Determine the domain of the function f(x)=1/3x^2+10x+8
Answers
f(x) = (1/3)x² + 10x + 8
Write the function in standard form for a parabola.
f(x) = (1/3)[x² + 30x] + 8
= (1/3)[ (x+15)²- 225] + 8
= (1/3)(x+15)² -75 + 8
f(x) = (1/3)(x+15)² - 67
This is a parabola with vertex at (-15, -67).
The axis of symmetry is x = -15
The curve opens upward because the coefficient of x² is positive.
As x -> - ∞, f -> +∞.
As x -> +∞, f -> +∞
The domain is all real values of x (see the graph below).
Answer: The domain is (-∞, ∞)
Related Questions
WILL GIVE BRAINEST
Identify one characteristic of exponential decay.
Answers
B. False. Common differences apply to arithmetic sequences which are not exponential in nature.
C. False. Decay curves slope downward. As you read them from left to right, they will drop down.
D. False. If r > 1, then we have exponential growth. It is effectively the opposite of choice A.
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So in summary, the final answer is choice A
Answer: A
Step-by-step explanation:
hannah and anthony are siblings who have ages that are consecutive odd integers. the sum of their ages is 92 . which equations could be used to find hannah's age,h, if she is the older sibling?
Answers
Hannah is older than her sibling, and their ages are consecutive odd integers. Therefore, h = an odd number and the sibling's age = h-2.
The sum of their ages is 92, therefore
h + (h-2) = 92
2h - 2 = 92
2h = 94
h = 47 years
Answer:
The equation to find Hannah's age is 2h - 2 = 92.
This yields Hannah's age as 47 years.
given b(x)=|x+4| what is b(-10)
Answers
Answer:
Given that b(x)=|x+4| value of b(-10) is:
6
Step-by-step explanation:
|We are given that:
b(x)=|x+4|
We have to find the value of b(-10)
Putting x= -10 in above equation, we get
b(-10)=|-10+4|
=|-6|
=6
Hence, given that b(x)=|x+4| value of b(-10) is:
6
It takes 40 min for a bus to travel the 36 miles from Framingham to Worcester. A car traveling from Worcester to Framingham moves 1.5 times as fast as the bus. If the car and the bus start moving towards each other simultaneously, after how many minutes will they meet?
Answers
The velocity of the bus is:
velocity (bus) = 36 miles / 40 min
velocity (bus) = 0.9 miles / min
Since the car is 1.5 times faster, so the velocity of the car is:
velocity (car) = 1.5 * 0.9 miles / min
velocity (car) = 1.35 miles / min
At the meeting point, the sum of the distance is equal to 36 miles. Therefore:
1.35 t + 0.9 t = 36
2.25 t = 36
t = 16 min
So they will meet after 16 minutes.
0.6 is 10 times as much as what
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0.6 is 10 times as much as 0.06.
What is multiplication?Multiplication is the general procedure in mathematics in which we multiply two or more numbers to each other to find a new multiplied number.
Multiplication gives us a resultant number that will be very big as compared to the number which is going to be multiplied if and only if the number which is going to be multiplied is more than one.
Let's say 0.6 is 10 times as much as x
Then,
0.6 = 10x
x = 0.6/10 = 0.06
Hence "0.6 is 10 times as much as 0.06".
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Harvey invested $6000 for 2 years in a savings account paying simple interest with a yearly interest rate of 5.5%. How much simple interest did he earn.
Answers
Harvey earned a simple interest of $660 over 2 years on his $6000 investment.
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Since, We know that;
Simple interest is calculated using the formula:
I = P r t
Where: I = Interest earned P = Principal amount (amount invested) r = Annual interest rate t = Time period (in years)
Now, In this case,
Harvey invested $6000 for 2 years at an annual interest rate of 5.5%.
So, using the formula:
I = 6000 x 0.055 x 2
I = $660
Therefore, Harvey earned a simple interest of $660 over 2 years on his $6000 investment.
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What is the property tax of 1.6% on property assessed at $85,000?
1,360
5,312
13,600
53,125
Answers
Answer:
$1,360.
Step-by-step explanation:
We are asked to find the amount of property tax at a rate of 1.6% assessed at $85,000.
Let us find 1.6% of 85,000 to find the amount of property tax.
[tex]\text{Amount of property tax}=\frac{1.6}{100}\times 85,000[/tex]
[tex]\text{Amount of property tax}=0.016\times 85,000[/tex]
[tex]\text{Amount of property tax}=1,360[/tex]
Therefore, the property tax will be $1,360 and 1st option is the correct choice.
