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The solution of the system would be (3,6).

Lets solve the problem,

Other equation: y = 1/3x+5

Slope-Intercept Form: y = mx + b

Slope Formula:

y2-y1/x2-x1 = m

Have to find equation now:

m = (6 - 5)/(3 - 0)

m = 1/3

y = 1/3x + b

5 = 1/3(0) + b

b=5

y = 1/3x + 5

Lets put the substituition method here,

1/3x + 5 = -1/3x + 7

2/3x + 5 = 7

2/3x = 2

x = 3

y = 1/3(3) + 5

y = 1 + 5

y = 6

Therefore the coordinates are (3,6)

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(a) To solve the differential equation -xy, we can use separation of variables. By integrating both sides and applying the initial condition when x=0, y=50, we can find the particular solution.

(b) The value of x for which y is decreasing can be determined by analyzing the sign of the derivative of y with respect to x.

(a) Given the differential equation -xy, we can use separation of variables to solve it. Rearranging the equation, we have dy/y = -xdx. Integrating both sides, we get ∫(1/y)dy = -∫xdx. This simplifies to ln|y| = -\(x^{2}\)/2 + C, where C is the constant of integration. Exponentiating both sides, we have |y| = e^(-\(x^{2}\)/2 + C) = e^C * e^(-\(x^{2}\)/2). Since y > 0, we can drop the absolute value and write the solution as y = Ce^(-\(x^{2}\)2). To find the particular solution, we use the initial condition y(0) = 50. Substituting the values, we have 50 = Ce^(-0^2/2) = Ce^0 = C. Therefore, the particular solution to the differential equation is y = 50e^(-\(x^{2}\)/2).

(b) To determine the values of x for which y is decreasing, we analyze the sign of the derivative of y with respect to x. Taking the derivative of y = 50e^(-\(x^{2}\)/2), we get dy/dx = -x * 50e^(-\(x^{2}\)/2). Since e^(-\(x^{2}\)2) is always positive, the sign of dy/dx is determined by -x. For y to be decreasing, dy/dx must be negative. Therefore, -x < 0, which implies that x > 0. Thus, for positive values of x, y is decreasing.

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Answer:

a) \(2.036x^-\frac{1}{3}\)

b) \(\frac{x^2}{\sqrt{x+1} }\)

Step-by-step explanation:

For a cube, all the sides are equal. Let the length of each side be L

a) The volume of a cube (V) = L³

For the first cube:

V = 270x in³

270x = L³

L = ∛(270x) = \(6.463x^\frac{1}{3}\)

For the second cube:

V = 32x² in³

32x² = L³

L = ∛(32x²) = \(3.175x^\frac{2}{3}\)

Ratio of length = \(\frac{6.463x^\frac{1}{3} }{3.175x^\frac{2}{3} }=2.036x^-\frac{1}{3}\)

b) The surface area of a cube (s) = 6L²

For the first cube:

s = 6x⁴ ft²

6x⁴ = L²

L = √6x⁴= 2.45x²

For the second cube:

s = 6(x + 1) ft²

6(x + 1) = L²

L = √6(x + 1)= 2.45√(x + 1)

Ratio of the length = \(\frac{2.45x^2}{2.45\sqrt{ (x + 1)}} =\frac{x^2}{\sqrt{x+1} }\)

34% of the data in a normal distribution is more than 1 standard deviation above the mean.

In a normal distribution, about 68% of the data falls within one standard deviation above or below the mean. This means that roughly 34% of the data falls one standard deviation above the mean.

To be more precise, we can use the empirical rule or the 68-95-99.7 rule, which states that:

Approximately 68% of the data falls within one standard deviation of the mean.

Approximately 95% of the data falls within two standard deviations of the mean.

Approximately 99.7% of the data falls within three standard deviations of the mean.

Therefore, if we assume that the normal distribution is perfectly symmetrical, we can estimate that roughly 34% of the data falls more than one standard deviation above the mean.

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The transformation of System A into System B is:

Equation [A2]+ Equation [A 1] → Equation [B 1]"

The correct answer choice is option D

How can we transform System A into System B?

To transform System A into System B as 1 × Equation [A2] + Equation [A1]→ Equation [B1] and 1 × Equation [A2] → Equation [B2].

System A:

-3x + 4y = -23 [A1]

7x - 2y = -5 [A2]

Multiply equation [A2] by 2

14x - 4y = -10

Add the equation to equation [A1]

14x - 4y = -10

-3x + 4y = -23 [A1]

11x = -33 [B1]

Multiply equation [A2] by 1

7x - 2y = -5 ....[B2]

So therefore, it can be deduced from the step-by-step explanation above that System A is ultimately transformed into System B as 1 × Equation [A2] + Equation [A1]→ Equation [B1] and 1 × Equation [A2] → Equation [B2].

The complete image is attached.

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The distance from a to the line passing through b and c is 7/5.

To find the distance from a point to a line, you can use the cross product and the dot product.

First, find the vector pointing from a to b and the vector pointing from b to c:

u = b - a = (3, -5, 0) - (0, 3, -5) = (3, -8, 5)

v = c - b = (3, 0, -5) - (3, -5, 0) = (0, 5, -5)

Next, find the cross product of these two vectors, which gives a vector orthogonal to the plane defined by the line:

n = u x v = (-40, 0, 40)

Finally, find the dot product of n and a - b, which gives the magnitude of the projection of a - b onto n:

d = |n . (a - b)| / |n| = |(-40, 0, 40) . (-3, -8, -5)| / |(-40, 0, 40)| = 57 / √(40^2 + 40^2) = 57 / √1600 = 57 / 40 = 7/5

Therefore, the distance from a to the line passing through b and c is 7/5.

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Answer:

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The angle formed by a tangent and secant is half the difference of the intercepted arcs:

Find the measure of ∠MLJ by substituting 4 for x in the angle measure:

The value of x to the nearest hundredth from the following values: 20.1820.1810.0410.0413.5113.5111.1511.1516.66 is calculated as to be equal to 11.16.

We will need to identify the value that is closer to x. The numbers from 10.04 to 16.66 are greater than 10.04 and less than 20.18. Therefore, the number closest to x is 11.15, which is greater than 10.04 and less than 13.51.

To find the value of x to the nearest hundredth, we round up to the nearest hundredth since 11.15 is closer to 11.16 which is greater than 11.15. Rounding up 11.15 to the nearest hundredth is 11.16.

Therefore the value of x to the nearest hundredth is 11.16.

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The exact values of the remaining trigonometric functions of θ are:

cos θ = 5/13

tan θ = 12/5

csc θ = 13/12

sec θ = 13/5

cot θ = 5/12

Given that sin θ = 12/13 and θ is in quadrant I, we can determine the values of the remaining trigonometric functions as follows:

cos θ:

In quadrant I, cos θ is positive. We can use the Pythagorean identity \(sin^2 θ + cos^2 θ = 1\) to find the value of cos θ:

\(cos^2 θ = 1 - sin^2 θcos^2 θ = 1 - (12/13)^2cos^2 θ = 1 - 144/169cos^2 θ = (169 - 144)/169cos^2 θ = 25/169\)

Since cos θ is positive in quadrant I, we take the positive square root:

cos θ = √(25/169)

cos θ = 5/13

tan θ:

tan θ is the ratio of sin θ to cos θ:

tan θ = sin θ / cos θ

tan θ = (12/13) / (5/13)

tan θ = 12/5

csc θ:

csc θ is the reciprocal of sin θ:

csc θ = 1 / sin θ

csc θ = 1 / (12/13)

csc θ = 13/12

sec θ:

sec θ is the reciprocal of cos θ:

sec θ = 1 / cos θ

sec θ = 1 / (5/13)

sec θ = 13/5

cot θ:

cot θ is the reciprocal of tan θ:

cot θ = 1 / tan θ

cot θ = 1 / (12/5)

cot θ = 5/12

Therefore, the exact values of the remaining trigonometric functions of θ are:

cos θ = 5/13

tan θ = 12/5

csc θ = 13/12

sec θ = 13/5

cot θ = 5/12

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Answer:

Step-by-step explanation:

The figure has 5 sides. Therefore the formula to solve it is (n - 2)*180

(5 - 2)*180 = 3*180 = 540

That is the total of the interior angles so

x + 86 + 140 + 138 + 59 = 540

x + 423 = 540                            Subtract 423 from both sides

x = 540 - 423

x = 117

according to question the solution is :

13.6 - 20.2 + 8 - (-38.5) = 59.9.

To solve this expression, we can follow the order of operations, which is a set of rules that tells us which mathematical operations to perform first. The order of operations is:

Perform any calculations inside parentheses or brackets.

Evaluate exponents or roots.

Perform multiplication or division from left to right.

Perform addition or subtraction from left to right.

Using this order of operations, we can simplify the expression as follows:

13.6 - 20.2 + 8 - (-38.5)

= 13.6 - 20.2 + 8 + 38.5 (Note: two negative signs make a positive sign)

= (13.6 + 8) - 20.2 + 38.5 (Rearranging terms)

= 21.6 - 20.2 + 38.5 (Adding the terms in parentheses)

= 59.9 (Performing the addition and subtraction from left to right)

what is expression?

In mathematics, an expression is a combination of numbers, variables, and operators that represents a mathematical relationship or a calculation. For example, the expression 3x + 5 is a mathematical expression that represents a linear relationship between the variable x and the constant values 3 and 5, where 3x represents three times the value of x and 5 is a constant value added to the product.

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To find the volume of the solid, we first need to sketch the region enclosed by the two parabolic cylinders and the two planes.

The two parabolic cylinders intersect at the points (-1,0,0) and (1,0,0), and the planes intersect at the point (1,-2,3).

Next, we need to find the limits of integration for x, y, and z. We can see that the region is symmetric about the yz-plane, so we only need to consider the positive values of x.

The parabolic cylinders have a common vertex at the origin and open downwards, so the limits of integration for y are -x^2+1 and x^2-1.

The planes have a common line of intersection, which is parallel to the vector <3,3,-1>. We can use this information to find the limits of integration for z.

The plane 3x+3y-z+14=0 intersects the yz-plane at y=(-14/3), and we can find the corresponding value of x using the equation 2=x+y+z. This gives us x=(-20/3).

The plane x+y+z=2 intersects the yz-plane at y=2-x, which gives us x=0.

Therefore, the limits of integration for x are 0 to (-20/3). The limits of integration for y are -x^2+1 to x^2-1. The limits of integration for z are given by the planes 3x+3y-z+14=0 and x+y+z=2.

Using the formula for the volume of a solid obtained by subtracting two volumes, we have:

V = ∭[2-x-y] dV - ∭[3x+3y+14] dV

where the first integral is taken over the region enclosed by the parabolic cylinders and the second plane, and the second integral is taken over the region enclosed by the two planes.

We can evaluate these integrals using the limits of integration we found above. The integrals will involve iterated integrals of the form ∫∫∫ f(x,y,z) dz dy dx.

The final answer for the volume of the solid is the difference between the two integrals.

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Answer:

5.1 cm

Step-by-step explanation:

(Probable) Question;

Given a circle with center O and radius 2.4 cm. P is a point on the tangent that touches the circle at point Q, such that the length of the tangent from P to Q is 4.5 cm. Find the length of OP

The given parameters are;

The radius of the circle with enter at O, \(\overline{OQ}\) = 2.4 cm

The length of the tangent from P to the circle at point Q, \(\overline{PQ}\) = 4.5 cm

The length of OP = Required

By Pythagoras's theorem, we have;

\(\overline{OP}\)² = \(\overline{OQ}\)² + \(\overline{PQ}\)²

∴ \(\overline{OP}\)² = 2.4² + 4.5² = 26.01

\(\overline{OP}\) = √26.01 = 5.1

The length of OP = 5.1 cm

Answer: The average person doesn't live 1 million hours. 1 million hour is 114 year. That is much more than 78 years. 1 million ours is too much. You would need 683280 to make it 78 years.

Answer:

A. $7.46

Step-by-step explanation:

184.54 - 5.50 = 179.04

179.04 / 24 = 7.46

The answer WITHOUT SUBTRACTING THE DELIVERY FEE is: $7.69 (B).

If you're supposed to subtract the delivery fee, then the answer is $7.46 (A).

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Hope this helps!

Have a great day and God bless! :)

The amount of interest earned on a deposit of $60.00 at a rate of 9% per annum for 2 years is $108.

As per the given problem:

Amount deposited = $60.00

Interest rate per year = 9%

The formula for calculating the interest is given by:

Interest = (Principal × Rate × Time)/100

Where Principal is the initial amount invested or deposited

Rate is the percentage of interest that you earn per annum

Time is the duration for which you want to calculate the interest

Putting the values in the above formula, we get:

Interest = (60 × 9 × 2)/100= (108 × 1)/1= $108

So, the amount of interest earned on a deposit of $60.00 at a rate of 9% per annum for 2 years is $108.

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Answer:

4x=7/2-5/6

4x=21-5/6

4x=16/6

x=8/12

x=2/3

x=0.6666.....

Answer:

ten lakh sixty nine thousand and twenty three point two seven

Answer:

Sin0= y/r

X= -4 and r= 9 (radius is also the hypotenuse)

In quadrant II y is positive

X^2 +y^2 = r^2

-4^2 + y^2 = 9^2

16 + y^2 = 81

Y^2 = 81-16

Y^2 = 65

Y= sqrt65

Sin0= sqrt65/9

Step-by-step explanation:

Answer:

Step-by-step explanation:

One that has the next least in common with the rest.

Answer: Check explanation

Step-by-step explanation: -g-6, 9d+3, -12y+20, 14n-29, -2c, x+21/2

Answer:

1. -g-6

2.  9d+3

3. -12y+20

4. 14n-29

5. -2c

6. x+21/2

Step-by-step explanation:

The largest integer less than 2010 that has a remainder of 5 when divided by 7, a remainder of 10 when divided by 11, and a remainder of 10 when divided by 13. is 1440

Given, a number less than 2010 that has a remainder of 5 when divided by 7, a remainder of 10 when divided by 11, and a remainder of 10 when divided by 13.

On using the Chinese remainder theorem. As, the numbers 7, 11, 13 are pairwise coprime.

Firstly, an integer  m  such that  m−5  is divisible by 7 and  m−10  is divisible by 11 .

The Chinese remainder theorem says that all integers that work will be of the form  54+7⋅11⋅k=54+77k  for any integer  k .

Next an integer  n  such that  n−10  is divisible by 13 and  n−54  is divisible by 77.

Then, by the Chinese remainder theorem, all the integers that also work are of the form  439+13⋅77⋅k=439+1001k .

Hence, the positive integers satisfying the condition are: 439, 439 + 1001 = 1440, 1440 + 1001 = 2441, and so on.

The largest integer less than 2010 is 1440.

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The height of the trapezoidal welcome mat that Polly Ester can create with 1114 ft2 of material, with bases of 5 ft and 4 ft, is approximately 247.56 ft.

To find the height of the trapezoidal welcome mat, we can use the formula for the area of a trapezoid, which is:

\($A = \frac{(b_1 + b_2)}{2} \cdot h$\)

where A is the area, \(b_1\) and \(b_2\) are the lengths of the parallel bases, and h is the height.

We know that the bases of the welcome mat are 5 ft and 4 ft, so we can substitute these values into the formula:

1114 = (5 + 4) / 2 * h

Simplifying this equation, we get:

1114 = 4.5h

Dividing both sides by 4.5, we get:

h = 1114 / 4.5

h ≈ 247.56 ft

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Answer:

11335.40 not sure po sa answer

Answer:

dont forget the point of contact dedo I show you how w

Answer:

187.775

Step-by-step explanation:

20.3×9.25=

187.775

The expression that represents the value of sin C - cos C is s-r

From the triangle ABC, since sin B = r and cos B = s.=, hence;

If m<C is the reference angle, then;

Opposite side= s

Adjacent side = r

Hypotenuse = 1

Sin C = s and cos C = r

Hence the expression that represents the value of sin C - cos C is s-r

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