What does r equal?
Answer: r = ________

The width of the frame is 2.4 inches

Let w represent the width of the frame

Then the area of the frame is:

(w + 5)(w + 7) = 69.56

Rewrite it in Standard form of a quadratic equation:

w² + 12w + 35 = 69.56

w² + 12w - 34.56 = 0

Use Quadratic Formula to solve for w:

w =  (-b±√(b²-4ac))/(2a)

w =  (-12±√(12²-4×1×(- 34.56)))/(2×1)

w = (-12±√(144+138.24))/(2)

w = (-12±16.8)/2

w = -6 ± 8.4

w = -6 + 8.4 or -6-8.4

w = 2.4 or w = -14.4

Since the width cannot be negative.

Thus, w = 2.4 inches

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Answer:Mathematics2 minutes ago

+5 pts

J31) what are the undefined values for sinx cosx / 1 - sin²x , where 0 ≤ x < 2pi ? how?

Step-by-step explanation:

To calculate the percent change of two numbers such as 99 to 71, you use the Percent Change Formula, where a is the start value and b is the end value. When we insert a = 99 and b = 71 in the formula above, then we get the following that we can simplify and solve to get the percent change from 99 to 71.

Change ≈ -28.2828%

Answer:

C

Step-by-step explanation:

Put in the form y/x and you should have equivalent fraction

12/4 = 3

15/5 = 3

18/6 = 3

When the fractions are simplified, they all equal 3.

Answer: 7/12

Step-by-step explanation:

Based on the given conditions, formulate: 3/4 - 1/4

Find the common denominator and write the numerators above the common denominator: 9/12 - 2/12

Calculate the product or quotient:

Write the numerators over the common denominator: 9-2                                          

                                                                                          12

Calculate the sum or difference: 7/12

Answer: 7/12

Answer:

A) 5

B) X-3

C) 2X+Y

step by step:

base x height = area

A Height= (5x+20) ÷ (x+4)= 5

B Base= (8x-24) ÷ 8 = x-3

C Height= (12x+6y) ÷ 6 = 2x+y

The solution is

Parallelogram A : Base = x + 4 ; Height = 5

Parallelogram B : Base = x - 3 ; Height = 8

Parallelogram C : Base = 6 ; Height = 2x + y

A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure

The four types are parallelograms, squares, rectangles, and rhombuses

Properties of Parallelogram

Opposite sides are parallel

Opposite sides are congruent

Opposite angles are congruent.

Same-Side interior angles (consecutive angles) are supplementary

Each diagonal of a parallelogram separates it into two congruent triangles

The diagonals of a parallelogram bisect each other

Given data ,

Let the area of the parallelogram be A = Base x Height

So , Substituting the values in the equation , we get

a)

Let the parallelogram be A

Now , Area = 5x + 20

Base = x + 4

So , the height = Area / Base

Height = 5

b)

Let the parallelogram be B

Now , Area = 8x - 24

Height = 8

So , the Base = Area / Height

Height = x - 3

c)

Let the parallelogram be C

Now , Area = 12x + 6y

Base = 6

So , the height = Area / Base

Height = 2x + y

Hence , the equations are solved

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Therefore , the solution of the given problem of unitary method comes out to be total amount spent by Ria £129.58.

By multiplying the value about one unit by the quantity of units required, one can apply the unit technique to solve a problem. The unit procedure is used to separate a single entity integer from a given many, to put it simply. One pen, or 400 rupees, would be needed to purchase 40 needle. There might be a common way to verify this. only one nation. Anything has a unique feature. Algebra, grid logic, and its laminates and reverse are all identical terms used to describe mathematical analysis.

Here,

Given : Ria purchases 19 books for £6.82 apiece.

Thus,

Total cost of book = 19 * 6.82

=> 129.58

Therefore , the solution of the given problem of unitary method comes out to be total amount spent by Ria £129.58.