Which function has an inverse that is also a function? a {(–1, 3), (0, 4), (1, 14), (5, 6), (7, 2)} b {(–1, 2), (0, 4), (1, 5), (5, 4), (7, 2)} c {(–1, –2), (0, 4), (1, 3), (5, 14), (7, 4)} d {(–1, 4), (0, 4), (1, 2), (5, 3), (7, 1)}
Answers
and expression that is a function, and has an inverse that is also a function, will have no x-repeats, and no y-repeats either, so the pairs will be unique for the set, let's do some checking then,
[tex]\bf a \qquad\{(-1, 3), (0, 4), (1, 14), (5, 6), (7, 2)\}\\\\ b \qquad\{(-1, 2), (0, \stackrel{\downarrow }{4}), (1, 5), (5, \stackrel{\downarrow }{4}), (7, 2)\}\impliedby \begin{array}{llll} \textit{notice the } y-rep eats\\ \textit{thus, no dice} \end{array}[/tex]
[tex]\bf c \qquad\{(-1, -2), (0, \stackrel{\downarrow }{4}), (1, 3), (5, 14), (7, \stackrel{\downarrow }{4})\}\impliedby \begin{array}{llll} \textit{notice the } y-rep eats\\ \textit{thus, no dice} \end{array}\\\\ d \qquad\{(-1, \stackrel{\downarrow }{4}), (0, \stackrel{\downarrow }{4}), (1, 2), (5, 3), (7, 1)\}\impliedby \begin{array}{llll} \textit{notice the } y-rep eats\\ \textit{thus, no dice} \end{array}[/tex]
Answer:
Which function has an inverse that is also a function? a {(–1, 3), (0, 4), (1, 14), (5, 6), (7, 2)} b {(–1, 2), (0, 4), (1, 5), (5, 4), (7, 2)} c {(–1, –2), (0, 4), (1, 3), (5, 14), (7, 4)} d {(–1, 4), (0, 4), (1, 2), (5, 3), (7, 1)}
Step-by-step explanation:
It is called the inverse or reciprocal function of f to another function f − 1 that fulfills that:
If f (a) = b, then f − 1 (b) = a.
The inverse of a function when it exists is unique, so that neither "X" nor "Y" can be repeated.
If we analyze the possibilities, in the case of b, c, and d, the value 4 of the "Y" is repeated twice; in the case of a, that does not happen, therefore the answer is: a {(–1, 3), (0, 4), (1, 14), (5, 6), (7, 2) }
Find the area of one segment formed by a square with sides of 6" inscribed in a circle.
(Hint: use the ratio of 1:1: to find the radius of the circle.)
Answers
now, bear in mind that, we could simply get the area of the whole circle with that radius, and tease out a quarter, because the segment is just using up a quarter of the circle, because the angle made is 90°, and then subtract the triangle from that sector, and what's leftover is the segment.
[tex]\bf \stackrel{\textit{area of the circle}}{A=\pi r^2}\implies A=\pi (3\sqrt{2})^2\implies A=\pi 3^2\sqrt{2^2}\implies A=18\pi \\\\\\ \textit{now one-quart of that is }\cfrac{18\pi }{4}\implies \cfrac{9\pi }{2}\impliedby \textit{sector's area}[/tex]
[tex]\bf \stackrel{\textit{area of the triangle}}{A=\cfrac{1}{2}bh}\implies A=\cfrac{(3\sqrt{2})(3\sqrt{2})}{2}\implies A=\cfrac{3^2\sqrt{2^2}}{2}\\\\\\A=\cfrac{18}{2}\implies A=9\impliedby \textit{area of that triangle}\\\\ -------------------------------\\\\ \stackrel{sector's area}{\cfrac{9\pi }{2}}~~-~~\stackrel{\textit{area of the triangle}}{9}\implies \cfrac{9\pi -18}{2}\impliedby \textit{segment's area}[/tex]
or you can always just use the area of a segment, with the radius and angle given.
[tex]\bf \textit{area of a segment of a circle}\\\\ A=\cfrac{r^2}{2}\left[\cfrac{\theta \pi }{180}-sin(\theta ) \right] \\\\\\ \begin{cases} r=3\sqrt{2}\\ \theta =90 \end{cases}\implies A=\cfrac{(3\sqrt{2})^2}{2}\left[\cfrac{90 \pi }{180}-sin(90^o ) \right][/tex]
a rectangular flower garden has area of 32 square feet. if the width of the garden is 4 feet less than the length, what is the perimeter, in feet, of the garden?
