Which fraction is NOT equivalent to 4/12?
A. 1/3 B. 12/30 C. 8/24 D. 16/48
What is the first step to writing an equation of a line when given two points?
I'm in high school and need help with this problem. 2x +y = -13 x= 3x+y
Hi! Please help... a woman drops a front door key to her husband from their apartment window several stories above the ground. the function h=-16t^2 +64 gives the height h of the key in feet, t seconds after she releases it.
A/ how long does it take the key to reach the ground?
B/ what are the reasonable domain and range for the function h? ...?
Answer:
It would take 2 seconds to the key to reach the ground.
The domain the function is: 0≤t≤2 or in interval notation [0,2].
The range of the function is: 0≤h≤64 or in interval notation [0,64].
Step-by-step explanation:
The provided function is: [tex]h=-16t^2 +64[/tex]
Where h represents the height and t represents the time.
Part(A) how long does it take the key to reach the ground?
When key will be at ground, the height will be 0.
Substitute the value of h=0 in above equation and solve for t.
[tex]-16t^2 +64=0[/tex]
[tex]-16(t^2 -4)=0[/tex]
[tex](t^2 -2^2)=0[/tex]
[tex](t+2)(t-2)=0[/tex]
[tex]t+2=0\ or\ t-2=0[/tex]
[tex]t=-2\ or\ t=2[/tex]
Ignore the negative value of t.
Hence, it would take 2 seconds to the key to reach the ground.
Part (B) what are the reasonable domain and range for the function h?
Time and Distance should be a positive number.
Thus, the value of t and h should be greater or equal to 0.
From the part (a) we know that the after 2 second the key will hit the ground so the value of t can be greater or equal to 0 but should be less or equal to 2.
Thus, the domain the function is: 0≤t≤2 or in interval notation [0,2].
The maximum height of the key will be at t=0.
Thus the maximum value of h can be 64 and minimum value can be 0.
The range of the function is: 0≤h≤64 or in interval notation [0,64].
Name the property of 11xn=1
. To change the shape of a function, you need to _____ or compress it.
A. compress
B. stretch
C. shift
D. flip
Answer:
B. Strech
Step-by-step explanation:
Stretching can change the shape of something such as a function.
Slope is - 3 And (0,-4) is on the line
The Sugar Sweet Company is going to transport its sugar to market. It will cost
$4500 to rent trucks, and it will cost an additional $175 for each ton of sugar transported. Let C represent the total cost (in dollars), and let S represent the amount of sugar (in tons) transported. Write an equation relating C to S. Then use this equation to find the total cost to transport 19 tons of sugar.
The des moines register recently reported the ratings of high school sportsmanship as complied by the iowo high school athletic association. For each school, the participants and coaches were rated by referees, where 1= superior, and 5= unsatisfactory. A regression analysis of the averages scores given to football players and coaches is shown below.
interpret the value of the correlation between the ratings of coaches and participants.
Which graph represents a reflection of f(x) = 2(0.4)x across the y-axis?
Answer: The correct option is A.
Explanation:
The given function is,
[tex]f(x)=2(0.4)^x[/tex]
To find the graph of this function after the reflecting across y-axis, first we have to find the graph of the equation.
The value of the function is 2 when x=0, so, the graph of given equation intersect the y-axis at 2.
In the equation [tex](0.4)^x[/tex]. Since [tex]0<0.4<1[/tex], so the given function is decreasing function.
[tex]f(x)\rightarrow 0 \text{ as }\rightarrow \infty[/tex]
[tex]f(x)\rightarrow \infty \text{ as }\rightarrow -\infty[/tex]
The value of f(x) is always positive, so the graph of f(x) is always above the x-axis. Thus, the graph must be above the x-axis after reflection across y-axis.
So, the option (2) and (4) and incorrect.
When we reflect the graph across the y-axis then,
[tex]f(x)\rightarrow \infty \text{ as }\rightarrow \infty[/tex]
[tex]f(x)\rightarrow 0 \text{ as }\rightarrow -\infty[/tex]
It means when x approaches to large negative number the f(x) approaches to 0 and when x approaches to large positive number the f(x) approaches to infinite.
Therefore, the correct option is show in first graph.
Answer:
a
Step-by-step explanation:
Which of the following is not a valid postulate or theorem for proving triangles congruent?
A. SSA
B. ASA
C. AAS
D. SAS
The valid postulates and theorems for proving triangles congruent are ASA, AAS, and SAS. The SSA postulate is not a valid postulate.
Explanation:The valid postulates and theorems for proving triangles congruent are ASA (Angle-Side-Angle), AAS (Angle-Angle-Side), and SAS (Side-Angle-Side).
The SSA (Side-Side-Angle) postulate, also known as the ambiguous case of the Law of Sines, is not a valid postulate for proving triangles congruent because it can result in two different triangles or no triangle at all.
