Which of the following can be the sides of a right triangle?
(i) 2.5 cm, 6.5 cm, 6 cm
(ii) 2 cm, 2 cm, 5 cm
(iii) 1.5 cm, 2cm, 2.5 cm
In the case of right-angled triangles, identify the right angles

Answer:

a) 4 cosx^4 - cos²2x=0

We can start by splitting the equation into two parts:

4 cosx^4 = cos²2x

cosx^4 = (1/4)cos²2x

From here, we can use the identity:

cos²2x = (cos 2x)² = (2cos²x -1)²

So, we have:

cosx^4 = (1/4)(2cos²x -1)²

Now we can square root both sides:

cosx^2 = (1/2) (2cos²x -1)

Now we square both sides again:

cos²x = (1/4) (2cos²x -1)

We can now subtract (1/4) from both sides and add cos²x to both sides:

(3/4)cos²x = (1/4)

We can now divide both sides by (3/4) to find the value of cosx:

cosx = sqrt(1/3)

So the solutions of the equation are x = (2n+1)π/3, where n is an integer.

b) sec x tan x =sqrt(2)

We know that sec x = 1/cosx and tan x = sinx/cosx.

So we can substitute these values into the equation:

1/cosx * sinx/cosx = sqrt(2)

This simplifies to:

sinx = sqrt(2)cosx

We can now divide both sides by cosx:

tan x = sqrt(2)

So the solutions of the equation are x = pi/4 + nπ, where n is an integer.

Note that the solutions are restricted to the domain where cos(x) is not equal to 0.

It is important to note that this solution is only a small part of the full solution set and that there might be more solutions in specific intervals.

Answer: [tex]12a^2-4a[/tex]

Step-by-step explanation:

[tex]f(-2a)=3(-2a)^2+2(-2a)=3(4a^2)-4a=12a^2-4a[/tex]

As per the formula of surface area of cube, the length of the cube is 5.45 meters.

The general formula to calculate the surface area of the cube is calculated as,

=> SA = 6a²

here a represents the length of cube.

Here we know that  the side of a cube with a surface area of 180 square meters than a cube with the surface area of 120 square meters.

When we apply the value on the formula, then we get the expression like the following,

=> 180 = 6a²

where a refers the length of the cube.

=> a² = 30

=> a = 5.45

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Therefore ,as a  result unitary method they just have sufficient flour to complete their recipes because they require roughly 4.08 c of wheat and only have 4 c.

In order to solve a problem using the unitary approach, you must first determine how much of a small subset there is, then multiply that number by two. Simply expression, the unit approach is utilized to isolate a common programming value from the a given set. For instance, 40 pens cost 400 rupees ($1.01) each, or Rs. It's possible that the method utilized to accomplish this will be governed by just one country. Each every thing has a distinctive quality. Its reciprocity and integration capabilities are the same (mathematics, algebra).

Here,

Given : Flour is available in 4c.

Eliza requires 2 1/3 cups of flour.

1 3/4 c of flour is required by Jaime.

All mixed numbers must first be converted into fractions before we can total the two amounts to determine if we have enough flour.

=> 2* 1/3 =7/3

=> 1* 3/4 = 7/4

Now, we add.

=> 7/3 +7/4

=> 28+21/ 12

=> 49/12

=> 4.08

As a result, they just have sufficient flour to complete their recipes because they require roughly 4.08 c of wheat and only have 4 c.

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Please share the correct question !!!

(x−2)2^=y   // this is incorrect mathematical expression

The correct question should be:

[tex](x-2)^{2} =y[/tex] , Find the value of "x"

step-by-step solution:

[tex](x-2)^{2} =y[/tex]

[tex](x-2)=y^{\frac{1}{2} }[/tex]

[tex]x=y^{\frac{1}{2} } + 2[/tex]   OR   [tex]x=\sqrt{y}+ 2[/tex]

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y³√45x⁷y⁵ in its simplest form is 3√5y⁵x³√x√y

An expression is combination of variables, numbers and operators.

The given expression is y³√45x⁷y⁵

y³√9×5 x⁷y⁵

In the given expression x and y are the variables.

=y³3√5x³.√x. y²√y.

=y⁵.3√5x³√y√x

=3√5y⁵x³√x√y

Hence,y³√45x⁷y⁵ in its simplest form is 3√5y⁵x³√x√y

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BD bisects angle ABC for the value of x = 4

An angle is a shape created by two rays that share a terminus and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are on the plane where the rays are located. The meeting of two planes also creates angles. Dihedral angles are these.

An angle is a shape created by two rays or lines that meet at the same terminal. The Latin word "angulus," which meaning "corner," is the source of the English term "angle." The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle.

In geometry, an angle bisector is a line that divides an angle into two equal angles. The term "bisector" refers to a device that divides an item or a form into two equal halves. An angle bisector is a ray that divides an angle into two identical segments of the same length.

Since 3x + 1 and 4x - 3 are angle bisectors so,

3x + 1 = 4x - 3

or, x = 4

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Answer:

Hope This Helps <3

Step-by-step explanation:

4-8 +2 = -11

6-3-7 = -4

1 +4-6 =  -1

2-7+6 = 1

A four-regular graph is a  quartic graph.

A quartic graph is an example of a polynomial function with a degree of four. The formula denotes a quartic function's equation: f(x) = ax4 + bx3 + cx2 + dx + e, where a, b, c, d, and e are constants. A quartic function's graph is a straight line with up to four turning points or extrema. The roots of the polynomial are also referred to as the graph's x-intercepts or the answers to the equation f(x) = 0.

The values of the constants a, b, c, d, and e, as well as whether an is positive or negative, determine the shape of the quartic graph. The graph starts out with an upward slope if it is positive and a downward slope if an is negative. Factorization, the square-root approach, or numerical techniques like the bisection method or the Newton-Raphson method can all be used to solve quartic equations.

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The solution to the linear system is [tex]|A_x|=\left[\begin{array}{cc}17&3\\9&-3\end{array}\right]{,|A|=\left[\begin{array}{cc}5&3\\-8&-3\end{array}\right]} ,|A_y|=\left[\begin{array}{cc}5&17\\-8&9\end{array}\right]\\[/tex]

An equation is a expression that shows the relationship between numbers and variables.

A linear system of equation:

Ax + By = C

Dx + Ey = F

Can be solved using:

[tex]|A_x|=\left[\begin{array}{cc}C&B\\F&E\end{array}\right]{,|A|=\left[\begin{array}{cc}A&B\\D&E\end{array}\right]} ,|A_y|=\left[\begin{array}{cc}A&C\\D&F\end{array}\right]\\\\Hence:\\\\x=\frac{|A_x|}{|A|} ,y=\frac{|A_y|}{|A|}[/tex]

Hence, for:

5x + 3y = 17

-8x - 3y = 9

[tex]|A_x|=\left[\begin{array}{cc}17&3\\9&-3\end{array}\right]{,|A|=\left[\begin{array}{cc}5&3\\-8&-3\end{array}\right]} ,|A_y|=\left[\begin{array}{cc}5&17\\-8&9\end{array}\right]\\[/tex]

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Answer:

47

Step-by-step explanation:

Factorise means to carry over the common number or letter to the outside of a set of brackets, whilst keeping the rest of the equation inside the brackets.

Answer:

Carry f to the outside, meaning that you would be left with f(4f +1).

We use the parallelogram-shaped sponge to create the T-shirt design. The area of the design is 66 square inches. 22 times we will use the sponge to create the design.

Parallelogram:

The term "parallelogram" comes from the Greek word "parallelogram on" which means "surrounded by parallel lines". A parallelogram is a quadrilateral bounded by parallel lines. A shape with opposite sides parallel and equal. Parallelograms fall into three main types: squares, rectangles, and rhombuses, each with its own characteristics.

According to the Question:

Area of the parallelogram-shaped sponge = base × height

                                                                        = 3 inches × 1 inch

                                                                        = 3 square inches

And,

Area of design = 66 square inches

Now,

Number of times to use the sponge to create the design

= Area of design ÷ Area of parallelogram-shaped sponge

= 66 square inches ÷ 3 square inches

= 22 Times

Therefore,

The sponge can be used 22 times to create the design.

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Answer:

B) [tex]2^2 \times 5 \times 37[/tex]

Step-by-step explanation:

[tex]740=2 \times 370=2^2 \times 185=2^2 \times 5 \times 37[/tex]

Answer:

40m + 40

Step-by-step explanation:

8(5m+5)

40m + 40

The hexagon's side length is 4.5 inches whereas the equilateral triangle's side length is 9.

While an exterior angles are equivalent to the sum of the twin interior angles that become not directly adjacent to it, the inside angles necessarily add up to 180°. By lowering the inclination of the target vertex from 180°, one may also get a triangle's exterior angle.

The equilateral triangle's side length is 9 inches.

The hexagon's sides measure 4.5 inches long.

The equilateral triangle's side length is equal to 1.4x plus 2.

Perimeter = 3(1.4x + 2) = 4.2x + 6 as a result.

The hexagon's side length is equal to 0.5x plus 2.

The perimeter is 6(0.5x + 2) = 3x + 12 as a result.

the perimeters being equal.

So,\s4.2x + 6 = 3x + 12

4.2x - 3x = 12-6

1.2x = 6\sx = 5

Hence,

The equilateral triangle's side length is equal to 1.4x + 2 = 1.4(5) + 2 = 9 inches.

The hexagon's side length is equal to 0.5x + 2 (or 0.5(5) + 2; or 4.5 inches).

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The complete question is-

An equilateral triangle has a side length of 1.4x + 2 inches. A regular hexagon has a side length of 0.5x + 2 inches. The perimeters are equal. What is the side length of the triangle? What is the side length of the hexagon? Show your work.

Answer:

2:5

I am not sure if it is correct answer

The next year's population to the nearest individual will be 140,014. The solution has been obtained by using arithmetic operations.

What are arithmetic operations?

There are four fundamental mathematical operations for all real numbers in mathematics, and they are as follows:

1. Obtaining the sum of the numbers through addition ('+').

2. Subtraction using the sign "-" where the difference between the numbers is produced.

3. Multiplication ('×'), which results in the numbers' product.

4. The division ('÷') operation where the quotient of the numbers is determined.

According to the question, the population of a city increases by 2.2% per year and this year's population is 137,000.

Let the population of next year be 'x'

Therefore, we get the following

⇒137,000 + 137,000(2.2%) = x

⇒137,000 + 3014 = x

⇒140,014 = x

Hence, the next year's population to the nearest individual will be 140,014.

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The value of 0/infinity is Zero but not undetermined value.

Generally zero in numerator and any other number in the denominator gives the result zero always. i.e 0/ x where x is any other number and the number can be real, imaginary or complex. But the case with infinity is different as zero upon infinity gives the result as zero only it's because infinity is never can be a member of set of number. Because infinity is  just an expression that is greater than any assignable quantity or countable number. In mathematics, the concept of infinity describes something  larger than the natural number. It usually describes something without a limit. This concept is not only used in the mathematics but also in physics. In mathematics and physics, this concept is utilized in a wide range of fields. The term infinity can also be employed for an extended number system.

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Therefore , the solution of the given problem of integer comes out to be 1/100 = 0.01

Zero, a positive integer, or a negative integer denoted by a minus sign are all examples of integers. A negative number is the additive reciprocal of a positive number that it corresponds to. A bold Z or a bold "mathbb Z" is frequently used in mathematical notation to denote a group of integers. A positive, negative, or zero integer—not a fraction—is referred to as an integer (pronounced IN-tuh-jer). The numbers -5, 1, 5, 8, 97, and 3,043 are examples of integers. 1.43, 1 3/4, 3.14, and other numbers are non-integer examples. Integers are a collection of integers and their antipodes. Decimals and fractions are not part of the set of integers.

Here,

=> 1/4 =0.25

=> 1/20 = 0.05

=> 1/25 = 0.04

=> 1/50 = 0.02

=> 1/100 = 0.01

Therefore , the solution of the given problem of integer comes out to be 1/100 = 0.01

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In order for the number to form a terminating decimal, 2 and 5 must be its only prime factors. Obviously any number less than [tex]0.01[/tex] or any value of [tex]n > 100[/tex] will not have a nonzero hundredths digit.

We now count the possibilities for [tex]n[/tex]:

[tex]5^0 : 2^0, 2^1,..., 2^6 \rightarrow 7 \text{ values}\\5^1 : 2^0, 2^1,..., 2^4 \rightarrow 5 \text{ values}\\5^2 : 2^0, 2^1, 2^2 \rightarrow 3 \text{ values}[/tex]

for a subtotal of [tex]15[/tex] values.

However, some of these have a nonzero tenths digit and a zero hundredths digit. In other words, we need to remove all of the single-digit terminating decimals from this list. These are [tex]\dfrac{1}{1} = 1.00,\dfrac{1}{2} = 0.50,\dfrac{1}{5}=0.20, \text{ and }\dfrac{1}{10} = 0.10 \implies 4 \text{ values}[/tex]

which means the final answer is [tex]15-4=11[/tex].

If a triangle has a perimeter of 48 kilometers. Two of the sides measure 12 kilometers and 20 kilometers. The length of the third side is 16.

Let x km represent  the length of the third side

Let Length of other two sides is  12 km  and  20 km.

Hence,

Perimeter of triangle = Sum of all sides =  48 km

12 + 20 + x = 48

32 +x = 48

x = 48 - 32

x = 16

Therefore we can conclude that the length of the third side is 16.

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I do not think that eleri can cover a distance of 1 km.

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.

The Distance Formula itself is actually derived from the Pythagorean Theorem which is a 2 + b 2 = c 2 {a^2} + {b^2} = {c^2} a2+b2=c2 where c is the longest side of a right triangle (also known as the hypotenuse) and a and b are the other shorter sides (known as the legs of a right triangle).

In the abov equestion,

for 1 lap eleri cover a distance of 400m

for 2 laps she will cover a distance of 800m

since

800m<1km

So eleri cannot cover a distance more than 800 m

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The final integral is [tex]=5\left[x\arctan \left(\frac{1}{x}\right)-\left(-\frac{1}{2}\ln \left|1+x^2\right|\right)\right]_1^{\sqrt{3}}[/tex]

Numerical integrals are used to express concepts like volume, area, and displacement when infinitely small amounts of data are combined. Integral location is the integration process.

The signed area of the region in the plane that is circumscribed by the graph of a specific function between two points on the real line can be used to describe definitive integrals. Areas above the plane's horizontal axis are often positive, whereas those below it are typically negative.

[tex]\\\\\int _1^{\sqrt{3}}5\arctan \left(\frac{1}{x}\right)dx=\frac{5\left(2\sqrt{3}\ln \left(2\right)+2\pi -\sqrt{3}\pi \right)}{4\sqrt{3}}\quad \left(\mathrm{Decimal:\quad }\:2.34037\dots \right)\\\\=5\cdot \int _1^{\sqrt{3}}\arctan \left(\frac{1}{x}\right)dx\\\\=5\left[x\arctan \left(\frac{1}{x}\right)-\left(-\frac{1}{2}\ln \left|1+x^2\right|\right)\right]_1^{\sqrt{3}}x_{123} \\\\=5\left[x\arctan \left(\frac{1}{x}\right)-\left(-\frac{1}{2}\ln \left|1+x^2\right|\right)\right]_1^{\sqrt{3}}[/tex]

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Correct Question:

[tex]\int _{\:1}^{\sqrt{3}}5\cdot \arctan \left(\frac{1}{x}\right)dx[/tex]

As you can see from the picture, the probability of getting one head and one tail on the toss of two coins is 0.5. There are two different ways that this can happen.

The likelihood of getting one head and one tail on a coin flip is 0.5, as seen in the image. There are two ways in which this might occur. 50% of each coin is equal to 1/2.

There are four possible results for two coins: heads/heads, tails/tails, tails/tails, etc. Each outcome has a theoretical chance of 1/4, or.25. Half of the time, you'll receive heads.

Since the occurrence is complementary and equally likely to occur, it is already known that the probability is half/half, or 50%. As a result, there is a 50% chance of receiving either heads or tails. Take the four-coin experiment into consideration. 

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An inequality for the statement "The sum of two numbers is less than 2." is x + y < 2.

An inequality for the statement "If we subtract the second number from the first, the difference is greater than 1" is x - y > 1.

The two numbers are 1/2 and 3/2 or 0.5 and 1.5.

In order to write a system of inequalities to describe this situation, we would assign variables to the first number and second number respectively, and then translate the word problem into algebraic equation as follows:

Based on the information provided, we can logically deduce that there are two (2) system of inequalities with respect to the constraints for this situation.

Sum of two numbers is less than 2 ⇒ x + y < 2.

The difference is greater than 1 when we subtract the second number from the first number;

x - y > 1

In conclusion, a graph that represents system of inequalities is shown in the image attached below.

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Since 3 doughnuts is more expensive than and closer to pricing at 2, Sally can only eat 2 doughnuts.

In economics, marginal utility refers to the addition of pleasure or benefit utility a buyer gets by purchasing an extra unit of a good or service. When marginal utility is greater than or equal to price, total utility is maximized. Minimum Utility MU It speaks about increased utility as a result of consuming an extra unit of a commodity.

The change in overall utility is known as marginal utility.

When she accepts two donuts, her marginal utility is three (8–5=3).

Her marginal utility for eating three donuts is 1 (9 – 8).

Since 3 is more expensive than and closer to price at 2, she should only eat 2 doughnuts.

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Answer: Dilation by 1/4 and translation

Step-by-step explanation:

Answer:

x (the number) = 19

Step-by-step explanation:

We can translate this into a linear equation. We will use x as our variable (a number). We have:

4x + 21 = 6x - 17

We will add 17 to both sides, and subtract 4x from both sides, giving us:

38 = 2x

Then dividing both sides by 2 gives us:

x = 19

So, x (the number) = 19.

Hope this helped!

Please give Brainliest if possible!

Answer:

4x + 21= -17+6x

-2x= -38

x=19

Answer:

a) In order to write the ratio h:k in its simplest form, we need to find the greatest common divisor (GCD) of h and k and divide both h and k by that value.

The GCD of 2 and 6 is 2.

So the simplified ratio h:k is 2/2:6/2 = 1:3

b) In order to write the ratio k:l in its simplest form, we need to find the greatest common divisor (GCD) of k and l and divide both k and l by that value.

The GCD of 6 and 9 is 3.

So the simplified ratio k:l is 6/3:9/3 = 2:3

Answer:

the ratio of h and k in simplest form is 1:3

the ratio of k and l is 2:3

Answer:

Step-by-step explanation:

Hello, I am the same guy that told you that your previous question had no image.

Ok, so slope formula is m = (y₂ - y₁)/(x₂ - x₁)

Two coordinates on the given line is (-2 , 1) and (3, 5)

Just substitute the values there.

m = (5 - 1)/(3 + 2)

= 4/5

slope/m = 4/5

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