The value of p is 60°.
What is a Triangle?A triangle is a polygon with three sides and three vertices.
Sum of all the angles of the triangle is 180°.
Given, the triangle ABC;
∠A = p + 49° + ∠CAB = 180°
∠CAB = 180° - p - 49°
And the sum of all the angles of the triangle is 180°.
∠CAB + ∠CBA + ∠BCA = 180°
180° - p - 49° + p - 15° + p -16° = 180°
p = 60°
Therefore, Evaluation of p is 60°
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NEEP HELP ASAP LAST DAY OF SCHOOL PLS SHOW YOUR WORK
A rectangular field is 80 meters wide and 120 meters long. Give the length and width of another rectangular field that has the same perimeter but a larger area.
Width= ----- Meters
Length= ------ Meters
The width of the new rectangular field would be 0 meters, which means it would essentially be a line segment.
To find the length and width of another rectangular field that has the same perimeter but a larger area, we can use the following steps:
1. Calculate the perimeter of the given rectangular field:
Perimeter = 2 * (Length + Width)
= 2 * (120 meters + 80 meters)
= 2 * 200 meters
= 400 meters
2. Divide the perimeter by 2 to find the equal sides of the new rectangular field. Since the perimeter is divided equally into two sides, each side would be half of the perimeter length:
Side length = Perimeter / 2
= 400 meters / 2
= 200 meters
3. Now, we have the side length of the new rectangular field. However, we need to determine the length and width that would yield a larger area. One way to achieve this is to make one side longer and the other side shorter.
4. Let's assume the length of the new rectangular field is 200 meters. Since both sides have the same length, the width can be calculated using the formula for the perimeter:
Width = Perimeter / 2 - Length
= 400 meters / 2 - 200 meters
= 200 meters - 200 meters
= 0 meters
5. Therefore, the width of the new rectangular field would be 0 meters, which means it would essentially be a line segment. However, note that the question asks for a rectangular field with a larger area. Since the width cannot be zero, we can conclude that it is not possible to have a rectangular field with the same perimeter but a larger area than the given field.
In summary, it is not possible to find another rectangular field with the same perimeter but a larger area than the rectangular field with dimensions 80 meters wide and 120 meters long.
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hiii! does anyone stan nct? if so what's your favorite unit and bias? :D
Answer:
i not a nctzen yet but i want to be!
Step-by-step explanation:
i am a multistan but there are just too many handsomeness in nct that i cant even keep track of
right now im just trying my best to learn some of their names which i cant even remember lol
Answer:
U and Jeno and Jaemin
Step-by-step explanation:
Find three vectors u, v, w € R² such that {u, v, w} is linearly dependent, and each pair {u, v}, {u, w} and {v, w} is linearly independent. Justify your answer.
the vectors u = [1, 0], v = [0, 1], and w = [1, 1] satisfy the conditions where {u, v, w} is linearly dependent, and each pair {u, v}, {u, w}, and {v, w} is linearly independent.
To find three vectors u, v, w ∈ R² such that {u, v, w} is linearly dependent while each pair {u, v}, {u, w}, and {v, w} is linearly independent, we can choose the vectors carefully. Let's consider the following vectors:
u = [1, 0]
v = [0, 1]
w = [1, 1]
To justify our answer, we need to show that {u, v, w} is linearly dependent and each pair {u, v}, {u, w}, and {v, w} is linearly independent.
First, we can see that u and v are standard basis vectors in R², and they are linearly independent since no scalar multiples of u and v can result in the zero vector.
Next, we observe that u + v = w, meaning that w can be expressed as a linear combination of u and v. Therefore, {u, v, w} is linearly dependent.
Finally, we check the remaining pairs: {u, w} and {v, w}. In both cases, we can observe that the two vectors are not scalar multiples of each other and cannot be expressed as linear combinations of each other. Hence, {u, w} and {v, w} are linearly independent.
In summary, the vectors u = [1, 0], v = [0, 1], and w = [1, 1] satisfy the conditions where {u, v, w} is linearly dependent, and each pair {u, v}, {u, w}, and {v, w} is linearly independent.
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NEED HELP ASAP WILL GIVE BRAINLY IF CORRECT
Answer:
500/40125/vDensitym/vI hope this helps!
