Answers
Given:
The functions are:
(1) [tex]h(x)=\sqrt{1-x}[/tex]
(2) [tex]x+y=4[/tex]
(3) [tex]x^2+y^2=16[/tex]
To find:
The domain of given functions.
Solution:
Domain is the set of input and x -values.
Value under the square root must be positive because if the number under square root is negative, then it is a complex or imaginary number.
(1) [tex]h(x)=\sqrt{1-x}[/tex]
The function is defined if
[tex]1-x\geq 0[/tex]
[tex]1\geq x[/tex]
The function is defined for all real values of x which are less than or equal to 1.
Therefore, the domain of the function is (-∞,1].
(2) [tex]x+y=4[/tex]
It is a linear function and linear function is defined for all real values of x.
Therefore, the domain of the function is (-∞,∞).
(3) [tex]x^2+y^2=16[/tex]
It can be written as
[tex]y^2=16-x^2[/tex]
[tex]y=\pm \sqrt{16-x^2}[/tex]
It is defined if
[tex]16-x^2\geq 0[/tex]
[tex]16\geq x^2[/tex]
[tex]4\geq x\geq -4[/tex]
This function defined for all real values of x from -4 to 4.
Therefore, the domain of the function is [-4,4].
Related Questions
Daysi buys a video game on sale. If the video usually costs $30.00, and it
was on sale for 25% off, how much did Daysi pay?
Answers
Answer:
$22.5
Step-by-step explanation:
The original price is $30 and it's on sale for 25% off. Since 25% is a quarter of the total price, I divided 30÷4=7.5. $7.5 is 25% of $30, so 7.5 is the amount taken off the original price. To find what Daysi paid, I subtracted 30-7.5=22.5. $22.5 is the result after the 25% off, so Daysi paid $22.5.
If you roll a 6-sided die 6 times, what is the best prediction possible for the number of times you will roll a two?
Answers
Answer:The best prediction is 1/6 of the times or one time of the six that you will roll a two..
This is because without any interference, each of the six numbers of the dice will have same theoretical probability (which is the probability or chances that is expected.
Helppp! 20 points!
Find m
m
Answers
Answer:
M∠ABC=58°
Step-by-step explanation:
The sum of Angle ∠ABD and Angle ∠DBC
37°+21°=58°
The measure of angleABC=37+21=58degrees
value of -2 ( x + 5 )
Answers
i am smart
What is the constant in the
expression below?
15 – 4b
A
B
С
Answers
Answer:
15 is the constant
Step-by-step explanation:
Does not have a variable next to it which means it remains a constant
easy:
what is the surface area of the rectangular prism?
L times W times H= 3 cm times 2 cm times 4 cm
Answers
Answer:
l x w do the the math
Step-by-step explanation:
there
Answer:
u said free poinstt on that persons answer so Hi
Step-by-step explanation:
Find the missing values
Answers
solve both problems please
Answers
Evaluate 3√343 + 3/4 3√-8
Answers
Answer:
5 1/2 is the answer, hope this helps
jerry observed 5 head in tosses of his coin. Do you think this was a fair coin?
Answers
A store owner spends 7x + 13 dollars on two orders of boxes of light bulbs, including shipping.
Part A
If she spends 3x + 5 dollars on the first order of light bulbs, which of the following represents how much she spends on the second order?
10x + 18
4x + 8
21x + 65
10x + 8
Part B
If the store owner spent a total of $90 on both orders, how much does a box of light bulbs cost in dollars? Enter the number in the box.
$
Answers
Answer:
Your answer is: X = 11
Your equation: 7x+30=90
If you subtract 7 from 90 you get 77.
If you divide 77 and 7 you get 11.
Step-by-step explanation:
Hope this helped : )
PLS SOMEONE HELP MEEE
Answers
Answer: 20
Explanation:
Explanation:
Please answer these three will be forever grateful and will make brainliest
Answers
5) 16q + 4
6) 3
i’m assuming the answer to 6 is there since i can’t see it in the screenshot ;)
help me please, i don’t get it loll
Answers
Answer:
subtract to find A
Step-by-step explanation:
6th grade math
help on numbers 4 5 6 plz help
Answers
Answer:
4) 6 students
5) 7 fewer students
6) No, you can not tell from the frequency table how many students ran a mile in exactly 12 minutes.
Step-by-step explanation:
4) you’d look at the row from 8:00-8:59.
5) Add the first two rows together (6+2=8), then subtract that by the sum of the last two rows (9+6=15), which is 7
6) There’s no pattern in the frequency table, and the data points would be plotted differently since it’d be from a range of times, not one set time.
Hope this helped, sorry if I’m wrong on #6 ;)
4. 8 students
5. 1 fewer student
6. Approximately 0.15 students
sarah baked a meatloaf she serves 2/4 of the meatloaf at the party. How much of the meatloaf remains?
Answers
Answer:
2/4 or 1/2 meatloaf
Step-by-step explanation:
2/4 simplified is 1/2 so she served half of a meatloaf. 1 - 1/2 = 1/2
Can anyone help me with this??
Answers
Answer:
find the cordinates of each letter or number then find witch is greater or less than when your answering it
Step-by-step explanation:
The Empire State Building in New York City is 1,454 feet tall. The observatory on the 86th floor is 404 feet from the top of the building. How high is the observatory above the ground?
Answers
Answer:
1,050 ft
Step-by-step explanation:
Which is an equation of a direct proportion
Answers
hope it helps!
