Step-by-step explanation:
Volume of rect prism = L X W X H = 4 X 9 X 10 = 360 cm^3
ASAP Please help me do a two column proof for this. I am struggling
∠A = ∠C in trapezoid ABCD with arcAB = arcCD, can be proven with the property of isosceles triangles.
How to prove the relation?Since arcAB = arcCD, the lengths of the two arcs are equal. This implies that the lengths of the segments subtended by these arcs, AB and CD, are also equal.
Let E and F be the midpoints of the non-parallel sides AD and BC, respectively. Connect E and F with a line segment EF.
Since E and F are midpoints, DE = EA and BF = FC. In addition, since AB = CD = L, we can say that:
DE + EA = BF + FC
EA = FC
So, by the Hypotenuse-Leg (HL) theorem of congruence, triangles AEF and CFE are congruent:
ΔAEF ≅ ΔCFE
Now, since the triangles are congruent, their corresponding angles are equal:
∠A = ∠C
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2㏒_[6](2)+3㏒_[6](3)+㏒_[6](12)
Answer: 4
Step-by-step explanation:
Given:
[tex]2log_62+3log_63+log_612[/tex]
Rewrite using the power property:
[tex]log_62^2+log_63^3+log_612[/tex]
Rewrite by adding the logarithms together (multiplying) since they all have a common base of 6:
[tex]log_6(2^2*3^3*12)[/tex]
Simplify by multiplying:
[tex]log_6(4*27*12)[/tex]
[tex]log_6(1,296)[/tex]
Evaluate the logarithm:
[tex]log_6(1,296)[/tex]
4
4. A fish tank is in the shape of a cuboid. It
has a base of width 80cm and length of 1.2 m.
Water is put into the tank to a depth of 70cm.
There are 700 000 small fish in the tank. Each
one of them needs a litre of water.
Is there enough water for the fish in the tank?
The volume of water in the tank won't be enough for the fish.
What is volume of a cuboid?A cuboid is a solid shape or a three-dimensional shape. The volume of a cuboid is expressed as;
V = l×w× h
where l is the length, w is the width and h is the height.
The volume of water needed by the fish is 700,000× 1litre = 700,000 litres.
The volume of water the tank can occupy is
V = l× b× h
V = 80× 1200× 70
V = 6,720,000cm³
in litres ;
V = 6,720,000/1000
V = 6720litres
therefore the volume water in the tank is not enough for the fish
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Please use Triangle Inequality to solve, I'm having a bit of trouble. I'd also appreciate if you just help me.
The value of x for the given triangle through which the perimeter of the given relation is satisfied is 10.
What about perimeter of triangle?
The perimeter of a triangle is the total length of its boundary, which is the sum of the lengths of its three sides. The perimeter can be thought of as the distance around the triangle, and it is measured in units of length such as centimeters, meters, or feet. The perimeter of a triangle is an important geometric property that is used in many practical applications, such as calculating the amount of fencing needed to enclose a triangular-shaped garden or determining the length of wire required to form a triangular circuit.
According to the given information:
The perimeter of triangle is sum of all sides of the triangle
In which,
2x + 4 + 3x - 8 + x - 2 = 54
6x - 6 = 54
6x = 60
x = 10
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at what rate is the base of the triangle changing when the altitude is 20 cm and the area is 120 cm2?
The rate at which the base of the triangle is changing when the altitude is 20 cm and the area is 120 cm^2 is 0 cm/s.
To solve this problem, we need to use the formula for the area of a triangle, which is:
A = (1/2)bh
Where A is the area, b is the base, and h is the altitude.
We know that the area is 120 cm^2 and the altitude is 20 cm. So we can plug in these values and solve for the base:
120 = (1/2)b(20)
240 = 20b
b = 12 cm
Now we need to differentiate both sides of the equation with respect to time (t):
dA/dt = (1/2)(db/dt)h
We are given the value of dh/dt (which represents the rate at which the altitude is changing) is 3 cm/s. We need to find db/dt (which represents the rate at which the base is changing).
