Answer:
a) [tex]\frac{dB}{dt} = \frac{5\pi}{4.2} \cdot \cos \left(2\pi\cdot \frac{t}{4.2} \right)[/tex], b) [tex]\frac{dB}{dt}\approx 5.595[/tex]
Step-by-step explanation:
a) The rate of change of the brightness of the Cepheid can be determined by deriving the function in time:
[tex]\frac{dB}{dt} = \left(\frac{2\pi}{4.2} \right)\cdot 0.25\cdot \cos (2\pi\cdot \frac{t}{4.2})[/tex]
[tex]\frac{dB}{dt} = \frac{5\pi}{4.2} \cdot \cos \left(2\pi\cdot \frac{t}{4.2} \right)[/tex]
b) The rate of increase after one day is:
[tex]\frac{dB}{dt} = \frac{5\pi}{4.2} \cdot \left(2\pi \cdot \frac{1}{4.2} \right)[/tex]
[tex]\frac{dB}{dt}\approx 5.595[/tex]
Quadrilateral BCDE is a kite. What is BF?
B
20
С
12
E
F
D
Answer:
32
Step-by-step explanation:
if u do pythagoras, sq root of 20^2-12^2=16
16x2=32
Ms. Ironperson and Mr. Thoro are making
Avenger posters to give children when they
visit Avenger Academy. Ms. Ironperson has
completed 12 posters and will complete 6
more per day. Mr. Thoro has not started yet
but can make 12 per day. At some point Mr.
Thoro will catch up and both will have finished
the same number of posters. When this does
happen, how many posters will each Avenger
have completed?
If x denotes the number of days and y denotes
the number of posters, what are the equations
needed to solve this problem? (7 points)
Answer:
y = 12 + 6x
y = 12x
Step-by-step explanation:
From the information provided, the following equations are derived:
y = 12 + 6x ------- Eqn 1
y = 12x ------- Eqn 2
Since Eqns 1 and 2 have the same subject, we equate them to solve for x. We have:
12x = 12 + 6x
Putting like terms together, we have:
12x - 6x = 12 ⇒ (12 - 6)x = 12
6x = 12 ⇒ x = 2
x = 2
Substitute x into Eqn 1 or 2
Eqn 1
y = 12 + 6x
y = 12 + 6(2) = 12 + 12
y = 24
Eqn 2
y = 12x
y = 12(2)
y = 24
It means that it will take Ms. Ironperson and Mr. Thoro 2 days apiece to produce the same number of posters at the current rate (which is 24 posters). Both Ms. Ironperson and Mr. Thoro will individually take 2 days to produce 24 Avenger posters apiece.
Problem 10: A tank initially contains a solution of 10 pounds of salt in 60 gallons of water. Water with 1/2 pound of salt per gallon is added to the tank at 6 gal/min, and the resulting solution leaves at the same rate. Find the quantity Q(t) of salt in the tank at time t > 0.
Answer:
The quantity of salt at time t is [tex]m_{salt} = (60)\cdot (30 - 29.833\cdot e^{-\frac{t}{10} })[/tex], where t is measured in minutes.
Step-by-step explanation:
The law of mass conservation for control volume indicates that:
[tex]\dot m_{in} - \dot m_{out} = \left(\frac{dm}{dt} \right)_{CV}[/tex]
Where mass flow is the product of salt concentration and water volume flow.
The model of the tank according to the statement is:
[tex](0.5\,\frac{pd}{gal} )\cdot \left(6\,\frac{gal}{min} \right) - c\cdot \left(6\,\frac{gal}{min} \right) = V\cdot \frac{dc}{dt}[/tex]
Where:
[tex]c[/tex] - The salt concentration in the tank, as well at the exit of the tank, measured in [tex]\frac{pd}{gal}[/tex].
[tex]\frac{dc}{dt}[/tex] - Concentration rate of change in the tank, measured in [tex]\frac{pd}{min}[/tex].
