Answers
Answer:
Domain: [- ∞, 4.5],
Range: [0.5, ∞]
Step-by-step explanation:
One approach is a graphical representation to solving the problem, which you can see as the two attachment's below. Clearly the domain would be on the interval [- ∞, 4.5] and the range would be on the interval [0.5, ∞]. There is another approach to this though,
We can determine the domain by finding what value for p makes the function undefined
Given : h(p) = (p + 3) / (2p - 9),
Value for p where denominator = 0 :
2p - 9 = 0,
2p = 9,
p = 9 / 2 = 4.5
And to determine the range we have to determine the set of values that corresponds with the domain. In this case it's p = 0.5.
Related Questions
Kaliska is jumping rope. The vertical height of the center of her rope off the ground R(t) (in cm) as a function of time t (in seconds) can be modeled by a sinusoidal expression of the form a cos(b. t) + d. , At t = 0, when she starts jumping, her rope is 0 cm off the ground, which is the minimum. After [tex]\frac{\pi }{12}[/tex] seconds it reaches a height of 60 cm from the ground, which is half of its maximum height. Find R(t). t should be in radians.
Answers
Answer:
R (t) = 60 - 60 cos (6t)
Step-by-step explanation:
Given that:
R(t) = acos (bt) + d
at t= 0
R(0) = 0
0 = acos (0) + d
a + d = 0 ----- (1)
After [tex]\dfrac{\pi}{12}[/tex] seconds it reaches a height of 60 cm from the ground.
i.e
[tex]R ( \dfrac{\pi}{12}) = 60[/tex]
[tex]60 = acos (\dfrac{b \pi}{12}) +d --- (2)[/tex]
Recall from the question that:
At t = 0, R(0) = 0 which is the minimum
as such it is only when a is negative can acos (bt ) + d can get to minimum at t= 0
Similarly; 60 × 2 = maximum
R'(t) = -ab sin (bt) =0
bt = k π
here;
k is the integer
making t the subject of the formula, we have:
[tex]t = \dfrac{k \pi}{b}[/tex]
replacing the derived equation of k into R(t) = acos (bt) + d
[tex]R (\dfrac{k \pi}{b}) = d+a cos (k \pi)[/tex] [tex]= \left \{ {{a+d \ for \ k \ odd} \atop {-a+d \ for k \ even}} \right.[/tex]
Since we known a < 0 (negative)
then d-a will be maximum
d-a = 60 × 2
d-a = 120 ----- (3)
Relating to equation (1) and (3)
a = -60 and d = 60
∴ R(t) = 60 - 60 cos (bt)
Similarly;
For [tex]R ( \dfrac{\pi}{12})[/tex]
[tex]R ( \dfrac{\pi}{12}) = 60 -60 \ cos (\dfrac{\pi b}{12}) =60[/tex]
where ;
[tex]cos (\dfrac{\pi b}{12}) =0[/tex]
Then b = 6
∴
R (t) = 60 - 60 cos (6t)
What is 3.59×6.2
PLEASE HELP QUICKLY AS POSSIBLE THANK YOU :)
Answers
In order to express the fraction 2/125 as a decimal, Meg will
first rewrite the fraction using a denominator that is a
power of 10. If she wants x to be a whole number, what is
the smallest power of 10 she can use?
Х
2
125
power of 10
A. 10
B.100
C. 1,000
D. 10,000
Answers
Answer:
B
Step-by-step explanation:
B because if it's 1000 then the number will be greater then the fraction.
Solve for x using
cross multiplication.
Answers
2. Solve the equation below and find the variation constant, k. Find y when x= 18, if y varies directly as x, and y=37 when x=5
*Round your answer to the nearest thousandth, if necessary.
Answers
Answer:
k = 7.4y = 133.2Step-by-step explanation:
To find the value of y when x= 18 we must first find the relationship between them
The statement
y varies directly as x is written as
[tex]y \: \: \alpha \: \: kx[/tex]
where k is the constant of proportionality
when y = 37
x = 5
Substitute the values into the above formula and solve for k
That's
37 = 5k
Divide both sides by 5
k = 7.4So the formula for the variation is
y = 7.4xWhen x = 18
y = 7.4(18)
We have the answer as
y = 133.2Hope this helps you
What is the measure of angle AOB?
