Find the value of x in x + y = 8 and x - y = 6

a) Find Zx and find the beam. The formula to calculate Zx is given as: Zx = Ix/cwhere c is the distance from the neutral axis to the most distant fiber.Zx = M/SWhere,M = F×e (F is the load on the beam and e is the distance from the extreme fiber to the centroid of the cross-section).

S = section modulus, Zx = (F × e)/0.66 = (1600 lb/ft × 4 ft)/0.66 = 9697.00 in³Zx = 9697.00 in³The beam required to support the load is W21 x 44.

b) Add the weightThe weight of the beam per foot is calculated as follows: W = A × weight of steel per cubic footW = 10.75 × 0.2833W = 3.049 lb/ft. Therefore, the total weight of the beam is:Weight of beam = 48 ft × 3.049 lb/ftWeight of beam = 146.35 lb.

c) Check for Zx again. The moment of inertia (Ix) is calculated as follows:

Ix = (bd³)/12Ix = (21 in × 44.5 in³)/12Ix = 21,454.38 in⁴.

The new Zx value is:Zx = Ix/cZx = 21,454.38 in⁴/22.25 inZx = 964.63 in³The new value of Zx is lower than the initial value of 9697.00 in³. Therefore, the section of W21 × 44 is safe and economical.

d) Check for deflection (Find the moment of inertia)The formula to calculate deflection is given as:δ = (5FL⁴)/(384EI)Where,δ = maximum deflection F = uniformly distributed loadL = length of beam,

E = modulus of elasticity I = moment of inertiaδ = (5 × 1600 lb/ft × (48 in/12)⁴)/(384 × 29,000,000 psi × 21,454.38 in⁴)δ = 1.35 in.

The deflection of the beam is less than span/240 = 48 in/240 = 0.20 in (given in the question).Therefore, the W21 × 44 beam is safe for the deflection criterion.

e) Check for shear : The maximum shear stress is given as:τmax = (3/2) × VQ/It

Where,V = maximum shear forceQ = first moment of area above the centroid axisI = moment of inertia of the beamt = thickness of the webτmax = (3/2) × VQ/Itτmax = (3/2) × (1600 lb/ft) × (10.75 in²)/((2 × 33.75 in⁴)/(0.25 in))τmax = 11,365.88 psi.

The maximum shear stress in the beam is less than the allowable shear stress for A36 steel (14,000 psi).

The lightest W shape to support a uniformly distributed line load of 1600 lb/ft on a simple span of 48 ft without exceeding the span/240 deflection criterion is W21 × 44.

The beam's weight is 146.35 lb, and its Zx value is 964.63 in³. The maximum deflection of the beam is 1.35 in, which is less than the deflection criterion of 0.20 in. Finally, the maximum shear stress in the beam is 11,365.88 psi, which is less than the allowable shear stress for A36 steel.

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Answer:

0,3

Step-by-step explanation:

   6x + 3y = 9

+  -6x + 4y = 12

=

7y = 21

y = 3

Replace 3 into one of the equations and solve for x

6x + 3(3) = 9

6x + 9 = 9

6x = 0

x = 0

Answer:

yeah 13 is the right answerrrrr

a) Mean: 38. b) Mean: 55.5. c) Mean: 132.05. d) Mean: 34.02. a) Median: 23, Range: 11. b) Median: 68, Range: 17. c) Median: 46, Range: 37.d)Median: 903.5, Range: 347. e) Median: 456, Range: 522.

a) For set a, the mean is calculated by adding all the numbers (24 + 45 + 38 + 56 + 27) and dividing the sum by the count (5), resulting in a mean of 38. The median is the middle value, which is 27 in this case, and the range is the difference between the highest value (56) and the lowest value (24), which is 32.

b) In set b, the mean is calculated by summing up all the numbers (24 + 31 + 17 + 39 + 9 + 171) and dividing by the count (6), resulting in a mean of 55.5. The median is the middle value, which is 39, and the range is the difference between the highest value (171) and the lowest value (9), which is 162.

