Given the piecewise function shown below, select all of the statements that are true.
The statements f(1) = 0 and f(-1) = 2 are true based on the piecewise function.
Options B and C are the correct answer.
We have,
The piecewise function:
f(x) = -x + 1, x < 0
f(x) = -2, x = 0
f(x) = x² - 1. x > 0
Now,
f(-2) = 0
False.
When x = -2, we are in the first condition, so f(-2) = -(-2) + 1 = 3, not 0.
f(1) = 0
True
When x = 1, we are in the third condition, so f(1) = (1)² - 1 = 0.
f(-1) = 2
True
When x = -1, we are in the first condition, so f(-1) = -(-1) + 1 = 2.
f(4) = 7
False.
When x = 4, we are in the third condition, so f(4) = (4)² - 1 = 15, not 7.
Therefore,
The statements f(1) = 0 and f(-1) = 2 are true.
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A child is to receive a dose of 0.5 teaspoon of cough medicine every 6 hours. If the bottle contains 24 doses, how many days will the medicine last?
how do you solve for 2w+8=-3+2w
!!PLEASE HELP!!
After school, Mike spends from 4:00 to 6:00 doing homework, eating, and playing sports. If he spends 65 minutes on homework and 15 minutes on eating, how much time does he have to play sports?
6×12=(6×7)+(6×_)=answer plz
Lisa and Alice are playing a game. Each player either receives or has to pay play money based on the result of their apin. The table lists how much a player reieves or pays for various spins.
Answer:
Outcome Bag of Gold Magic Wand
Relative frequency 0.32 0.68
The relative frequency of getting a bag of gold is .......... reasonably close
.32 is close to 30% so
Alison's claim about the theoretical probability is likely to be 2............true
Further, this means that the theoretical probability of getting a magic wand is most likely 3............1 - 30% = 70%
Step-by-step explanation:
Corresponding range of Celsius temperature C
What three ratios of the lengths of two segments equal?
(09.05) A golf ball is hit from the ground with an initial velocity of 208 feet per second. Assume the starting height of the ball is 0 feet. How long will it take the golf ball to hit the ground?
The amount of Time that it would take for the golf ball to hit the ground using the given parameters is; 13 seconds
How to solve projectile problems?
We are given;
Initial Velocity = 208 feet per second
Initial height = 0 ft
Now, the general equation to be used here is;
h(t)= -16t² + 208t
Factorizing the equation gives;
h(t) = -16t(t - 13)
At h = 0, we have;
-16t(t - 13) = 0
Thus;
t = 13 seconds
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Simplify:-3 1/2-(12 1/4)
8. Susie had $150 in her checking account. She wrote a check for $95 and another check for $85. What was the balance in her account after she wrote the check?
Commutative property across multiplication for 2x10x7
Ok folks 4 questions and 50 points up for grabs for correct answers....Need quickly thanks!!!
1. 2*0.8 = 1.6 PQ = 1.6
2. arctan(14/12) = 49.4 degrees
3. 15 * cos(70) = 5.1 feet
4. x = 30 * cos(40) = 22.9813 = 23.0 miles
y = 30 *sin(40) = 19.2836 = 19.3 miles
A home is to be built on a 56 foot 9 inch wide lot. The house is 5 feet 5 inches from the side of the lot and is 34 feet 10 inches wide. How far is the house from the other side of the lot?
Answer:
132
123
Step-by-step explanation:
An object is launched upward with an initial velocity of 64 feet per second from a platform 80 feet high. Write a model for the object? How many seconds until the maximum height is reached? What will be the maximum height? How many seconds until the object hits the ground
The model for the object's motion is [tex]h(t) = -16t^2 + 64t + 80[/tex]. It reaches its maximum height of 144 feet at 2 seconds. The object will hit the ground after 5 seconds.
To model the vertical motion of the object, we use the equation:
[tex]h(t) = -16t^2 + 64t + 80[/tex]
where:
h(t) is the height at time t64 ft/s is the initial velocity80 ft is the initial height[tex]16t^2[/tex] represents the effect of gravity (since the gravitational acceleration is approximately 32 ft/s2, and here it is halved to be per second squared)Time to Reach Maximum Height
The time to reach the maximum height can be found by using the formula:
[tex]t = \frac{v_0}{|g|} = \frac{64}{32} = 2 seconds[/tex]
Maximum Height
Plug t = 2 seconds into the height equation:
[tex]h(2) = -16(2)^2 + 64(2) + 80 = 144 feet[/tex]
Time to Hit the Ground
To find when the object hits the ground (h(t) = 0), solve:
[tex]-16t^2 + 64t + 80 = 0[/tex]
Using the quadratic formula:
[tex]t = \frac{-64\pm\sqrt{64^2-4(-16)(80)} }{2(-16)}[/tex]
Simplifies to:
t = 5 seconds (since the negative value does not make sense in this context)
The object will hit the ground after 5 seconds.
