A graph is shown below: A graph is shown. The values on the x axis are 0, 2, 4, 6, 8, and 10. The values on the y axis are 0, 4, 8, 12, 16, and 20. Points are shown on ordered pairs 0, 16 and 2, 12 and 4, 8 and 6, 4 and 8, 0. These points are connected by a line. What is the equation of the line in slope-intercept form?
Answers
Answer:
Graph is image, and equation is from the work result below:
Step-by-step explanation:
Take two points find the slope and y-intercept:
Slope = -2
Y-intercept = (0,16)
Equation =
y = − 2 x + 16
check work for one point (to make sure equation works):
(2,12)
y = -2x + 16
12 = -2(2) + 16
12 = -4 + 16
12 = 12
The equation is correct: y = − 2 x + 16
Image below are the points given:
Related Questions
NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW!!! PLEASE explain thoroughly. Chapter 9 part 1
1. How can you determine the end behaviors for a graph from the function? What are the possible behaviors?
2. How is solving a polynomial inequality different from a solving a polynomial equation? How do the solutions differ?
3. What is a composite function? How does order of the composite function play a role in solving the composition?
Answers
9514 1404 393
Explanation:
1. End behavior is the behavior of the function when the value of the independent variable gets large (or otherwise approaches the end of the domain). There are generally four kinds of end behavior:
the function approaches a constant (horizontal asymptote)the function approaches a function (slant asymptote, for example)the function oscillates between two of the above end behaviorsthe function tends toward +∞ or -∞Of these, behavior 2 will ultimately look like one of the others.
For polynomials, the function will always approach ±∞ as the independent variable approaches ±∞. Whether the signs of the infinities agree or not depends on the even/odd degree of the polynomial, and the sign of its leading coefficient.
For exponential functions, the end behavior is a horizontal asymptote in one direction and a tending toward ±∞ in the other direction.
For trig functions sine and cosine, the end behavior is the same as the "middle" behavior: the function oscillates between two extreme values.
For rational functions (ratios of polynomials), the end behavior will depend on the difference in degree between numerator and denominator. If the degree of the denominator is greater than or equal to that of the numerator, the function will have a horizontal asymptote. If the degree of the numerator is greater, then the end behavior will asymptotically approach the quotient of the two functions—often a "slant asymptote".
__
2. A polynomial inequality written in the form f(x) ≥ 0, or f(x) > 0, will be solved by first identifying the real zeros of the function f(x), including the multiplicity of each. For positive values of x greater than the largest zero, the sign of the function will match the sign of the leading coefficient. The sign will change at each zero that has odd multiplicity, so one can work right to left to identify the sign of the function in each interval between odd-multiplicity zeros.
The value of the function will be zero at each even-multiplicity zero, but will not change sign there. Obviously, the zero at that point will not be included in the solution interval if the inequality is f(x) > 0, but will be if it is f(x) ≥ 0. Once the sign of the function is identified in each interval, the solution to the inequality becomes evident.
As a check on your work, you will notice that the sign of the function for x > max(zeros) will be the same as the sign of the function for x < min(zeros) if the function is of even degree; otherwise, the signs will be different.
The solution to a polynomial inequality is a set of intervals on the real number line. The solution to a polynomial equation is a set of points, which may be in the complex plane.
__
3. A composite function is a function of a function, or a function of a composite function. For example f(g(x)) is a composite function. The composition can be written using either of the equivalent forms ...
[tex](f\circ g)(x)\ \Leftrightarrow\ f(g(x))[/tex]
It can be easy to confuse an improperly written composition operator with a multiplication symbol, so the form f(g(x)) is preferred when the appropriate typography is not available.
When simplifying the form of a composition, the Order of Operations applies. That is, inner parenthetical expressions are evaluated (or simplified) first. As with any function, the argument of the function is substituted wherever the independent variable appears.
For example, in computing the value f(g(2)), first the value of g(2) is determined, then that value is used as the argument of the function f. The same is true of other arguments, whether a single variable, or some complicated expression, or even another composition.
Note that the expression f(g(x)) is written as the composition shown above. The expression g(f(x)) would be written using the composition operator with g on the left of it, and f on the right of it:
[tex](g\circ f)(x)\ \Leftrightarrow\ g(f(x))[/tex]
That is, with respect to the argument of the composition, the functions in a composition expression are right-associative. For example, ...
for h(x)=2x+3, g(x)=x^2, f(x)=x-2 we can evaluate f(g(h(x)) as follows:
f(g(h(x)) = f(g(2x+3) = f((2x+3)^2) = (2x+3)^2 -2
It should be obvious that g(h(f(x)) will have a different result.
g(h(f(x)) = g(h(x-2)) = g(2(x-2)+3) = (2(x-2)+3)^2
The volume of a rectangular prism is the products it’s dimensions. If the dimensions of a rectangle prism are approximately 1.08 feet,5.25 feet, and 3.3 feet ,what is the approximate volume of the cube?Express your answer using an approximate level of accuracy.