Plugging in the values we know, we get:
dA/dt = (1/2)(db/dt)(20)
Solving for db/dt, we get:
db/dt = (2dA/dt)/h
Plugging in the values we know, we get:
db/dt = (2)(0)/20
db/dt = 0 cm/s
Since the area is constant (120 cm²) and the altitude is constant (20 cm), the base of the triangle is not changing. Therefore, the rate at which the base is changing is: 0 cm/s
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The shaded area of a circle is 25 cm squared. if the diameter of the circle is 10cm, determine what percentage of the circle is shaded
If the shaded area of a circle is 25 cm squared. if the diameter of the circle is 10cm, the percentage of the circle is shaded is: 31.83% .
What percentage of the circle is shaded?We can start by finding the area of the entire circle. The formula for the area of a circle is:
A = πr^2
where A is the area and r is the radius. Since the diameter of the circle is 10 cm, the radius is half of that, or 5 cm. Therefore, the area of the entire circle is:
A = π(5 cm)^2 = 25π cm^2
Next, we can find what percentage of the circle is shaded by dividing the shaded area by the total area of the circle and multiplying by 100:
Percentage shaded = (shaded area / total area) x 100
Percentage shaded = (25 cm^2 / 25π cm^2) x 100
Percentage shaded = 100 / π ≈ 31.83%
Therefore, approximately 31.83% of the circle is shaded.
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if you used this version of the equation (including your new conversion factor, how would this have changed the intercept of your log-log graph? what would its value have been?
The equation with the new substitutions and conversion factor is a'B'T' = (1/6) * (2/3)^(1/3) * a^(1/3) * d^(1/2)*a^6/6 where k is (1/6) * (2/3)^(1/3) * a^(1/3) * d^(1/2) The intercept value of the log-log graph would have been -1.108.
Starting with Equation 4: T = ka^6/6, we can substitute a = (d/k)^(1/6) and b = (2/3)^(1/2) * (d/k)^(1/3) to get
T = k[(d/k)^(1/6)]^6/6
T = k(d/k)^(1/2)/6
T = (k^(1/2)/6) * d^(1/2)
Now we can rearrange the equation so that a, b, and t are on the left side
a'B'T' = ka^6/6
(a/d)^(1/6) * b^(2/3) * T' = k[(a/d)^(1/6)]^6/6 * T'
(a/d)^(1/6) * (2/3)^(1/2) * (d/k)^(1/3) * T' = (k^(1/2)/6) * d^(1/2) * T'
(2/3)^(1/2) * (a/d)^(1/6) * d^(1/3) * T' = (k^(1/2)/6) * d^(1/2) * T'
(2/3)^(1/2) * (a/d)^(1/6) * d^(1/3) = k^(1/2)/6
k = [(2/3)^(1/2) * (a/d)^(1/6) * d^(1/3)]^2/6
k = (1/6) * (2/3)^(1/3) * a^(1/3) * d^(1/2)
With this new conversion factor, the intercept of the log-log graph would have changed. The intercept represents the value of T when a = 1 (since log(1) = 0). Using the new conversion factor, we have
T = (1/6) * (2/3)^(1/3) * d^(1/2) * a^(1/3)
T = (1/6) * (2/3)^(1/3) * d^(1/2)
log(T) = log[(1/6) * (2/3)^(1/3) * d^(1/2)]
log(T) = log(1/6) + log[(2/3)^(1/3)] + log(d^(1/2))
log(T) = log(1/6) + (1/3) * log(2/3) + (1/2) * log(d)
So the intercept of the log-log graph would be log(1/6) + (1/3) * log(2/3) = -1.108, assuming that d is held constant. This intercept represents the value of log(T) when log(a) = 0, or when a = 1. In other words, when a = 1, the predicted value of T would be 0.162 (or 16.2% of its maximum value).
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--The given question is incomplete, the complete question is given
" Plug the two substitutions into Equation 4 (T = ka^6/6)). Rearrange the equation so that a, b,t are on the left side of the equation and d remains on the right side, e.g. a'B'T' = ka^6/6 you will figure out what the "k" if you used this version of the equation (including your new conversion factor, how would this have changed the intercept of your log-log graph? what would its value have been?"--
Fruit Smoothle
O E. Talia can use 1
cup orange juice
cup yogurt
8 cup strawberries
8 cup blueberries
cup of ice
Blend all ingredients. Serve cold.
Makes 1 serving.
Which statement about the recipe is true? Mark all that apply.
cup strawberries to double the recipe.
O A. Talia can use
OB. Talia can use
OC. Talia can use
12 cup yogurt to make 3 servings.
cup blueberries to make 4 servings.
OD. Talia can use
1
cups orange juice to make 4 servings.
cup of ice to make 5 servings.
A. Talia can use 1 and 3/4 cup strawberries to double the recipe. B. Talia can use 1 and 1/3 cup yogurt to make 3 servings. D. Talia can use 2 cups orange juice to make 4 servings.
What is proportion?In statistics, a proportion is a fraction or a percentage that reflects the proportion of a population's or sample's members who share a particular attribute to the population's or sample's overall size. It is a kind of ratio where the denominator is the entire population or sample size and the numerator is the number of people who possess a specific trait or attribute.
From the given ingredients and the serving size we can see that the correct statement is:
A. Talia can use 1 and 3/4 cup strawberries to double the recipe.
B. Talia can use 1 and 1/3 cup yogurt to make 3 servings.
D. Talia can use 2 cups orange juice to make 4 servings.
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The complete question is:
PLS HURRY!!
The length of ribbons found at a seamstress are listed. 3, 6, 9, 11, 12, 13 What is the appropriate measure of variability for the data shown, and what is its value?
Thus, the appropriate measure of variability found for the given data is 10.
Explain about the range of the data:The difference here between maximum and smallest values in a data set is known as the range. Utilizing the exact same units as the data, it measures variability. More variability is shown by larger values.
The range in statistics refers to the distribution of your data between the lowest and greatest value in the distribution. It is a widely used indicator of variation. Measures of variability provide you with descriptive statistics for summarising your data set in addition to measurements of central tendency.Given length of ribbons:
3, 6, 9, 11, 12, 13
Minimum value = 3
Maximum value = 13
Actually, the range, which is determined by deducting the lowest value from the greatest value in the dataset, would be the proper measure of variability for this data.
Range = Maximum value - Minimum value
Range = 13 - 3
Range = 10
Thus, the appropriate measure of variability found for the given data is 10.
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In the diagram, ABC undergoes a dilation with D as the center of the dilation to create A’ B’ C’. What are possible scale factors of the dilation that will create a A’ B’ C’? Select all that apply.
The scale factor of the dilation must be greater than 1. if the image A'B'C' is bigger than the preimage ABC
What are possible scale factors of the dilationIf the image A'B'C' is bigger than the preimage ABC, then the scale factor of the dilation must be greater than 1.
In other words, the length of any segment in the image is larger than the corresponding segment in the preimage by the same factor.
Since D is the center of the dilation, we can use the ratio of the corresponding side lengths of the image and preimage triangles to find the scale factor.
For example, if we want to find the scale factor for A', we can use:
scale factor = B'C'/BC
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Harry is organizing a picnic. He can spend at most $24. 00 on beverages. Iced tea costs $2. 00 per gallon and lemonade costs $2. 50 per gallon. If x represents the number of gallons of iced tea and y represents the number of gallons of lemonade, which inequality shows the number of gallons of each drink that he can buy? Identify the number of gallons of iced tea that Harry can buy if he buys 5 gallons of lemonade.
Answer:
Harry can buy 5 gallons of lemonade and 5 gallons of iced tea and still have $1.50 left over from his original $24 dollar budget
Step-by-step explanation:
At a computer manufacturing company, they produce two different types of computers. They can make 70 laptops per day while making 55 desktops per day. The company has a total of 14 machines to make computers. They can make a total of 905 computers per day. How many machines make laptops and how many make desktops?
Write a system of equations and solve.
Answer:
Yo wassup bro, at this computer factory, they be making two types of computers, laptops and desktops. They churn out 70 laptops a day and 55 desktops a day. They got a total of 14 machines to make these computers. And they make a total of 905 computers a day. We gotta figure out how many machines are making laptops and how many are making desktops, ya know?
Alright, let's set up a system of equations to solve this. Let's call the number of machines making laptops "x" and the number of machines making desktops "y".
So, we got two equations here:
The total number of computers they make in a day is 905, so we can write: x laptops + y desktops = 905.
They got a total of 14 machines, so we can write: x + y = 14.
Now, let's solve this system of equations to find the values of x and y, man. Once we got those, we'll know how many machines are making laptops and how many are making desktops at this computer factory, yo!
the table shows several packages of assorted spools of thread available at a store. what is the price per spool of each kind of thread?
I'm sorry, but I cannot provide a definitive answer to your question as I do not have access to the table you are referring to.
However, in general, to find the price per spool of each kind of thread, you would need to know the total price of the package and the number of spools in the package.
To calculate the price per spool, you would divide the total price of the package by the number of spools in the package. For example, if a package costs $10 and contains 50 spools of thread, the price per spool would be $0.20 ($10 ÷ 50 = $0.20).
You can use this method to find the price per spool for each type of thread in the table you are looking at.
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HELP ME PLEASE!!!!!!!
Answer:
Step-by-step explanation:
Graph # Matching equation
1 |-3x|
2 |-x|
3 -|2x|
You can tell which one matches by finding the slope and whether the V points up or down
i need some help with this problem i don’t really understand it
Answer:
-34x+29
Step-by-step explanation:
[tex]7(5-x)-3(9x+2)=7.5-7x-3.9x-3.2=35-7x-27x-6\\=-34x+29[/tex]
4. The radius of a cylinder is 3x-2 cm. The height of the cylinder is x +3 cm. What is the
surface area of the cylinder? Use the formula A=2x²+2xrh.
02x (3x2+10x-8)
O 27(12x+7x-2)
O 27(12x²-2x+13)
O 27(12x²-5x-2)
Answer:
D: 27(12x² - 5x - 2).
Step-by-step explanation:
The formula for the surface area of a cylinder is: A = 2πr² + 2πrh
Given that the radius of the cylinder is 3x - 2 cm and the height is x + 3 cm, we can substitute these values in the formula and simplify:
A = 2π(3x - 2)² + 2π(3x - 2)(x + 3)
A = 2π(9x² - 12x + 4) + 2π(3x² + 7x - 6)
A = 18πx² - 24πx + 8π + 6πx² + 14πx - 12π
A = 24πx² - 10πx - 4π
A = 2π(12x² - 5x - 2)
Therefore, the answer is option D: 27(12x² - 5x - 2).
Answer:
D
Step-by-step explanation:
Solve the IVP given by y''+y=t, y(0)=1, y'(0)=-2
The solution to the IVP given by y''+y=t, y(0)=1, y'(0)=-2 is y(t) = cos(t) - (3/2) sin(t) + (1/2) t.
To solve the Initial Value Problem, we can use the method of undetermined coefficients, which involves assuming a particular form for the solution to the non-homogeneous equation y'' + y = t, and then finding the coefficients of the terms in that form by substituting it back into the equation.
First, we find the general solution to the homogeneous equation y'' + y = 0
The characteristic equation is r² + 1 = 0, which has solutions r = ±i. Therefore, the general solution to the homogeneous equation is
y_h(t) = c₁ cos(t) + c₂ sin(t),
where c₁ and c₂ are constants determined by the initial conditions.
Next, we assume a particular form for the non-homogeneous solution, based on the form of the right-hand side t. Since t is a linear function, we assume that the particular solution has the form
y_p(t) = a t + b.
Substituting this into the differential equation, we get
y''_p + y_p = t
2a + (at+b) = t.
Equating coefficients, we get
a = 1/2, b = 0.
Therefore, the particular solution is
y_p(t) = (1/2) t.
The general solution to the non-homogeneous equation is then the sum of the homogeneous and particular solutions
y(t) = y_h(t) + y_p(t)
= c₁ cos(t) + c₂ sin(t) + (1/2) t.
To determine the constants c₁ and c₂, we use the initial conditions:
y(0) = c₁ cos(0) + c₂ sin(0) + (1/2) (0) = c₁ = 1,
y'(0) = -c₁ sin(0) + c₂ cos(0) + (1/2) (1) = c₂ - (1/2) = -2,
so c₂ = -3/2.
Therefore, the solution to the IVP is
y(t) = cos(t) - (3/2) sin(t) + (1/2) t.
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‼️WILL MARK BRAINLIEST‼️
The average distance of electric cars is 275.
The range of the data set is 300.
How to solveGiven:
Average of the data set = 275Range of the data set = 300To find: Average distance of electric cars
Solution:
The average distance of electric cars can be calculated by finding the average of the data set containing the distances of electric cars. Let's assume that the data set is as follows:
250, 250, 250, 400, 300, 300, 350, 100
To find the average distance of electric cars, we can use the formula:
Average = (Sum of all the data points) / (Number of data points)
Substituting the given values, we get:
Average = (250 + 250 + 250 + 400 + 300 + 300 + 350 + 100) / 8
Average = 2200 / 8
Average = 275
Therefore, the average distance of electric cars is 275.
Now, let's calculate the range of the data set. The range is the difference between the maximum and minimum values in the data set. From the given data set, we can see that the minimum value is 100 and the maximum value is 400.
Range = Maximum value - Minimum value
Range = 400 - 100
Range = 300
Therefore, the range of the data set is 300.
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How do you find the period of a cosine function of the form y = cos bx?
The period of a cosine function of the form y = cos bx is equal to T= 2π/b where 'T' is the period of the cosine function and b is the coefficient of x in the function.
This formula tells us that the period of the cosine function is equal to the length of one complete cycle of the function.
it represents the distance along the x-axis for the cosine function to complete one full oscillation.
The period of a cosine function of the form y = cos bx, first identify the coefficient b.
Use the formula T= 2π/b to calculate the period 'T'.
For example,
Consider cosine function y = cos 2x,
The coefficient of x is 2.
Using the formula above, the period is equal to
Period = 2π/2
= π
So the period of the function y = cos 2x is π.
This implies that the cosine function completes one full oscillation every π units along the x-axis.
Therefore, the formula used to calculate the period of the cosine function y = cos bx is given by T= 2π/b.
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6²
Which theorem is shown by the diagram above?
a + b = c
C
D
a - b = c
a² + b² = c²
a²-b² = c²
The theorem is shown in a pythagoras theorem is c² = a² + b²
Which theorem is shown in a pythagoras theoremThe theorem shown in the Pythagorean theorem is "a² + b² = c²". This theorem is named after the ancient Greek mathematician Pythagoras, who is credited with discovering it.
The Pythagorean theorem applies to right-angled triangles and states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Mathematically, we can express this as:
c² = a² + b²
Where c is the length of the hypotenuse, and a and b are the lengths of the other two sides (called the legs) of the right-angled triangle.
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Can please someone help me ASAP? It’s due tomorrow. I will give brainliest if it’s all correct!!
Please do part a, b, and c
The sample space are:
{AR, AS, AT, AE, RA, RS, RT, RE, SA, SR, ST, SE, TA, TR, TS, TE, EA, ER, ES, ET}
The favorable outcomes care:
{RS, RT, SR, ST, TR, TS}
The probability is 0.3 or 30%
How to find the sample spacePart A:
The sample space represents all possible outcomes that can occur when two cards are randomly selected without replacement from the given pile of cards.
The sample space can be represented as follows:
{AR, AS, AT, AE, RA, RS, RT, RE, SA, SR, ST, SE, TA, TR, TS, TE, EA, ER, ES, ET}
Part B:
The favorable outcomes are those outcomes in which both cards are consonants. In this case, the consonants are R, S, and T.
The favorable outcomes can be represented as follows:
{RS, RT, SR, ST, TR, TS}
Part C:
To calculate the probability of selecting 2 cards that are consonants, we need to find the ratio of favorable outcomes to the sample space.
The number of favorable outcomes is 6, and the size of the sample space is 20.
Therefore, the probability of selecting 2 cards that are consonants is:
P(consonants) = favorable outcomes / sample space
P(consonants) = 6 / 20
P(consonants) = 0.3 or 30%
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Please help me with this homework
Answer: Circumference = 18 π cm
Step-by-step explanation:
We can use this formula to find the circumference of a circle:
➜ r is equal to the radius, also known as half the width of a circle.
C = 2πr
We will substitute our known values and solve for C by multiplying. Since the answer option includes π in our units, we do not multiply this into the 18.
C = 2πr
C = 2π(9)
C = 18 π cm
Answer: 18π
Step-by-step explanation:
The circumference of a circle is equal to 2πr, with r being equal to the radius. The radius of a circle is defined as the length from any point on the circle to its middlemost point. In this case, we are given the value of the radius as defined by the line. The radius equals 9, which we can plug into the equation.
C= 2πr
C = 2π(9)
C = 18π = 56.55
Hope this helps!
Ms. Yamato's gross pay is $2644. Her deductions total $548.30.
What percent of her gross pay is take-home pay?
A. 84%
B. 79%
C. 21%
D. 18%
Thus, the correct Percent response is B) 79%.
what is a percent?Percentage refers to a portion of every hundred. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, it is frequently shown using the percent sign, "%".
If you have 100 apples and distribute 10 of them, for instance, you have distributed 10% of your total apple supply.
We deduct Ms. Yamato's deductions from her gross income to determine her take-home pay:
$2644 - $548.30 = $2095.702.
By dividing her take-home pay by her gross pay and multiplying the result by 100%, we can determine what proportion of her gross pay is taken home:
($2095.70 / $2644) * 100% = 79%
Thus, the correct response is B) 79%.
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A factory has two assembly lines, M and N, that make the same toy. On Monday, only assembly line M was functioning and it made 900 toys.
On Tuesday, both assembly lines were functioning for the same amount of time. Line M made 300 toys per hour and line N made 480 toys per hour. Line N made as many toys on Tuesday as line M did over both days.
Write an equation that can be used to find the number of hours, t, that the assembly lines were functioning on Tuesday.
Answer: First choice 480t = 300t + 900
Step-by-step explanation:
A factory has two assembly lines, M and N, that make the same toy. On Monday, only assembly line M was functioning and it made 900 toys.
On Tuesday, both assembly lines were functioning for the same amount of time. Line M made 300 toys per hour and line N made 480 toys per hour. Line N made as many toys on Tuesday as line M did over both days.
Write an equation that can be used to find the number of hours, t, that the assembly lines were functioning on Tuesday.
ANS
Let say t is time in hrs for Which Both Assembly line worked
M made 300 toys per hr on Tuesday
Toys made on Tuesday at Assembly line M = 300 × t = 300t toys
N made 480 toys per hr on Tuesday
Toys made on Tuesday at Assembly line N = 480 × t = 480t toys
Toys Made by N on Tuesday = Toys made by M on Tuesday + Toys made by M on Monday
480t = 300t + 900
=> 180 t = 900
=> t = 900/180
=> t = 5 hr
N capacity on tuesday Per hour * t = M capacity on tuesday per hour * t + Toys made by M on Monday
N = N capacity on tuesday Per hour
M = M capacity on tuesday Per hour
=> t (N - M ) = 900
=> t = 900/(N-M)
Springtown Hardware kept an inventory of 697,500 lawnmowers in the past. With a change in management, the hardware store now keeps an inventory of 24% more lawnmowers. How many lawnmowers is that?
Thus, the number of current lawnmowers in the Springtown Hardware is 864,900.
Explain about the percentage:In mathematics, a percentage is a number or ratio that may be expressed as a fraction of 100. The Latin word "per centum," which meaning "per 100," is where the word "percent" comes from. % is the symbol used to represent percentages.
When a number is expressed in decimal form, you can calculate its percentage by multiplying it by 100. For instance, multiplying 0.5 by 100 gives you the percentage 50%.
Given data:
Springtown Hardware's inventory - 697,500 lawnmowers.
Current inventory of 24% more lawnmowers.
Current inventory = old inventory + 24% of old inventory
Current inventory = 697,500 + 24 % of 697,500
Current inventory = 697,500 + 24 * 697,500/ 100
Current inventory = 697,500 + 24* 6,975
Current inventory = 864,900
Thus, the number of current lawnmowers in the Springtown Hardware is 864,900.
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a man can hit his target 25% of the time if he fires 4 shots in succession what is the probability that he will hit his target
The probability that the man will hit his target at least once in 4 shots is calculated using the complementary probability of him missing all 4 shots. Since he hits his target 25% of the time, he misses it 75% of the time.
The probability of missing all 4 shots is (0.75)^4 = 0.3164.
Now, to find the probability of hitting the target at least once, subtract the probability of missing all shots from 1:
1 - 0.3164 = 0.6836 or 68.36%.
So, the probability that the man will hit his target at least once in 4 shots is approximately 68.36%.
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The length of one leg of a right triangle is 2 times the length of the other, and the
length of the hypotenuse is 12. What is the length of the longest leg?
Answer:
[tex]\frac{24\sqrt{5} }{5}[/tex]
Step-by-step explanation:
Let's start by assigning one of the unknown legs with the variable x.
We know that the other leg is 2 times the length of x, so we can write:
2x
We also know that the length of the hypotenuse is 12.
From here, we can use the Pythagorean Theorem.
Recall that the Pythagorean Theorem is:
[tex]a^2+b^2=c^2[/tex]
where a is the length of one leg, b is the length of the other leg, and c is the length of the hypotenuse.
