Find the value of x and rs if s is between r and t rs = 5x, st = 3x, and rt = 48
Answers
Answer: 6
Step-by-step explanation:
By the segment addition postulate,
5x + 3x = 48
8x = 48
x = 6
Related Questions
Which of the following shows the equation of a line with slope - 2 passing through (3,-2)?
(1) y = 2x +7
(3) y=-2x-1
(2) y = 2x - 8
(4) y=-2x+4
Answers
mx" + cx' + kx = F(t), x(0) = 0, x'(0) = 0 modeling the motion of a damped mass-spring system initially at rest and subjected to an applied force F(t), where the unit of force is the Newton (N). Assume that m = 2 kilograms, c = 8 kilograms per second, k = 80 Newtons per meter, and F(t) = 50 sin(6t) Newtons. Solve the initial value problem. x(t) = help (formulas) Determine the long-term behavior of the system (steady periodic solution). Is lim x(t) = 0? If it is, enter zero. If not, enter a function that approximates x(t) for very large positive values of t. For very large positive values of t, x(t) ≈ xsp(t) = 00+1 help (formulas)
Answers
The x(t) ≈ xsp(t) = (25/127)cos(6t) - (3/127)sin(6t) for very large positive values of t.
Given equation is mx''+cx'+kx=F(t), where m=2 kg, c=8 kg/s, k=80 N/m, and F(t)=50 sin(6t) Newtons.
We need to solve the initial value problem where x(0)=0, x'(0)=0. This is a second-order linear differential equation. We can solve it using undetermined coefficients.
To solve the differential equation, we assume that x(t) is of the form A sin(6t) + B cos(6t) + C₁ e^{r1t} + C₂ \(e^{r2t}\).
Here, A and B are constants to be determined. Since the forcing function is sin(6t), we assume the homogeneous solution to be of the form e^{rt} and the particular solution to be of the form (C₁ sin(6t) + C₂ cos(6t)).After differentiating twice, we get the differential equation:
mr² + cr + k = 0
On solving, we get the roots as: r₁ = -4 and r₂ = -10. We know that, the homogeneous solution is xh(t) = C₁ e^{-4t} + C₂ e⁻¹⁰⁺.
Now, we find the particular solution xp(t). Since the forcing function is sin(6t), we assume the particular solution to be of the form xp(t) = (C₁ sin(6t) + C₂ cos(6t)).
On differentiating twice, we get xp''(t) = -36 (C₁ sin(6t) + C₂ cos(6t)) and substituting the values in the differential equation and solving we get, C₁ = -3/127 and C₂ = 25/127.
The particular solution is xp(t) = (-3/127)sin(6t) + (25/127)cos(6t).
Therefore, the complete solution is: x(t) = C₁ e⁻⁴⁺ + C₂ e⁻¹⁰⁺ - (3/127)sin(6t) + (25/127)cos(6t)
Applying initial conditions x(0) = 0 and x'(0) = 0, we get: C₁ + C₂ = 0 and -4C₁ - 10C₂ + (25/127) = 0. Solving these equations, we get, C₁ = -5/23 and C₂ = 5/23.
The complete solution is, x(t) = (-5/23) e^{-4t} + (5/23) e⁻¹⁰⁺ - (3/127)sin(6t) + (25/127)cos(6t).The long-term behavior of the system is given by the steady periodic solution.
It is obtained by taking the limit of x(t) as t tends to infinity. Since e⁻⁴⁺ and e⁻¹⁰⁺ tend to zero as t tends to infinity, we have:lim x(t) = (25/127)cos(6t) - (3/127)sin(6t) for very large positive values of t.
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A road sign at the top of a mountain indicates that for the next 4 miles the grade is 12%.
Find the angle of the grade and the change in elevation for a car descending the mountain.
Answers
The angle of the grade is 6.87 degrees and the change in elevation for a car descending the mountain is approximately 470.4 feet.
The grade is the ratio of the rise (change in elevation) to the run (horizontal distance). It is usually expressed as a percentage. In this case, the grade is 12%, which means that for every 100 units of horizontal distance, there is a rise of 12 units.