Answers
Answer:
18.711
Step-by-step explanation:
Volume = L * W * H
V = 1.08 * 5.25 * 3.3
1.08 * 5.25 = 5.67
5.67 * 3.3 =
V = 18.711
using sets what is the intersection of a=(-2-1,0,1,7) I=(-2,-1,1,2,8)
Answers
Factor: x^3-2x^2-8x
1. (x-4)(x+2)
2. x(x+4)(x-2)
3. x(x-4)(x+2)
4. (x-4)(x^2+2x)
Answers
Answer:
x( x-4)(x+2)
Step-by-step explanation:
x^3-2x^2-8x
First factor out the greatest common factor x
x( x^2 -2x -8)
What 2 numbers multiply to -8 and add to -2
-4*2 = -8
-4+2 = -2
x( x-4)(x+2)
A research center is interested in investigating the height and age of children who are between 5 to 9 years old. In order to do this, a sample of 15 children is selected and the data are given below.
Age (in years) Height (inches)
7 47.3
8 48.8
5 41.3
8 50.4
8 51
7 47.1
7 46.9
7 48
9 51.2
8 51.2
5 40.3
8 48.9
6 45.2
5 41.9
8 49.6
Requried:
a. Develop a scatter chart with age as the independent variable. What does the scatter chart indicate about the relationship between the height and age of children?
b. Use the data to develop an estimated regression equation that could be used to estimate the height based on the age. What is the estimated regression model?
c. How much of the variation in the sample values of height does the model estimated in part (b) explain?
Answers
Answer:
Kindly check explanation
Step-by-step explanation:
Given the data:
Age(x)
7
8
5
8
8
7
7
7
9
8
5
8
6
5
8
Height (Y)
47.3
48.8
41.3
50.4
51
47.1
46.9
48
51.2
51.2
40.3
48.9
45.2
41.9
49.6
The estimated regression equation:
ŷ = 2.73953X + 27.91395
Where ;
X = independent variable
ŷ = predicted or dependent variable
27.91395 = intercept
C.) To obtain the variation in sample values of height estimated by the model, we obtain the Coefficient of correlation:
Using the online pearson correlation Coefficient calculator :
The correlation Coefficient is 0.9696.
which means that the regression model estimated in part (b) explains approximately (0.9696 * 100) = 96.96% = 97% of the variation in the height in the sample.
Kylie has a loyalty card good for a 13% discount at her local hardware store. What number should she multiply the prices on the tags by to find the price she would have to pay, before tax, in one step?
Answers
Answer:
.87
Step-by-step explanation:
She gets 13 off so 100-13 =87
She will pay 87%
Multiply by .87
Kylie must multiply the price by 0.87 to get the discounted price.
Given that,
Kylie has a loyalty card good for a 13% discount at her local hardware store. What number should she multiply the prices on the tags by to find the price she would have to pay, is to be determined.
The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
Here,
let the price be x,
Now,
According to the question,
discounted price = x - 13% of x
Discounted price = x - 0.13x
Discounted price = 0.87 x
The coefficient of the x represents the multiplication factor for Kylie.
Thus, Kylie must multiply the price by 0.87 to get the discounted price.
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If m2 DOC = 44º and m2 COB = 80°,
find the measure of the indicated arc in circle 0.
Find measure of arc DC.
Answers
Answer:
44°
Step-by-step explanation:
Given:
m<DOC = 44°
m<COB = 80°
Required:
Angle measure of arc DC
SOLUTION:
A central angle is said to be equal to the angle measure of the arc it intercepts or corresponds with. Therefore, angle measure of arc DC = m<DOC.
measure of arc DC = 44°
The radius of a right circular cylinder is increasing at the rate of 7 in./sec, while the height is decreasing at the rate of 6 in./sec. At what rate is the volume of the cylinder changing when the radius is 20 in. and the height is 16 in.
Answers
Answer:
[tex]\approx \bold{6544\ in^3/sec}[/tex]
Step-by-step explanation:
Given:
Rate of change of radius of cylinder:
[tex]\dfrac{dr}{dt} = +7\ in/sec[/tex]
(This is increasing rate so positive)
Rate of change of height of cylinder:
[tex]\dfrac{dh}{dt} = -6\ in/sec[/tex]
(This is decreasing rate so negative)
To find:
Rate of change of volume when r = 20 inches and h = 16 inches.
