solve for y for y+4x+6=2x^2

Answer:

Please find attached the required graph created with Microsoft Excel

4. The solution is x = -1, y = -2

5. Both equations represent the same line and the system of equation has Infinitely many solutions

6. The system of equation represent two parallel lines, therefore, the system of equation has no solutions

Step-by-step explanation:

4. The given system of equation are;

y = -3·x - 5...(1)

y = 9·x + 7...(2)

Equating both values of y from the two equations, gives;

9·x + 7 = -3·x - 5

12·x = -5 - 7 = -12

x = -12/12 = -1

x = -1

y = 9·x + 7 = 9 × (-1) + 7 = -2

y  = -2

5. y = -2·x - 5...(1)

6·x + 3·y = -15...(2)

Substituting the value of 'y' from equation (1) in equation (2), gives;

6·x + 3·y = 6·x + 3 × (-2·x - 5) = -15 = -15

Therefore, equations (1) and (2) are the same and has infinitely many solutions

6. y = -4·x + 3

8·x + 2·y = 8

Substituting the value of 'y' from equation (1) in equation (2), gives;

8·x + 2·y = 8·x + 2×(-4·x + 3) = 6

However, 8·x + 2·y = 8, therefore, equations (1) and (2) do not intersect and they have no common solution.

Answer:

23: 21\(\frac{23}{55}\)  25: 1\(\frac{44}{45}\)

Step-by-step explanation:

Question 23:

1) add the whole numbers together: 15+5=20

2)To add fractions, both need to have the same denominator. Find a number that is a multiple of both denominators (in this case 55)

\(\frac{9}{11}\) → \(\frac{45}{55}\) (multiply the numerator and denominator by 5)

\(\frac{3}{5}\) → \(\frac{33}{55}\) (multiply the numerator and denominator by 11)

3) add the fractions together

\(\frac{45}{55}\) + \(\frac{33}{55}\) = \(\frac{78}{55}\) (add the numerators)

4) Turn the improper fraction into a mixed number

Divide 78 by 55. You'll get a whole number and a remainder. The remainder is the new numerator: In this case 55 enters 78 once with a remainder of 23. Therefore:

1\(\frac{23}{55}\)

5) Add the whole numbers together to get the final answer:

20+1= 21

Answer: 21\(\frac{23}{55}\)

Question 25:

Follow the above steps but subtract instead of adding

Answer:

6.73 X 10 to the sixth power.

1.33 X 10 to the fifth power.

9.77 X 10 to the twenty-second power.

Step-by-step explanation:

ANSWER: -1/4

EXPLANATION:

4x-y=9

y=4x-9

(so slope/gradient of this line is 4 as y= mx+c and the coefficient of x here is 4)

(formula for perpendicular slopes) m1 multiplied by m2 = -1, where m= gradient

So, m1 x 4= -1

    m of perp line= -1/4

Answer:

±5

Step-by-step explanation:

-5k²+20k-30

if u look at the equation ±5 are the greatest common factors so we ±5(±k²±4k±6)

Answer:

A. How are GH and GI related?

B. Write an equation to solve for x.

C. Let's solve the equation...

GH : 2x

GI : x + 12

D. Now, that we solve for x, let's find the length of GH....

GH = 2x where, x = 12

Therefore, the length of GH is 24.

Answer The picture shows you where to place your line

Step-by-step explanation:

The curve equation as F(x,y) = (x - 2)^2 + y^2 and the indicated point as P(a, b).

The distance between the curve and point P can be expressed as the square root of the square of the difference in x-coordinates plus the square of the difference in y-coordinates.

So, the distance function can be written as \(D(x,y) = \sqrt((x - a)^2 + (y - b)^2)\).

To find the minimum distance, we need to minimize the distance function subject to the constraint F(x,y) = 0. We can set up the Lagrange equation as follows:
L(x, y, λ) = D(x,y) + λF(x,y)
Taking the partial derivatives with respect to x, y, and λ, we have:

\(dL/dx = (x - a) / \sqrt((x - a)^2 + (y - b)^2) + 2\lambda(x - 2)\)
\(dL/dy = (y - b) / \sqrt((x - a)^2 + (y - b)^2) + 2 \lambda y\)
\(dL/dλ = F(x,y) = (x - 2)^2 + y^2\)

Setting each of these derivatives equal to zero, we can solve the resulting system of equations to find the critical points. Once we obtain the critical points, we can calculate the distance for each of them using the distance function D(x,y).

