If x= 5 and y = 2, work out the value of a) 3x + y
b) 2x2
c) (x - y)2

Answer:

x+5 or 5+x

Step-by-step explanation:

It seems we are looking for a math expression that is the same as English expression you wrote.The sum is what we get when we add numbers. Therefore, we could restate the English expression as what do we get when we add 5 to the number x? While we do not know what specific number x represents, we do know that if we add 5 to the number x we get 5 plus x. Now the question can be restated as, "How do we write 5 plus the number x?" Do you know the answer now? Does 5 + x sound right? How about x + 5? Both of these expressions are correct as they both represent the sum of 5 and the number x.

Answer:

False.

Step-by-step explanation:

The formula that is used to find the area of a rectangle is given by :

A = l×b

Where,

l is length and b is breadth

If area of a rectangle is 6m², it means we need to find the factors of 6. The factors of 6 are 2 and 3. If we multiply 2 and 3, we get 6.

Other possibility can be 1 m by 6 m because if we muliply 1 m and 6 m, we get 6m².

It means there are more than one possibiliy about the length and breadth of the rectangle.

Hence, the given statement is not true.

Answer:

160mm²

Step-by-step explanation:

Finding the length/height:

Perimeter = 2(l+b)

2(l+40) = 88

2l + 80 = 88

2l = 8

l = 8/2 = 4

Hence, the length/height is 4 mm

Finding the area:

Area = l * b

= 4 * 40

= 160mm²

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Answer:

n = 0.0164321

Answer:

1051.6×10n

Step-by-step explanation:

Answer:

x=12/5

Step-by-step explanation:

2(2.5x+8)=26

5x+14=26

5x=12

x=12/5

Answer:

The value of \(x\):

\(x = 2\)

Step-by-step explanation:

Solve for \(x\):

\(2(2.5x + 8) = 26\)

-Divide both sides by \(2\):

\(2(2.5x + 8) = 26\)

\(2.5x + 8 = \frac{26}{2}\)

-Divide \(26\) by \(2\):

\(2.5x + 8 = \frac{26}{2}\)

\(2.5x + 8 = 13\)

-Subtract both sides by \(8\):

\(2.5x + 8 - 8 = 13 - 8\)

\(2.5x = 5\)

-Divide both sides by \(2.5\):

\(\frac{2.5x}{2.5} = \frac{5}{2.5}\)

Expand to the form \(\frac{5}{2.5} = 2\) by multiplying both the numerator and the denominator by \(10\):

\(\frac{5}{2.5} = 2\)

\(x = \frac{50}{25}\)

Then, you divide \(50\) by \(25\):

\(x = \frac{50}{25}\)

\(x = 2\)

So, the final answer would be \(x = 2\) .

Answer:

A

Step-by-step explanation:

the triangles share one angle and they have two equal sides

Answer:

No solution

Step-by-step explanation:

−4x − 4 = −4(x + 2)

We solve the parentheses

-4x-4=-4x-8

We add 4 to both sides, cancelling out the -4 on both sides

-4=-8

As this isn't true if using normal math, there is

N O   S O L U T I O N

The number of inches in 5 m is 196.85 inches

1 m = 100 cm

Therefore,

5 m = 5 × 100

5 m = 500 cm

2.54 cm = 1 inche

Therefore,

500 cm = 500 / 2.54

500 cm = 196.85 inches

Thus, there are 196.85 inches in 5 m

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Answer: 27:1

Step-by-step explanation:

The ratio of the volumes is equal to the cube of the ratio of the altitudes.

The measure of the major arc JLK will be 206°. Then the correct option is B.

The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.

The measure of the minor arc JK will be 154°.

Then the sum of the major arc and minor arc in a circle is 360°.

Then the major arc JLK will be given as,

JLK + JK = 360°

JLK + 154° = 360°

JLK = 206°

The measure of the major arc JLK will be 206°. Then the correct option is B.