Solution:
First of all, let us have a look at the formula for Volume:
[tex]V = \pi r^2h[/tex]
Differentiating it w.r.to 't':
[tex]\dfrac{dV}{dt} = \dfrac{d}{dt}(\pi r^2h)[/tex]
Let us have a look at the formula:
[tex]1.\ \dfrac{d}{dx} (C.f(x)) = C\dfrac{d(f(x))}{dx} \ \ \ (\text{C is a constant})\\2.\ \dfrac{d}{dx} (f(x).g(x)) = f(x)\dfrac{d}{dx} (g(x))+g(x)\dfrac{d}{dx} (f(x))[/tex]
[tex]3.\ \dfrac{dx^n}{dx} = nx^{n-1}[/tex]
Applying the two formula for the above differentiation:
[tex]\Rightarrow \dfrac{dV}{dt} = \pi\dfrac{d}{dt}( r^2h)\\\Rightarrow \dfrac{dV}{dt} = \pi h\dfrac{d }{dt}( r^2)+\pi r^2\dfrac{dh }{dt}\\\Rightarrow \dfrac{dV}{dt} = \pi h\times 2r \dfrac{dr }{dt}+\pi r^2\dfrac{dh }{dt}[/tex]
Now, putting the values:
[tex]\Rightarrow \dfrac{dV}{dt} = \pi \times 16\times 2\times 20 \times 7+\pi\times 20^2\times (-6)\\\Rightarrow \dfrac{dV}{dt} = 22 \times 16\times 2\times 20 +3.14\times 400\times (-6)\\\Rightarrow \dfrac{dV}{dt} = 14080 -7536\\\Rightarrow \dfrac{dV}{dt} \approx \bold{6544\ in^3/sec}[/tex]
So, the answer is: [tex]\approx \bold{6544\ in^3/sec}[/tex]
The products of (2,3) and (-2,-3) is
Answers
Answer:
(-4,-9)
Step-by-step explanation:
multiply (a,b)
How many solutions does the system of equations below have y=3x+2 y-2x=4
Answers
(2,8)
x=2
y=8
Answer:
Only one solution.
Step-by-step explanation:
y = 3x +2
y -2x =4
y - 2x = 4
=> y = 2x +4
y = 3x + 2
y = 2x + 4
Since both equations are not the same, so the answer cannot be "infinitely many solutions".
They both intersect each other 1 point, so it cannot be "no solutions".
So the answer is "Only 1 solution".
Part III- Percentage Problems
1. You currently have $4,500 saved in your bank account. You have decided to use $2700.
What percentage of your savings did you use? Show all your work to justify your answer.
2. An organization raises money for students who attend Berkeley College every year.
Currently, they have raised $11,250 which represents 45% of the money they raise.
Determine the amount of money the organization will raise in total. Show all your work
to justify your answer.
Answers
The percentage of your savings that I use is 60%
This shows that the amount of money the organization will raise in total is $25,000.
1) Given
Total amount saved = $4500
Amount used = $2,700
Percentage of money used = Amount used/Total amount saved × 100%
[tex]Percentage \ of \ money \ used = \frac{2700}{4500} \times 100\\Percentage \ of \ money = \frac{27}{45} \times 100\\Percentage \ of \ money \ used = \frac{2700}{45} \\Percentage \ of \ money \ used = 60 \%[/tex]
Hence the percentage of your savings that I use is 60%
2) Let the amount of money the organization will raise in total be x
Since the 45% of the money they raise represents $11,250, hence:
[tex]45\% \ of \ x = \$11,250\\0.45x = 11,250\\x = \frac{11250}{0.45}\\ x = 25,000[/tex]
This shows that the amount of money the organization will raise in total is $25,000
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What is the equation of the following line? Be sure to scroll down first to see all answer options.
A.
y = - 1/2x
B.
y = 1/2x
C.
y = 2x
D.
y = -6x
E.
y = 6x
F.
y = 3x
Answers
Answer:
y=-6x
Step-by-step explanation:
Choose the expression that is equivalent to -4 - (-9).
A 4 + 9
B 4 - 9
C -4 + 9
D -4 + (-9)
Answers
Answer:
d
Step-by-step explanation:
[tex]\\ \sf\longmapsto -4-(-9)[/tex]
[tex]\\ \sf\longmapsto -4+9[/tex]
Option C is correct .
Note:-
(-)(-)=(+)(+)(-)=(-)(-)(-)=(+)(+)(+)=(+)Allowance bank received a deposit of 28,000 and is free to lend out 25,480 what is the reserve rate?