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[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{1}~,~\stackrel{y_1}{-6})\qquad (\stackrel{x_2}{-8}~,~\stackrel{y_2}{-4})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(~~-8 - 1~~)^2 + (~~-4 - (-6)~~)^2} \implies d=\sqrt{(-8 -1)^2 + (-4 +6)^2} \\\\\\ d=\sqrt{( -9 )^2 + ( 2 )^2} \implies d=\sqrt{ 81 + 4 } \implies d=\sqrt{ 85 }\implies d\approx 9.22[/tex]

Answer:

Step-by-step explanation:

set 1 is the work, then 60 works finish 1/21 per day. [tex]\frac{1}{21*60}[/tex] is the work for per workers. so, the days for 70 workers is [tex]\frac{21*60}{70}=18[/tex] days.

it will spend 18 days to complete

The area of ΔADC is equal to 6 unit².

The total area that is bounded by a triangle's three sides is referred to as the triangle's area. In essence, it is equal to 1/2 of the height times the base, or A = 1/2 b h.

A abc = A adc because the areas of the initial and reflected triangles are equal.

Using the formula area=1/2 base height, determine the area of triangle ABC.

ABC in a triangle:

base = 4 units + AC

height = 3 units + BE

AΔ= abc = 1/2×4×3 =6 unnit²

Hence,

 ΔADC = 6 unit²

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On applying the midpoint theorem the values of x, y, and z are 2, 10 and 8 respectively.

What is the mid-point theorem?

According to the midpoint theorem, the line segment connecting any two triangle sides' midpoints is parallel to and equal to half of the third side.

The outer triangle is ABC and the inner triangle is DEF.

It can be seen that sides AB, BC and AC are equally divided such that AD=DB,

BE=EC and

CF=FA.

So, this proves that point D, E and F are the middle points of AB, BC and AC respectively.

Now, according to the midpoint theorem -

DF = 1/2(BC)

Plugging in the values -

x = (5x-6)/2

2x = 5x-6

2x-5x = -6

-3x = -6

x = 2

Now, for side DE -

DE = 1/2(AC)

Plugging in the values -

12 = (2z+8)/2

24 = 2z+8

24-8 = 2z

16 = 2z

z = 8

Now, for side EF -

EF = 1/2(AB)

Plugging in the values -

y = 20/2

y = 10

Therefore, the values obtained are x=2, y=10 and z=8.

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Therefore, F = c * M1 * M2 / d^2 when the force F of attraction between two bodies varies jointly as the weights of the two bodies and inversely as the square of the distance between them using the C constant.

Distance is the sum of an object's movements, regardless of direction. Distance may be defined as the amount of space an item has covered, regardless of its beginning or finishing position.

Direction is characterized as the course that anything follows, the route that must be taken to go to a certain location, the direction in which something is beginning to take shape or the direction you are facing.

F = c * M1 * M2 / d^2

Where,

F is the force of attraction,

M1 and M2 are the weights of the two bodies,

d is the distance between the two bodies,

and c is the proportionality constant.

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We get the number of bananas as 8 and the number of mangoes as 4.

The general equation of a straight line is -

y = mx + c

{m} - slope.

{c} - intercept along the y - axis.

Given is that Chee and her children went into a grocery store and she bought $12 worth of bananas and mangos. Each banana costs $0.50 and each mango costs $2. She bought twice as many bananas as mangos.

We can write the system of equations as -

x = 2y               .....  (1)

(1/2)x + 2y = 12   ..... (2)

We can write equation (2) as -

(1/2) x 2y + 2y = 12

3y = 12

y = 4

then -

x = 8

Therefore, we get the number of bananas as 8 and the number of mangoes as 4.

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Therefore the cost of each pair of incense is 2.4 in terms of x.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

An ordered pair of integers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. For instance, you might express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls) There are 1 in 4 boys and 3 in 4 girls.

Let x be the cost of one pair of incense.

We know that the total amount spent on apples and oranges is the same as the total cost of 12 pairs of incense. Therefore:

(cost of apples + cost of oranges) = 12x

We also know that the cost of the apples is 3x the cost of the incense, and the cost of the oranges is 2x the cost of the incense. Therefore, we can substitute these values into the equation:

(3x + 2x) = 12x

5x = 12x

x = 12/5 or 2.4

So the cost of each pair of incense is 2.4 in terms of x.

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Answer:

Step-by-step explanation:

-x+6=-2(x+2)-5

Solve for x

-x + 6 = -2(x + 2) - 5

-x + 6 = -2x - 4 - 5

x = -15

------------------------

- (-15) + 6 = -2(-15 + 2) - 5

21 = 21

x = -15

The area of the circular base of the fountain is 179 square feet.

