sketch the graph of each function. Then State the domain, range and increasing, decreasing intervals. Part 2
Answers
Problem 17
The graph is shown below.
The domain is [tex]x \ge -1[/tex] which is found by solving [tex]x+1 \ge 0[/tex]. This is done to ensure that the stuff under the square root is not negative. Note the left-most point of the graph has x = -1 as its x coordinate.
The domain in interval notation is [tex][-1, \infty)[/tex] we have a square bracket at -1 and a curved parenthesis at infinity.
The range is [tex]y \le 3[/tex] based on what the graph shows. This is directly tied to the +3 at the end of the function. The parent's function max value is y = 0, so that plus 3 shifts everything up 3 units so that the new translated function has a max of y = 3.
The range in interval notation is [tex](-\infty, 3][/tex] we use a square bracket to include 3 as part of the interval.
Throughout the entire function, the curve is going downhill as we move from left to right. The graph shows this. We could also use a table of values to see that as x gets bigger, y gets smaller.
So the function is never increasing. The function decreases on the interval (-1, infinity) which is the entire domain.
=====================================================
Problem 18
The graph is shown below. It's in a separate attachment.
The domain and range are the set of all real numbers. The graph shows that the curve extends forever to the left and right. Also, the graph extends forever upward and downward (regardless if that growth seems really slow).
The domain and range in interval notation is [tex](-\infty, \infty)[/tex] to indicate the entire real number line.
The graph goes uphill as we read from right to left, so the function is increasing on the interval [tex](-\infty, \infty)[/tex]. In other words, no matter where you are, you're going uphill if you move from left to right. This rules out the function ever decreasing.
We can use a table of values to see that the function is increasing if we cannot rely on the graph. As x gets bigger, so does y.
Answer:
1)
The angle of inclination is the angle between the horizontal and the ramp.
Using the sine ratio in the right triangle formed by the ground and the ramp
let x be the angle of inclination, then
sinx = \frac{opposite}{hypotenuse}
hypotenuse
opposite
= \frac{0.7}{4.2}
4.2
0.7
, then
x = sin^{-1}sin
−1
(\frac{0.7}{4.2}
4.2
0.7
) ≈ 10° ( to the nearest degree )
(2)
Again there is a right triangle between the ground and the vertical height of the kite, with hypotenuse being length of string.
let y be the height of the kite and x the horizontal distance, then
sin27° = \frac{opposite}{hypotenuse}
hypotenuse
opposite
= \frac{y}{176}
176
y
( multiply both sides by 176 )
176 × sin27° = y , then
y ≈ 80m ( to the nearest metre ) ← height of kite
and
cos27° = \frac{adjacent}{hypotenuse}
hypotenuse
adjacent
= \frac{x}{176}
176
x
( multiply both sides by 176 )
176 × cos27° = x , then
x ≈ 157m ( to the nearest metre ) ← horizontal distance
Related Questions
a bacteria culture doubles every 3 minutes. if 400 bacteria started, how long will it take before there are 2000 in the culture?
Answers
Answer:
15 minutes
Step-by-step explanation:
400 to 2000(x5)
so, 3 times 5 is equal to 15 min
Whoever is awake I need help with math points and brainlest
Answers
Answer:
the first one or A. hope this helps.
Step-by-step explanation:
given that angle one is approximately equal to angle two, and angle three is approximately equal to angle one, prove line xy is parallel to line wv (using the statements and reasons columns)
Answers
Answer :
Statements :-
1. Segment XY is parallel to segment WV.
2. Angle 1 is congruent to angle 2.
3. Angle 3 is congruent to angle 1.
4. Angle XMY is congruent to angle VMW.
Reasons :-
1. Given
2. Given
3. Given
4. SSS (Side-Side-Side)
Hope this helps, thank you !!
What is the answer to the question?
Answers
Answer:
exponential function i think
Step-by-step explanation:
QUESTION: A survey of students in a homeroom class explored the
relationship between gender and participation in the school band. What
is a reasonable conclusion to draw from the data?*
Answers
Answer:
ill say its c but im not that sure
Step-by-step explanation:
How many boxes did Lamar sell?
How many boxes did Jina sell?
Answers
PLEASE HELLPPPPPPPPPPPPPPPPPPPPPPPPPPP
Answers
Answer:
a) 33
B) 65?
C) 60?
D) Becuase its the same shape just smaller.
E) 14, its cut in half
Step-by-step explanation:
be careful if you use these, its been a while since I geometry.
Which set of values for x makes the inequality 12−x<7 true
Answers
Answer:
[tex]\{x:x>5\}[/tex]
Step-by-step explanation:
Given
[tex]12 - x < 7[/tex]
Required
Values of x that make it true
First: solve the inequality.