[tex]V[/tex] - Volume of the tank, measured in gallons.
The following first-order linear non-homogeneous differential equation is found:
[tex]V \cdot \frac{dc}{dt} + 6\cdot c = 3[/tex]
[tex]60\cdot \frac{dc}{dt} + 6\cdot c = 3[/tex]
[tex]\frac{dc}{dt} + \frac{1}{10}\cdot c = 3[/tex]
This equation is solved as follows:
[tex]e^{\frac{t}{10} }\cdot \left(\frac{dc}{dt} +\frac{1}{10} \cdot c \right) = 3 \cdot e^{\frac{t}{10} }[/tex]
[tex]\frac{d}{dt}\left(e^{\frac{t}{10}}\cdot c\right) = 3\cdot e^{\frac{t}{10} }[/tex]
[tex]e^{\frac{t}{10} }\cdot c = 3 \cdot \int {e^{\frac{t}{10} }} \, dt[/tex]
[tex]e^{\frac{t}{10} }\cdot c = 30\cdot e^{\frac{t}{10} } + C[/tex]
[tex]c = 30 + C\cdot e^{-\frac{t}{10} }[/tex]
The initial concentration in the tank is:
[tex]c_{o} = \frac{10\,pd}{60\,gal}[/tex]
[tex]c_{o} = 0.167\,\frac{pd}{gal}[/tex]
Now, the integration constant is:
[tex]0.167 = 30 + C[/tex]
[tex]C = -29.833[/tex]
The solution of the differential equation is:
[tex]c(t) = 30 - 29.833\cdot e^{-\frac{t}{10} }[/tex]
Now, the quantity of salt at time t is:
[tex]m_{salt} = V_{tank}\cdot c(t)[/tex]
[tex]m_{salt} = (60)\cdot (30 - 29.833\cdot e^{-\frac{t}{10} })[/tex]
Where t is measured in minutes.
Find the exact solution of 3x^2+7=28
[tex]\text{Solve:}\\\\3x^2+7=28\\\\\text{Subtract 7 from both sides}\\\\3x^2=21\\\\\text{Divide both sides by 3}\\\\x^2=7\\\\\text{Square root both sides}\\\\\sqrt{x^2}=\sqrt7\\\\x=\pm\sqrt7\\\\\boxed{x=\sqrt7\,\,or\,\,x=-\sqrt7}[/tex]
Analyze the function for domain, range, continuity, symmetry, boundedness, extrema, and asymptotes. f(x)=-2cot x
Answer:
(See explanation below for further details)
Step-by-step explanation:
The domain of the function is:
[tex]x \in \mathbb{R} - \{ \pm \pi \cdot i \}[/tex] for [tex]i \in \mathbb{N}_{O}[/tex]
The range of the function is:
[tex]f(x) \in \{-\infty, +\infty \}[/tex]
There are no absolute extrema and such function is not bounded.
Function is symmetric, whose period is π.
Lastly, the set of asymptotes is:
[tex]x = \pm \pi \cdot i[/tex], for [tex]i \in \mathbb{N}_{O}[/tex]
Answer:
Step-by-step explanation:
edge
determine whether the forces in the pair are pulling at right angles to each other for the values. a-3.4 and b=2.6, which are legs of a right triangle, find c, the hypotenuse, to the nearest tenth
Answer:
4.3 units
Step-by-step explanation:
In this question we use the Pythagorean Theorem which is shown below:
Data are given in the question
Right angle
a = 3.4
b = 2.6
These two are legs of the right triangle
Based on the above information
As we know that
Pythagorean Theorem is
[tex]a^2 + b^2 = c^2[/tex]
So,
[tex]= (3.4)^2 + (2.6)^2[/tex]
= 11.56 + 6.76
= 18.32
That means
[tex]c^2 = 18.56[/tex]
So, the c = 4.3 units
A hiker starts at an elevation of 65 feet and descends 30 feet to the base camp . What is the elevation of the base camps ?
