Answer:
10
Step-by-step explanation:
jose is x,so the penelope is 4x, eliot is x-3,
so :
x+4x+x-3=57,
then:
6x=60, x=10
The period of a pendulum is the time the pendulum takes to swing back and forth. The function Upper L equals 0.81 t squared relates the length L in feet of a pendulum to the time t in seconds that it takes to swing back and forth. A convention center has a pendulum that is 50 feet long. Find the period.
The period of a 50-foot pendulum can be found by plugging the given length into the provided pendulum function and solving for the time variable. This gives a final result after taking the square root of the division between the length and a constant.
Explanation:To find the period of a pendulum using the given length, we use the given function Upper L equals 0.81 t squared where L is the length in feet and t is the time in seconds that the pendulum takes to swing back and forth. In this case, the length of the pendulum is given as 50 feet. We plug this into the equation and solve for t:
50 = 0.81 * t^2
Rearranging this equation gives us:
t^2 = 50 / 0.81
Then we calculate the square root of this to find t:
t = sqrt(50 / 0.81)
The final answer after calculations gives the period of the pendulum.
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The period of the pendulum at the convention center, which is the time it takes to swing back and forth, is approximately 7.862 seconds. This is calculated using the given mathematical function relating length to swing time.
Explanation:The given function that relates the length L of the pendulum to the swinging time t is Upper L = 0.81 t squared. If the pendulum at the convention center is 50 feet long (L = 50), we can substitute that into the equation to find the time it takes to swing (t), which in other words is the period we are trying to determine.
So, 50 = 0.81 * t squared. Solving this equation for t, we divide both sides of the equation by 0.81 to isolate t squared. This will give us t squared = 50/0.81
t = sqrt(50/0.81) ≈ 7.862. This means that the period of the convention center's pendulum is approximately 7.862 seconds.
It’s important to note that the only factors that affect the period of a simple pendulum are its length and the acceleration due to gravity, and the pendulum performs simple harmonic motion.
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What is 15 x 11? Bjnsjxjscjsnjsnjcnsjncjsncj
Answer:
165
Step-by-step explanation:
During a sale atthe book store sold for 3$ and magazinssold for2.50. Jan spent 16$ and bought a total of 6 books and magazines. How many of each did she buy.
Answer:
6 books and 10 magazines
Step-by-step explanation:
Lanette drove 248 miles in 4 hours. At the rate, how many hours will it take her to drive a additional 93miles.
Answer:
1.5 hours
Step-by-step explanation:
using the relationship between distance/ speed / time
distance = speed × time
speed = [tex]\frac{distance}{time}[/tex] = [tex]\frac{248}{4}[/tex] = 62 mph
travelling at this rate then
time = [tex]\frac{distance}{speed}[/tex] = [tex]\frac{93}{62}[/tex] = 1.5 hours
This set of points is on the graph of a function.
{(−2, 5), (−1, 2), (0, 1), (2, 5)}
Which points are on the graph of the inverse?
Select each correct answer.
(−5, 2)
(2, −1)
(0, 1)
(5, 2)
Answers: (B) (2, -1) and (D) (5, 2)
Step-by-step explanation:
Inverse is when the x's and y's are swapped
Given: (-2, 5), (-1, 2), (0, 1), (2, 5)
Inverse: (5, -2), (2, -1) (1, 0), (5, 2)
The correct answer would be options (B) (2, -1) and (D) (5, 2)
What is an inverse function?The inverse function is defined as a function obtained by reversing the given function.
To determine the inverse of a function, all you have to do is switch where x and y are and resolve for y.
Given that the set of points is on the graph of a function.
{(−2, 5), (−1, 2), (0, 1), (2, 5)}
We have to find the inverse of the function below :
{(−2, 5), (−1, 2), (0, 1), (2, 5)}
When the values of x and y are switched, the inverse is true.
(-2, 5) ⇒ (5, -2),
(-1, 2) ⇒ (2, -1),
(0, 1) ⇒ (1, 0),
(2, 5) ⇒ (5, 2)
Hence, the points {(5, -2), (2, -1) (1, 0), (5, 2)} are on the graph of the inverse.