PLEASE HELP
Find the value of x in the triangle shown below.
Answer:
82^o
Step-by-step explanation:
74 + 24 = 98
180 - 98 = 82^o
Hope it helps!
When data is positively skewed the mean will be?
Which of the following statements about XY and XZ is true?
2
6
8
X(1, -1)
Y(8, -2)
4
Z(-5.-5)
00
do
10
12
14
Answer:
\(\boxed{\textsf{ The correct option is \textbf{Option (D)} .}}\)
Step-by-step explanation:
For complete solution kindly refer to the attachment .
Related Information :-
• Midpoint formula :-
The midpoint formula for points (x1,y1) and (x2,y2) is ,
\(\boxed{\sf Midpoint =\bigg( \dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\bigg) }\)
• Section Formula :-
The coordinate of point dividing the line joining points (x1,y1) and (x2,y2) in ratio m:n is ,
\(\boxed{\sf Section\ Formula = \bigg(\dfrac{nx_1+mx_2}{m+n},\dfrac{ny_1+my_2}{m+n}\bigg)}\)
Can you answer this math homework? Please!
Step-by-step explanation:
\(x + 3y = 7 \\ 2x + 4y = 8 \\ x = 7 - 3y \\ 2(7 - 3y) + 4y = 8 \\ 14 - 6y + 4y = 8 \\ 14 - 2y = 8 \\ - 2y = - 6 \\ y = 3 \\ x = 7 - 3(3) \\ x = 7 - 9 \\ x = - 2\)
Answer:
2x+3y=7x4
x+4y=8x3
8x+12y=27
3x+12y=24
8x-3x =5x
+12y-+12y=0
27-24=3
5x/5 3/5x
answer = x = 3/5
y=1.85
Eva can type 120 words in 3 minutes. If w represents the number of words she can type in 8 minutes, what proportion could NOT be used to find the value of w?
Answer:
minute per words because it would be in accurate.
Arik invested $500 in a savings account that earns 6.25% interest compounded monthly. Assuming there are no other deposits or withdrawals, what is the total amount in his account after 4 years?
The total amount that would be found in the account after 4 years, would be $ 641. 69
How to find the total amount ?The total amount after 4 years in Arik's account can be found by the formula :
= A = Amount invested x ( 1 + r /n )ⁿ
The variables are:
Amount invested = $ 500
r = 6.25% = 0. 0625
n = 12
t = 4 years
The total amount is then :
A = 500 x ( 1 + 0. 0625 / 12 ) ^ ⁽¹² ˣ ⁴ ⁾
A = $ 641. 69
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Given the right triangle, evaluate: sin 0.
Answer: B. 5/13
This is the same as writing \(\frac{5}{13}\)
==========================================================
Reason:
We have two given sides of this right triangle. Use the pythagorean theorem to find the missing side.
a = 5 and b = 12 are the two known legs; c is the unknown hypotenuse
\(a^2+b^2 = c^2\\\\c = \sqrt{a^2+b^2}\\\\c = \sqrt{5^2+12^2}\\\\c = \sqrt{25+144}\\\\c = \sqrt{169}\\\\c = 13\\\\\)
The hypotenuse is exactly 13 units long. This is a 5-12-13 right triangle.
Now we can compute sine of theta
\(\sin(\text{angle}) = \frac{\text{opposite}}{\text{hypotenuse}}\\\\\sin(\theta) = \frac{5}{13}\\\\\)
This points us to choice B as the final answer.
----------------
Extra Info (optional)
5/12 is the value of tan(theta) since it's opposite/adjacent12/5 is the value of cot(theta), the reciprocal of tangent12/13 is the value of cos(theta), because cos = adjacent/hypotenuseSuppose the motion of a spring-mass system is described by u(t)=5e −3t
cos(2t)+12e −3t
sin(2t). Is this system underdamped, critically damped, or overdamped? Describe how you arrived at your conclusion.
The system is underdamped because ζ < 1, which means that the system will oscillate about the equilibrium point, but with gradually decreasing amplitude.
Given the expression of motion of spring-mass system
u(t)=5e^−3tcos(2t)+12e^−3tsin(2t).
To determine whether the system is underdamped, overdamped, or critically damped, we need to find out the damping ratio first. We can obtain the damping ratio by using the following expression-
ζ= (b/2m)
where b = damping constant
m = mass
Next, we need to find out the natural frequency of the system, ωn given by:
ωn = sqrt(k/m)
Here, k is the spring constant. The motion of the system is described as
u(t)=5e^−3tcos(2t)+12e^−3tsin(2t)
We can identify a pattern in the motion of the system as
u(t) = e^−3t (a cos(2t) + b sin(2t))
= e^−3tA cos (2t - φ)
(by the identity a cos(x) + b sin(x) = A cos(x - φ))
where A^2 = a^2 + b^2, and
tan(φ) = b/a
So, we have
A^2 = 5^2 + 12^2
= 169
and
tan φ = 12/5.
=> φ = 67.38 degrees
Now we can substitute the values of b and m to find the value of damping ratio ζ
ζ= (b/2m)
= φ
= tan^-1 (12/5)
Thus the value of damping ratio is 0.859. Now we can use the following conditions to determine whether the system is overdamped, critically damped, or underdamped:
If ζ < 1, the system is underdamped
If ζ = 1, the system is critically damped
If ζ > 1, the system is overdamped
Here, ζ = 0.859, which is less than 1. Therefore, the system is underdamped.
Thus, the system is underdamped because ζ < 1, which means that the system will oscillate about the equilibrium point, but with gradually decreasing amplitude.
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HELP HELP HELP
Quick algebra 1 question for 50 points!
1. Provide a brief overview of graphing a linear equation using slope.
2. Create 2 original problems and solve it using the graphing a linear equation using slope method, show your work as you solve the problem and explain each step.
The standard equation of a straight line is given by y = mx + b, where m is the slope (rate of change) and b is the y intercept of the line.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The standard equation of a straight line is given as:
y = mx + b
Where m is the slope (rate of change) and b is the y intercept of the line.
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cindy bought 7/8 yards of ribbon at the craft store . jacob bought 4/5 the length of ribbon as cindy. how many yards of ribbon did jacob buy.
Answer:
7/10
Step-by-step explanation:
adults should consume 21 to 38 grams of ________ daily.
Answer: fiber
Step-by-step explanation:
excessive consumption may lead to diarrhea, too less may result in constipation, heart disease and sometimes cancer
What is the approximate volume of this sphere?
Don't forget to use the formula: V=43πr3
A 392.5 cm3
B 523.3¯ cm3
C 3,140 cm3
D 4,186.6¯ cm3
Answer:
Step-by-step explanation:
The formula is incorrect. V = 4πr³/3
Radius r = 10/2 = 5 cm
V = 4πr³/3 ≈ 4×3.14×5³/3 = 523⅓ cm³
The volume of the sphere is 523.3 cm³ if the diameter of the sphere is 10 cm option (B) is correct.
What is a sphere?It is defined as three-dimensional geometry when half-circle two-dimensional geometry is revolved around the diameter of the sphere that will form.
We have the diameter of the sphere shown in the picture,
Let's denote the diameter of the sphere as D then,
D = 10 cm
the radius r will be half the diameter.
r = 10/2 ⇒5 cm
The formula for finding the volume of the sphere is given:
\(\rm V = \frac{4}{3} \pi r^3\\\\\rm V = \frac{4}{3} \pi 5^3\) (r = 5 cm)
\(\rm V =\frac{4}{3} \pi 75\)
V = 166.66π
V = 166.66×3.14 (π = 3.14)
V = 523.31 cm³
Thus, the volume of the sphere is 523.3 cm³ if the diameter of the sphere is 10 cm option (B) is correct.
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The number of micro-organisms in a culture triples every 3hrs. If there were 2 micro-organisms present at noon, how many were there tomorrow the same time assuming that all micro-organisms survive?
There will be 13,122 micro-organisms present at noon the next day
The number of hours between noon today and noon tomorrow is 24 hours.
The micro-organisms triple every 3 hours. The first thing you need to do therefore, is to find the number of 3 hour intervals in 24 hours.
= 24 hours / 3
= 8 three hour intervals
The micro-organisms started with 2 and will triple every 3 hour intervals.
