what is the value of y

Answer: 5 were triangles :)

Answer: 08:00

Step-by-step explanation:

If you want breakfast to be ready at 08:15 and the cooking time is 15 minutes, you need to start cooking at:

08:15 - 00:15 = 08:00

So you need to start cooking at 08:00 in order to have breakfast ready by 08:15.

The solution to the system of equations using matrices is x = 45, y = 15, and z = 30.

A scalar value that can be calculated from a matrix's elements is the determinant. When a square matrix is used to transform vectors, the determinant is a measurement of how much the matrix "stretches" or "shrinks" space. In linear algebra, the determinant is employed in a variety of operations, including as the computation of a matrix's inverse, the description of a matrix's eigenvalues and eigenvectors, and the resolution of linear equation systems. In specifically, the existence of a unique solution, the absence of a solution, or an unlimited number of solutions to a system of linear equations can be determined using the determinant of the coefficient matrix.

The given equation are:

2x -y + 3z = 180

-4x + 2y + 3z = 225

3x - 4y = 270

Writing the equations in matrix form we have:

[tex]\begin{bmatrix} 2 & -1 & 3 \\ -4 & 2 & 3 \\ 3 & -4 & 0 \end{bmatrix} \begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} 180 \\ 225 \\ 270 \end{bmatrix}[/tex]

Multiplying the inverse of the coefficient matrix we have:

[tex]\begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} 2 & -1 & 3 \\ -4 & 2 & 3 \\ 3 & -4 & 0 \end{bmatrix}^{-1} \begin{bmatrix} 180 \\ 225 \\ 270 \end{bmatrix}[/tex]

Now,

[tex]\begin{bmatrix} 2/23 & 5/46 & -3/23 \\ 2/23 & 1/23 & 5/23 \\ -3/23 & -5/46 & 2/23 \end{bmatrix}[/tex]

Multiplying this by the vector on the right-hand side gives:

[tex]\begin{bmatrix} x \ y \ z \end{bmatrix} = \begin{bmatrix} 2/23 & 5/46 & -3/23 \\ 2/23 & 1/23 & 5/23 \\ -3/23 & -5/46 & 2/23 \end{bmatrix} \begin{bmatrix} 180 \\ 225 \\ 270 \end{bmatrix} = \begin{bmatrix} 45 \\ 15 \\ 30 \end{bmatrix}[/tex]

Hence, the solution to the system of equations is x = 45, y = 15, and z = 30.

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The value of p(B/A) represents the probability that event B will occur given that event A has occurred.

It is a measure of conditional probability, which is calculated using the formula:

p(B/A) = p(A ∩ B) / p(A)

Where:

Therefore, To calculate the value of p(B/A), you need to know the probabilities of A and B, as well as the probability that both occur together.

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The composite functions (f/g)(x) and (f-g)(x) are (2x-1)/√(3x-5) and (2x-1) -√(3x-5)

To calculate (f/g)(x), we need to divide f(x) by g(x):

(f/g)(x) = f(x)/g(x) = (2x-1)/√(3x-5)

The domain of (f/g)(x) is the set of all x-values for which the denominator √(3x-5) is not equal to zero and non-negative

3x-5 ≥ 0, or x ≥ 5/3

Therefore, the domain of (f/g)(x) is x ≥ 5/3.

To calculate (f-g)(x), we need to subtract g(x) from f(x):

(f-g)(x) = f(x) - g(x) = (2x-1) - √(3x-5)

The domain of (f-g)(x) is the set of all x-values for which the expression inside the square root is non-negative:

3x-5 ≥ 0, or x ≥ 5/3

Therefore, the domain of (f-g)(x) is x ≥ 5/3.

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Answer:

Axis of symmetry =1

vertex =(1,2)

y intercept =0

min/max= -6,2

domain= 0,1,2

range =y≥1,2

Answer: 4.8%

Step-by-step explanation: the total amount of pens in the drawer is (10+12+3)  = 25

the amount of red pens in the drawer is 3

the probability of picking out a red pen from the drawer = 3/25

the amount of blue pens in the drawer is 10

the probability of picking out a red pen from the drawer = 10/25

the probability of picking out a red pen then a blue pen afterwards = (10/25 x 3/25) = 4.8%

Answer:

Step-by-step explanation:

yes because quadrilaterals have 4 sides and so do all squares

hope this answered your question

Answer:

380 weight

Step-by-step explanation:

please brilliant answer me

the area of the trapezoid is 10√3 km² (approximately 17.3 km²).To find the area of a trapezoid, we use the formula A = (1/2) * (b₁ + b₂) * h

what is trapezoid ?

A trapezoid is a quadrilateral with at least one pair of parallel sides. The parallel sides are called the bases of the trapezoid, and the other two sides are called the legs. The height (or altitude) of a trapezoid is the perpendicular distance between the two bases. The formula for the area of a trapezoid

In the given question,

To find the area of a trapezoid, we use the formula:

A = (1/2) * (b₁ + b₂) * h

where A is the area, b₁ and b₂ are the lengths of the parallel sides of the trapezoid, and h is the height (or perpendicular distance between the parallel sides).

In this case, we are not given the height, but we can still find the area if we make some assumptions. Let's assume that the trapezoid is isosceles, which means that the two non-parallel sides are equal in length. Then we can draw an altitude from one of the vertices to the opposite base, which will bisect the base and create two right triangles.

Using the Pythagorean theorem, we can find the length of the altitude:

a² + (b₁ - b₂)² = (2a)²

Simplifying and solving for a, we get:

a² + (b₁- b₂)² = 4a²

3a² = (b₁ - b₂)²

a = (1/√3) * |b₁ - b₂|

Since we know that the sum of the non-parallel sides is 10 km, we can write:

b₁ + b₂ = 10

Let's assume that b1 is the longer base, so we can write:

b₁ = 8 km

b₂ = 10 - b₁ = 2 km

Substituting these values into the formula for the altitude, we get:

a = (1/√3) * |8 - 2| = (1/√3) * 6 = 2√3 km

Now we can use the formula for the area of a trapezoid to find the area:

A = (1/2) * (b1 + b2) * h

A = (1/2) * (8 + 2) * 2√3

A = 10√3 km²

Therefore, the area of the trapezoid is 10√3 km² (approximately 17.3 km²).

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The intervals on which the function Is constant are [-4, -3] and [3, 6]

A function is considered constant over an interval if the function has the same output for all the inputs within that interval.

In other words, the function does not change over that interval.

Using the above as a guide, we have the following:

The function does not change over the intervals [-4, -3] and [3, 6]

Hence, the intervals are [-4, -3] and [3, 6]

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greatest common factor, which is 18.

What is greatest common factor?

The largest factor that all of the numbers share is known as the greatest common factor (GCF) of a set of numbers.

One way to do this is to list the factors of both 36 and 90 and find their common factors. The factors of 36 are:

1, 2, 3, 4, 6, 9, 12, 18, 36

The factors of 90 are:

1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90

The common factors of 36 and 90 are:

1, 2, 3, 6, 9, 18

Therefore, the greatest common factor of 36 and 90 is 18.

To reduce the fraction 36/90, we can divide both the numerator and denominator by 18:

36 ÷ 18 = 2

90 ÷ 18 = 5

So, 36/90 can be reduced to 2/5 by dividing both the numerator and denominator by their greatest common factor, which is 18.

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if csc(x) = 7 and x is in quadrant II, then cos(x/2) = -√((7 - 4√(3))/14).

How to solve the question?

We can start by using the reciprocal identity of csc to find the sin of x.

csc(x) = 7 can be rewritten as sin(x) = 1/7

Next, we can use the Pythagorean identity to find the cosine of x:

cos²(x) = 1 - sin²(x) = 1 - (1/7)²= 48/49

Since x is in quadrant II, cosine is negative, so cos(x) = -√(48/49) = -4√(3)/7

Now we can use the half-angle identity for cosine to find cos(x/2):

cos(x/2) = ±√((1 + cos(x))/2)

We know that cos(x) is negative and that x is in quadrant II, which means that x/2 is also in quadrant II.

Therefore, cos(x/2) = -√((1 - 4√(3)/7)/2)

We can simplify this expression by rationalizing the denominator:

cos(x/2) = -√((7 - 4√(3))/14)

In summary, if csc(x) = 7 and x is in quadrant II, then cos(x/2) = -√((7 - 4√(3))/14).

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There are 52 quarters and 15 half-dollars

Let's represent the number of half-dollars as "x" and the number of quarters as "y".

From the problem statement, we know that:

x + y = 67 (because there are a total of 67 coins)

y = 3x + 7 (because the number of quarters is 7 more than three times the number of half-dollars)

We can use substitution to solve for x:

x + (3x + 7) = 67

4x + 7 = 67

4x = 60

x = 15

So there are 15 half-dollars. We can use this to find the number of quarters:

y = 3x + 7

y = 3(15) + 7

y = 52

So there are 52 quarters.

Therefore, there are 52 quarters and 15 half-dollars.

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According to the given information, the function has no cusp.

What is a function?

A function is a relation between a set of inputs and a set of possible outputs, with the property that each input is related to exactly one output.

The given piecewise function is:

c(x) = 39, when x ≤ 6

c(x) = 39 + 5(x - 6), when x > 6

A cusp is a point on the graph where the function changes direction very abruptly, like a sharp turn. This happens when the derivative of the function is not defined at that point.

The derivative of the function is:

c'(x) = 0, when x ≤ 6

c'(x) = 5, when x > 6

Since the derivative is defined and continuous at x = 6, there is no cusp at that point. Therefore, the function has no cusp.

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You can plot the box and whisker plot using these values:

Step 1: Order the data set from smallest to largest:

12, 19, 28, 32, 34, 38, 45, 47, 50, 56

Step 2: Calculate the lower quartile (Q1), median (Q2), and upper quartile (Q3):

Q1 (25th percentile): The value that separates the lowest 25% of the data from the rest. Since we have 10 data points, the first quartile will be the average of the 2.5th and 3.5th data points. In our case, it's the average of the 2nd and 3rd data points:

Q1 = (19 + 28) / 2 = 23.5

Q2 (50th percentile or median): The value that separates the lowest 50% of the data from the rest. Since we have an even number of data points, the median will be the average of the 5th and 6th data points:

Q2 = (34 + 38) / 2 = 36

Q3 (75th percentile): The value that separates the lowest 75% of the data from the rest. Since we have 10 data points, the third quartile will be the average of the 7.5th and 8.5th data points. In our case, it's the average of the 7th and 8th data points:

Q3 = (45 + 47) / 2 = 46

Step 3: Calculate the interquartile range (IQR):

IQR = Q3 - Q1 = 46 - 23.5 = 22.5

Step 4: Determine the whiskers:

Lower whisker limit: 23.5 - 1.5 * 22.5 = -10

Upper whisker limit: 46 + 1.5 * 22.5 = 79.5

Our data points are all within these limits, so the lower whisker is at the smallest value, 12, and the upper whisker is at the largest value, 56.

Now, you can plot the box and whisker plot using these values:

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create a box and whisker plot for the following set of data

12, 19, 28, 32, 34, 38, 45, 47, 50, 56

Answer: less than

Step-by-step explanation:

Answer:

3 and -16

Step-by-step explanation:

To find two numbers that add up to 13 but multiply to -48, we can start by making a list of the factors of -48:

1, -1, 2, -2, 3, -3, 4, -4, 6, -6, 8, -8, 12, -12, 16, -16, 24, -24, 48, -48

We can see that the only two numbers in this list whose sum is 13 are 3 and -16. To verify that these numbers multiply to -48, we can simply multiply them together:

3 x (-16) = -48

Therefore, the two numbers that add up to 13 but multiply to -48 are 3 and -16.

Answer: -3, 16

Step-by-step explanation:

Step-by-step explanation:

36^3/4   *    36 ^-1/4    =   36 ^( 3/4 - 1/4 )  =  36 ^1/2 = sqrt (36 ) = 6

Answer:

$5040

Step-by-step explanation:

Apply the formula

SI = (Principal)(Rate)(Time)

= 6000×0.12×7

= $5,040

Answer:

93/2

Step-by-step explanation:

93/2 = 46.5

82/3 = 27.3

45/2 = 22.5

Answer:

93/2

Step-by-step explanation:

93/2=279/6

82/3=164/6

45/2=135/6

The polynomial function of least degree that has zeros of x=0, x=2i, and x=3, and with all coefficients real is:

Since the zeros of the polynomial function are given as

x=0, x=2i, and x=3,

we can write the function in factored form as follows:

f(x) = a(x-0)(x-2i)(x-3)

where

a is a constant coefficient and the factors correspond to the given zeros.

Since all coefficients must be real, we know that the complex conjugate of 2i, which is -2i, must also be a zero of the function. Therefore, we can rewrite the function as:

f(x) = a(x-0)(x-2i)(x+2i)(x-3)

Expanding this expression gives:

f(x) = a(x² + 4)(x-3)

Multiplying out the brackets and collecting like terms, we get:

f(x) = ax³ - 3ax² + 4ax - 12a

To find the value of 'a', we can use the fact that the coefficient of the x³ term is 1. Thus, we have:

a = 1/(1*4) = 1/4

Substituting this value of 'a' in the above expression, we get:

f(x) = (1/4)x³ - (3/4)x² + x - 3

Therefore, the polynomial function of least degree that has zeros of x=0, x=2i, and x=3, and with all coefficients real is:

Option A: f(x) = x² - 3x³ + 4x² - 12x

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The correct answer is (1,1) because both of the lines meet together at these numbers

Answer:

[tex]3( {2}^{2} ) - {2}^{2} + 4 = 12[/tex]

[tex] {2}^{3} + b( {2}^{2} ) + 43(2) - 126 = 4b - 204[/tex]

[tex]4b - 32 = 12[/tex]

[tex]4b = 44[/tex]

[tex]b = 11[/tex]

For this value of b, these graphs will intersect at (2, 12). Please use your graphing calculator to confirm that this is the only point of intersection.