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Answer:

First find slope. m = (y2 - y1)/(x2 - x1) = (6 -1)/(-6 --3) = 5/-3. then. use. y - y1 =. m (x - x1). which gives. y - 1 = -5/3(x - 3)

Step-by-step explanation:

To accurately calculate the values of sinx, cosx, and tanx we use trigonometric functions.

To find sin(x), cos(x), and tan(x) in a right triangle with side lengths d, e, and f, we first need to identify which sides are opposite, adjacent, and hypotenuse relative to angle x. Let's assume that side d is opposite to angle x, side e is adjacent to angle x, and side f is the hypotenuse.
Now, we can use the definitions of the trigonometric functions:
1. sin(x) = opposite/hypotenuse = d/f
2. cos(x) = adjacent/hypotenuse = e/f
3. tan(x) = opposite/adjacent = d/e
These are the expressions for sin(x), cos(x), and tan(x) in terms of the given side lengths d, e, and f.

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The three conditions for a function to be continuous at a point x=a are:

a) The function is defined at x=a.

b) The limit of the function as x approaches a exists.

c) The limit of the function as x approaches a is equal to the value of the function at x=a.

The continuity of a function can be analyzed by observing its graph. However, as the graph is not provided, a specific discussion about its continuity cannot be made without further information. It is necessary to examine the behavior of the function around the point in question and determine if the three conditions for continuity are satisfied.

The function f(x) = { *** is not defined in the question. In order to discuss its continuity, the function needs to be provided or described. Without the specific form of the function, it is impossible to analyze its continuity. Different functions can exhibit different behaviors with respect to continuity, so additional information is required to determine whether or not the function is continuous at a particular point or interval.

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Answer:

(-2,6)

Step-by-step explanation:

Answer:His error lies in  the subtraction of 12 from 8 , he wrote 4 instead of -4 , as 8-12 gives -4 instead of 4.

Step-by-step explanation:

Step 1

Rewriting this to a mathematical expression 2 cubed (3 minus 1) + 4 (8 minus 12) and solving correctly gives

2³(3-1)+ 4(8-12)

=8(2) + 4(-4)

= 16 +(-16)

16-16=0

Step 2-----Jacki's evaluation

2³(3-1)+ 4(8-12)

 = 2³(2) +4(4)

= 8(2) +16= 16+ 16 =32

His error lies in  the subtraction of 12 from 8 , he wrote 4 instead of -4 , as 8-12 gives -4 instead of 4.

Answer:

C

Step-by-step explanation:

I took the test ;)

The value the seasonal index (SI) for Q4 is 0.63.

To find the seasonal index (SI) for Q4, the first step is to calculate the average of the ratio-to-moving average for each quarter.

The formula for calculating seasonal index is as follows:

Seasonal Index = Average of Ratio-to-Moving Average for a Quarter / Average of Ratio-to-Moving Average for all Quarters

To find the seasonal index (SI) for Q4:

1: Calculate the average of the ratio-to-moving average for Q4.Q4 average = (0.65 + 0.65) / 2 = 0.65S

2: Calculate the average of the ratio-to-moving average for all quarters.All quarters average = (0.87 + 1.30 + 1.50 + 0.65 + 0.77 + 1.36 + 1.35 + 0.65) / 8 = 1.03

3: Calculate the seasonal index for Q4.Seasonal Index for Q4 = Q4 Average / All Quarters Average= 0.65 / 1.03 = 0.6311 (rounded to 2 decimal places)

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Given statement solution is :- If you conclude to reject the null hypothesis (H0), there are two possible errors you may be making: Type I Error,

Type II Error. It's important to note that these errors are inherent in hypothesis testing and are not necessarily indicative of mistakes or negligence on the part of the researcher. The goal is to minimize both types of errors, but there is typically a trade-off between them.

If you conclude to reject the null hypothesis (H0), there are two possible errors you may be making:

Type I Error: This occurs when you reject the null hypothesis even though it is true. In other words, you conclude that there is a significant effect or relationship when, in fact, there is no such effect or relationship in the population. The probability of making a Type I error is denoted by the significance level (usually denoted as α), and it is typically set before conducting the hypothesis test.

Type II Error: This occurs when you fail to reject the null hypothesis even though it is false. In other words, you fail to identify a significant effect or relationship that actually exists in the population. The probability of making a Type II error is denoted by β, and it is related to the power of the test (1 - β).

It's important to note that these errors are inherent in hypothesis testing and are not necessarily indicative of mistakes or negligence on the part of the researcher. The goal is to minimize both types of errors, but there is typically a trade-off between them.

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Answer:

Tim has $50. 15+15=30-35=5

Tim has $5 left

Answer:

3y - x = 3

Step-by-step explanation:

The slope intercept form of the equation is expression is y = mx+c

m is the slope

c is the y inercept

From the graph

c = 1

Using the coordinates (-3, 0) and (0, 1)

m = 1-0/0-(-3)

m = 1/3

Get the required equation

y = 1/3x + 1

Multiply through by 3

3y = x + 3

3y - x = 3

Hence the required equation is 3y - x = 3

Answer:

20% off 45.00 is 36.00

Step-by-step explanation:

The difference is $9.00

Answer:

$36

Step-by-step explanation:

20% of $45 is $9.

$45 - $9 = $36

The value of the composite function (g o f)(6) is 3

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

f(x) = 2x + 3

g(x) = 1/5x

A. Find f(6)

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

f(6) = 2 * 6 + 3

So, we have

f(6) = 15

For the function (gof)(6), we have

g(x) = 1/5x

This gives

(g o f)(6) = 1/5 * 15

Evaluate

(g o f)(6) = 3

Hence, the composite function has a solution of 3

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Complete question

Given that f(x) = 2x + 3 and g(x) = 1/5x

Compute (gof)(6)

A. Find f(6)

B. substitute the value of g(x) into the function f(x) in place of x

If the value exceeds\($0.200$\) by the tolerance of \($0.020$\) on either side, a repair cost of \($\$150$\)is incurred.

\($L(x) = 150(x - T)$\) option b.

The Taguchi loss function measures the cost or loss associated with deviations from a target value in a quality characteristic.

In this case, the specification for the quality characteristic is \($0.200 \pm 0.020$\).

If the value exceeds \($0.200$\) by the tolerance of \($0.020$\)on either side, a repair cost of $\$150$ is incurred.

Based on this information, the Taguchi loss function for this example is given by:

b.\($L(x) = 150(x - T)$\)

In the given options, option b represents the correct Taguchi loss function. The loss function is a linear function where the loss increases linearly with the deviation from the target value.

The coefficient of \($150$\) represents the cost of repair per unit deviation.

This loss function is appropriate for the given scenario as it accurately captures the cost associated with deviations from the target value.

The Taguchi loss function provides a quantitative measure to assess the impact of variations in the quality characteristic and helps in making decisions regarding process improvement and optimization.

In this case, it allows for evaluating the cost implications of exceeding the specified tolerance and guides decision-making on whether repairs are necessary based on the associated costs.

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Answer:

Step-by-step explanation:

Feb 8, 2017 - an=12n(n+1). Explanation: These are recognisable as triangular numbers, but let's use a general method for finding matching polynomial ...

1 answer

Answer:

Step-by-step explanation:

a 2x-6/5=4

2x-6=20

2x=26

x=13

b 7-2x/4=9

-2x=8

x=-4

With one third of a serving remaining, there are 17 servings are there in a box that holds 13 cups.

Given that:

Each cup holds a bit more than 1 serving, so we know there are at least 13 servings in a box.

We need to know how many servings of 3/4 cup can be obtained from 13 cups.

now we need to divide 13 by 3/4

=13 ÷ 3/4  

= 13 × 4/3

= 52/3

= 17\(\frac{1}{3}\)

With one third of a serving remaining, there are 17 servings total.

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Based on the SAS similarity theorem, the right option is: C) ΔVML ∼ ΔUMT.

In order to determine if two triangles are similar, find out if the ratio fo their corresponding side lengths are equal, that is, their lengths must be proportional to each other if they are similar triangles.

The SAS states that if two pairs of sides of two triangles are proportional to each other, and they have a pair of corresponding congruent included angles, then they are similar triangles.

Given the image showing the two triangles, we have the following measures:

VM = 14, which is corresponding to UM = 49

LM = 8, which is corresponding to TM = 28

VM/UM = 14/49 = 2/7

LM/TM = 8/28 = 2/7

This means the two sides are proportional.

Also, angles VML and UMT are congruent to each other based on the vertical angles theorem.

Therefore, we can state that the ΔVML ∼ ΔUMT by SAS. The right option is C.

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The Steady-state gain can be found using the formula Kp = lim s->0 G(s).

A. (a) The inverse Laplace transform of the function 8 /s² (s+2) is given by f(t) = 8(t - e^(-2t)).

B. (a) To find the inverse Laplace transform of 8 /s² (s+2), we can use partial fraction decomposition and inverse Laplace transform tables.

First, we express the function in partial fraction form as follows: 8 /s² (s+2) = A/s + B/s² + C/(s+2).

To find the values of A, B, and C, we can equate the coefficients of corresponding powers of s in the numerator and denominator. This leads to the equations A + 2B + 2C = 0, A = 8, and B = -8.

Substituting the values of A and B into the equation A + 2B + 2C = 0, we find C = 4.

Now, we have the partial fraction decomposition as: 8 /s² (s+2) = 8/s - 8/s² + 4/(s+2).

Using inverse Laplace transform tables, we find the inverse Laplace transforms of each term: L⁻¹{8/s} = 8, L⁻¹{8/s²} = 8t, and L⁻¹{4/(s+2)} = 4e^(-2t).

Finally, we combine the inverse Laplace transforms of each term to obtain the inverse Laplace transform of the original function: f(t) = 8(t - e^(-2t)).

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Answer: y-4=-3(x+4) or y=-3x-8

Step-by-step explanation:

To find the equation of the line with a given point and slope, we can fill them into the point-slope formula. The point-slope formula is y-y₁=m(x-x₁).

y-4=-3(x-(-4))            [multiply]

y-4=-3(x+4)

Another equation could be slope-intercept form. It is y=mx+b.

y-4=-3(x+4)              [distribute]

y-4=-3x-12                [add both sides by 4]

y=-3x-8

Now, we know that the equation is y=-3x-8 or y-4=-3(x+4).

Answer:

500

Step-by-step explanation:

the dimensions of the circle and square that produce a minimum total area are 1.12 and 2.24 respectively

given that

the combined perimeter of a circle and square is 16cm

let side length of the square is s

let radius of the circle with r

So, the perimeter (P) and the area (A) of the shape are:

P= 4s + 2\(\pi\)r

A = \(s^{2}\) + \(\pi\)\(r^{2}\)

given that perimeter is 16

so, 4s +2\(\pi\)r = 16

divide by 4

s +0.5\(\pi\)r = 4

s = 4 - 0.5\(\pi\)r

substitute s value in area

A =  \((4-0.5\pi r)^{2}\) + \(\pi\)r

A = 16 - 4\(\pi\)r +0.25\((\pi r)^{2}\) +\(\pi\)\(r^{2}\)

A =16 - 4\(\pi\)r + (0.25 \(\pi ^{2}\) + \(\pi\))\(r^{2}\)

differentiate with respect to r

A' = 0 - 4\(\pi\) +2 (0.25 \(\pi ^{2}\) + \(\pi\))r

A' = - 4\(\pi\) +2 (0.25 \(\pi ^{2}\) + \(\pi\))r

now A' =0

- 4\(\pi\) +2 (0.25 \(\pi ^{2}\) + \(\pi\))r =0

2 (0.25 \(\pi ^{2}\) + \(\pi\))r =  4\(\pi\)

divide both sides by 2

(0.25 \(\pi ^{2}\) + \(\pi\))r = 2\(\pi\)

r = \(\frac{2\pi }{0.25\pi ^{2} +\pi }\)

r = \(\frac{2\pi }{\pi (0.25\pi +1)}\)

substitute  \(\pi\) =3.14

r = 2/(0.25(3.14)+1)

r = 1.12

substitute r value in s

s = 4 - 0.5 * 3.14 *1.12

s =2.24

Hence, the dimensions of the circle and square that produce a minimum total area are 1.12 and 2.24 respectively

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Answer:

z(x+y)

Step-by-step explanation:

Answer:

Step-by-step explanation:

Z(x+y)