Your question was incomplete, but the complete question was attached below.

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The possible dimensions (length and width) of the field are:(10 m × 13 m) or (13 m × 10 m) and (11 m × 12 m) or (12 m × 11 m).

Given that Aaron has 47m of fencing to build a three-sided fence around a rectangular plot of land that sits on a riverbank. The fourth side of the enclosure would be the river.

The area of the land is 266 square meters.To find the possible dimensions (length and width) of the field, we can use the given information.The length of fencing required = 47 m.

Since the fence needs to be built on three sides of the rectangular plot, the total length of the sides would be 2l + w = 47.1. When l = 10 and w = 13, we have:

Length of the field, l = 10 m Width of the field, w = 13 mArea of the field = l × w = 10 × 13 = 130 sq. m2. When l = 11 and w = 12,

we have:Length of the field, l = 11 m

Width of the field, w = 12 m

Area of the field = l × w = 11 × 12 = 132 sq. m

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The given rectangular equation is.

(y = x - 3\)

We know that the polar coordinate system uses r and θ instead of x and y.

In the rectangular coordinate system,

y = x - 3.

we can substitute y with (r sin θ) and x with (r cos θ) to obtain the equivalent polar equation.

=r sin θ = r cos θ - 3

Plot the origin (0, 0)2. Draw a line at an angle of

= (π/4 radians) from the x-axis.

Draw a circle with radius 3 centered at the origin.4.

Wherever the line intersects the circle is a point on the graph of the polar equation.

Repeat steps 2-4 for angles 45° to 225°.6.

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Answer:

7.5

Step-by-step explanation:

The values 15ft, 13ft and x are the sides of a right triangle;

According to pythagoras theorem;

15² = 13²+x²

x² = 15² - 13²

x² = 225 -169

x² = 56

x = √56

x = 7.48

Hence the value of x to the nearest tenth is 7.5 to the nearest tenth

Answer:

C

Step-by-step explanation:

In part (a), we are required to show that the line integral is independent of path and use a potential function to evaluate it. The line integral is given by ∫C (z² + 2xy)dx + (x²)dy + (2xz)dz, where C runs from (2,1,3) to (4,-1,0).

In part (b), we have to perform a similar analysis for the line integral ∫C (2x cos z - x²) dx + (z-2y)dy + (y – x² sin z)dz, where C runs from (3,-2,0) to (1,0, π).

(a) To show that the line integral is independent of path, we need to demonstrate that it depends only on the endpoints and not the specific path taken. We can do this by finding a potential function f(x, y, z) such that the gradient of f equals the given vector field. Calculating the partial derivatives, we find that f(x, y, z) = xz² + x²y + C, where C is a constant. To evaluate the line integral, we can use the potential function. Evaluating f at the endpoints and subtracting the values, we obtain f(4,-1,0) - f(2,1,3) = (16)(0) + (16)(-1) + C - (4)(9) - (4)(1) - (2)(27) - C = -25. Hence, the line integral is independent of path and its value is -25.

(b) Similar to part (a), we seek a potential function for the vector field. By integrating the given components, we find f(x, y, z) = x² cos z - xy + yz - x² sin z + C, where C is a constant. Using the potential function, we evaluate f at the endpoints and find f(1,0,π) - f(3,-2,0) = (1)² cos(π) - (1)(0) + (0)(π) - (1)² sin(π) + C - (3)² cos(0) - (3)(-2) + (0)(0) - (3)² sin(0) - C = 14. Hence, the line integral is independent of path and its value is 14.

The line integral in part (a) is independent of path and evaluates to -25, while the line integral in part (b) is also independent of path and its value is 14.

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Answer: infinetly many solutions

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

We can use the slope formula to find the slope

m = ( y2-y1)/(x2-x1)

    = (3-3)/(-3-3)

    = 0/-6

    =0

Answer:

m = 0

Step-by-step explanation:

Use the slope formula: \(m=\frac{y_2-y_1}{x_2-x_1}\\\)

\(\frac{3-3}{3-(-3)}\\\\ \frac{0}{6}\\\\0\)

Therefore, the slope of the line is 0.

*Note that if the y values do not change as x changes, it is evidence that the slope is 0.*

The maximum output of the roll crusher in tons per hour for material less than 1 in. is 40 tons per hour. The amount of the roll crusher output in the range of 1 in. to ½ in. is 20 tons per hour, and the amount less than ½ in. is 10 tons per hour.

To determine the maximum output of the roll crusher, we need to consider the size reduction process and the efficiency of the screen.

Maximum Output of the Roll Crusher: The jaw crusher has a 2½ in. opening, and the screen has 1½-in. openings. Therefore, the maximum size of the material entering the roll crusher is 1½ in. Since the roll crusher is set at 1½ in., it can effectively crush the material to a size less than 1 in. without any recycle of oversize material.

The efficiency of the screen is given as 85%, which means that 85% of the material passing through the jaw crusher will pass through the screen and the remaining 15% will go to the roll crusher.

The maximum output of the roll crusher can be calculated as follows: Maximum Output = (Output from Jaw Crusher) x (Efficiency of Screen) = (40 in. x 22 in.) x (85%) = 880 in.^2 x 0.85 = 748 in.^2

Since the roll crusher is set at 1½ in., the maximum output in tons per hour can be calculated using the following formula: Maximum Output (tons per hour) = Maximum Output (in.^2) x Roll Crusher Setting (in.) x Roll Crusher Efficiency (tons per in.^2) = 748 in.^2 x 1.5 in. x 40 tons per in.^2 = 44,880 tons per hour ≈ 40 tons per hour

Amount of Roll Crusher Output: To determine the amount of roll crusher output in the range of 1 in. to ½ in. and less than ½ in., we need to consider the size reduction process and the size of the roll crusher setting.

Since the roll crusher is set at 1½ in., the amount of roll crusher output in the range of 1 in. to ½ in. can be calculated as follows: Amount in Range (1 in. to ½ in.) = Maximum Output (tons per hour) x Roll Crusher Setting Range Efficiency = 40 tons per hour x (1 - 0.85) = 40 tons per hour x 0.15 = 6 tons per hour

The amount of roll crusher output less than ½ in. can be calculated as follows: Amount less than ½ in. = Maximum Output (tons per hour) x (1 - Roll Crusher Setting Range Efficiency) = 40 tons per hour x (1 - 0) = 40 tons per hour

The maximum output of the roll crusher in tons per hour for material less than 1 in. is 40 tons per hour. The amount of the roll crusher output in the range of 1 in. to ½ in. is 6 tons per hour, and the amount less than ½ in. is 40 tons per hour.

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Answer:

Mean=19.5

Step-by-step explanation:

Mean= (16x1 + 17x4 + 19x4 + 21x1 + 22x2 + 23x1 + 25x1)/14=273/14=19.5

Answer:

No, Tony is not correct. Solving the inequality tells us that x is greater than or equal to 37.5 . Since the class must wash a whole number of cars, they need to wash at least 38 cars.

Step-by-step explanation:

This is the sample response

(I just took the assignment lol)

Answer:

The solution to the inequality is x Greater-than-or-equal-to 37.5.

For this situation, only whole number solutions make sense.

Tony needs to round up to 38.

Step-by-step explanation:

El valor que satisface D es 188.

El modelo matemático será así:

D/d = 12(resto 8)

si escribimos 8 como resto de D, entonces:

(D-8) /d=12

D-8= 12d o se puede escribir D= 12d+8

luego sustituya D= 12d+8 por D+d= 203

D+d= 203

(12d +8) +d= 203

13d= 203-8

13d= 195

re=15

sustituir d=15 en D+d= 203

D+d= 203

D+15=203

D=203-15

D=188

El modelo matemático es una forma de interpretación humana al traducir o formular problemas existentes en forma matemática, de modo que el problema pueda resolverse utilizando las matemáticas.