In triangle ABC

a) The value of x = 29⁰

b) The angle c equal to 93⁰

A triangle is a closed plane figure that is formed by connecting three line segments, also known as sides, at their endpoints. The three endpoints, or vertices, where the sides of the triangle meet are not collinear. Triangles are important in mathematics and geometry because they are the simplest polygon that can exist in two-dimensional space.

In a triangle, the sum of all interior angles is always 180 degrees. Therefore, we can use this fact to find the value of x and angle c.

We know that:

angle a = 35⁰

angle b = 52⁰

angle c = 3(x+2)⁰

Using the fact that the sum of all interior angles in a triangle is 180 degrees, we can write:

angle a + angle b + angle c = 180

Substituting the values we know, we get:

35 + 52 + 3(x+2) = 180

Simplifying the equation, we get:

87 + 3x + 6 = 180

3x + 93 = 180

3x = 87

x = 29

Therefore, x = 29⁰

To find angle c, we can substitute the value of x into the equation we were given for angle c:

angle c = 3(x+2)

angle c = 3(29+2)

angle c = 3(31)

angle c = 93

Therefore, angle c is equal to 93⁰.

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Answer:

finding the perimeter, you sumthe distance all round that is 7+7.5+17.8+6=38.3

38.3 is the perimeter

we can place 10 marbles with a radius of 1 1/2 inches in a box that is 5” by 5” by 6”.

How to solve the question?

To calculate the maximum number of marbles that can be placed in the given box, we need to first determine the volume of the box and the volume of a single marble.

The volume of the box is calculated by multiplying its three dimensions, which gives us:

5 x 5 x 6 = 150 cubic inches

The volume of a marble can be calculated using the formula for the volume of a sphere:

(4/3) x π x r³

where r is the radius of the marble. Since the radius of the marble is given as 1 1/2 inches, we convert it to a decimal form by adding 1 to 1/2, which gives us a radius of 1.5 inches. Substituting this value into the formula, we get:

(4/3) x π x 1.5³ ≈ 14.14 cubic inches

Now, we divide the volume of the box by the volume of a single marble to find the maximum number of marbles that can be placed in the box:

150 ÷ 14.14 ≈ 10.61

Since we cannot have a fraction of a marble, we round down to the nearest whole number, which gives us a maximum of 10 marbles that can be placed in the box.

Therefore, we can place 10 marbles with a radius of 1 1/2 inches in a box that is 5” by 5” by 6”.

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The equation of the normal plane is 4y = 4π, or equivalently, y = π.

The word osculate comes from the Latin osculatus, which is a past participle of the verb osculari, which means "to kiss." Thus, an osculating plane is one that "kisses" a submanifold.

To find the osculating plane and normal plane of the curve x = sin 2t, y = t, z = cos 2t at the point (0, π, 1), we need to follow these steps:

Step 1: Find the first and second derivatives of the curve with respect to t.

x' = 2cos2t

y' = 1

z' = -2sin2t

x'' = -4sin2t

y'' = 0

z'' = -4cos2t

Step 2: Evaluate the derivatives at t = π.

x'(π) = 2cos2π = 2

y'(π) = 1

z'(π) = -2sin2π = 0

x''(π) = -4sin2π = 0

y''(π) = 0

z''(π) = -4cos2π = -4

So the velocity vector at the point (0, π, 1) is v = ⟨2, 1, 0⟩, the acceleration vector is a = ⟨0, 0, -4⟩, and the curvature vector is κv = ⟨0, 4, 0⟩.

Step 3: Use the velocity and acceleration vectors to find the normal vector of the osculating plane.

The normal vector of the osculating plane is given by the cross product of the velocity and acceleration vectors:

n = v × a = ⟨2, 1, 0⟩ × ⟨0, 0, -4⟩ = ⟨4, 0, 0⟩

Step 4: Use the normal vector and the point (0, π, 1) to find the equation of the osculating plane.

The equation of the osculating plane is given by:

4(x - 0) + 0(y - π) + 0(z - 1) = 0

Simplifying, we get:

4x - 4 = 0

So the equation of the osculating plane is 4x = 4, or equivalently, x = 1.

Step 5: Use the curvature vector to find the normal vector of the normal plane.

The normal vector of the normal plane is given by the curvature vector:

n' = κv = ⟨0, 4, 0⟩

Step 6: Use the normal vector and the point (0, π, 1) to find the equation of the normal plane.

The equation of the normal plane is given by:

0(x - 0) + 4(y - π) + 0(z - 1) = 0

Simplifying, we get:

4y - 4π = 0

So, the equation of the normal plane is 4y = 4π, or equivalently, y = π.

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The answer to the question is   O 216 square units