There are 8 three hour intervals so the number of micro-organisms at noon the next day is:
= Beginning number of micro-organisms x 3 ^ number of three hour intervals
= 2 x 3⁸
= 13,122 microorganisms
In conclusion, there will be 13,122 micro-organisms.
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Write an explicit formula for the geometric formula: 1,-3,9,-27…..Find a18
An explicit formula for the geometric sequence is aₙ = (-3)ⁿ⁻¹.
The eighteenth term is -129,140,163.
How to calculate the nth term of a geometric sequence?In Mathematics, the nth term of a geometric sequence can be calculated by using this mathematical expression:
aₙ = a₁rⁿ⁻¹
Where:
aₙ represents the nth term of a geometric sequence.r represents the common ratio.a₁ represents the first term of a geometric sequence.Note: The nth term of a geometric sequence is equal to the explicit formula for the geometric sequence.
Next, we would determine the common ratio as follows;
Common ratio, r = a₂/a₁
Common ratio, r = -3/1
Common ratio, r = -3.
Now, we can calculate the nth term (explicit formula) of this geometric sequence as follows:
aₙ = a₁rⁿ⁻¹
aₙ = 1(-3)ⁿ⁻¹
aₙ = (-3)ⁿ⁻¹
a₁₈ = (-3)¹⁸⁻¹
a₁₈ = (-3)¹⁷
a₁₈ = -129,140,163.
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State the property of integer represented by the following mathematical statement
22 x ( 3 - 7 ) = 22 x 3 – 22 x 7
Answer:
The distributive property
Step-by-step explanation:
When you have a number on the outside of a set of parenthesis, you can remove the parenthesis by multiplying the term on the outside by each of the terms on the inside. This is known as the distributive property.
let x be a random variable with the probability distribution below. find e(x) and ex2 and then, using these values, evaluate e(2x 1)2.
E(X) = 1.88. E(X^2) = 11.12. E((3X + 2)^2) = 126.64. To find E(X) and E(X^2), we will use the provided probability distribution for the random variable X.
E(X) is the expected value of X and can be calculated by multiplying each value of X by its corresponding probability and summing them up. Let's perform this calculation:
E(X) = (-2 * 0.18) + (4 * 0.38) + (6 * 0.12)
= -0.36 + 1.52 + 0.72
= 1.88
Therefore, E(X) = 1.88.
E(X^2) is the expected value of X^2 and can be calculated by multiplying each value of X squared by its corresponding probability and summing them up. Let's perform this calculation:
E(X^2) = ((-2)^2 * 0.18) + (4^2 * 0.38) + (6^2 * 0.12)
= (4 * 0.18) + (16 * 0.38) + (36 * 0.12)
= 0.72 + 6.08 + 4.32
= 11.12
Therefore, E(X^2) = 11.12.
Now, let's evaluate E((3X + 2)^2) using the values of E(X) and E(X^2) obtained in the previous step.
E((3X + 2)^2) = E(9X^2 + 12X + 4)
= 9E(X^2) + 12E(X) + 4
Substituting the values of E(X^2) = 11.12 and E(X) = 1.88:
E((3X + 2)^2) = 9 * 11.12 + 12 * 1.88 + 4
= 100.08 + 22.56 + 4
= 126.64
Therefore, E((3X + 2)^2) = 126.64.
Please note that the final answer is subject to the accuracy of the provided probability distribution and the calculations performed.
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Incomplete Question:
Let X be a random variable with the probability distribution below. Find
E(X)
and
EX2
and then, using these values, evaluate
E(3X+2)2.
x
−2
4
6
f(x)
18
38
12
Find E(X).
E(X)=
(Simplify your answer.)
Find EX2.
EX2=
(Simplify your answer.)
Evaluate
E(3X+2)2.