90=20+70 use the distributive property and the GCF OF 20 and 70 to write another related expression for 90 could you write another expression with a different common factor?
Final answer:
To write another expression for 90 using the distributive property and the GCF of 20 and 70, distribute the GCF to each term. Another expression with a different common factor can be written by multiplying each term by a different common factor.
Explanation:
To write another expression for 90 using the distributive property and the GCF of 20 and 70, we can rewrite 90 as (20 + 70). Using the distributive property, we can distribute the GCF to each term inside the parentheses, resulting in 20*(GCF of 20 and 70) + 70*(GCF of 20 and 70). The GCF of 20 and 70 is 10, so the expression becomes 20*10 + 70*10, which simplifies to 200 + 700, equaling 900.
Yes, we can write another expression with a different common factor. Let's say we use the GCF of 20 and 70, which is 10, to rewrite the expression. Instead of multiplying each term by 10, we can multiply 20 and 70 by a different common factor, such as 5. This gives us 20*5 + 70*5, which is equal to 100 + 350, resulting in 450.
your grandmother is in the hospital and is on a liquid diet. After examining her chart, a mistake is found stating that her weight is 500kg. what is the equivalent weight in pounds
The population of a city in Alabama increases every year by 11.5 percent. If the population in 2011 was 4.8 million, what will its population be in 2016?
A)2.6 million
B)2.76 million
C)8.27 million
D)220 million
PRE-CAL/CAL MASTER NEEDED
f ( 2x − 1 ) = 4x^2 − 10x + 6
from f(x)=x^2-3x+2, h(x)=2x-1, f(h(x))
How is this: f ( 2x − 1 ) = 4x^2 − 10x + 6 derived from ^
if the quotient of -20 and 4 is decreased by 3 what number results
quotient is division
-20/4 = -5
-5 -3=
-8
the number is -8
simplify the expression 3xy(2x+5y)
What is the e-file rejection error for an Invalid bank account or routing transit numbers?
Answer;
The Error code "0019".
Explanation;
-The e-file rejection error for an invalid bank account or routing transit numbers is error code "0019".
-This error code may be caused by a variety of reasons and is present in tax accounting software, where an e-file sent to the IRS is rejected, hence the error name. An incomplete installation might be one of the several reasons behind an e-file rejection error.
Simplify and determine the coefficient of (-x)(3y)(-2x).
a.-4
b.1/3
c.1
d.4
well.. i just got the same problem.. With the same multiple choice.. I'm going to put one. I might update with my score on the test after i finish. (this is an old question that i thought i might answer with my guess)
Determine if the number is divisible number 15
Will the opposite of a opposite always be positive?
Yes, the opposite of an opposite will always return you to the original value, making it positive if you started with a positive number.
The question refers to the concept of opposites in Mathematics. When considering opposite numbers, the opposite of a positive number is negative, and vice versa. To answer the query, let’s break it down into steps.
First Opposite: The opposite of a positive number, say +5, is -5.Second Opposite: The opposite of -5 is, again, +5.So, yes, the opposite of an opposite will always be positive if you start with a positive number. Similarly, the opposite of an opposite will be negative if you start with a negative number, returning to the original number. This concept is crucial in understanding signed numbers and their roles in arithmetic and algebra.
what is 15.2 rounded to the nearest tenth
charlie wants to order lunch for his friend. hell order 5 sandwiches and a $3 kids meals for his little brother. charlie has $28. how much can he spend on each sandwich if they are all the same price?
Answer:4 or less
Step-by-step explanation:
6x+3>27
Evaluate the expression for the given value.
36 ÷ m when m = 9
A.
324
B.
45
C.
27
D.
4
Simplify by dividing negative three over eight divided by five over nine..
A. negative fifteen over seventy-two.
B. fifteen over seventy-two.
C. negative twenty-seven over forty.
D. twenty-seven over forty.
Answer:
-27/40
Step-by-step explanation:
What is the answer to 8=56, 7=42, 6=30, 5=20, 3=?