which statement compares the graphs of f(x) and g(x) over the interval [0, 5]?
A) The graph of f(x) always exceeds the graph of g(x) over the interval [0, 5]
B) The graph of g(x) always exceeds the graph of f(x) over the interval [0, 5]
C) The graph of f(x) exceeds the graph of g(x) over the interval [0, 4], the graphs intersect at a point between 4 and 5, and then the graph of g(x) exceeds the graph of f(x)
D) The graph of g(x) exceeds the graph of g(x) over the interval [0, 4], the graphs intersect at a point between 4 and 5, and then the graph of f(x) exceeds the graph of g(x)
we can see that
For x is 0, 1, 2, 3 ,4
f(x) is 0 , 1 , 4, 9 , 16
g(x) is -2 , -1 , 1 , 5 , 13
so, g(x) is greater than f(x) for x is 0, 1, 2, 3 ,4
It means that f(x) exceeds g(x) on [0,4]
But for x=5
f(x) is 25
g(x) is 29
Here, we can see that g(x) exceeds f(x) at x=5
so, there must be intersection point between x=4 and x=5
so, option-C.........Answer
Each option describes different behaviors and relationships between the two functions over the interval [0, 5]. Without further details, we can only conceptualize the scenarios provided.
To compare the graphs of f(x) and g(x) over the interval [0, 5], we can evaluate the options provided:
Option A: The graph of f(x) always exceeds the graph of g(x) over the interval [0, 5]Option B: The graph of g(x) always exceeds the graph of f(x) over the interval [0, 5]Option C: The graph of f(x) exceeds the graph of g(x) over the interval [0, 4], the graphs intersect at a point between 4 and 5, and then the graph of g(x) exceeds the graph of f(x)Option D: The graph of g(x) exceeds the graph of f(x) over the interval [0, 4], the graphs intersect at a point between 4 and 5, and then the graph of f(x) exceeds the graph of g(x)Without the exact equations or a graph to analyze, we cannot definitively determine which option is correct. However, we can conceptualize the scenarios described:
Option A suggests f(x) is consistently greater than g(x) throughout the interval. Option B suggests the opposite. Option C introduces an intersection point, where f(x) transitions from being greater to less than g(x). Option D indicates g(x) is initially greater, with a reversal after an intersection between 4 and 5.
If we had the graphs or more specific information, we could more precisely identify the correct statement.
find the slope of the line containing the following two points
The slope is -22/9. Use the formula (y2-y1)/(x2-x1)
(-1/3 +4)/(-1/3-7/6)
Name two points on a line that has a slope of 5/8
The two points on a line such that it has a slope 5/8 is:
(0,0) and (8,5)
Step-by-step explanation:We know that the slope of a line is the ratio of the change in the y-coordinates to the change in the x-coordinates.
Now, let us assume that the equation of a line with slope 5/8 be given by:
[tex]y=\dfrac{5}{8}x[/tex]
Hence, the point (0,0) lie on the line.
( since, when x=0 we have:
[tex]y=\dfrac{5}{8}\times 0\\\\y=0[/tex] )
and also the point (8,5) lie on the line.
( when x=8 we have:
[tex]y=\dfrac{5}{8}\times 8\\\\y=5[/tex] )
How many congruent triangles do the midsegments of an equilateral triangle partition the triangle into? Explain.
Answer:
4
Step-by-step explanation:
Let us consider an equilateral triangle ABC. Now, we will define midsegments:
A midsegment of a triangle is a segment that connects the midpoints of two sides of a triangle (here triangle ABC). This segment has two special properties. It is always parallel to the third side, and the length of the midsegment is half the length of the third side.
Refer the attached image:
Now, from the definition of midsegment we can see that:
[tex]PQ=\frac{1}{2}BC[/tex]
[tex]\therefore PQ=BR[/tex]
and PQ is also parallel to BR.
Now, again from the definition of midsegment we can see that:
[tex]QR=\frac{1}{2}AB[/tex]
[tex]\therefore QR=PB[/tex]
and QR is parallel to PB.
therefore, PQBR forms a parallelogram
And a diagonal of a parallelogram divides it into two congruent triangles.
Hence, triangle 2 (triangle PBR) is congruent to triangle 4(triangle PQR).