E(3X+2)2=
(Simplify your answer.)
please make sure answer is correct and answer quickly.
n the metric system, each millimeter increment is equal to _____.A. 1/1000 of a centimeterB. 1/100 of a centimeterC. 1/10 of a centimeterD. 10 centimeters
The answer is C. 1/10 of a centimeter.
can someone see and answer this
Answer:
I can’t see the picture well please make it more detailed
Step-by-step explanation:
Answer: Its A
explanation:
Im good at math
Can i have brainliest please?
the area under the normal curve between the 20th and 70th percentiles is
The area under the normal curve between the 20th and 70th percentiles is then calculated as Area = CDF(z₂) - CDF(z₁)
To find the area under the normal curve between the 20th and 70th percentiles, we need to determine the corresponding z-scores for these percentiles and then calculate the area between these z-scores.
The normal distribution is characterized by its mean (μ) and standard deviation (σ). In order to calculate the z-scores, we need to standardize the values using the formula:
z = (x - μ) / σ
where x is the value, μ is the mean, and σ is the standard deviation.
First, let's find the z-score corresponding to the 20th percentile. Since the normal distribution is symmetrical, the 20th percentile is the same as the lower tail area of 0.20. We can use a standard normal distribution table or statistical software to find the z-score associated with this area.
Let's assume that the z-score corresponding to the 20th percentile is z₁.
Next, we find the z-score corresponding to the 70th percentile. Similarly, the 70th percentile is the same as the lower tail area of 0.70. Let's assume that the z-score corresponding to the 70th percentile is z₂.
Once we have the z-scores, we can calculate the area between these z-scores using the cumulative distribution function (CDF) of the standard normal distribution. The CDF gives us the area under the curve up to a particular z-score.
The area under the normal curve between the 20th and 70th percentiles is then calculated as:
Area = CDF(z₂) - CDF(z₁)
where CDF(z) is the cumulative distribution function evaluated at z.
It is important to note that the CDF values can be obtained from standard normal distribution tables or by using statistical software.
In summary, to find the area under the normal curve between the 20th and 70th percentiles, we follow these steps:
Determine the z-score corresponding to the 20th percentile (z₁) and the z-score corresponding to the 70th percentile (z₂).
Calculate the area using the formula: Area = CDF(z₂) - CDF(z₁), where CDF(z) is the cumulative distribution function of the standard normal distribution evaluated at z.
By performing these calculations, we can determine the area under the normal curve between the specified percentiles.
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What is the equation of a line that is parallel to y=2/3x-7 and passes through (12,2)?
Group of answer choices
A. y=2/3x-6
B. y=2/3x+12
C. y=2/3x-7
D. y=-3/2x+12
Answer:
The answer is option AStep-by-step explanation:
Equation of a line is y = mx + c
where
m is the slope
c is the y intercept
To find the equation of the parallel line we must first find the slope of the original line
From the question the original line is
y = 2/3x - 7
Comparing with the general equation above
Slope = 2/3
Since the lines are parallel their slope are also the same
Slope of parallel line = 2/3
So the equation of the line using point
(12 , 2 ) and slope 2/3 is
\(y - 2 = \frac{2}{3} (x - 12) \\ y - 2 = \frac{2}{3} x - 8 \\ y = \frac{2}{3} x - 8 + 2\)
We have the final answer as
\(y = \frac{2}{3} x - 6 \\ \)
Hope this helps you
A 64-ounce container of juice costs $5.76. What is the cost per ounce?
The cost per ounce of the juice is $0.0.9 using unitary method.
What is unitary method?The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unitary method, in its most basic form, is used to calculate the value of a single unit from a specified multiple. The unitary technique can be used to complete it. Additionally, after determining the value of a single unit, we can increase that value by the number of units needed to determine the value of the additional units. What is division?One of the four fundamental arithmetic processes, or how numbers are combined to create new numbers, is division. The other processes are addition, subtraction, and multiplication. The reverse of multiplying is division.
In this question,
64-ounce container of juice costs $5.76. I
ounce of juice costs = 5.76/64= $0.09
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derive the expressions for intensity transmittivity and reflectivity given in equations (10.29) and (10.30), respectively.
Transmittivity = I_transmitted / (I_reflected + I_transmitted) & Reflectivity = I_reflected / (I_reflected + I_transmitted)
How to derive the expressions for intensity transmittivity and reflectivity?Hi! To derive the expressions for intensity transmittivity and reflectivity given in equations (10.29) and (10.30), respectively, follow these steps:
1. Define the terms:
- Transmittivity (T): The fraction of incident light transmitted through a medium.