Answer:
the elevation of base camp is 35 ft
Step-by-step explanation:
Starting at 65 feet elevation, and the descending 30 feet to reach base camp, that means that base camp is at: 65 ft - 30 ft = 35 ft elevation
Answer:
35 feet
Step-by-step explanation:
65 feet- 30 feet= 35 feet is the elevation of the base
Please answer this correctly
Answer:
514 square meters
Step-by-step explanation:
Consider the length of p;
[tex]11 * p * 3 = 528,\\33 * p = 528,\\p = 528 / 33 = 16 meters[/tex]
11, 3, and p act as the length, width, and height of this rectangular prism. We can apply the volume formula length * width * height, and thus made 11 * p * 3 equivalent to the volume 528. Now let us determine the surface area;
[tex]Area of Side 1 = 16 * 11 = 176 square meters,\\Area of Side 2 = 3 * 16 = 48 square meters,\\Area of Side 3 = 11 * 3 = 33 square meters,\\\\Surface Area = 2 * ( 176 ) + 2 * ( 48 ) + 2 * ( 33 ) = 352 + 96 + 66 = 514 square meters[/tex]
Hope that helps!
Answer:
514 square meters
Step-by-step explanation:
Since the volume of a rectangular prism is the product of the width, length, and height, 11*3*p=528. Therefore, p=528/(11*3)=16. Now, you can find the surface area. The surface of a rectangular prism is made up of 3 pairs of rectangles. One pair has dimensions of 11 by 3, one pair has dimensions of 16 by 3, and the last pair has dimensions of 16 by 11. The surface area of this figure is therefore:
[tex]2(11\cdot 3)+2(16\cdot 3) + 2(16\cdot 11)=66+96+352=514 m^2[/tex]
Hope this helps!
If f(x) = 4–1 and g(x) = 8x, which expression is equivalent to (g-1)(3)?
O 8-3-(4 + 3)
08-3-(4-32
813)-4432
O 6(3) 4-32
Answer:
Option (3)
Step-by-step explanation:
Given functions are f(x) = 4 - x² and g(x) = 6x
We gave to find the expression for (g - f)(3).
(g - f)(x) = g(x) - f(x)
= 6x - (4 - x²)
= 6x - 4 + x²
By substituting x = 3 in this expression,
(g - f)(x) = 6(3) - 4 + (3)²
Therefore, option (3) will be the answer.
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Question
Unit 2 Tutorials
Question 20
Mark this question
For the arithmetic sequence beginning with the terms (-2,0,2,4,6,8...), What is the sum of the first
18 terms?
0 238
0 340
o 304
0 270
Sove and continue
Answer:
270
Step-by-step explanation:
For any arithmetic sequence
nth term is given by
nth term = a + (n-1)d
where a is first term,
d is common difference
d is given by nth term - (n-1)th term
sum of n terms given by
sum = n/2(2a + (n-1)d)
________________________________________________
Given arithmetic sequence
-2,0,2,4,6,8...
first term a = -2
lets take third term as nth term and second term as (n-1)th term to find common difference d.
d = 2 - 0 = 2
using a = -2 , d = 2, n = 18
thus, sum of first 18 terms = n/2(2a + (n-1)d)
=18/2( 2*(-2) + (18-1) 2)
=9 ( -4 + 34)
=9 ( 30) = 270
Thus, sum of first 18 terms is 270.
In triangle FGH, F = 830 inches, g = 460 inches and h=500 inches. Find the measure of angle H
to the nearest degree.
9514 1404 393
Answer:
32°
Step-by-step explanation:
The law of cosines can be used for this:
h^2 = f^2 +g^2 -2fg·cos(H)
cos(H) = (f^2 +g^2 -h^2)/(2fg)
cos(H) = (650,500/763,600)
H = arccos(6505/7636) ≈ 31.5826°
Angle H is about 32°.
Fifteen different Thursday evening programs reported that a commercial cost an average of $169,000 with a standard deviation of $81,000. What is the 95% confidence interval for the true mean
Answer:
The 95% confidence interval for the true mean is between $0 and $342,729
Step-by-step explanation:
We have the standard deviation for the sample, so we use the t-distribution to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 15 - 1 = 14
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 14 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.1448
The margin of error is:
M = T*s = 2.1448*81000 = 173,729.
In which s is the standard deviation of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 169,000 - 173,729 = -4,... = $0(cannot be negative)
The upper end of the interval is the sample mean added to M. So it is 169,000 + 173,729 = $342,729
The 95% confidence interval for the true mean is between $0 and $342,729
A machine has four components, A, B, C, and D, set up in such a manner that all four parts must work for the machine to work properly. Assume the probability of one part working does not depend on the functionality of any of the other parts. Also assume that the probabilities of the individual parts working are P(A) = P(B) = 0.93, P(C) = 0.95, and P(D) = 0.92. Find the probability that the machine works properly.A) 0.8128B) 0.2441C) 0.8217D) 0.7559
Answer:
D) 0.7559
Step-by-step explanation:
Independent events:
If two events, A and B are independent:
[tex]P(A \cap B) = P(A)*P(B)[/tex]
In this question:
Four independent events, A, B, C and D.
So
[tex]P(A \cap B \cap C \cap D) = P(A)*P(B)*P(C)*P(D)[/tex]
Find the probability that the machine works properly.
This is the probability that all components work properly.
[tex]P(A \cap B \cap C \cap D) = P(A)*P(B)*P(C)*P(D) = 0.93*0.93*0.95*0.92 = 0.7559[/tex]
So the correct answer is:
D) 0.7559
What is 27 ÷ 4 rounded to the nearest tenth?
Answer:
6.8
Step-by-step explanation:
27 / 4 = 6.75, which rounded to the nearest tenth, is 6.8.
which equation represents a line perpendicular to the line shown on the graph
Answer:
y = 1/4x + (any number)
Step-by-step explanation:
m = -8/2 = -4, the equation shown is y = -4x + 8
perpendicular is y = 1/4x + (any number), you didn't say where the line was perpendicular.
ملی
A man left one-fifth of his property to his
Son , one third to his daughter
and remaining
to his wife. If his wife got 35ooo RS what was the
worth of his total property?
Answer:
Rs 75,000
Step-by-step explanation:
Let the total value of property be x
If one-fifth of that is given to son
property with son = 1/5 of total value of property = 1/5 of x = x/5
If one-third of that is given to daughter
property with daughter = 1/3 of total value of property = 1/3 of x = x/3
remaining property after giving the portions to son and daughter
= total value of property - property with son -property with daughter
= x - x/5 - x/3
taking LCM of 5 and 3 (15)
= (15x - 3x - 5x)/15
= 7x/15
Given that remaining property was given to wife
property with wife = 7x/15
it is given that wife got 35000 Rs
thus,
7x/15 = 35,000
7x = 35,000*15 = 525,000
x = 525,000/7 = 75,000
Thus, total worth of property =Rs 75,000 Answer
Answer:
Rs 75,000
Step-by-step explanation:
Let the total value of property be x
If one-fifth of that is given to son
property with son = 1/5 of total value of property = 1/5 of x = x/5
If one-third of that is given to daughter
property with daughter = 1/3 of total value of property = 1/3 of x = x/3
remaining property after giving the portions to son and daughter
= total value of property - property with son -property with daughter
= x - x/5 - x/3
taking LCM of 5 and 3 (15)
= (15x - 3x - 5x)/15
= 7x/15
Given that remaining property was given to wife
property with wife = 7x/15
it is given that wife got 35000 Rs
thus,
7x/15 = 35,000
7x = 35,000*15 = 525,000
x = 525,000/7 = 75,000
Thus, total worth of property =Rs 75,000 Answer
Chris Evans drives 300 miles per week in his Honda Civic that gets 22 miles per gallon of gas. He
is considering buying a new fuel-efficient car for $20,000 (after trade-in of your Honda Civic)
that gets 50 miles per gallon. Insurance prerniums for the new car and old care are $900 and
$500 per year respectively. If he decides to keep his car, he will need to spend $1200 on repairs
per year. Assume gas costs $3.50 per gallon over a 5-year period,
a, what is the cost of the old car?
b. what is the cost of the new car?
