The vertex is (-1,0), range is (-inf,0], increasing on (-inf,-1), decreasing on (1,inf)
The key aspects of the function [tex]f(x) = - x^2 - 2x - 1[/tex] are as follows:
Vertex: The vertex of a quadratic function is the point where the function changes from increasing to decreasing, or vice versa. To find the vertex, we can complete the square or use the vertex formula. In this case, the vertex is (-1,0).
Range: The range of a function is the set of all possible output values. Since the leading coefficient in f(x) is negative, the parabola opens downwards, so the range is all numbers less than or equal to 0, or (-inf,0].
Increasing/Decreasing: A quadratic function is increasing to the left of its vertex and decreasing to the right of its vertex. Therefore, f(x) is increasing on (-inf,-1) and decreasing on (-1,inf).
Domain: The domain of a function is the set of all possible input values. For quadratic functions, the domain is all real numbers, so the domain of f(x) is all real numbers.
Therefore, The vertex is (-1,0), range is (-inf,0], increasing on (-inf,-1), decreasing on (1,inf).
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the table shows the prices for different party toy packages from the Tomtown Toy Company.Which item costs the least per toy? Explain your reasoning
Answer:
Dominoes costs the least per toy.
Step-by-step explanation:
From the given table it is clear that
Cost of 6-pack of Dominoes = $3.98
Cost of 1-pack of Dominoes = [tex]\frac{\$3.98}{6}\approx \$0.663[/tex]
The cost of 1-pack of Dominoes is $0.663.
Cost of 12-pack of Peg Games = $9.99
Cost of 1-pack of Peg Games = [tex]\frac{\$9.99}{12}=\$0.8325[/tex]
The cost of 1-pack of Peg Games is $0.8325.
Cost of 24-pack of Mini Footballs = $17.98
Cost of 1-pack of Mini Footballs = [tex]\frac{\$17.98}{24}\approx $0.75[/tex]
The cost of 1-pack of Mini Footballs is $0.75.
$0.663 is less than $0.8325 and $0.75. It means dominoes costs the least per toy.
Which number is a perfect cube A 3 B 15 C 64 D567
Hamburger costs $1.50 per pound and soy costs $1.00 per pound. The school cafeteria uses 50 more pounds of soy than hamburger and spends $350 a week. How much soy does the school use?
Graph y=− 4/7 x+1 .
where would 2015 be on a mod 7 clock
Christopher recorded the low temperature each day for 1 week and recorded his results in this table. Day Sunday Monday Tuesday Wednesday Thursday Friday Saturday Low −5 °F −8 °F −6 °F −8 °F −3 °F 2° F 7° F What is the average low temperature for the week? Enter your answer in the box.
In 8 months, 55.6 gallons were used. Find the unit rate.
Answer:
6.95 gallons/month
Step-by-step explanation:
We are given that In 8 months, 55.6 gallons were used
Amount used in 8 months = 55.6 gallons
We are supposed to find amount used per month i.e. unit rate
So, Amount used in 8 months = 55.6 gallons
Amount used in 1 month = [tex]\frac{55.6}{8}[/tex] gallons
Amount used in 1 month = [tex]6.95[/tex] gallons
So, 6.95 gallons were used in 1 month
Hence the unit rate is 6.95 gallons/month
math question down below
Please help
An animal shelter spends $5.50 per day to care for each cat and $8.00 per day to care for each dog. Angel noticed that the shelter spent $54.00 caring for cats and dogs on Monday. Angel found a record showing that there were a total of 8 cats and dogs on Monday. How many cats were at the shelter on Monday?
In the diagram AB is parallel to CD. What is the term for the line that intersects the two parallel lines?
Answer:
its been 3 years but the answer is b
Step-by-step explanation:
Light travels at 3.0 x 105 km/s. The sun is 1.5 x 108 km from Earth. How long does it take for the sun's light to reach Earth?
Answer:
It takes 8 minutes and 20 seconds for the light to travel this distance
Step-by-step explanation:
Velocity is calculated as:
V= d/t (1)
Where d is distance and t is time. As we want to find time t we must simplify (1) for t
t= d/V (2)
We replacethe values given:
t=d/V=1.5*10^8/3.0*10^5=5*10^3 = 500 seconds
As there are 60 seconds in a minute we find
minutes = 500/60 = 50/6 = 25/3 = 8 2/3 or 8 minutes 20 seconds
Estimate each product 33.6 x 82.1
Jack and Jessica and the same amount last week.Jack earned $18 per hour and had $41 taken away from his check for Taxes. Jessica earned $15 an hour and had to $17 deducted from her pay. how many hours did they each work in order to get paid the same amount
There are 25 students in the class. ten students have sports practice after school. What is the ratio of students that do have practice, to those that do not?
Help ASAP plz
The odometer on your family car reads 20,186.7 after going
62.3 miles. How many miles were on the odometer before
going 62.3 miles?
What is the slope of the graph for the equation y = -5x + 8? A. 0 B. -5 C. 8
what is 10/4 as a mixed number
The fraction 10/4 written as a mixed number is 2 1/2
Given the improper fraction :
10/4To convert to a mixed number ; divide Numerator by denominator and express the remainder as a fraction
10/4 = 2 2/4
Express in its simplest form:
2 2/4 = 2 1/2Hence, the mixed number value is 2 1/2
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what is the answer to
3(4x+6)+7x
The simplified value of the given expression 3(4x+6)+7x, is 19x+18
What is an expression?Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.