Answers
length= x
width=x-4
area = 32
length * width=32
x(x-4)=32
x^2 - 4 x -32=0
(x-8)(x+4)=0
x=8 feet
length=8 feet
width=4 feet
perimeter=2(len+wid)
=2(8+4)
2*12=24 feet
To find the perimeter of the rectangular flower garden, we first need to find its dimensions. Once we have the length and width, we can calculate the perimeter by using the formula: P = 2(length + width). Therefore, the perimeter of the garden is 4x - 8 feet.
Explanation:To find the perimeter of the rectangular flower garden, we first need to find its dimensions. Let's use x to represent the length of the garden.
According to the problem, the width of the garden is 4 feet less than the length, so the width would be x - 4.
The area of the garden is 32 square feet, so we can set up the equation: x * (x - 4) = 32.
We can solve this equation by factoring or by using the quadratic formula to find the length.
Once we have the length and width, we can calculate the perimeter by using the formula: P = 2(length + width).
Substituting the values, we get P = 2(x + x - 4), which simplifies to P = 4x - 8.
Therefore, the perimeter of the garden is 4x - 8 feet.
The expression 62.4d - 210 gives the number of Indian rupees you receive when you exchange $d at the local currency exchange.
How many Indian rupees do you receive when you exchange $13?
Answers
62.4 (13) - 210
811.2 - 210
601.2 rupees for $13
I need help with this problem
HELP PLEASE URGENT NEED TO PASS THIS CLASS
Answers
Answer is y = 1/3x - 1
m = rise/run = 1/4
y = 1/4 x + 1
A building has 4 offices. There are 4 people in each of the offices. Each person has 4 chairs. How many chairs are in the building? Enter your answer in the box.
Answers
4x4x4=64
= 16 x 4
= 64
64 is your answer
hope this helps
A line has a slope of -1/2 and a y-intercept of –2.
what is the x-intercept of the line?
Answers
y = (slope)x + (y-intercept)
y = -1/2x - 2
x-intercepts occur when y = 0
0 = -1/2x - 2
2 = -1/2x
x = -4
Thus, the x-intercept is at (-4,0)
Output all of the numbers and their squares between 1 and 10 using a do while loop
Answers
If Sandy has 288 tiles and wants one-half of the tiles divided evenly into three different colors (green, yellow, burgundy). How many green tiles does she need?
Answers
In this case, 1/6 of 288 tiles - or 288 ÷ 6 - gives us a result of 48 green tiles.
The required number of green tiles is 48
Given that,
Sandy has 288 tiles and wants one-half of the tiles divided evenly into three different colors (green, yellow, burgundy), How many green tiles she need is to be determined.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
Here,
total number of tiles = 288
half of the tiles = 288 / 2 = 144
Now this half number of tiles is divided into 3 equal parts, in (green, yellow, burgundy)
= 144 / 3
= 48
So, she needs 48 green tiles.
Thus the required number of green tiles is 48.
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Find the measures of two angles, one positive and one negative, that are coterminal with pi divided by five.
Answers
The coterminal angles differ from the given angle by 2π and -2π.
The lower coterminal angle is
[tex] \frac{ \pi }{5}-2 \pi = - \frac{9 \pi }{5} [/tex]
The higher coterminal angle is
[tex] \frac{ \pi }{5} +2 \pi = \frac{11 \pi }{5} [/tex]
Answer: [tex]- \frac{9 \pi }{5} . \, \frac{11 \pi }{5} [/tex]
A pineapple is 7 times as heavy as an orange. The pineapple also weighs 870 grams more than the orange. What is the total weight in grams for the pineapple and the orange?
Answers
A student must take one physics, one chemistry, and one mathematics course during their junior year of high school. There are three courses to choose from for physics (P1, P2, P3), two courses to choose from for chemistry (C1, C2), and two courses to choose from for mathematics (M1, M2). How many possible combinations are there for the three physics, chemistry, and mathematics courses a student could select?
Answers
P1 C1 M1
P1 C1 M2
P1 C2 M1
P1 C2 M2
So there are 4 possible choices with P1. Since there are 3 choices of P, there are 3*4 total combinations, or 12. In general, you can multiply the number of possibilities together to see how many total combinations can occur, I just wanted to illustrate why that works.
Sixteen more than a number is 48 which equation models this sentence
A 16n = r8
B n - 16 = 48
C n + 16 = 48
D n ➗ 16 =48
Answers
So C. n + 16 = 48
What is 32,020.20 rounded to the nearest square mile
Answers
you have to round up the whole number in this situation because its asking for nearest mile
There are about 4200 college presidents in the United States, and they have annual incomes with a distribution that is skewed instead of being normal. Many different samples of 40 college presidents are randomly selected, and the mean annual income is computed for each sample. What is the approximate shape of the sample means?
Answers
Final answer:
The distribution of sample means for college presidents' incomes, based on many different samples of size 40, will approximate a normal distribution due to the Central Limit Theorem.
Explanation:
The question regarding the distribution of sample means for college presidents' incomes pertains to a concept in statistics known as the Central Limit Theorem. When dealing with a population whose distribution is skewed, the distribution of sample means tends to become approximately normal if the sample size is large enough, which is usually considered to be over 30. As multiple samples of size 40 are taken in this case, the distribution of the sample means for the college presidents' annual incomes should approximate a normal distribution.
How many boxes of carrots are left? 75 boxes − 68 boxes = 7 boxes
Answers
i dont know why you would ask thisquestion
The question pertains to a basic subtraction operation where the student is left with 7 boxes of carrots after subtracting 68 boxes from an initial count of 75 boxes.
The subject of the question is mathematics, specifically involving subtraction and the concept of determining the number of items remaining after a reduction. The mathematical operation presented in the question is 75 boxes - 68 boxes = 7 boxes, which indicates that when you start with 75 boxes of carrots and remove 68 boxes, you are left with 7 boxes of carrots.
This type of problem is common in elementary mathematics and does not involve complex concepts such as permutations, probability, or statistical distributions.
Find the point p where the line x = 1 + t, y = 2t, z = -3t intersects the plane x + y - z = 3.
Answers
x = 1 + t
y = 2t
z = -3t
The plane is x + y - z = 3
If the lines intersect the plane at a point p, then the lines should satisfy the equation of the plane.
That is,
(1 + t) + (2t) - (-3t) = 3
1 + t + 2t + 3t = 3
1 + 6t = 3
6t = 2
t = 1/3
Therefore the coordinates of the point p are
x = 1 + 1/3 = 4/3
y = 2(1/3) = 2/3
z = -3(1/3) = -1
That is p (4/3, 2/3, -1)
Answer: The point p has coordinates (4/3, 2/3, -1)
how many times more respondents chose silver than red round to the nearest tenth if necessary silver 0.2 red 0.09
Answers
Answer: 2.2
Step-by-step explanation:
Given : Proportion of choosing silver = 0.2 =0.20.
Proportion of choosing red= 0.09
Clearly, 0.20> 0.09
Now, the number of times more respondents chose silver than red will be :-
[tex] n=\dfrac{0.20}{0.09}\\\\=\dfrac{20}{9}\\\\=2.22222\approx2.2\ \text{ Rounded to the nearest tenth}[/tex]
Hence, 2.2 times the respondents chose silver than red.
Ralph sold brownies for $0.66 a piece in order to earn money to buy baseball cards. If the cards cost $0.90 per pack, and if Ralph had no money left over after buying them, what is the least number of brownies he must have sold?
Answers
Hope this Helps
For the number 4768.325, what is the sum of the tens digit and the tenths digit
Answers
the tenths digit = 0.3
sum = 60 + 0.3 = 60.3
answer
60.3
the leukemia and lymphoma society sponsors a 5k race to raise money it receives 55 per race and 10,000 in donations but it must spend 15 per race entry to cover the cost of the race write and solve an inequality
Answers
Hmm i think its this 55,000 >= 40x+5,000 because it needs atleast 55,000
Which explains 55,000>= second receives 55 per race but spend 15 race in other terms 55x-15x= 40 x
So 55,000>=40x third 10,000 in donations sponsers a 5,000 race 10,000-5,000=5,000 so 55,000>=40x+5,000
Also to find x 55,000>=40x+5,000 subtract 5,000
50,000>=40x now divide by 40
50,000/40>=x
X<= 1,250
Which of the following numbers is the smallest?
4/9
0.44
3/7
400%
Answers
can you do it on paper please? that would be helpful.
you could type it in though.
that's ok too.
Answers
-3x < 12 - 4
-3x < 8
-3x/-3 < 12/-3
x > -4 the inequality sign is flipped when divided by a negative.