A circle's area is equal to its radius, r, squared, then multiplied by the mathematical constant pi: A = pi x r2.

A cylinder has two bases that are two congruent circles at the top and bottom. The radius r of a cylinder is only the radius of the circular bases, and the height h of a cylinder is the perpendicular distance between these bases.

Combined area of the walkway and fountain: (3.14)112=379.94 ft2.

Fountain area: (3.14)8*2=200.96 feet

Walkway area: 379.94-200.96=178.98 square feet, which is also rounded to 179 square feet.

The area of the circular base of the fountain is 179 square feet.

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Answer: original price: £400

Step-by-step explanation:

20/100 × original price = £80

Original price = £80 ÷ 20/100

                      = £400

Answer:

C. x=68 and y=112

Step-by-step explanation:

We can find that x=68 by adding 52 and 60 together which would get us 112. Then subtracting 112 from from 180 leaving us with our sum of 68, which means x=68. Then we find the value of y by adding the two interior angles on the opposite sides of the triangle. So 52+60=112. This makes y=112.

-Hope this helped

Answer:

x = 68

y = 112

Step-by-step explanation:

The interior angles of a triangle add to 180º.

Using this knowledge, we can solve for x:

52º + 60º + xº = 180º

↓ subtract 52º and 60º from both sides

xº = 180º - 52º - 60º

xº = 68º

x = 68

The interior and corresponding exterior angles of a triangle are supplementary (they add to 180º).

Using this knowledge, we can solve for y:

xº + yº = 180º

↓ substitute for solved x-value

68º + yº = 180º

↓ subtract 68º from both sides

yº = 112º

y = 112

Answer:

<1 and  <2  are Complementary Angles

m<1  + <2  = 90 degrees

Step-by-step explanation:

<1 and  <2  are Complementary Angles

m<1  + <2  = 90 degrees

Have a great day!

Since, angle 1 and 2 sums up to make 90 degrees, hence Angle 1 and 2 are complementary angles.

Complementary angles are those whose combined angle is exactly 90 degrees. 30 degrees and 60 degrees, for instance, are complementary angles.

Angles that add up to 180 degrees are referred to as supplementary angles. For instance, angle 130° and angle 50° are complementary angles since the sum of these two angles is 180°. In the same way, complementary angles sum to 90 degrees.

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Kate needs to buy 453.6 ft2 of mulch for her 12 ft radius garden, which is equal to 76.3 cubic feet when multiplied by the desired depth.

Kate needs to purchase 453.6 cubic feet of mulch for her garden. To figure this out, she needs to first calculate the area of her garden using the formula A = πr2, where A is the area of the garden and r is the radius. In this case, the area of Kate’s garden is 453.6 ft2. For example, if she wants to put down 2 inches of mulch, she would need to purchase 453.6 ft2 x 0.167 ft = 76.3 cubic feet. This calculation can be adjusted depending on the depth of mulch desired. For example, if Kate wants to put down 3 inches of mulch, she would need to purchase

453.6 ft2 x 0.25 ft = 113.4 cubic feet

A = πr2

A = π(12)2

A = 453.6 ft2

Mulch = A x depth

Mulch = 453.6 ft2 x 0.167 ft

Mulch = 76.3 cubic feet

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Personal assets are the list of things which are owned by any person for the present or the future use such as house , saving accounts, Cash etc.

Therefore, the personal assets represent the valuable  items owned by any individual for present or the future use.

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a. The graphical representation of the oscillation of the weight suspended from a spring is a sine wave, with the displacement of the weight on the y-axis and time on the x-axis. The equation involving the situation would be y = Asin(2pift + phi) where A is the amplitude of the oscillation (3 cm in this case), f is the frequency of oscillation (3 cycles per second in this case), t is the time elapsed since the weight was released, and phi is the phase offset (0 in this case).

b. To find the displacement of the spring after 2.5 seconds, we can substitute 2.5 seconds for t in the equation: y = Asin(2pift + phi) = 3sin(2pi32.5 + 0) = 3sin(15pi) = 3*0 = 0 cm. So the displacement of the spring after 2.5 seconds is 0 cm.

By definition, period of oscillation of an oscillator is the time interval that the oscillating object needs to pass through its equilibrium position with velocity in the same direction.

