The length of a rectangle is twice its width. When the length is increased by 5 and the width is decreased by 3 , the new rectangle will have a perimeter of 52 . Find the dimensions of the original rectangle.

Answer:

52ft

Step-by-step explanation:

You divide the box in 2 pieces and multiply the numbers by the separate boxes that you made, then you add them.

5x2= 10

8-2= 6 -----> 7x6= 42

10 + 42 = 52

Answer: The first box is 56 The second box is 4 and the last is 52

Step-by-step explanation: The total area of the full rectangle is 8×7=56

The area of the small cut out portion is 2×2=4

The area of the remaining figure is 56-4=52

The quadrilateral ABCD is similar to quadrilateral EFGH because ABCD ∼ EFGH .

The quadrilateral ABCD is similar to quadrilateral EFGH and we can see this because quadrilateral EFGH is an enlarged version of quadrilateral ABCD.

We know this because  there is a scale factor which is:

= Corresponding side of EFGH / Side of ABCD

= 21 / 14

= 1. 5

When this scale factor multiplies any of the sides of ABCD, it gives the side of EFGH that corresponds so they are similar.

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The value of the error for Z, where x = 5.9 +/- 0.5 and y = 2.1 +/- 0.2, with one decimal place is 4.

To calculate the error in Z, we need to consider the uncertainties in both x and y. The error in Z can be determined by propagating the uncertainties using the formula for error propagation.

In this case, Z is given by the equation Z = x/y. To propagate the uncertainties, we use the formula for relative error:

ΔZ/Z = sqrt((Δx/x)^2 + (Δy/y)^2)

Given the uncertainties Δx = 0.5 and Δy = 0.2, and the values x = 5.9 and y = 2.1, we substitute these values into the formula:

ΔZ/Z = sqrt((0.5/5.9)^2 + (0.2/2.1)^2) = sqrt(0.0089 + 0.0181) ≈ 0.134

Multiplying this value by 100 to convert it to a percentage, we get approximately 13.4%. Rounding to one decimal place, the value of the error is 4.

Therefore, the value of the error for Z, with one decimal place, is 4.

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Step-by-step explanation:

members of "M" = 2,3,5,7,11

members of "N" = 1,2,3,4,6,12

M∪N = 1,2,3,4,5,6,7,11,12

M∩N = 2,3

intersection is the overlapping numbers in the sets

union is the set with all the numbers but they cannot be duplicates

The members of "M" \(=\) \(2,3,5,7,11\)

The members of "N" \(= 1,2,3,4,6,12\)

M∪N \(= 1,2,3,4,5,6,7,11,12\)

M∩N \(= 2,3\)

What is Prime number ?

A prime number is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number.

According to questions, M = {Prime integers between \(1\) and \(11\)}

and N = { factors of \(12\)}.

We have to find the members of M, the members of N, M∪N and M∩N.

M = {Prime integers between \(1\) and \(11\)} \(=\)\(2,3,5,7,11\)

N = { factors of \(12\)} \(= 1,2,3,4,6,12\)

 So, M∪N \(= 1,2,3,4,5,6,7,11,12\)

and M∩N \(= 2,3\)

Hence, we can conclude that

The members of "M" \(=\) \(2,3,5,7,11\)

The members of "N" \(= 1,2,3,4,6,12\)

M∪N \(= 1,2,3,4,5,6,7,11,12\)

M∩N \(= 2,3\)

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Step-by-step explanation:

'a' region is    53  out of (53+81+106+85 + 64 = 389)

53/389 ths of the 360 degree circle would be the  a's

53/389  * 360 =    49 degrees

Answer:

X =35

Step-by-step explanation:

To solve:

Step-by-Step Explanation:

First of all, Cross Multiplying:

\(5(5x - 8) = 3(11x - 9)\)

Now expanding the parentheses,

\(25x - 40 = 33x - 27\)

Shifting 33x to the Left hand side of the equation.

\(25x - 33x = - 27 + 40\)

This is Equal to:

\( - 8x = 13\)

And dividing -8 both sides,

\(x = \dfrac{ - 13}{8} \)

~\( \large{ \blue{ \sf{FadedElla}}}\)

Answer:

\(0\geq 0\)

Step-by-step explanation:

\(3x+9\geq 9+3x\\3x\geq 9+3x-9\\3x\geq 3x\\0\geq 0\)

Answer:  -3x+5y=-2 = x=5/3y+2/3  

3x+7y=26 = x=-7/3y+26/3

Step-by-step explanation:

Answer:

A (4,2)

Step-by-step explanation:

edge

Answer:

third one is the correct answer

The probability that the mean amount of cereal per box in a case is less than 18 ounces is 0.2743 for a random variable following a normal distribution.