The correct answer would be options (B) (2, -1) and (D) (5, 2)
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Arjun can type 40 words per mintue.Dalia can type 55 words per mintue.If Arjun and dalia each type for 30 mintues,about how many more words will Dalia type
Answer: 450 words
Step-by-step explanation:
Arjun: [tex]\dfrac{40 words}{1minute} \times\dfrac{30minutes}{} = 1200 words[/tex]
Dalia: [tex]\dfrac{55 words}{1minute} \times\dfrac{30minutes}{} = 1650 words[/tex]
Dalia - Arjun
= 1650 - 1200
= 450
I have tryed to find this problem and I can't everytime I try the numbers that are to high for the answer what I'm I doing wrong the problem is 51/2*21/3=
Answer:
1071/2
when you multiply the top you get 1071 and when you multiply the bottom you get 6. But if u want to simplify the answer could be 357/2
Plzzz give brainlest and thank me
Answer:
178.5
Step-by-step explanation:
First, Do 51/2, which is 25.5
Second do 25.5*21, which is 535.5
Third, do 535.5/5, which would be 178.5
So, the answer is 178.5
Hope this helps :)
The cone shown has a diameter of 18 m and a slant height of 15 m which choice is closest to the lateral surface area
Answer:
[tex]423.9 m^2[/tex] is the required lateral surface area of the cone.
Step-by-step explanation:
The lateral surface area of cone is:
[tex]\pi\cdot r\sqrt{h^2+r^2}[/tex]
Slant height is l which is [tex]l=\sqrt{h^2+r^2}[/tex]
We have given diameter 18 m
Since, radius is half of diameter so r=18/2 =9
Slant height l =15
[tex]\pi=3.14[/tex]
On substituting the values in the formula we get:
[tex]3.14\cdot 9\cdot 15[/tex]
On simplification we get:
[tex]3.14\cdot 135[/tex]
Further simplification will give:
[tex]423.9 m^2[/tex] is the required lateral surface area of the cone.
Jaime has 6 quarters and some dimes in his pocket . The total value of the coins in 4.50. How many dimes does he have in his pockets
Hi there! :)
Answer:
Jaime has 30 dimes in his pocket.
Step-by-step explanation:
First off, you need to know that:
A quarter is equal to = $0.25
A dime is equal to = $0.10
Jaime has 6 quarters, which means that he has 6 times $0.25:
6 × 0.25 = $1.50
Jaime has a total of $4.50 → Subtract the amout of money represented by the quarters and you'll be left with the amout of money represented by the dimes:
4.50 - 1.50 = $3
Jaime has $3 worth of dimes in his pocket. In order to know how many dimes $3 represents, you'll need to divide "3" by 0.10, which is what 1 dime is worth:
3 ÷ 0.10 = 30 → YOUR ANSWER
There you go! I really hope this helped, if there's anything just let me know! :)
ΔABC is an equilateral triangle. m∠A = (3x - 12)°. Solve for x. A) 14 B) 19 C) 20 D) 24
Answer:
option (d)
Step-by-step explanation:
An equilateral triangle is a triangle whose all the sides are equal and all the angles are same.
There are three angles in a triangle and the according to the property of the angles of a triangle, the angle sum of a triangle is 180°.
So, in an equilateral triangle, the measure of each angle is 60°.
[tex]3x-12= 60[/tex]
3x = 60 + 12
3x = 72
x = 24
option (d)
The rectangle below has an area of x^2-11x+30x 2 −11x+30x, start superscript, 2, end superscript, minus, 11, x, plus, 30 square meters and a length of x-5x−5x, minus, 5 meters. what expression represents the width of the rectangle?
Answer:
[tex](x-6)[/tex] meters
Step-by-step explanation:
We have been given that the area of a rectangle is [tex]x^2-11x+30[/tex] square meters and a length of [tex](x-5)[/tex] meters.
Since the area of a rectangle is product of its width and length.
[tex]\text{Area of rectangle}=\text{Width of rectangle*Length of rectangle}[/tex]
We can find width of our rectangle by dividing area of rectangle by length of rectangle.