Answers
Answer:
let angle AOB and angle COD be x
the it would be
x+x+110=180
2x+110=180
2x=180-110
2x=70
x=70/2
x=35 degree.
hope it will help you.
The table below shows the number of color pages a printer prints out over a period of time.
Printed Pages in Color
Time (min), x
2
6
8
18
Number of pages, y
3
9
12
27
What is the constant of variation?
Two-thirds
Three-halves
2
3
Answers
Answer:
The answer is three halves why proof is in the step by step explanation.
Step-by-step explanation:
Answer:
The answer is
3
_
2
Because y is over x
y
_
x
Step-by-step explanation:
The gasoline consumption of a small car is advertised as 16.3 km/L (1L=1liter). How many miles per gallon is this? One mile is 1.609 km and one gallon is 3.788 L.
Answers
Answer:
38.38 miles per gallon
Step-by-step explanation:
16.3 km/L to miles per gallon
1 mile = 1.609 km
16.3 km = 16.3/1.609 = 10.13 miles
1 gallon = 3.788 L
1 L = 1/3.788 = 0.2639 gallon
therefore,
16.3 km/L = 10.13/0.2639 = 38.38 miles per gallon
can someone please help me with this :) i only have one more try to get it right and if not i get 0/10
Answers
Answer: [tex]\sqrt[5]{27}[/tex], fifthroot(27) [according to your picture, I think there will be no space between fifth and root]
Step-by-step explanation:
concept to know: any exponent that is performed in fraction, the numerator will be the real exponent for the base, while the denominator will be the root
-------------------------------------
[tex]27^{\frac{1}{5}[/tex]
This has 1 as the numerator and 5 as the denominator.
1 can be ignored because any number to the 1 power is equal to itself.
5 is the root for 27
[tex]\sqrt[5]{27}[/tex]
Hope this helps!! :)
Please let me know if you have any question
What are the coordinates for the origin of the coordinate plane? (0.1) (1,0) (1,1) 0 (0.0)
Answers
Step-by-step explanation:
Remember: the origin is at the very center of the graph: (0,0). Not (0,1), (1,0), or 0. The first two options are not at the center. (0,1) takes us one unit above the middle, and (1,0) takes us one unite to the right of the origin. The number 0 is not used to find a point. So, our final answer is: (0,0).
expansion of (−1−2√3)^2
Answers
(- 1 - 2√3)²
applicating (a - b)² = a² + b² - 2ab
a = - 1
b = 2√3
so:
(- 1 - 2√3)² =
(- 1)² + (2√3)² - 2(- 1)(2√3) =
1 + (2² * √3²) + 2(2√3) =
1 + (4 * 3) + 4√3
ps. √x² = x1 + 12 + 4√3 = 13 + 4√3
Line t passes through points (10, 4) and (7, 9). Line u is parallel to line t. What is the slope of line u?
Answers
Answer: 3/5
Step-by-step explanation:
concept to know: the slope of perpendicular line is always opposite reciprocal
----------------------
Step 1. Find the slope of line t
(y2-y1)/(x2-x1)
=(4-9)/(10-7)
=-5/3
-------------------
Step 2. Apply the concept
Opposite reciprocal of (-5/3)=3/5
Hope this helps!! :)
Please let me know if you have any question
Hi guys, can anyone help me with this, Thanks a lot:)
Answers
Answer:
k = 1/9
Step-by-step explanation:
In order for the function to be continuous at x=9, the values of the two expressions must be the same at x=9.
The first expression evaluates to ...
