Is centroid and Circumcentre same?

Answer: y=x−2 y = x − 2

Step-by-step explanation:

The area of the rectangular paper left after two semi circles are cut out of it is 186.96 cm².

A rectangle is a closed 2-D shape, having 4 sides, 4 corners, and 4 right angles (90°).The opposite sides of a rectangle are equal and parallel.

To caluculate the area of the paper that remains, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the area of the paper left is 186.96 cm².

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The transformed equation of  is  y = x³ is y =-1/7(x+8)³

Given that :

The equation of y=x^3 and Vertical compression by a factor of 1/7 ,horizontal shift 8 units to the left, reflection across the x axis

Applying the given transformations, we have:

To have a vertical compression by a factor of 1/7, we need to multiply the function by 1/7. So, we have:

y=1/7x³

We must add 8 to x in order to have a horizontal shift of 8 units to the left. We thus have:

y=1/7(x+8)³

A reflection over the x-axis would be the final step, we need to multiply the function by −1. So, we have:

y= -1/7(x+8)³

Therefore, the transformed equation is y= -1/7(x+8)³

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The slope of the perpendicular line to the equation 5x - 4y = -24, is: 4/5.

The slope values of two lines which lie perpendicular to each other on a coordinate plane are always negative reciprocals to each other.

Rewrite the equation, 5x - 4y = -24 in slope-intercept form:

5x - 4y = -24

-4y = 5x - 24

Divide both sides by -4

-4y/-4 = 5x/-4 - 24/-4

y = -5/4x + 6

The slope of y = -5/4x + 6 is -5/4. The negative reciprocal of -5/4 is 4/5. Thus, the slope of the line that is perpendicular to the equation of the given line is: 4/5.

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The greatest counting number that is a factor of both 96 and 120 but has no common factor with 105 other than 1 is 2.

The given number are 96 and 120.

The GCF (Greatest Common Factor) of two or more numbers is the greatest number among all the common factors of the given numbers. The GCF of two natural numbers x and y is the largest possible number that divides both x and y without leaving any remainder.

The factors of given number are

The factors for the number 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, and 96.

The factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60 and 120.

The factors of 105 are 1, 3, 5, 7, 15, 21, 35 and 105.

Therefore, the greatest counting number that is a factor of both 96 and 120 but has no common factor with 105 other than 1 is 2.

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The various types of inverse function are the inverse of trigonometric functions, rational functions, hyperbolic functions and log functions

If the function is denoted by ‘f’ or ‘F’, then the inverse function is denoted by f⁻¹or F⁻¹.

A function accepts values, performs particular operations on these values and generates an output. The inverse function agrees with the resultant, operates and reaches back to the original function.

The various types of inverse function are:

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The area of the path is 456 square feet

The formula for determining area of a rectangle is given as;

A = lw

Where;

Now, substitute the values into the formula, we have;

Area of the rectangle  = 40 × 70

Area of the rectangle = 2800 square feet    (1)

Bordered fence with a 4 ft path so dimensions 44 ft by 74 ft

Area of rectangular garden with Path = 44 × 74

= 3256 square feet       (2)

Area of the walk = (2) - (1) = 3256 - 2800 = 456 square feet

Hence, the value is 456 square feet

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Answer:

it depends im pretty sure that you mean y and x cord  so answer is 0 x 6 y

Step-by-step explanation:

or 0 X so width or y height 6 Y

Answer:

The height of the 4th bounce would be 4.7458321; rounded would be 4.8.

Step-by-step explanation:

We can figure this question out by first converting the 83% into a decimal, by bringing back 2 decimal places:

0.83.

And then setting up this equation:

0.83 x 10 = 8.3

Now, this is for 1 bounce. We have to do this 4 more times:

0.83 x 8.3 = 6.889

3rd time:

0.83 x 6.889 = 5.71787

4th time:

0.83 x 5.71787 = 4.7458321.

Now, we can round this answer to:

4.8

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The number of nickels and the number of dimes that Joseph has are 12 and 5 respectively.

An equation of degree one is known as a linear equation.

A linear equation of two variables can be represented by ax + by = c.

Let the no. of nickels be N and no. of dimes be D.

∴ N + D = 17...(i) and 0.05N + 0.1D = 1.45...(ii)

Multiplying (ii) by 100 we get 5N + 10D = 145...(iii)

Now multiply (i) by 5 we get 5N + 5D = 85...(iv)

Now subtracting (iv) from (iii) we get,

5D = 60.

D = 12 hence N = 5.

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Reflection then translation are rigid transformation can map triangle ABC onto triangle Fed.

What is congruent?

Congruence of triangles: 2 triangles square {measure} aforesaid to be congruent if all 3 corresponding sides square measure equal and every one the 3 corresponding angles square measure equal in measure. These triangles may be slides, rotated, flipped and turned to be looked identical. If repositioned, they coincide with one another. The image of congruity is’ ≅’.

Main body:

It has been given in the question that Δ ABC and ΔFED are congruent by SSS congruence theorem.

ΔFED is the picture image of ΔABC and slightly shifted towards left.

Therefore, we can tell about the transformations that if ΔABC is reflected on x-axis and translated towards left, it can map ΔFED.

Hence ,Option B is the answer.

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In order to show that △ ABC ≅ △ DEF by SAS congruence, we need the sides of triangles ABC and DEF with the angle between the respective sides.

Triangle congruence: Two triangles are said to be congruent if all three of their corresponding sides and all three of their corresponding angles have the same measurements. Slide, twist, flip, and turn these triangles to create an identical appearance. They are in alignment with one another when moved. "" is the congruence symbol. When two figures are comparable to one another in terms of their size and shape, this is what mathematicians mean by congruence. In essence, there are four congruence principles that demonstrate if two triangles are congruent. However, locating all six dimensions is essential. As a result, the congruence of triangles can be assessed using just three of the six variables.

Congruency Requirements:

SSS (Side-Side-Side)

SAS (Side-Angle-Side)

ASA (Angle-Side-Angle)

AAS (Angle-Angle-Side)

RHS (Right angle-Hypotenuse-Side) 

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The equation that best defines the length of the equal piece is 4x+2¹-12

We should know that an equation is a mathematical model that shows the equality of two sides of an expression

Based on the given condition 12-24=4*x

Applying multiplicative distribution -12=4x

Rearrange the equation 4x=-12

Calculate the product of the quotient x=-3

Now 24feet divided by -3 =-4

Since it deals with length =4

In conclusion the equation that determines the length of each equal piece is  4x+2¹-12

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The relation:

(9, -1) (4,2) (5,3) (8, -1) (3, 0)

Is a function, because each element of the domain appears only once.

A relation maps elements from a set, called the domain, into elements from another set, called the range.

Such that the element x being mapped into the element y is written as:

(x, y).

A relation is a function only if each element in the domain is mapped into only one element of the range.

Here we have the relation:

{  (9, -1) (4,2) (5,3) (8, -1) (3, 0)}

We can see that no element of the domain appears twice, so yes, this is a function.

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The true statements are

The side length of the transparent cube is given as

Length = 10 millimetres

The volume of the cube is calculated as

Volume = Length³

Substitute the known values in the above equation, so, we have the following representation

Volume =10³

Evaluate

Volume = 1000 cubic millimetres

1000 cubic millimetres and 30 cubic millimetres do not have the same value

So, the co-worker is incorrect.

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Answer:

The integers could be 8 and 4, just checked with a calculator

Total 56 pencils are needed for the exam.

Multiplication is one of the arithmetic operation used to find total numbers of items or things.

Given,

Total students in the classroom = 28

Total number of pencils needed by each student for the exam=2 pencils

Total number of pencils needed for the exam are,

= Total student ×  Number of pencils needed by each student

= 28 × 2

= 56 pencils

Hence , The total number of pencils needed by the students for the exam would be 56 .

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Answer:

11 pizza rolls

6 chicken wings

Answer:

11 pizza Rolls and 6

Step-by-step explanation:

Answer:

We can be able to use compatible numbers to estimate the quotient of 925/29 if the whole number that is part of the decimal is less than the divisor, we need to be able to rename the decimal.

Step-by-step explanation:

Option A is correct that is ASA postulate AC bisects ∠DAB and CA bisects ∠DCB then we proved ΔDAC≅ΔABC.

Given that,

We have to find the missing reasons in the two column.

Given

AC bisects ∠DAB and CA bisects ∠DCB

Prove

ΔDAC≅ΔABC

Statement                                                          Reasons

1. AC bisects ∠DAB                                           Given

2. ∠DAC≅∠BAC                                              definition of angle bisects

3.AC≅AC                                                         reflexive property
4.CA bisects ∠DCB                                           given

5. ∠DCA≅∠BCA                                              definition of angle bisects

6. ΔDAC≅ΔABC                                               ASA postulate

Therefore, Option A is correct that is ASA postulate AC bisects ∠DAB and CA bisects ∠DCB then we proved ΔDAC≅ΔABC.

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Answer:

expanded: 7+0.08

standard: 7.08

Step-by-step explanation:

The hundredths place is the second digit after the decimal, so 8 hundredths is 0.08.

Answer:

0.80

Step-by-step explanation:

The hundredth is 2 digits after the decimal.

Rounding 0.799, we want 0.xx

Look at the third digit, 9, meaning we round up.

However, since the second digit after the decimal is also a 9, we can make that a 0 by adding 1 to the first digit after the decimal.

We get 0.80

Applying the definition of an Isosceles triangle, given that isosceles triangle TIC has a vertex angle I of 90 degrees, the measure of angle T is 45 degrees.

In geometry, an isosceles triangle is a triangle that has at least two sides of equal length. Sometimes it is specified as having exactly two sides of equal length, and sometimes as having at least two sides of equal length, the latter version thus including the equilateral triangle as a special case. Examples of isosceles triangles include the isosceles right triangle, the golden triangle, and the faces of bipyramids and certain Catalan solids.

The two equal sides are called the legs and the third side is called the base of the triangle. The other dimensions of the triangle, such as its height, area, and perimeter, can be calculated by simple formulas from the lengths of the legs and base. Every isosceles triangle has an axis of symmetry along the perpendicular bisector of its base. The two angles opposite the legs are equal and are always acute, so the classification of the triangle as acute, right, or obtuse depends only on the angle between its two legs.

An Isosceles triangle has a vertex angle and two equal base angles.

Given that triangle TIC is an isosceles triangle:

angle I is the vertex angle = 90 degrees

angle T is a base angle

angle C is also a base angle

Thus:

angle C and angle T are congruent or equal to each other.

Therefore,

    Angle T = (180 - 90)/2

⇒ Angle T = 90/2

⇒ Angle T = 45 degrees.

applying the definition of an isosceles triangle, given that isosceles triangle TIC has a vertex angle I of 90 degrees, the measure of angle T is 45 degrees.

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Answer:

160 minutes can be spent on long distance calls each month.

Step-by-step explanation:

first we know that there is standard charge of $17 for basic service, $0.05 cost per minute with a budget of $25.

let's write that into an equation to solve for (a) which will be number of minutes.

17 + a(0.05) = 25

solving:

17 + a(0.05) = 25

carry across the 17 whilst changing the sign, or some people is also thought to minus on both sides to get rid of a certain variable.

a(0.05) = 25 - 17

a(0.05) = 8

carry across the multiplication of 0.05 which will then turn into division, or divide by 0.05 on both sides to remove it.

[tex]a = \frac{8}{0.05} [/tex]

a = 160

therefore 160 minutes can be spent on long distance calls each month.

You can redefine your answer more simply to hours by dividing by 60, which gives 2 hours and 40 minutes

Answer:

add up the exponents of each term and select the highest sum.

Answer: -23

Step-by-step explanation:

[tex]jk^2 -m=(-5)(2^2)-3=-5(4)-3=-20-3=-23[/tex]

=================================================

Work Shown:

[tex]A = P*e^{rt}\\\\A = 4000*e^{0.07*7}\\\\A \approx 6529.26487982264\\\\A \approx 6529.26[/tex]

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Explanation:

Let your calculator handle the constant 'e's value, rather than typing in the numbers 2.718... so you can get the most accuracy possible. It's like how many calculators have a [tex]\pi[/tex] button for similar reasoning. If your calculator doesn't have an 'e' button, then this should be sufficient

e = 2.71828182846

By the way, it's a bit odd how your teacher didn't require you to round to the nearest cent. Something like 6423.12590591 should round to 6423.13

There are four basic properties of numbers: commutative, associative, distributive, and identity.

1.Commutative Property

a. Addition

. When two numbers are added, the sum is the same regardless of the order in which the numbers are added.

3 + 5 = 8       or       5 + 3 = 8

b. Multiplication. When two numbers are multiplied together, the product is the same regardless of the order in which the numbers are multiplied.

3 x 5 = 15       or       5 x 3 = 15

2.Associative Property

a. Addition. When three or more numbers are added, the sum is the same regardless of the way in which the numbers are grouped.

6 + (4 + 3) = 13   or   (6 + 4) + 3 = 13

b. Multiplication. When three or more numbers are multiplied, the product is the same regardless of the way in which the numbers are grouped.

6 x (4 x 3) = 72   or   (6 x 4) x 3 = 72

3.Distributive Property

The sum of two numbers times a third number is equal to the sum of each addend times the third number.

5 x (7 + 2) = 45   or   5 x 7 + 5 x 2 = 45

4.Identity Property

a. Addition. The sum of any number and zero is that number.

12 + 0 = 12

b. Multiplication, The product of any number and one is that number.

18 x 1 = 18

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Using trigonometric ratio the distance to the control tower is 750.7ft

In trigonometry, there are six trigonometric ratios, namely, sine, cosine, tangent, secant, cosecant, and cotangent. These ratios are written as sin, cos, tan, sec, cosec(or csc), and cot in short.

The values of these trigonometric ratios can be calculated using the measure of an acute angle, θ in the right-angled triangle given below. This implies that the value of the ratio of any two sides of the triangle here depends on angle C.

Using trigonometric ratio, the distance is

tan θ = opposite / adjacent

tan 47 = x / 700

x = 700 tan 47

x = 750.7 ft

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The area of the larger floor is 64 square units when w = 8 and l = 8. which is the correct answer would be an option (B).

To compare the values, we must first calculate each given situation. The area of any given rectangle is length times width.

If w = 7 and l = 9

A = l × w = 8 × 6 = 48

If w = 8 and l = 8

A = l × w = 8 × 8 = 64

So, the second case would obtain a larger area.

Therefore, the area of the larger floor is 64 square units when w = 8 and l = 8.

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