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Explanation:
The given piecewise function is
[tex]f(x) = \begin{cases}-4x+3 \ \text{ if } \ x < 3\\-x^3 \ \text{ if } \ 3 \le x \le 8\\3x^2+1 \ \text{ if } \ x > 8\end{cases}[/tex]
At first piecewise functions may be strange confusing things, but they aren't so bad. I like to think of it like this: f(x) is a function that changes its identity based on what the input x is. We have three situations
f(x) = -4x+3 when x < 3f(x) = -x^3 when [tex]3 \le x \le 8[/tex]f(x) = 3x^2+1 when x > 8In a sense, we have three different functions but they are combined somehow.
If x is smaller than 3, then we go for the first definition. Or if x is between 3 and 8, then we go for the second definition. Or if x is larger than 8, then we go for the third definition.
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f(-5) means f(x) when x = -5. We see that -5 is smaller than 3, so x = -5 makes x < 3 true. We'll use the first definition
f(x) = -4x+3
f(-5) = -4(-5)+3
f(-5) = 20+3
f(-5) = 23
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Now the input is x = 12. This is larger than 8. In other words, x = 12 makes x > 8 true. We'll use the third definition
f(x) = 3x^2+1
f(12) = 3(12)^2+1
f(12) = 3(144)+1
f(12) = 432+1
f(12) = 433
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Side notes:
We won't use the second definition since we don't have any x inputs between 3 and 8To say "less than or equal to" on a keyboard, you can write "<=" without quotes. For example, [tex]x \le 5[/tex] is the same as x<=5PLEASE HELP I HAVE 30 POINTS Part A: If (6^2)^x = 1, what is the value of x? Explain your answer. (5 points) Part B: If (6^0)^x = 1, what are the possible values of x? Explain your answer. (5 points)
Answer:
Part A: 0
Part B: All real numbers
Step-by-step explanation:
Part A:
We have:
[tex](6^2)^x=1[/tex]
First, let's evaluate the square:
[tex]36^x=1[/tex]
Now, what to the xth power will equal 1?
Remember the fact that anything (except for 0) to the zeroth power is 1.
Therefore, our x is 0:
[tex]36^0=1[/tex]
Part B:
We have:
[tex](6^0)^x=1[/tex]
Like mentioned previously, anything to the zeroth power is 1. Thus:
[tex]1^x=1[/tex]
Now, 1 is a special base because 1 to any (real) power is still going to be 1. For example:
[tex]1^0=1,1^1=1,1^{999},\text{ and } 1^{\pi}=1[/tex]
Therefore, our values of x is all real numbers.
And we're done!
Middle schoolers help!!!!!!!Witch expresion has the same value has the model bellow!
Answer:
Its the second one 4-(-8)
please answer B and C i will mark u brainiest
Answer:
B: the translation can be represented as (x,y) (x-2,y-2)
C: figure c was translated from quad 2 to quad 4
hope that helps.
The label on Emma's muffin said that one serving provided 6 grams of fat, which is 10% of the recommended daily amount. What is the total recommended daily amount of fat?
0.6 because 6 divided by 10% is 0.6
How to solve
- 2b
-- 5(b-6)
(b + 2) • (b - 1) • (b - 3)
Answer:
-2b
-5b+30
Step-by-step explanation:
-2b
-5×b= -5b
-5×-6= (+)30
cancels out the negative because a negative times a negative is a positive
NEED HELP ASAP PLEASE ON ALL OF THEM !!!!
En el Número 258.324, el 25 son de miles. ¿Es Verdadero o Falso?¿Por que?
Answer:
Ok amigo, entonces es falso porque los miles son 5 ahora, la parte 25 está en la marca de diez mil más inteligente, por favorStep-by-step explanation:
How could you add -13 + 10?
The area of a rectangle is 25/42 and its width is 5/6. What is the length? ASAP
Answer:
[tex]length = \frac{25}{28} [/tex]Step-by-step explanation:
Let the length of the rectangle be l
Area of a rectangle = length × width
From the question
Area = 25/42
width = 5/6
Substitute the values into the above formula and solve for the length
That's
[tex]length = \frac{area}{width} [/tex]So we have
[tex]length = \frac{25}{42} \div \frac{4}{6} \\ = \frac{25}{42} \times \frac{6}{4} \\ = \frac{25}{7} \times \frac{1}{4} [/tex]We have the final answer as
[tex] \frac{25}{28} [/tex]Hope this helps you
I need Help plz...!!!!
Answer:
B.21.3 is the correct answer
Step-by-step explanation:
1/2*x+1/4*x=16
x/2+x/4=16
2x+x/4=16
3x/4=16
3x=16*4
3x=64
x=21.3
Hope it is helpful for you
if it is follow me and
mark me as a brainest
Answer:
Answer: Option B.
Step-by-step explanation:
Hey there!!
Let's simply solve it.
Given,
[tex] \frac{1}{2} x + \frac{1}{4} x = 16[/tex]
Now, take LCM.
[tex] \frac{2x + x}{4} = 16[/tex]
Multiply 16 by 4.
[tex]3x = 16 \times 4[/tex]
or, 3x = 64.
Divide 64 by 3.
[tex]x = \frac{64}{3} [/tex]
x= 21.33
Therefore, your answer is option B.
Hope it helps...
Find the width and height of a newer 65" television screen with an aspect
ratio of 16:9.