[tex]\dfrac{\sqrt{9}-3}{-9}=-\dfrac{3-3}{9}=0[/tex]
The second expression needs to have the same value:
[tex]1 -k(9) = 0\\\\1 = 9k\\\\\boxed{k=\dfrac{1}{9}}[/tex]
Answer:
[tex]k=1/9[/tex]
Step-by-step explanation:
A function is continuous at a point if and only if:
[tex]\lim_{x \to n} f(x)=f(n)[/tex]
So, we have the piecewise function:
[tex]f(x) = \left\{ \begin{array}{lI} \frac{\sqrt{x} -3}{-9} & \quad0< x <9 \\ 1-kx & \quad x\geq 9 \end{array} \right.$$[/tex]
And we want to find the value of k such that the function is continuous.
First, find the left hand limit of f(x):
[tex]\lim_{x\to9^-} f(x)[/tex]
Since we're coming from the left, we'll use the first equation. Thus:
[tex]=\lim_{x\to9^-} \frac{\sqrt{x}-3}{-9}[/tex]
Direct substitution:
[tex]=\frac{\sqrt{9}-3}{-9}[/tex]
Simplify:
[tex]=\frac{3-3}{-9}[/tex]
Subtract and divide:
[tex]=\frac{0}{-9}=0[/tex]
So, what this tells us is that for the function to be continuous, the right hand limit as f(x) approaches 9 from the right must also be equal to 0.
Therefore:
[tex]\lim_{n \to 9^+} 1-kx=0[/tex]
Direct substitution:
[tex]1-9k=0[/tex]
Subtract 1 from both sides:
[tex]-9k=-1[/tex]
Divide both sides by -9:
[tex]k=1/9[/tex]
Therefore, the value of k is 1/9.
So, our equation in the end is:
[tex]f(x) = \left\{ \begin{array}{lI} \frac{\sqrt{x} -3}{-9} & \quad0< x <9 \\ 1-\frac{1}{9}x & \quad x\geq 9 \end{array} \right.$$[/tex]
Please help!!!! 40 POINTS 1. By the square root property, if k is a real number and x^2=k, then what is x equal to? (See picture) 4. Solve x^2=64. What property did you use? (See picture)
Answers
Answer:
x = ± sqrt(k)
x = ± 8 by the square root property
Step-by-step explanation:
x^2 = k
K is a real number
Take the square root of each side
sqrt(x^2) = ± sqrt(k)
x = ± sqrt(k)
Letting k = 64
x = ± sqrt(64)
x = ± 8 by the square root property
Answer:
x = ± √k
x = ± √8 by the square root property
Step-by-step explanation:
x² = k
where k is a real number
square root of each side
√x² = ± √k
x = ± √k
let k = 64
x = ± √64
therefore
x = ± 8 by the square root property
When do lunar eclipses occur?
Answers
Step-by-step explanation:
Lunar eclipses can only happen when the Moon is opposite the Sun in the sky, a monthly occurrence we know as a full Moon.
If $4x=3y$, what is the value of $\frac{2x+y}{3x-2y}$?
Answers
Answer:
10
Step-by-step explanation:
Solving $4x=3y$ for $x$ gives $x = \frac{3}{4}y$. Substituting this into the desired expression gives\begin{align*}\frac{2x+y}{3x-2y} &= \frac{2\left(\frac34\right)y + y}{3\left(\frac34y\right) - 2y}\\
&=
\frac{\frac32y + y}{\frac94y - 2y} = \frac{\frac52y}{\frac{y}{4}} \\
&=\frac{5}{2}\cdot 4 = \boxed{10}.\end{align*}
Answer:
10
Step-by-step explanation:
Substitution and simplification
1. What are the coordinates of the midpoint of the line segment with endpoints (2,5) and (4. – 7)?
O (-2. - 2)
O (-1. - 6)
O (6, - 2)
O (3. - 1)
Answers
Answer:
(3,-1)
Step-by-step explanation:
(2+4)/2. (5-7)/2
6/2. - 2/2
3,-1
the product of a number and 8
Answers
Answer:
[tex]8n[/tex]
Step-by-step explanation:
The answer would be [tex]8n[/tex] because [tex]8*n[/tex] = [tex]8n[/tex]
I need help finding the domain and range, I already know is not a function
Answers
Answer:
Domain: [-4, 4]
Range: [-3, 5]
Function? No
Step-by-step explanation:
Domain is all x-values that can be inputted in the graph that returns an output.
Range is all y-values that are outputted when x is inputted.
A function has to pass the Vertical Line Test.
An investigator predicts that dog owners in the country spend more time walking their dogs than do dog owners in the city. The investigator gets a sample of 21 country owners and 23 city owners. The mean number of hours per week that city owners spend walking their dogs is 10.0. The standard deviation of hours spent walking the dog by city owners is 3.0. The mean number of hours country owners spent walking theirs dogs per week was 15.0. The standard deviation of the number of hours spent walking the dog by owners in the country was 4.0. Do dog owners in the country spend more time walking their dogs than do dog owners in the city?
Answers
Answer:
Yes dog owners in the country spend more time walking their dogs than do dog owners in the city
Step-by-step explanation:
From the question we are told that
The sample size from country is [tex]n_1 = 21[/tex]
The sample size from city is [tex]n_2 = 23[/tex]
The sample mean for country is [tex]\= x_1 = 15 [/tex]
The Sample mean for city is [tex]\= x_2 = 10[/tex]
The standard deviation for country is [tex]\sigma _1 = 4[/tex]
The standard deviation for city is [tex]\sigma _2 = 3[/tex]
Let the level of significance is [tex]\alpha = 0.05[/tex]
The null hypothesis is [tex]H_o : \mu_1 = \mu_2[/tex]
The alternative hypothesis is [tex]H_a : \mu_1 > \mu_2[/tex]
The pooled standard deviation is mathematically represented as
[tex]s = \sqrt{ \frac{s_1 ^2 * (n_1 - 1 ) + s_2 ^2 * (n_2 - 1 )}{ df} }[/tex]
Here df is the degree of freedom which is mathematically represented as
[tex]df = n_1 + n_2 - 2[/tex]
[tex]df = 21 + 23 -2 [/tex]
[tex]df = 42[/tex]
So
[tex]s = \sqrt{ \frac{4 ^2 * (15.0 - 1 ) + 3 ^2 * (10 - 1 )}{ 42} }[/tex]
[tex]s = 3.5[/tex]
Generally the test statistics is mathematically represented
[tex]t = \frac{\= x_1 - \= x_2 }{ s * \sqrt{\frac{1}{n_1} +\frac{1}{n_2} } }[/tex]
[tex]t = \frac{ 15 -10 }{ 3.5 * \sqrt{\frac{1}{ 21 } + \frac{1}{23} } }[/tex]
[tex]t = 4.733[/tex]
Generally the p-value is obtained from the student t-distribution table table , the value is
[tex]P(T > 4.733)= t_{4.733, 42 } = 0.000013 [/tex]
From the calculation we see that
[tex]p-value < \alpha[/tex]
So we reject the null hypothesis
Hence we can conclude that there is sufficient evidence to support the claim that dog owners in the country spend more time walking their dogs than do dog owners in the city
00:00
Hakim is making birdhouses. Each birdhouse uses
7
What is the total length of wood Hakim will need to build 5 birdhouses?
Į yard of wood.
4 3 yards
5 [ yards
1 yards
og yards
Answers
Answer:
[tex]4\frac{3}{8}[/tex] yards of wood
Step-by-step explanation:
The correct question is Hakim is making birdhouses. Each birdhouse uses 7 /8 yard of wood. What is the total length of wood Hakim will need to build 5 birdhouses?