[tex]\text{Width of rectangle}=\frac{\text{Area of rectangle}}{\text{Length of rectangle}}[/tex]
Let us substitute our given values in above formula.
[tex]\text{Width of rectangle}=\frac{x^2-11x+30}{x-5}[/tex]
Let us factor out numerator by splitting the middle term.
[tex]\text{Width of rectangle}=\frac{x^2-6x-5x+30}{(x-5)}[/tex]
[tex]\text{Width of rectangle}=\frac{x(x-6)-5(x-6)}{(x-5)}[/tex]
[tex]\text{Width of rectangle}=\frac{(x-6)(x-5)}{(x-5)}[/tex]
Upon cancelling out x-5 from numerator and denominator we will get,
[tex]\text{Width of rectangle}=(x-6)[/tex]
Therefore, the expression [tex](x-6)[/tex] meters represents width of the rectangle.
Answer:
the answer is x - 6, have a nice day
The product of the roots of $2x^2 - 7x + N = 0$ is $-5.$ Find $N.$
By the fundamental theorem of algebra, we can factorize the quadratic as
[tex]2x^2-7x+N=2(x-r_1)(x-r_2)[/tex]
so that expanding the right hand side gives
[tex]2x^2-7x+N=2x^2-2(r_1+r_2)x+2r_1r_2[/tex]
[tex]\implies\begin{cases}-2(r_1+r_2)=-7\\2r_1r_2=N\end{cases}[/tex]
We're told that the product of the roots is -5, or [tex]r_1r_2=-5[/tex], so we get
[tex]2(-5)=N=-10[/tex]
The value of N for given conditions is -10. It can be calculated as shown below.
Given that:The quadratic equation given is: [tex]2x^2 -7x + N = 0[/tex]
The product of roots of given equation is: -5
To find: Value of N
Explanation for product of roots and Calculations:For quadratic equation [tex]ax^2 + bx + c = 0[/tex], we have:
[tex]\text{Product of roots} = \dfrac{c}{a}\\\\\text{Sum of roots} = \dfrac{-b}{a}[/tex]
For given quadratic equation, we have:
a = 2, b = -7, c = N
Thus, by above formula:
[tex]\text{Product of roots} = \dfrac{c}{a} = \dfrac{N}{2} = -5\\\\N = -5 \times 2 = -10[/tex]
Thus, value of N for given conditions is -10.
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A line has a slope of -4/5. Which ordered pairs can be points on the line is perpendicular to this line
Answer:
Any ordered pairs which have a slope of 5/4.
Step-by-step explanation:
The line has a slope of -4/5 which means the y values have a difference of -4 and the x values have a difference of 5. If the line is perpendicular to this line then its slope must be the negative reciprocal which is 5/4. Any points which have a difference in y values of 5 and a difference of x values of 4 will be on some line perpendicular to the original.
Show you work for full credit Use the SUBSITUTION method or ELIMINATION method to solve this system of equations:
IF YOU THINK YOUR SMART OR AT A HIGH RANK THEN ANSWER 3 QUESTIONS FOR ME....BTW I'LL GIVE YOU BRAINLIEST.
1. Ronald is making hats and scarves for charity. He has enough yarn to make 5 hats and 8 scarves. It takes him 12 hours to knit a hat and 6 hours to knit a scarf; he has 20 hours to knit.
Let x represent the number of hats made. Let y represent the number of scarves made.
Which inequalities are among the constraints for this situation?
Select each correct answer.
A) y≤8
B) 12x+6y≤20
C) x≤5
D) 5x+8y≤20
E) x+y≤20
2. Which ordered pairs lie on the graph of the exponential function f(x)=2^(x+4) −8?
Select each correct answer.
A) (−2,−4)
B) (2, 56)
C) (8, 0)
D) (24, 1)
3. The expression 15.85(1+x) gives the total cost of a toy, where x is the sales tax written in decimal form.
What does 1 + x represent in the expression?
A) percent of original price being paid in tax
B) cost of toy
C) percent of tax
D) amount of tax
Answer:
B, D, E- 12 per hat so 12x / 6 per scarf 6x
A - Graph then find the order pair on the line
?
