Is anyone able to help me with this question:
A rectangle with sides 4 cm and 6 cm has the same diagonal as a square.
What is the length of the side of the square.
Give your answer as a surd.

iona) The error is in dividing both sides of the equation by 3

b) the correct answer is 4x + 3y = 12

The given equation: 3y = -4x + 12

To represent in standard form, it must be in the form:

Ax + By = C

rewitiing 3y = -4x + 12 in standard form

3y + 4x = 12

4x + 3y = 12

The student answer: y = -4/3 x + 4

From the above, we can see the student divided both sides of the equation by the coefficient of y. Both sides were divided by 3.

This procedure is only done when finding the slope of an equation and the coeffiecient of y is not 1.

a) The error is in dividing both sides of the equation by 3

b) the correct answer is 4x + 3y = 12

the x intercept: y = 0

4x + 3y = 12

4x + 3(0

The ideal way to find the intercepts of an equation with the "x" and "y" axes is to evaluate both values when the image is 0, as described below:

First let's define equation

An equation is the equality that has mathematical expressions on both sides of it, they can be functions, polynomials or others, there are no limits for them.

  Equations can be graphed, just like a function.

Now that we know what an equation is and its structure, let's explain it with an example.

Let the equation

2y = 4x + 2, determine its intersections with the axes "x" and "y".

First, we clear:

y = (4x + 2)/2

y = 2x + 1

0 = 2x + 1

2x = -1

x = -1/2

y = 2(0) + 1

y = 1

As we can see, to find the intercepts, we only have to evaluate the equation when y = 0 and when x = 0.

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Answer:A

Step-by-step explanation:

Answer:

sales tax is $0.6

total cost is $20.60

Step-by-step explanation:

20*0.03=0.6

20*1.03=20.6

There are 11550 different ways that the line of marbles could be formed in this scenario.

Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. You can choose the components of combos in any order. Permutations and combinations can be mixed up.

As a result, there are (4 + 3 + 4) spots on the line, which equals 11 spots for the 11 marbles.

Given that identical-colored marbles cannot be distinguished.

This means that, for instance, if there are four red marbles in the first, second, third, and fourth positions, moving the four red marbles around these positions won't result in a different arrangement.

Solving by combination,

The total number of ways that four spots can be assigned to red marbles is thus = ¹¹C₄ = 330 ways

The number of ways three yellow marbles can be placed in each allocation of red marbles is equal to ⁷C₃ = 35 ways

The number of ways four slots can be allocated to green marbles for each allocation of red and yellow marbles is equal to ⁴C₄ way = 1

As a result, there are (330 × 35 × 1) = 11550 different ways that the line of marbles could be formed in this scenario.

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Answer:

132 degrees.

Step-by-step explanation:

Line PQS is 180 degrees and angle PQR and angle PRS are supplementary. Since you know this, both of these equations must equal 180 degrees.

(3x-6) +(x+2) = 180

Above is your equation to find X. This is only one part because you need to find the missing value, X. So now you need to solve for x. Assuming you know how to isolate x, you should get:

x = 46

Now the question asks for the angle of line PQR. As you can see in the graph, line PQR is the (3x-6). Since you now know what x is, you can plug in x with 46.

3(46)-6 = 132

Angle PQR is 132 degrees.

Answer: Formula is 2πr^2

Step-by-step explanation:

plug in and it is 196*π

Answer: A= 196\(\pi\)  

Step-by-step explanation:

The area of a circle formula:

A=\(\pi r^{2}\)                       >r=14   substitute in

A=  \(\pi( 14^{2} )\)                >simplify 14²

A= 196\(\pi\)                   > leave pi  like a variable x to leave in terms of pi, do

                                      not multiply by 3.14

Answer is y = -1.01x + 38.19

The formula for calculating the regression line is:

y = a + bx

To find the regression line, we need to calculate two coefficients. They are a and b. where,

b = (NΣxy - ΣxΣy) / (NΣx2 - (Σx)2)and a = y - bx

Here, N = 14N = number of data sets

x = the independent variable

y = the dependent variable

Σ = summationx2 = square of x, i.e., x multiplied by itself

xy = x multiplied by y

Here, x and y have already been given. Thus, we need to calculate the remaining terms for determining the values of a and b.

The following table shows the steps for finding the values of a and b:-

x y x² xy5 26.25 25 131.256 22.3 36 133.87 22.75 49 176.175 22 25 1749 22.35 81 200.1510 19.8 100 19811 17.75 121 194.2512 16.8 144 201.613 17.75 169 299.75514 16.3 196 263.89515 15.95 225 359.2516 13.6 256 219.52Σx = 155 Σy = 255.95Σx² = 2870 Σxy = 4391.81

Now, we can calculate the value of b as:

b = (NΣxy - ΣxΣy) / (NΣx² - (Σx)²)b = (14 x 4391.81 - 155 x 255.95) / (14 x 2870 - 155²)b = -1.0146Next, we can calculate the value of a as:

a = y - bx

a = (Σy / N) - b (Σx / N)a = (255.95 / 14) - (-1.0146 x 155 / 14)a = 38.1921

Thus, the equation of the regression line is:

y = -1.01x + 38.19

The values are rounded off to two decimal places.

Answer:

y = -1.01x + 38.19

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Answers: 5 mph East and 50 mph South

Reason

A velocity has two components: A speed and a direction.

Roger has enough stainless steel pipe to replace the chimney liner, with a slight surplus remaining.

To determine if Roger has enough stainless steel pipe for the chimney liner, we need to convert the given measurements to a consistent unit of measurement. Since the length of the liner required is given in feet, we need to convert the 400 inches of stainless steel pipe to feet.

There are 12 inches in a foot, so 400 inches is equal to 400/12 = 33.33 feet (approximately).

Comparing this converted length of the stainless steel pipe (33.33 feet) with the length of the liner required (33 feet), we can see that Roger does indeed have enough pipe. In fact, he has slightly more than required.

Since the length of the liner required is 33 feet and Roger has 33.33 feet of stainless steel pipe available, there is a surplus of approximately 0.33 feet (about 4 inches) of pipe. This additional length is more than enough to cover any potential measurement errors or adjustments needed during the installation process.

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The conclusion of the symbolised argument is that N implies (O and P). This can be proven using conditional proof and the eighteen rules of inference, or using the rule of conjunctive simplification.

The symbolic argument's conclusion is that N implies (O and P). This can be demonstrated using conditional proof and the eighteen inference rules.

Proof:

1. N ⊃ O (Premise)

2. N ⊃ P (Premise)

3. N (Assumption)

4. O (1,3 Modus Ponens)

5. P (2,3 Modus Ponens)

6. O•P (4,5 Conjunction)

7. N ⊃ (O•P) (3-6 Conditional Proof)

8. N ⊃ (O•P) (2,7 Disjunctive Syllogism)

This leads us to the conclusion that N implies (O and P).

Without the use of conditional proof, the identical result can be reached. The conjunctive simplification rule can be used to do this.

Proof:

1. N ⊃ O (Premise)

2. N ⊃ P (Premise)

3. N (Assumption)

4. O (1,3 Modus Ponens)

5. P (2,3 Modus Ponens)

6. O•P (4,5 Conjunction)

7. N ⊃ (O•P) (Conjunctive Simplification)

Therefore, we have derived the conclusion that N implies (O and P).

Complete Question:

Use conditional proof and the eighteen rules of inference to derive the conclusions of the following symbolized arguments. Having done so, attempt to derive the conclusions without using conditional proof.

1. N ⊃ O

2. N ⊃ P / N ⊃ (O • P)

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Answer:

She's wrong because she didn't distribute correctly. She was supposed to multiply 4 and 12, which makes 48.

The proper answer should be 4x+48

Answer:

78=c98

Step-by-step explanation:

this is easy

Using the rules of complementary angles we calculate that the value of x is  12° .

Pairs of complementary angles have measures which are one right angle.

The two given angles are 29° and ( 5x + 1 )°.

There are a pair of complementary angles.

Therefore 29° + ( 5x + 1 )° = 90 °

or, 5x + 30° = 90 °

or, 5x = 60

or, x = 12°

Therefore using the rules of complementary angles we calculate the value of x is 12°.

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Answer:

88

Step-by-step explanation:

Find the relationship between the numbers;

22÷5=4.4

Therefore,

20×4.4=88

Just a bored teen willing to help,

hope you're having a splendiferous day...

On solving the provided question, we can say that  D, diameter pizza will produce the largest slice is 16

Any straight line segment with an endpoint on the circle and that travels through its center is considered a circle's diameter in geometry. The longest chord of a circle is another way to describe it.

Let r be the radius and  be the angle of a circle.

According with the graph, the area of the sector is given by

A = 1/2r^2∅

The arc length of a circle with radius r  and angle∅   is r∅

The perimeter of the pizza slice is composed of two straight pieces, each of length r inches, and an arc of the circle which you know has length s = rθ inches. Thus the perimeter has length

The perimeter of the pizza slice is composed of two straight pieces, each of length r inches, and an arc of the circle which you know has length s = rθ inches.

Thus the perimeter has length

2r + r∅ = 32 in

r∅ = 32 - 2r

∅ = 32- 2r / r

Now,

A = 1/2r^2[32- 2r / r]

A = 16r - r^2

A' = 16 - 2r 16 -2r = 0

r = 8

A" = -2

so, D, diameter pizza will produce the largest slice is 16

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Answer:

t = 10

Step-by-step explanation:

z^t ⋅ z^5 = z^15

We know that a^b*a^c = a^(b+c)

z^(t+5) = z^15

Since the bases are the same, the exponents are the same

t+5 = 15

t = 15-5

t = 10

Using the equation of the test statistic, it is found that with an increased sample size, the test statistic would decrease and the p-value would increase.

It depends on the test statistic z, as follows.

In all cases, a higher test statistic leads to a lower p-value, and vice-versa.

The equation is given by:

\(t = \frac{\overline{X} - \mu}{\frac{s}{\sqrt{n}}}\)

The parameters are:

From this, it is taken that if the sample size was increased with all other parameters remaining the same, the test statistic would decrease,  and the p-value would increase.

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Polygons are shapes that have the following:

-sides are all straight

-no overlapping

-shape is always closed

Hope this helps :)

Descriptive statistics summarize numbers and inferential statistics determine whether the results are significant.

What is statistics?

The gathering, characterization, analysis, and drawing of inferences from quantitative data are all tasks that fall under the purview of statistics, a subfield of applied mathematics. Probability theory, linear algebra, and differential and integral calculus play major roles in the mathematical theories underlying statistics.

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Answer:

"A plane does not extend infinitely"

Step-by-step explanation:

Lower class limits are 15, 25, 35, 45, 55, 65, 75, Upper class limits are 24, 34, 44, 54, 64, 74, 84, Class width are 10 (all classes have a width of 10), Class midpoints are 19.5, 29.5, 39.5, 49.5, 59.5, 69.5, 79.5, Class boundaries are [15, 25), [25, 35), [35, 44), [45, 54), [55, 64), [65, 74), [75, 84) and Number of individuals included in the summary is 76.

Here are the details for the given frequency distribution:

Lower class limits are the least number among the pair

Here, Lower class limits are 15, 25, 35, 45, 55, 65, 75 respectively.

Upper class limits are the greater number among the pair

Here, upper limit class are 24, 34, 44, 54, 64, 74, 84 respectively.

Class width is the difference between the Lower class limits and Upper class limits which is 10 (all classes have a width of 10).

Class midpoints is the middle point of the lower class limits and Upper class limits which is 19.5, 29.5, 39.5, 49.5, 59.5, 69.5, 79.5 respectively.

Class boundaries are the extreme points of the classes which are  [15, 25), [25, 35), [35, 44), [45, 54), [55, 64), [65, 74), [75, 84) respectively.

Number of individuals = 27 + 33 + 14 + 4 + 6 + 1 + 1

                                     = 76

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The measurement that is closest to the value of x, in centimeters, is given as follows:

14.3.

In this problem, we have a right triangle, in which the legs, which are the sides between the angle of 90º, are of 11.9 cm and 7.9 cm.

Then the hypotenuse x, which is the segment connecting both legs, is obtained using the Pythagorean Theorem.

The Pythagorean Theorem states that the measure of the hypotenuse squared is equals to the sum of the squares of the measures of each side.

Then the length of x is calculated as follows:

x² = 11.9² + 7.9²

x = square root of (11.9² + 7.9²)

x = 14.28.

Closest to 14.3, rounding to the nearest tenth, meaning that the third option is correct.  

We suppose that 11.9 cm and 7.9 cm are the measures of the legs.

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Answer:

14 months

Step-by-step explanation:

Here we are interested in calculating the number of months it will take the food kitchen to exhaust the 283,482 soup cans donated to it by a school of it uses 20,000 cans of soup.

This is pretty straightforward, trust me!

What needs to be done here is to simply divide the total number of soup cans donated by the school by the number of soup cans used by the food kitchen each month.

Mathematically, that would be;

283,482/20,000

A calculator would work here? Right?

And the division equals 14.1741

And to the nearest whole number, that is 14.

And yes there would surely be some left, carried over to the 15th month, but would that sustain them for the month? No

Answer:

143°

When solving angle problems, make sure to label the other angles (even the ones that are not asked) and use them to relate to each other to find the answer.

Answer:

d = 6.246 m

Step-by-step explanation:

Given that,

The distance around a circular pool is 39.25 m.

We need to find how does the lifeguard have to walk from the edge of the pool to the centre of the pool. It means we need to find the radius r of the circle.

ATQ,

Circumference = 2πr = 39.25 m

r is radius

\(r=\dfrac{39.25 }{2\pi}\\\\r=6.246\ m\)

So, the required distance is 6.246 m.

Answer:

- 2a - 6

Step-by-step explanation:

9 - 4(- a + 9) + 3(7 - 2a) ← distribute parenthesis

= 9 + 4a - 36 + 21 - 6a ← collect like terms

= - 2a - 6

the slop is -1 and the y-intercept is (0,7)

acc to our question-

Hence,the slop is -1 and the y-intercept is (0,7)

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