Answers
Answer:
Reserve rate = 9%
Step-by-step explanation:
Reserve ratio/rate is the percentage of deposits which commercial banks are required to keep as cash, as directed by the central banks.
first, let us calculate the reserve amount as follows:
Reserve = Deposit - (free amount to lend out)
Reserve = 28,000 - 25,480 = $2,520
[tex]Reserve\ rate = \frac{Reserves}{Deposits} \times100\\Reserve\ rate = \frac{2520}{28000} \times100\\=\frac{252000}{28000} =9\%[/tex]
Therefore the reserve rate = 9%
In the expression 3x2 + y − 5, which of the following choices is the exponent in the term 3x2?
Answers
Answer:
2
Step-by-step explanation:
The term 3x² has 2 as an exponent, the correct option is C.
What are Exponents?Exponents are the base raised by power, it is written in the superscript of a number.
The expression is 3x² +y-5
The term 3x² has 2 as an exponent.
Therefore, the correct option is C.
The missing options are
A.3x2
B. y
A 2
C. -5
D. None of these choices are correct.
To know more about Exponents
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x − 6 ≤ 3 solve for x please
Answers
Answer:
x ≤ 9
Step-by-step explanation:
x − 6 ≤ 3
Add 6 to each side
x − 6+6 ≤ 3+6
x ≤ 9
Answer:
x ≤ 9
I hope this helps!
if 405 is to be divided among three persons A, B, C in the ratio of 3:5:7, how much money does each one get? Express them in percentages.
Answers
Step-by-step explanation:
Pls Mark me
Brainliest!!!!price.
A shopkeeper marks the price of his her goods 40 % above the cost price and
allows 20% discount. If his her purchase price of an item is Rs 6.000. how much
should a customer pay for it levying 13 % VAT!
e 990 the honorariter
Answers
Answer:
73%
Step-by-step explanation:
HaLP a beggar in need
Answers
Answer:
C) 2
Step-by-step explanation:
From the point (2,0), the next point on the graph is up 2, right 1, meaning that the slope is a positive 2.
What are the roots for x?
Answers
Answer:
B
Step-by-step explanation:
Use the quadractic equation, x=-b+or-sqrtb^2-4ac/2a, then simplify.
I'm really sorry that it looks messy, I don't know how to make my text look better :(
wo independent samples have been selected, 100 observations from population 1 and 76 observations from population 2. The sample means have been calculated to be x⎯⎯⎯1=11.9 and x⎯⎯⎯2=12.9. From previous experience with these populations, it is known that the variances are σ21=27 and σ22=23. (a) Determine the rejection region for the test of
Answers
Answer:
[tex]\text{Critical Region} = z<-1.96\ \text{or}\ z>1.96[/tex]
Step-by-step explanation:
A test for the difference between two population means is to be performed.
As the population variances are known, the z-test will be used.
The hypothesis can be defined as follows:
H₀: μ₁ = μ₂ vs. Hₐ: μ₁ ≠ μ₂
Assume that the significance level of the test is, α = 0.05.
The critical region can be defined as follows:
The critical value of z for α = 0.05 is:
[tex]z_{\alpha/2}=z_{0.05/2}=z_{0.025} =-1.96\\\\z_{1-\alpha/2}=z_{1-0.05/2}=z_{0.975} =1.96[/tex]
Use a z-table.
[tex]\text{Critical Region} = z<-1.96\ \text{or}\ z>1.96[/tex]
Simplify: 9h-12h=54-23
A. 3h=-77
B.3h= 31
C.-3h= -31
D.-3h= 31
Answers
Answer:
c is the answer
Step-by-step explanation:
-3h = 31
-9h-12h = -3h
54-23= 31
Answer:
[tex]\boxed{C. -3h = 31}[/tex]
Step-by-step explanation:
Hey there!
9h - 12h = 54 - 23
Simplify
-3h = 31
C. -3h = 31
Hope this helps :)
Please help. I’ll mark you as brainliest if correct
Answers
Answer:
bonds: $65,000
cd's: $30,000
stocks: $20,000
Step-by-step explanation:
b + c + s = 115000
0.045b + 0.0325c + 0.082s = 5540
b = c + 35000
b = 65,000
c = 30,000
s = 20,000
1+9+40-40+40+10x2 equals what?
Answers
Answer:
70
Step-by-step explanation:
1+9+40-40+40+10*2
----------------------- 20
10+40-40+40+20
50 (-40+40 cancels out to 0) +20
50+20= 70
(Following PEMDAS)
Multiply, add, subtract.
if you were to instead go through it left to right, you would get 120, which is incorrect.
A group of pirates captures Kevin, Lisa, Matt and Neal, and forces them to play a game. They each roll a fair 6-sided-die once. If the product of their roll is a multiple of 3, they all have to walk the plank, but otherwise they are safe. What is the probability that they survive? A)2/3 B)16/81 C)145/1296 D)65/81 E)625/1296 PLZ answer been waiting. I'll give 30 points
Answers
Answer: Option B, 16/81
Step-by-step explanation:
So we have 4 prisoners, they will roll a fair six side die and the product of the four rolls must NOT be a multiple of 3.
We know that every integer number can be "decomposed" into a product of prime numbers.
Then a number N, that is divisible by 3, can be written as:
N = 3*k
Where k is another integer.
Here we will have a product of 4 numbers, each of them are in between 1 and 6.
Now, if only one of the prisoners rolls a 3, then the product of the rolls will always be a multiple of 3. And if one of the rolls is 6 the same will happen, because 6 = 3.2
Then the probability of surviving is when in none of the four rolls we have a 3 or a 6.
Then we must have a 1, 2, 4 or 5.
The probability of 4 outcomes out of 6, is:
P = 4/6.
But we have 4 rolls, so we have that probability four times, and the joint probability will be equal to the product of the probabiliities for each roll, then the probability of surviving is:
P = (4/6)^4 = (2/3)^4 = 16/81
Answer:
16
Step-by-step explanation:
The position of an object at time t is given by s(t) = -9 - 3t. Find the instantaneous velocity at t = 8 by finding the derivative. I think its either -3 or -36
Answers
Answer:
[tex] \boxed{\sf Instantaneous \ velocity \ (v) = -3} [/tex]
Given:
Relation between position of an object at time t is given by:
s(t) = -9 - 3t
To Find:
Instantaneous velocity (v) at t = 8
Step-by-step explanation:
To find instantaneous velocity we will differentiate relation between position of an object at time t by t:
[tex] \sf \implies v = \frac{d}{dt} (s(t))[/tex]
[tex] \sf \implies v = \frac{d}{dt} ( - 9 - 3t)[/tex]
Differentiate the sum term by term and factor out constants:
[tex] \sf \implies v = \frac{d}{dt} ( - 9) - 3 (\frac{d}{dt} (t))[/tex]
The derivative of -9 is zero:
[tex] \sf \implies v = - 3( \frac{d}{dt} (t)) + 0[/tex]
Simplify the expression:
[tex] \sf \implies v = - 3( \frac{d}{dt} (t))[/tex]
The derivative of t is 1:
[tex] \sf \implies v = - 3 \times 1[/tex]
Simplify the expression:
[tex] \sf \implies v = - 3 [/tex]
(As, there is no variable after differentiating the relation between position of an object at time t by t so at time t = 8 is of no use.)
So,
Instantaneous velocity (v) at t = 8 is -3
Find a linear inequality with the following solution set. Each grid line represents one unit. (Give your answer in the form ax+by+c>0 or ax+by+c>=0 where a, b, and c are integers with no common factor greater than 1.) Help please!! I have to finish it by tonight!! Thank you!!
Answers
Answer:
Below
Step-by-step explanation:
First let's find the equation of the doted line.
Notice that the line is crossing these points:
● (0,1)
● (1,2)
The equation of the line has the following form:
● y = ax+c
C is the y-intercept wich is given by the output of 0.
Notice that the output of 0 is 1.
● y = ax+1
● a = rise / run = (2-1)/(1-0) = 1
So y = x + 1
■■■■■■■■■■■■■■■■■■■■■■■■■■
Notice that the line divide the plan into 2 areas.
● y > x+1 => x+1-y < 0
● y < x+1 => x+1 -y > 0
To khwo wich one that represent the shaded area take a point and replace x and y by its coordinates
● (-1,2)
● -1+1-2 = 0-2 = -2
It is a negative value so the inequality is
● y > x+1
giving brainliest! :)
Answers
Answer:
239=5
478=10
956=20
Step-by-step explanation:
Gianna's car can travel 478 mi with 10 gallons of gas
so, 47.8 mi with 1 gallon
by dividing 239 by 47.8 miles/gallon we get the answer 5 miles.
if we multiply 20 gallons by 47.8 mi/gallon #e get the answer 956 miles.
easy weasy
From -13°C to 15°C.
a. -28°C
b. -2°C
C. 28°C
d. 2°C
Answers
ccccccccccccccccccccccc
Answer:
Option B
-13°c-2°c= 15°c
hope it helps
3x^2+4x-5 find the coefficient
Answers
HELLO THERE
3 and 4 is the answer
I hope I helped