5(4 · 3 + 3 · 4)= 300 120 480

[tex]\displaystyle \lim_{x\to -4}~\cfrac{~~ \frac{1 }{4 }+\frac{1}{x} ~~}{4+x} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{~~ \frac{1 }{4 }+\frac{1}{x} ~~}{4+x}\implies \cfrac{~~ \frac{4+x}{4x} ~~}{4+x}\implies \cfrac{~~ \frac{4+x}{4x} ~~}{\frac{4+x}{1}}\implies \cfrac{4+x}{4x}\cdot \cfrac{1}{4+x}\implies \cfrac{1}{4x} \\\\[-0.35em] ~\dotfill\\\\ \displaystyle \lim_{x\to -4}~\cfrac{1}{4x}\implies \cfrac{1}{4(-4)}\implies -\cfrac{1}{16}[/tex]

105 watts

The middle wattage is found by taking the average of the highest and lowest wattages. To find the average, you add the two numbers together and then divide by 2. In this case, the lowest wattage is 60 and the highest is 150, so when we add these two numbers together, we get 210. Then, when we divide 210 by 2, we get 105. So the middle wattage is 105 watts.

When triangle ABC is dilated to triangle A'BC then the line A'B' has the equation 2z+ 3y = 10.

Parallel lines are any two or more lines that all lie in the same plane and never cross one another. They are equally spaced apart and have the same incline. No matter how far we extend a parallel line, it will never meet another parallel line.

Given that the triangle ABC is dilated to get the triangle A'BC.

If the triangle is dilated then, AB is parallel to A'B'.

So, the slopes of the two line are equal.

The equation of the AB is 2x + 3y = 5.

Converting into the standard equation of line:

y = - 2/3 x + 5/3

The slope of the line is -2/3.

From the given options, the line that has slope -2/3 when converted to standard form is:

2z+ 3y = 10

Hence, when triangle ABC is dilated to triangle A'BC then the line A'B' has the equation 2z+ 3y = 10.

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The differentiation of the f(x) = g(x)/h(x), using the quotient rule, indicates that the value of f'(2) = 20/81

The Quotient Rule for finding the derivative of a ratio of two functions, [tex]f(x) = \frac{g(x)}{h(x)}[/tex] that are differentiable is presented as follows;

[tex]f'(x) = \frac{h(x) \cdot g'(x) - g(x) \cdot h'(x)}{h(x)^2}[/tex]

The equation of the lines are found as follows;

The points on the line g(x) are; (1, 2), and (3, 6)

Therefore, we get;

Slope of the line = (6 - 2)/(3 - 1) = 2

Equation of the line is; y - 2 = 2·(x - 1) = 2·x - 2

y - 2 = 2·x - 2

y = 2·x - 2 + 2 = 2·x

The equation of the line is presented as follows;

g(x) = 2·x

Points on the graph of the function h(x) when x = 2 are; (2.5, 5), and (0, 2.5)

Slope of the graph of h(x) when x = 2 is; (2.5 - 5)/(0 - 2.5) = 1

The equation of the line is therefore; y - 5 = 1·(x - 2.5) = x - 2.5

y - 5 = x - 2.5

y = x - 2.5 + 5 = x + 2.5

h(x) = x + 2.5

f(x) = g(x)/h(x)

The value of f'(x) using the quotient rule, is therefore;

f'(x) = (h(x)·g'(x) - g(x)·h'(x))/(h(x))²

g'(x) = 2

h'(x) = 1

Therefore;

f'(x) = ((x + 2.5)×2 - 2·x  × 1)/(x + 2.5)² = (2·x + 5 - 2·x)/((x + 2.5)²)

(2·x + 5 - 2·x)/((x + 2.5)²) = 5/(x + 2.5)²

f'(2) = 5/(2 + 2.5)² = 20/81

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Answer:

x=15

Step-by-step explanation:

2x-17=13

2x=30

x=15

Hope this helped! :)

Answer:

15

Step-by-step explanation:

2x - 17 = 13

Add 17 to both sides:

2x = 30

Divide both sides by 2:

[x = 15]

Answer:  x = 7

Step-by-step explanation:

    [tex]\frac{2x}{7} =\frac{6}{3}[/tex]

we cross multiply, we get

2x(3) = 6(7)

   6x = 42

     x = 7

The boat speed in still water is 2 km/hr.