c) For set c, the mean is calculated by adding all the numbers (125 + 136 + 174 + 116 + 164 + 3.8 + 9.2 + 6.7 + 11.5) and dividing by the count (9), resulting in a mean of 132.05. The median is the middle value, which is 136, and the range is the difference between the highest value (174) and the lowest value (3.8), which is 170.2.

d) In set d, the mean is calculated by summing up all the numbers (73 + 75 + 7.0 + 8.1 + 8.0) and dividing by the count (5), resulting in a mean of 34.02. The median is the middle value, which is 8.1, and the range is the difference between the highest value (75) and the lowest value (7.0), which is 68.

e) Finally, for set e, the median is the middle value, which is 456, and the range is the difference between the highest value (631) and the lowest value (109), which is 522.

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Given that a rectangle has an area of 345 square millimeters and a base of 15 millimeters, find the height.

Area of a Rectangle = b x h

So, to find the height, we would reverse it by dividing the area by the base.

Work:

345/15 = 23

So, 23 would be our height.

Thus, the height of the rectangle is 23 millimeters.

Answer:

23 millimeters

Step-by-step explanation:

The area of a rectangle can be found using the following formula.

a=b*h

We know that the area is 345 square millimeters and the base is 15 millimeters, but we don't know that the height is.

a=345

b=15

Substitute these variables into the formula.

345=15*h

We want to find out what the height, or h is.  In order to do this, we have to get h by itself. Perform the opposite of what is being done to the equation. Keep in mind, everything done to one side, has to be done to the other.

h is being multiplied by 15. The opposite of multiplication is division, so divide both sides by 15.

345/15=15*h/15

345/15=h

23=h

Add appropriate units. In this case, the units are millimeters.

h=23 millimeters

The height of the rectangle is 23 millimeters.

She will travel a distance of 62.8 feet × 5 revolutions = 314 feet.

Calculate the circle of the carousel (the distance around the outside) and multiply it by the number of revolutions to determine how far Sierra will move after five rotations.

The following equation can be used to determine the carousel's circumference:

Circumference = 2πr

Where "radius" refers to the carousel's radius and "" is an irrational integer roughly equivalent to 3.14. (in this case, 10 feet).

Substitute the values in the above equation, we get

Circumference = 2 × 3.14 × 10 feet

Circumference = 62.8 feet

Since Sierra will make five revolutions, she will travel a distance

= 62.8 feet × 5 revolutions = 314 feet.

Remember that this is only an estimate because the precise distance may have varied slightly depending on the carousel's speed and Sierra's position on it, among other things.

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Answer:

13a² + 5

Step-by-step explanation:  

Not 100% but 90% sure. Work on Picture.

if f(x, y, z) = 4\(x\)\(y^{2}\)\(z^{3}\) arcsin (xz) , the value of fₓzᵧ is "24xyz²√(1-x²z²)".

To find fₓzᵧ, we differentiate f(x,y,z) partially with respect to x, then z, and finally y.

First, we take the partial derivative of f with respect to x:

fₓ = 4y²z³(arcsin(xz)) + 4xy²z³(1-x²z²)⁻ᵐ

where m = 1/2 * (1 - x²z²)⁻ⁿ, n = -1/2

Next, we take the partial derivative of fₓ with respect to z:

fₓz = 12xyz²(arcsin(xz)) + 4y²z²(1-x²z²)⁻ᵐ + 8xy²z²x(1-x²z²)⁻ⁿ

Finally, we take the partial derivative of fₓz with respect to y:

fₓzᵧ = 24xyz²√(1-x²z²)

Therefore, fₓzᵧ = 24xyz²√(1-x²z²) is the solution, where x, y, and z are the values of the given function f.

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Answer:

  49°

Step-by-step explanation:

The marked angles are "vertical" angles. They have the same measure.