Mathematical expressions have only numbers and operators, while algebraic expressions have both numbers and variables in terms, separated by operators in between.
For example, 4m + 5 is an expression where 4m and 5 are the terms and m is the variable of the given expression separated by the arithmetic sign +.
Given that, is an expression 3(4x+6)+7x, we need to simplify it,
3(4x+6)+7x
By the Distributive property, multiplying by 3,
3(4x+6)+7x
= 12x+18+7x
Rearranging the terms,
= 12x+7x+18
Adding the like terms,
= 19x+18
Hence, the simplified value of the given expression 3(4x+6)+7x, is 19x+18
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Nathan helps out in the family pet shop on Saturdays. He must separate a shipment of 112 fish into nine bowls. Does Nathan have enough bowls if each bowl can fit no more than 12 fish? Explain why.
In 2001, the population of the United States was about 2/7 billion people. It is projected that by 2025, there will be 1/3 billion people in the United States. How much will the population increase by 2025?
Pleeeeeeaaaaase show steps
Subtract the starting population from the increased population:
1/3 -2/7
Rewrite the fractions to have a common denominator:
7/21 - 6/21 = 1/21 billion increase.
Convert 4500 feet per second to miles per hour.
5280 ft = 1 mi
Round to the nearest hundredth.
Enter your answer in the box.
2. Which conjecture is true?
A. An even number plus 3 is always even.
B. An even number plus 3 is always prime.
C. An even number plus 3 is always odd.
D. A prime number plus 3 is always even
C. An even number plus 3 is always odd.
Prime number: A number that can only be divided by 1 and itself. For example 7, 11, etc
Odd number: Any number that cannot be divided by 2. For example 3, 5, 7, etc
Even number: Any number than can be divided by 2. For example: 4, 6, 8, etc
If we add 2,4,6 or 1000 to 3, the resultant will be always odd. If we add 2 to 3, we will get 5 which is an odd number. If we add 8 to 3, you will get 11 which is an odd number.
So, the conjecture is :
An even number plus 3 is always odd.
Therefore the correct option is (c).
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negative 50 plus 300 minus 50 minus 100
find the discriminant and determine the number of real solutions : 4x^2 + 7x - 15 = 0
Ebert used to make a $22 an hour, but got a 10% raise. how much more will he make in a 40 hour work week with the raise?
Jenny's frog made one jump of 2.34 meters. Christina's frog made jumps of 1.22 meters and 0.89 meters. How much further did Jenny's frog jump in one jump than Christina's frog in two jumps combined? 0.23 m 0.33 m 1.12 m 1.45 m
took the k12 test it 0.23
Greg builds a new pond which has a volume of 7.35 m3. It is 4.2 m long and 50 cm deep. What is the width of the pond?
volume = length x width x depth
50cm = 0.5 m
7.35 = 4.2 x 0.5 x X
7.35 = 2.1 x X
x = 7.35 / 2.1
x = 3.5
width = 3.5 meters
Answer: 3.5 meters
Step-by-step explanation:
Given : The volume of a new pond = [tex]7.35\ m^3[/tex]
The length of a new pond = 4.2 m
The depth of the pond = 50 cm =0.5 m
Let the width of the pond be 'w'.
The volume of cuboid is given by :_
[tex]V=l\times h\times w\\\\\Rightarrow\ 7.35=4.2\times0.5\times w\\\\\Rightarrow\ w=\dfrac{7.35}{0.5\times4.2}\Rightarrow\ w=3.5[/tex]
Hence, the width of the pond = 3.5 meters
If g(x)= 2x-1, and h(x)= square root of x, find (goh)(9)
Answer:
The [tex](goh)(9)=5[/tex]
Step-by-step explanation:
We need to find out the [tex](goh)(9)[/tex]
Given:- [tex]g(x)=2x-1[/tex] and [tex]h(x)=\sqrt{x}[/tex]
First we need to find out the composition of (gof)(x)
Replace x in function g(x) with h(x) as;
[tex](goh)(x)=2(h(x))-1[/tex]
[tex](goh)(x)=2(\sqrt{x})-1[/tex]
Now put x=9 , in above to get the [tex](goh)(9)[/tex]
[tex](goh)(9)=2(\sqrt{9})-1[/tex]
[tex](goh)(9)=2(3)-1[/tex]
[tex](goh)(9)=6-1[/tex]
[tex](goh)(9)=5[/tex]
Therefore, [tex](goh)(9)=5[/tex]
f y = 16x, which table shows the values of y for different values of x?
x 0 2 4
y 0 18 20
x 0 2 4
y 0 8 4
x 0 2 4
y 0 32 64
x 0 2 4
y 0 16 32
Answer:
D
Step-by-step explanation:
One-third of the dairy cattle on a farm are in the barn. Three-fifths of the beef cattle are in the barn. There are 30 dairy cattle and 15 beef cattle in the barn. How many more dairy cattle are on the farm than beef cattle?