A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution. The normal distribution appears as a “bell curve” on a graph.

Given,

X is a random variable denoting the actual amount of cereal in each box.

Mean, \(\mu\)=18.03 ounces

Standard deviation, \(\sigma\)=0.05 ounces

To determine the probability that the mean amount of cereal per box in a case is less than 18 ounces= P(X<18)

\(P(\frac{X-\mu}{\sigma} < \frac{18-\mu}{\sigma})\)

\(P(z < 18-18.03/0.05)=P(z < -0.6)\)

\(P(z < -0.6)=0.2743\)

Thus, the probability that the mean amount of cereal per box in a case is less than 18 ounces is 0.2743

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The area of a square is given by the formula A = side^2, where side represents the length of one side of the square.

In this case, the length of a side is 3a^5. So, we can substitute this value into the formula: A = (3a^5)^2. Expanding the expression, we get: A = 9a^10. Therefore, the area of the square with a side length of 3a^5 is 9a^10 square units. It's worth noting that the area is expressed in terms of a variable, 'a,' indicating that the actual value of the area depends on the value assigned to 'a.'

If 'a' is a specific number or variable with a defined value, you can substitute that value to obtain a numerical result for the area.

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Answer:

\(LMN = 14.2\)cm

Step-by-step explanation:

Given

\(r = OL = NO = MO = LO =6cm\) -- radius

\(LM = 6.3cm\) -- arc

\(\angle MON = 75^o\)

(see attachment)

Required

The length of arc LMN

First, we calculate the length of arc MN using:

\(MN = \frac{\alpha}{360} * 2\pi r\) --- length of arc

In this case:

\(\alpha = \angle MON = 75^o\)

So, we have:

\(MN = \frac{75}{360} * 2 * 3.14* 6\)

\(MN = \frac{75* 2 * 3.14* 6}{360}\)

\(MN = \frac{2826}{360}\)

\(MN = 7.85\)

So, the length of arc LMN is:

\(LMN = LM + MN\)

\(LMN = 6.3 + 7.85\)

\(LMN = 14.15\)

Answer:

D

Step-by-step explanation:

14.2

Answer:

706 out 2201

Step-by-step explanation:

the total number of the passengers in the cabin out of the total number of the passengers that were on board.

I hope this helps you..!

Answer:

-7

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

-2d + 2e - 2

Step-by-step explanation:

Combine like terms. Like terms are terms with the same variable as well as same amount of said variables. Set the expression:

4d - 6d + 6e - 4e + 4 - 6

(4d - 6d) = -2d

(6e - 4e) = 2e

(4 - 6) = -2

-2d + 2e - 2 is your answer.

~

Answer:

x ≥ 48

Step-by-step explanation:

If a line parallel to one side of a triangle contacts the other two sides of the triangle, the line proportionally splits these two sides. If DE = BC, then ADDB=AEEC.

If a line parallel to one side of a triangle contacts the other two sides, the two sides are proportionately divided.

The formula for a proportional equation is y = kx. The letters y and x denote the variables in the equation. The letter k represents the proportionality constant, which is fixed.

Because matching angles produce the AA similarity shortcut, when a line is drawn parallel to one side of a triangle, two similar triangles are generated. Because the triangles are comparable, the parallel line segments are proportionate segments.

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Answer:

231.59 years

Step-by-step explanation:

To model this situation we are going to use the exponential decay function:

f(t)= a (1-b)^t

where f(t) is the final amount remaining after t years of decay

a is the final amount

b is the decay rate in decimal form

t is the time in years

For Substance A:

Since  we have 300 grams of the substance, a=300. To convert the decay rate to decimal form, we are going to divide the rate by 100%:

r = 0.15/100 = 0.0015. Replacing the values in our function:

f(t) = a (1-b)^t

f(t) = 300 (1-0.0015)^t

f(t) = 300 (0.9985)^t equation (1)

For Substance B:

Since we have 500 grams of the substance, a= 500. To convert the decay rate to decimal form, we are going to divide the rate by 100%:

r=0.37/100= 0.0037. Replacing the values in our function:

f(t) = a (1-b)^t

f(t)= 500 (1-0.0037)^t

f(t)=500(0.9963)^t equation (2)

Since they are trying to determine how many years it will be before the substances have an equal mass M, we can replace f(t) with M in both equations:

M=300(0.9985)^t equation (1)

M=500(0.9963)^t equation (2)

We can conclude that the system of equations that can be used to determine how long it will be before the substances have an equal mass, M, is :

{M=300(0.9985)^t

{M=500(0.9963)^t

The differentiation dy/dx = (4x^3 - 6x y^8) / (15x^2 y^10). The sloe of the tangent line to this function at the point (0,3) is 0.

To find the derivative of the function y^3 x^2y^5 - x^4 = 27 with respect to x using implicit differentiation, we apply the product rule and the chain rule:

d/dx(y^3 x^2y^5) - d/dx(x^4) = d/dx(27)

Using the power rule and the chain rule, we can find the derivatives of each term:

3y^2 x^2y^5 + 2y^3 x^2(5y^4 dy/dx) - 4x^3 = 0

Simplifying this expression, we get:

15x^2 y^10 dy/dx + 6x y^8 = 4x^3

Now we can solve for dy/dx by isolating it on one side of the equation:

15x^2 y^10 dy/dx = 4x^3 - 6x y^8

dy/dx = (4x^3 - 6x y^8) / (15x^2 y^10)

To find the slope of the tangent line to the function at the point (0,3), we substitute x = 0 and y = 3 into the expression we just found:

dy/dx = (4(0)^3 - 6(0)(3)^8) / (15(0)^2 (3)^10) = 0

So the slope of the tangent line to the function at the point (0,3) is 0.

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Answer:

-10

Step-by-step explanation:

h(-4) = 2(-4)+7 which equals -1

g(h(-4)) = -1²-9 which equals -10

Answer:

hello brother or sister can you please send a picture of the graph in provided but if not there are no specific calculations on reflection so you have to be smart on it and try imagining it or have your own scratch

Answer:

b=15

Step-by-step explanation:

7(b+1)=2*56 (we cross multiply)

7b+7=112

7b=105

b=15

Answer:

X=6

Step-by-step explanation:

Answer:

7⅔ window cleaner

Step-by-step explanation:

23 =3w

x= 1w

3x =23

x= 7⅔ window cleaner

Answer:

∠ JFK = 57°

Step-by-step explanation:

∠ JFK and ∠ GFH are vertically opposite and congruent , then

∠ JFK = ∠ GFH = 57°

Step-by-step explanation:

y=4x + 3

it should have another one

The approximate value of x(t), which indicates the location of coordinate the ladder's foot at time t seconds, is 6.85. 7

Coordinates are numerical lengths or angles that uniquely identify locations on two-dimensional (2D) surfaces or in three-dimensional (3D) space ( 3D ). Mathematicses, scientists, and engineers frequently employ a variety of coordinate systems.

The location in the cartesian plane will be determined by the coordinate points. A point's distance from the y axis is known as the x-coordinate, also known as the abscissa, and its distance from the x-axis is known as the y-coordinate, also known as the ordinate.

based on the information provided,

x = the distance between the wall and the bottom of the ladder

y = distance of the top of the ladder from the ground

x² + y² = 25²

x² + 7² = 25²

x² = 625 -49 = 429

y = √576

Differentiating the equation with respect to time t gives

2x dx/dt + 2y dy/dt = 0

dx/dt = -y dy/dt / x

 = -√576 * (2) / 7

= 6.85 feet per second approximately.

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Answer:

17 inches

Step-by-step explanation:

The given shape is square pyramid.

Given,

Height (H) = 8 in

Base side's length (s) = 30 in

To find : Slant height (l)

Formula

l² = H² + (s/2)²

l² = 8² + (30/2)²

l² = (8 x 8) + 15²

l² = 64 + (15 x 15)

l² = 64 + 225

l² = 289

l² = 17 x 17

l² = 17²

l = 17 in

To predict the cost of driving 1800 miles per month, substitute 1800 in the given function C(d) = 0.2d + 280C(1800) = 0.2 (1800) + 280= $640 per month. Therefore, the cost of driving 1800 miles per month is $640.

(b) Graph is shown below:(c)The slope of the graph represents the rate of change of the cost of driving a car per mile. The slope is given by 0.2, which means that for every mile Lynn drives, the cost increases by $0.2.The y-intercept of the graph represents the fixed cost (amount she pays even if she does not drive).

The y-intercept is given by 280, which means that even if Lynn does not drive the car, she has to pay $280 per month.The linear function gives a suitable model in this situation because the monthly cost increases as the number of miles driven increases.

This is shown by the positive slope of the graph. The fixed cost is also included in the function, which is represented by the y-intercept. Therefore, a linear function is a suitable model in this situation.

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