Answer:
see below
Step-by-step explanation:
65 inches is the diameter of the screen
We have a right triangle for a tv with the side length of 16x and 9x
Using the Pythagorean theorem
a^2 +b^2 = c^2
(16x)^2 + (9x)^2 = 65^2
256x^2+ 81x^2 = 4225
Combine like terms
337x^2 = 4225
Divide each side by 337
x^2 =4225/37
Take the square root of each side
x =65sqrt(337)/337
x =3.54077562
The width is 16 times this
width =56.65240991
height is 9 times this
height = 31.86698058
an adult panda will eat at least 20 pounds of bamboo every day. What an inequality that expresses this situation.
Answer:
is greater than or equal to 20
What is 7.96 repeating as a mixed number in simplest form
Answer:
Ion even know jus need points
Step-by-step explanation:
. A basketball coach is interested in measuring a player’s vertical jumping ability. While standing
and reaching up, the player’s hand reaches the 4-in. mark on the scale. When jumping, the player
can reach the 19-in. mark. What is the player’s vertical jumping ability?
Answer:
The player's vertical jump ability is 15 inches
Step-by-step explanation:
The mark on the scale which the player's hand can reach while standing = 4-in which is the standing reach
The mark on the scale the player's hand can reach when jumping = 19-in
Therefore, the player's vertical jumping ability is given as the difference between the height the players hand can reach when jumping and the height which the player's hand can when standing,
Which gives;
The player's vertical jump ability = 19 inches - 4 inches = 15 inches
The player's vertical jump ability = 15 inches.
terry earn $35.75 for working for 5 hours. how much did terry earn per hour
Answer:
Step-by-step explanation
Divide 35.75 and 5 and you get 7.15 an hour .
Please help. What is the answer to the Algebra 2 question
Answer:
(- ∞,1]
Step-by-step explanation:
a plane intersects a sphere 5cm away from the center of the sphere. the cross section is a circle whose diameter is 12 cm. determine the radius of the sphere PLEASE ANSWER
A basketball concession stand sells soda for $1.50, a bag of popcorn for $.50, and a candy bar for $1.25. At one game, 17 fewer candy bars were sold than bags of popcorn. That same night, the number of sodas sold was 7 more than the number of candy bars and bags of popcorn sold altogether. If the concession stand made $130 that night, how many of each item were sold?
Answer:
87 I am getting points yayyyy
Plz help! Ive been stuck on this for hours!!!!
Answer:
h[tex]\geq[/tex]8
Step-by-step explanation:
h-(-2)[tex]\geq[/tex]10=h+2[tex]\geq[/tex]10
subtract 2 on both sides to get h[tex]\geq[/tex]8
What is equivalent to -36 -8
Answer:
B
Step-by-step explanation:
It's not A because the 8 is positive.
It's not C because the 36 is positive.
And it's not D because both numbers are positive.
A bicyclist travels at a constant speed of 18 miles per hour for a total of 27minutes. Choose the function, the domain and the range according to the situation.
Answer:
domain is (xo ≤ x ≤ 0.45 )
range is (xo ≤ y ≤ 8.1 )
Step-by-step explanation:
given data
constant speed = 18 miles per hour
total time = 27 minutes = 0.45 hour
solution
we consider here Domain number of hours = x and Range distance traveled = y
we apply here distanace formula that is
Distance = speed × time .........................1
put here value
Distance = 18 × 0.45 = 8.1 miles
and no of hours x = 0 to 0.45 hours
so here
So domain is (xo ≤ x ≤ 0.45 )
and
Distance is 0 to 8.1 miles
So range is (xo ≤ y ≤ 8.1 )
Kenji scores 23 points per coin. After collecting a total of 2 coins, how many points will Kenji have scored in all?
Answer:
46
Step-by-step explanation:
23 x 2 = 46
Hope this helps!
help w this / asap!
Answer:
The answer should be p >= 7
Is 7.87400787401 a rational or irrational number?
If f (x) = -2x-3 and g (x) =x^2+5x find g (2) -f(3)
Match up each scenario with the equation that models the word problem.
Jeff is 3 years less than Tony's age.
y = x-3
Skate rental charges an additional $3.
y = 3x
Marie buys balloons for a party that
are $3.00 each
y = x + 3
Please helpp
Answer:
Marie is y=3x
Jeff is y=x-3
Skate is y=x+3
Step-by-step explanation:
Answer: y=37
Step-by-step explanation:
3072.9
What is 2x+x+7x+4y-2y
Answer:
2x +x +7x +4y -2y= 3x +7x +2y=10x +2y= 2×(5x +y)There are 200 pupils in year 11.
125 are female, of these 68 have school dinners.
52 boys have school dinners.
Use this information to complete the frequency tree.
Answer:
Sbsnsndndndjjbsndmmdmddndndn
Step-by-step explanation:
Bsbsnsjsjskdkck
Is 4.85912 rational number
3. Factor x2 + 5x + 6.
Answer:
( x+3) (x+2)
Step-by-step explanation:
x^2 + 5x + 6.
What two numbers multiply to 6 and add to 5
(3*2) = 6
3+2 = 5
( x+3) (x+2)
Answer:
[tex]\left(x+2\right)\left(x+3\right)[/tex]
Step-by-step explanation:
[tex]x^2+5x+6\\\\\mathrm{Break\:the\:expression\:into\:groups}\\=\left(x^2+2x\right)+\left(3x+6\right)\\\\\mathrm{Factor\:out\:}x\mathrm{\:from\:}x^2+2x\mathrm{:\quad }x\left(x+2\right)\\\\\mathrm{Factor\:out\:}3\mathrm{\:from\:}3x+6\mathrm{:\quad }3\left(x+2\right)\\=x\left(x+2\right)+3\left(x+2\right)\\\\\mathrm{Factor\:out\:common\:term\:}x+2\\=\left(x+2\right)\left(x+3\right)[/tex]