Answer:
old car $20,909new car: $29,960Step-by-step explanation:
At 300 miles per week, Chris drives 300×52 = 15,600 miles per year. His gas cost can be figured as ...
(5 years)×(miles per year)÷(miles/gallon)×($ per gallon) = $273,000/(miles per gallon)
__
a) old car cost = repair cost + gas cost + insurance cost
= 5($1200) + $273,000/22 + 5($500) ≈ $20,909 . . . over 5 years
__
b) new car cost = purchase cost + gas cost + insurance cost
= $20,000 + $273,000/50 +5($900) = $29,960 . . . over 5 years
Find the equation for the plane through the points Upper P 0 (5 comma 4 comma 5 ), Upper Q 0 (negative 5 comma negative 1 comma negative 4 ), and Upper R 0 (negative 2 comma 1 comma negative 2 ). The equation of the plane is nothing.
Answer:
The equation of the plane is
8(x - 5) - 7(y - 4) - 5(z - 5) = 0
8x - 7y - 5z + 13 = 0
Step-by-step explanation:
Given 3 points, P(x₁, y₁, z₁), Q(x₂, y₂, z₂), and R(x₃, y₃, z₃).
We can calculate the equation of the plane through those points as
a(x - x₀) + b(y - y₀) + c(z - z₀) = 0, where (x₀, y₀, z₀) are the coordinates of any one of the points P, Q, or R, and <a,b,c> is a vector perpendicular to the plane.
The vector perpendicular to the plane is obtained by writing vector PQ and PR and taking the cross or vector product.
For this question,
P = (5, 4, 5)
Q = (-5, -1, -4)
R = (-2, 1, -2)
PQ = (-5, -1, -4) - (5, 4, 5) = (-10, -5, -9)
= (-10î - 5ĵ - 9ķ)
PR = (-2, 1, -2) - (5, 4, 5) = (-7, -3, -7)
= (-7î - 3ĵ - 7ķ)
PQ × PR is then
| î ĵ ķ |
|-10 -5 -9|
|-7 -3 -7|
= î [(-5×-7) - (-9×-3)] - ĵ [(-10×-7) - (-9×-7)] + ķ [(-10×-3) - (-7×-5)]
= î (35 - 27) - ĵ (70 - 63) + ķ (30 - 35)
= 8î - 7ĵ - 5ķ
Hence, (a, b, c) = (8, -7, -5)
And using point P as (x₀, y₀, z₀) = (5, 4, 5)
The equation of the plane is
a(x - x₀) + b(y - y₀) + c(z - z₀) = 0
8(x - 5) - 7(y - 4) - 5(z - 5) = 0
8x - 40 - 7y + 28 - 5z + 25 = 0
8x - 7y - 5z = 40 - 28 - 25 = -13
8x - 7y - 5z + 13 = 0
Hope this Helps!!!
Help needed please!!!!!!!!
Olivia recorded the prices of 10 paperback books and 10 hard cover books. Her data is shown.
Paperback: $6.99, $7.49, $12.99, $9.99, $5.99, $8.99, $9.99, $10.00, $3.99, $4.99
Mean: 8.14
Hard cover: $9.99, $12.99, $34.99, $16.99, $15.00, $19.99, $9.99, $10.99, $18.99, $24.99
Mean: 17.49
Which statement is true given the data?