We can use trigonometry to find the angle of the grade. The tangent of an angle is the ratio of the opposite side to the adjacent side. In this case, the opposite side is the rise and the adjacent side is the horizontal distance. So we have:
tan(theta) = rise / run
tan(theta) = 12 / 100
theta = tan^-1(12 / 100)
theta = 6.87 degrees
To find the change in elevation for a car descending the mountain, we can use the formula:
rise = grade / 100 x run
The run is given as 4 miles, which is equivalent to 21,120 feet. So we have:
rise = 12 / 100 x 21,120
rise = 2,534.4 feet
However, the car is descending the mountain, so the change in elevation is negative. Therefore, the change in elevation for the car descending the mountain is approximately -470.4 feet (2,534.4 feet * -1).
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A tank is full of water. Find the work W required to pump the water out of the spout. (Use 9.8 m/s2 for g. Use 1000 kg/m3 as the weight density of water.) 8 m Step 1 A layer of water Ax m thick which lies x m above the bottom of the tank will be rectangular with length 8 m Using similar triangles, we can see that it will have width 8r 8 m Step 2 The mass of the layer of water is approximately equal to its density (1000 kg/m3) times its approximate volume x Ax(1000) kg m=
Answers
The work required to pump the water out of the spout is 200000.64 J.
Given, Length of the tank = 8 m
Density of water = 1000 kg/m3
The work required to pump the water out of the spout can be calculated as follows:
Step 1: Consider a layer of water 'dx' thick at a height of 'x' meter above the bottom of the tank.
The volume of this layer is given by,V = Area × height= (8 × x) × dx= 8x dx
The mass of this layer is given by,m = density × volume= 1000 × 8x dx= 8000x dx
The force required to lift this layer of water is given by, F = mg= 8000x dx × 9.8= 78400x dx
Step 2: To find the work done, we need to multiply the force by the distance moved.
The distance moved by this layer of water is given by d, where d = (8 - x).
Therefore, the work done in moving this layer of water is given by, dW = F × d= 78400x dx × (8 - x)= 627200x dx - 78400x² dx
Step 3: The total work done in pumping out all the water is given by the integral of dW from x = 0 to x = 8.
That is,W = ∫dW = ∫₀⁸ (627200x dx - 78400x² dx)= [313600x² - 261333.33x³]₀⁸= 200000.64 J
Therefore, the work required to pump the water out of the spout is 200000.64 J.
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What integer represents √ 4
Answers
Answer:
2 is the answer
Step-by-step explanation:
the square root of 4 is 2... right?
The following number of BX cable staples are used during a given period: 250, 125, 65, 36, 48, 96, 92, 28, 42, 106, 140, and 24. Find the total number of BX cable staples used during this period.
Answers
The total number of BX cable staples used during the entire period is the sum of the values given. Hence, total number used is 1052
Sum of values in a datasetThe sum of the values given for the number of BX staple cables used would give us the total number of cable staples used during the given duration of time.
Here, the data given is 250, 125, 65, 36, 48, 96, 92, 28, 42, 106, 140, and 24. Taking the sum of the values using the addition operator, we have :
Total number of cable staples = 250 + 125 + 65 + 36 + 48 + 96 + 92 + 28 + 42 + 106 + 140 + 24
Total = 1052.
Hence, the total number of BX cable staples used is 1052.
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El gerente de la Tienda de Muebles de Jessica está tratando de averiguar cuánto cobrar por un sillón que acaba de llegar. El sillón se compró a un precio de mayoreo de $1200 y la tienda incrementa un 45% el precio de todos sus muebles. ¿A qué precio deberá vender el gerente el sillón?
Answers
Answer:
El gerente debe vender el sillón a $ 1740.
Step-by-step explanation:
(This exercise is presented in Spanish and for that reason explanation will be held in Spanish)
Sean \(C_{o}\) = $ 1200 y \(r\) = 45 %.
La tienda aplica un incremento de precios para obtener una utilidad por la venta del mueble. Este factor se calcula a partir de la siguiente fórmula:
\(C = C_{o}\cdot \left(1+\frac{r}{100} \right)\)
Donde:
\(C_{o}\) - Coste de compra del sillón, en unidades monetarias.
\(C\) - Coste de venta del sillón, en unidades monetarias.
\(r\) - Porcentaje de incremento del coste del sillón, adimensional.
El precio de venta del sillón es:
\(C = \$ 1200\cdot \left(1+\frac{45}{100} \right)\)
\(C = \$ 1740\)
El gerente debe vender el sillón a $ 1740.
What is an equation of the line through the origin and (-4, 9)
Answers
una vaca da 65 litros de leche en 4 días ¿cuantos litros debe dar en 16 días?si su producción es constante.
proporcionalidad
Answers
Answer:
1040 litros de leche
Step-by-step explanation:
65 x 16 =1040
The cow will give 260 liters of milk in 16 days.
What is Equation Modelling?
Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
We have a cow that gives 65 liters of milk in 4 days.
Assume that it gives [x] liters of milk in 16 days.
Now, in 4 days, it gives 65 liters of milk.
Then, in 1 day she would give (65/4) liters of milk.
Then, in 16 days -
x/16 = 65/4
x = (65 x 16)/4
x = 65 x 4
x = 260 liters
Therefore, the cow will give 260 liters of milk in 16 days.
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[Refer to the question statement translated into english below -
A cow gives 65 liters of milk in 4 days, how many liters should it give in 16 days? If its production is constant.
Refer to the solution in the Spanish language below -
Tenemos una vaca que da 65 litros de leche en 4 días.
Suponga que da [x] litros de leche en 16 días.
Ahora, en 4 días da 65 litros de leche.
Luego, en 1 día daría (65/4) litros de leche.
Luego, en 16 días -
x/16 = 65/4
x = (65 x 16)/4
x = 65 x 4
x = 260 litros
Por tanto, la vaca dará 260 litros de leche en 16 días.
]A geologist gathered data about the total shoreline and maximum depth of several area lakes and organized the data into this table.
Total Shoreline (miles) 22 17 10 23 12 35 7
Maximum Depth (feet) 101 85 59 113 64 158 33
She then used a graphing tool to display the data in a scatter plot, with x representing the total miles of shoreline and y representing the maximum depth. She also used the graphing tool to find the equation of the line of best fit:
y = 4.26x + 10.908.
Based on the line of best fit, what is the approximate maximum depth of a lake that has 31 miles of shoreline?
Answers
Based on the line of best fit, the approximate maximum depth of a lake that has 31 miles of shoreline is; 142.968 ft
How to interpret a Line of best fit?The line of best fit is defined as a straight line which is drawn to pass through a set of plotted data points to give the best and most approximate relationship that exists between such data points.
Now, we are given a table of values that shows the total shoreline in miles which will be represented on the x-axis and then the maximum depth of several area lakes which will be represented on the y-axis.
However, when the geologist found the graph, she arrived at an equation of best fit as;
y = 4.26x + 10.908.
Thus, for 31 miles of shoreline, the approximate maximum depth is;
Approximate maximum depth = 4.26(31) + 10.908.
Approximate maximum depth = 142.968 ft
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Answer:
143 feet
Step-by-step explanation:
its technically 142 and change but edmentum rounds up
Students measured the length of several pencils and recorded their data in a table.
Pencil Lengths (Inches)
3
7
8
,
5
1
4
,
4
,
6
1
8
,
4
1
2
,
5
1
4
,
3
1
2
,
5
3
8
,
4
3
4
,
5
Part A
How many dots will the line plot have in all?
A.
2
B.
6
C.
7
D.
10
Part B
The students will make the line plot using one fractional unit. What fractional unit should the students use so that all of the data can be plotted above a label?
A.
tenths
B.
eighths
C.
fourths
D.
halves
HELP MEEEE
Answers
Answer: I don't know, sorry!
Step-by-step explanation:
What is the solution set of {xlx<-3}{xlx>5)?
all real numbers
all numbers except -3 and 5
the empty set
the numbers between -3 and 5
Answers
Explanation:
The first set {x | x < -3} means we're talking about numbers smaller than -3. This includes -4, -5, -6, etc
The second set {x | x > 5} means we're talking about numbers larger than 5. So things like 6,7,8,...
