First, we can use the points (4,3) and (20,15) to find the slope of the line:
[tex]\begin{gathered} s=\frac{m_2─m_1}{j_2─j_1}=\frac{15─3}{20─4}=\frac{12}{16}=\frac{3}{4} \\ s=\frac{3}{4} \end{gathered}[/tex]Now we can find the relation function using the point (4,3) and the slope s=3/4
[tex]\begin{gathered} m─m_1=s(j─j_1) \\ \Rightarrow m─3=\frac{3}{4}(j─4)=\frac{3}{4}j─(\frac{12}{4})=\frac{3}{4}j─3 \\ m=\frac{3}{4}j \end{gathered}[/tex]therefore, the equation to describe the relationship between J and M is m=3/4j
A fair coin is flipped 10 times. Each flip is independent.
What is the probability of getting exactly eight heads?
Answer:
8 out of 10.
Step-by-step explanation:
if you flip a coin independent then it doesn't matter what the other outcomes are. So if it's a one out of two chance every time then it's 8 /10.
which of the following coordinates represent a point on the Y - axis choose all that apply
Question 7:
The y-axis on a graph is the vertical line on a graph, it represents the dependent variable.
Any point on the y-axis of a graph, has an x-value of zero.
Therefore, from the list given, any coordinate with an x-value of zero is on the y-axis.
Apply the point form: (x, y)
The following coordinates represent a point y-axis:
(x, y) ==> (0, -4)
(x, y) ==> (0, 3)
ANSWER:
(0, -4)
(0, 3)
i need help with my homework please check work when done I NEED HELP WITH THE QUESTION IN BLUE
Amount invested by Katelyn = $4000
rate = x%
time = x + 2 years
n = number of times compounded
n = annually = 1
We need to find the function that models the total amount
To find the function, we will apply the compound interest formula:
[tex]\begin{gathered} $$FV\text{ = P(1 +}\frac{r}{n})^{nt}$$ \\ \\ P\text{ = 4000} \\ t\text{ = x + 2} \\ n\text{ = 1} \\ \text{ r = x\% = x/100} \\ FV=\text{ total amount } \end{gathered}[/tex]substitute the values into the formula:
[tex]\begin{gathered} FV=\text{ 4000\lparen 1 + }\frac{\frac{x}{100}}{1})^{1\times(x\text{ + 2\rparen}} \\ \\ FV=\text{ 4000\lparen1 + }\frac{x}{100})^{x+2} \end{gathered}[/tex][tex]FV=\text{ 4,000\lparen}\frac{100+\text{ }x}{100})^{x\text{ +2}}\text{ }[/tex]let the function that represents the total amount = f(x)
[tex]f(x)=\text{ 4000\lparen}\frac{\text{ }x+\text{ 100}}{100})^{x\text{ +2}}\text{ }[/tex]Mid point of -2,11 and 18,-1
The midpoint of (-2, 11) and (18, -1) is:
[tex]\begin{gathered} \bar{x}=\frac{-2+18}{2}\rightarrow\bar{x}=8 \\ \\ \bar{y}=\frac{11-1}{2}\rightarrow\bar{y}=5 \end{gathered}[/tex]Point (8,5)
A ride sharing company offers two options: riding in small cars that can carry up to 3 passengers each, or riding in large vans that can carry up to 6 passengers each. A group of 27 people is going to use the ride sharing service to take a trip. The trip in a small car costs $10 and the trip in a large van costs $15. The group ends up spending $80 total.What do x and y represent?
Answer:
x = no of people in a small car
y = number of people in a van
Explanation:
The relevant information in the problem is that the total number of people is 27 and that the small car costs $10 and the large van $15.
If we call x the number of people in a small car, and y the number in the large van then the following equations can be obtained
[tex]\begin{gathered} x+y=27 \\ 10x+15y=80 \end{gathered}[/tex]The first equation simply says that the total number of people is 27 and the second equation says that the total cost of the trip is $80.
Hence,
x = no of people in a small car
y = number of people in a van
Find the ordered pair $(x,y)$ if
\begin{align*}
x+y&=(3-x)+(3-y),\\
x-y &=(x-2)+(y-2).
\end{align*}
Thanks
In accordance with the system of linear equations, the ordered pair is (x, y) = (1, 2).
How to find the values associated to an ordered pair
Ordered pairs are constructions characterized by two components, typically real numbers. The most common form of notation is (x, y). In this problem we need to resolve a system of linear equations to obtain the needed values. We find a system of two equations and two variables:
x + y = (3 - x) + (3 - y)
x - y = (x - 2) + (y - 2)
First, simplify each expression of the system:
First equation:
x + y = 6 - x - y
2 · x + 2 · y = 6
x + y = 3
Second equation:
x - y = (x - 2) + (y - 2)
x - y = x + y - 4
- 2 · y = - 4
y = 2
Second, substitute in the first equation:
x + 2 = 3
x = 1
The ordered pair is (x, y) = (1, 2).
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A chemist is using 363 milliliters of a solution of acid and water. If 13.6% of the solution is acid, how many milliliters of acid are there? Round your answer to the nearest tenth.
If 13.6% of the solution is acid ,then 49.4 milliliters of acid are there .
In the question;
it is given that
the total solution of acid and water is 363 milliliters .
and also it is given that 13.6% of the solution is acid ,
which means
the amount of acid in solution = 13.6% of total solution
Substituting the values , and
on solving further ,
we get
amount of acid in solution = 0.136×363 ......as 13.6% = 0.136
= 49.368
≈ 49.4 milliliter
Therefore , if 13.6% of the solution is acid ,then 49.4 milliliters of acid are there .
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an industrial manufacturing company uses an inverted conical (cone-shaped) tank to dispense liquid into containers. the tank measure 24 inches with a base radius of 48 inches. if the liquid flows out of the tank at a rate of 40 cubic inches per minute, at what rate is the height of the liquid falling when the height of the liquid is 10 inches deep?
If the liquid flows out of the tank at a rate of 40 cubic inches per minute, the height of the liquid will decrease at rate 0.0318 in./minute
Referring to the attached picture, the two triangles in a cone are similar. Hence,
r/h = 48/24
or
r = 2h.
The volume of the liquid is given by:
V = 1/3 . πr²h
Substitute r = 2h,
V = 1/3 . π(2h)²h = 4/3 . πh³
Take the derivative with respect to t
dV/dt = 4/3 . 3πh² . dh/dt
dV/dt = 4 . πh² . dh/dt
Substitute dV/dt = -40 and h = 10
-40 = 4 . π(10)² . dh/dt
dh/dt = - 0.0318 in./minute
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Solve for X round to nearest tenth
Answer:
the answer for this question is 35.0
The perimeter of a square can be found using p=n+n+n+n
Answer: Well, yes. It's more like p = s + s + s + s. "S" = side. "P" = perimeter.
So, this is theoretically true if your variable for a side just happened to be "n".
You also put, "The perimeter of a square", A simpler way to put this is
P = s4 or in your case P = n4.
Because this shape is a square all side lengths and angles will be congruent, and therefore will all be the same (which is why we are able to multiply one side by four.)
Hope this helps. :)
To eliminate the x terms and solve for y in the fewest steps, by which constants should the equations be multiplied by before adding the equations together?
First equation:
Second equation:
The first equation should be multiplied by 3 and the second equation by -5.
The first equation should be multiplied by 3 and the second equation by 5.
The first equation should be multiplied by 7 and the second equation by -6.
The first equation should be multiplied by 7 and the second equation by 6.
Answer: the answer is c)The first equation should be multiplied by 7 and the second equation by -6.
Step-by-step explanation:edge 2022
Answer:
C
Step-by-step explanation: -6
Martha has 4 different colored pens in her bag. After she uses a pen she just throws it back into bag. If she does this 5 day a week, how many different ways can she use the pens for the week?.
By likelihood, she can utilize the pens in 1024 distinct ways during the week.
Probability is the study of possible outcomes of events, together with the probabilities and distributions of those occurrences.
Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.
To calculate probability, divide the total number of outcomes by the total number of possible possibilities. There are differences between probability and odds.
Odds are computed by dividing the likelihood that an event will occur by the likelihood that it won't.
From the stated circumstance,
Total ways = [tex]4^{5}[/tex]= 1024
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Given f(x)=x+2 and g(x)=4-x^2 find the following (g o f)(x)
Given functions are
[tex]\begin{gathered} f(x)=x+2 \\ g(x)=4-x^2 \end{gathered}[/tex]Then,
[tex]\begin{gathered} (g\circ f)(x)=g(f(x)) \\ =g(x+2) \\ =4-(x+2)^2 \\ =4-(x^2+4x+4) \\ =4-x^2-4x-4 \\ =-(x^2+4x) \end{gathered}[/tex]Thus,
[tex](g\circ f)(x)=-(x^2+4x)[/tex]Scientists are studying the temperature on a distant planet. They find that the surface temperature at one location is 45 ° Celsius. They also find that the temperature decreases by 7 ° Celsius for each kilometer you go up from the surface. Let T represent the temperature (in Celsius), and let H be the height above the surface (in kilometers). Write an equation relating T to H , and then graph your equation using the axes below.
The equation relating T to H is H = 45 - 7T.
What is temperature?Temperature simply means the degree of hotness and coldness in a body.
In this case, they find that the surface temperature at one location is 45 ° Celsius. They also find that the temperature decreases by 7 ° Celsius for each kilometer you go up from the surface.
Let T = the temperature (in Celsius).
Let H = the height above the surface (in kilometers).
The equation will be:
H = 45 - (7 × T)
H = 45 - 7T
The axes aren't given and can't be graphed.
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Solve the given linear equation.14x + 4 = 8x + 23x =
We have to solve this linear equation for x:
[tex]\begin{gathered} 14x+4=8x+23 \\ 14x-8x+4-4=8x-8x+23-4 \\ 6x+0=0x+19 \\ 6x=19 \\ x=\frac{19}{6} \\ x\approx3.16\ldots \end{gathered}[/tex]The answer is x=19/6
PLEASE HELP ASAPPP!!!!!!!!!!!!!!!!!!!!!
PLEASE HELP ASAP!!!!
The quadratic function f(x) has roots of −4 and 2 and point (1, −5) lies on f(x). What is the equation of f(x)?
f(x) = (x − 2)(x + 4)
f(x) = (x − 2)(x − 4)
f(x) = 4(x − 2)(x + 4)
f(x) = 4(x − 2)(x − 4)
The function has an equation of f(x) = (x + 4)(x - 2)
How to determine the equation of f(x)?The given parameters in the question are
Roots = -4 and 2
Point = (1, -5)
The above parameters can be rewritten as
Roots: x = -4 and x = 2
Point: (x, y) = (1, -5)
A quadratic equation can be represented as
f(x) = a * (x - Roots)
Where Roots: x = -4 and x = 2
The above parameters imply that we have the following equation
y = a(x + 4)(x - 2)
From the question, we have
(x, y) = (1, -5)
This gives
-5 = a(1 + 4)(1 - 2)
Divide
a = 1
Substitute a = 1 in y = a(x + 4)(x - 2)
y = (x + 4)(x - 2)
Hence, the equation of the quadratic function f(x) is f(x) = (x + 4)(x - 2)
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Answer: The answer would be A: f(x) = (x − 2)(x + 4)
Step-by-step explanation: I got it right on my test
X=
/////////////////////
Answer: [tex]x=15[/tex]
Step-by-step explanation:
By the consecutive interior angles theorem,
[tex]150+3x-15=180\\\\3x-15=30\\\\3x=45\\\\x=15[/tex]
Find the slope of the line that passes through the following points: (-4,-2) and (-3,5)
What is the solution to this equation?
5(x-3) = 21
A x =
OB x=
36
5
D x=
65
6
5
24
OC X= 5
18
5
Answer:
x = 7.2
Step-by-step explanation:
[tex]5(x - 3) = 21[/tex]
[tex]x - 3 = 4.2[/tex]
[tex]x = 7.2[/tex]
What is the solution of the system of equations below?
y+2x=2 y+4x=0
GIVING 100 POINTS PLEASE HELP
Answer: (-1, 4)
Step-by-step explanation: y=-2x+2, y=-4x Solve for the first variable in one of the equations, then substitute the result into the other equation.
Answer this question using SUBSTITUTION:
Substitution is a method to solving a system of equations through substituting one of the variables for another equation.
y + 2x = 2
y + 4x =0 (rewrite this equation so y is isolated: y =4x)
Since y=4x you can substitute the y in y +2x =2 and solve for x:
4x + 2x =2
6x = 2
x = [tex]\frac{1}{3}[/tex]
Now, plug in x into y =4x:
y = 4 ([tex]\frac{1}{3}[/tex]) = [tex]\frac{4}{3}[/tex] or [tex]1\frac{1}{3}[/tex]
x= [tex]\frac{1}{3}[/tex]
y = [tex]\frac{4}{3}[/tex] or [tex]1\frac{1}{3}[/tex]
Chocolate milk Riley mix five scoops of chocolate powder with 3 cups of milk Brooke mixes 6 cups of chocolate powder with 4 cups of milk whose mixture is more chocolatey explain how you know
This mixture has an extra scoop of chocolate ice cream so will taste more chocolatey than 3 scoops of chocolate ice cream and 2 cups of milk.
The line containing the points (14, 15) and (20, 24) crosses the y-axis at what point?
The linear equation that passes through the points (14, 15) and (20, 24) crosses the y-axis at y = -6.
How to get the y-intercept?
A general linear equation can be written as:
y = m*x + b
Where m is the slope and b is the y-intercept.
If the line passes through two points (x₁, y₁) and (x₂, y₂), then the slope can be written as:
m = (y₂ - y₁)/(x₂ - x₁).
In this case the line passes through (14, 15) and (20, 24) so the slope is:
m = (24 - 15)/(20 - 14) = 9/6 = 3/2
y = (3/2)*x + b
To find the y-intercept we can replace the values of one of the points, like (14, 15)
15 = (3/2)*14 + b
15 = 3*7 + b
15 = 21 + b
15 - 21 = b
-6 = b
The y-intercept is -6.
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what is the effect on the graph of the function f(x) = x² when f(x) is changed to f(x + 8) ?A) shifted upB) shifted leftC) shifted right D) shifted down
Solution
- The rule for this transformation is given below:
[tex]\begin{gathered} f(x)\to f(x+h) \\ when\text{ h is positive, then, the graph is shifted left} \\ when\text{ h is negative, then, the graph is shifted right} \end{gathered}[/tex]- Based on this rule, f(x + 8) will shift the graph 8 units to the left
Final Answer
Shifted left (OPTION B)
Is (x-3) a factor of 2x^3 -4x^2-6?
1) (Type yes or no in the first blank)
2) What is the remainder?
(Type the answer in the second blank)
1. x - 3 is not a factor
2. The remainder is 32.
1. How to determine if x - 3 is a factor of 2x³ - 4x² - 6?Using the remainder theorem, which states that for a polynomial p(x), if x - a is a factor, then p(a) = 0.
So, p(x) = 2x³ - 4x² - 6 If x - 3 is a factor, then
p(3) = 0
So, substituting x = 3 into the equation, we have
p(3) = 2x³ - 4x² - 6
= 2(3)³ - 4(2)² - 6
= 2(27) - 4(4) - 6
= 54 - 16 - 6
= 54 - 22
= 32
Since p(3) ≠ 0.
x - 3 is not a factor
2. What is the remainder?Since p(3) = 32,
The remainder is 32.
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insert parentheses to make the expression true
4×2+3×2=32
Answer:
4 * ( 2 + 3 * 2) = 32
Step-by-step explanation:
The strategy I used in this question is generally trial and error. The most important thing here to remember is to follow the order of operations. If you think a little out of the box, then you will see the answer. To solve, first multiply 3*2, then add two, which should result in 8. 4*8 is 32, which makes the equation true.
A ball, dropped vertically falls d metres in t seconds
d is directly proportional to the square of t
The ball drops 125 metres in the first 5 seconds
How far does the ball drop in nthe next 9 seconds?
The distance covered in the next 9 seconds is 405 meters
How to determine the distance coveredThe variation statement is given as
d is directly proportional to the square of t
This means that
d = kt²
Where k represents the constant of variation
Using the parameters in the question, we have
When d = 125, t = 5
Substitute d = 125, t = 5 in d = kt²
This gives
125 = k x 5²
Evaluate
k = 5
So, we have
d = 5t²
After 9 seconds, we have
t = 9
Substitute t = 9 in d = 5t²
Here, we have
d = 5 x 9²
This gives
d = 405
Hence, the distance is 405 meters
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In one year, a school uses 13,480 pieces of white paper, 7,880 fewer pieces of blue paper thanwhite paper, and 1,500 fewer pieces of yellow paper than blue paper. How many pieces of paperdoes the school use in all?
Answer:
23,180 pieces
Explanation:
The number of white paper used = 13,480 pieces
Since they used 7,880 fewer pieces of blue paper than white paper
The number of blue paper used = 13,480 - 7880 =5,600 pieces
They also used 1,500 fewer pieces of yellow paper than blue paper.
The number of yellow paper used = 5,600-1500 =4100 pieces
Therefore. the total number of pieces of paper
=13,480 + 5,600 + 4100
=23,180 pieces
explain how you got the answer
Slope - 2/3
y - intercept : (0,3)
x | y
0 | 3
3 | 1
The radioactive substance cesium-137 has a half-life of 30 years. The amount A(t) (in grams) of a sample of cesium -137 remaining after t years is given by the following exponential function.A (t) = 523 (1/2)^t/30Find the initial amount in the sample and the amount remaining after 100 years.Round your answers to the nearest gram as necessary.Initial amount:Amount after 100 years:
After 100 years:
Replace t by 100:
A (t) = 523 (1/2)^t/30
A (100) = 523 (1/2)^100/30 = 523 (1/2) ^10/3 = 51.88 =52 grams
The initial amount of the sample is 523
24. Anna went bowling. She spent less than or equal to $30, but spent more
than $25. Create a number line that shows all the possible amounts that
Anna may have spent at the bowling alley.
All the possible amounts that Anna may have spent at the bowling alley are presented on the number line.
What is a number line?In mathematics, a numbered line is a straight line with numbers organized at regular intervals or sections throughout its breadth. The beginning of period is frequently shown laterally and may be shifted in any position.
Anna visited a bowling alley. She did not spend less than or equal to $30, but she did spend more than $25.
The inequality is given as,
$25 < x ≤ $30
All the possible amounts that Anna may have spent at the bowling alley are presented on the number line.
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