Do you agree with the rules of the council on tall buildings and urban habitat regarding spires and antennae? Are the Petronas towers really taller than the Sears tower?
Answers
Answer:
Yes, I agree
The Petronas Towers are taller than the Sears tower
Step-by-step explanation:
The rule regarding spires and antenna of the Council on tall buildings and Urban Habitat states that "an antenna is just functional - something with a technical purpose stuck on the top of a building after it is finished while spires are considered a continuation of the form of the building.
According to the Council, the Petronas Towers are taller than the Sears Tower because spires are included in a building's architecture while antennae are not.
The architectural height of the Petronas towers is 1,483ft
The architectural height of the Sears (now Willis) tower is 1,450ft
question is in the pic
Answers
Answer:
I would say A.
Step-by-step explanation:
Both of the bakeries' data does seem symmetric, so use the mean.
Hope it is correct!
Answer:
Prolly A
Step-by-step explanation:
so sorry if I'm wrong hope I'm right
Michelle has 2/3 of her monthly allowance left. She plans to save 1/4 of the money she has left . What fraction of the original allowance does she plan to save
Answers
Answer: The fraction of the original allowance does she plan to save = [tex]\dfrac16[/tex]
Step-by-step explanation:
Let x = original monthly allowance
Monthly allowance left = [tex]\dfrac23x[/tex]
She plans to save = [tex]\dfrac14[/tex] of (Monthly allowance left)
= [tex]\dfrac14\times\dfrac23x[/tex]
[tex]=\dfrac{2}{12}x\\\\=\dfrac{1}{6}x[/tex]
i.e. the fraction of the original allowance does she plan to save = [tex]\dfrac16[/tex]
can u pls help me ill give brainliest
Answers
Answer:
<
Step-by-step explanation:
What is the unit rate of 450 miles in 7 hours?
Answers
Answer:60 mph
Step-by-step explanation:
Answer: 60 mph (miles per hour)
Explain:
You can get the same answer as what it shows from the internet, but a faster way to explain why this is the answer is dividing 420 to 7, and that equals 60 miles per hour. Have a good day!.
Peter, Bridget and Caroline share some sweets in the ratio 6:3:2. Peter gets 56 more sweets than Caroline. How many sweets are there altogether?
Answers
Answer:
The scale in the ratio given considers the case that there are 9 sweets (2 + 3 + 4), however, to answer our question, we need to scale up the ratio, so that we can work out the share when we have 36 sweets
Step-by-step explanation:
Ratios are a way of displaying the proportional split of a value and they are very similar to fractions. In the example above, we see that for every 2 sweets Amy has, Beth gets 3 and, Colin will get 4. Like fractions, this proportion will stay the same regardless of the scale of the ratio. The scale in the ratio given considers the case that there are 9 sweets (2 + 3 + 4), however, to answer our question, we need to scale up the ratio, so that we can work out the share when we have 36 sweets. So, what scale factor do we need to get it from a total of 9 sweets to a sum of 36 sweets? We know that 9 multiplied by 4 gives us 36, therefore, we can use a scale factor of 4. Remember how whatever is done to the denominator of a fraction has to be done to the numerator? Ratios like to behave the same way, so now that we have scaled up the sum of the ratio, we need to scale up the individual values by 4 – (2x4) : 3x4 : 4x4. Once we work it out we get the new ratio 8:12:16. You can check if you’re right by adding up the new values and you will see that 8 + 12 + 16 = 36, which is the value that the 9 was initially scaled up to. So we now know that when sharing the 36 sweets, Amy will get 8 sweets, Beth will get 12 sweets and Colin will get 16.
Which set of ordered pairs (x, y) could represent a linear function?
A = {(0,-5), (3,-2), (6,0), (9,3)}
B = {(-7,5), (-5,4), (1,1), (5, -1)}
C = {(-7,-4), (0, -1), (4,1), (6,2)}
D = {(-2,3), (0,2), (2,0), (4, -2)}
which on is the right answer?
Answers
Answer:
A.
Step-by-step explanation:
Graphed them
i hope this helps :)
8/x = 32
..................
Answers
Answer:
Step-by-step explanation:
x= 1/4
At Burger Haven, 11 of the last 44 customers wanted cheese on their burgers. Considering this data, how many of the next 256 customers would you expect to want cheese?
Answers
Answer:
64
Step-by-step explanation:
11 out of 44 = 25%
11 ÷ 44 = 0.25 = 25%
25% × 256 = 64
Write the domain AND range of the following graph.
Answers
Answer:
Domain: (-∞,∞), Range: [2,∞)
can someone help me pls );
Answers
Answer:
Hope it helps you,
Step-by-step explanation:
As the figure can be split in to 3 geometric figure,
Rectangle , Triangle and Semi circle ,
So first find the area of these figures then add up them ,
Area of rectangle = Length * width
Length = 20m m and width = 14 mm
hence
Area of rectangle = 20*14 = 280 mm^2
Now ,
Are of Circle = [tex]\\ \pi *d^{2} /4[/tex]
Then Area of semi circle = [tex]\\ \pi *d^{2} /8[/tex]
Hence we have d= 20mm
Putt in semi circle formula we get,
Area of Semi Circle= (3.14)*400/8 = 157 mm^2
Now area of triangle = 1/2 * length*width
length =32-20 = 12 mm
width = 14 mm
putt in the formula we get ,
Area of triangle = 1/2*12*14 = 84 mm^2
Now add these 3 Areas to get total Area,
Total Area = 84+157+280 = 521 mm^2