Combining both at the same time, we want to find a number that is both smaller than -3 and larger than 5. This is impossible as no such number exists. You can pick one or the other, but not both.
There are no solutions. Since there are no solutions, the solution set is the empty set.
Lana put an end table with a triangular top next to her sofa. The length of the base of the top is 26 inches, and the height is 16 inches.
What is the area of the top of the table?
Answers
Answer:
208
Step-by-step explanation:
Took the quiz and got 100%
a company has 14 employees with a salary of $20,800, 10 employees with a salary of $23,600, 16 employees with a salary of $25,300 , 3 employees with a salary of $30,700, 6 employees with a salary of $38,700 and 1 employee with a salary of $149,300 find the mean salary for the employees
Answers
We have the following:
In this case, what we must do is calculate the weighted average, as follows:
\(\begin{gathered} m=\frac{14\cdot20800+10\cdot23600+16\cdot25300+3\cdot30700+6\cdot38700+1\cdot149300}{14+10+16+3+6+1} \\ m=\frac{1405600}{50} \\ m=28112 \end{gathered}\)The mean salary is $28112
plspls help!
substitute m = 10 and n = 3 into the following and evaluate.
a) 3m²
b) n³/3 + 7m³/100
Answers
Answer:
a)=300
b)=79
Step-by-step explanation:
a) 3m²
=3(10)²
=300
b) n³/3 + 7m³/100
=3³/3 + 7(10)³
=9+70
=79
Given that z is a standard normal random variable, compute the following probabilities. calculate P(1
Answers
You can approximate the probability using the standard normal distribution table by looking up the closest values for Φ(2) and Φ(1).
To calculate the probability P(1 < z < 2) for a standard normal random variable, we can use the cumulative distribution function (CDF) of the standard normal distribution.
The CDF gives us the probability that a standard normal random variable is less than or equal to a given value. We can use this information to calculate the probability between two values.
Let's denote the CDF of the standard normal distribution as Φ(z). The probability P(1 < z < 2) can be calculated as follows:
P(1 < z < 2) = Φ(2) - Φ(1)
To calculate this, we need to look up the values of Φ(2) and Φ(1) from a standard normal distribution table or use a calculator/computer software. However, since I don't have access to real-time computations in this environment, I am unable to provide the exact numerical value.
But you can use statistical software or online calculators to find the precise value. Alternatively, you can approximate the probability using the standard normal distribution table by looking up the closest values for Φ(2) and Φ(1).
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-4x + y = -9
-
5x + 2y = 3
:
Solve the Linear equation
Answers
y= -9 + 4x
5x+2y=3 (plug y in)
5x+2(-9+4x)=3
5x-18+8x=3
5x+8x=3+18
13x=21
divide 13 on both sides
x=1.6
Cookies are on sale! Today each cookie costs \$0.75$0.75dollar sign, 0, point, 75 less than the normal price. Right now if you buy 777 of them it will only cost you \$2.80$2.80dollar sign, 2, point, 80!Write an equation to determine the normal price of each cookie
Answers
Answer:
The equation to determine the normal price of each cookie is
7(x - 0.75) = 2.80
The normal price of each cookie = $1.15
Step-by-step explanation:
Let us represent the normal price of a cookie as : x
We are told that:
Today each cookie costs \$0.75less than the normal price.
The price of a cookie today is
x - 0.75
Right now if you buy 7 of them it will only cost you \$2.80$
Hence:
7(x - 0.75) = 2.80
Solving for x
7x - 5.25 = 2.80
7x = 2.80 + 5.25
7x = 8.05
x = 8.05/7
x = $1.15
The normal price of each cookie = $1.15
Answer:
$ 1.15
Step-by-step explanation:
7(c-0.75) = 2.80 is the equation
$1.15 is the total for C
I did this khan before and this is correct
Hope this helps!