Similarly, triangle 3 (triangle QRC) and triangle 1 (triangle APQ) are congruent to triangle 4 (triangle PQR), Therefore, there are 4 congruent triangles formed when midsegments of an equilateral triangle partition the triangle.
The midsegments of an equilateral triangle partition it into four smaller congruent triangles, due to the Triangle Midsegment Theorem and the Third theorem of congruence for triangles.
When the midsegments of an equilateral triangle are drawn, they connect the midpoints of the sides of the triangle. These segments will each be parallel to one side of the triangle and half its length, according to the Triangle Midsegment Theorem. Drawing all three midsegments partitions the equilateral triangle into four congruent smaller triangles. Each smaller triangle will be similar to the original equilateral triangle.
By the Third theorem of congruence for triangles (which is often referred to as SSS or side-side-side), if three sides of one triangle are congruent respectively to the corresponding sides of another triangle, the two triangles are congruent. In this case, each smaller triangle formed by the midsegments shares a side with the original triangle and has the other two sides equal in length to the midsegments, which are congruent to each other by construction.
Therefore, all four smaller triangles are congruent to each other.
a spherical container with a radius of 4 ft is filled with gas that costs$12 per cubic foot what is the total value of the gas in the container
We calculate the volume of the sphere to find the amount of gas it can hold, then we multiply this volume by the price per cubic foot to get the total cost of the gas, which is $3216.96.
Explanation:The problem is asking us to determine the total value of gas in a spherical container given the radius of the sphere (container) and the cost of gas per cubic foot.
Firstly, we need to calculate the volume of the sphere using the formula: V = 4/3 * pi * r^3, where r is the radius of the sphere. Substituting the given radius, V = 4/3 * pi * 4^3 = 268.08 cubic feet
Then, we find the total value of the gas by multiplying the volume of the gas by the cost per cubic foot. So, the total value = volume * cost = 268.08 * 12 = $3216.96
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The total value of the gas in the container is $3216.96.
Explanation:To find the total value of the gas in the container, we first need to calculate the volume of the gas.
The formula to find the volume of a sphere is V = (4/3) * π * r^3, where r is the radius of the sphere.
Plugging in the given radius of 4 ft, we get V = (4/3) * π * (4^3) = 268.08 ft^3.
Next, we multiply the volume of the gas by the cost per cubic foot to find the total value.
Multiplying 268.08 ft^3 by $12/ft^3, we get a total value of $3216.96.
Therefore, the total value of the gas in the container is $3216.96.
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If f(x)=5x-3 and f(x)=7, what is the value of x?
5x - 3 = 7
Add 3 to both sides.
5x = 10
Divide both sides by 5.
x = 2
The value of x is 2.
What is 12x - 5 = 127
Here is your equation:
[tex]12x-5=127[/tex]
You're trying to find x, and to do that, the variable must be alone. That means you need to cancel out everything with it. The only thing with the variable 12x is -5. To cancel that out, you have to do the opposite of it, which is +5. Add 5 to both sides.
[tex]12x-5+5=127+5 \\12x=132[/tex]
12x(12 times x) is equal to 132. You need to find x. You have to do the opposite of times 12, which is divide by 12. Divide both sides by 12.
[tex]\frac{12x}{12} = \frac{132}{12} \\ \\x=11[/tex]
Your answer is x is equal to 11 ; x = 11
If you have any questions, feel free to ask in the comments! :)
what is the slope of the line? (Slope from equation)
7x+2y=5
thanks.
Answer:
The slope is -7/2.
Step-by-step explanation:
Convert to slope-intercept form (y = mx + b where m = the slope)
7x + 2y = 5
2y = -7x + 5
Divide both sides by 2:-
y = (-7/2)x + 5/2
so slope m = -7/2
chris is 3 years older than jacob. Nathan is 18 years old. two years ago the sum of all their ages was 59 years old how old is jacob?
Today 2 years ago
Chris: x + 3 (x + 3) - 2 = x + 1
Nathan: 18 (18) - 2 = 16
Jacob: x (x) - 2 = x - 2
Chris + Nathan + Jacob = sum
x + 1 + 16 + x - 2 = 59
2x - 15 = 59 added like terms (x and x) and (1, 16, and -2)
2x = 74 added 15 to both sides
x = 37 divided both sides by 2
Answer: Jacob is 37 yrs old
what is t(6) for the function t(n)=0.009n
a)0.054
b)0.0096
c)6.009
What is 3/8 + b/3= 5/12
Final answer:
To solve the equation 3/8 + b/3 = 5/12 for b, we find a common denominator, combine the fractions, and then isolate and solve for b. The solution for b is 1/8.
