solve the following Simultaneous equation
Using any suitable method
x+6y=2, 3x +2y =10​

Answer:

\(x=\dfrac{2}{3},-\dfrac{3}{2}\)

Step-by-step explanation:

Given equation:

\(6x^2+5x-6=0\)

First, factor the left side of the given equation.

To factor a quadratic in the form \(ax^2+bx+c\) find two numbers that multiply to \(ac\) and sum to \(b\):

\(\implies ac=6\cdot-6=-36\)

\(\implies b=5\)

So the two numbers are: 9 and -4

Rewrite \(b\) as the sum of these two numbers:

\(\implies 6x^2+9x-4x-6=0\)

Factorize the first two terms and the last two terms separately:

\(\implies 3x(2x+3)-2(2x+3)=0\)

Factor out the common term \((2x+3)\):

\(\implies (3x-2)(2x+3)=0\)

To solve for x:

\(\begin{aligned}\implies (3x-2) & =0 & \implies (2x+3) & = 0\\3x & = 2 & 2x & = -3\\x & = \dfrac{2}{3} & x & = -\dfrac{3}{2}\end{aligned}\)

Therefore:

\(x=\dfrac{2}{3},-\dfrac{3}{2}\)

200.60 interest does andy’s account earn.

Let x be the amount of interest earned by Andy's account.

According to the problem, Andy's account earns 0.3% more interest than Marty's account, which means that Andy's account earns the same amount plus an additional 0.3% of that amount. Mathematically, we can express this as:

x = 200 + 0.3% of 200

Simplifying the right-hand side of the equation, we get:

x = 200 + 0.003 × 200

x = 200.60

Therefore, the answer is option 1: 200.60.

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A. P(6, then 1) = 1/90

B. P(even, then 5) = 1/18

C. P(8, then odd) = 1/18

D. P(3, then prime) = 2/45

E. P(prime, composite) = 4/15

F. P(even, then 3, then 5) = 1/144

Given:

Total number of cards: 10

A. P(6, then 1):

P(6, then 1) = 1/10 x 1/9

= 1/90

B. P(even, then 5):

Number of favorable outcomes: 5 x 1 = 5

P(even, then 5) = 5/10 x 1/9

= 1/18

C. P(8, then odd):

Number of favorable outcomes: 1 x 5 = 5

P(8, then odd) = 1/10 x 5/9

= 1/18

D. P(3, then prime):

Number of favorable outcomes: 1 x 4 = 4

P(3, then prime) = 1/10 x 4/9

= 2/45

E. P(prime, composite):

Number of favorable outcomes: 4 x 6 = 24

P(prime, composite) = 4/10 x 6/9

= 4/15

F. P(even, then 3, then 5):

Number of favorable outcomes: 5 x 1 x 1 = 5

P(even, then 3, then 5) = 5/10 x 1/9 x 1/8

= 1/144

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\( \sf \longrightarrow \: 5 \bigg( \: n - \frac{1}{10} \bigg) = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: 5 \bigg( \: \frac{n}{1} - \frac{1}{10} \bigg) = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: 5 \bigg( \: \frac{10 \times n - 1 \times 1}{1 \times 10} \bigg) = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: 5 \bigg( \: \frac{10n - 1}{ 10} \bigg) = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: \: \frac{50n - 5}{ 10} = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: \: 2(50n - 5) =1(10) \\ \)

\( \sf \longrightarrow \: \: 2(50n - 5) =10 \\ \)

\( \sf \longrightarrow \: \: 100n - 10=10 \\ \)

\( \sf \longrightarrow \: \: 100n =10 + 10\\ \)

\( \sf \longrightarrow \: \: 100n =20\\ \)

\( \sf \longrightarrow \: \:n = \frac{2 \cancel{0}}{10 \cancel{0}} \\ \)

\( \sf \longrightarrow \: \:n = \frac{1}{5} \\ \)

Answer:-

To solve the equation \(\sf 5(n - \frac{1}{10}) = \frac{1}{2} \\\) for \(\sf n \\\), we can follow these steps:

Step 1: Distribute the 5 on the left side:

\(\sf 5n - \frac{1}{2} = \frac{1}{2} \\\)

Step 2: Add \(\sf \frac{1}{2} \\\) to both sides of the equation:

\(\sf 5n = \frac{1}{2} + \frac{1}{2} \\\)

\(\sf 5n = 1 \\\)

Step 3: Divide both sides of the equation by 5 to isolate \(\sf n \\\):

\(\sf \frac{5n}{5} = \frac{1}{5} \\\)

\(\sf n = \frac{1}{5} \\\)

Therefore, the solution to the equation \(\sf 5(n - \frac{1}{10})\ = \frac{1}{2} \\\) is \(\sf n = \frac{1}{5} \\\), which corresponds to option (d).

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♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Answer:

can i have a photo, please?

Step-by-step explanation:

Answer:

{3, 4}

Step-by-step explanation:

"M(x)=(2x-6)(x-4) true statements when M(x)=0 when x= ?" asks us to find the "roots" of M(x); that is, the x values at which M(x) = 0.  Thus, we set

(2x - 6)(x - 4) = 0, which is equivalent to 2(x - 3)(x - 4) = 0.

Thus, x - 3 = and x = 3; also x - 4 = 0, so that x = 4.  

The roots of M(x) are {3, 4}

Using the language of the original problem:  "true statements when M(x)=0 when x="              the correct results, inserted into the blanks, are x = 3 and x = 4.

We have the identity

\((a + b)^2 = a^2 + 2ab + b^2 = a^2 + ab + b (a + b) \\\\ ~~~~ \implies a + b = \sqrt{a^2 + ab + b (a + b)} \\\\ ~~~~ \implies a + b = \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b \sqrt{\cdots}}}}\)

assuming \(a+b\ge0\).

For the numerator, let \(b=1\), so \(a\ge-1\), which means

\(a^2 + a = x \implies a = \dfrac{-1 + \sqrt{1 + 4x}}2\)

and so

\(\sqrt{x + \sqrt{x + \sqrt{x + \sqrt{\cdots}}}} = \dfrac{-1 + \sqrt{1 + 4x}}2 + 1 = \dfrac{1 + \sqrt{1 + 4x}}2\)

For the denominator, let \(b=-1\) so that \(a\ge1\). Now

\(a^2 - a = x \implies a = \dfrac{1 + \sqrt{1 + 4x}}2\)

so that

\(\sqrt{x - \sqrt{x - \sqrt{x - \sqrt{\cdots}}}} = \dfrac{1 + \sqrt{1 + 4x}}2 - 1 = \dfrac{-1 + \sqrt{1 + 4x}}2\)

So, in the integral we can simplify and evaluate it to

\(\displaystyle \int_0^{2021} \frac{\sqrt{x + \sqrt{x + \sqrt{x + \sqrt{\cdots}}}}}{1 + \sqrt{x - \sqrt{x - \sqrt{x - \sqrt{\cdots}}}}} \, dx \\\\ ~~~~~~~~ = \int_0^{2021} \frac{\frac{1 + \sqrt{1 + 4x}}2}{1 - \frac{1 - \sqrt{1+4x}}2} \, dx \\\\ ~~~~~~~~ = \int_0^{2021} \frac{1 + \sqrt{1 + 4x}}{1 + \sqrt{1 + 4x}} \, dx \\\\ ~~~~~~~~ = \int_0^{2021} dx = \boxed{2021}\)

The directional derivative of f = x²yz³ along vector i + 2j + 2k at x = \(e^{-t}\) , y = 1 + 2 sin t , z = t -cost at t =0 is 2/3.

Given that the functions are,

x = \(e^{-t}\)

y = 1 + 2 sin t

z = t - cos t

At t = 0 the point will be,

x = e⁰ = 1

y = 1 + 2 sin 0 = 1

z = 0 - cos 0 = -1

So the point is (1, 1, -1).

The vector is,

a = i + 2j + 2k

unit vector of a = (i + 2j + 2k)/√(1² + 2² + 2²) = (i + 2j + 2k)/3

Given the function is, f = x²yz³

Grad. f = 2xyz³.i + x²z³.j + 3x²yz².k

directional derivative is given by

= (Grad. f)*(unit vector of a) at (1, 1, -1)

= (2xyz³.i + x²z³.j + 3x²yz².k)*(i + 2j + 2k)/3 at (1, 1, -1)

= (2xyz³ + 2x²z³ + 6x²yz²)/3 at (1, 1, -1)

= (-2 - 2 +6)/3

= 2/3

Hence required directional derivative is 2/3.

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The question is incomplete. The complete question will be -

"The directional derivative of f= x^2 y z^3 along vector i + 2j + 2k at x = e^-t , y = 1 + 2 sin t , z = t -cost at t =0"

The value of x is 1.75 and y is 5. The solution is obtained using properties of congruent triangles.

What is a congruent triangle?

Two triangles that are congruent will have precisely the same three sides and three angles.

The dimensions of the triangles' sides and angles determine whether two or more triangles are congruent. A triangle's size is determined by its three sides, and its shape by its three angles. Pairs of corresponding sides and corresponding angles in two triangles are said to be equal if they are congruent. They share a similar size and shape. In triangles, there are numerous congruence conditions.

The triangles are congruent by SAS congruency because

AC = CD (Given)

∠ACB = ∠DCE ( Vertically opposite angles)

BC = CE  (Given)

Thus, Triangle ABC ≅ Triangle DEC

Since, the triangles are congruent, therefore

⇒AC = CD

⇒4y-6 = 2x+6   ...(1)

Also, BC = CE

⇒3y+1 = 4x

⇒(3y+1)/4 = x    ...(2)

Now, substituting the value of x in (1), we get,

⇒4y-6 = 2(3y+1)/4+(6)

⇒4y-6 = (6y+2 +24)/4

⇒16y-24 = 6y+2 +24

⇒10y = 50

⇒y = 5

Now putting the value of y in (2), we get

⇒(3(2)+1)/4 = x

⇒7/4 = x

⇒ x = 1.75

Hence, the value of x is 1.75 and y is 5.

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The coordinate of point B is (√3, 1 ).

The coordinate of point C is (3√3/2,  3/2).

The coordinate of points of B and C is calculated by applying the following formula as follows;

The given coordinate of point A;

A = ( √3/2, 1/2)

Fromm the given coordinate of point A, we can see that;

The coordinate of point B is calculated as;

point B; x-axis = (√3/2 x 2) = √3

point B; y axis = 1

B = (√3, 1 )

The coordinate of point C is calculated as;

point C; x-axis = (√3/2 x 3) = 3√3/2

point C; y axis = 3/2

C = (3√3/2,  3/2)

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The rate of the first athlete is greater than the rate of the second athlete.

To determine if the rate of the first athlete is greater than, less than, or equal to the rate of the second athlete, we need to compare their average speeds.

The average speed of an athlete is calculated by dividing the distance traveled by the time taken.

For the first athlete who runs 3 miles in 24 minutes, the average speed can be calculated as:

Speed1 = Distance1 / Time1 = 3 miles / 24 minutes = 1/8 miles per minute.

For the second athlete who runs 4 miles in 33 minutes, the average speed can be calculated as:

Speed2 = Distance2 / Time2 = 4 miles / 33 minutes.

To make a comparison, we need to convert both rates to a common unit. Let's convert both rates to miles per minute:

Speed2 =\((4 miles / 33 minutes) * (24 minutes / 24 minutes)\) = (96 miles / 792 minutes) ≈ 0.1212 miles per minute.

Comparing the two rates, we see that Speed1 (1/8 miles per minute) is greater than Speed2 (0.1212 miles per minute). The rate of the first athlete is greater than the rate of the second athlete.

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Answer:

A. f(25) = 15

Step-by-step explanation:

there are three functions given,

1st.

3√x  .............replace x with 25 cause f(25)

3√25

3*5

15 ......given that x≥9, so 15 falls above 9 and is correct

2nd.

-| 2x |

-| 2(25) | .....replace x here as well

- |50|

-50 .......given that 0<x<9, but it doesn't fall between 0 and 9 so wrong.

3rd.

13 .......given x≤0, 13 doesn't fall under or equal to 0 but is above so wrong.

Therefore can be concluded answer is 15

Answer:

A 15

Step-by-step explanation:

The constant differences between the consecutive terms are 2 (a); 2 (b), -3 (c), 7 (d), 1(e), and 6(f).

In math, the constant difference can be defined as the number that defines the pattern of a sequence of numbers. This means that number that should be added or subtracted to continue with the sequence.

Due to this, to determine the constant difference it is important to observe the pattern and find out the number that should be added. For example, if the sequence is 2, 4, 6, 8, there is a difference of 2 between each of the numbers and this is the constant difference.

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Answer:

D. 48x

Step-by-step explanation:

sana nakatulong

Blanks to be filled by 4,3,8 and 3.

Multiplication in mathematics is the same as adding equal groups. As we multiply, there are more items in the group. The product, the two factors, and the product are all components of a multiplication problem. The numbers 6 and 9 are the factors in the multiplication equation 6 x 9 = 54, and 54 is the result.

Given Data

           3 __ 8

×            7 8 4

_____________

       1 _    9 2

    2 7 __ 4

_   4 3  6

_____________

 2  7 2 8 __ 2

_____________

Solving

Multiplying and adding,

           3 _4_ 8

×            7 8 4

_____________

       1 3_    9 2

    2 7 _8_ 4

_   4 3  6

_____________

 2  7 2 8 _3_ 2

_____________

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if Jenny chooses to buy from Daikin, the monthly installment price would be approximately RM98.89, and the total installment price to be paid would be approximately RM1,779.98 (18 monthly installments * RM98.89).

Calculating the loan amount for each brand by subtracting the down payment from the cash price:

Loan amount for Daewoo = RM1,899 - RM300 = RM1,599

Loan amount for Daikin = RM1,699 - RM300 = RM1,399

Loan amount for Mitsubishi = RM1,999 - RM300 = RM1,699

Calculating the interest charge for each brand:

Interest charge for Daewoo = Loan amount for Daewoo * Interest rate = RM1,599 * 0.04 = RM63.96

Interest charge for Daikin = Loan amount for Daikin * Interest rate = RM1,399 * 0.04 = RM55.96

Interest charge for Mitsubishi = Loan amount for Mitsubishi * Interest rate = RM1,699 * 0.04 = RM67.96

To find the monthly installment price, divide the total amount (cash price + interest charge) by the number of monthly installments:

Monthly installment price for Daewoo = (Cash price of Daewoo + Interest charge for Daewoo) / Number of monthly installments = (RM1,899 + RM63.96) / 18 ≈ RM107.22

Monthly installment price for Daikin = (Cash price of Daikin + Interest charge for Daikin) / Number of monthly installments = (RM1,699 + RM55.96) / 18 ≈ RM98.89

Monthly installment price for Mitsubishi = (Cash price of Mitsubishi + Interest charge for Mitsubishi) / Number of monthly installments = (RM1,999 + RM67.96) / 18 ≈ RM116.72

Therefore, if Jenny chooses to buy from Daikin, the monthly installment price would be approximately RM98.89, and the total installment price to be paid would be approximately RM1,779.98 (18 monthly installments * RM98.89).

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The volume of the sphere is approximately 3431.82 cubic miles.

To find the volume of a sphere, we need the radius of the sphere. The length of a great circle is the circumference of the sphere, which is related to the radius by the formula C = 2πr, where C is the circumference and r is the radius.

In this case, we are given that the length of the great circle is 60 miles. We can use this information to find the radius of the sphere.

C = 2πr

60 = 2πr

Divide both sides of the equation by 2π:

r = 60 / (2π)

r = 30 / π

Now that we have the radius, we can use the formula for the volume of a sphere:

V = (4/3)πr³

V = (4/3)π(30/π)³

V = (4/3)π(27000/π³)

V = (4/3)π(27000/π³)

V = (4/3)π(27000/π³)

V = (4/3)(27000/π²)

V = (4/3)(27000/9.87) (approximating π to 3.14)

V ≈ 3431.82 cubic miles

Therefore, the volume of the sphere is approximately 3431.82 cubic miles.

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Question

You are given the great circle of a sphere is a length of 60 miles. What is the volume of the sphere?

The figure that would make the following "a reflection in line k." is: A. first figure.

In Geometry, a reflection can be defined as a type of transformation which moves every point of the object by producing a flipped but mirror image of the geometric figure.

Generally speaking, reflections and dilations are types of transformation that preserve angle measure. Additionally, reflection can be used to preserve the direction the vertices (coordinates) that are traced around a geometric figure.

In this context, we can reasonably infer and logically deduce that the first figure is a transformation that would produce a reflection in line k because it preserves the direction of its vertices.

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The length of the arc of a circle of radius 12 is 37.68.

The arc of a circle is defined as the part or segment of the circumference of a circle.

To calculate the arc of the circle, we the formula below.

Formula:

Where:

From the question,

Given:

Note: 360° = 2π radian

Substitute these values into equation 1

Hence, the length of the arc is 37.68.

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Answer:

transitive property

Step-by-step explanation:

Answer:

The first is not equivalent, second is.

Step-by-step explanation:

2x-3.9x+7.5=5.9x+7.5

The first is not equivalent, second is.

To find the umber of shares Lisa owns we need to calculate how many shares 40 % represents from the total 1,200 shares.

Written without exponents, you'd have

   abbbcc   and    aabbc

Both have one a, two b's, and one c.

The GCF is \(ab^2c\), since those are the greatest factors they all have in common.

Answer:

You can use the vertical line test, which means anywhere you put it on the graph it should only pass through the line once.

Step-by-step explanation:

This insures that the graph does not have two of the same x values. However if it has two points that have the same x values that means it will not be a function.

Answer:

rate goes up every 50 dollars for eatch number of deposits