- Reflectivity (R): The fraction of incident light reflected by a medium.
- Intensity (I): The power per unit area of light.
2. Consider a light wave incident on a medium with intensities I_incident, I_reflected, and I_transmitted.
3. Based on the conservation of energy, the sum of the reflected and transmitted intensities should equal the incident intensity:
I_incident = I_reflected + I_transmitted
4. Define the transmittivity and reflectivity expressions:
- Transmittivity (T) = I_transmitted / I_incident
- Reflectivity (R) = I_reflected / I_incident
5. Substitute the intensity values into the expressions from step 4:
- T = I_transmitted / (I_reflected + I_transmitted)
- R = I_reflected / (I_reflected + I_transmitted)
6. Rearrange the equations to isolate I_reflected and I_transmitted:
- I_transmitted = T * (I_reflected + I_transmitted)
- I_reflected = R * (I_reflected + I_transmitted)
These are the expressions for intensity transmittivity (Equation 10.29) and reflectivity (Equation 10.30) based on the given information. Note that these expressions may vary depending on the specific context or system being analyzed.
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1. According to Luban, moral injuries and physical injuries are similar in that they share most characteristics except for which of the following:
A. Pain and suffering
B. Loss of functionality
C. Disfigurement
D. None of the others –they share all characteristics
According to Luban, moral injuries and physical injuries are similar in that they share most characteristics except for the pain and suffering caused by physical injuries.
What are Luban?
Luban is an American lawyer and philosopher. He is known for his work on just war theory and international law. Luban argues that moral injuries and physical injuries are similar in that they share most characteristics except for the pain and suffering caused by physical injuries.
Moral injuries:
Moral injuries are injuries caused by actions that violate a person's moral or ethical values.
Physical injuries:
Physical injuries are injuries caused by physical trauma, such as a broken bone or a cut.
Moral injuries and physical injuries are similar in many ways. Both can cause pain and suffering, loss of functionality, and disfigurement. Both can also have long-lasting effects on a person's health and well-being.
However, moral injuries are different from physical injuries in one important way
they do not cause physical pain and suffering.Moral injuries are caused by actions that violate a person's moral or ethical values.
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Hello
Thank you :)
y=3x²+10
is this a function?
Justify your answer.
Can anyone help? can’t figure this one out
Answer:
d = 47°
Step-by-step explanation:
Image is attached
Sum of angles drawn along a straight line = 180°:
The angle drawn in pink : 180° - 112° = 68°
The angle drawn in green: 180° - 66° = 114°
The angle drawn in yellowish orange: 180° - 23° = 157°
The angle marked in purple: 180° - 102° = 78°
The figure drawn in the center is a 5-sided irregular pentagon
∴ Sum of interior angles in a 5-sided polygon = (n - 2) ×180°
= (5 - 2) × 180°
= 540°
The four angles calculated above will assist in calculating the fifth remaining angle of the pentagon (which is marked in light blue):
68° + 114° + 78° + 157° + angle in light blue = 540°
Angle in light blue = 540° - 68° - 114° - 78° - 157°
= 123°
Sum of angles drawn along a straight line = 180°:
Angle marked in dark blue = 180° - 123°
= 57°
Now focus on the angles present inside the triangle
Sum of interior angles of a triangle = 180°
= d + 76° + 57° = 180°
d has to be isolated and made the subject of the equation:
d = 180° - 76° - 57°
d = 47°
A water tank holds 944 gallons but is leaking at a rate of 5 gallons per week. A second water tank holds 1,180 gallons but is leaking at a rate of 9 gallons per week. After how many weeks will the amount of water in the two tanks be the same?
Answer:
59
Step-by-step explanation:
The equation is
944 - 5x = 1180 - 9x
Notice what is being said. You start with 944 gallons and take off 5 per week
You also start with 1180 gallons and take on 9 per week.
You want to know when the two are equal. The second tank is larger, but it leaks more. That's what's going to bring about equality.
Add 9x to both sides
944 - 5x + 9x = 1180
944 + 4x = 1180
Subtract 944 from both sides.
4x = 1180 - 944
4x = 236
Divide by 4
x = 236/4
x = 59 weeks