Explanation:
The equation presented by the student is 3/8 + b/3 = 5/12. To solve for b, we must first get a common denominator for the fractions to combine them. In this case, the common denominator is 24, since it is the least common multiple of 8 and 3. Multiplying each term by 24 yields:
(3/8)*24 + (b/3)*24 = (5/12)*24
9 + 8b = 10
Next, we isolate the variable b by subtracting 9 from both sides of the equation:
8b = 10 - 9
8b = 1
Finally, divide both sides by 8 to solve for b:
b = 1/8
Thus, the value of b that satisfies the given equation is 1/8.
What is the value of f?
6f-12= -4f+6
[tex]6f-12=-4f+6\qquad|\text{add 12 to both sides}\\\\6f=-4f+18\qquad|\text{add 4f to both sides}\\\\10f=18\qquad|\text{divide both sides by 10}\\\\\boxed{f=1.8}[/tex]
Tiffany has $54. She is shopping for umbrellas that cost $12 each. She writes the following equation to model the situation. Place Value Chart
Answer:
4 umbrellas
Step-by-step explanation:
Number of Umbrellas Total Money
1 $12
2 $24
3 $36
4 $48
She can't go over $48 because $48 + $12 is $60, which is more than she has ($54). So the max amount of umbrellas she can buy is 4.
is 20x9x5 a associative or distributive property?
A toll collector on a highway receives $8 for cars and $9 for buses. At the end of a 4-hour period, she collected $368. How many cars and buses passed through the toll booth during that period? Select ALL THAT APPLY: 40 cars and 5 buses!!37 cars and 8 buses!!22cars and 21 buses!!28 cars and 16 buses!!0 cars and 41 buses!!46 cars and 0buses!!4cars and 37 buses!! 10 cars and 32 buses!! 1car and 40 buses!!19 cars and 24 buses
Applying the concept of Algebra, the toll collector processed 40 cars and 5 buses during a 4-hour period. This is found by checking each option against the equations 8c + 9b = 368 and c + b = total number of vehicles (where c = cars and b = buses).
Explanation:To solve this problem, we need to find the number of cars and buses that make up the total toll collected, which is $368. We can set up a system of equations to solve for the two variables: number of cars (c) and number of buses (b).
So, we have two equations: 8c + 9b = 368 and c + b = total number of vehicles. By checking each option, only 40 cars and 5 buses match these equations, because 8*40 + 9*5 = 368.
So, the toll collector processed 40 cars and 5 buses during the 4 hour period.
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How many solutions does the equation have?
9z+10=1−3(5−3z)
9z + 10 = 1 - 3(5 - 3z) use distributive property
9z + 10 = 1 + (-3)(5) + (-3)(-3z)
9z + 10 = 1 - 15 + 9z
9z + 10 = -14 + 9z subtract 9z from both sides
10 = -14 FALSE
NO SOLUTION
Answer: zero solutions.
Answer:
[tex] \sf \: z = no \: solution[/tex]
Step-by-step explanation:
Given equation,
→ 9z + 10 = 1 - 3(5 - 3z)
Now the value of z will be,
→ 9z + 10 = 1 - 3(5 - 3z)
→ 9z + 10 - 1 = -15 + 9z
→ 9z + 9 = -15 + 9z
→ 9z - 9z = -15 - 9
→ 0 = -24
→ [ z = no solution ]
Hence, there is no solution.
WILL GIVE BRAINLIEST. is my answer correct
I’m pretty sure you are
finding terms of an arithmetic sequence with a recursive formula
a1 =12 an= an-1+7
Hey there!!
Recursive formula :
... a( n ) = a ( n - 1 ) + 7
The first term is 12
To find the second term, we will need to substitute 2 in place of ' n '
2 term :
... a( 2 ) = a ( 2 - 1 ) + 7
... a( 2 ) = a( 1 ) + 7
We know a( 1 ) = 12
... a( 2 ) = 12 + 7
... 19 is the second term and we will need to use this to find the other terms.
Hope my answer helps!
Is (2,10) a solution of the equation y = 9x
This line is already in slope-intercept form.
The slope of the line is 9, and the y-intercept is 0.
Because of this, we can find every y value for any x value simply by replacing x with the value of the x coordinate.
By replacing x with 2, we can see what the y coordinate would be when x is 2.
9(2) = 18
The y value would be 18, which is not 10, meaning (2, 10) is not a solution to the equation.
The point (2,10) is not a solution to the equation y = 9x because when x is substituted into the equation, it results in y = 18, not y = 10 as in the point.
To determine if the point (2,10) is a solution to the equation y = 9x, we need to substitute the x-value from the point into the equation and see if the corresponding y-value matches the one in the point. Let's substitute x = 2 into the equation:
y = 9 x 2
y = 18
For the point (2,10), the y-value is 10, which does not equal the calculated y-value of 18. Therefore, the point (2,10) is not a solution to the equation y = 9x.
Which choice solves the problem?
1467÷7=
A) 29 with a remainder of 4
B) 207 with a remainder of 4
C) 209
D) 209 with a remainder of 4
D) 209 with a remainder of 4
The question is about the division of 1467 by 7. The answer is '209 with a remainder of 4'.
Explanation:This question is about division in mathematics. To solve this, we will divide 1467 by 7. Division is really repeated subtraction. You subtract 7 from 1467 as many times as you can until you get a number smaller than 7. That number is called the 'remainder', and the number of times you could subtract is the 'result' of the division.
After the division, the quotient is 209 and the remainder is 4. Therefore, the correct option is 'D) 209 with a remainder of 4'.
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A total value of $6,000 is invested into two simple interest accounts. The annual simple interest rate on one account is 9%; on the second account, the annual simple interest rate is 6%. How much should be invested in each account so that both accounts earn the same amount of annual interest.
hello there this one was tricky i looked at it for sevrel minutes and solve dit
the answer is 50%
To obtain the same annual interest on both accounts, $3,600 should be invested at 9%, and $2,400 should be invested at 6%.
Explanation:To solve this problem, we need to use the formula for simple interest, which is I = PRT, where P is the principal amount (the initial amount of money), R is the annual interest rate in decimal form, and T is the time the money is invested for in years. Here, we want both accounts to earn the same annual interest, so we'll let x be the amount of money invested at 9%, and 6000 - x be the amount of money invested at 6%. The annual interest for both should be the same, so:
x × 0.09 = (6000 - x) × 0.06
Solving for x, we get x = $3,600. So, $3,600 should be invested at 9%, and $2,400 ($6,000 - $3,600) should be invested at 6% to obtain the same annual interest.
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Solve each system by substitution. Show ALL work!!!!
1) y=2x-1
6x-3y=7
Solution:
Work:
To solve the given system of equations by substitution, 'y' from the first equation is substituted into the second, resulting in x = 4/3. Substituting this into the first equation yields y = 5/3. Therefore, the solution to the system is x = 4/3, y = 5/3.
Explanation:To solve the given system of equations by substitution, we will start with the first equation y = 2x - 1 and substitute it into the second equation 6x - 3y = 7.
Substituting 'y' from the first equation into the second, we get: 6x - 3(2x - 1) = 7.
Solving this, we find 'x': 6x - 6x + 3 = 7 => x = 7/3 = 4/3.
Next, we substitute 'x' into the first equation to find 'y': y = 2(4/3) - 1 = 8/3 - 1 = 5/3.
So, the solution to the system of equations is x = 4/3, y = 5/3.
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Becky gets $5.00 a week for chores, and helps with chores for 4 weeks. If Becky wants to spend only half of her money, how much will she have left to save?
$5.00 x 4 = $20.00.
$20.00 divided by 2 = $10.00
She will have $10.00 to save.
Hope I helped!
Good Luck!
Can someone find the unit rate of $46 for 5 toys, and add an explanation and how to do it?!?!? ASAP HELP!!
Not sure if I am right but I looked online for you and it said divide the numerator and the denominator by the given rate so I guess you do 46 divided by 5 I'm sorry if I am wrong nd let me know
The unit rate of $46 for 5 toys is calculated by dividing the total cost by the number of toys, resulting in $9.20 per toy.
This question demands complete basic understanding of mathematical concepts in general and division in particular.