Answer:
C
Step-by-step explanation:
Harasti was inspired to build his hotels after he saw seahorses living in old fishing traps. What is the volume of a fishing trap that is 2 feet wide, 5 feet long, and 3 feet tall?
HELP ME DO THIS !!!!
Answer:
volume of rectangular prism = 30 ft³
Step-by-step explanation:
The fishing trap he wants to build to house sea houses are mostly rectangular prism. The traps are mostly glass like. The volume of the fishing trap will be the volume of the rectangular prism.
volume of rectangular prism = LWH
where
L = length
W = width
H = height
volume of rectangular prism = LWH
Length = 5 ft
width = 2 ft
Height = 3 ft
volume of rectangular prism = 5 × 2 × 3
volume of rectangular prism = 10 × 3
volume of rectangular prism = 30 ft³
A polygon will be dilated on a coordinate grid to create a smaller polygon. The polygon is dilated using the origin as the center of dilation. Which rule could represent this dilation
Answer:
(x, y) → (4/5 x, 4/5 y)
Question:
The answer choices to determine the rule that represent the dilation were not given. Let's consider the following question:
A polygon will be dilated on a coordinate grid to create a smaller polygon. The polygon is dilated using the origin as the center of dilation. Which rule could represent this dilation?
A) (x, y) → (0.5 − x, 0.5 − y)
B) (x, y) → (x − 7, y − 7)
C) (x, y) → ( 5/4 x, 5/4 y)
D) (x, y) → (4/5 x, 4/5 y)
Step-by-step explanation:
To determine the rule that could represent the dilation, we would multiply each coordinate by a dilation factor (a constant) to create a dilation. Since the dilation would be used to create a smaller polygon, the constant multiplied with the coordinates of x and y would be less than 1.
Let's check the options out.
In option (A), the coordinates is subtracted from the constant (0.5).
In option (B), the constant (7) is subtracted from the coordinates.
In option (C), the coordinates are multiplied by constant (5/4).
But 5/4 = 1.25. This is greater than 1.
In option (D), the coordinates are multiplied by constant (4/5).
4/5 = 0.8
The constant multiplied with the coordinates of x and y is less than 1 in option (D) = (x, y) → (4/5 x, 4/5 y)
4/5 = 0.8
0.8 is less than 1
What is the probability of selecting the 4 of spade or black diamond from a deck of 52 playing cards?
a) 2/52
b) 4/52
c) 3/52
d) 1/5
Answer:
b
Step-by-step explanation:
Answer:
he
Step-by-step explanation:
hi
What is the solution to this equation?
3x - 7 + 4x = 28
O A. x= 35
O B. x = 21
O c. x= 5
O D. x= 3
Answer:
x = 5
Step-by-step explanation:
3x - 7 + 4x = 28
Combine like terms
7x -7 = 28
Add 7 to each side
7x - 7 +7 = 28+7
7x = 35
Divide each side by 7
7x/7 = 35/7
x = 5
Solve the inequality and graph the solution set. Write the answer in interval notation. Write your answer in exact simplified form
0> 20x+2>-32
what is the solution?
Answer:
The solution is [tex]\:\left(-\frac{17}{10},\:-\frac{1}{10}\right)[/tex].
Step-by-step explanation:
An inequality is a mathematical relationship between two expressions and is represented using one of the following:
≤, "less than or equal to"<, "less than">, "greater than" ≥, "greater than or equal to"To find the solution of the inequality [tex]0>\:20x+2>\:-32[/tex] you must:
[tex]\mathrm{If}\:a>u>b\:\mathrm{then}\:a>u\quad \mathrm{and}\quad \:u>b\\\\0>20x+2\quad \mathrm{and}\quad \:20x+2>-32[/tex]
First, solve [tex]0>20x+2[/tex]
[tex]\mathrm{Switch\:sides}\\\\20x+2<0\\\\\mathrm{Subtract\:}2\mathrm{\:from\:both\:sides}\\\\20x+2-2<0-2\\\\\mathrm{Simplify}\\\\20x<-2\\\\\mathrm{Divide\:both\:sides\:by\:}20\\\\\frac{20x}{20}<\frac{-2}{20}\\\\\mathrm{Simplify}\\\\x<-\frac{1}{10}[/tex]
Next, solve [tex]20x+2>-32[/tex]
[tex]20x+2-2>-32-2\\\\20x>-34\\\\\frac{20x}{20}>\frac{-34}{20}\\\\x>-\frac{17}{10}[/tex]
Finally, combine the intervals
[tex]x<-\frac{1}{10}\quad \mathrm{and}\quad \:x>-\frac{17}{10}\\\\-\frac{17}{10}<x<-\frac{1}{10}[/tex]
The interval notation is [tex]\:\left(-\frac{17}{10},\:-\frac{1}{10}\right)[/tex] and the graph is:
I need help
On these two
Answer:
10.
A. 10240
6.
B. 2^18 = 262144
Step-by-step explanation:
b) A man purchased 5 dozen of eggs at Rs 5 each. 10 eggs were broken and he
sold the remaining at Rs 5.70 each. Find
(ii) Profit or loss percent.
(i) his total profit or loss.
Answer:
Dear User,
Answer to your query is provided below
(i) Total Loss = Rs.15
(ii) Loss percent = 5%
Step-by-step explanation:
Eggs purchased = 5x12 = 60
Total Cost = 60x5 = Rs 300
Eggs Broken = 10
Eggs Broken cost = 10x5= Rs. 50
Eggs sold = 60-10 = 50
Egg Sale cost = 50x5.70 = Rs 285
(i) Total Loss = C.p. - S.p. = 300 - 285 = 15
(ii) Loss Percent = (Loss/CP)x100 = (15/300)x100 = 5%
Solve the equation. 4c = 3
Answer:
Brainelist~~~!!!
Step-by-step explanation:
4c=3
c=3/4
c=0.75
The solution of the linear equation 4·c = 3, obtained by solving for the variable c is; c = 3/4
What is a linear equation?A linear equation is an equation that can be expressed in the form; y = m·x + c
The equation 4·c = 3 is a linear equation
In order to solve the equation 4·c = 3 for the variable c, the variable c needs to be isolated to one side of the equation, by dividing both sides of the equation by 4 as follows;
4·c = 3
(4·c)/4 = 3/4
c = 3/4
Therefore, the solution of the equation, 4·c = 3 is; c = 3/4
Learn more on linear equations here: https://brainly.com/question/30338252
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A school needs 1,860 pencils for its students. The pencils are sold in boxes of 12. How many boxes does the school need to order?
Answer:
Step-by-step explanation:
155
The number of boxes required by the school to order is 155.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
We have been given that the school needs 1,860 pencils for its students. Also, the pencils are sold in boxes of 12.
We need to find the school needs to requires boxes to order.
Total number of pencil = 1,860
Number of boxes = 12
Therefore, boxes needed = 1,860 / 12
= 155
Hence, the number of boxes required by the school to order is 155.
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If 3 boxes of apples weigh 105 pounds, how much would 2 boxes of apples weigh?
Answer:
70 pounds
Step-by-step explanation:
3 boxes= 105 pounds
2boxes= x pounds
Cross Multiply
3*x=105 *2
3x=210
3x/3=210/3
x=70 pounds
Answer:
70
Step-by-step explanation:
105/3=35
35x2=70
So 70 is the answer
What is the area of the rhombus?
Answer: 24 square units
Explanation: The diagonals are 4+4 = 8 and 3+3 = 6 units long. Multiply the diagonals to get 8*6 = 48. Then divide this in half to get 48/2 = 24.
An alternative is to find the area of one smallest triangle, and then multiply that by 4 to get the total area of the rhombus. You should find the area of one smallest triangle to be 0.5*base*height = 0.5*4*3 = 6, which quadruples to 24.