Problem 1
Answer: Choice A, Choice B, and choice C
---------
Explanation:
x = number of hats made,
12*x = total time to knit just hats (12 hrs to do 1 hat)
y = number of scarves made
6*y = total time to knit just scarves (6 hrs to do 1 scarf)
In total, it takes 12x+6y hours to knit everything (scarves+hats) and we want this total time to be 20 or less, so this means choice B is one of the answers
Choice A and choice C are also answers because they restrict how many scarves and hats we can make. Choice A says we can make at most 8 scarves. Choice C says the max number of hats we can make is 5.
The other inequalities won't apply so they can be crossed off the list.
=============================
Problem 2
Answer: choice A and choice B
---------
Explanation:
If you plug in x = -2 and simplify, you'll end up with f(x) = -4, so that helps confirm A is one of the answers. Choice B is the other answer because x = 2 leads to f(x) = 56
In contrast, if you plugged in x = 8, you'd end up with 4088 which is way off of the y coordinate 0 listed. The same story happens with x = 24 but the result is much much larger.
=============================
Problem 3
To be honest, I'm not sure what to make of this problem. If x is the decimal form of the sales tax, then 1+x would be the multiplier to help get the total cost. For example, if x = 0.02 then 1+x = 1+0.02 = 1.02, meaning that the final cost (after tax) is 102% of the original cost (before tax)
1+x isn't the amount of tax as that would be 15.85*x
The percent of tax would be 100*x (eg: x = 0.02 so 100*x = 100*0.02 = 2% tax rate)
The cost of the toy is given to be 15.85 so that answer is out as well.
=============================
Will mark you as brainiest
if right!! Please Please answer this question! I need it done by 4 P.M. Eastern Time
Which answers describe the end behaviors of the function modeled by the graph?
f(x)=−3^(x+2)−2
Select each correct answer.
As x increases without bound, f(x) increases without bound.
As x decreases without bound, f(x) approaches the line y=−2.
As x increases without bound, f(x) approaches the line y=−2.
As x increases without bound, f(x) decreases without bound.
This is a multiple choice question, so there might be 2 answers.
Answer:
Option B and D are correct.
Step-by-step explanation:
Given the function: [tex]y=f(x) = -3^{x+2}-2[/tex]
End behavior states that a polynomial function is the behavior of the graph of as approaches positive infinity or negative infinity.
As [tex]x \rightarrow \infty[/tex] in the given function, then [tex]f(x) \rightarrow -\infty[/tex]
and
As [tex]x \rightarrow -\infty[/tex] in the given function, then [tex]y=-2[/tex]
Therefore, as x increases without bound , f(x) decreases without bound
and as x decreases without bound , f(x) approaches the line y =-2
If property damage due to erosion along the coast is $60 million each year, how many money would be spent in 4 years?
What is the solution of the system?
Use the substitution method.
{3x+2y=11x−2=−4y
The only solution is (12, −52) .
The only solution is (4, −12) .
There is no solution.
There are an infinite number of solutions.
Answer: [tex]\bold{\text{b.}\bigg(4,-\dfrac{1}{2}\bigg)}[/tex]
Step-by-step explanation:
x - 2 = -4y → x = 2 - 4y
3x + 2y = 11
3(2 - 4y) + 2y = 11 replaced "x" with (2 - 4y)
6 - 12y + 2y = 11 distributed "3" on left side
6 - 10y = 11 added like terms (-12y + 2y)
- 10y = 5 subtracted "6" from both sides
y [tex]= -\dfrac{1}{2}[/tex] divided both sides by -10
Next, solve for x:
x = 2 - 4y
[tex]= 2 - 4(-\frac{1}{2} )[/tex]
= 2 + 2
= 4
Answer:
your answer would be b
Step-by-step explanation:
Tickets to a baseball game cost $22 each and parking costs $10. What is the equation of the line that represents the cost of attending the game?
x - number of games
22x - cost of x tickets
10 - parking cost
The equation:
[tex]y=22x+10[/tex]
Answer:
y = 22x + 10
Step-by-step explanation:
Given,
The cost of each ticket = $ 22,
Let x be the number of tickets,
Then, the cost of x tickets = x × cost of each ticket
= 22x dollars,
Now, parking cost = $ 10,
So, the total cost of attending the game ( say y ) = cost of all tickets + parking cost
⇒ y = 22x + 10
Which is the required equation.
If xy= -20 -2y= -6. What's the value of x
Answer:
x = -6 2/3 or -20/3
Step-by-step explanation:
So we know:
-2y = -6
Divide -2 on both sides
y = 3
Plug that into the other equation:
3x = -20
divide 3 on both sides
x = -20/3 or -6 2/3
(r3 +6r2 −21r−18)÷(r−3) solve using synthetic division
Answer:
y = x^2 + 9x + 6 No remainder.
Step-by-step explanation:
The divisor will be 3 The sign on the divisor switches.
3 || 1 + 6 - 21 - 18 ||
3 27 + 18
================================
1 9 6 0
The answser is x^2 + 9x + 6
Janine is packing carrots. Each large box holds 20 2-pound bags of carrots. If Janine has 800 bags of carrots, how many boxes can she fill?
Answer: 40 Boxes
Step-by-step explanation: All you need to do is divide 800 by 20.
Answer:
40
Step-by-step explanation:
Blueberries are on sale for $2.80 per pint. The regular price is $3.50 per pint. What is the percent of decrease? Select from the drop-down menu to correctly complete the statement.
0.2
0.25
0.7
20
25
70
Answer:
it is 20% can you mark me brainless
Step-by-step explanation:
Select all that apply.
Solve for x , 0 < x < 360. 1/sin^2x = 4
answer choices (choose all that apply)
30
150
210
330
Answer:
30,150, 210 ,330
Step-by-step explanation:
1/sin^2x = 4
Multiply each side by sin^2x
1 = 4 sin^2 x
Divide each side by 4
1/4 = sin^2 x
Take the square root of each side
sqrt(1/4) = sqrt(sin^2 x)
±sqrt(1/4) = sin x
±1/2 = sinx
Take the inverse sin of each side
arcsin (1/2) = arcsin (sin x) and arcsin(-1/2) = arcsin (sin x)
30 = x -30 = x
But this is not between 0 and 360,
so we add 360
-30+360 = 330
We also have to look at the other locations where sin x = 1/2
Taking the arcsin only gives values between -90 and 90
Since we are looking at the sin value, we take 180 - the value given
180 -30 = 150
180 --30
180+30 = 210
So our values are 30, 150,210,330
A square of area 36cm is cut to make two rectangles a and b the ratio of area a to b is 2:1 work ou the dimensions of rectangles a and b
Answer:
The dimensions of rectangle a are 6x4 and dimensions of rectangle b are 6x2.
Step-by-step explanation:
We are given a square with area 36 squared cm. Therefore, dimension of the square will be 6 cm.
The square is cut into two rectangles with areas in the ratio 2:1.
Let the dimensions of the rectangles be 6*a and 6*b. Therefore, we can set up the ratio of areas as:
[tex]\frac{6a}{6b}=\frac{2}{1} \\a=2b[/tex]
Moreover, we can set the combined area of rectangles equal to the area of square to form another equation:
[tex]6a+6b=36\\a+b=6[/tex]
Using substitution method, we can solve for 'a' and 'b' as shown below:
[tex]2b+b=6\\3b=6\\b=2[/tex]
And
[tex]a=2b\\a=2(2)\\a=4[/tex]
Therefore, dimensions of the two rectangles are 6x4 and 6x2, respectively.
Consider the scatter plot.
Consider the scatter plot. The line of best fit is
The line of best fit is y = 0.75x + 5.
Choose the best representation for the y-intercept.
The y-intercept of the line of best fit shows that when time started, the distance was 0.75 feet.
The y-intercept of the line of best fit shows that after 0.75 minutes, the distance was 5 feet.
The y-intercept of the line of best fit shows that when time started, the distance was 5 feet.
The y-intercept of the line of best fit shows that when time started, the distance was 0 feet.
Answer:
The correct answer option is: The y-intercept of the line of best fit shows that when time started, the distance was 5 feet.
Step-by-step explanation:
We are given a scatter plot with a best fit line as shown on the given graph.
The equation of the best fit line is given by:
y = 0.75x + 5
So with the help of the equation and by looking at the given graph, we can conclude about the representation of the y intercept that the the y-intercept of the line of best fit shows that when time started, the distance was 5 feet.
Since the distance shown on the y axis is already 5 when the time started at 0 minutes.
Suppose there are 10 green, 8 brown, 3 yellow, 8 blue, and 6 red candies in a bag. If you randomly pick out one candy, what is the probability it is red or yellow?
Answer:
9/35, 0.257 or 25.7%Step-by-step explanation:
The basic and simple way to calculate the probability of an event happening is by using this equation:
Number of desired outcomes------------------------------------------------- = Probability Number of all possible outcomesOur desired outcomes are picking either red or yellow candies. The number of desired outcomes in this case is the total number of red and yellow candies. 6 red + 3 yellow = 9
Number of desired outcomes = 9
Number of all possible outcomes in this case is the total number of candies in the bag. 10 green + 8 brown + 3 yellow + 8 blue + 6 red = 35
Number of all possible outcomes = 35
Use the formula and we get that the probabbility of drawing out a yellow or red candy is: 9/35, 0.257 or 25.7% (those are 3 different ways to write the probability)
What is the justification for each step in solving the inequality?
3x+5/8≥4x−1/2
Select from the drop-down menus to correctly justify each step.
3x+5/8≥4x−1/2 Given
3x≥4x−9/8 ?????
−x≥−9/8 ?????
−x/−1≥−9/8/−1 ?????
x≤9/8 ?????
Chose from
Multiplication or Division property of order
Distributive property
Addition or Subtraction property of order
Step-by-step explanation:
[tex]3x+\frac{5}{8}\geq 4x-\frac{1}{2}[/tex]
Subtract 5/8 on both sides
To subtract 5/8 we make the denominators same
[tex]3x\geq 4x-\frac{1*4}{2*4}-\frac{5}{8}[/tex]
Addition or Subtraction property of order is used
[tex]3x\geq 4x-\frac{9}{8}[/tex]
Subtract 4x on both sides
Addition or Subtraction property of order is used
[tex]-x\geq -\frac{9}{8}[/tex]
Now divide both sides by -1
Multiplication or Division property of order is used
[tex]\frac{-x}{-1} \geq \frac{-\frac{9}{8}}{-1}[/tex]
Multiplication or Division property of order is used
[tex]x\leq \frac{9}{8}[/tex]
Final answer:
The justification for solving the inequality involves using the Addition or Subtraction property of order to combine like terms and isolate the variable, and the Multiplication or Division property of order to solve for the variable, with an important note that dividing both sides by a negative number reverses the inequality symbol.
Explanation:
The justification for each step in solving the inequality 3x + 5/8 ≥4x − 1/2 can be broken down as follows:
3x + 5/8 ≥4x − 1/2 Given
3x ≥4x − 9/8 Addition or Subtraction property of order, subtracting 5/8 from both sides
−x ≥ − 9/8 Addition or Subtraction property of order, subtracting 4x from both sides
−x / −1 ≥ −9/8 / −1 Multiplication or Division property of order, dividing both sides by −1
x ≤9/8 Multiplication or Division property of order, understanding that dividing by a negative number reverses the inequality symbol
Each step involves manipulating the inequality while maintaining the balance, and the direction of the inequality changes when both sides are multiplied or divided by a negative number.
How to solve
3 log 2x=4
Answer:
= 5 * 10 ^ 1/3
Step-by-step explanation:
3 log 2x=4
Divide each side by 3
3/3 log 2x=4/3
log 2x=4/3
Raise each side to the power of 10
10 ^(log 2x)=10 ^(4/3)
2x = 10 ^(4/3)
Divide by 2
2/2x = 1/2 * 10 ^(4/3)
x = 1/2 * 10 ^4/3
10 ^ 4/3 = 10 * 10 ^ 1/3
x = 1/2 ( 10) 10 ^ 1/3
= 5 * 10 ^ 1/3
Please help me simplify this! I have no idea how to solve this question! Thank you if you do!