ILL GIVE BRAINIEST find the solption for each system of equations using substitution. check ur solution in both original equations and make sure equations are in slope intercept form before u set them equal

y= -2x+6 and y=3x-4


check:

The marked price of the article is Rs18000

From the question, we have the following parameters that can be used in our computation:

Discount = 15%

VAT = 13%

Amount paid = Rs 17289

Using the above as a guide, we have the following

Amount paid = Marked price * (1 - discount) * (1 + VAT)

Substitute the known values in the above equation, so, we have the following representation

17289 = Marked price * (1 - 15%) * (1 + 13%)

So, we have

Marked price = 17289/[(1 - 15%) * (1 + 13%)]

Evaluate

Marked price = 18000

HEnce, the price is Rs18000

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The probability that the product operates, given that none of the integrated circuits are defective, is approximately 0.4577 or 45.77%.

To determine the probability that the product operates, we need to find the probability that none of the integrated circuits are defective.

Given that there are 38 integrated circuits and the probability of any integrated circuit being defective is 0.03, we can calculate the probability of a single integrated circuit being non-defective as:

P(non-defective) = 1 - P(defective) = 1 - 0.03 = 0.97

Since the integrated circuits are independent, the probability of all 38 integrated circuits being non-defective is simply the product of the individual probabilities:

P(product operates) = P(non-defective)^38

P(product operates) = 0.97^38 ≈ 0.4577

Therefore, the probability that the product operates, given that none of the integrated circuits are defective, is approximately 0.4577 or 45.77%.

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The number of free variables in the solution of the given matrix are as follow:

Attached matrix.

1. First matrix has one free variable x₃.

2. Second matrix has three free variable x₂ , x₃ , x₄.

3. Third matrix has one free variable x₃ , x₄ , x₅

4. Fourth matrix has two free variable x₂ , x₃.

Number of free variables for the corresponding matrix are :

1. First matrix has two pivot element at first and second column , it implies number of free variable is one that x₃.

2. Second matrix has one pivot element in the first column therefore there are three free variable in the second, third and fourth column x₂ , x₃ , x₄.

3. Third matrix has  two pivot element at first and second column so

there are three free variable in the  third ,fourth , and fifth column  x₃ , x₄, x₅.

4. Fourth matrix has one pivot element in the first column therefore it has  two free variables in the second and third column x₂ and x₃.

Therefore, the free variables present in the corresponding matrix are :

1. First matrix : one free variable.

2. Second matrix : three free variables.

3. Third matrix : one free variable.

4. Fourth matrix : two free variables.

The above question is incomplete, the complete question is:

For each matrix, consider the corresponding system of linear equations. how many free variables are there in the solution?

Matrix are attached.

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Answer:

I think it is C.

Step-by-step explanation:

Please mark brainliest I am knew at this

Recursive sequence would produce the sequence 2,-6, 34 is a1 = 2 and an = 2an-1 - 4

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Given:

In the triangular base of the pyramid,

Base = 4m

Height = 7m

Area of base = 1/2 x Base x Height

=> 1/2 x 4 x 7 = 14 m^2

Now, Volume of Triangular Pyramid = 1/3 x Area of Base x Height

= 1/3 x 14 x 5

= 1/3 x 70

= 23.33 m^2 or 23 1/3 m^2

Answer:

$0.20/lb

Step-by-step explanation:

2.99/15 = 199333

.20/lb

Answer:

A. X∪Y = {25, 36, 49}

B. X∩Y = ∅ i.e empty set

C. X' = {21, 22, 23, 24, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48}

D. X′∩Y∩Z = ∅

Step-by-step explanation:

We'll begin by determining the universal set (ε), set X, set Y and set Z.

This can be obtained as follow:

ε = {whole numbers less than 50 but greater than 20}

ε = {21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49}

X = {perfect squares}

X = {25, 36, 49}

Y = {factors of 12}

Y = ∅ i.e empty

Z = {prime numbers}

Z = {23, 29, 31, 37, 41, 43, 47}

A. Determination of X∪Y

X = {25, 36, 49}

Y = ∅

X∪Y =?

X∪Y => combination of elements in set X and Y without repeating any element in both X and Y.

X∪Y = {25, 36, 49}

B. Determination of X∩Y

X = {25, 36, 49}

Y = ∅

X∩Y =?

