the volume of the cone rounded to the nearest tenth, and then explain how you calculated it.
Answer:
Volume of a cone = 1/3•pi r•r•h
V = 1/3•pi•2•2•8
V = 33.49333333333333
V = 33.5 inches squared
I hope this helps! Have a good day! :)
The volume of the considered cone whose heigth is 8 inches and radius of the base is 2 inches is 33.5 cubic inches approximately.
How to find volume of a right circular cone?Suppose that the radius of considered right circular cone be 'r' units.
And let its height be 'h' units.
Then, its volume is given as:
[tex]V = \dfrac{1}{3} \pi r^2 h \: \rm unit^3[/tex]
Right circular cone is the cone in which the line joining peak of the cone to the center of the base of the circle is perpendicular to the surface of its base.
The missing image for this problem is attached below.
For this case, the radius is of 2 inches, and height is of 8 inches, thus, the volume of the considered cone is:
[tex]V = \dfrac{1}{3} \pi r^2 h \: \rm unit^3 \approx \dfrac{1}{3} \times 3.14 \times (2)^2 \times 8 \approx 33.51 \approx 33.5 \: \rm in^3[/tex]
(rounded to the nearest tenth, which is first place to right of the decimal point.
Thus, the volume of the considered cone whose heigth is 8 inches and radius of the base is 2 inches is 33.5 cubic inches approximately.
Learn more about volume of a cone here:
https://brainly.com/question/26093363
Find the area of the polygon.
Answer:
95 m
Step-by-step explanation:
you can split the shape into three pieces so it is 4x5, 4x5, and 11x5. Add the products for the area which is 95 m
Paul bought 4 DVDs for $9.95 each. What was his total cost?
A.$39.90
B.$40.80
C.$39.80
D.$38.80
Errin bought stock in XYZ Corporation for $100 per share. One month later the stock was up 10%. After another month the stock fell 10%. a. What was the price of the stock after the first month? b. What was the price of the stock after the second month?
Answer:
350 sum
Step-by-step explanation:
1. The equation of a circle is x² + y² - 4x +2y-11-0. What are the center and the radius of the circle?
www
Show your work.
Answer:
[tex]\mathfrak{\huge{\orange{\underline{\underline{AnSwEr:-}}}}}[/tex]
Actually Welcome to the concept of Circles,
so we get as,
centre as ==> ( -g, -f) ==> (2,-1)
How do i Write (3x^3)^2 WITHOUT exponents
Answer:
(3x³)² = 9x⁶ = 3 × 3 × x × x × x × x × x × x
Thus, The answer is
3 × 3 × x × x × x × x × x × x
Answer:
3 * 3 * y * y * y * y * y * y
Step-by-step explanation:
(3y³)²
Multiply 3 by 3 and y six times
3 * 3 = 9
y * y * y * y * y * y
The answer should be
3 * 3 * y * y * y * y * y * y
I hope this helps!
help its for calculus
Answer:
maybe its e(1/y)
Answer:
it should be e(1/y)
Evaluate (2 minus 5 i) (p + q) (i) when p = 2 and q = 5 i.
29 i
29 i - 20
- 21 i
29
Ed Galaxy- Operations with whole numbers and decimals
Answer:
0.6
Step-by-step explanation:
1.0l-0.4l=0.6L
Multiple choice easy question. Please answer.
Answer:
I belive it should be # 3 i might be wrong thow.
Step-by-step explanation:
Answer:
2
Step-by-step explanation:
Car one rotated 90 degrees counterclockwise would be to car 4
then, it rotated 180 degrees clockwise would be car 2.
the answer is Car 2
Please Help Me ASAP.
Answer:
x > -10
Step-by-step explanation:
5 - 3x > 35
-5 -5
-3x > 30
[tex]\frac{-3x > 30}{-3}[/tex]= x > -10
Find x.
Round to the nearest tenth:
31°
у
X
400 ft
x = [ ? ]ft
Answer:
x = 466.7 fty = 240.3 ftFirst find the inner angle:
90° - 31°59°using sine rule:
[tex]\sf sin(x)= \dfrac{opposite}{hypotensue}[/tex]
[tex]\hookrightarrow \sf sin(59)= \dfrac{400}{x}[/tex]
[tex]\hookrightarrow \sf x = \dfrac{400}{sin(59)}[/tex]
[tex]\hookrightarrow \sf x = 466.6533[/tex]
[tex]\hookrightarrow \sf x = 466.7[/tex] ( rounded to nearest tenth )
====================================
using tan rule:
[tex]\sf tan(x)= \dfrac{opposite}{adjacent}[/tex]
[tex]\hookrightarrow \sf tan(59)= \dfrac{400}{y}[/tex]
[tex]\hookrightarrow \sf y= \dfrac{400}{ tan(59)}[/tex]
[tex]\hookrightarrow \sf y= 240.344[/tex]
[tex]\hookrightarrow \sf y= 240.3[/tex]
Answer:
y = 466.7 ft (nearest tenth)
Step-by-step explanation:
Using the Alternate Interior Angle Theorem
the angle inside the triangle that is opposite the side [tex]y[/tex] is 31°
Using the cos trig ratio:
[tex]\sf cos(\theta)=\dfrac{A}{H}[/tex]
where:
[tex]\theta[/tex] is the angleA is the side adjacent the angleH is the hypotenuseGiven:
[tex]\theta[/tex] = 31°A = 400 ftH = [tex]x[/tex]Substitute given values and solve for x:
[tex]\sf \implies cos(31)=\dfrac{400}{x}[/tex]
[tex]\sf \implies x=\dfrac{400}{cos(31)}[/tex]
[tex]\sf \implies x=466.7\:ft\:(nearest\:tenth)[/tex]
Determine the simple interest earned p=$2000 r=4.6% T=4 years
Answer:
[tex]\boxed{\sf{I=368}}[/tex]Step-by-step explanation:
Use a simple interest formula.
Simple interest formula:
⇒ I=PrtP stands for principal R stands for interest rateT stands for interest time(P): Principal =$2000(R): Interest Rate =4.6%(T): Interest Time =4→ 2000*4.6%4
You have to convert 4.6% into a decimal form.
→ 4.6%=0.046
→ I=2000*0.046*4
Solve.
Multiply the numbers from left to right.
→ 2000*0.046*4=368
Therefore, the correct answer is 368.I hope this helps you! Let me know if my answer is wrong or not.
How much should you invest in an account that pays 6% annual interest compounded continuously if you want exactly $8000 after four years?
Answer:
$6239
Step-by-step explanation:
A(t) = P•e^rt
Substitute with 6% 0.06, t with 4 and A(t) with 8,000 to find the value of P.
8, 000 = P•e^0.06•4
8, 000 = P•e^0.24
8, 000 = P•1.27
P = 6, 293
Find the axis of symmetry and the vertex of the graph of the function.
g(x) = 2x^2+12x+4
so hmmm from the equation we can see that is in "x terms" so the independent variable is "x", that tells us the parabola is a vertical one, leading term's coefficient is "2", that means it opens upwards like a bowl.
on a vertical parabola the axis of symmetry is the x-coordinate of its vertex, let's find the vertex of this one.
[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{2}x^2\stackrel{\stackrel{b}{\downarrow }}{+12}x\stackrel{\stackrel{c}{\downarrow }}{+4} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{ 12}{2(2)}~~~~ ,~~~~ 4-\cfrac{ (12)^2}{4(2)}\right)\implies \left( -3~~,~~4-\cfrac{144}{8} \right) \\\\\\ (-3~~,~~4-18)\implies (\stackrel{x}{-3}~~,~~-14)~\hfill \stackrel{\textit{axis of symmetry}}{x=-3}[/tex]
probability pls hurry(13)
Answer:
A (3/16)
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
[tex]\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}[/tex]
The spinner is evenly divided and numbered from 1 through 8.
[tex]\sf \implies Probability\:of\:landing\:on\:any\:number= \dfrac18[/tex]
There are 4 even numbers (2, 4, 6 and 8)
[tex]\sf \implies Probability\:of\:landing\:on\:an\:even\:number= \dfrac48=\dfrac12[/tex]
There are 3 numbers less than 4 (1, 2 and 3)
[tex]\sf \implies Probability\:of\:landing\:on\:a\:number\:less\:than\:4=\dfrac38[/tex]
Therefore, the probability of landing of an even number and then on a number of less than 4 is:
[tex]\sf \implies Probability=\dfrac12 \times \dfrac38=\dfrac{3}{16}[/tex]
What is the length of this key to the nearest quarter inch?
3 inches
314 inches
312 inches
334 inches
Key laying horizontally with vertical markers indicating the left and right ends of the key.
the length of the key will be 3 inched long because it is laying horizontally
Use a net to find the surface area of the cylinder. Use 3.14 for pie
Answer:
62.83
nearest tenth 62.8
Simplify: 4/15+7/8-11/12
Answer:
[tex]\frac{9}{40}[/tex]
Step-by-step explanation:
LCD: 120
[tex]\frac{4}{15} +\frac{7}{8} -\frac{11}{12}[/tex]
[tex]\frac{32}{120} +\frac{105}{120} -\frac{110}{120}[/tex]
[tex]\frac{27}{120}[/tex]
[tex]\frac{9}{40}[/tex]
Hope this helps!
Answer:
9/40
hope this helps.
What is 9n=1(98-2n) equal to? Id really appreciate if you could answer both though
PLEASE HELP ME OUT AND PLEASE
Answer:
65⁰ because the opposite angles of parallelogram are equal...
1) A user must be at least 13 years old to set up a video-sharing account.
Let x be the age in years of a user who can set up an account.
Which inequality represents the situation?
Answer: x [tex]\geq[/tex] 13
Step-by-step explanation: quite simple actually, since the user must be AT LEAST 13 years old to set up the account, the equation would be X is greater than or equal to 13.
Hope this helps
Lilit and Sergio sold candles for a class trip. On the first day, Lilit sold 8 candles and Sergio sold 10 candles. For the next three days, both sold another 3 candles each day.PLEASE HELP
Answer:
Lilit- 17 candles
Sergio- 19 candles
Step-by-step explanation:
this is the most probable answer.
The original price is $125. The sale price is $81.25. How much was the discount as a percent?
Answer: 35%
Step-by-step explanation:
Start by subtracting the original price by the sale price.
125-81.25=43.75
Now divide that amount by the original price.
[tex]\frac{43.75}{125} =0.35[/tex]
Multiply that value by 100 for the answer
0.35×100=35
35%
Answer:
Discount Percent = 35.00 %
Step-by-step explanation:
125-81.25=43.75 actual discount
43.75/125 = 0.35 actual discount / original
0.35 as percentage = 35%
You took a test and got 12 points on it. The next week, you retook it and got 25% more points than before. How many points did you get when you retook it?
Answer:
15 points
Step-by-step explanation:
12 divied by .25 =3
so there for it would be 15 points
Answer:
The answer is 15 points. Have a great day:)
If you can help me with this please and thank you
Answer:
1) im not sure
2) im not sure
3) 72 degrees
Step-by-step explanation:
Suppose there are 20 equally-sized marbles in a bag. Six marbles are blue, seven red, three of them orange, three of them black, and one green. If you choose a red marble, you win nothing. Selecting a blue marble will win you 25 cents. Selecting an orange marble will win you 50 cents, selecting a black marble will cost you a dollar, and if you choose the green one, you win three dollars.
Answer:
i dont know what youre trying to answer but if your trying to answer how much money can you get if you get all of the marbles you get $9
just blue- $1.50
just orange- $1.50
just black- $3
just green- $3
red=$0