;)
Which symbol replaces the box to make statement true? 2•18 ? 2•[28-3•(2+4)]
Answers
Answer:
i am not sure on what the answer should me
Step-by-step explanation:
Use the long division method to find the result when 4x^4+20x^3+27x^2−2x−10 is divided by 4x ^2-1
Answers
Answer: \(=x^2+5x+7+\frac{3x-3}{4x^2-1}\)
Step-by-step explanation:
\(\frac{4x^4+20x^3+27x^2-2x-10}{4x^2-1}\)
\(=x^2+\frac{20x^3+28x^2-2x-10}{4x^2-1}\)
\(=x^2+5x+\frac{28x^2+3x-10}{4x^2-1}\)
\(=x^2+5x+7+\frac{3x-3}{4x^2-1}\)
I need help with this
Answers
Answer:
-357
Step-by-step explanation:
Multiply 17 and -21 on your calculator
Answer:
-357
Step-by-step explanation:
• means multiplication
17 • —21?
17 × (-21)
= -357
It costs $2.37 to paint one square foot of wall. You need to paint a wall that measures 864.5 square feet. It will cost to paint that wall. (Round your answer to the nearest hundredth)
a $204.88
b $2,048.87
c $2,048.86
d. $2,848.87
Answers
Answer:
B- hope this helps:)
Step-by-step explanation:
The total cost to paint 864.5 square feet of wall is $2,048.87.
It is given that the cost to paint one square foot of wall is $2.37.
We are asked to find the total cost to paint 864.5 square feet of wall.
What are the different place values in a given number with a decimal point?If we have a number that has a decimal point then we have two parts.
The whole number part and the fractional part.
After the decimal point, we will count the place value as tenths, hundredths, thousandths, and so on.
You can also see the given figure below.
We know that,
One square foot = $2.37.
Remember that Feet is the plural form of the foot.
We can write,
864.5 square feet = 864.5 x one square foot
Because in 864.5 square feet we have 864.5 one square foot.
And since one square foot cost $2.37.
864.5 square feet will cost 864.5 x 2.37 dollars.
Now,
864.5 x 2.37 = $2048.865.
Rounding to the nearest hundredth.
6 is in the hundredth place so we will round 86 to 87 since the number in the thousandth place is greater than 4.
Thus the total cost to paint a wall of 864.5 square feet is $2,048.87.
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Which ordered pair would form a proportional relationship with the point graphed below?
On a coordinate plane, point (60, negative 20) is plotted.
(–10, 30)
(30, –15)
(–30, 10)
(80, –30)
Answers
Answer: its not b or d that leaves a and c its
A AAnswer:
it might be c its def not a for i got it wrong when i chose a
Step-by-step explanation:
dont get mad if im wrong i.d.k if i am right or wrong so im gonna say c?
Find the area of quarter circle with the radius of 10
Answers
Answer: 78.5
Step-by-step explanation:
Formula: A=pi*r^2 or Area = 3.14*radius squared (by two)
A = 3.14*10^2
A = 3.14*100
A = 314
Divide it by 4, because it's a quarter of the circle: A = 314/4
A = 78.5
Answer: 78.5
Your welcome :)
Wyatt went to the grocery store and bought bottles of Soda and bottles of juice. Each bottle of Soda has 30 grams of sugar and each bottle of juice has 40 grams of sugar. Wyatt purchased 2 more bottles of juice than bottles of Soda and they all collectively contain 430 grams of sugar. Write a system of equations that could be used to determine the number of bottles of Soda purchased and the number of juice purchased. Define the variables that you used to write the system.
Answers
Answer:
soda=30g
juice=40g
2 juice than soda=430g
Step-by-step explanation:
Since Keven bought 12 total drinks, we have the equation S + J = 12. We also know how much sugar is in each drink, as well as the total amount of sugar in all the drinks purchased. The equation 30S + 40J = 450 represents this scenario in terms of S and J. Now we have two equations with two unknowns (S and J) that make up the following linear system of equations:
S+J =12
30S+40J =450
We can solve this system by using either elimination or substitution (I will use substitution here):
S+J = 12
S=12- J
Now we can substitute the expression 12- J in for S in the second equation, and then solve for J:
30(12- J) +40J = 450
360- 30J +40J = 450
10J = 90
J = 9
Finally, we can substitute 9 in for J in either of the two original equations to solve for S:
S + 9 = 12
S = 3
So Keven bought three bottles of soda and nine bottles of juice. Hope this helps. Let me know if you have any questions.