To find the unit rate of $46 for 5 toys, you divide the total cost by the number of toys. This calculation will give you the cost of one toy. Here's how it's done step-by-step:
Write down the total cost for all the toys, which is $46.Write down the total number of toys, which is 5.Divide the total cost by the number of toys to find the unit rate: $46 / 5 toys = $9.20 per toy.So, as per the above explaination, the unit rate is $9.20 per toy.
Which sequence of transformations creates a similar, but not congruent, triangle?
A Rotation and translation
B Dilation and rotation
C Reflection and rotation
D Translation and reflection
Answer:
It would be B.
Step-by-step explanation:
Dilation is the only transformation that is NOT congruent. It is similar.
Andrew deposited $500 in a savings account that offers an interest rate of 6.5%, compounded continuously. Andrew's initial deposit will grow to $543 in ___ months.
Answer:
The answer is 15 months.
Step-by-step explanation:
p = $500
r = 6.5% or 0.065
A = $543
t = ?
The formula to be used here is :
[tex]A=pe^rt[/tex]
[tex]t=(log(A/p)/log(e))/r[/tex]
Putting the values in formula we get:
[tex]t=(log(543/500)/log(e))/0.065[/tex]
[tex]t=(log(1.086)/log(e))/0.065[/tex]
This gives t = 1.3 years
In months it will be 1 year(12 months) + 3 months = 15 months.
Hence, the answer is 15 months.
Answer:
15 months
Step-by-step explanation:
examine the diagram on the right and explain how it illustrates the value of n^+n/2
the key is to write [tex]n^2 + n[/tex] as [tex]n(n+1)[/tex] which can be easily seen as an area of a rectangle with one side length n and the other (n+1). That explains the rectangle made of dots - 3 x 4
Now you only have half of them because of the 1/2. So that explains the lower "triangle" of dots being greyed out - they do not count in the area (upper triangle). So the count of the dark dots corresponds to the original expression.
For n=5 you can draw a similar rectangular matrix with 5 x 6 dots. And count only the upper triangular part.
How do you use elimination in math?
In order to use the elimination method, you have to create variables that have the same coefficient—then you can eliminate them. Next add the equations, and solve for y or x. Once you find out the value of either y or x you can substitute into one of the original equations to find x or y.
A dog takes 3 steps to walk the same distance for which a cat takes 4 steps. If 1 step of the dog covers 1/2 door how many feet will the cat cover on 24 steps?
Answer:
9 feet will the cat cover on 24 steps.
Step-by-step explanation:
Given: A dog takes 3 steps to walk the same distance for which a cat takes 4 steps.
⇒ 3 steps of dog=4 steps of Cat
If 1 step of the dogs cover [tex]\frac{1}{2}[/tex] feet
then,
4 steps of cat=3 steps of dog
24 steps of cat=[tex]\frac{3}{4}\times(24)[/tex]=18 steps of dog
Also, 1 step of the dogs cover=[tex]\frac{1}{2}[/tex] feet
18 steps of the dogs cover=9 feet
therefore, 24 steps of cat will cover 9 feet .
A roller coaster car rapidly picks up speed as it rolls doen a slope. As it starts down the slope, it's speed is 4m/s. But 3 seconds later, at the bottom of the slope, it's speed is 22m/s. What is its average acceleration?
The average is 18m/s.
The average acceleration of the roller coaster car is [tex]\( 6\, \text{m/s}^2 \)[/tex].
The average acceleration of the roller coaster car is calculated using the formula:
[tex]\[ a = \frac{{v_f - v_i}}{{\Delta t}} \][/tex]
where [tex]\( v_f \)[/tex] is the final velocity, [tex]\( v_i \)[/tex] is the initial velocity, and [tex]\( \Delta t \)[/tex] is the time interval over which the acceleration occurs.
Given:
[tex]- Initial velocity (\( v_i \)) = 4 m/s \\- Final velocity (\( v_f \)) = 22 m/s\\ - Time interval (\( \Delta t \)) = 3 s[/tex]
Plugging in the values:
[tex]\[ a = \frac{{22\, \text{m/s} - 4\, \text{m/s}}}{{3\, \text{s}}} \] \[ a = \frac{{18\, \text{m/s}}}{{3\, \text{s}}} \] \[ a = 6\, \text{m/s}^2 \][/tex]