El uso principal de los modelos matemáticos es ayudar a las personas a comprender los problemas y simplificarlos para que puedan resolverse.

, los siguientes son algunos de los usos que se obtienen al utilizar un modelo matemático, a saber:

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Answer:

wrong

Step-by-step explanation:

10 /5 = 2

5/10 = 0.5

The street can be represented in slope intercept form as follows:

y = x + 4

Linear equation can be represented in slope intercept form as follows:

y = mx + b

where

Parallel lines have the same slope.

The street goes by the name y = x + 17.

The slope of the street is 1.

Therefore, the street parallel to that one should have the same slope.

The street can be represented in slope intercept form is as follows:

y = x + 4

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Answer:

i think true

Each model should be produced on a weekly basis to maximize net profit is $75,900.

What is Net profit?

In both business and accounting, net income or profit is an entity's revenue less cost of goods sold, costs, depreciation and amortisation, interest, and taxes for a certain accounting period.

As given,

Number of products sold:

T ≥ 1.5G

Maximize Profit Z = 150T + 130G

Labor Constraint:

Labor hours Available:

Production Department:

Number of labor hours available per day = 58 × 7 = 406

Number of days in a week = 5

Number of lobor ours available per week = 406 × 5 = 2030

Assembly Department:

Number of labor hours available per day = 25 × 7 = 175

Number of days in a week = 5

Number of labor hours available per week = 175 × 5 = 875.

Labor hours Required:

Labor hours required for G1 model:

Labor hours required at Production department = 3.5G

Labor hours required at assembly department = 2G

Labor hours required for T1 model:

Labor hours required at Production department = 4T

Labor hours required at Assembly department = 1.5T

Total labor hours required at Production department = 3.5G + 4T

Total labor hours required at Assembly department = 2G + 1.5T.

Constraint:

Labor hours required ≤ Labor hours Available.

Production department Labor constraint

3.5G + 4T ≤ 2030

Assembly department Labor constraint:

2G + 1.5T ≤ 875

The function:

Maximum Profit Z = 150T +130G

Constraint:

3.5G +4T ≤ 2030

2G + 1.5T ≤ 875

T ≥ 1.5G

Suppose that for example:

10.5G +12T = 6090

 16G + 12T = 7000

Solve both equations simultaneously,

5.5G = 7000 - 6090

5.5G = 910

    G = 910/5.5

    G = 363

Since, T > G

Hence,

T = 363,

G = 165

Calculate Profit:

150T + 130G = 150 × 363 + 130 × 165

                     = 54450 + 21450

                     = 75900

Hence, each model should be produced on a weekly basis to maximize net profit is $75,900.

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Answer:

\(\dfrac{x+9}{x+1}\)

Step-by-step explanation:

\(\dfrac{2x+4}{x+1}+\dfrac{-x+5}{x+1}= \\\\\\\dfrac{2x+4-x+5}{x+1}= \\\\\\\dfrac{x+9}{x+1}\)

Hope this helps!

The sum of the given fraction is \(\frac{x+9}{x+1}\)

\(= \frac{2x+4}{x+1} + \frac{-x+5}{x+1}\\\\ = \frac{2x+4-x+5}{x+1} \\\\= \frac{x+9}{x+1}\)

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The required distance of object far from 25° and 55° are 103.71feet and 163.88feet respectively.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

Given the trigonometry identity;

d=94 secθ.

If the object is sighted at an angle of  25°, then;

d=94 sec25

d = 94 × 1/cos25

d = 94 × 1.1033

d = 103.71feet

If the object is sighted at an angle of  55°, then;

d=94 sec55

d = 94 × 1/cos55

d = 94 × 1.7434

d = 163.88feet

Hence the required distance of object far from 25° and 55° are 103.71feet and 163.88feet respectively.

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