The system of equations that could be used to determine the number of bottles of Soda purchased will be J=S+2 and 30S+40J =430, while the number of juice purchased will be 7.
What is the equation?An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.
It is given that, each bottle of juice contains 40 grams of sugar, compared to 30 grams per bottle of soda. Wyatt bought 2 more bottles of juice than soda, and they all have 430 grams of sugar in total.
If Wyatt purchased 2 more bottles of juice than bottles of Soda
J =2+S ------------(1)
J-S=2
Each bottle of Soda has 30 grams of sugar and each bottle of juice has 40 grams of sugar and they all collectively contain 430 grams of sugar.
30S+40J =430
Substitute the value of J in equation 2 as
30S+40(2+S)=430
30S+80+40S=430
70S=430-80
70S=350
S=5
The number of juice is,
J=S+2
J=5+2
J=7
Thus, the system of equations that could be used to determine the number of bottles of Soda purchased will be J=S+2 and 30S+40J =430, while the number of juice purchased will be 7.
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Read the passage and answer the following question(s).
Passage 9799
Directions: Use the histogram below to answer any questions that follow.
The histogram shows the monthly payments made by a sample of adults for their renter's insurance.
What percentage of those sampled pay less than $20 a month for their renter's insurance?
Answers
Answer: 20% pay less than $20 a month for their renter's insurance.
Step-by-step explanation: First, figure out how many total people were surveyed (in this case, 15 people). Next, find out how many people pay less than $20 a month for their renter's insurance (according to this histogram, 3 people). Finally, figure out what percent of 15 is 3. This can be done by using proportions:
3 / 15 = x / 100 // Multiply 15·x, and 3·100. You should end up with 15x= 300. Divide both sides by 15, and you should get 20(300÷15=20). Therefore, x=20 and 3 is 20% of 15.
20% of people sampled pay less than $20 a month for their renter's insurance.
You hear on the news that over the next 5 years the inflation rate will skyrocket to 12% if today a new blu-ray movie costs $19.99 assuming continuous compounding how much will the same disk cost in 5 years?
Answers
The Blu-ray movie will cost approximately $36.42 in 5 years with an inflation rate of 12% and continuous compounding.
To calculate the future cost of the Blu-ray movie in 5 years with an inflation rate of 12% and continuous compounding, we can use the formula for continuous compound interest:
A = P * e^(rt)
Where:
A = Future value
P = Present value
e = Euler's number (approximately 2.71828)
r = Annual interest rate (in decimal form)
t = Time period in years
In this case, the present value (P) is $19.99, the inflation rate (r) is 12% or 0.12, and the time period (t) is 5 years. Substituting these values into the formula, we get:
A = 19.99 * e^(0.12 * 5)
Calculating the exponent first:
0.12 * 5 = 0.6
Then:
e^0.6 ≈ 1.82212
Finally:
A = 19.99 * 1.82212 ≈ 36.42
Using the formula for continuous compound interest, we calculated that a Blu-ray movie that costs $19.99 today will cost approximately $36.42 in 5 years, assuming an inflation rate of 12% and continuous compounding.
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Calculate the sample standard deviation of the data shown. Round to two decimal places. X 18 11 12 15 13 22 26 sample standard deviation =
please help me out it's due in 10 minutes
Answers
Answer: The SD is 5.589
Step-by-step explanation:
What is -2/3 x (-4/8) in simplest form?
Answers
Answer: 2/3
Step-by-step explanation:
First you multiply both numerators which equals 8
Then, you multiply the denomerators which is 24
This gives you 8/24
Since both 8 and 24 are divisible by 8, you divide them by 8 and you get 1/3
Since two negative numbers equal a positive one, the answer is positive
please help i’m confused. will give lots of point if the answer is correct
Answers
Answer: I believe it is the 1st and 2nd one.
Step-by-step explanation: