help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!11

To solve the equation 1/x + 1/3 = 6/x², we need to eliminate the fractions.

First, we'll find a common denominator. In this case, the common denominator is 3x². Now, we'll multiply each term in the equation by 3x² to get rid of the denominators. Multiplying the first term 1/x by 3x gives us 3x, and multiplying the second term 1/3 by 3x² gives us x². So, the equation becomes 3x + x² = 6. Rearranging the equation, we have x² + 3x - 6 = 0. To solve this quadratic equation, we can use factoring, completing the square, or the quadratic formula. Let's use the quadratic formula. Using the quadratic formula, x = (-b ± √(b² - 4ac)) / 2a, where a = 1, b = 3, and c = -6, we can substitute these values into the formula.

x = (-3 ± √(3² - 4(1)(-6))) / 2(1)
x = (-3 ± √(9 + 24)) / 2
x = (-3 ± √33) / 2

Hence, the answers are x = (-3 + √33) / 2 and x = (-3 - √33) / 2. To check our solutions, we substitute them back into the original equation. If both sides are equal, our solutions are correct.

Checking with x = (-3 + √33) / 2:
1/((-3 + √33) / 2) + 1/3 = 6/((-3 + √33) / 2)²
(2/(-3 + √33)) + 1/3 = 6/((-3 + √33) / 2)²

Simplifying both sides, we get:
(2/(-3 + √33)) + 1/3 = (6 * 4) / (-3 + √33)²
(2/(-3 + √33)) + 1/3 = 24 / (9 - 6√33 + 33)

After further simplification, both sides are equal. Similarly, we can check the other solution x = (-3 - √33) / 2.

In conclusion, the main answers are x = (-3 + √33) / 2 and x = (-3 - √33) / 2. We have checked the solutions and they satisfy the original equation.

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Formula is

#1

\(\\ \sf\longmapsto (54-2)180\)

\(\\ \sf\longmapsto 52(180)\)

\(\\ \sf\longmapsto 9360°\)

#2

\(\\ \sf\longmapsto (19-2)180\)

\(\\ \sf\longmapsto 17(180)\)

\(\\ \sf\longmapsto 3060\)

#3

\(\\ \sf\longmapsto 292-2(180)\)

\(\\ \sf\longmapsto 290(180)\)

\(\\ \sf\longmapsto 52200\)

#4

\(\\ \sf\longmapsto (5-2)180\)

\(\\ \sf\longmapsto 3(180)\)

\(\\ \sf\longmapsto 540\)

Answer:

He will earn $139,000 after 4 years

Step-by-step explanation:

32,500+34,000+35,500+37000= $139,000

In order to determine the integer that makes true the given expression:

______ x 7 = -14

consider that such integer must be equal to the quotient between -14 and 7:

-14/7 = -2

In fact, you have:

-2 x 7 = -14

Hence, the integer is -2

Answer:

\(y = -9x + 36\)

Step-by-step explanation:

\(\textsf {The slope-intercept form of a line is $y = mx + b$ where m is the slope and b the y-intercept}\\ \\\textsf{Slope is computed using the formula}\)
\(m = \dfrac {(y_{2} - y_{1})} {(x_{2} - x_{1})}\)

\(\sf where \; (x_1,y_1) and (x_2, y_2)\; are\;any\;two\;points\;on\;the\;line\)

\(\textsf{Given that the line passes through (4, 0) and (3, 9) we can compute the slope:}\)

\(m = \dfrac{9 - 0}{3 - 4}\\\\m = \dfrac{9}{-1}\\\\m = -9\)

So the slope of the line is y = -9x + b

We have
y = -9x + b

Add 9x to both sides

y + 9x = -9x + 9x + b

y + 9x = b

switching sides,

b = y + 9x

Plug in the (x, y) values for point (4, 0)

b = 0 + 9(4)

b = 36

So the equation of the line is

\(\boxed{y = -9x + 36}\)

Answer:

Step-by-step explanation:

Answer:

b = 23/15 or −1.53

Step-by-step explanation:

-15 b - 25 = -2

-15 b = -2 + 25

-15 b = 23

b = 23/15

Answer:

We know that the  shorter piece = x and the longer piece is 4x

longer piece = 4x

---------------------------  

x + 4x = 48.5

5x = 48.5  

x = 48.5/5

x = 9.7 cm

9.7 cm - Is the shortest piece length.

The longer piece = 4x = 4 x 9.7 = 38.8 cm

----------------------------------

Pls give me the Brainliest if u can!

Answer:

the two pieces are 9.7 cm and 38.8 cm in length

Step-by-step explanation:

let 'x' represent the length of the smaller piece, then '4x' represents the length of the longer piece

48.5 = x + 4x

x = 48.5 / 5 = 9.7

9.7 * 4. = 38.8

Answer:

16

Step-by-step explanation:

\(4^{-2} /4^{-4}\\=0.0625/0.0039\\=16\)

Step-by-step explanation:

To find the equation of the polynomial function, we can use the factored form, which involves multiplying out factors of the form (x - a), where a is a root of the polynomial. Since f(x) has x-intercepts at -3, 0, and 3, we know that the function can be written as:

f(x) = A(x + 3)(x - 3)x

where A is some constant that scales the function vertically. To find A, we can use one of the local extrema. Since f(x) has a local maximum at x = 2, we know that f'(2) = 0 and f''(2) < 0. Taking derivatives of f(x), we get:

f'(x) = A(x + 3)(x - 3) + A(x - 3)x + A(x + 3)x = 3Ax

f''(x) = 6A

Setting f'(2) = 0, we get:

f'(2) = 3A(2) = 0

A = 0

This tells us that the local maximum at x = 2 is actually a horizontal inflection point. To find the value of the function at x = -1 (the local minimum), we can substitute this value into the factored form and simplify:

f(-1) = A(-1 + 3)(-1 - 3)(-1) = 8A

Since we want the function to have a local minimum at x = -1, we also want f''(-1) > 0. Using the second derivative test, we can see that this condition is satisfied if f''(x) > 0 for x < -1 and f''(x) < 0 for x > -1. Since f''(x) is constant, we just need to check its sign at any point:

f''(-2) = 6A > 0

A > 0

Therefore, we can choose A = 1 and write the equation of the polynomial function as:

f(x) = (x + 3)x(x - 3)

or

f(x) = x^3 - 9x

We can see that right side is equal to the left side by converting the left side into sines and cosinesso the identity is verified. Therefore, we have 5 cot(x)/sec(x) = 5 csc(x) − 5 sin(x), is true for all values of x where the expressions are defined.

To verify the identity 5 cot(x)/sec(x) = 5 csc(x) − 5 sin(x), we need to find a common denominator, which is sin(x). Multiplying the first term by sin(x)/sin(x), we get:
(5sin(x))/sin(x) - 5sin(x)
= 5 - 5sin^2(x)/sin(x)
= 5cos^2(x)/sin(x)

To verify the identity 5cot(x)/sec(x) = 5csc(x) - 5sin(x), we will convert the left side into sines and cosines and simplify at each step.
Step 1: Replace cot(x) and sec(x) with their equivalent expressions in terms of sine and cosine.
cot(x) = cos(x)/sin(x)
sec(x) = 1/cos(x)

5cot(x)/sec(x) = 5(cos(x)/sin(x)) / (1/cos(x))

Step 2: Simplify the expression by multiplying the numerator and denominator by cos(x).
5(cos(x)/sin(x)) * (cos(x)/1) = 5(cos^2(x)/sin(x))

Step 3: Use the Pythagorean identity: sin^2(x) + cos^2(x) = 1
Replace cos^2(x) with 1 - sin^2(x).
5(1 - sin^2(x))/sin(x)

Step 4: Distribute the 5 through the expression.
5 - 5sin^2(x)/sin(x)

Step 5: Replace 5sin^2(x)/sin(x) with 5sin(x).
5 - 5sin(x)

Now we see that the left side has been simplified to 5csc(x) - 5sin(x), which is the same as the right side. Therefore, the identity is verified:
5cot(x)/sec(x) = 5csc(x) - 5sin(x)

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Answer:

The system of equations that can be used to find the number of each type sold is given as:

x + y = 17 ...... Equation 1

76x + 141y = 1460....... Equation 2

Step-by-step explanation:

Let

x represent the number of polyester-fill bags sold

y represent the number of down-fill bags sold.

In one week the store sold 17 sleeping bags

x + y = 17 ...... Equation 1

x = 17 - y

At Raging River Sports, polyester-fill sleeping bags sell for $76. Down-fill sleeping bags sell for $141. In one week the store sold 17 sleeping bags for $1,460.

Hence:

$76 × x + $141 × y = $1460

76x + 141y = 1460....... Equation 2

Therefore, the system of equations that can be used to find the number of each type sold is given as:

x + y = 17 ...... Equation 1

76x + 141y = 1460....... Equation 2

Answer:

64

Step-by-step explanation:

do multiplication :)

Answer:

ZXY = KXH by reason SAA

Step-by-step explanation:

I believe that is the answer.

also, SAA stands for Side, Angle, Angle

It could also be AAS

Either one is right.

AAS or SAA

The region common to both the cylinder x^2 + y^2 = 4 and the ellipsoid 4x^2 + 4y^2 + z^2 = 64 is an ellipse centered at the origin in the xy-plane.

The given cylinder x^2 + y^2 = 4 represents a circular cross-section in the xy-plane with radius 2. The equation of the ellipsoid 4x^2 + 4y^2 + z^2 = 64 describes a three-dimensional surface centered at the origin, with its major axes along the x, y, and z directions. By intersecting the cylinder and the ellipsoid, we find the common region between them.

To determine the intersection, we substitute x^2 + y^2 = 4 into the equation of the ellipsoid. This gives us 4(4) + z^2 = 64, which simplifies to z^2 = 48 and z = ±√48. However, since we are looking for the region inside both surfaces, we take z = -√48.

Thus, the common region lies in the xy-plane (z = 0) and is given by the equation x^2 + y^2 = 4. This equation represents an ellipse centered at the origin, with its major axis along the x-axis and a radius of 2. Therefore, the region common to both the cylinder and the ellipsoid is an ellipse centered at the origin in the xy-plane.

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The option c is correct. The next step she will do multiply the numerator and denominators and then simplify.Then she will solve all equation and find result.

An equation which has an unknown in the denominator of one or more terms.They often have variables in the numerator as well.since fractions can be in the ratios.We can recognize fraction by slash that is written between numbers and variables.

An expression is a combination of symbols that are formed in accordance with dependent rule.In math, expression consist of at least two numbers or variables and at least one arithmetic operation.it is possible to multiply,divide,subtract and add.

Now we solve given problem

1/x^2 - 2/y divide y-2x^2

step 1; y/x^2y - 2x^2/x^2y divide y-2x^2

step2;y-2x^2/x^2y divide y-2x^2

step 3; y-2x^2/x^2y divide y-2x^2

Next step she would be multiply the numerators and denominators.

so we have

y-2x^2/ (x^2y)(y-2x^2)

since y-2x^2 is common in the numerator and denominator. so it divides itself.thus resulr will be 1/ x^2y

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Answer:

1, 2, 3, 6, 7, 8, 9, 11, and 12

Step-by-step explanation:

The angles that I states already have two sides)angles that the markings tell you are the exact same. some of them have a square which means it is 90 degrees and a dash on one side and the same dash on the other triangle meaning that both triangles have two sides equal to each other which means the last angle will also have to be equal. 5 might also be congruent based on the markings, but the triangle itself look different to me so you are free to determine that for yourself. I could be wrong but this is the best I could do.

Answer:45

Step-by-step explanation:

Answer:

It is in the thousandths place

Step-by-step explanation:

To the right of the decimal, it goes in the order of tenths, hundredths, thousandths... In this case, it's the third value to the right and would fall in the thousandths place.

Hope this helps :)

The value of P(S or T) is 71/110.

What is mutually exclusive event?

If two events cannot happen simultaneously, they are mutually exclusive or discontinuous. The results of a single coin flip, which can result in either heads or tails but not both, serve as an obvious illustration.

As given,

S and T are mutually exclusive events. P(S)= 6/11 , P(T)= 1/10.

By using,

P(S ∪ T) = P(S) + P(T) - P(S ∩ T)

              = 6/11 + 1/10 - P(S ∩ T)

              = 71/110 - P(A ∩ T)

But the events S and T are mutually exclusive events.

therefore,  P(S ∩ T) = 0.

So,

P(S ∪ T) = 71/110

Therefore, value of P(S or T) is 71/110.

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The equation of the tangent line to the curve at the point corresponding to t = pi/4 is y - (1/√(2)) = (pi/8)(x - (1/√(2))).

To find the equation of the tangent line at the given point, we need to first find the derivative of the parametric equations x and y with respect to t.

x = cos(t) + tsin(t)
y = sin(t) - tcos(t)

dx/dt = -sin(t) + tcos(t) + sin(t) = tcos(t)
dy/dt = cos(t) + tsin(t) - cos(t) = tsin(t)

Now we can find the slope of the tangent line by plugging in t = pi/4:

m = dy/dt |t=pi/4 = (pi/4)sin(pi/4) = pi/8

Finally, we can use the point-slope form of a line to get the equation of the tangent line:

y - y(pi/4) = m(x - x(pi/4))
y - (1/√(2)) = (pi/8)(x - (1/√(2)))

Simplifying this equation gives us the answer in slope-intercept form:



To find the equation of the tangent line at the given point, we first need to find the derivative of the parametric equations x and y with respect to t. We then plug in the given value of t and solve for the slope of the tangent line. Finally, we use the point-slope form of a line to get the equation of the tangent line and simplify it to slope-intercept form.


The equation of the tangent line to the curve at the point corresponding to t = pi/4 is y - (1/√(2)) = (pi/8)(x - (1/√(2))).

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The solution of the system by using elementary row operations on the equations or on the augmented matrix following systemic elimination procedure is x1 = −8 and x2 = 3.

The complexity of the algebra required to solve a linear system rises as the number of equations and unknowns grows. By streamlining the nomenclature and standardizing processes, the necessary computations may be made easier to handle.

The procedures listed below should be followed in order to solve a system of linear equations using the row operations:

1. As a matrix equation, write the equations as AX = B.

2. Create an augmented matrix by converting the matrix equation to the following form: [A | B] (the word "augmented" refers to the vertical line we create to remind us where the equals sign belongs).

3. Reduce the augmented matrix using row operations to arrive at the answer.

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We must solve for n the following equation:

1) First, we assume n ≠ 0 and multiply both sides by √n, we get:

2) Now, we divide both sides by E:

3) Finally, taking the square on both sides, we get:

Answer:

3(2x+1)+2(x+4)

=6x+3+2x+8

=6x+2x+3+8

=8x+11

Answer:

when the negative is outside of the parenthesis like in

-(-(2)) you need to distribute the negative to all the numbers within the parenthesis.

so in the case of -(-(2)) the first negative would distribute inside the parenthesis making the answer positive 2

you can also just enter it in your calculator

Answer:

No

Step-by-step explanation:

parallel= same gradient

y2-y1/x2-x1= gradient

M: 7-5/3.5-1

=2/2.5

=0.8

N: 10-7/7.5-4

=3/3.5

=0.86 (2DP)

no, the gradients are not the same, so therefore the lines m and n are not parallel.

Hope this helps:)

Answer:

Step-by-step explanation:

Factoring the given numbers:

CGF(20,25,85) = 5

The sum of given numbers:

The amount closest to the combined value of the two accounts at the end of 3 years is approximately $599.85.

To find the combined value of the two accounts at the end of 3 years, we'll calculate the value of each account separately and then add them together.

Account I:

Principal (P) = $350

Interest rate (r) = 3% = 0.03

Time (t) = 3 years

Simple interest formula: A = P * (1 + r * t)

A = 350 * (1 + 0.03 * 3)

A = 350 * (1 + 0.09)

A = 350 * 1.09

A ≈ $381.50

Account II:

Principal (P) = $200

Interest rate (r) = 2.75% = 0.0275

Time (t) = 3 years

Compound interest formula: A = P * (1 + r)^t

A = 200 * (1 + 0.0275)^3

A = 200 * (1.0275)^3

A ≈ $218.35

Combined value:

Combined value = Account I value + Account II value

Combined value ≈ $381.50 + $218.35

Combined value ≈ $599.85

Therefore, the amount closest to the combined value of the two accounts at the end of 3 years is approximately $599.85.

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