The required length of the rectangle is 12/5 feet and the width is 9/5 feet.
What is the equation model?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
Here,
Let's denote the length of the rectangle as L and the width as W.
From the problem statement, we know that:
3L = 4W (equation 1)
We also know that the perimeter P is given by:
P = 2L + 2W = 8 2/5 feet
Multiplying both sides by 5 to get rid of the fraction, we get:
10L + 10W = 42
Dividing by 2, we get:
5L + 5W = 21 (equation 2)
Now we can use equations 1 and 2 to solve for L and W.
First, we can substitute equation 1 into equation 2 to get an equation in terms of W:
5L + 15L/4 = 21
Multiplying both sides by 4, we get:
20L + 15L = 84
35L = 84
L = 84/35 = 12/5 feet
Now we can substitute the value of L into equation 1 to get the value of W:
3L = 4W
3(12/5) = 4W
W = 9/5 feet
Therefore, the length of the rectangle is 12/5 feet and the width is 9/5 feet.
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Joel has a goal to practice his clarinet for 4 1/2 hours per week. The list below shows the number of hours Joel has practiced so far this week.
Monday: 1 1\2 hours
Wednesday: 1 1\4 hours
Thursday: 1 hour
How many more hours does Joel need to practice this week to meet his goal?
Answer: 3/4 hour
Step-by-step explanation: Add them all to get 3 3/4. subtract that from 4 1/2.
calculate the exact value of cos (a+b) given that cos a= 3/5 with 0<a< π/2 and Sin b = - 8/17 with 3π / 2 <b < 2 π
The value of cos (a+b) when cos a= 3/5 with 0<a< π/2 and Sin b = - 8/17 with 3π / 2 <b < 2 π, is 0.906.
What is triangle angle sum theorem?According to the triangle angle sum theorem, the sum of all the angle(interior) of a triangle is equal to the 180 degrees. The formula for cos compound angle using angle sum theorem can be given as,
[tex]\cos (a+b)=\cos (a)\cos (b)-\sin (a)\sin (b)[/tex]
The exact value of cos (a+b) has to be find out. It is given that,
[tex]\cos a= \dfrac{3}{5}[/tex]
The value of a is lies between 0<a< π/2. The value of other side of the triangle using the Pythagoras theorem,
[tex]5^2={x^2+3^2}\\x^2=25-9\\x=\sqrt{16}\\x=4[/tex]
Thus, the value of sin a is 4/5 from the trigonometry ratio. the value of sine b is,
[tex]\sin b = -\dfrac{8}{17}[/tex]
The value of b is lies between 3π / 2 <b < 2 π. The value of the other side of the triangle using the Pythagoras theorem,
[tex]17^2={(-8)^2+y^2}\\y^2=289-64\\y=\sqrt{225}\\y=15[/tex]
Thus, the value of cos b is, 15/17. Put the values in above formula,
[tex]\cos (a+b)=\cos (a)\cos (b)-\sin (a)\sin (b)\\\cos (a+b)=\dfrac{3}{5}\times\dfrac{15}{17}-\dfrac{4}{5}\times\dfrac{-8}{17}\\\cos (a+b)=\dfrac{9}{17}+\dfrac{32}{85}\\\cos (a+b)=0.906[/tex]
Thus, the value of cos (a+b) when cos a= 3/5 with 0<a< π/2 and Sin b = - 8/17 with 3π / 2 <b < 2 π, is 0.906.
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what is equal to 13 centimeters.
Answer:
5.11811 inches
Step-by-step explanation:
Find the median of the following data: 19, \ 21, \ 18, \ 17, \ 18, \ 22, \ 4619, 21, 18, 17, 18, 22, 46
Check the picture below.
Hey culture starting with 5000 bacteria after four hours ago to 5500 bacteria predict how many bacteria will be present after 13 hours. Round to the nearest whole number
it will be 3375 bacteria my ducky
From the given figure, find the value of x:-
Please can someone answer it I need it...
I'll mark as BRAINLIEST...
Answer:
90°
Step-by-step explanation:
Angle subtended by diameter from circumference is a right angle(Circle Theorem)
How can you use
probability to draw conclusions about the
likelihood that something will occur?
(Probability)
The closer the probability is to 1, the more likely it is to occur and the closer the probability is to 0, the less likely it is to occur.
ProbabilityThis is the likelihood that an event will occur.
Probability of an event occuring is calculated thus P(event) = event space/sample space.The event space is the set of desired outcomes in which the event can occur while the sample space is the set of all possible outcomes.Now, the probability P(x) of an event x is in the range 0 ≤ P(x) ≤ 1 where P(x) = 0 implies that the event cannot occur and P(x) = 1 implies that the event will definitely occur.To draw conclusions about the likelihood that something will occurFor an event will occur, it value must be close to 1. For example, a probability P(x) = 0.38 is less likely to occur than a probability P(x) = 0.78.So, the closer the probability is to 1, the more likely it is to occur and the closer the probability is to 0, the less likely it is to occur.
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find the equation of the circle which passes through points
(3,-1), (3,9) and (-2,4)
please help me out, simple
Answer:
Answer is 45⁰
Step-by-step explanation:
The angle ATB IS 45⁰
26 rooms on 2 floors = ____ rooms on 4 floors
Answer:
There would be 104 rooms on 4 floors in total.
Step-by-step explanation:
If there were 26 rooms on 2 floors, then you multiply 26 x 4, the result would be 104 rooms on 4 floors in total.
Answer:
52 rooms
Step-by-step explanation:
you could set up a proportion to solve this
26 rooms/ 2 floors = ?/4 floors
to find the answer for the question mark you can divide the amount of rooms by floors and get 13.
With the 13 you can multiply that by 4 to get 52 rooms. You basically used the 13 as the amount of increase
i hope this helped
if you have anymore questions feel free to ask again:3
Solve the following system of equations:
{−3x+4y=7, 7x−12y=−11
Provide your answer below:
Tim’s weight was 320 pounds in 2010 and is 180 pounds in 2020. What is the slope?
Answer:
-14
Step-by-step explanation:
We have two points
(2010, 320) and ( 2020, 180)
The slope is
m= ( y2-y1)/(x2-x1)
= ( 180-320)/(2020-2010)
= -140/10
= -14 lbs/ year
if the tempture is 39.2 degrees F what would the tempture be in celsius
Answer:
4 degrees celsius
Step-by-step explanation:
A father is four times as old as his son. In two years the will have been five times as old as his son was two years ago. How old is the father?
Answer:
Q13)A man is four times as old as his son. After 20 years, he will be twice as old as his son at that time. Find their present ages. Present age of the father is = 4 x = 4 × 10 = 40 4x=4\times10=40 4x=4×10=40 years.
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Mayra bought x grams of rice.
Anika bought 1/3 more than Mayra bought.
Select ALL of the equations that represent the relationship between the amount of rice that Mayra bought, x, and the amount of rice that Anika bought, y.
y = 4/3x
y = 2/3x
y = x - 1/3x
y = x + 1/3x
y = 1/3x
Answer:
i think last one is the right answer
Step-by-step explanation:
y=1/3x
Suppose that 22% of people own dogs. If you pick two people at random, what is the probability that they both own a dog? Round to 2 places.
pls help me i really need help
Answer:
hey pls help me I urgently need help
Find the value of y.
Answer:
this is your answer hope u like it
A circle has its center at (2,-4). The radius of the circle extends to the
point (2,5). What is the approximate circumference of the circle?
⚫️114 units
⚫️14 units
⚫️28 units
⚫️57 units
Check the picture below, so the circle looks more or less like so, with a radius of 9.
[tex]\textit{circumference of a circle}\\\\ C=2\pi r~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=9 \end{cases}\implies C=2\pi (9)\implies C\approx 57[/tex]
A credit card company receives numerous phone calls throughout the day from customers reporting fraud and billing disputes. Most of these callers are put “on hold” until a company operator is free to help them. The company has determined that the length of time a caller is on hold is normally distributed with a mean of 2.5 minutes and a standard deviation 0.5 minutes. If 1.5% of the callers are put on hold for longer than x minutes, what is the value of x?
Using the normal distribution, it is found that the value of x is of 3.585.
Normal Probability DistributionIn a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of XIn this problem, the mean and the standard deviation are given, respectively, by [tex]\mu = 2.5, \sigma = 0.5[/tex].
The value of x is the 100 - 1.5 = 98.5th percentile, which is X when Z = 2.17, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]2.17 = \frac{X - 2.5}{0.5}[/tex]
[tex]X - 2.5 = 0.5(2.17)[/tex]
[tex]X = 3.585[/tex]
Hence the value of x is of 3.585.
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what is 6 dived by 20?
Answer:
0.3
Step-by-step explanation:
Answer:
6 divided by 20 is 0.3
(your welcome)
Medication with strength 125 mg/5 mL has been ordered at 25 mg/kg. The patient weighs 215 lb. How much should be
administered? (If less than 1, round to the nearest hundredth; otherwise, round to the nearest tenth.)
The amount of mg required per kg for the patient is 2,438.1mg/kg
Ratios and proportionsProportions are ratios of two integers.
Given the medication with a strength 125mg/5ml which has been ordered at 25 mg/kg.
For a patient that weighs 215lb, the weight in kg will be 97.5224kg
Since 25mg = 1 kg
x = 97.5224kg
x = 25 * 97.5224
x = 2,438.06
Hence the amount of mg required per kg for the patient is 2,438.06mg/kg
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GIVING BRAINLIEST + STARS
I know A to B is 20m/s but what is C to D?
Answer:
See below ↓↓
Step-by-step explanation:
A to B
Avg. speed = Distance covered / Time takenAvg. speed = 200 m / 10 sAvg. speed = 20 m/sC to D
Avg. speed = Distance covered / Time takenAvg. speed = (500 - 200) m / (60 - 30) sAvg. speed = 300 m / 30 sAvg. speed = 10 m/sMr. Ferarra is planning a field trip to the history museum for all of the students at his middle school. The school's buses can only transport 144 students. Mr. Ferarra needs to rent more buses for the remaining 290 students.
Answer:
[tex]s - 144 = 290[/tex]
[tex]s = 434[/tex]
Step-by-step explanation:
the keyword is remaining. Meaning the teacher slready has 144 reserved but needs to get 290 spots more.
please help me i dont know the answer to this one
Answer:
centroid (2, 2.666666666...)
circumcenter (2, 1.75)
orthocenter (2, 2.5)
Step-by-step explanation:
the coordinates of the centroid of a triangle are
((x1 + x2 + x3)/3, (y1 + y2 + y3)/3)
so, we have
(-4 + 2 + 8)/3 = 6/3 = 2 = x
(0 + 8 + 0)/3 = 8/3 = y = 2.666666666...
the circumcenter is the crossing point of the lines going perpendicular through the midpoint of each side.
the orthocenter is the crossing point of the lines going perpendicular on each side through the opposing vertices (the heights of the triangle).
so, we need to calculate additionally the slopes of 2 sides and their midpoints before we can get these 2 centers. the third side would only confirm the result but not provide additional information.
A = (-4, 0), B = (2, 8), C = (8, 0)
midpoint D of AC = ((-4 + 8)/2, (0+0)/2) = (2, 0)
the slope of AC is
(y2 - y1)/(x2 - x1) = (0 - 0)/(8 - -4) = 0/12 = 0 (a flat line)
the slope of the perpendicular line is -1/slope of original line. which is -1/0 = -infinity.
but don't worry, that means it is a constant line x = ...
and since it has to go through the midpoint D, the perpendicular line is x = 2
midpoint E of BC = ((2+8)/2, (8+0)/2) = (5, 4)
the slope of BC is
(0-8)/(8-2) = -8/6 = -4/3
so, the slope of the perpendicular line is 3/4.
that line is then y = 3/4 x + b
it has to go through the midpoint E
4 = 3/4 × 5 + b = 15/4 + b
16 = 15 + 4b
4b = 1
b = 1/4
so, the full perpendicular line is
y = 3/4 x + 1/4
crossing both perpendicular lines is simply using the first in the second equation :
y = 3/4 × 2 + 1/4 = 6/4 + 1/4 = 7/4 = 1.75
for the orthocenter we can use the same slopes, but the lines go now through the opposing vertices instead through the side midpoints.
so, line 1 is going through B, which makes it also x = 2.
line 2 is going through A, so
0 = 3/4 × -4 + b
0 = -1 + b
b = 1
line 2 is then
y = 3/4 x + 1
crossing these 2 lines gives us
y = 3/4 × 2 + 1 = 6/4 + 4/4 = 10/4 = 5/2 = 2.5
is it possible to write vector (-5,6) as a linear combination of vectors (1,2) and (3,4)
Answer:
Step-by-step explanation:
-5i+6j=x(1i+2j)+y(3i+4j)
-5=x+3y(multiply by 2)
6=2x+4y
-10=2x+6y
subtract
16=-2y
y=-8
-5=x+3(-8)
x=-5+24=19
-5i+6j=19(i+2j)-8(3i+4j)
so we can write (-5,6) as a linear combination of (1,2) and (3,4)
The length of a rectangle is 10 ft less than three times the width, and the area of the rectangle is 77ft^2 . Find the dimensions of the rectangle.
Answer:
The dimensions of rectangle are 11 feet and 7 feet.Step-by-step explanation:
Given, The length of a rectangle is 10 ft less than three times the width, and the area of the rectangle is 77 ft²
Let's assume width of rectangle be x feet and Length of rectangle be 3x - 10. Using the formula of area of the rectangle we'll find the dimensions of the Rectangle.
[tex] \\ \dashrightarrow{ \red{\underline{\underline{\sf{Area (rectangle) = Length \times width }}}}} \\ \\ [/tex]
Substituting the required values:
[tex]\dashrightarrow \: \: (3x-10)(x) = 77 \\ [/tex]
[tex]\dashrightarrow \: \: 3x^2 - 10x = 77 \\ [/tex]
[tex]\dashrightarrow \: \: 3x^2 -10x -77 = 0 \\ [/tex]
[tex]\dashrightarrow \: \:3x^2 + 11x -21x -77 = 0 \\ [/tex]
[tex]\dashrightarrow \: \: x(3x+11)-7(3x+11) = 0 \\ [/tex]
[tex]\dashrightarrow \: \: (x-7)(3x+11) = 0 \\ [/tex]
[tex]\dashrightarrow \: \: { \red{\underline{\underline { x = 7 \: or \: \dfrac{-11}{3}}}} } \\ \\ [/tex]
Hence,
Width of rectangle = x = 7 feetLength of rectangle = 3x -10 = 3(7) - 10 = 11 feet[tex] \therefore[/tex] The required dimensions of rectangle are 11 feet and 7 feet.
The dimensions of the given rectangle with an area of 77 ft^2 and given dimensions are; Length = 11 ft and Width = 7 ft
How to find the Area of a rectangle?
Formula for area of a rectangle is;
A = Length * Width
We are given;
Length; L = 3W - 10
Thus;
Area; A = W(3W - 10)
Thus;
W(3W - 10) = 77
3W² - 10W - 77 = 0
Using online quadratic equation calculator, we have;
W = 7
Thus;
L = (3*7) - 10
L = 11 ft
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The length of the term is one year. Calculate the principal if the maturity value is $4,500 and the simple interest is $350.
Answer:
Easy! The answer is $4,150
Step-by-step explanation:
The $350 is interest so we will take that away from the maturity value to get 4,150!
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TriangleABC and triangle DEC are
A. Similar
B. Not similar
Answer:
i guess not similar....
Step-by-step explanation:
A.
B.
5x
x
=20
=4
1) How can we get Equation BBB from Equation AAA?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
Multiply/divide both sides by the same non-zero constant
(Choice B)
B
Multiply/divide both sides by the same variable expression
(Choice C)
C
Add/subtract the same quantity to/from both sides
(Choice D)
D
Add/subtract a quantity to/from only one side
2) Based on the previous answer, are the equations equivalent? In other words, do they have the same solution?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
Yes
(Choice B)
B
No
Answer:
Divide both sides by 5.
Step-by-step explanation:
Divide both sides by same non-zero constant.