Thus, the correct answer is A. SSA.
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Solve the differential equation using the method of undetermined coefficients
a) 4y"- 4y'-3y= cos2x
help please?
solve for Y
a(y+c)=b(y-c)
solve for W
A=lw+wh+lh
...?
**!!!STUCK ON 2 QUESTIONS!!!!
The time is takes to mow the lawn at a large park m(x) varies inversely with the numbers of workers assigned to the job x. It takes 90 minutes to complete the job when 3 workers are assigned to it.
which equation can be used to find the time to complete the job when x workers are assigned to it?
A.) m(x)= 270/x
B.) m(x) = 270x
C.) m(x) = 30/x
D.) m(x) = 30x
2. Suppose that H(x) varies inversely with x and H(x)=50 when x =0.25
What is H(x) when x =2?
A.) 0.5
B.) 6.25
C.) 12.5
D.) 24
Can you also provide how you got the answer as well :)
Answer:
1. Which equation can be used to find the time to complete the job when x workers are assigned to it?
A.) m(x) = 270/x
2. Suppose that H(x) varies inversely with x and H(x)=50 when x =0.25
What is H(x) when x =2?
B.) 6.25
Step-by-step explanation:
1. We know when x=3 (workers), m(x)= 90 min (time is takes to mow the lawn at a large park) and we know m(x) varies inversely with x, this means when m(x) increases so x decreases. This is obtained with a division over x.
Now, we can replace to know what is the correct answer:
[tex]m(x)=\frac{y}{x} (1) \\90=\frac{y}{3} \\90*3=y[/tex]
[tex]y=270[/tex]
The answer is A.
[tex]m(x)=\frac{270}{x}[/tex]
We can confirm if we replace x=3 in the equation before. Our answer should be 90.
[tex]m(x)=\frac{270}{3}=90[/tex]
2. Suppose that H(x) varies inversely with x and H(x)=50 when x =0.25
We know H(x) varies inversely with x, this means when H(x) increases so x decreases. This is obtained with a division over x. Now, we need to find the constant in the numerator.
Now, we can replace in the eq (1) to know the constant in the numerator:
[tex]H(x)=\frac{y}{x}\\50=\frac{y}{0.25} \\50*0.25=y[/tex]
[tex]y=12.5[/tex]
Now, we can replace in the eq (1) to find H(x) when x=2
[tex]m(x)=\frac{y}{x}[/tex]
[tex]m(x)=\frac{12.5}{2}[/tex]
[tex]m(x)=6.25[/tex]
The answer is B.) 6.25
Which answer shows these decimals written in order from greatest to least? 46.95
48.1
46.581
What is the midpoint of 0.7 0.8?
Two particles are fixed to an x axis: particle 1 of charge -1.00 x 10-7 C is at the origin and particle 2 of charge +1.00 x 10-7 C is at x = 17.1 cm. Midway between the particles, what is the magnitude of the net electric field?
...?
The following data values represent a population. What is the variance of the values?
8, 10, 14, 12
A.22
B.11
C.5
D.10
Answer:
It’s actually 5
Step-by-step explanation:
Ape x
The product of 9 and a number is 12 less than three times that number.
What is the number?
Which of the following options is an equivalent function to f(x) = 3(2)3x?
f(x) = 3(8)x
f(x) = 24x
f(x) = 27(8)x
f(x) = 3(8x)
The correct option is A: [tex]\( \boxed{f(x) = 3(8)^x} \).[/tex]
To determine which option is equivalent to the given function f(x) = [tex]3(2)^{3x} \),[/tex] we will simplify the given function and compare it to each option.
The given function is:
[tex]\[ f(x) = 3(2)^{3x} \][/tex]
We can rewrite the exponent part using properties of exponents:
[tex]\[ (2)^{3x} = (2^3)^x = 8^x \][/tex]
So the function becomes:
[tex]\[ f(x) = 3 \cdot 8^x \][/tex]
Now, let's compare this to each of the given options:
Option A: [tex]\( f(x) = 3(8)^x \)[/tex]
This is exactly the same as our simplified function. Therefore, Option A is equivalent to [tex]\( f(x) = 3(2)^{3x} \).[/tex]
Option B: [tex]\( f(x) = 24^x \)[/tex]
This is not equivalent because it implies a different base raised to the power of x.
Option C:[tex]\( f(x) = 3(8x) \)[/tex]
This is not equivalent because it multiplies by 27 instead of 3.
Option D: [tex]\( f(x) = 3(8x) \)[/tex]
This is not equivalent because it implies multiplying 8 by x, not raising 8 to the power of x.
Therefore, the correct answer is:
[tex]\( \boxed{f(x) = 3(8)^x} \).[/tex]
The complete question is here:
Which of the following options is an equivalent function to f(x) = 3(2)3x?
A. f(x) = 3(8)x
B. f(x) = 24x
C. f(x) = 27(8)x
D. f(x) = 3(8x)
-1.4n + 2.1 = 6.58
what is n
Solve the system of equations and choose the correct ordered pair.
3x + 2y = 12
6x + 3y = 21
A. (4, 3)
B. (4, 0)
C. (2, 3)
D. (3, 2)
Answer:
C.
Step-by-step explanation:
We are going to solve it with substitution, that is, we are going to clear one variable and then replace it in the other equation. Then,
[tex]3x + 2y = 12[/tex]
[tex]3x = 12-2y[/tex]
[tex]x = \frac{12-2y}{3}[/tex]
[tex]x = \frac{12}{3}-\frac{2y}{3}[/tex]
[tex]x = 4-\frac{2y}{3}.[/tex]
Now, we replace that x value in the equation 6x + 3y = 21:
[tex]6(4-\frac{2y}{3}) + 3y = 21[/tex]
[tex]24-\frac{12y}{3} + 3y = 21[/tex]
[tex]24-4y + 3y = 21[/tex]
[tex]24-y = 21[/tex]
[tex]-y = 21-24[/tex]
[tex]-y = -3[/tex]
[tex]y = 3.[/tex]
Finally, we replace the y value found to find x.
[tex]x = 4-\frac{2*3}{3}[/tex]
[tex]x = 4-2[/tex]
[tex]x = 2.[/tex]
So, the solution is (x,y)=(2,3). Then, the answer is C.
a factory makes 1200 pounds of potato chips in four hours at this rate how many pounds of potato chips will a factory make in 10 hours
A factory producing 1200 pounds of chips in four hours will yield 3000 pounds when operating for 10 hours, assuming a consistent production rate.
Explanation:The given problem pertains to rate, which allows the determination of how much of something can be done in a specific amount of time. In this case, the rate of potato chip production is 1200 pounds every four hours. To find out how many pounds of potato chips can be produced in 10 hours, we first need to determine the hourly rate of production.
Firstly, we determine the hourly production rate of the factory by dividing the total produce by the time spent. That is 1200 pounds / 4 hours = 300 pounds/hour.
At this hourly rate, the amount of potato chips that can be produced in 10 hours can be calculated by multiplying the hourly rate by the number of hours, which is 300 pounds/hour * 10 hours = 3000 pounds.
So, a factory that produces 1200 pounds of potato chips in four hours will make 3000 pounds of potato chips in 10 hours.
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keisha is reading a 325 page book at a rate of 25 pages per day. use a point slipe equation to determine whether she will finish reading the book in 10 days.
Using the point slope equation, it is determined that Keisha will not finish reading the 325 pages book in 10 days if she is reading at a rate of 25 pages per day.
Explanation:The subject of this question is Mathematics and it involves solving a problem using a point slope equation.
Let's denote the total number of pages in the book as 'y' and the number of pages that Keisha can read per day as 'm'. We know that y=325 and m=25. The point slope equation in this case would be y=mx, where 'x' represents the number of days. In this case, we are trying to find out whether x=10.
Substituting the known values into the equation we get: 325=25*10. This simplifies to 325=250.
Since 325 does not equal 250, we can conclude that Keisha will not complete reading the book in 10 days.
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The formula for an object's final velocity is f=i−gt f=i−gt . Solve for t.
answer: (f-i)/-g=t
I hope it helps~
which correctly describes the root of the following cubic equation? x^3-3x^2+4x-12=0
Answer:
The equation has one real root and two complex roots.
Step-by-step explanation:
The given equation is
[tex]x^3-3x^2+4x-12=0[/tex]
The above equation is true form x=3, therefore (x-3) is a factor of above equation.
Use long division or synthetic division method to divide the equation by (x-3).
[tex](x-3)(x^2+4)=0[/tex]
Equate each factor equal to zero.
[tex]x-3=0[/tex]
[tex]x=3[/tex]
Therefore 3 is a real root of the equation.
[tex]x^2+4=0[/tex]
[tex]x^2=-4[/tex]
[tex]x=\sqrt{-4}[/tex]
[tex]x=\pm 2i[/tex]
2i and -2i are complex roots of the equation.
Therefore the equation has one real root and two complex roots.
4 questions that I don't understand how to do. Help please?
page 128 slopes and intercepts
Mark all of the statements that are true.
(will attach graph shortly)
a. The range for this function is the set {3}.
b. This graph is not a function because the value of y is the same for every value of x.
c. The domain for this function is all real numbers.
d. The domain for this function is the set {3}.
e. All real numbers are in the range of this function.
***CHOOSE ALL THAT APPLY!! And please explain!! :)
i am the only number between 41 and 49 that has 5 as a factor. what number am i?