PLEASE EXPLAIN AND SHOW ALL YOUR WORK

The right angle lies opposite to the greater side that is 6.5 cm. Therefore, the given sides are not of a right- angled triangle.

step1

for checking a triangle can be made by these sides you have to check if the longest side is smaller than or equal to the sum of other two sides i.e.

2.5cm+7cm=9.5cm

8.5cm>6.5cm

which means the triangle can be made by these sides

step2

As we know,

In a Right-angled Triangle: By Pythagoras Theorem,

hypotenuse² = base² + perpendicular²

As we know the hypotenuse is the longest side of the triangle, So

Hypotenuse = 6.5 cm

Verifying the Pythagoras theorem,

6.5²= 7²+ 2.5²

42.25=49+6.25

42.25=55.25

Hence it is not  a right-angled triangle.

The Right-angle lies on the opposite of the longest side (hypotenuse) So the right angle is at the place where 2.5 cm side and 7 cm side meet.

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Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.

cos (61 degrees) = c/19

plug in cos(61) degrees into your calculator to get .484

484 = c/19

Multiply both sides by 19 to isolate c by itself.

9.20 = c

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Step-by-step explanation:

Rewrite in slope-intercept form. Subtract x x from both sides of the equation. Divide each term in −y=5−x - y = 5 - x by −1 - 1 and simplify.

Here is a math function to find the height of a stack of x chairs:

y = (x/10)h

y = (x/10)h

where:

This function calculates the total height of the stack by dividing the number of chairs in the stack (x) by 10, and then multiplying by the height of one chair (h).

This is because we have assumed that groups of 10 chairs will take up one unit of height.

Alternatively, if the number of chairs in the stack is not divisible by 10, we can use the ceiling function to round up to the nearest multiple of 10

y = ceil(x/10)h

where:

ceil(x) = smallest integer greater than or equal to x

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Our Pythagorean triplets will be (3,4,5) and (6,8,10).

So what is the Pythagorean triplet?

The square of the greatest number in a Pythagorean triplet equals the sum of the squares of the other two numbers.

The greatest side in a right-angled triangle is called the hypotenuse.

So, in our first triplet (3,4,5) the greatest side is 5. So, hypotenuse = 5.

=  [tex]hypotenuse^{2}[/tex] = [tex]5^{2}[/tex] = 25.

Now, [tex]3^{2}[/tex] + [tex]4^{2}[/tex] = 9 + 16 = 25.

So, [tex]5^{2}[/tex] = [tex]3^{2}[/tex] + [tex]4^{2}[/tex].

Thus (3,4,5) is a Pythagorean triplet.

In the second case (6,8,10) hypotenuse = 10.

= [tex]hypotenuse^{2}[/tex] = [tex]10^{2}[/tex].

Now, [tex]6^{2}[/tex] + [tex]8^{2}[/tex] = 36 + 64 = 100.

So, [tex]10^{2}[/tex] = [tex]6^{2}[/tex] + [tex]8^{2}[/tex].

Thus (6,8,10) is a Pythagorean triplet.

In the Third case (8,10,12) Hypotenuse = 12.

= [tex]hypotenuse^{2}[/tex] = [tex]12^{2}[/tex] = 144.

Now, [tex]8^{2}[/tex] + [tex]10^{2}[/tex] = 64 + 100 = 164.

So, [tex]12^{2}[/tex] [tex]\neq[/tex] [tex]8^{2}[/tex] + [tex]10^{2}[/tex].

Thus (8,10,12) is not a Pythagorean Triplet.

Therefore our two results (3,4,5) and (6,8,10) are Pythagorean triplets.

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The number of orders of magnitude that the kilogram is as heavy as the microgram is 10⁹.

The kilogram and the microgram are multiples of the gram which is the basic unit for measuring the mass of objects.

The kilogram is a higher multiple of the gram whereas the microgram is a smaller multiple of the gram.

1 kilograms = 1000 grams

1 microgram = 1/1000000 gram

Hence,

1 microgram = 1/1000000 * 1/1000 kilograms

Therefore, the ratio of kilograms to micrograms is 10⁹ : 1

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Therefore ,the solution to the given problem of linear equation comes out to be m =1,b =24, z = 21 and r =-7.

A function is said to be linear if it can be written algebraically as y=mx+b. The y-intercept is m, and the slope is B. Because y and x are both elements in the previous sentence, it is widely termed to as a 2 different equation system. Linear equations featuring two variables are known as bivariate equations. Two examples of the many applications of linear equations are x + z = 2 , 3z - y + z = 3. If a mathematical equation has the form y=mx+b, where m stands for the slope and b for the y-intercept, it is said to be linear. The equation is represented as Y=mx+b, where m denotes the elevation and b the y-intercept.

Here,

Given :

=> 6m =6

=> m =1

2)

=>b/-8 =-3

=> b =24

3)

=>3/7 * z  =9

=> z = 9 * 7 /3

=> z = 21

4)

=> -5/7 *r = 5

=> r =-7

Therefore ,the solution to the given problem of linear equation comes out to be m =1,b =24, z = 21 and r =-7.

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To meet, Armand and Jill will both travel for an equal length of time.

50t + 60t = 247.5 is the formula used to calculate the time, t, required for their meeting.

To meet Armand, Jill will travel 135 miles.

given that

Despite being 247.5 miles apart, Armand and Jill are heading in the same direction.

50 mph is the speed at which Armand is moving.

and Jill's vehicle is moving at a 60 mph pace.

Allow them to connect after t hours.

We understand that Distance=Speed*Time.

Armand traveled 50 miles, thus.

Jill traveled 60 t of distance.

Now that they are moving in that direction, do the following:

50t+60t=247.5--------------

(a)

1)To meet, Armand and Jill will both travel the same distance.

The value of 50t and 60t will differ for the same t, hence this statement is false.

2)Jill and Armand will both travel for an equal length of time to meet.

This is accurate because they will collide at the same time.

3)50t + 60t = 247.5 is the formula used to determine how long it will take for them to meet.

This statement is true.

4)They won't meet until 4.5 hours have passed.

We will calculate the value of t using equation (a) and determine if t=4.5 or not.

As 50t+60t=247.5

⇒ 110t=247.5

⇒ t=247.5/110=2.25

As a result, it will take 2.25 hours for them to finally meet.

Option 4 is therefore unsuitable.

5)To meet Armand, Jill will travel 135 miles.

Jill must travel 60 miles to meet Armand.

As t=2.25

60t = 60 x 2.25 = 135 miles.

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Margie worked for 47 hours.

The given table is about the times recorded on the timesheet for the week.

We have to calculate the total time she worked for.

From 7:05 to 3:58

If 7:05 is a.m. then 3:58 will be 15:58 pm.

By subtraction of these timings we can get the number of hours she has worked.

15:58 - 07:05 = 8:53 (8 hours 53 minutes)

From 7:30 a.m. to 17:01 pm

17:01 - 07:30 = 9:31 (9 hours 31 minutes)

From 8:01 a.m. to 17:32 pm

17:32 - 08:01 = 09:31 ( 9 hours 31 minutes)

From 07:22 a.m. to 16:46 pm

16:46 - 07:22 = 09:24 (9 hours 24 minutes)

From 6:55 am to 16:31 pm

16:31 - 06:55 = 9:36 (9 hours 36 minutes)

Therefore, total time she worked = 8:53 + 9:31 + 9:31 + 9:24 + 9:36 = 44:175 (44 hours 175 minutes)

Now we will convert minutes to hours

175 minutes = 2 hours 55 minutes

So total working hours = 44 hours + 2 hours 55 minutes = 46 hours 55 minutes ≈ 47 hours

Therefore, Margie worked for 47 hours.

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The value of x for the given expression is found as 2189/3.

The stated expression is-

3x − 2 = 3^7

Obtain the value of 3^7 by solving its power.

3x − 2 = 2187

(3x − 2) + 2  = 2187 + 2

3x − 2 + 2  = 2189

3x  = 2189

3x / 3  = 2189 / 3

x = 2189/3

Thus, the value of x for the given expression is found as 2189/3.

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The correct question is-

Solve 3x − 2 = 3^7 and find the value of x.

It is possible to construct a triangle whose sides are 4.5 cm 6 cm and 7.5 cm because the sum of two sides are greater than third sides.

In the given question, we have to check that it is possible to construct a triangle whose sides are 4.5 cm 6 cm and 7.5 cm.

To check whether the given sides can make a triangle or not, we have to check that the sum of two sides always grater than the third side.

To check this we firstly add the 4.5 and 6

4.5 + 6 > 7.5

10.5 > 7.5

Now we add 6 and 7.5

6 + 7.5 > 4.5

13.5 > 4.5

Now we add 4.5 and 7.5

7.5 + 4.5 > 6

12 > 6

It is possible to construct a triangle whose sides are 4.5 cm 6 cm and 7.5 cm because the sum of two sides are greater than third sides.

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The price of one orange is £0.45 and one cauliflower is £1.1.

An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation. This math operation can be addition, subtraction, multiplication, or division. For example, the phrase “6 added to some number” can be written as the expression x + 6, where the variable x represents the unknown number.

Let's consider the price of one orange be x and price of one cauliflower is y.

so, from given conditions,

2x + y = 2

y = 2 - 2x         - ( 1 )

4x + y = 2.90   - ( 2 )

substitute equation (1) in equation (2),

4x + 2 - 2x = 2.90

4x - 2x = 2.90 - 2

2x = 0.90

x = 0.90 / 2

x = 0.45

now, put the value of x in equation ( 1 ),

y = 2 - 2 × 0.45

y = 2 - 0.9

y = 1.1

Therefore, the price of one orange is £0.45 and one cauliflower is £1.1.

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A U B= { If x is a factor of 6 and y is a prime number}, then The collection of elements that belong to either set A or set B, or to both sets A and B, is the union of the two sets A and B.

[tex]$A=\{x \leq 5 ; x \in N\}$[/tex]

[tex]$: \mathrm{A}=\{1,2,3,4,5\}$\\$\therefore \mathrm{A} \mid=5$[/tex]

The following sets have been entered by you:

A = {(x: If x is a factor, then 6)}

B ={ ( y, where y is a prime number ) }.

A and B are combined to form:

[tex]$A \cup B$[/tex] = { If x is a factor of 6 and y is a prime number}, then

The collection of elements that belong to either set A or set B, or to both sets A and B, is the union of the two sets A and B. We discover togetherness in two steps: STEP 1: Compile a list of each component from each set.

[tex]$$\{(x: \text { xisafactorof } 6), y: \text { yisaprimenumber }\}$$[/tex]

Remove any components that are duplicates in step 2 to obtain:

[tex]$$A \cup B=\{(x: \text { xisafactorof } 6), y: \text { yisaprimenumber }\}$$[/tex]

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The scale factor is greater than 1.

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Yes, the given statement that prime number is infinite is true.

As given in the question,

Let us consider there are finite prime numbers.

The finite prime numbers be P₁ , P₂, P₃ , ......., Pₙ

Now let us consider there exist a number which represents the product of all the given numbers

P =  P₁ × P₂ × P₃ × .......× Pₙ

To make P as a prime number add 1 to it.

P = P₁ × P₂ × P₃ × .......× Pₙ + 1

It represents that P is the next prime numbers to the given 'n' prime number.

This implies that

Out supposition is wrong.

Therefore, there exist infinite number of prime numbers.

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So on solving the provided question we can say  that factors 8 = 1,2,4,8 factor 20 = 1,2,4,5,10,20

Any natural number other than 1 with just itself and the number 1 as its divisors is considered a prime factor. Actually, 2, 3, 5, 7, 11, and so on are some of the first prime numbers. an amount that has been multiplied to produce another amount. By dividing 15 by 3 and 5, for instance, we get 3 5 = 15. main elements: Prime factors include all factors that are prime but are not composite. A few prime factors of 30 are 2, 3, and 5. Only 2 and 3 are prime factors of 12, so listing 2 twice as 2 2 3 (or 22 3) is necessary to factorize 12. The sum of 2 + 3 is not 12.

here,

factors 8 = 1,2,4,8

factor 20 = 1,2,4,5,10,20

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Answer: 4x+y-6=0

Step-by-step explanation:

To find the equation of the line that is parallel to 4x+y+1=0, we need to work in terms of slope-intercept form, which is y=mx+b.

4x+y+1=0       [subtract both sides by 4x]

y+1=-4x          [subtract both sides by 1]

y=-4x-1

Our original equation is in terms of y=mx+b.

The properties of parallel lines is that they NEVER touch. Therefore the slope must be the same. The y-intercept can be different though.

y=-4x+b           [plug in (1,2)]

2=-4(1)+b          [multiply]

2=-4+b             [add both sides by 4]

b=6

We can fill in our equation now.

y=-4x+6

We need to make our equation match the original, so let's manipulate it.

y=-4x+6           [add both sides by 4x]

4x+y=6            [subtract both sides by 6]

4x+y-6=0

Therefore 4x+y-6=0 is the answer.

A 2 3 aspect ratio is an image size format that refers to the proportion of width to height.

Ratio is a comparison between two or more quantities expressed as a fraction, or a set of relative quantities. It is used to compare the size of one number to another, or to compare changes over time. Ratios can be expressed in words, as fractions, or as decimals. Ratios are an important concept in mathematics, used to analyze data and solve problems.

It is commonly used in photography and video and is expressed as two numbers separated by a colon. The first number represents the width and the second number represents the height. For example, a 2 3 aspect ratio would be expressed as 2:3, meaning that the width is twice as wide as the height. This aspect ratio is also known as the "Golden Ratio" and is often used for print and digital media.

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Answer:

Step-by-step explanation:

area of trapezoid = 1/2 (a + b) h

where 'a' and 'b' are parallel sides.

and 'h' is height.

                 area     = 1/2 (9 + b) 18.9

                  226.8 = 1/2 (9 + b) 18.9

                   226.8 × 2 = (9 + b) 18.9

                     453.6 = (9 + b) 18.9

                     453.6 ÷ 18.9 = (9 + b)

                        24 = (9 + b)

                          b = 15 millimeters

Answer:

B 4 times

Step-by-step explanation:

since the area is

side length × side length,

any doubling of the side length is included twice in this multiplication.

2×2 = 4

and so, answer B is correct. the new area will be 4 times the old one.

The value of the multiplication of the given fractions  [tex](\frac{1}{2} - \frac{2}{5}) * (- \frac{5}{7} + \frac{1}{14} )[/tex] is -9/ 140.

In mathematics, a fraction is used to denote a portion or component of the whole. It stands for the proportionate pieces of the whole. Numerator and denominator are the two components that make up a fraction.

A fraction multiplied by another fraction, an integer, or a set of variables is referred to as a fraction. The steps for multiplying fractions are as follows:

Add the numerator to the numerator to multiply. Add the denominator to the denominator and multiply. If necessary, simplify the fractions.

The multiplication of the given numbers is:

[tex](\frac{1}{2} - \frac{2}{5}) * (- \frac{5}{7} + \frac{1}{14} ) \\\\(\frac{5-4}{10} ) * (\frac{-10 + 1}{14} )\\\\\frac{1}{10} * \frac{- 9}{14} \\\\\frac{-9}{140}[/tex]

Hence, value of the multiplication of the given fractions [tex](\frac{1}{2} - \frac{2}{5}) * (- \frac{5}{7} + \frac{1}{14} )[/tex] is -9/ 140.

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Answer:

Step-by-step explanation:

x and y​ are not proportional and the value of the card in 2011​ is $33.14.

Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other. That constant is known as the "constant of proportionality".

Given that, when he retired in 2000 his card was worth ​$7.73. The value has increased by ​$2.31 each year since then.

Let the value of the card y in dollars and the number of years x the player has been in retirement.

Now equation is y=7.73+2.31x

When x=1

y=$10.04

When x=2

y=7.73+2.31(2)

y=$12.35

When x and y are proportional

1/10.04 ≠2/12.35

Now, the value of the card in 2011​

y=7.73+2.31(11)

y=$33.14

Hence, x and y​ are not proportional and the value of the card in 2011​ is $33.14.

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Answer:

Last option: 5/8

Step-by-step explanation:

sin(angle) = opposite / hypotenuse

So, sin(B) = 4/6.4 = 20/32 = 10/16 = 5/8

Hope this helps!

As a result, the graph illustrating how one face's side width and diameter are linearly associated is the resolution to the given linear equation problem.

One degree is the highest number of levels that can be employed in a linear model. Nonlinearity is the property of any equation having a theoretical extent of at least two. On a map, there is a horizontal line with a straightforward equation. The graph shows the curve that a nonlinear equation produces.

Here,

the side lengths and perimeter of one face are linearly connected.

formula for lines

A regular model is described by the equation y = mx + b.

If b is in fact the y intercept and m is the changing rate, then y and x are variable.

One face's length and perimeter have a linear relationship, as seen by the graph.

As a result, the graph illustrating how one face's edge length or perimeter are linearly associated is the answer to the given linear equation problem.

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Sequences can start at either 0 or 1, depending on the specific sequence and the conventions used.

In mathematics, there are two main ways to number the elements of a sequence: zero-indexing and one-indexing. In zero-indexing, the first element of a sequence is assigned the index 0, the second element is assigned the index 1, and so on. This is the standard convention used in computer science and programming.

On the other hand, in one-indexing, the first element of a sequence is assigned the index 1, the second element is assigned the index 2, and so on. This is the standard convention used in mathematics and many other fields.

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The product is the answer to a multiplication problem.

You can obtain the result by repeatedly adding the whole number of groups in the problem. This is known as repeated addition. We are aware that multiplication is the term used to describe repeated addition. On a number line, we start at 0 and go steadily to the right side of the number line to multiply integers. Multiplication is one of the four basic mathematical operations, along with addition, subtraction, and division. In arithmetic, multiply refers to continuously adding sets of the same size. In mathematics, multiplying the numbers yields the product of two or more integers.

The multiplication of two integers in mathematics represents the repeated addition of one number in respect to another. These numbers can be natural numbers, fractions, integers, whole numbers, etc. M is either added to itself 'n' times or subtracted from itself when m is multiplied by n.

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Total cost of dinner including tip = $861.40

In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.

Given

Cost of the dinner = $730

Amount tipped to the caterers = 18% of 730

                                                   = 18/100 × 730

                                                   = $131.40

Total cost of dinner = 730 + 131.40

Total cost of dinner = $861.40

Hence, $861.40 is the total cost of the dinner including tip.

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An example of a pattern rule is "add 3" which means that to find the next term in a sequence, you add 3 to the previous term.

A pattern rule is a mathematical relationship used to find the value of each term in a sequence. To describe certain sequences, a pattern rule can be established. This is an algebraic equation that enables you to quickly find the value of a term in a sequence using its rank.

To write a rule for a sequence, you need to identify the pattern. This involves looking at the differences between the numbers and seeing if there is a pattern of increasing or decreasing numbers. Once you have identified the pattern, you can then write a rule that expresses that pattern.

Examples of pattern sequences include the Fibonacci sequence (1,1,2,3,5,8,13,21,34, etc.), the even numbers (2,4,6,8,10, etc.), and the multiples of 3 (3,6,9,12,15, etc.).

To describe the pattern of a sequence, you need to look at the differences between the numbers and the pattern of increases or decreases. For example, in the Fibonacci sequence, the pattern is that each number is the sum of the two numbers before it so 1+1=2, 1+2=3, 2+3=5, etc.

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One common trick for memorizing the 8 times table is to pair it with the 4 times table.

For example, 8 x 4 = 32, so 8 x 5 = 40 because 5 is one more than 4. Similarly, 8 x 6 = 48 because 6 is two more than 4, and so on. Another trick is to think of it as 8 x 10 = 80 and then subtract 8. For example, 8 x 7 = 80 - 8 = 72.

The eight times table trick states that when you multiply eight by a number between one and five, the result always begins with a digit one lower than the number from one to five. The answer begins with a digit that is two less than the number from 6 to 10 when multiplying 8 by a number between 6 and 10.

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