Speed is a measure of how fast an object is moving. It is defined as the distance traveled by an object in a given amount of time. Speed is a scalar quantity, meaning it only has magnitude and does not have direction. It is typically expressed in units of distance per time, such as meters per second (m/s) or miles per hour (mph). The formula for speed is speed = distance / time. It is important to distinguish speed from velocity, which is a vector quantity that includes both magnitude (speed) and direction.

The formula to calculate the speed of the boat in still water is:

speed = distance / (time up + time down)

To use this formula, we first need to find the distance traveled upstream and downstream. Let's assume that the distance traveled upstream and downstream is the same, so we can use the average of the two times: (30 min + 10 min) / 2 = 20 min.

Next, we need to convert the time to hours. 20 minutes is equal to 20/60 = 1/3 hours.

Now, let's calculate the distance using the current speed of 2 km/hr:

distance = current speed * time

distance = 2 km/hr * 1/3 hours = 2/3 km

Finally, we can use the formula to calculate the boat speed:

speed = distance / time = 2/3 km / (1/3 hours) = 2 km/hr

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Answer:

x<-5

Step-by-step explanation:

-(2+2x)-2>6

-(2+2x)>8

2+2x<-8

2x<-10

x<-5

The required volume of the given right rectangular prism is 2x³ - 4x² cubic units.

Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.

here,
From the figure,
Volume = length × width × height
            = [2x - 4] × x × x
            = [2x³ - 4x²]

Thus, the required volume of the given right rectangular prism is 2x³ - 4x² cubic units.

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The correct value of the measure of the exterior angle is 72 degrees

You should understand that when one side of a polygon is produced, the angle so formed is called an exterior angle

Note also that two opposite interior angles equal to one exterior angle

This implies that

x+30=2x-12

Collecting like terms

x-2x=-12-30

-x=-42

the value of x is 42

Then substitute x for the exterior angle

2(42)-12

84-12 = 72

The exterior angle is 72 degrees

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The statement "the sum of measures of angles B and A is 130 degrees" is  correct. Therefore, option A, B and E are the correct answer.

An isosceles trapezoid can be defined as a trapezoid in which non-parallel sides and base angles are of the same measure. In other words, if two opposite sides (bases) of the trapezoid are parallel, and the two non-parallel sides are of equal lengths, then it is an isosceles trapezoid.

Given that, an isosceles trapezoid ABCD has two parallel sides AB and CD and m∠A = 65°.

Correct statements are

The sum of measures of angles B and A is 130 degrees.

The measure of angle D is 115 degrees.

The sum of measures of angles B and C is 180 degrees.

Therefore, option A, B and E are the correct answer.

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7. m<2 = 138° based on the definition of vertical angles.

8. m<3 is supplementary to angle 8

9. The measure of angle 2 = 50°

10. The value of x = 20

A supplementary angle is a pair of angles whose sum is equal to 180 degrees. In other words, two angles are supplementary if they add up to a straight angle.

For example, if one angle measures 70 degrees, its supplement would be 180 - 70 = 110 degrees.

7. m<2 = 138° (reason: vertical angles are equal).

8. m<3 is supplementary to angle 8 because angle 3 and 5 are supplementary, and angle 5 is congruent to angle 8.

9. 5x + 55 = 2x + 100 (corresponding angles are equal)

Find x:

5x - 2x = -55 + 100

3x = 45

x = 15

m<2 = 180 - (5x + 55) (linear pair is equal to 180 degrees)

Plug in the value of x

m<2 = 180 - (5(15) + 55)

m<2 = 180 - 130

m<2 = 50°

10. 45 + 5x + 35 = 180 (supplementary angles)

5x + 80 = 180

5x = 180 - 80

5x = 100

x = 20

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Answer:350

Step-by-step explanation: 280/4=70

280+70=350

Answer:

350

Step-by-step explanation:

The percentage is converted to decimal place and then multiplied by 280

[tex]280(\frac{125}{100} )=280(1.25)=350[/tex]

Hope this helps.

The point (-2 3/4, -4 1/2) is plotted below.

Coordinates are the set of points in a geometrical plane or space, which is used to denote the exact point in the coordinate plane or space.

The given point is (-2 3/4, -4 1/2).

Both the coordinates are in the mixed number form.

-2 3/4 = -(2 × 4 + 3) / 4 = -11/4 = -2.75

-4 1/2 = -(4 × 2 + 1) / 2 = -9/2 = -4.5

So the point is (-2.75, -4.5).

Hence the given point is (-2.75, -4.5) which is marked in the coordinate plane as shown below.

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The given trigonometric equation is csc²x-1 =cotx/tanx is proved LHS=RHS.

A trigonometric equation is one that involves one or more of the sixs sine, cosine, tangent, cotangent, secant, and cosecant. Some trigonometric equations, like x = cos x, can be solved only numerically, through successive approximations.

The given trigonometric equation is csc²x-1 =cotx/tanx.

Here, csc²x-1 =cosx/sinx ÷ sinx/cosx

csc²x-1 =cosx/sinx × cosx/sinx

csc²x-1 =cos²x/sin²x

csc²x-1 =cot²x

We know that, cot²x+1=csc²x

So, cot²x=cot²x

Hence, proved LHS=RHS.

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Answer:

9:8

Step-by-step explanation:

We know that 72:64

If you multiply 9 by 8 you get 72, so you know that the answer will have to be simplified by 8.

64/8 = 8

Therefore your answer for this will be 9:8

Answer:

2x+3 i think

The answer is 506 not to sure since I haven't done this in a while

Answer:

506

Step-by-step explanation:

According to the order of operations(or PEMDAS), you would first evaluate the exponent in the problem: [tex]8^3[/tex]. [tex]8^3[/tex] is equivalent to [tex]8*8*8[/tex], which is just 512. Therefore, the equation would now be 512 - 9 * 2 ÷ 3

Next step would be to do out the multiplication and division left to right. First is 9 * 2 which is 18. Then that is divided by three to get 6. The equation would now be 512 - 6.

512 - 6 is just 506.

Answer:

5000

Step-by-step explanation:

800/16% = 5000

Answer:

f(x)= (X+5)^2

Step-by-step explanation:

pls, tell me if wrong have a good day/night<3

An equation of the line that passes through the point (1, -3) and has a slope of -3 in slope-intercept form is y = 2x + 3.

Mathematically, the standard form of the equation of a straight line is given by this mathematical expression;

y = mx + c

Where:

Next, we would determine the slope of this straight line by using this mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (15 - 3)/(2 - (-4))

Slope (m) = 12/6

Slope (m) = 2.

Therefore, the equation in slope-intercept form is given by:

y = mx + c

y = 2x + 3

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The updated median is 56.37 and the updated IQR is 17.66.

The median is the value in the middle of a data set, meaning that 50% of data points have a value smaller or equal to the median and 50% of data points have a value higher or equal to the median. For a small data set, you first count the number of data points (n) and arrange the data points in increasing order.

Given that, one employee recorded the measurements for the lengths of 55 different wood boards.

Median =58.37 and IQR=19.66

Someone discovers the measuring tape used started at 2 inches instead of 0.

The interquartile range is given by the difference between the 75th percentile(value that is greater than 75% of the measures) and the 25th percentile.

This means that each piece of wood is actually 2 inches shorter than the value recorded by the employee.

This means that the length of each wood is less than 5. However, the difference between the 75th percentile and the 25th percentile will stay the same, since both were subtracted by 2.

So, IQR=19.66-2 =17.66

Therefore, the updated median is 56.37 and the updated IQR is 17.66.

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The value of {x} is equivalent to +55.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is that -

" - {-(x)} is 55 units to the right of 0".

It is given that -

- {-(x)} = {x}                                 ..... ( 1 )

We can rewrite -

{x} is 55 units to the right of 0.

As an equation, we can write -

0 + 55 = {x}

{x} = + 55

Therefore, the value of {x} is equivalent to +55.

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Answer: 2808 ft.

Step-by-step explanation:

72(39) = 2808

Answer:

Area for a rectangle is Length * Width or A=l*w

Length= 72ft
width= 39ft

72*39= 2808

The area of the rectangular room is 2808

Step-by-step explanation:

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Answer: The mass of one mole of a substance is equal to its molar mass in grams. The molar mass of a substance is the mass of one mole of that substance and is usually expressed in atomic mass units (amu) or grams per mole (g/mol).

One mole of a substance contains Avogadro's number of particles, which is approximately 6.022 x 10^23.

Since the mass of one doughnut is given in grams (74 g), we can assume that this is the molar mass of the substance in question. So, the mass in grams of one mole of the substance is:

Mass of one mole = 74 g

So, the answer to two significant figures is:

Mass of one mole = 74 g (rounded to two significant figures).

Step-by-step explanation:

a)

C = 23.8°C

b)

F = 113°F

c)

F = -4°F

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

a) 75°F

b) 45°C

c) -20°C

Conversion formulas:

C = (F - 32) / 1.8

F = 1.8C + 32

Now,

75°F

C = (F - 32) / 1.8

C = (75 - 32) / 1.8

C = 23.8°C

45°C

F = 1.8C + 32

F = 1.8 x 45 + 32

F = 113°F

-20°C

F = 1.8C + 32

F = 1.8 x (-20) + 32

F = -4°F

Thus,

The temperature conversion is given above.

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Answer:

7. √149 ft or 12.2 ft

8. 5√2 m or 7.07 m

9. √36.75 in. or 6.06 in.

Step-by-step explanation:

7.

a² + b² = c²

7² + 10² = x²

49 + 100 = x²

x² = 149

x = √149

x ≈ 12.2

Answer: √149 ft or 12.2 ft

8.

perimeter = 20 m

side = perimeter/4 = 5 m

a² + b² = c²

5² + 5² = x²

25 + 25 = x²

x² = 50

x = 5√2

Answer: 5√2 m or 7.07 m

9.

a² + b² = c²

3.5² + x² = 7²

12.25 + x² = 49

x² = 49 - 12.25

x² = 36.75

x = √36.75 = 6.06

Answer: √36.75 in. or 6.06 in.

Answer:

  7.  12.2 ft

  8.  7.07 m

  9.  6.06 in

Step-by-step explanation:

You want the hypotenuse of at right triangle with legs 7 and 10 ft, the diagonal of a square with perimeter 20 m, and the altitude of an equilateral triangle with side length 7 inches.

These problems all make use of the Pythagorean theorem, which tells yo the relation between sides a, b and hypotenuse c of a right triangle is ...

  a² +b² = c²

The length of the leash (c) is ...

  c² = (7 ft)² +(10 ft)² = 149 ft²

  c = √149 ft ≈ 12.2 ft

The leash is about 12.2 feet long.

Each side of the square is 1/4 of the perimeter, so is 5 m. The diagonal is the hypotenuse of a right triangle with legs that length. Its measure is ...

  c = √(5² +5²) = 5√2 ≈ 7.07 . . . . meters

The length of the diagonal is about 7.07 meters.

The altitude of an equilateral triangle is a perpendicular bisector of one side. Its length is ...

  b = √(c² -a²)

  b = √(7² -3.5²) = √36.75 ≈ 6.06 . . . . inches

The altitude of the triangle is about 6.06 inches.

__

Additional comment

The triangles of problems 8 and 9 are known as the two "special" right triangles.

The side lengths of an isosceles right triangle (angles 45°-45°-90°) have the ratios 1 : 1 : √2.

The side lengths of a triangle with angles 30°-60°-90° have the ratios 1 : √3 : 2.

That is, the diagonal of the square is √2 times its side length, and the altitude of the equilateral triangle is (√3)/2 times is side length.

It can be useful to remember these triangles and their side ratios.

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On solving the provided question, we can say that Therefore, the function has an average rate of change of -1.

The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, inside functions, and on functions.

The function has an average rate of change of -1.

R = 4-5/1-0

R = -1

Therefore, the function has an average rate of change of -1.

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Answer: Let's call the length of the rectangular court "L" and the width "W". Then, the perimeter of the court is 2 * (L + W) = 148 feet, so 2 * L + 2 * W = 148 feet.

And, according to the coach's estimate, the athlete ran a total of 4 * L + 7 * W = 353 feet.

We can use these two equations to find the dimensions of the court. Solving the first equation for W:

W = (148 - 2 * L) / 2.

Substituting this expression for W into the second equation:

4 * L + 7 * (148 - 2 * L) / 2 = 353

Expanding and simplifying the right side of the equation:

4 * L + 74 - 7 * L = 353

-3 * L = -279

L = 93 feet.

Finally, using the expression for W from the first equation:

W = (148 - 2 * L) / 2 = (148 - 2 * 93) / 2 = 32 feet.

So the dimensions of the sports court are 93 feet by 32 feet.

Step-by-step explanation:

Answer:

60.48

Step-by-step explanation:

Answer:51.52

Step-by-step explanation: