let f be a differentiable function with f(1)=−2. the graph of f′, the derivative of f, is shown above. which of the following statements is true about the line tangent to the graph of f at x=1 ?

Answer:

f(x) = 2 + 7.5 sin(x/3 + pi/4)

Step-by-step explanation:

f(x) = 2 + 3 sin(x/3 + pi/4)

  Amplitude: 3

2.5 * 3 = 7.5

Function that has an amplitude that is two and half times the size of the function f(x) = 2 + 3 sin(x/3 + pi/4)

   f(x) = 2 + 7.5 sin(x/3 + pi/4)

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In ΔOPQ, o = 10 cm, p = 67 cm, ∠Q=24,∠P=152.

A triangle in geometry is a three-sided polygon with three edges and three vertices.

The fact that a triangle's internal angles add up to 180 degrees is its most crucial characteristic.

This characteristic is known as the triangle's angle sum property.

If ABC is a triangle, it is written as ABC, where A, B, and C represent the triangle's vertices.

In Euclidean geometry, a triangle is a two-dimensional shape that is represented by three non-collinear points in a single plane.

A closed, two-dimensional shape is a triangle. It is a polygon with three sides. Straight lines make up all of the sides.

The vertex is the intersection of two straight lines. The triangle therefore has three vertices.

Hence, In ΔOPQ, o = 10 cm, p = 67 cm, ∠Q=24,∠P=152.

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The length of side o is, 48.6 inches.

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

In ΔNOP,

⇒ n = 61 inches, m ∠N = 140° and m ∠O = 31°.

Now, Let the length of side o = x

So, By sine rule, we get;

⇒ sin N / n = Sin O / o

Substitute all the values, we get;

⇒ sin140°/  61 = sin 31° / x

⇒ 0.64 / 61  = 0.51 / x

⇒ x = 0.51 × 61 / 0.64

⇒ x = 48.6 inches

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The amount of money Mina will receive in dollars is $13.33 USD.

Mina returned from a trip and needs to exchange 18 pounds  GBP back to USD. She finds that the current exchange rate is 1.35 pounds GBP to $1.00 USD.

Therefore, the amount of money Mina will receive in dollars can be calculated as follows:

Therefore,

1.35 pounds = 1.00 dollars

18 pounds = ?

cross multiply

Therefore,

amount of money in dollars she will receive =  18 × 1.00 / 1.35

amount of money in dollars she will receive = 18 / 1.35

Therefore,

amount of money in dollars she will receive = 13.33 dollars

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6 sin² (x) - 5 cos(x) — 7 = 0 for all solutions 0 < x < 2π :  x = π

[tex]& \sin ^2 x-5 \cos x=5 \\[/tex]

[tex]& 1-\cos ^2 x-5 \cos x=5 \\[/tex]

[tex]& \cos ^2 x+5 \cos x+4=0 \\[/tex]

[tex]& \cos ^2 x+\cos x+4 \cos x+4=0 \\[/tex]

[tex]& \cos x(\cos x+1)+4(\cos x+1)=0 \\[/tex]

[tex]& (\cos x+1)(\cos x+4)=0 \\[/tex]

[tex]& \cos x+1=0 \quad(\because \cos x \neq-4) \\[/tex]

[tex]& \cos x=-1 \\[/tex]

[tex]& \cos x=\cos \pi \\[/tex]

[tex]& x=(2 k+1) \pi[/tex]

Where, k is any integer i.e  k = 0 ± 1, ± 2, ± 3,....

But x ∈[0,2π)  hence setting k = 0 we get the solution

x = π

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The value of x and y in the equation is (x,y) = (68,2) (optionA)

Simultaneous equations are two or more algebraic equations that share variables e.g. x and y . They are called simultaneous equations because the equations are solved at the same time. For example, below are some simultaneous equations: 2x + 4y = 14 4x − 4y = 4.

x= 60+4y equation 1

7x + 12y = 500 equation 2

rearranging the equation

x- 4y = 60

7x+12y = 500

using elimination method

7x-28y = 420 equation 3

7x+12y = 500 equation 4

subtract equation 4 from 3

-40y = -80

divide both sides by -40

y = -80/-40

y= 2

substitute 3 for y in equation 1

x = 60+4(2)

x= 60+8

x= 68

Therefore the value of x and y is 68 and 2 respectively.

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The answer choices which correctly represent equations which model the total yards of fabric Sophie will buy is; x + y = 28, 28 - x = y and 28 - y = x.

It follows from the attached table, where x represents the yards of red fabric she buys and y represents the yards of blue fabric she buys.

It follows that the following x and y pairs are possible; (1, 27), (2, 26), (3, 25) and (4, 24).

On this note, it can be inferred that in each of the red and blue fabric pairs; x + y = 28.

Ultimately, the equations which model the total yards of of fabric Sophie will buy as required are; x + y = 28, 28 - x = y and 28 - y = x.

Complete question; The given answer choices are; x+y=28, 28+x=y, x-y=28, 28-x=y and 28-y=x.

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n!-(n-1)!=16(n-2)! by factorizing it by  n!  and dividing it by n! we get n is equal to 2 .

The intersection point in mathematics is the location on the y-axis where the slope of the line passes. a point where a line or curve's y-axis crosses it. This is demonstrated using the equation for the straight line, Y = mx+c, where m denotes the slope and c the y-intercept. The equation's intercept form highlights the line's slope (m) and y-intercept (b). The slope is m and the y-intercept is b when an equation has the intercept form (y=mx+b). It is also possible to rewrite some equations so that they resemble slope intercepts. For example, the slope and y-intercept are both modified to 1 if y=x is rewritten as y=1x+0.

given

n! + (n+1)! = (n+2)!

Let us rewrite:

n!+ (n+1)n! = (n+2)(n+1)n!

Factorize n!

n!(1+n+1) = (n+2)(n+1)n!

Divide by n!

==> n+2 = (n+2)(n+1)

No divide by (n+2)

==> 1= n+1

==> n = 0

to verify substitute with n=0

==> 0! + 1! = 2!

==> 1+1 = 2

==> 2=2

n!-(n-1)!=16(n-2)! by factorizing it by  n!  and dividing it by n! we get n is equal to 2 .

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height of pentagonal prism is h unit.

The prism is one that has two pentagonal bases from which one acts as bottom and the other acts as top. The pentagonal prism has five rectangular sides. This prism has 10 vertices and 15 edges. It is also said five-sided polygon prism.

given, area of pentagonal prism = 34 square unit

volume of pentagonal prism = 180.2 cubic unit

we know the formula for the area of the pentagonal prism.

Total surface area = 5ab + 5hb

Volume of pentagonal prism = 5/2 a b h

where, a =apothem length

b = base length

h = height of the prism

according to the given statement, 34 = 5 a b + 5 h b

          180.2 = 5/2 a b h

from the above two equation, we get, the height of prism = h unit.

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The total weight of the items is 29.25 lb.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

The wight of one can = 13 1/2 = 27/2 pounce

and, number of cans in one case = 12

So,  total weight of the items

= 1/16 ( 27/2 x 12 x 2)+ 4x 2.375

= 1/16 ( 324) + 9.5

= 81/4 + 9.5

= 20.25+ 9.5

= 29.25 lb

Hence, the weight is 29.25 lb.

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Polynomial function R is the difference of two​ degree-2 polynomial functions P and Q. the possible degree of Polynomial R is

A polynomial function is a function in an equation, such as the quadratic equation or the cubic equation, that only uses non-negative integer powers or only positive integer exponents of a variable.

A polynomial function of degree 2 is a quadratic function.

The degree of polynomials can only increase during multiplication, when polynomials are added or subtracted the result will have a degree which is at most the degree of the functions operated on.

Polynomial of degree zero are constants and hence is possible in the case

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complete question

Polynomial function R is the difference of two degree-2 polynomial functions P and Q. What are the possible degrees for R? Explain.

Select the correct choice below and fill in the answer box to complete your choice.

(Type an integer or a decimal. Use a comma to separate answers as needed)

A. The possible degree(s) is/are    because it must be equal to the greater of the degrees of P and Q.

B. The possible degree(s) is/are    because it must be equal to the lesser of the degrees of P and Q.

C. The possible degree(s) is/are     because it must be less than the degree of either P or Q

D. The possible degree(s) is/are    because it cannot be higher than the degree of either P or Q but it can be less depending on which terms cancel

Therefore ,the solution to the given problem of angles comes out to be

∠K= 66 degree,LK length = 2√2 unit LK length = 2√2 unit.

In Geometrical, an angled is a structure made up of two rays, known as the angle's face, that converging at the vertex, or center, of the angle. It is feasible for two beams to form an angle within a plane depending on where they are placed. An angle is also created when two planes intersect. The nomenclature to them is diahedral angles. In plane geometry, light rays or lines with the same ending can have many different forms, or angles. The Latin word "angulus," which means "horn," is where the word "angle" in English comes from. The vertex, also known as the vertex of the angle, is the point at where the two rays meet.

Here,

Given: A right angle triangle MKL

∠M = 24 degree

and ∠K =90 degree

Thus,

=> ∠L + ∠M  +∠K =180

=> 90 + 24 + ∠K = 180

=>∠K =180-114

=> ∠K= 66 degree

and

LK length = 2√2 unit

LK length = 2√2 unit

Therefore ,the solution to the given problem of angle comes out to be

∠K= 66 degree,LK length = 2√2 unit LK length = 2√2 unit.

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Answer:

x=0 or x=pi / x=πn

Step-by-step explanation:

cos2x + 3 = 4

subtract 3 from both sides

cos2x = 1

take the inverse cos/arccos of both sides

arccos(cos2x) = arccos(1)

2x=0 or 2x=2pi

divide both sides by 2

x=0 or x=pi

beyond (0,2pi) for every possible answer you should do x=(pi)n since any multiple of pi gives you the same answer

A collection of seven geometric objects known as the Tangram is composed of five triangles (two tiny, one medium, and two large), a square, and a parallelogram.

In the given question, we have to find how many triangles are there in a 7 piece.

As we know that a collection of seven geometric objects known as the Tangram is composed of five triangles (two tiny, one medium, and two large), a square, and a parallelogram.

A dissection problem called a tangram is made up of seven flat polygons, or tans, that are combined to make various shapes. The goal is to use each of the seven parts separately to duplicate a pattern that is typically found in a puzzle book.

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Answer:

79 degree

Step-by-step explanation:

A triangle is 180 degrees

We know that angle D and F is equal to each other

180 - 22 = 158 degree

158 / 2 = 79 degree

So, m<F = 79 degree

Answer:

v/202

Step-by-step explanation:

formula: leg² + leg² = hyp²

11² + 9² = hyp²

121 + 81 = hyp²

202 = hyp²

v/202 = v/hyp²

hope this makes sense

The quotient of the division problem is (x + 1)/(x +2). The result is obtained by determining the factors of the two quadratic equations.

The quadratic equation can be expressed as

ax² + bx + c = 0

Where c is a constant.

To find the factors of a quadratic equation, follow these steps!

Find the quotient of (x² + 2x + 1)/(x² + 3x + 2) = 0!

For quadratic equation x² + 2x + 1:

The common factors: (x + 1)(x + 1)

For quadratic equation x² + 3x + 2:

The common factors: (x + 2)(x + 1)

The quotient of the quadratic equations is

(x² + 2x + 1)/(x² + 3x + 2) = 0

(x + 1)(x + 1)/(x + 2)(x + 1) = 0

(x + 1)/(x + 2) = 0

Hence, the quotient of the quadratic equations is (x + 1)/(x + 2) = 0.

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The formula to calculate the quotient of 2 3 and 2 9 is written as 2 3 divided by 2 9, or 2 3 / 2 9.

To calculate the answer, first divide 2 by 9, which is equal to 0.22. Then multiply 0.22 by 3, which is equal to 0.66. The final answer is 0.66.

In order to solve this problem, the division operation was used. The first number, 2 3, was divided by the second number, 2 9. The division operation was used to determine how many times the second number could fit into the first number. The answer of 0.66 means that 2 9 can fit into 2 3 0.66 times. This answer can be written as 0.66, or as a fraction, 2/3.

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The equation of the line with points (0.0) and (-3,-7) is y = 7/3 * x

A coordinate system is a method for determining how to position points or other geometrical objects on a manifold, such as Euclidean space, uniquely using one or more integers, or coordinates.

The study of geometry using coordinate points is known as coordinate geometry (also known as analytical geometry). Finding the distance between two points, breaking lines into m:n segments, locating a line's midpoint, computing a triangle's area in the Cartesian plane, and other operations are all feasible using coordinate geometry.

The points are (0,0) and (-3, - 7)

The equation of the line will be

y - 0 = (-7 - 0)/(-3-0) * (x - 0)

⇒y = 7/3 * x

The equation of the line with points (0.0) and (-3,-7) is y = 7/3 * x

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By solving the algebraic expression A=125^x/(1+125^x)​ the answer is 8/35.

When addition, subtraction, multiplication, division, and other mathematical operations are performed on variables and constants, the result is a mathematical statement known as an algebraic expression. Any combination of terms that have undergone operations like addition, subtraction, multiplication, division, etc. is known as an algebraic expression (or variable expression).

given that 5^x/(1+5^x)=2/5

or (1+5^x)/5^x = 5/2

⇒ 1/5^x + 1 = 5/2

⇒ 1/5^x = 5/2 - 1

⇒ 1/5^x = (5-2)/2

⇒ 1/5^x  = 3/2

or 5^x = 2/3

now,

A = 125^x/(1+125^x)

⇒ A = (5^3)^x/{1+(5^3)^x}

⇒ A = 5^3x/(1+5^3x)

⇒ A = (5^x)^3/{1+(5^x)^3}

⇒ A = (2/3)^3/{1+(2/3)^3}

⇒ A = (8/27)/(1+8/27)

⇒ A = (8/27)/{(27+8)/27}

⇒ A = (8/27)/(35/27)

⇒ A = 8/35

So that A=125^x/(1+125^x)​ = 8/35

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We can define a function f(x) with a domain of all real numbers (−[infinity],[infinity]) and a range of [-11,3].

Let's start by defining our function f(x):

f(x) = [-11,3]

Now, let's define our new function g(x):

g(x) = f(6x) + 1

This means that the range of g(x) is the range of f(x) plus 1, so the range of g(x) is [-67, 19]. In interval notation, this can be expressed as [-67, 19].

We can define a function f(x) with a domain of all real numbers (−[infinity],[infinity]) and a range of [-11,3]. To generate a new function, g(x), we can define it by g(x) = f(6x) +1. This means that the range of g(x) is the range of f(x) plus 1, so the range of g(x) is [-67, 19]. To express this in interval notation, we can write [-67, 19]. This means that the output of g(x) lies between the values -67 and 19. This new range can be found by multiplying each value in the range of f(x) by 6 and then adding 1 to each value. Therefore, the range of g(x) is [-67, 19] in interval notation.

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As per the area of rectangle, the required length of rope is 36.66 square meter.

The formula to calculate the area of rectangle is written as,

=> A = l x b

Where l refers the length and b refers the breadth.

Here we have given that a florist want to put a rope around his rectangular garden with the dimensions 7. 8m by 4. 7m.

In order to put the rope we have to find the area of the garden,

The area of the garden is calculated by using the area of rectangle formula, as 7.8 as length and 4.7 as breadth

=> A = 7.8 x 4.7

=> A = 36.66

Therefore, 36.66 square meter is required.

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The probability that the child will select a pair of sunglasses both times is; 1/25

We are given the contents of the toy chest as;

7 puzzles

4 squishy balls

5 pairs of play sunglasses

9 fidget spinners

Total toy chest = 7 + 4 + 5 + 9

= 25

Probability of first choice being sunglasses = 5/25 = 1/5

Probability of second choice being sunglasses = 5/25 = 1/5

P(two choices being sunglasses) = 1/5 * 1/5 = 1/25

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To make a model of corresponding angles using toothpicks or straws, you can take two pieces of the material and place them next to each other at the same angle.

When two parallel lines are intersected by another line, corresponding angles are the angles that are created in matching corners or corresponding corners with the transversal.

To make a model of co-interior angles, you can place the two pieces of material on top of each other, with one inside the other at the same angle. To make a model of alternate angles, you can place the two pieces of material on opposite sides of a straight line, with one angle facing up and the other angle facing down.

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Complete question

make a model of corresponding angles using toothpicks or straws

Answer:

There are six types of triangles based on their side lengths:

Equilateral Triangle: A triangle with all sides of equal length. For example, a triangle with sides of 3cm each is an equilateral triangle.

Isosceles Triangle: A triangle with two sides of equal length. For example, a triangle with sides of 2cm, 2cm, and 3cm is an isosceles triangle.

Scalene Triangle: A triangle with no sides of equal length. For example, a triangle with sides of 2cm, 3cm, and 4cm is a scalene triangle.

Acute Triangle: A triangle with all angles measuring less than 90 degrees. For example, a triangle with angles measuring 60, 75, and 45 degrees is an acute triangle.

Right Triangle: A triangle with one angle measuring exactly 90 degrees. For example, a triangle with angles measuring 45, 45, and 90 degrees is a right triangle.

Obtuse Triangle: A triangle with one angle measuring more than 90 degrees. For example, a triangle with angles measuring 90, 45, and 45 degrees is an obtuse triangle.

Step-by-step explanation:

Answer: There are 4 quarts in a gallon so to convert 5 gallons to quarts you would multiply 5 x 4 = 20 quarts.

The Least Common Multiple (LCM) of 4 and 10 is 20, and the Highest Common Factor (HCF) of 4 and 10 is 2.

HCF is the highest integer that can divide 4 and 10 is 2. HCF stands for Highest Common Factor.

Now, 4 and 10 can be expressed as:

4 = 2 × 2 

10 = 2 × 5 

The common prime factor is 2. 

Therefore HCF (4, 10) = 2

The Least Common multiple simply known as LCM is the smallest or the least positive integer that is divisible by the given set of numbers.

Similarly, Calculating the LCM, 4 and 10 can be expressed as;

4 = 2 x 2

10 = 2 x 5

LCM (4, 10) = 2 x 2 x 5 = 20

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Answer:

Below

Step-by-step explanation:

From 10 000 to 99 999   there are 90 000 numbers of which half are even  = 45 000  even 5-digit numbers