Let's substitute the values. We have:
[tex]x^2+(2x^2)=12^2=\\x^2+4x^2=144=\\5x^2=144=\\x^2=\frac{144}{5}=\\x=\frac{12}{\sqrt{5} }[/tex]
Let's rationalize the denominator by multiplying the numerator and denominator by [tex]\sqrt{5}[/tex], like so:
[tex]\frac{12}{\sqrt{5} } =\\\frac{12\sqrt{5} }{5}[/tex]
Therefore, [tex]x=\frac{12\sqrt{5} }{5}[/tex]
Let's solve for 2x:
[tex]2x=\\2(\frac{12\sqrt{5} }{5})=\\ \frac{24\sqrt{5} }{5}[/tex]
So, the length of the longest leg is [tex]\frac{24\sqrt{5} }{5}[/tex]
One gallon of paint covers 400 square feet. What is the least amount of paint needed to paint the walls of a room in the shape of a rectangular prism with a length of 17 feet, a width of 15 feet, and a height of 12 feet? Write your answer as a decimal. Gal
We need at least 3.465 gallons of paint to paint the walls of this room.
The area of the two rectangular faces on either end of the prism is:
length x height = 17 x 12 = 204 square feet
The area of the two rectangular faces on the sides of the prism is:
width x height = 15 x 12 = 180 square feet
The area of the top and bottom faces of the prism is:
length x width = 17 x 15 = 255 square feet
The total surface area of the prism is:
2(204) + 2(180) + 2(255) = 1386 square feet
Now, we divide surface area by coverage of one gallon of paint:
1386 / 400 = 3.465
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q= 2-4t/t+3
make t the subject of the formula
(please include steps!!!!) ty
Therefore (t) can be written as **(2 - 3Q) / (Q + 4)**.
Define Q?Within the given equation, Q is a variable. It stands for an unknowable amount or value that can be ascertained by equation-solving.
What exactly is variable?A quantity that can take on any one of a number of values is referred to as a variable. A variable in mathematics is a symbol or letter that denotes an unknowable amount or value. The variable Q in the given equation stands for an unknowable quantity or value that can be ascertained by resolving the equation.
The equation is as follows:
Q = (2 - 4t) / (t + 3)
When we divide both sides by (t + 3), we obtain:
Q(t + 3) = 2 - 4t
When we increase the left side of the equation, we obtain:
Qt + 3Q = 2 - 4t
The result of adding 4t to both sides of the equation is:
Qt + 3Q + 4t = 2
Combining related concepts gives us:
t(Q + 4) = 2 - 3Q
The result of dividing both sides by (Q + 4) is:
t = (2 - 3Q) / (Q + 4)
t can therefore be written as **(2 - 3Q) / (Q + 4)**.
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the time it takes to cover the distance between two cities by car varies inversely with the speed of the car. the trip takes hours for a car moving at . how long does the trip take for a car moving at ?
The time takes by car to cover the distance between two cities by car varies inversely with the speed of car. Total 5 hours will consume to complete the trip with a car moving at 40 mph.
Time is taken in traveling a particular distance is proportional to the distance traveled which means more distance covered in more time.
The speed of an object is defined as the 'distance traveled per unit time'. Formula is written as [tex]Speed(s ) = \frac{Distance(d)}{Time(t)}[/tex]
Distance(d) = Speed(r)×Time(t)Time(t) = Distance(d)/Speed(s)Now, Speed of car (s) = 50 miles per hour
Car takes 4 hours to complete the trip. Let the distance travelled by car in 4 hour during the trip be 'x'. Applying the speed formula, [tex]50 mph = \frac{ x}{4 \: \: hours}[/tex]
=> x = 4 × 50 miles
=> x = 200 miles
Now, if the speed of car (s') = 40 mph in the trip. We have to determine the time taken by car to complete the trip with 40 mph speed. So, we know the speed of car and total distance travelled by car on trip. Using the time formula,[tex]time ( t') = \frac{distance (x) }{ speed( s')} [/tex]
=> [tex] time (t') = \frac{ 200 \: miles}{ 40 \: mph}[/tex]
= 5 hours.
Hence, required value of time is 5 hours.
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Complete question :
The time it takes to cover the distance between two cities by car varies inversely with the speed of the car. The trip takes four hours for a car moving at 50 mph. How long does the trip take for a car moving at 40 mph?