  ∠TGF = ∠HGM = 49°

_____

You don't need to know the value of p to answer this question. It is 7.

Answer:

∠TGF = 49°

Step-by-step explanation:

From the diagram, we get that ∠TGF is equal to ∠MGH because they are  vertical angles.

Hence,

⇒ ∠TGF = ∠MGH

⇒ ∠TGF = 49°

Step-by-step explanation:

mean score means the sum of all 6 scores divided by the number of games : 6.

sum6/6 = 15

sum6 = 15×6 = 90

(sum6 + x)/7 = 16

sum6 + x = 16×7 = 112

90 + x = 112

x = 22

they scored 22 points in the 7th game.

Answer:

D

Step-by-step explanation:

D, it has a right angle and it shows us that the hypotenuse is congruent and the leg is also congruent.

Answer:

Step-by-step explanation:

Step one:

given data

principal= $450

rate= 7.5%= 0.075

time = 3 years.

Step two:

the simple interest formula is

A=P(1+rt)

Substituting we have

A=450(1+0.075*3)

A=450(1+0.225)

A=450(1.225)

A=551.25

The answer is $551.25

Answer:

2, 3, 4, 5

Step-by-step explanation:

Answer:

I believe 4 of these are correct,

answer choice, 2,3,4and

Step-by-step explanation:

2 and 3 are correct because of the inverse of the parallel theorem and answer choice 4 is just a straight line has an angle of 180. Since angle 3 corresponds to angle 7 also meaning they are congruent. We can say angle 1 and 7 add up to 180. As for answer 5, it is the same side interior thereom

Within the Symphony No. 5, right at the beginning (0:00) of this excerpt, the music starts with the introductory section, the so-called "exposition."

The exposition is a crucial section in the sonata form structure commonly found in classical symphonies. It is the initial part of the movement where the main thematic material is introduced and developed. In the case of Symphony No. 5, the excerpt begins with the exposition, which serves as an introduction to the musical ideas that will be further developed throughout the movement. During the exposition, the composer presents the primary themes and motifs that will shape the rest of the piece. It establishes the tonal center and introduces contrasting elements that create tension and interest. In Symphony No. 5, the introductory section of the exposition sets the stage for the thematic material that will unfold, capturing the listener's attention and establishing the musical foundation for the rest of the movement. This section is often characterized by its distinctive melodies, harmonic progressions, and rhythmic patterns that define the musical identity of the symphony.

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a) The GCF of 63 and 36 is 9

b)

a) To find the GCF of 63 and 36, we do the following:

Write 63 and 36 as follows:

The common factors are:

Therefore, the Greatest Common Factor (GCF) is 9

b) To find the factor 63 - 36

The foci of the ellipse given by the equation 225x^2 + 144y^2 = 32400 can be found by identifying the major and minor axes of the ellipse and using the formula for the foci coordinates. The foci of the ellipse are located at (±c, 0). Therefore, the foci are approximately (±15.87, 0).

The equation of the ellipse can be rewritten in standard form:

(225x^2)/32400 + (144y^2)/32400 = 1

We can identify the major and minor axes of the ellipse by comparing the coefficients of x^2 and y^2. The square root of the denominator gives the lengths of the semi-major axis (a) and semi-minor axis (b) of the ellipse.

a = sqrt(32400/225) = 24

b = sqrt(32400/144) = 18

The foci of the ellipse can be calculated using the formula:

c = sqrt(a^2 - b^2)

c = sqrt(24^2 - 18^2)

c = sqrt(576 - 324)

c = sqrt(252)

c ≈ 15.87

The foci of the ellipse are located at (±c, 0). Therefore, the foci are approximately (±15.87, 0).

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Answer:

1. 600 cm^3

2. 24 cm^3

3. 540 cm^3

4. 1476 cm^3

Step-by-step explanation:

1. rectangular prism volume equation is: V = lwh, where l = length, w = width, h = height. Substitute known values into this equation: V = 5 x 8 x 15 and we get V = 600 cubic cm.

2. V = (1/2)bhl, where the base and height are dimensions of the triangle. V = (1/2)6 x 2 x 4 and we get V = 24 cubic cm

3. V = Bh, where B is the base area and h is the perpendicular height. V = 45(12). So, V = 540 cm^3

4. Same thing with this one: V = Bh. Substitute known values into this equation: V = 82(18), which means V = 1476 cm^3

Answer:

where is the dot plot also describe if it increases or decreases

Answer:

w = 59

Step-by-step explanation:

90 + 31 +w = 180

121 +w = 180

w = 180 - 121

w = 59

Answer:

-18

Step-by-step explanation:

The absolute value is only on the 9, and the absolute value of positive 9 is positive 9. Multiply by negative 2 and you get -18.

Answer:

(x+3)^2 + (y-12)^2 =root 5

Step-by-step explanation:

Assumming you meant equation of the circle with center ()

$5 for 1 shirt

y = cost

x = number be shirts

10y = 2x

5y = x

Answer: x = 45

Step-by-step explanation:

3/5x+1/3x=42

9x+5x = 630

14x = 630

x = 45

Answer:

(-2,-7)

alternatively

x: -2

y: -7

The inverse Laplace transform of F(s) = (s^2 - 25) / (3s) is f(t) = t/3 - 25/3.

To find the inverse Laplace transform of F(s) = (s^2 - 25) / (3s), we can apply the properties of Laplace transforms and the inverse Laplace transform formula. Firstly, we can rewrite the expression as F(s) = (s^2) / (3s) - 25 / (3s).

Using the property of linearity, we can split the expression into two separate terms: (s^2) / (3s) and -25 / (3s).

The inverse Laplace transform of (s^2) / (3s) can be found using the formula for the inverse Laplace transform of s^n / (as), which gives us t^(n-1) / (a^(n-1) * (n-1)!). In this case, n = 2 and a = 3, so the inverse Laplace transform of (s^2) / (3s) is (t^(2-1)) / (3^(2-1) * (2-1)!) = t / 3.

The inverse Laplace transform of -25 / (3s) can be found using the property of scaling, which states that the inverse Laplace transform of -kF(s) is -k f(t). Therefore, the inverse Laplace transform of -25 / (3s) is -25/3.

Combining the results, we have f(t) = t / 3 - 25/3 as the inverse Laplace transform of F(s).

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Answer:

\(BD = 19\)

Step-by-step explanation:

Given

\(CD = 2x\)

\(BD = 3x + 4\)

\(BC = 2x -1\)

Required

Find BD

Since C is on BD, we have:

\(BD = BC + CD\)

Substitute values for BD, BC and Cd

\(3x + 4 = 2x - 1 + 2x\)

Collect Like Terms

\(3x - 2x - 2x = -1 - 4\)

\(-x = -5\)

Multiply through by -1

\(x = 5\)

Substitute 5 for x in \(BD = 3x + 4\)

\(BD = 3 * 5 + 4\)

\(BD = 19\)

Answer:

Step-by-step explanation:

cost price x .60 = 80

80/.60 = 133.33 was the cost price

The dimensions 36 x 27 inches are too small to allow a 48-inch piece of glass to fit through it.

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a) -43, -12, -1 1/2

b) 1 1/2. 12, 43

c) it is different

a) -1 1/2, -12, -43

from the least to the greatest:

The higher a negative number , the lesser the value of the number

-43, -12, -1 1/2

b) The absolute values of -1 1/2, -12, -43:

1 1/2, 12, 43

absolute values from least to greatest:

1 1/2. 12, 43

The order of the rational numbers in part (a) is different from the order of the numbers' absolute values in part (b)

c) Absolute values of a negative number gives a positive number. The higher a posititve number, the greater its value. While a higher negative number has a lower value. This makes the result in ordering the data different