Find the cosine of angle x
X
W
90
72
V
Simplify your answer and write it as a proper fraction, improper fraction, or whole number

In order to factor our polynomial must be written in a way that we will factor out the greatest common factor

A polynomial is an expression made up of variables, constants, and exponents that are combined using mathematical operations like addition, subtraction, multiplication, and division.

A polynomial function is one that involves only non-negative integer powers or positive integer exponents of a variable in an equation such as the quadratic equation, cubic equation, and so on. For example, 2x+5 is a polynomial with an exponent of one.

To be a polynomial term, an expression must contain no square roots of variables, no fractional or negative powers on variables, and no variables in the denominators of any fractions.

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The solution to the system of equations is x = 4, y = 2, and z = 3.

The step-by-step solution to your question using the inverse method:

Express the system of equations in matrix form.

The system of equations can be expressed in matrix form as follows:

[A][x] = [b]

where

[A] = [1 1 1; 0 2 5; 2 5 -1]

[x] = [x; y; z]

[b] = [6; -4; 27]

Find the inverse of the matrix [A].

The inverse of the matrix [A] can be found using Gaussian elimination. The steps involved are as follows:

1. Add 4 times the second row to the third row.

2. Subtract 2 times the first row from the third row.

3. Divide the third row by 3.

This gives the following inverse matrix:

[A]^-1 = [1/3 1/6 -1/3; 0 1/3 -1/3; 0 0 1]

Solve the system of equations using the inverse matrix.

The system of equations can be solved using the following formula:

[x] = [A]^-1[b]

Substituting the values of [A] and [b] gives the following solution:

[x] = [A]^-1[b] = [1/3 1/6 -1/3; 0 1/3 -1/3; 0 0 1][6; -4; 27] = [4; 2; 3]

Therefore, the solution to the system of equations is x = 4, y = 2, and z = 3.

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Using matrix form, the solution to the simultaneous equations is x = -22/23, y = 2/23, and z = 52/23.

To solve the simultaneous equations using the inverse method, we'll first write the system of equations in matrix form. Let's define the coefficient matrix A and the column matrix X:

A = [[1, 1, 1], [0, 2, 5], [2, 5, 1]]

X = [[x], [y], [z]]

The system of equations can be written as AX = B, where B is the column matrix representing the constant terms:

B = [[6], [-4], [27]]

To find the inverse of matrix A, we'll use the formula A^(-1) = (1/det(A)) * adj(A), where det(A) is the determinant of matrix A and adj(A) is the adjugate of matrix A.

First, let's find the determinant of matrix A:

det(A) = 1(2(1) - 5(5)) - 1(0(1) - 5(2)) + 1(0(5) - 2(5))

      = 1(-23) - 1(-10) + 1(-10)

      = -23 + 10 - 10

      = -23

The determinant of A is -23.

Next, let's find the adjugate of matrix A:

adj(A) = [[(2(1) - 5(1)), (2(1) - 5(1)), (2(5) - 5(0))],

         [(0(1) - 5(1)), (0(1) - 5(2)), (0(5) - 2(0))],

         [(0(1) - 2(1)), (0(1) - 2(2)), (0(5) - 2(5))]]

      = [[-3, -3, 10],

         [-5, -10, 0],

         [-2, -4, -10]]

Now, let's find the inverse of matrix A:

A^(-1) = (1/det(A)) * adj(A)

      = (1/-23) * [[-3, -3, 10],

                   [-5, -10, 0],

                   [-2, -4, -10]]

      = [[3/23, 3/23, -10/23],

         [5/23, 10/23, 0],

         [2/23, 4/23, 10/23]]

Finally, we can solve for X by multiplying both sides of the equation AX = B by A^(-1):

X = A^(-1) * B

 = [[3/23, 3/23, -10/23],

    [5/23, 10/23, 0],

    [2/23, 4/23, 10/23]] * [[6], [-4], [27]]

Performing the matrix multiplication, we have:

X = [[(3/23)(6) + (3/23)(-4) + (-10/23)(27)],

    [(5/23)(6) + (10/23)(-4) + (0)(27)],

    [(2/23)(6) + (4/23)(-4) + (10/23)(27)]]

Simplifying the expression, we get:

X = [[-22/23],

    [2/23],

    [52/23]]

Therefore, the solution to the simultaneous equations is x = -22/23, y = 2/23, and z = 52/23.

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Answer:

5

Step-by-step explanation:

0 is 10ths 5 is 100ths

Step-by-step explanation:

We know that the formula for slope is y=mx+b, with m equaling the slope itself and b equaling the y-intercept. Since the slope is -4, we can safely say that the equation starts off as y=-4x.

The y-intercept is (0,2). This means that the x-coordinate is 0 and the y-coordinate is 2, so the y-intercept is 2. Since 2 is being added, the equation is y=-4x+2

Answer:

y=-4x+2

Answer:

A

Step-by-step explanation:

Answer:

A. y=3x+4

Step-by-step explanation:

(y+5)=3(x+3)

y+5=3x+9

y=3x+9-5

y=3x+4

Answer:

B) P = 42; A = 84

Step-by-step explanation:

Perimeter:

You have two right triangles, so you need to find the third side length.

\(a^{2}\) + \(b^{2}\) = \(c^{2}\)

\(5^{2}\) + \(12^{2}\) = \(c^{2}\)

25 + 144 = \(c^{2}\)

169 = \(c^{2}\)

\(\sqrt{169}\) = \(\sqrt{c^{2} }\)

13 = c

The top right missing outside length is 13

We do the same thing to find the missing bottom outside.

\(a^{2}\) + \(b^{2}\) = \(c^{2}\)

\(12^{2}\) + \(9^{2}\) = \(c^{2}\)

144 + 81 = \(c^{2}\)

225 = \(c^{2}\)

\(\sqrt{225}\) = \(\sqrt{c^{2} }\)

15 = c

The perimeter of triangle xyz is 5 + 9 + 13 + 15 = 42 units

Area:

a = 1/2 bh

a= 1/2 (5 + 9) (12)

a = 1/2 (14)(12)

a = 84 \(units^{2}\)

Helping in the name of Jesus.

Answer:

a)  $498

b) $1052

c) $554

Step-by-step explanation:

to find the median of lower half of data:  find median of all the data, then find middle value from the minimum value to the median (not including median)

to find the median of upper half of data:  find median of all the data, then find middle value from the median to the maximum value (not including median)

interquartile range (IQR) is the difference of the two

To satisfy the requirement the equations can be:

x+y= 0

x-y= 0

the solution of this system of equations is the pair (0,0) which has an x-coordinate of 0.

The result is not statistically significant.

To test the hypothesis is the mean SAT score is less than 1520 at 5% significance level.

The null hypothesis is

H₀ : μ ≥ 1520

The alternative hypothesis is

Hₐ : μ ≤ 1520

then the test statistic is,

t = (x - μ)/(s/√n)

 = (1501 - 1520)/(53/√20)

t = - 1.603

The t-test statistic is - 1.603.

Degree of freedom n - 1 = 20 - 1 = 19

Hence the t-critical value is -1.792.

The conclusion is that the t value corresponds to sample statistics is not fall in the critical region, so the null hypothesis is not rejected at 5% level of significance. There is insignificance evidence indicates that the mean SAT score is less than 1520.

The result is not statistically significant.

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The solution to the initial value problem dx/dt = ax with x(0) = x0, where a = −5/2 or 3/2, and x0 = 1/4 is x(t) = (1/4) e^(-5/2t) or x(t) = (1/4) e^(3/2t), respectively.

The initial value problem dx/dt = ax with x(0) = x0, where a = −5/2 or 3/2, and x0 = 1/4 can be solved using the formula x(t) = x0 e^(at).
Substituting the given values, we get x(t) = (1/4) e^(-5/2t) or x(t) = (1/4) e^(3/2t).
To check the validity of these solutions, we can differentiate both sides of the equation x(t) = x0 e^(at) with respect to time t, which gives us dx/dt = ax0 e^(at).
Substituting the given value of a and x0, we get dx/dt = (-5/2)(1/4) e^(-5/2t) or dx/dt = (3/2)(1/4) e^(3/2t).
Comparing these with the given equation dx/dt = ax, we can see that they match, thus proving the validity of the initial solutions.
In summary, the solution to the initial value problem dx/dt = ax with x(0) = x0, where a = −5/2 or 3/2, and x0 = 1/4 is x(t) = (1/4) e^(-5/2t) or x(t) = (1/4) e^(3/2t), respectively.

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Step-by-step explanation:

well it could be -10 < x < 10

or -9 ≤ x < 10

or -10 < x ≤ 9

or -9 ≤ x ≤ 9

The centroid of an octant of a solid sphere is located at the point (r/3, r/3, r/3), where r is the radius of the sphere.

An octant is one-eighth of a solid sphere, so it is formed by cutting the sphere into eight equal parts along the x, y, and z axes. The centroid of a solid is the point at which the mass of the solid is evenly distributed, and for an octant of a sphere, this point is located at (r/3, r/3, r/3).

This can be determined by using the formula for the centroid of a solid, which is the average of the x, y, and z coordinates of all the points in the solid. For an octant of a sphere, the x, y, and z coordinates all range from 0 to r, so the average of these coordinates is r/3.

In conclusion, the point representing the centroid is (r/3, r/3, r/3).

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→ Let the width of the rectangle = x inches

∵ The length of the rectangle is 3 less than 7 times the width

∴ The length of the rectangle = 7(x) - 3

→ The perimeter of the rectangle P = 2(length + width)

∵ The perimeter is 58 inches

→ Add 6 to both sides

→ Divide both sides by 16 to find x

Answer:

E

Step-by-step explanation:

\(\lim_{x \to 0} f(1-x^2)=\lim_{x \to 1} f(x)\)

which does not exist.

Answer:     Ok I'm assuming you got this question from FLVS. There answer is NOT correct. Perpendicular lines are lines that intersect two given points at about 90 degrees. Think of it like this, the slope is 3. Perpendicular slopes are opposite, so the opposite reciprocal of 3 is -1/3. Now plug in x. X should render 3. -1/3 times (-6) = 2. Now adding 5 or 6 like you guys put is wrong because 5 + 2 =7. NOT 3. So y = -1/3 (-6) = 2. Now -y = 2 + 1 =3.

So the correct answer is y = - 1/3 x +1.

The distance between a point on a sphere and another point is found by considering the shortest distance between the two points, which passes through the center of the sphere.

As a result, to find the point on the sphere that is farthest from the point (-2,28,-11), the line that passes through the center of the sphere and the point (-2,28,-11) must be determined. To determine the coordinates of the center of the sphere, we need to know the radius of the sphere, which is sqrt(5776)=76. Therefore, the center of the sphere is (0,0,0). Let P be the point on the sphere farthest from the point (-2,28,-11). Draw a straight line through P and the center of the sphere, O. The distance between P and O, which is the radius of the sphere, is 76. Let the vector pointing from O to P be called {u}. Then, {u} = (x,y,z). The point P is obtained by scaling {u} by a scalar k. That is, {p} = k{u}. To maximize the distance between P and (-2,28,-11), we can maximize |{p} - (-2,28,-11)|^{2} or equivalently maximize |{p}|^{2} + |(-2,28,-11)|^{2}. Recall that |{u}| = sqrt{x^{2}+y^{2}+z^{2}} = 76. Then, the squared distance from {p} to (-2,28,-11) is:|{p}|^{2} + |(-2,28,-11)|^{2} = (kx+2)^{2} + (ky-28)^{2} + (kz+11)^{2}. We can differentiate the squared distance with respect to k and set it equal to zero to obtain the value of k that maximizes the distance. We have:(2kx+4)x + (2ky-56)y + (2kz+22)z = 0.This is a linear equation in k, which can be solved for k. Once k is found, we can find the coordinates of P by {p} = k{u}.

By solving the linear equation in k, we obtain k=-10. Therefore, {p} = (-10x, -10y, -10z). The point P on the sphere farthest from the point (-2,28,-11) is (-960,-150,550).

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The computation is that the width is 21.5 feet and the height is 12.5.

Let the height = h

Let the width = (3 × h) - 16 = 3h - 16

Therefore, the dimensions will be:

h + 3h - 16 = 34

4h = 34 + 16

4h = 50

Divide

h = 50/4

h = 12.5

Therefore width = 3h - 16 = 3(12.5) - 16

= 37.5 - 16

= 21.5

The width is 21.5 feet and the height is 12.5.

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a) Area = √[s(s-a)(s-b)(s-c)] b) the area of the land 225.83 m^2 c) the total cost for the fencing the land three times at the rate of Rs. 25 per meter of the wire. is  Rs. 43,500

a) The formula to find the area of a triangle when all sides are not equal is Heron's formula:

Area = √[s(s-a)(s-b)(s-c)]

where s is the semi-perimeter of the triangle, and a, b, and c are the lengths of its sides.

To find the semi-perimeter, we add up the three sides and divide by 2:

semi-perimeter = (8+9+10)/2 = 27/2

Now we can substitute into the formula:

b) Area = √[27/2(27/2-8)(27/2-9)(27/2-10)]

= √[27/2(11/2)(9/2)(7/2)]

= √(27^2/4 * 11 * 9 * 7) / 4

= √51030.1875

≈ 225.83 m^2

b) To fence the land three times, we need to find the perimeter of the triangle and multiply by 3:

Perimeter = 8x + 9x + 10x = 27x

We know that the perimeter is 540 m, so we can solve for x:

27x = 540

x = 20

Now we can find the actual lengths of the sides:

8x = 8(20) = 160

9x = 9(20) = 180

10x = 10(20) = 200

The total length of wire needed to fence the land three times is the perimeter multiplied by 3:

Total length of wire = 3(160 + 180 + 200) = 1740 m

The cost of the wire is Rs. 25 per meter, so the total cost is:

Total cost = 1740 * 25 = Rs. 43,500

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The exact form would be:

2 over 11

Decimal Form:

0.18

Heres an image

Answer:

24*3-30=x

Step-by-step explanation:

Answer:

8-5 times R

Step-by-step explanation:

you subtract 8-5 to get that answer and then you do less than twice the number r i think this is correct hope it helps :)

Step-by-step explanation:

I hope this help comment me please

mark me brainest

Answer:

37/100 = 0.37 (the first one)

Step-by-step explanation:

a percentage is out of 100.

If you divide 37 by 100, you get 0.37

Answer:

37%=0.37=37/100

Step-by-step explanation:

Convert the percentage to an equivalent decimal number by placing the percentage sign with x1/100. The decimal equivalent to the percentage by moving the decimal 2 places to the left from the convert postion.

Answer:

8)y=2x-3

9)y= -1/2+4

Step-by-step explanation:

The word "or" in probability implies that we use the addition rule, also known as the "or rule."

The addition rule states that the probability of either of two events A or B occurring is given by the sum of their individual probabilities minus the probability of their intersection. Mathematically, P(A or B) = P(A) + P(B) - P(A and B).

Example: Let's consider the probability of rolling a 4 or an even number on a fair six-sided die. The probability of rolling a 4 is 1/6, and the probability of rolling an even number is 3/6 (as there are three even numbers out of six). The probability of rolling a 4 and an even number (intersection) is 1/6, as the number 4 is the only one that satisfies both conditions. Applying the addition rule, we get P(4 or even) = 1/6 + 3/6 - 1/6 = 3/6 = 1/2.

The addition rule allows us to calculate the probability of at least one of two events occurring when the word "or" is used. By summing the individual probabilities and subtracting the probability of their intersection, we can determine the overall probability.

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Answer:

y = -2x + 12

Step-by-step explanation:

Slope-intercept form

\(y=mx+b\)

where:

Therefore, to find the slope-intercept form of the given linear equation, isolate y:

\(\implies 4x+2y=24\)

\(\implies 4x+2y-4x=-4x+24\)

\(\implies 2y=-4x+24\)

\(\implies \dfrac{2y}{2}=\dfrac{-4x}{2}+\dfrac{24}{2}\)

\(\implies y=-2x+12\)

Answer:

y = -2x + 12

Step-by-step explanation:

Given equation,

→ 4x + 2y = 24

The slope-intercept form is,

→ y = mx + b

Converting into slope-intercept form,

→ 4x + 2y = 24

→ 2y = -4x + 24

→ y = (-4x + 24)/2

→ [ y = -2x + 12 ]

Hence, the solution is y = -2x + 12.

The solution to the inequality f(x) ≤ 0 is the interval [-6, 2]. In other words, the values of x that satisfy the inequality are those that lie between -6 and 2, inclusive.

To solve the inequality f(x) ≤ 0, we need to find the values of x for which the function f(x) is less than or equal to zero.

We start by factoring the quadratic expression f(x) = x^2 + 4x - 12:

f(x) = (x + 6)(x - 2)

Setting this expression to zero, we get:

(x + 6)(x - 2) = 0

This gives us two solutions: x = -6 and x = 2.

Now, we need to determine the sign of f(x) in the intervals between these two solutions. We can use a sign chart to do this:

x f(x)

-∞ +

-6 0

2 0

+∞ +

From the sign chart, we see that f(x) is positive for x < -6 and for x > 2, and it is negative for -6 < x < 2.

To summarize, the solution to the inequality f(x) ≤ 0 for the function f(x) = x^2 + 4x - 12 is the interval [-6, 2].

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