To solve the system of linear equations by elimination, we need to eliminate one of the variables by multiplying one or both equations by a constant so that the coefficients of one of the variables are equal in both equations. Then, we can subtract one equation from the other to eliminate that variable and solve for the remaining variable.
In this case, we can eliminate y by multiplying the first equation by -7 and the second equation by 6, so that the coefficients of y are equal in both equations:
-28x - 42y = -336
18x + 42y = 306
Adding these two equations together, we get:
-10x = -30
Dividing both sides by -10, we get:
x = 3
Now that we have solved for x, we can substitute this value into one of the original equations to solve for y. Using the first equation, we get:
4x + 6y = 48
4(3) + 6y = 48
12 + 6y = 48
Subtracting 12 from both sides, we get:
6y = 36
Dividing both sides by 6, we get:
y = 6
Therefore, the solution to the system of linear equations is x = 3 and y = 6.
Marlene wants to enclose her circular vegetable garden with fencing to keep rabbits from eating the vegetables. if the diameter of her garden is 14 feet, how much fencing will she need to buy if fencing is sold by the linear foot?
Marlene will need to buy approximately 44 feet of fencing to enclose her circular vegetable garden.
To determine the amount of fencing Marlene needs, we'll need to calculate the circumference of her circular vegetable garden. Here's a step-by-step explanation:
1. Given the diameter of the garden is 14 feet, we can find the radius by dividing the diameter by 2: Radius = Diameter / 2 = 14 feet / 2 = 7 feet.
2. Now, we will use the formula for the circumference of a circle, which is: Circumference = 2 * pi * radius.
3. Plug in the radius value we found in step 1: Circumference = 2 * pi * 7 feet.
4. Calculate the circumference: Circumference ≈ 2 * 3.1416 * 7 feet ≈ 43.98 feet.
5. Since fencing is sold by the linear foot, Marlene needs to buy approximately 44 linear feet of fencing to enclose her circular vegetable garden and keep the rabbits away.
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2. A scientist placed 100 bacteria in a petri dish. The number of bacteria triples every 12 hours. What is the equivalent hourly rate?
Let's call the initial number of bacteria in the petri dish as $N_0 = 100$. After 12 hours, the number of bacteria triples, which means there are now $3N_0$ bacteria. After another 12 hours, the number of bacteria triples again, which means there are now $3(3N_0) = 9N_0$ bacteria.
We can see a pattern here that after every 12 hours, the number of bacteria is multiplied by 3. Let's calculate the number of bacteria after 1 hour:
$\sf\implies\:N_1 = N_0 \times 3^{1/12}$
After simplifying:
$\sf\implies\:N_1 = 100 \times 3^{1/12}$
Using a calculator, we can find that $\sf\:3^{1/12} \approx 1.1548$. Therefore:
$\sf\implies\:N_1 \approx{\boxed{115.48}}$
So the equivalent hourly rate at which the number of bacteria is increasing is approximately 15.48% per hour.
In general, if the number of bacteria triples every $t$ hours, the equivalent hourly rate can be calculated as:
$\sf\implies\:r = 3^{1/t} - 1$
where $r$ is the hourly rate expressed as a decimal.
[tex]\begin{align}\huge\colorbox{black}{\textcolor{yellow}{\boxed{\sf{I\: hope\: this\: helps !}}}}\end{align}[/tex]
[tex]\begin{align}\colorbox{black}{\textcolor{white}{\underline{\underline{\sf{Please\: mark\: as\: brillinest !}}}}}\end{align}[/tex]
[tex]\textcolor{lime}{\small\textit{If you have any further questions, feel free to ask!}}[/tex]
[tex]\huge{\bigstar{\underline{\boxed{\sf{\color{red}{Sumit\:Roy}}}}}}\\[/tex]
Verify that the function f(x) = -4x^2 + 12x - 4ln x attains an absolute maximum and absolute minimum on
[1/2,2].
Find the absolute maximum and minimum values.
To verify that the function f(x) = -4x^2 + 12x - 4ln x attains an absolute maximum and absolute minimum on [1/2,2], we can use the Extreme Value Theorem.
First, we need to check if the function is continuous on the interval [1/2,2] and differentiable on the open interval (1/2,2).
The function is continuous on [1/2,2] because it is a polynomial and the natural logarithm function is continuous on its domain.
To check if it is differentiable on (1/2,2), we need to take the derivative:
f'(x) = -8x + 12 - 4/x
This is defined and continuous on the open interval (1/2,2).
Now we can find the critical points by setting f'(x) = 0:
-8x + 12 - 4/x = 0
Multiplying both sides by x and rearranging, we get:
-8x^2 + 12x - 4 = 0
Dividing by -4, we get:
2x^2 - 3x + 1 = 0
This factors as (2x - 1)(x - 1) = 0, so the critical points are x = 1/2 and x = 1.
We also need to check the endpoints of the interval:
f(1/2) = -4(1/4) + 6 - 4ln(1/2) = 2 - 4ln(1/2)
f(2) = -4(4) + 12(2) - 4ln(2) = 8 - 4ln(2)
Now we can compare the function values at the critical points and endpoints to find the absolute maximum and minimum:
f(1/2) = 2 - 4ln(1/2) ≈ 5.39
f(1) = -4(1) + 12(1) - 4ln(1) = 8
f(2) = 8 - 4ln(2) ≈ 0.31
So the absolute maximum value is 8, which occurs at x = 1, and the absolute minimum value is 0.31, which occurs at x = 2.
Therefore, the function f(x) = -4x^2 + 12x - 4ln x attains an absolute maximum and absolute minimum on [1/2,2], and the absolute maximum value is 8 and the absolute minimum value is 0.31.
To verify that the function f(x) = -4x^2 + 12x - 4ln(x) attains an absolute maximum and minimum on the interval [1/2, 2], we will first find its critical points by taking the first derivative and setting it to zero, and then evaluate the function at the critical points and endpoints.
The first derivative of f(x) is:
f'(x) = -8x + 12 - 4/x
Setting f'(x) to zero, we have:
-8x + 12 - 4/x = 0
Multiplying by x to remove the fraction, we get:
-8x^2 + 12x - 4 = 0
Dividing by -4, we have:
2x^2 - 3x + 1 = 0
Factoring, we get:
(x-1)(2x-1) = 0
This gives us the critical points x = 1 and x = 1/2.
Now, we evaluate f(x) at the critical points and endpoints:
f(1/2) = -4(1/2)^2 + 12(1/2) - 4ln(1/2)
f(1) = -4(1)^2 + 12(1) - 4ln(1)
f(2) = -4(2)^2 + 12(2) - 4ln(2)
Calculating these values, we get:
f(1/2) ≈ 5.386
f(1) = 4
f(2) ≈ -4
The absolute maximum value is ≈ 5.386 at x = 1/2, and the absolute minimum value is ≈ -4 at x = 2.
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The set of numbers 1 7 11 and 36 contains values for m what value of m makes the inequality 4m + 8 < 36 true
The value of m that makes the inequality 4m + 8 < 36 true is m = 1 for the set of numbers 1 7 11 and 36 contains values for m.
An inequality is a mathematical expression in which the values on the left side of an equation are not equal to the values on the right side, but instead are either greater than or less than the values on the right side.
To find the value of m that makes the inequality 4m + 8 < 36 true, given the set of numbers {1, 7, 11, 36},
Isolate the variable m in the inequality. Subtract 8 from both sides:Now, we know that the value of m should be less than 7. From the given set of numbers {1, 7, 11, 36}, only 1 is less than 7. Therefore, the value of m that makes the inequality true is m = 1.
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A square based pyramid has a side length of 10 inches and a volume of 3300 inches^3. What is the height of the pyramid?
the height of the pyramid is 99 inches.
(explain)
To solve this problem, we can use the formula for the volume of a square pyramid which is:
Volume = (1/3) x (base area) x (height)
Since the base of our pyramid is a square with a side length of 10 inches, the base area would be:
Base area = (side length)^2 = 10^2 = 100 square inches
Substituting the values given in the problem, we get:
3300 = (1/3) x 100 x height
Multiplying both sides by 3, we get:
9900 = 100 x height
Dividing both sides by 100, we get:
height = 99 inches
Therefore, the height of the pyramid is 99 inches.
Pls respond quick | what is the value of the expression? c711
a)330
b)1,663,200
c)5040
d)7920
The value of the expression 11C7 is 330. This can be calculated using the formula for combinations, which is nCr = n!/r!(n-r)!, where n is the total number of objects and r is the number of objects being selected. So, the correct answer is A).
To calculate the value of the expression 11C7, we need to use the formula for combinations or binomial coefficients, which is
nCr = n! / (r! * (n-r)!)
where n is the total number of items, r is the number of items to be chosen, and ! denotes the factorial operation (the product of all positive integers up to n).
In this case, we have
n = 11 and r = 7
So, we can substitute these values into the formula
11C7 = 11! / (7! * (11-7)!)
= 11! / (7! * 4!)
= (11 * 10 * 9 * 8 * 7 * 6 * 5) / (4 * 3 * 2 * 1)
= 330
Therefore, the value of the expression 11C7 is 330. So, the correct answer is A).
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--The given question is incomplete, the complete question is given
"Pls respond quick | what is the value of the expression? ₁₁C₇
a)330
b)1,663,200
c)5040
d)7920"--
order: baraclude (entecavir) 0.5mg PO daily. The drug is an oral
solution with strength of 0.05 mg/mL. How many mL will you
administer?
10mL of the baraclude oral solution to the patient.
To determine the amount of the oral solution of baraclude (entecavir) to administer, we need to use the following formula:
Amount to administer (mL) = Desired dose (mg) / Strength (mg/mL)
In this case, the desired dose is 0.5mg and the strength is 0.05mg/mL. Plugging in these values, we get:
Amount to administer (mL) = 0.5mg / 0.05mg/mL = 10mL
Therefore, you will administer 10mL of the baraclude oral solution to the patient.
Hi! To calculate the number of mL to administer, you need to consider the prescribed dose and the strength of the oral solution. The order is for Baraclude (entecavir) 0.5mg PO daily, and the solution's strength is 0.05 mg/mL.
To find the required mL, divide the prescribed dose by the solution's strength:
0.5 mg (prescribed dose) ÷ 0.05 mg/mL (solution's strength) = 10 mL
You will administer 10 mL of Baraclude (entecavir) oral solution daily.
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a ⃗=⟨-9,6⟩ and b ⃗=⟨3,1⟩. What is the component form of the resultant vector 1/3 a ⃗- 2b ⃗ ?
Show all your work.
please answer this, with full work. even if the answer is incorrect the work is the most important part
The resultant component of the vector addition is (-9, 0).
What is the resultant component of the vectors?The resultant component of the vector is calculated as follows;
a = (-9, 6)
b = (3, 1)
The result of 1/3a = ¹/₃ (-9), ¹/₃(6) = (-3, 2)
The result of 2b = 2(3, 1) = (6, 2)
The result of the vector addition is calculated as follows;
1/3a - 2b
= (-3, 2) - (6, 2)
= (-3 -6, 2 -2)
= (-9, 0)
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¿Como la gastronomia puede ayudarnos a convivir armoniosamente?
Gastronomy is a way of promoting understanding among different cultures, and of bringing people and traditions closer together.
The practise of choosing, preparing, presenting, and consuming exquisite cuisine. The foundation of gastronomy lies in the connections between food, culture, and tradition. Gastronomy has emerged through time as a more potent cultural force than language or other influences among the peoples of the world.
Molecular gastronomy is a relatively recent branch of science that studies the physical and chemical changes that take place during cooking. Molecular cuisine is the name of the new culinary movement based on this emerging discipline.
Nowadays, the world may be broken down into separate gastronomic zones, where different cuisines are popular and similar cooking techniques are used. Throughout much of Southeast Asia, rice is the main food. The abundant and creative use of spices to give meals an extra flavour is what makes Indian and Indonesian cuisine unique. The prevalent ingredient in Mediterranean recipes is olive oil.
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Complete question:
How can gastronomy help us live harmoniously?
Angle pair: exterior. Solve for x
Answer:
11
Step-by-step explanation:
Because of the parallel lines 5x=6x-11, so x=11.
Step-by-step explanation:
this is the answer being alternate exterior angles
Find each value or measure.
assume all lines that appear
to be tangent are tangent.
mztuv =
u
т.
539
v
s.
145º
The measure of angle TUV, given that line segment UT is tangent to circle V, and angle VTS is 145, is 55°.
Based on the information provided, you are looking to find the measure of angle TUV, given that line segment UT is tangent to circle V, and angle VTS is 145º.
Since UT is tangent to circle V, it means that angle UTV is a right angle (90º). Now, we know that the sum of the angles in a triangle is 180º. Therefore, to find the measure of angle TUV (m∠TUV), we can use the following formula:
m∠TUV + m∠UTV + m∠VTS = 180º
Substitute the given values:
m∠TUV + 90º + 145º = 180º
Solve for m∠TUV:
m∠TUV = 180º - 90º - 145º
m∠TUV = -55º
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EMERGENCY HELP NEEDED!!! WIL MARK BRAINLEST!!!
F (X) = X + 3
G (X) = 7X + 4
WHAT DOES (F + G) (X) EQUAL??
The solution to the composite function (f + g)(x) is: 8x + 7
How to solve Composite Functions?Composite functions are said to occur when the output of one function is used as the input of another. If we have a function f and another function g, it means that the function fg(x), said as “ f of g of x”, is the composition of the two functions.
Now, we are given two functions as:
f(x) = x + 3
g(x) = 7x + 4
Thus, we can say that:
(f + g)(x) = f(x) + g(x)
= x + 3 + 7x + 4
= 8x + 7
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Consider this equation
(4x)^1/3 - x =0
The first step in solving this equation is to ____
The second step is to____
Solving this equation for x initially yields____
Checking the solutions shows that____
The first step in solving the equation is to isolate the radical term, and the second step is to eliminate the radical by raising both sides to the power of 3. Solving this equation for x initially yields x = 0, x = 2, and x = -2. Checking the solutions shows that it is not a real solution.
The first step in solving the equation (4x)[tex]^{1/3}[/tex] - x = 0 is to isolate the radical term by adding x to both sides of the equation. This gives us
(4x)[tex]^{1/3}[/tex]= x.
The second step is to raise both sides of the equation to the power of 3, which eliminates the radical. This results in 4x = x³.
Solving this equation for x initially yields x = 0, x = 2, and x = -2.
Checking the solutions shows that only x = 2 is a valid solution, as plugging it back into the original equation yields (4*2)[tex]^{1/3}[/tex] - 2 = 0. However, plugging in x = 0 results in a division by zero, and plugging in x = -2 yields a negative number under the radical, which is not a real solution.
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For each set of data, describe the shape of the
distribution and determine which measures of
center and spread best represent the data.
15. 28, 13, 23, 34, 55, 38, 44, 65, 49, 33, 50, 59,
67, 45
The shape of the distribution in histogram is skewed left and mean=43.071429 and standard deviation= 15.886445 are used together to measure the center and spread of the data.
What is histogram?
A grouped frequency distribution with continuous classes is graphically represented by a histogram. It is an area diagram, and its size is proportional to the frequencies in the associated classes. Due to the base's coverage of the spaces between class boundaries, all of the rectangles in such representations are contiguous.
We can make a sideways histogram. (makes it easier if typing text, but if you are writing on paper then you don't have to make it sideways) Each row will represent a range of 10 (1st row is 10 to 19, 2nd row is 20 to 29, etc)
=> 13 23 28 33 34 38 44 45 49 50 55 59 65 67
The data looks like it is slightly skewed left (hump towards the right [down]). The mean and the standard deviation are used together to measure the center and spread of the data.
Mean = [tex]\frac{ 13+23+28+33+34+38+44+45+49+50+55+59+65+67}{14}=\frac{603}{14}[/tex] = 43.071429
Standard deviation = 15.886445
Hence the shape of the distribution in histogram is skewed left and mean=43.071429 and standard deviation= 15.886445 are used together to measure the center and spread of the data.
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I need help I have no idea how to do this
Answer:
x=6
Step-by-step explanation:
5x+150=180
-150 -150 (subtract 150 from both sides)
5x=30
x=6
Answer:
x = 6
Step-by-step explanation:
Supplementary angles add up to 180 degrees, and lines A and B are parallel, so:
180 - 150 = 30
30/5 = x
6 = x
625y2+400y-36+20z-z2
Answer:
The expression 625y^2 + 400y - 36 + 20z - z^2 can be rearranged and simplified as follows:
625y^2 + 400y - 36 + 20z - z^2
= (25y)^2 + 2(25y)(8) + 8^2 - 8^2 - 36 + 20z - z^2 (adding and subtracting (25y)(8) and 8^2 inside the parentheses)
= (25y + 8)^2 - (8^2 + 36) + 20z - z^2 (expanding the squared term and simplifying)
= (25y + 8)^2 - 100 + 20z - z^2 (simplifying)
Therefore, the simplified form of the expression is:
(25y + 8)^2 - 100 + 20z - z^2.
Note that this expression can also be written as:
(5y + 2)^2(5y - 12)^2 - (z - 10)(z + 10),
Using the difference of squares factorization. However, this is not necessarily simpler than the previous form, and it depends on the context and the purpose of the expression.
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Carlos spots an airplane on radar that is currently approaching in a straight line, and that will fly directly overhead. the plane maintains a constant altitude of 7275 feet. carlos initially measures an angle of elevation of 20°
∘
to the plane at point aa. at some later time, he measures an angle of elevation of 37°
∘
to the plane at point bb. find the distance the plane traveled from point aa to point bb. round your answer to the nearest foot if necessary.
The distance the plane traveled from point A to point B is approximately y - x:
Distance = y - x
≈ 14046.99 feet - 20246.71 feet
≈ -6200.72 feet.
To find the distance the plane traveled from point A to point B, we can use trigonometry and the concept of similar triangles.
Let's denote the distance from point A to the plane as x, and the distance from point B to the plane as y. We are given the altitude of the plane (constant) as 7275 feet.
At point A, Carlos measures an angle of elevation of 20 degrees to the plane, and at point B, he measures an angle of elevation of 37 degrees to the plane.
Using trigonometry, we can set up the following equations:
tan(20 degrees) = 7275 / x,
tan(37 degrees) = 7275 / y.
We can rearrange these equations to solve for x and y:
x = 7275 / tan(20 degrees),
y = 7275 / tan(37 degrees).
Using a calculator, we can evaluate these expressions:
x ≈ 20246.71 feet,
y ≈ 14046.99 feet.
Therefore, the distance the plane traveled from point A to point B is approximately y - x:
Distance = y - x
≈ 14046.99 feet - 20246.71 feet
≈ -6200.72 feet.
Since the distance cannot be negative, we can round the absolute value of the result to the nearest foot:
Distance ≈ 6201 feet.
To find the distance the plane traveled from point A to point B, we can use trigonometry and the concept of similar triangles.
Let's denote the distance from point A to the plane as x, and the distance from point B to the plane as y. We are given the altitude of the plane (constant) as 7275 feet.
At point A, Carlos measures an angle of elevation of 20 degrees to the plane, and at point B, he measures an angle of elevation of 37 degrees to the plane.
Using trigonometry, we can set up the following equations:
tan(20 degrees) = 7275 / x,
tan(37 degrees) = 7275 / y.
We can rearrange these equations to solve for x and y:
x = 7275 / tan(20 degrees),
y = 7275 / tan(37 degrees).
Using a calculator, we can evaluate these expressions:
x ≈ 20246.71 feet,
y ≈ 14046.99 feet.
Therefore, the distance the plane traveled from point A to point B is approximately y - x:
Distance = y - x
≈ 14046.99 feet - 20246.71 feet
≈ -6200.72 feet.
Since the distance cannot be negative, we can round the absolute value of the result to the nearest foot:
Distance ≈ 6201 feet.
Therefore, the distance the plane traveled from point A to point B is approximately 6201 feet.
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d – 10 – 2d + 7 = 8 + d – 10 – 3d
d = –5
d = –1
d = 1
d = 5
Answer:
d=1
Step-by-step explanation:
(i have to write this cuz i cant write less than 20 words)
There are 2 squares, 2 triangles, 2 hexagons, and 2 circles in a teacher's bag of shapes. If a student randomly selects 1 shape from the bag, what is the probability that student selects a circle?
How do i solve for surface area on a rectangular prism
To solve for the surface area of a rectangular prism, you'll need to find the area of each of its six faces and add them together.
A rectangular prism has three pairs of faces: two each for length (L), width (W), and height (H).
First, find the area of the two faces with dimensions L x W. The area is calculated by multiplying length by width: A₁ = L * W. Since there are two such faces, the total area for these is 2A₁ = 2(L * W).
Next, find the area of the two faces with dimensions L x H. The area is calculated by multiplying length by height: A₂ = L * H. The total area for these faces is 2A₂ = 2(L * H).
Finally, find the area of the two faces with dimensions W x H. The area is calculated by multiplying width by height: A₃ = W * H. The total area for these faces is 2A₃ = 2(W * H).
To find the total surface area of the rectangular prism, add the areas of all six faces together: Surface Area = 2A₁ + 2A₂ + 2A₃ = 2(L * W) + 2(L * H) + 2(W * H).
So, the formula for the surface area of a rectangular prism is Surface Area = 2(L * W + L * H + W * H).
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At the airport, there are three counters for checking the luggage. the employees at each counter work independently with the time for each customer modeled as an exponential distribution. the average time is one minute for one counter, two for the next, and three minutes for the third. an actuary, who is next in line, will take the next available counter, i. e. the minimum of the three. what is the variance of the actuary's wait time
The variance of the actuary's wait time is 36 / 121.
How to calculate the varianceFrom the information, at the airport, there are three counters for checking the luggage. the employees at each counter work independently with the time for each customer modeled as an exponential distribution. the average time is one minute for one counter, two for the next, and three minutes for the third. an actuary, who is next in line, will take the next available counter,
From the complete question, the variance of the actuary's wait time will be:
= 1 / (11/6)²
= (6/11)²
= 36 / 121
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And number d -
is q(x) the equation of a line?
Justify your answer.
Answer: for d the answer is yes
Step-by-step explanation:
a line is in the form of y=mx+c or y=mx+b, as p(x)=3x+5 then the equation passes by being compatible with the general equation of a line
Step-by-step explanation:
1d.
yes.
f(x) = 2x + 3
g(x) = x + 2
p(x) = f(x) + g(x) = (2x + 3) + (x + 2) = 3x + 5
p(x) is still a linear function (highest exponent of x is 1). therefore it is a line.
Tres cargas puntuales, q1=5uc,q3=5uc y q2=-2. 0uc, se encuentran en los vértices de un triángulo rectángulo la longitud de los catetos del triángulo es de 10 cm cuál es la fuerza resultante sobre q3
La fuerza resultante sobre q3 debe calcularse considerando la interacción de las cargas q1, q2 y q3.
How to calculate the resultant force on q3?Para determinar la fuerza resultante sobre q3, debemos calcular la magnitud y la dirección de las fuerzas ejercidas por q1 y q2 sobre q3.
Usando la Ley de Coulomb, podemos calcular la fuerza entre dos cargas puntuales utilizando la fórmula: F = k * (|q1| * |q2|) / r^2, donde k es la constante de Coulomb, |q1| y |q2| son los valores absolutos de las cargas, y r es la distancia entre las cargas.
Dado que las cargas q1 y q3 son iguales, y q2 tiene una carga negativa, las fuerzas ejercidas por q1 y q2 en q3 tendrán direcciones opuestas. Debido a la simetría del triángulo rectángulo, las fuerzas tendrán componentes horizontales y verticales iguales en magnitud.
La magnitud de la fuerza resultante sobre q3 se calcula sumando las magnitudes de las fuerzas ejercidas por q1 y q2. La dirección de la fuerza resultante será la misma que la de las fuerzas individuales ejercidas por q1 y q2.
Por lo tanto, para calcular la fuerza resultante sobre q3, debemos encontrar la magnitud de la fuerza ejercida por q1 y la magnitud de la fuerza ejercida por q2, y luego sumarlas. La dirección será la misma que las fuerzas individuales.
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A clown made purple and green balloon animals at a party. He kept track of the requests.
What is the probability that a randomly selected balloon animal is green and is shaped like a dog?
The probability that a randomly selected balloon animal is green and shaped like a dog is 0.231.
What is the probability?The probability is found using the data table given below:
Purple and giraffe = 3; Purple and dog = 3; Green and giraffe = 4; Green and dog = 3
Out of the total number of balloon animals made, the number of green dog balloon animals is 3.
The probability of randomly selecting a green dog balloon animal is found using the formula:
Probability = (number of green dog balloon animals) / (total number of balloon animals)Probability = 3 / (3 + 3 + 4 + 3) = 3/13
Probability = 0.231
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find the exact values of the side lengths b & h
The value of the side lengths b and h in the right-angle triangle is [tex]3\sqrt{2} , and[/tex] 8.
What is a trigonometric ratio, exactly?Trigonometric ratios are the ratios of a right triangle's sides. The sine (sin), cosine (cos), and tangent are three often used trigonometric ratios. (tan).
The given figure is a right-angle triangle.
To find the value of b and h we need to apply the trigonometric ratio.
In the first triangle,
[tex]cos45 = \frac{adjacent}{hypotenuse}[/tex]
[tex]cos45 = \frac{b}{6}[/tex]
[tex]\frac{1}{\sqrt{2} } = \frac{b}{6}[/tex]
[tex]b = \frac{1}{\sqrt{2} } * 6[/tex]
[tex]b = 3\sqrt{2}[/tex]
In the second triangle
[tex]cos60 = \frac{adjacent}{hypotenuse} \\cos60 = \frac{4}{h} \\\frac{1}{2} = \frac{4}{h} \\h= 2 *4\\h = 8[/tex]
Therefore the value of the b and h is [tex]3\sqrt{2}[/tex] , and 8 respectively.
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The figure shown is composed of two congruent triangles and a square Measurements are given in inches 6 in 5 in 4 in A 5 in What is the total area of the figure in square inches 5 in 4 in 5 in
Answer:
60 square inches
Step-by-step explanation:
Pt refers to Pythagoras Theorem. You know two sides of a right angled triangle, how do you find the 3rd side? Pythagoras Theorem. Then the rest is easy. Just do the area of all of the 4 triangles and the area of the square and add them up
HELP
Tom and Kim are playing a game in which they use a spinner with 10 sectors. One of the sectors says, "$0," four
say, "S100," three say, "$200," and two say, "$500. " Use a table to show the probability distribution.
Here is the probability distribution table:
|Outcome|Probability|
|-------|-----------|
|$0 |1/10 |
|S100 |4/10 |
|$200 |3/10 |
|$500 |2/10 |
To create the table, you simply list each possible outcome (in this case, the different amounts that could be won on the spinner), and then calculate the probability of each outcome occurring. In this case, there are 10 sectors in total, so the probability of landing on each sector is 1/10. There is 1 sector that says "$0," so the probability of getting that outcome is 1/10.
There are 4 sectors that say "S100," so the probability of getting that outcome is 4/10, or 2/5. Similarly, there are 3 sectors that say "$200," so the probability of getting that outcome is 3/10, or 3/10.
And finally, there are 2 sectors that say "$500," so the probability of getting that outcome is 2/10, or 1/5.
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4. what is the difference in the measures of center?
5. what is the variability of grades each week?
6. what conclusions can you draw about the test?
Measures of center are statistical tools used to determine the central tendency of a dataset, including mean, median, and mode.
The difference between these tools is how they capture the central tendency.
Variability of grades refers to how much grades fluctuate from week to week, which can be measured using statistical tools such as range, variance, and standard deviation. Without specific information about the test, it is not possible to draw conclusions.
However, analyzing the measures of center and variability can provide insights into student performance and grading consistency.
Further analysis, such as comparing grades to class averages or identifying patterns over time, may reveal additional information.
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Un hacendado compro "5" pollos y "8" conejos por $517,00 y una semana despues a los mismos precios compro "8" pollos y "11" por $761. 00 HALLAR EL COSTO DE UN POLLO Y DE UN CONEJO NOTA: Resolver por el metodo de sustitucion
Using substitution method, the cost of a chicken is $44.56 and the cost of a rabbit is $36.78.
Let's use the substitution method to solve the problem.
Let's assume that the cost of a chicken is "x" dollars and the cost of a rabbit is "y" dollars.
From the first statement, we know that:
5x + 8y = 517 --- equation (1)
And from the second statement, we know that:
8x + 11y = 761 --- equation (2)
Now we can solve for one of the variables in terms of the other from one of the equations, and then substitute that expression into the other equation to solve for the remaining variable.
Solving equation (1) for "y", we get:
y = (517 - 5x) / 8
Now we can substitute this expression for "y" into equation (2), and solve for "x":
8x + 11[(517 - 5x) / 8] = 761
Multiplying both sides by 8 to eliminate the fraction, we get:
64x + 11(517 - 5x) = 6088
Expanding the brackets, we get:
64x + 5687 - 55x = 6088
Combining like terms, we get:
9x = 401
Dividing both sides by 9, we get:
x = 44.56
So the cost of a chicken is $44.56.
Now we can substitute this value for "x" into equation (1) to solve for "y":
5(44.56) + 8y = 517
Simplifying, we get:
222.80 + 8y = 517
Subtracting 222.80 from both sides, we get:
8y = 294.20
Dividing both sides by 8, we get:
y = 36.78
So the cost of a rabbit is $36.78.
Therefore, the cost of a chicken is $44.56 and the cost of a rabbit is $36.78.
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help I want to get this done
Answer:
j: 0, m: (-4)
Step-by-step explanation:
RECALL:
Rational function is the func. expressed by polynomials p(x) and q(x) as:
p(x)/q(x) where q(x) is non-zero
j(m+4) must be non zero, or
j(m+4)≠0
j≠0 and m+4≠0
j≠0 and m≠(-4)