What is the domain of the function graphed below?
Answers
Answer:
(-2,4] and [7,α)
Step-by-step explanation:
the domain is open at -2 but closed at 4 and also closed at 7 but open till infinity..
The domain of the given function is (-2,4] U [7, ∞), which is the correct option (B).
What is a piecewise function?A piecewise-defined function (also known as a piecewise function or a hybrid function) is a function defined by multiple sub-functions, each of which applies to a different interval of the main function's domain (a sub-domain).
The graph is given in the question, as shown
f(x) = x²+1 if (-2,0]
This the sub-function define between the interval (-2,0].
f(x) = -1 if (0, 4]
This the sub-function define between the interval (0, 4].
f(x) = -(x-7)² if [7, ∞)
This the sub-function define between the interval [7, ∞).
Thus, the domain of the given function is (-2,4] U [7, ∞).
Learn more about the piecewise function here:
https://brainly.com/question/12700952
#SPJ7
Related Questions
3c + 2 = -22
whats c?
Answers
3c+ 2= -22
⇔3c = -22 -2
⇔3c = -24
⇔c= -24/3
⇔c=- 8
Answer:
3c= -22-2
3c= -24
c= -24/3
c= -8
Step-by-step explanation:
if x=3√8, find the value of 1/x
plz its urgent
Answers
Answer:
[tex]\frac{1}{x} =\frac{1}{3\sqrt{8} } =\frac{1(\sqrt{8})}{3\sqrt{8}(\sqrt{8})} =\frac{\sqrt{8}}{3*8} =\frac{\sqrt{8}}{24} =\frac{\sqrt{(2)(2)(2)}}{24}=\frac{2\sqrt{2} }{2(12)} =\frac{\sqrt{2} }{12}[/tex]
Evaluate the function.
f(x) = -4x2 + 5x
Find f(6)
Answers
Answer:
f(6) = -114
Step-by-step explanation:
f(x) = -4x² + 5x
f(6) = -4(6)² + 5(6)
f(6) = -4(36) + 30
f(6) = -114 + 30
f(6) = -114
Answer:
-114
Step-by-step explanation:
to evaluate the function f(x) to find f(6) means to substitute x by 6
f(x) = -4x² +5x
f(6) = -4*6² +5*6
f(6) = -144 + 30
f(6) = -114
What is the equation of a circle with its center at (−6,−3) and a radius of 12?
Answers
Answer:
(x+6)^2 + ( y +3)^2 = 144
Step-by-step explanation:
The equation of a circle is given by
(x-h)^2 +(y-k)^2 = r^2 where (h,k) is the center and r is the radius
(x- -6)^2 + ( y - -3)^2 = 12^2
(x+6)^2 + ( y +3)^2 = 144
Answer:
x² + y² + 12x +6y - 99 = 0
Step-by-step explanation:
Given :
Centre = (-6,-3) Radius = 12 ,Using the Standard equation of circle ,
( x - h)² + (y-k)² = r² ( x +6)² + (y+3)² = 12² x² + 36 + 12x + y² + 9 + 6y = 144 x² + y² + 12x + 6y +45-144 = 0 x² + y² + 12x +6y - 99 = 0On 1 st March, 2020 Mr. Mohit started a Furniture business in GANDHI NAGAR Mr. Mohit invested Rs 50,00,000.
Answers
Answer:
Answer to the following question is as follows;
Step-by-step explanation:
Given:
Amount invested by Mr. Mohit = Rs. 50,00,000
Computation:
Books of (...... LTD)
Journal entries
Date Particular Debit Credit
March 1 Cash A/C Dr. 50,00,000
To Capital A/C Cr. 50,00,000
(Being Amount invested in new business)
what is 121 divided by 57,246
Answers
Answer:2.1136848
Step-by-step explanation:
Answer:
0.00211368479
Step-by-step explanation:
Please help with this problem.
Answers
Answer:
( 10 m n^3) ^2
Step-by-step explanation:
100 m^2 n^6
Break into pieces
What number times itself gives 100
10*10 = 100
m*m = m^2
n*n*n*n*n*n = n^6 Breaking into two parts
n^3 * n^3 = n^6
( 10 m n^3) ^2
Answer:
[tex](10mn^3)^2[/tex]
Step-by-step explanation:
The square root of 100 is 10.
Divide the exponents of [tex]m^2 n^6[/tex] by 2.
You get: [tex]mn^3[/tex]
Put them together and add on the ^2
You get [tex](10mn^3)^2[/tex]
I hope this helps!
What is 3/4 as a percentage
Answers
Answer:
75%
Step-by-step explanation:
A percent is a value out of 100.
Change the fraction [tex]\frac{3}{4}[/tex] to an equivalent fraction with the denominator equal to 100.
[tex]\frac{3}{4}[/tex] × [tex]\frac{25}{25}[/tex] = [tex]\frac{75}{100}[/tex]
This fraction represents a percent.
[tex]\frac{75}{100}[/tex] = 75%
ASAP PLEASE HELP MEEEEEEEEEEEEEEEEEEEEEEEEEE
Answers
Answer:
the answer is -9/16.....
Answer:
2/18
Step-by-step explanation:
When solving a quadratic in the form a x squared + b x + c = 0 we are really finding the x–intercepts. These x–intercepts are also called roots. What is another term for roots or x-intercepts? a. exponents c. zeros b. quadratics d. variables Please select the best answer from the choices provided A B C D
Answers
This is because you plug 0 into X to get the Y answer which is your x-intercept
A rectangle prism has length 12 centimeters and width 4 centimeters. If its surface area is 467 square centimeters, what is the height of the prism
Answers
Answer:
11.59 centimeters
Step-by-step explanation:
Use the formula for the surface area of a rectangular prism: A = 2(wl + hl + hw)
Plug in the surface area, length, and width. Then, solve for h:
A = 2(wl + hl + hw)
467 = 2((4)(12) + h(12) + h(4))
467 = 2(48 + 12h + 4h)
467 = 2(48 + 16h)
467 = 96 + 32h
371 = 32h
11.59 = h
So, the height of the prism is approximately 11.59 centimeters
Si consideramos que el planeta Tierra tiene forma esférica y un radio de 6 371 km, ¿cuál es el área total del planeta Tierra?
Answers
Respuesta:
5.101 × 10⁸ km²
Explicación:
Primer paso: Información provista
Radio del planeta Tierra (r): 6371 km
Paso 2: Calcular el área del planeta Tierra
Si suponemos que el planeta Tierra tiene forma esférica, podemos calcular su área (A) usando la siguiente fórmula.
A = 4 × π × r²
A = 4 × π × (6371 km)² = 5.101 × 10⁸ km²
-4b + 8c + 12 - 8b -2c & simplify
Answers
Answer:
Combine like terms
-4b + 8c + 12 - 8b -2c
-4b - 8b + 8c - 2c + 12
-12b + 6c + 12
6(-2b + c + 2)
A polynomial p has zeros when x = 5, x = -1, and x = -1/4
What could be the equation of p?
A. p(x) = (x +5)(x + 1)(4x + 1)
B. p(x) = (x - 5)( x + 1)(4x + 1)
C. p(x) = (x + 5)(x - 1)(4x - 1)
D. p(x) = (5x)(-1x)( - 1/4x)
Answers
Answer:
[tex]x=5[/tex] ⇒ [tex](x-5)=0[/tex]
[tex]x=-1[/tex] ⇒[tex](x+1)=0[/tex]
[tex]x=-1/4[/tex] ⇒ [tex](x+1/4)=0[/tex] ⇒ [tex](4x+1)=0[/tex]
[tex]p(x)=(x-5)(x+1)(4x+1)=0[/tex]
[tex]Option(B)[/tex]
-------------------------
Hope it helps...
Have a great day!!
Answer:
p(x) = (x-5) (x+1)(4x+1)
Step-by-step explanation:
We know the equation for a polynomial with zeros is written as
f(x) = a( x-b1) (x-b2)...... where b are the zeros
We have zeros x = 5, x = -1, and x = -1/4
p(x) = a( x-5) (x- -1) (x - -1/4)
p(x) = a (x-5) (x+1) (x+1/4)
Let a = 4
p(x) = 4 (x-5) (x+1) (x+1/4)
p(x) = (x-5) (x+1)(4x+1)
please help!!!!!! 50 points!!
Answers
Area of first rectangle= 5×2=10units
Area of second rectangle= 3×2= 6 units
Area of third rectangle = 5×2= 10 units
Now,
Total area of figure = 10+6+10= 26units✓
Answer:
26
Step-by-step explanation:
we want to figure out the area of the composite figure notice that the composite figure contains three rectangles therefore in order to find the area of the composite figure we need find the area of the rectangles first
finding the area of the first & last rectangles:
the first and last rectangles are congruent therefore they will have the same area thus
[tex] \displaystyle A _{ \rm 1)rect} = A _{ \rm 3)rect} = l \times w[/tex]
from the figure we obtain:
[tex]l = 5[/tex][tex]w = 2[/tex]thus substitute:
[tex] \displaystyle A _{ \rm 1)rect} = A _{ \rm 3)rect} = 5\times 2[/tex]
simplify multiplication:
[tex] \displaystyle A _{ \rm 1)rect} = A _{ \rm 3)rect} = 10[/tex]
finding the area of the middle rectangle:
the middle rectangle has a length and width of 3 and 2 respectively Thus
[tex] \displaystyle A _{ \rm 2)rect} =3 \times 2[/tex]
simplify multiplication:
[tex] \displaystyle A _{ \rm 2)rect} =6[/tex]
finding the area of the composite figure:
[tex] \rm \displaystyle A _{ \rm composite} = A _{ \rm 1)rect} + A _{ \rm 2)rect} + A _{ \rm 3)rect} [/tex]
substitute what we got:
[tex] \rm \displaystyle A _{ \rm composite} = 10 + 6 + 10[/tex]
simplify addition:
[tex] \rm \displaystyle A _{ \rm composite} = \boxed{ 26}[/tex]
hence,
the answer is 26 square units
Could someone help me arrange these pairs of points in increasing order of the slopes of the lines joining them. (15, 30) and (20, 40) (12, 32) and (18, 48) (27, 12) and (72, 32) (45, 15) and (60, 20) (27, 2) and (243, 18) (18, 63) and (24, 84) (63, 9) and (84, 12).
Answers
Answer:
(e) (27, 2) and (243, 18)
(g) (63, 9) and (84, 12)
(d) (45, 15) and (60, 20)
(c) (27, 12) and (72, 32)
(a) (15, 30) and (20, 40)
(b) (12, 32) and (18, 48)
(f) (18, 63) and (24, 84)
Step-by-step explanation:
Required
Arrange in increasing order of slope
Slope (m) is calculated using:
[tex]m = \frac{y_2 -y_1}{x_2 - x_1}[/tex]
So, we have:
(a) (15, 30) and (20, 40)
[tex]m = \frac{40 -30}{20- 15}[/tex]
[tex]m = \frac{10}{5}[/tex]
[tex]m =2.00[/tex]
(b) (12, 32) and (18, 48)
[tex]m = \frac{48 -32}{18- 12}[/tex]
[tex]m = \frac{16}{6}[/tex]
[tex]m = 2.67[/tex]
(c) (27, 12) and (72, 32)
[tex]m = \frac{32-12}{72- 27}[/tex]
[tex]m = \frac{20}{45}[/tex]
[tex]m = 0.44[/tex]
(d) (45, 15) and (60, 20)
[tex]m = \frac{20-15}{60- 45}[/tex]
[tex]m = \frac{5}{15}[/tex]
[tex]m = 0.33[/tex]
(e) (27, 2) and (243, 18)
[tex]m = \frac{18-2}{243- 27}[/tex]
[tex]m = \frac{16}{216}[/tex]
[tex]m = 0.07[/tex]
(f) (18, 63) and (24, 84)
[tex]m = \frac{84-63}{24- 18}[/tex]
[tex]m = \frac{21}{6}[/tex]
[tex]m = 3.50[/tex]
(g) (63, 9) and (84, 12)
[tex]m = \frac{12 -9}{84- 63}[/tex]
[tex]m = \frac{3}{21}[/tex]
[tex]m = 0.14[/tex]
From least to greatest slope, the pair of points are:
(e) (27, 2) and (243, 18)
(g) (63, 9) and (84, 12)
(d) (45, 15) and (60, 20)
(c) (27, 12) and (72, 32)
(a) (15, 30) and (20, 40)
(b) (12, 32) and (18, 48)
(f) (18, 63) and (24, 84)
Answer:
From least to greatest slope, the pair of points are:
(e) (27, 2) and (243, 18)
(g) (63, 9) and (84, 12)
(d) (45, 15) and (60, 20)
(c) (27, 12) and (72, 32)
(a) (15, 30) and (20, 40)
(b) (12, 32) and (18, 48)
(f) (18, 63) and (24, 84)
Step-by-step explanation:
Consider the following 8 numbers, where one labelled x
is unknown.
27, 20, 34,
x, 7, 47, 26, 41
Given that the range of the numbers is 63,
work out 2 values of x
Answers
Answer: 70 and -16
==========================================================
Explanation:
For now, we'll assume x is the largest value (aka the max)
Let's sort the values from smallest to largest.
7, 20, 26, 27, 34, 41, 47, x
We see that 7 is the smallest item, so,
range = max - min = x - 7
Set this equal to 63 and solve for x
x-7 = 63
x = 63+7
x = 70
So x could be equal to 70.
---------------------------
Next, we'll assume that x is the smallest value
That means the min is x and 47 is now the max
max - min = range
47 - x = 63
-x = 63-47
-x = 16
x = -16
So if x is the smallest value, then it must be -16
----------------------------
Finally, we'll let x be somewhere between 7 and 47
Unfortunately, we can't pin down a specific value here since we could have lots of possible values. Three such examples are x = 8, x = 9, and x = 10. There are many others.
If your teacher is looking for 2 values only, then I would refer to the previous two sections and ignore this section entirely.
Which of the following number is not a perfect cube? 64 or 729 or 800 or 1331 can some1 say it fastt plsss
Answers
Answer:
800
Step-by-step explanation:
9.28 is answer of cube 800
Miss pat bake cupcakes for the school's Tuck Shop .each baking tray can hold one doesen cupcake .she wants to bake 48 cupcakes .how many trays of cupcakes she will need to bake?
A .1
B. 2
C.3
Answers
Given that,
→ She wants to bake 48 cupcakes.
We have to find,
The number of trays of cupcakes she will need to bake.
The formula we use,
→ No. of cupcakes ÷ One dozen
Then we can divide,
→ 48 ÷ 12
→ 4 trays
Thus, none of the option is correct.
The difference between the length and width of a rectangle is 7 units. The perimeter is 50 units. Find the dimensions.
Answers
Answer:
Step-by-step explanation:
Hello!
(x +x+7)*2 = 50
(2x+7)*2 = 50
4x+14= 50
4x= 50-14
4x= 36
x= 36/4
x= 9
9 et 16cm
Please help :) angles
Answers
Answer:
y = 95
Step-by-step explanation:
The exterior angle is equal to the sum of the opposite interior angles
y+25 = 120
y = 120-25
y = 95
PLEASE HELP, AND FAST! I WILL GIVE BRAINLIEST!!
Given the expression: 6x10 − 96x2
Part A: Rewrite the expression by factoring out the greatest common factor.
Part B: Factor the entire expression completely. SHOW THE STEPS OF YOUR WORK.
Answers
Answer:
Step-by-step explanation:
factor the numerical coefficients (6 and 96)
HCF 6 and 96 is 6
HCF x^10 and x^2 = x^2
HCF: 6x^2
(6* x^8*x^2 - 16*6 x^2) Take out the highest common factor
6x^2 (x^8 - 16)
12 5/6 - 3 5/12 - 1 1/2 =??