X∩Y => elements common to both set X and Y

X∩Y = ∅ i.e empty

C. Determination of X′

ε = {21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49}

X = {25, 36, 49}

X' =?

X' => elements in the universal set but not found in set X.

X' = {21, 22, 23, 24, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48}

D. Determination of X′∩Y∩Z

X' = {21, 22, 23, 24, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48}

Y = ∅

Z = {23, 29, 31, 37, 41, 43, 47}

X′∩Y∩Z =?

X′∩Y∩Z => elements common to set X', Y and Z

X′∩Y∩Z = ∅

Answer:

(A) 125.6 m

Step-by-step explanation:

They are asking the circumference of a circle with a radius of 20. The formula for the circumference of a circle is:

\(C=2\pi r\), where C is the circumference and r is the radius.

Plug in \(r=20\) to get:

\(C=40\pi\) which is approximately 125.6.

Hope this helps :)

The rocket peaks at approximately 2805.7 meters above sea-level.

The function h(t) = −4.9t² + 232t + 374, describes the height, in meters above sea-level, of the rocket as a function of time, t.

We are given the function: h(t) = −4.9t² + 232t + 374

Let's first determine when the rocket splashes down:

When the rocket splashes down, h(t) = 0.

We can set h(t) to 0 and solve for t: 0 = −4.9t² + 232t + 374

Solving this quadratic equation using the quadratic formula:

\(t=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\)

\(t=\frac{-232\pm\sqrt{232^2-4(-4.9)(374)}}{2(-4.9)}\)

\(t\approx48.2 \:s\:\text{or}\:9.6 \:s\)

Since time cannot be negative, we must choose the positive solution: t ≈ 48.2 s.

Therefore, the rocket splashes down after approximately 48.2 seconds.

The vertex of the parabola represents the maximum height of the rocket above sea-level.

Let's begin by finding the x-coordinate of the vertex of the parabola, which represents the time at which the rocket reaches its peak.

To find the time t at the vertex of the parabola, we can use the formula:

\(t=-\frac{b}{2a}\)

\(t=-\frac{232}{2(-4.9)}\)

\(t\approx23.7 \:s\)

The rocket reaches its peak after approximately 23.7 seconds.

Now we need to find the height h(t) at this time t = 23.7s:

h(23.7) = −4.9(23.7)² + 232(23.7) + 374 ≈ 2805.7 meters

Therefore, the rocket peaks at approximately 2805.7 meters above sea-level.

The rocket splashes down after approximately 48.2 seconds.

The rocket peaks at approximately 2805.7 meters above sea-level.

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Answer:

  78 square feet

Step-by-step explanation:

You want the surface area of a rectangular prism 1 ft high by 4 ft long and 7 ft wide.

The surface area is given by ...

  SA = 2(LW +H(L +W))

  SA = 2(4·7 +1(4 +7)) = 2(28 +11) = 78 . . . . square feet

The surface area of the prism is 78 square feet.

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The solution to the equation given as 1.8(b-5.3)-4.2=5.8(b-2.3) is b = -0.1

From the question, the equation is given as

1.8(b-5.3)-4.2=5.8(b-2.3)

Rewrite the equation properly

This is represented as follows

1.8(b - 5.3) - 4.2 = 5.8(b - 2.3)

Open the brackets in the above equation

So, we have

1.8b - 9.54 - 4.2 = 5.8b - 13.34

Collect the like terms in the equation

So, we have

1.8b - 5.8b = 9.54 + 4.2 - 13.34

Evaluate the like terms in the equation

So, we have

-4b = 0.4

Divide by -4

b = -0.1

Hence, the solution is b = -0.1

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The solution to the equation 1.8(b-5.3)-4.2=5.8(b-2.3) will be; b = -0.1

An equation is an expression that shows the relationship between two or more numbers and variables.

We have been given an equation as;

1.8(b-5.3)-4.2=5.8(b-2.3)

Rewrite the equation properly  as follows;

1.8(b - 5.3) - 4.2 = 5.8(b - 2.3)

Open the brackets in the equation, we have

1.8b - 9.54 - 4.2 = 5.8b - 13.34

Now Collect the like terms in the equation

1.8b - 5.8b = 9.54 + 4.2 - 13.34

Evaluate the like terms in the equation;

-4b = 0.4

Now Divide by -4

b = -0.1

Hence, the solution is; b = -0.1

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Step-by-step explanation:

2 negatives equal a positive a positive and a negative equals a negative

2 positives equals a positbe

Using the exponential regression feature of the calculator to find the equation of the regression line, we get that \($$y = 0.8996 e^{1.3759x}.$$\)

Given data, $$\begin{array}{|c|c|} \hline x & y\\ \hline 1 & 2.20\\ 2 & 3.60\\ 3 & 5.90\\ 4 & 9.70\\ 5 & 15.90\\ 6 & 26.00\\ \hline \end{array}.$$

The equation of the form is y = 1 + aebx;

Thus, the required equation is \($$y = 1 + 0.8996 e^{1.3759x}.$$\)

Finally, putting x = 7, we get

\($$y = 1 + 0.8996 e^{1.3759(7)} \approx 156.76.$$\)

Thus, the required equation is\($$y = 1 + 0.8996 e^{1.3759x}.$$\)Finally, putting x = 7, we get

\($$y = 1 + 0.8996 e^{1.3759(7)} \approx 156.76.$$\)

So, the value of y at x = 7 is approximately 156.76.

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Answer:

D

Step-by-step explanation:

If you think of the x-axis as your horizontal line, you can see that there is more than one value for x for y=0.

For instance, (-2,0), (0,0), (0,2).

The transformation of the function f(x) = log2(x) involves shifting 2 units up and vertically compressing by a factor of 0.4.

Which function represents the transformation g(x)?

The following equation can be used to represent the transformation:

g(x) = 0.4*log2(x) + 2

Therefore, the function that represents the transformation g(x) is:

g(x) = 0.4*log2(x) + 2

To understand the transformation of the function f(x) = log2(x) into g(x), we need to first understand the individual transformations involved.

Vertical compression: When a function is vertically compressed by a factor 'a', its output values get multiplied by 'a'. This means that the function's range gets compressed by a factor of 'a'. In this case, the function f(x) = log2(x) is vertically compressed by a factor of 0.4. So, the output values of f(x) get multiplied by 0.4, which compresses the range of the function by a factor of 0.4.

Vertical shift: When a function is shifted 'b' units up or down, its output values get increased or decreased by 'b'. This means that the function's range gets shifted up or down by 'b'. In this case, the function f(x) = log2(x) is shifted 2 units up. So, the output values of f(x) get increased by 2, which shifts the range of the function 2 units up.

Putting these two transformations together, we get the transformation of the function f(x) = log2(x) into g(x) as follows:

g(x) = 0.4*log2(x) + 2

This equation represents a vertical compression of the function f(x) by a factor of 0.4, followed by a vertical shift of 2 units up.

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Complete question:

To solve;

we will use the formula;

where a is the base and h is the height

From the diagram, a = 4 and h=3

substituting into the formula;

A= 16 + 8√13

A= 16 + 28.8444

A=44.844 units²

Answer:

n + n*1.30 = 69

The number is 30

Step-by-step explanation:

We have a number n

increased by 130%

n + n*130%

is 69

n + n*1.30 = 69

Combine like terms

2.30n = 69

Divide by 2.30

2.30n/2.3 = 69/2.3

n =30

When the volume of a spherical balloon is increasing at a constant rate of 10 cubic meters per hour, radius is increasing can be determined using the derivative of the volume with respect to time.

To find the rate at which the radius is increasing, we need to relate the volume and the radius of the spherical balloon. The volume of a sphere is given by the formula V = (4/3)πr^3, where V is the volume and r is the radius.

Taking the derivative of the volume with respect to time will give us the rate of change of the volume, which is 10 cubic meters per hour in this case. Let's denote the rate of change of the radius as dr/dt.

Differentiating the volume equation with respect to time, we have dV/dt = 4πr^2 (dr/dt). Since the volume is increasing at a constant rate of 10 cubic meters per hour, we can substitute dV/dt with 10.

10 = 4πr^2 (dr/dt)

Now, we can solve for dr/dt, which represents the rate at which the radius is increasing. Plugging in the given radius of 5 meters, we have:

10 = 4π(5^2)(dr/dt)

10 = 100π(dr/dt)

Simplifying the equation, we find:

dr/dt = 10/(100π)

dr/dt = 1/(10π) meters per hour

Therefore, when the radius is 5 meters, the rate at which it is increasing is approximately 1/(10π) meters per hour.

Answer:

41

Step-by-step explanation:

15+26=41

Answer:

41 minutes

Step-by-step explanation:

If she jogged 15 minutes more on Sunday than Saturday, we can find how many minutes she jogged on Sunday by adding 15 to Saturday's amount:

So, add 15 to 26:

15 + 26

= 41

So, she jogged 41 minutes on Sunday.

Answer:

4 years

Step-by-step explanation:

Given data

Simple interest= $400

Principal= $2000

Rate= 5%

The simple interest formula is given as

SI=PRT/100

substitute and solve for T

400=2000*5*T/100

cross multiply

400*100= 10000*T

40000=10000T

T= 40000/10000

T= 4 years

Hence the time taken is 4 years

(i) Jitra All Black Berhad Income Statement for the years 2019 and 2020SalesRevenueCost of salesGross profitOperating expensesSalariesRentUtilitiesDepreciationOperating incomeInterest expense.

Earnings before tax (EBT)Income tax (20%)Net income (Profit or loss)2019 $ 1,200,000 $ 780,000 $ 420,000 $ 140,000 $ 100,000 $ 60,000 $ 20,000 $ 100,000 $ 20,000 $ 80,000 $ 16,000 $ 64,0002020 $ 1,500,000 $ 975,000 $ 525,000 $ 175,000 $ 125,000 $ 75,000 $ 25,000 $ 150,000 $ 30,000 $ 120,000 $ 24,000 $ 96,000.

(ii) Jitra All Black Berhad Balance Sheet as at 31 December 2019LiabilitiesAssetsCurrent liabilitiesAccounts payableWages payableInterest payableAccrued expenses.

Total current liabilitiesLong-term liabilitiesLoan payableTotal liabilitiesCurrent assetsCashAccounts receivableInventoryTotal current assetsFixed assetsPlant and equipmentLess:

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Data collected at the same, or approximately the same point in time are  Cross- sectional data

In statistics and econometrics, cross-sectional data, or a cross section of a study population, is a type of data gathered by monitoring numerous subjects (such as individuals, firms, countries, or regions) at one point or throughout the course of time. It's also possible that the analysis disregards variations in time. Cross-sectional data analysis often entails contrasting the variations among pre-selected respondents.

For instance, if we wanted to determine the prevalence of obesity in a population, we could randomly select a sample of 1,000 people (also referred to as a cross section of that population), measure their height and weight, and then determine what proportion of that sample falls under the definition of obesity. With the use of this cross-sectional sample, we are able to get a current picture of that group. Be aware that based on a single cross-sectional sample, we cannot determine whether the prevalence of obesity is rising or falling; we can only describe the current proportion.

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a) The time it takes for the ball to hit the ground is given as follows: 2.5 seconds.

b) The time it takes for the maximum height is of: 1 second.

c) The maximum height is of: 36 feet.

d) The equation would be of: h(t) = 30 + 32t - 16t².

The quadratic function for the ball's height is given as follows:

h(t) = 20 + 32t - 16t².

In which:

The coefficients are given as follows:

a = -16, b = 32, c = 20.

Then the discriminant is of:

D = b² - 4ac

D = 32² - 4 x (-16) x 20

D = 2304.

The positive root gives the time it takes for the ball to hit the ground, as follows:

t = (32 + sqrt(2304))/32

t = 2.5 seconds.

The time to reach the maximum height is the t-coordinate of the vertex, hence:

t = -b/2a

t = -32/-32

t = 1 second.

The maximum height is of:

h(1) = 20 + 32 - 16

h(1) = 36 feet.

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Answer:

3.2 units to nearest tenth.

Step-by-step explanation:

cos 29 = x /3.7      (cosine = adjacent side / hypotenuse)

x = 3.7 * cos 29

= 3.236

Answer:

What happens when h is positive?

The asymptote of the graph shifts right by that amount.

What happens when h is negative?

The asymptote of the graph shifts left by that amount.

What happens when k is positive?

The entire graph shifts up by that amount.

What happens when k is negative?

The entire graph shifts down by that amount.

Answer:

1.)c

2.)d

3.)a

4.)b

Step-by-step explanation:

Answer:

-21z-35t+21g

Step-by-step explanation:

-7x3z=-21z

-7x5t=-35t

-7x-3g=21g

Answer: Now, I'm not so sure about the identify and inconsistent part, so I took a guess.  Sorry if I'm wrong!

a. x = -8 (identify)

b. x = 6 (identify)

c. x = 5 = -1  (inconsistent)

d. x = 6 (identify)

d. (the second d;  it looks like there are 2 d's) x = 5 (identify)

e. 1 = -1 (inconsistent)

f. x =  \(\frac{2}{3}\) (identify)

g. x = -3 (identify)

h. 5x+5 = 5x+5 (identify)

i. I don't know, sorry :/

Step-by-step explanation:

a. 7x +5 = 2x - 35

  -2x        -2x   (Subtract the smaller number with the x)

 5x +5 = -35

      -5      -5

      5x = -40

         x = -8    (Divide 5 with 5x and -40)

b. \(\frac{x}{3}\) - 7 = -5

   x - 21 = -15   (Multiply 3 with x/3, -7, and -5)

          x = 6

c. 4x +5 = 4x -1

   -4x       -4x

            5 = -1

d. \(\frac{5(x-3)}{2}\) -1 = 14

10(x-3) -2 = 28  (Multiply all numbers by 2)

10x -30 -2 = 28   (Combine -30 and -2)

    10x -32 = 28

          +32  +32

           10x = 60

               x = 6

d. 3 (x-1) +2 = x+9

    3x -3 +2 = x+9

           3x -1 = x+9  (Subtract x from both sides b/c x is basically 1x)

           -x        -x

          2x -1 = 9

               +1  +1

               2x = 10

                  x = 5  (Divide 2 from both sides)

e. 4x-(2x-1) = x+5+x-6

4x -2x +1 = x+5+x-6  (Mulitply the negative sign w/ 2x and -1. The negative sign is basically a -1.  So, a negative times a negative is a positive)

        2x+1 = 2x -1 (You can stop here or keep going)

        -2x     -2x

              1 = -1

f. 5(2x-6)+2=(4x+3)=8x-9

10x-30+8x+6 = 8x-9

18x - 24 = 8x - 9

      +24         +24

       18x = 8x + 15

      -8x      -8x

      10x = 15  (Divide 10 by both sides)

          x = \(\frac{2}{3}\)

g. \(\frac{2x+5}{6}\) = \(\frac{x}{18}\)

   6x = 18(2x+5)

    6x = 36x+90

    -6x   -6x

      0 = 30x + 90

    -90          -90

    -90 = 30x  (Divide 30 by both sides)

      -3 = x

h. \(\frac{10x-4}{2}\) +7 = 5(x+1)

\(\frac{2(5x-2)}{2}\) +7 = 5(x+1)  (The 2 cancels out)

 5x - 2 + 7 = 5(x+1)  (Combine like terms and do distributive property)

        5x+5 = 5x+5  (We can stop here because each side is the same)

i. I'm so sorry, I don't quite know :/

To calculate compound interest, we use the formula:

\(A = P(1 + \frac{r}{n})^{nt}\)

Where:

A = the final amount (including principal and interest)

P = the principal amount (the initial loan)

r = the annual interest rate (as a decimal)

n = the number of times that interest is compounded per year

t = the number of years

In this case, Tom borrowed $6,000 at a 3% interest rate for 2 years. Let's calculate the compound interest:

P = $6,000

r = 3% = 0.03

n = 1 (compounded annually)

t = 2 years

\(A = 6000(1 + \frac{0.03}{1})^{1 \cdot 2}\\\\= 6000(1 + 0.03)^2\\\\= 6000(1.03)^2\\\\\approx 6000(1.0609)\\\\\approx \$6,365.40\)

The final amount (including principal and interest) is approximately $6,365.40. To calculate the compound interest, we subtract the principal amount:

Compound Interest = A - P = $6,365.40 - $6,000

Compound Interest ≈ $365.40

Therefore, the correct answer is:

Compound Interest ≈ $365.40.

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Answer:

x=27

because

3x-4y=65

replace the y with 4

3x-4(4)=65

-4(4)= -16

3x-16=65

add the 16 to both sides

3x=81

divide both by 3 and you get x=27

Step-by-step explanation: