A wire that is 40 cm long is bent into the shape of a rectangle whose width is x cm.

(i) Find an expression, in terms of x, for the area, A cm², of the rectangle. Find the x-intercepts on the graph of A against x.
(ii) Find the x-intercepts on the graph of A against x.
(iii) Find the maximum area that can be formed.
(iv) Show that this maximum area is only possible if the shape formed is a square.

How do I solve (iii) and (iv)? Thank you!​

Yes, it is possible to relate a given quantity to an indicated amount using more than one symbol because variables are often used to represent unknown quantities and different symbols can be used.

If you want to find the volume of a cylinder, you can use the formula V = πr^2h, where V represents the volume, r represents the radius, h represents the height, and π represents pi. Using different symbols to represent the same quantity can be helpful in different situations and can make the mathematics clearer and more concise.

For example, instead of using the symbol V to represent the volume of a cylinder, you could use the symbol V₁. This can make it clear that the volume being calculated is the volume of a cylinder, and not the volume of some other shape.

In conclusion, using different symbols to represent the same quantity can help to make the mathematics clearer, more concise, and more specific to the problem being solved.

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254 degrees is the coterminal to 614°

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

Coterminal angles are angles in standard position (angles with the initial side on the positive x-axis) that have a common terminal side.

To find coterminal angles when given a positive angle, subtract 360 degrees to the given angle until you get an angle between 0 and 360.

614-360=254

254 lies between 0 and 360 degrees.

Hence, 254 degrees is the coterminal to 614°

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Answer: (-8,104)

you have to find the component form of the resultant vector.

Sum of angles,

∠6 +∠2 +∠5 = 180°

Alternate angles are angles that occur on opposite sides of the transversal line and have the same size. There are two different types of alternate angles, alternate interior angles and alternate exterior angles.

Given,

y || x

To prove,

∠5 +∠2 +∠6 = 180°

∠1, ∠2, ∠3 are on straight line,

∠1 +∠2 +∠3 = 180°

∠1 = ∠5    (alternate angles on transversal AC)

∠3 = ∠6    (alternate angles on transversal AB)

∠5 +∠2 +∠6 = 180°

Hence, ∠5 +∠2 +∠6 = 180° is proved.

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Answer:

18x + 346

Step-by-step explanation:

8(x+12) + 10(x+25)

8x + 96 + 10x + 250

18x + 346

1). The two adjacent angles are ∠1 and ∠2.

2). The two vertically opposite angles are ∠1 = ∠3.

3). The value of x will be 10.

Perpendicular lines, intersecting lines, transversal lines, and other types of lines will be covered. An angle is a shape formed by two rays emerging from a common point. In this field, you may also come across alternate and corresponding angles.

1.) The two adjacent angles will be:-

∠1 and ∠2

The two angles are just next to each other which is why they are adjacent angles.

2). The two vertically opposite angles are ∠1 = ∠3. They are opposite to each other so their values will also be the same.

3). The value of x will be calculated as:-

9x = 90

x = 90 / 9

x = 10

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The terms of the sequence are t1 = 8, t10 = 39.5 and t23 = 85

From the question, we have the following function definition that can be used in our computation:

tn=3.5n+4.5

Using the above as a guide, we have the following equations:

t(1) = 3.5(1) + 4.5 = 8

t(10) = 3.5(10) + 4.5 = 39.5

For 85,, we have

3.5n+4.5 = 85

This gives

3.5n = 80.5

Dvide by 3.5

n = 23

Hence, 85 is the 23rd term of the sequence

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The difference between the sample standard deviation (s) and the population standard deviation (σ) will generally be greater for the data set with fewer data values.

This is because the sample standard deviation is an estimate of the population standard deviation, and with a smaller sample size, the estimate is likely to be less accurate.
In this case, the data set with 20 data values has a smaller sample size, so the difference between s and σ will be greater for this data set compared to the data set with 50 data values. The larger the sample size, the more representative the sample is of the population and the more accurate the estimate of the population standard deviation is likely to be.
It's worth noting that while the sample standard deviation is a useful measure of variability in the sample, it is not the same as the population standard deviation, which is a true measure of the variability in the population. The sample standard deviation can be used to make inferences about the population standard deviation, but it is important to consider the sample size and other factors that may affect the accuracy of the estimate

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Answer:

9.4 ounces of oat meal

Step-by-step explanation:

37.6 x 10 = 376

4 x 10 = 40

we do this to get rid of the decimal

376/40=188/20=94/10=47/5=9(2/5)=9.4 ounces of oat meal

Answer:

[tex]\displaystyle \sqrt{3}\biggr[\cos\biggr(\frac{11\pi}{9}\biggr)+i\sin\biggr(\frac{11\pi}{9}\biggr)\biggr][/tex]

Step-by-step explanation:

Use the nth-root formula for complex numbers in polar form

[tex]\displaystyle \sqrt[n]{r}\biggr[\text{cis}\biggr(\frac{\theta+2\pi k}{n}\biggr)\biggr]\\ \\\\\sqrt[2]{3}\biggr[\text{cis}\biggr(\frac{\frac{4\pi}{9}+2\pi(1)}{2}\biggr)\biggr]\\ \\\\\sqrt{3}\biggr[\text{cis}\biggr(\frac{2\pi}{9}+\pi\biggr)\biggr]\\\\\\\sqrt{3}\biggr[\text{cis}\biggr(\frac{11\pi}{9}\biggr)\biggr][/tex]

[tex]\displaystyle \sqrt{3}\biggr[\cos\biggr(\frac{11\pi}{9}\biggr)+i\sin\biggr(\frac{11\pi}{9}\biggr)\biggr][/tex]

Note that this is one of the square roots of the complex number with k = n-1 = 2-1 = 1, but is the only applicable answer to this problem.

Erika has 6.53 kilograms of apples, which is more than the 6 kilograms she needed for the recipe. Therefore, she has enough apples to make the recipe.

To determine if Erika has at least 6 kilograms of apples, we need to add the weight of all three bags of apples. The total weight of the apples is:

It is given that:

There is 2.56 kg of red apples.

There is 1.18 kg of green apples.

And, 2.79 kg of yellow Apples.

Therefore,

2.56 kg + 1.18 kg + 2.79 kg = 6.53 kg

Erica needs a certain number of apples for her recipe, i.e. 6 kg. She goes to her store and chooses three different bags of apples: a 2.56 kg bag of red apples, a 1.18 kg bag of green apples, and a 2.79 kg bag of yellow apples.

To determine if you have enough apples, you must add up the weight of all three bags. The total weight of the apples is 6.53 kg. This means that Erika has more than 6 kg of apples she needs and has enough for the recipe. It's important to note that Erica has a surplus of apples that can come in handy if she needs more apples for recipes or later.

Combining different types of apples can also add variety and flavor to your recipe.

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Two details are that support the response:

The oak is revered as a cosmic repository of knowledge represented by its imposing might. It develops at its own pace, gradually yet steadily. Due of its size and longevity, oak is frequently connected with dignity, nobility, and knowledge as well. Since the very beginnings of human interaction with oaks, a highly potent symbolic picture of oaks has emerged, in which these trees have come to be connected with immortality, power, consistency, perseverance, fertility, justice, and honesty.

Two responses are:

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For the trigonometric function -0.575 = cos c the value is obtained as c = 2.18340 + 2πn and c = 2.18340 - 2πn.

What is trigonometric function?

Simply put, trigonometric functions also referred to as circular functions are the functions of a triangle's angle. This means that these trig functions provide the relationship between the angles and sides of a triangle.

The trigonometric function is -

-0.575 = cos c

The value for c is -

cos c = -0.575

c = arccos (-0.575)

c = 2.18340 + 2πn

In radians the value of c is -

c = 2.18340 + 2πn and c = 2.18340 - 2πn

In degrees the value of c is -

c = 125.1° + 360° and c = 125.1° - 360°

Therefore, the value of c is c = 2.18340 + 2πn.

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Answer:

£ 162

Step-by-step explanation:

Ratio:

    Ratio of money = 2 : 3

Edward receives two parts of the money and Thomas receives three parts of the money.

Edward's share = 2x

Thomas share = 3x

Thomas receives £243 which is three parts. Find 'x'.

           Thomas share = £ 243

                              3x  = 243

         Divide both sides by 3,

                                 x = 243 ÷ 3

                                 x = 81

Now, find Edward's share.

Edward's share = 2x

                          = 2*81

                         = £ 162

Answer:

£ 162

Step-by-step explanation:

Ratio:

   Ratio of money = 2 : 3

Edward receives two parts of the money and Thomas receives three parts of the money.

Edward's share = 2x

Thomas share = 3x

Thomas receives £243 which is three parts. Find 'x'.

          Thomas share = £ 243

                             3x  = 243

        Divide both sides by 3,

                                x = 243 ÷ 3

                                x = 81

Now, find Edward's share.

Edward's share = 2x

                         = 2*81

                        = £ 162

The triangle ABC is equal to triangle ADE by Angle-Angle-Side theorem.

What are triangles?

Triangles are a particular sort of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional figure shown here. An example of a 3-sided polygon is a triangle. The total of a triangle's three angles equals 180 degrees. One plane completely encloses the triangle.

In triangle ABC and ADE -

It can be seen that ∠B = ∠E.

Also the line segment AB is equal to line segment AE.

AB = AE

The angles ∠BAC and ∠DAE are vertically opposite to each other.

So, they are also equal.

∠BAC = ∠DAE

Angle-Angle-Side is abbreviated as AAS. The triangles are said to be congruent when two angles and a non-included side of one triangle match the corresponding angles and sides of another triangle.

Therefore, Δ ABC ≅ Δ ADE according to AAS theorem.

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For the significance test given, the error will be a type one error.

The results of tests for statistical significance show whether apparent variations in assessment results are the product of random variation or sampling mistake. The given parts can be answered as -

a) The analysis of the given question was conducted with a likelihood of .05 for a type one error. This is because the level of significance for it is .05 as well. Therefore, such a situation implies that regardless of whether the null hypothesis is correct and accurate there is still a five percent chance that it will be incorrect or will be rejected.

b) The probability that a representative sample will be equally extreme or more intense than the one that was correctly predicted is known as the p-value when the null hypothesis is true. In this case, the p-value is only .03 and drops below the .05 criterion of significance. This reveals that the generic parameter-supported null thesis is categorically rejected. This study would thus, further result in the rejection of the null hypothesis.

c) A decision error from the test could be either a Type I error or a Type II error. While a Type II error happens when the null hypothesis is true but not rejected, a Type I error happens when the opposite is true. Since the null hypothesis was true but was rejected by chance in this situation, any judgement error that the test produced would be of the Type I variety.

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Answer: 132 degrees

Step-by-step explanation: 180 degrees ( the degree of a straight line) - 48 equals 132

Answer:

Step-by-step explanation:

7+m>5

Answer:

m = -2

Step-by-step explanation:

yes.

Answer: no

Step-by-step explanation:

jose added the same variable, (n) to the left side that he subtracted from the right side. so the eqation is not correct

The cost of a restricted pass is equals to £35 and the cost of a full pass is equals to £20.

We have, Brian and Bob visit a ski resort.

In case of Brain,

Number of full passes = 3

Number of restricted passes = 4

In case of Bob,

Number of full passes = 2

Number of restricted passes = 3

Let " £r" and " £p" be the cost of each full pass and restricted pass. Then, on basis of problem,

Total cost of passes in case of brain = £185

=> 3p + 4r = 185 --(1)

Similarly, Total cost of passes in case of bob

= £130

=> 2p + 3r = 130 --(2)

Now, equation (1) and (2) formed a system of two linear equations. We have to calculate the value of "r" and "p" . So, using the Elimination method,

Multiplying the equation (1) and equation (2) by 2 and 3 respectively and then equation (2) from (1) to eliminate the variable "p".

=> 2(3p + 4r) - 3(2p + 3r) = 2× 185 - 3× 130

=> 6p + 8r - 6p - 9r = 370 - 390

=> -r = - 20

=> r = 20

then from equation (1) , 3p + 4(20) = 185

=> 3p = 185 - 80 = 105

=> p = 105/3 = 35

Hence, the required values of r = £20 and p = £35.

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Answer:

C. 5 hours

Step-by-step explanation:

We know

One delivery driver can complete a route in 6h

The rate is 1/6

One delivery driver can complete a route in 5h

The rate is 1/5

To solve this, we use the equation

rate + rate = together rate

1/6 + 1/5 = 1/y

10/60 + 12/60 = 1/y

22/60 = 1/y

y =  5 hours

So, the answer is C. 5 hours

Answer:

shown below

Explanation:

you can take the y-intercept and plot that right away. The y intercept for this equation is 1, so you plot a point at (0,1). Then you can use the slope to find your next point. You can put the slope, 6, into a fraction form, making it  “6/1” then you use rise/run and go up 6, over 1, and plot your next dot at (7,1). You then take a straight edge and graph the line that intercepts both points. It looks like the picture below.

When we want to find all the points on a surface where the tangent plane is horizontal, we are essentially looking for the points where the surface has a horizontal slope. The points on the surface where the tangent plane is horizontal are the points (0, 0, 0).

To find these points, we can use the partial derivative test. First, we calculate the partial derivatives of the surface function with respect to x and y, and set them equal to zero. These equations will give us the x and y values of the points where the slope is zero.

Next, we plug these values back into the original surface function to obtain the z-coordinate of the points. These are the points on the surface where the tangent plane is horizontal.

For example, let's consider the surface function z = x^2 + y^2. To find the points on this surface where the tangent plane is horizontal, we need to find the x and y values where the partial derivatives of z with respect to x and y are equal to zero.

Taking the partial derivative of z with respect to x, we get:

∂z/∂x = 2x

Setting this equal to zero, we get: 2x = 0

Solving for x, we get x = 0.

Taking the partial derivative of z with respect to y, we get:

∂z/∂y = 2y

Setting this equal to zero, we get: 2y = 0

Solving for y, we get y = 0.

Therefore, the points on the surface where the tangent plane is horizontal are the points (0, 0, 0).

In summary, when we want to find all the points on a surface where the tangent plane is horizontal, we can use the partial derivative test and set the partial derivatives of the surface function with respect to x and y equal to zero. We can then plug these values back into the original surface function to obtain the z-coordinate of the points.

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Answer:

x²+y²+2xy

Step-by-step explanation:

Hope it helps! If it did, please thank, rate and mark brainliest!

Answer:

O x² + 2xy + y². The result of squaring a binomial is the sum of the square of the first term in the binomial, the product of twice the first term and the second term and the square of the second term: (x + y)² = x² + 2xy + y².

Answer: 23

Step-by-step explanation:

This is another parallel line theorem that is important. Over here, we will need to use the concept of corresponding angles (refer to images below). In corresponding angles, they are equal. So we know the corresponding angle to [tex]x + 1[/tex] will be equal to [tex]x + 1[/tex] since corresponding angles are equal.

Now we have to use the fact that angles on a line add up to 180°. Keeping this in mind, we can now solve it like this:

[tex](x + 1) + (7x-5) = 180\\x + 1 + 7x - 5 = 180\\8x - 4 = 180\\8x = 184\\x = 23\\\\[/tex]

Once again, if there is anything you don't understand, please reply back :)

Expression is; 29 - x = 16 an expression to represent this situation.

Where in mathematics is an expression?

An expression in mathematics is made up of a mixture of variables, numbers, and functions (such as addition, subtraction, multiplication or division etc.) In some ways, phrases and expressions are comparable.

                               Term is a mathematical concept that refers to a constant, a single variable, or a mixture of variables and constants along with multiplication or division. Example of an algebraic expression: 3x + 9; 5x + 10

We are told that at lunchtime, it was 29 degrees Celsius and that by sunset, the temperature had dropped to 16 degrees Celsius.

Let the drop be x.

Thus;

29 - x = 16

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The complete question is -

On Tuesday at lunchtime, it was 29 degrees Celsius. By sunset, the temperature had dropped to 16 degrees Celsius. Please write an expression for the situation, and draw a number line diagram.

Answer:

6902.97m³

Step-by-step explanation:

volume of a sphere =4/3πr³

=4/3×3.142×13×13×13=9203.965m³

1/4×9203.965=2300.99125m³

9203.965-2300.99125=6902.974

=6902.97m³

If Bill does not really know if the concept will be viable, so he develops a limited menu and has friends and family fill out a questionnaire to gather information. Bill is using creation in action.

What is questionnaire?

A questionnaire is a type of research tool used to collect data from respondents for a survey or statistical analysis. It consists of a set of questions (or other forms of prompts). Typically, a research questionnaire will have both closed-ended and open-ended questions. Long-term, open-ended inquiries provide the respondent the chance to go into more detail. The Statistical Society of London created the research questionnaire in 1838. Although statistical analysis of the replies is frequently the goal of questionnaire design, this is not always the case.

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