Answers
Answer:47/12
=3.9167
Step-by-step explanation:
Step-by-step explanation:
I hope this will help you
stay safe
What expression is equal to (3 x 5) x 4
Answers
Answer:
60
Step-by-step explanation:
Step 1:
3 x 5 = 15
Step 2:
15 x 4 = 60
Answer:
well 3. x 5 is 15, then multiply by 4 to get 60.
Step-by-step explanation:
( x + 3 )( y + 2 ) = xy - 5
( x + 2 )( y - 3 ) = xy
Answers
Answer:
xy+2x+3y+6=xy-5 .............(1)
xy-3x+2y-6=xy.....,.,(2)
2x+3y=-11
-4x+2y=6
first equation multiply by 2
(2)*(2x+3y)=-11
4x+6y=-22
-4x+2y=6
8y=-16 y=(-2),,,,, x=(-2,5)
Ivan sabe que pir su salud debe tomar agua hervida , lleno 3 botellas de agua hervida para empezar los lleno de 7,2 L usando 3 botellas grandes y 5 botellas pequeñas , no lleno otra botella ya que le faltaba 0,5L pero lleno una pequeña mas y le quedaron 0,3L de ahua hervida para tomar ¿Cuanta agua hervida tenia al inicio ivan?
Answers
Answer:
Al inicio Iván tenía 8.1 litros de agua hervida.
Step-by-step explanation:
Dado que Iván sabe que por su salud debe tomar agua hervida, y llenó 3 botellas de agua hervida para empezar con 7,2 L usando 3 botellas grandes y 5 botellas pequeñas, y no llenó otra botella ya que le faltaba 0,5L pero llenó una pequeña mas y le quedaron 0,3L de agua hervida para tomar, para determinar cuánta agua hervida tenia al inicio Iván se debe realizar el siguiente cálculo:
Botella grande = -0.5 litros
Botella chica = +0.3 litros
0.5 + 0.3 = 0.8
Así, la diferencia entre una botella grande y una botella chica es de 0.8 litros.
3X + 5(X - 0.8) = 7.2
3X + 5X - 4 = 7.2
8X = 7.2 + 4
X = 11.2 / 8
X = 1.4
3 x 1.4 + 5 x 0.6 = 7.2
7.2 + 0.6 + 0.3 = 8.1
Por lo tanto, al inicio Iván tenía 8.1 litros de agua hervida.
For each hour he babysits, Anderson earns $1 more than half of Carey's hourly rate. Anderson earns $6 per hour. Which equation can be used to solve for Carey's hourly rate, c? 18 + ?T = 24 What number should be the coefficient of t?
Answers
Answer:
The total earnings of Carey in t tours is 12 t - 2 .
Step-by-step explanation:
For each hour he babysits, Anderson earns $1 more than half of Carey's hourly rate. Anderson earns $6 per hour. Which equation can be used to solve for Carey's hourly rate, c? 18 + ?T = 24 What number should be the coefficient of t?
Anderson earns $1 more than half of Carey's hourly rate.
Anderson hourly rate = $ 6
Let Carey's hourly rate is p. Let the time is t hours.
So, Anderson rate is
[tex]6 t = \frac{p t}{2} +1\\\\2\times 6 t = p t + 2 \\\\p t = 12 t - 2[/tex]
what is the measure of arc MP
Answers
Answer:
[tex]m\widehat{MP}=118^{\circ}[/tex]
Step-by-step explanation:
In any circle, the measure of an inscribed angle (an angle created when the intersection of two chords is on the circle) is equal to half of the arc it forms. In this case, [tex]\angle MPN[/tex] is an inscribed angle that forms [tex]\widehat{MN}[/tex]. Therefore, the measure of arc MN must be twice the measure of angle MPN:
[tex]m\widehat{MN}=2\cdot m\angle MPN,\\m\widehat{MN}=2\cdot 31^{\circ}=62^{\circ}[/tex]
Since we want to find the measure of arc MP, we need to know that there are 360 degrees in a circle. Since [tex]\overline{PN}[/tex] is a diameter of the circle (line that has two endpoints on the circle and that passes through the center of the circle), each side of [tex]\overline{PN}[/tex] must be 180 degrees.
Therefore, we have:
[tex]m\widehat{MN}+m\widehat{MP}=180^{\circ},\\62^{\circ}+m\widehat{MP}=180^{\circ},\\m\widehat{MP}=\boxed{118^{\circ}}[/tex]
If [tex]x[/tex] is real and p=[tex]\frac{3(x^{2} +1)}{2x-1}[/tex], prove that [tex]p^{2}[/tex]-3(p+3) ≥ 0
Answers
Answer:
[tex]{ \tt{p=\frac{3(x^{2} +1)}{2x-1}}} \\ { \tt{p(2x - 1) = 3( {x}^{2} + 1) }} \\ { \tt{2px - p = 3 {x}^{2} + 3 }} \\ { \tt{3 {x}^{2} - (2p)x + (p + 3) = 0}} [/tex]
By factorization :
[tex]{ \tt{ ( {p}^{2} - 3)( p + 3) \: is \: the \: zero}}[/tex]
Since the roots are real, they're greater than zero ( 0 < x ≤ +∞ ):
[tex]{ \tt{ ({p}^{2} - 3})(p + 3) \geqslant 0}[/tex]
Janine is considering buying a water filter and a reusable water bottle rather than buying bottled water. Will doing so save her money?
First, determine what information you need to answer this question, then click here to display that info (along with other info).
How much water does Janine drink in a day? She normally drinks 6 bottles a day, each 16.9 ounces.
How much does a bottle of water cost? She buys 24-packs of 16.9 ounce bottles for $2.79.
How much does a reusable water bottle cost? About $10.
How long does a reusable water bottle last? Basically forever (or until you lose it).
How much does a water filter cost? How much water will they filter?
A faucet-mounted filter costs about $28 and includes one filter cartridge. Refill filters cost about $33 for a 3-pack. The box says each filter will filter up to 100 gallons (378 liters)
A water filter pitcher costs about $22 and includes one filter cartridge. Refill filters cost about $20 for a 4-pack. The box says each filter lasts for 40 gallons or 4 months
An under-sink filter costs $130 and includes one filter cartridge. Refill filters cost about $60 each. The filter lasts for 500 gallons.
Which option is cheapest over one year (365 days)?
The cheapest option saves her over a year.
Answers
9514 1404 393
Answer:
faucet filter is cheapest$205.78 savings first year; $232.78 savings in subsequent yearsStep-by-step explanation:
The variable cost per gallon (128 floz) is ...
water bottles: $2.79/((24×16.9 floz)/(128 floz/gal)) = $0.88 /gal
faucet filter cartridge: $33/(3×100 gal) = $0.11 /gal
filter pitcher: $20/(4×40 gal) = $0.125 /gal
under-sink filter: $60/(500 gal) = $0.12 /gal
a) The cheapest option over the year is the faucet filter.
__
b) The cost of setting up the faucet filter includes the cost of a reusable bottle ($10) and the cost of the faucet mount (less the value of the accompanying cartridge), $28 -11 = $17. The total in addition to the recurring cost is then ...
setup cost = $10 + 17 = $27
and the first-year cost will be ...
$27 + $0.11 g . . . . . where g is the number of gallons used.
The amount of water used in a year (365 days) is ...
(365 days/year)×(6×16.9 oz/day)×(1 gal/(128 oz)) = 289.148 gal/year
Then the cost per year for water bottles is ...
(289.148 gal/year)·($0.8804733 /gal) = $254.59 /year
The cost for the first year for the faucet filter is ...
$27 + ($0.11/gal)(289.148 gal) = $58.81
Janine's first-year savings using a faucet filter will be about ...
$254.59 -58.81 = $205.78
Her savings over subsequent years will be $27 per year more than this.