Answer: Given that the amount of wood need to produce one bird house is 7/8 yard, for 5 birdhouse, the amount of wood needed would be 5 times the number needed for one birdhouse. It is given by:
Amount of wood needed for 5 birdhouse = 5 × amount of wood for 1 birdhouse
Amount of wood needed for 5 birdhouse = 5 × 7/8 yards = 35/8 = [tex]4\frac{3}{8}[/tex] yards of wood
A bag has 13 red candies 7 pink candy 12 orange candies what is the possibility that you will choose an orange candy at random
Answers
Answer:
12/32, 3/8, or 37.5%
Step-by-step explanation:
Add the candies in the bag together
13+7+12=32
12 out of the thirty-two are orange
12/32
After dividing by 4 to simplify, you get
3/8
3÷8 will give us the decimal which we can then turn into a percentage
37.5%
12/32, 3/8, or 37.5%
Hope this helps :-)
If each chip has a length of 35 nanometers (nm), how many would you need to circle the Earth. Which has a radius of 6,371 km? (Show all your workings. Final answer MUST be in scientific notation.)
Answers
Answer:
1144.18 e-12 chips
Step-by-step explanation:
Conversation rate of nanometers
1 nanometers =1* 10^-12 km
35 nanometers= 35 *10^-12
Radius of earth= 6371 km
Circumference of earth = 2πr
Circumference= 2*22/7*6371
Circumference=40046.29 km
The number of chips to be used to circle the earth
= 40046.29/35 *10^-12
=1144.18 *10^-12
= 1144.18 e-12 chips
Operations on Rational and Irrational Numbers
Answers
Answer:
the second option 5 2/3
Step-by-step explanation:
since 0.3 with a line over it is equal to 2/3 and 3+2 is 5 our answer would be 5 2/3
Answer:
6
Step-by-step explanation:
Will give brainliest if you complete all of them
Answers
Answer:
14 is 4
15 is check your self
in Google
Simplify: 5x+2(3−2x)+7
Answers
Answer:
x + 13
Step-by-step explanation:
5x + 2(3 - 2x) +7
Distribute the 2 into (3 - 2x)
5x + 6 - 4x + 7
Combine like terms
x + 13
PEMDAS is an acronym that refers to the sequence of operations to be employed when solving equations with multiple operations. The given expression 5x+2(3−2x)+7 when simplified will be equal to x+13.
What is PEMDAS?PEMDAS is an acronym that refers to the sequence of operations to be employed when solving equations with multiple operations. PEMDAS is an acronym that stands for P-Parenthesis, E-Exponents, M-Multiplication, D-Division, A-Addition, and S-Subtraction.
The given expression 5x+2(3−2x)+7 can be simplified as shown below.
5x + 2(3−2x) + 7
Open the parenthesis,
= 5x + 6 − 4x + 7
Bring the like terms together,
= 5x − 4x + 7 + 6
Add the like terms,
= x + 13
Hence, The given expression 5x+2(3−2x)+7 when simplified will be equal to x+13.
Learn more about PEMDAS here:
https://brainly.com/question/36185
#SPJ2
FOR THE FUNCTION F(X) =6x - 8 what is f(3)?
Answers
Replace x in the equation with 3
6(3) -8 = 18 -8 = 10
The answer is 10
Answer:
10
Step-by-step explanation:
To find f(3), substitute 3 in the function
f(3) = 6*3 - 8
= 10
(Please help fast!) ..........
Answers
Answer:
the sum would be located 2 notches to the right from 0.
Step-by-step explanation:
since the notches are already split up into 5, you just count 2 notches to the left (since its negative) and then count 4 notches to the right and then you land on your sum :) btw I like your profile picture
— 6— (—12) help me plz
Answers
Answer:
Hey there!
-6-(-12)
-6+12
6
Hope this helps :)
Answer:
[tex]6[/tex]
Step-by-step explanation:
[tex]-6-(-12)[/tex]
[tex]-6+12[/tex]
Since 12 - 6 is equal to 6, -6 + 12 would be 6.
[tex]=6[/tex]
Now you have your answer!
Hope this helps!
What is standard form for 400,000+60,000+5,000+100
Answers
Answer:
[tex]\boxed{\bold 4.651 \times {10}^{5}}}[/tex]
Step-by-step explanation:
[tex]400000 + 60000 + 5000 + 100 \\ = 465100[/tex]
Now write it in standard form.
[tex]465100 \\ = 4.651 \times {10}^{5} [/tex]
hope this helps you.
will give the brainliest!
follow~Hi1315~