[tex]12 - x < 7[/tex]
Collect Like Terms
[tex]- x < 7-12[/tex]
[tex]- x < -5[/tex]
Multiply both sides by -1
[tex]-1 * - x < -5 * -1[/tex]
[tex]x > 5[/tex] --- The inequality changes when multiplied by a negative value
So, the solution implies that the value of x is greater than 5 (i.e. 6, 7, 8..)
Hence, the set is:
[tex]\{x:x>5\}[/tex]
Which graph represents the function f(x) = 4|x|?
Answers
Answer:
The 2nd one
Step-by-step explanation:
It is a compression, because you are multiplying by a whole number greater than 1, therefor the line will look thinner
Sweet Orange
$1.29/lb
What's the final price of 8 pounds of oranges? Assume that the tax is regular and that your
membership gives you an extra 10% off. *
Answers
10.32x10%
10.32x0.10=1.03
10.32-1.03=9.29
I need to know the answer ASAP
Answers
Q2) Four O’clock
Subtract 7−5x from 2−3x . What is the difference?
Answers
Answer:
7−5x from 2−3x
Step-by-step explanation:
you flip them and get 2−3x 7−5x. try it that way...
i forgot to bring a piece of paper, im on the road
Elijah invested $280 in an account paying an interest rate of 2.1% compounded
continuously. Assuming no deposits or withdrawals are made, how long would it
take, to the nearest tenth of a year, for the value of the account to reach $360?
Answers
Answer: 12
Step-by-step explanation:
Hi! Please i need your help!. Thank you to those who help and answer correctly
Answers
Answer:
I believe there are 5
Step-by-step explanation:
if there are 4 friends and Mary then that makes 5 people in total.
The power, P (watts), of a car engine is proportional to the square of its speed, s (m/s).
When s = 35, P = 1760.
Work out the power (to 1 DP) when the speed is 40 m/s
Answers
Answer:
P = 2288 W
Step-by-step explanation:
The power, P (watts), of a car engine is proportional to the square of its speed i.e.
[tex]P\propto s^2[/tex]
or
[tex]P=ks^2[/tex]
Put s = 35, P = 1760 to find k.
[tex]k=\dfrac{P}{s^2}\\\\k=\dfrac{1760}{35^2}\\\\k=1.43[/tex]
Now put k = 1.43 and s = 40. So,
[tex]P=1.43\times (40)^2\\\\P=2288\ W[/tex]
So, the new power is 2288 W when the speed is 40 m/s.
Find an equation of the straight line that is perpendicular to y=2x+1 and passes through the point (-2,5)
Answers
Answer:
y = -1/2x + 4
Step-by-step explanation:
to answer this question you need to find the slope and the y-intercept
to find the slope of a line that is perpendicular to another line you take the opposite and reciprocal of the slope of the first line
in this case the slope of the initial line is 2; therefore, the opposite reciprocal is -1/2
knowing slope ('m') = -1/2 and having the point (-2, 5) can give us the y-intercept of the new line; we start with:
y = mx + b and then plug the values in so find the y-intercept ('b')
5 = (-1/2)(-2) + b
5 = 1 + b
b = 4
put it all together: y = -1/2x + 4
Jackie has $250 in her bank account and makes $25 every time she babysits. Write an expression in simplest form representing how much Jackie has in her account after babysitting t times
Answers
Step-by-step explanation:
y = 25t + 250
y is the total amount
t is number of times babysitting
What is 23% over a 100
Answers
Answer:
0.0023 or 23 / 10000
Step-by-step explanation:
23% = 0.23
0.23 / 100 = 0.0023
Answer:
23
Step-by-step explanation:
anything over 100 s a percent
like 15/100 is 15%
Katie uses 12 cups of flour and sugar to make cookies. The amount of flour is four more than three times the amount of sugar. How many cups of flour are in this recipe?
The solution is?
Answers
Answer:
146
Step-by-step explanation:
because 3times the cups is 36
so four times more 36
There are 13 cups of flour in this recipe when Katie uses 12 cups of flour and sugar to make cookies. The amount of flour is four more than three times the amount of sugar.
Let's assume the amount of sugar used in the recipe is represented by the variable "s."
According to the given information, the amount of flour used is four more than three times the amount of sugar. In mathematical terms, this can be expressed as:
Flour = 3s + 4
Now, we know that Katie uses 12 cups of flour in the recipe. We can set up an equation to solve for the amount of sugar:
12 = 3s + 4
Subtracting 4 from both sides of the equation:
12 - 4 = 3s
8 = 3s
Dividing both sides by 3:
8/3 = s
s = 2.67
Since the number of cups of sugar must be a whole number, we can round the value to the nearest whole number. Thus, s ≈ 3.
Now, we can find the amount of flour by substituting the value of sugar into the equation:
Flour = 3s + 4
Flour = 3(3) + 4
Flour = 9 + 4
Flour = 13
Therefore, there are 13 cups of flour in this recipe.
To know more about flour click here :
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Simplify
(5 - 4x) (6 + 7x)
Answers
Answer:
30+11x−28x2
Step-by-step explanation:
it is 30+11x-28x2
Find the quotient: 68/6
Answers
Answer:
The answer is 11. 2 is the remainder
Step-by-step explanation:
hope this helps
Adult tickets to the fall play cost $6 and student tickets cost $3. The drama class sold 25 more student tickets than adult tickets to the fall play. If the class collected $660 from ticket sales, how many student tickets were sold?
The drama class sold how many tickets?
The solution is?
Answers
9514 1404 393
Answer:
90 student tickets65 adult ticketsStep-by-step explanation:
For many "mixture" problems, it is convenient to use a variable for the quantity of the highest contributor. Here, we can use 'a' to represent the number of adult tickets, because adult tickets cost the most. Then the number of student tickets is (a+25), and the total revenue is ...
6a +3(a+25) = 660
9a +75 = 660
9a = 585
a = 65
(a+25) = 90
The drama class sold 90 student tickets and 65 adult tickets.
Calculate the value of x
35 degree 2x+16 4x+3
Answers
180 miles in 4 hours at what rate how long will it take to drive 270 miles
Answers
Answer:
6
Step-by-step explanation:
180 / 4 = 45
45mi = 1hr
270 / 6 = 45
3 How many more cake
pops does the neighbor need to sell so that Callie can make a
profit of $5.00? Show
your
work.
Answers
Answer:
you didint explainded well
Step-by-step explanation:
What type of function is f(x)=2(1/7)^x?
Linear
Exponential Decay
Exponential Growth
None of the Above
Answers
Answer:
B) Exp. Decay
Step-by-step explanation:
Because the term getting raised to a power is under 1, the function immediately starts going down and approaches negative infinity as x approaches infinity.
The type of function is f(x)=2(1/7)^x is Exponential Decay, the correct option is B.
What is a function?Function is a type of relation, or rule, that maps one input to specific single output.
In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable). In mathematics and the physical sciences, functions are indispensable for formulating physical relationships.
Linear function is a function whose graph is a straight line
We are given that;
Function; f(x)=2(1/7)^x
Now,
The function has the form f(x)=abx
where a and b are constants and b is between 0 and 1. In this case, a is 2 and b is 1/7, which is less than 1. This means that the function decreases as x increases.
Therefore, by the given function the answer will be Exponential Decay.
Learn more about function here:
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sketch the graph of each function. Then State the domain, range and increasing, decreasing intervals. Part 3.
Answers
Answer:
19) Domain: - ∞ < x < ∞ 20) Domain: - ∞ < x < ∞
Range: - ∞ < y < ∞ Range: - ∞ < y < ∞
Increases throughout Decreases throughout
Step-by-step explanation:
Given the parent function " y = ∛x" we know that the first graph should have a vertical shift down 2 units, and a horizontal shift 4 units to the right. There is no vertical stretch since there is no coefficient. (Check first graph)
Domain: - ∞ < x < ∞
Range: - ∞ < y < ∞
Increases throughout
______________________________
For the second graph there should be a vertical shift down three units, a horizontal shift 1 unit to the left, and a vertical stretch by a factor of - 1. (Check second graph)
Domain: - ∞ < x < ∞
Range: - ∞ < y < ∞
Decreases throughout
Solve each equation.
40 = -8(x + 2)
Answers
Answer:
x = -7
Step-by-step explanation:
it’s right!
The area of a circle is 9πft^2. What is the circumference in feet?
Answers
Answer:
98
Step-by-step explanation:
Answer:
6π ftStep-by-step explanation:
Area:
A = πr²Circumference:
C = 2πrSubstitute values in area:
πr² = 9πr² = 9r = 3 ftCircumference is:
C = 2π*3 = 6πFrom a board 8 feet in length, Emmet cut two 2 ⅓ foot bookshelves. How much of the board remained?
Answers
Answer:
3 2/5
I converted these into decimals, because I find it easier ^.^
We have an 8 feet board, and we twice remove 2 1/3 from that number.
8 - 2 1/3 = 5.7
5.7 - 2 1/3 = 3.4 or 3 2/5
~Hope this helps~