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Answer:

B. 3/4

Step-by-step explanation:

Let the equation of line be represented as A

Now , the value of A is

Let the first point be P = P ( -3 , 4 )

Let the second point be Q = Q ( 1 , 7 )

Now , the slope of the line between the two points is given by the formula ,

Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 7 - 4 ) / ( 1 - ( -3 ) )

On simplifying the equation , we get

Slope m = 3 / 4

The decimal form of n/350 terminates after 49 integer values of n between 1 and 349 inclusive.

The technique of expressing all numbers as a product of primes is known as prime factorization. As an example, suppose we have the number 20. We may divide this into two categories. "Well, that's 4 times 5," we may remark. Also, 5 is a prime number. The number four is not a prime number. All numbers are made up of prime numbers. "Factors" are numbers that are multiplied to generate another number. As an example. "Prime factorization" is the process of determining which prime numbers multiply to produce the original number.

Here,

first, find the prime factorization of 350. (2*5^2*7)

then we need to find all multiples of 7 that are between 1 and 350.

the first multiple of 7/350.

The first multiple of 7 between 1 and 350 is 7.

so 7/350=0.02.

Then, drop the two zeros and find out what is 100% (1 whole, ignoring the percent) /2.

Then, we get 49.

49 integer values of n between 1 and 349 inclusive does the decimal representation of n/350 terminate.

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Exponential graph is identified by its curve.

An exponential graph is a graph that shows a rapid increase or decrease of a value over time, where the rate of change is proportional to the current value. It is usually represented by a curve that bends upward or downward.

The key characteristic of an exponential graph is that the Y-axis is on a logarithmic scale, and the curve of the graph is a steep curve going either up or down. The equation of an exponential graph is usually of the form y = ab^x, where a is the initial value, b is the growth or decay factor, and x is the independent variable.

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(a) Since cosθ = 7/12 and sinθ < 0, we can find the other four trigonometric functions as follows:

sinθ = √(1 - cos²θ) = √(1 - (7/12)²) = √(1 - 49/144) = -√(95/144)

tanθ = sinθ / cosθ = (-√(95/144)) / (7/12) = -4√(5/18)

cotθ = 1 / tanθ = -1 / (-4√(5/18)) = 1/(4√(5/18))

secθ = 1 / cosθ = 1 / (7/12) = 12/7

cscθ = 1 / sinθ = -1 / (-√(95/144)) = √(95/144)

(b) Since tanθ = 4/3 and θ is in Quadrant III, we can find the other five trigonometric functions as follows:

cosθ = √(1 / (tan²θ + 1)) = √(1 / (16/9 + 1)) = √(9 / 25) = 3/5

sinθ = cosθ * tanθ = (3/5) * (4/3) = 4/5

cotθ = 1 / tanθ = 1 / (4/3) = 3/4

secθ = 1 / cosθ = 1 / (3/5) = 5/3

cscθ = 1 / sinθ = 1 / (4/5) = 5/4

Trigonometric functions are a set of functions that relate the angles of a right triangle to the ratios of the sides of the triangle. The six most commonly used trigonometric functions are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc).

The sine function, represented by sin, gives the ratio of the side opposite the angle to the hypotenuse. The cosine function, represented by cos, gives the ratio of the adjacent side to the hypotenuse. The tangent function, represented by tan, gives the ratio of the opposite side to the adjacent side.

The cotangent function, represented by cot, gives the ratio of the adjacent side to the opposite side. The secant function, represented by sec, gives the ratio of the hypotenuse to the adjacent side, and the cosecant function, represented by csc, gives the ratio of the hypotenuse to the opposite side.

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A composite function is a type of function that is made up of two or more other functions. It is created by combining two or more functions together. The resulting function can be written as a single expression, or as a composition of multiple functions.

A composite function is a type of function that is formed by combining two or more other functions. It is created by combining two or more functions together using the mathematical operations of addition, subtraction, multiplication, division, or composition. The resulting function can be written as a single expression, or as a composition of multiple functions. A composite function is often used to simplify a complex problem, or to manipulate and analyze data. For example, if a data set contains two sets of data, a composite function could be used to combine the two sets of data into a single expression. Additionally, composite functions can be used to solve problems that involve multiple variables, as the resulting function can be used to represent the relationship between the variables. Furthermore, composite functions can be used to create graphs, which can be used to further analyze the data.

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