1/3 x 5/8 = ?

Please explain step by step to get marked

Answer:

804.25

Step-by-step explanation:

Area of a circle is pi(r)^2

so if the radius is 16, that makes it pi(16)^2= pi(256) = 804.25

Answer:

1/4

Step-by-step explanation:

1/2 times 1/2

1/2 because there is 3 odds and 3 evens

the total is 6

3/6 equals to 1/2

so 1/2 times 1/2 is 1/4

1. The Fill ups are as follow:

AB² +  BC² = AC. AD + AC. CD

2. Segment addition postulate

The relationship between the three sides of a right-angled triangle is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem. The Pythagoras theorem states that the square of a triangle's hypotenuse is equal to the sum of its other two sides' squares.

Given:

BC/ AC = CD/ BC and AB/ AC = AD/ AB

Now, BC² = AC. CD  and AB² = AC. AD

Using, Addition Property of Equality

AB² +  BC² = AC. AD + AC. CD

and, AB² +  BC² = AC (AD + CD)  [factor]

AD + CD = AD (segment addition postulate)

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PLATO

i got it correct :)

A common denominator is a shared multiple of the denominators of the fractions involved when adding or subtracting fractions. It enables fraction comparison and addition/subtraction.

Simplification is the process of reducing a fraction to its simplest form by dividing the numerator and denominator by their greatest common divisor. This is done to represent fractions in the simplest terms viable.

Conversion: The process of transferring a fraction from one form to another while retaining its equal value is known as conversion. Finding a common denominator or expressing a fraction in terms of a specified unit or fraction may be required.

Fraction Addition/Subtraction: When adding or subtracting fractions, a common denominator is required. This entails determining a common multiple of

To rewrite the expression 3 + 1/5 + 2/3 using fifteenths as the common denominator, we need to find a common denominator for 5 and 3, which is 15 (since 5 and 3 are both factors of 15).

First, let's convert the fractions 1/5 and 2/3 to fifteenths:

\((\frac{1}{5})(\frac{3}{3}) = \frac{3}{15}\)

\((\frac{2}{3})(\frac{5}{5}) = \frac{10}{15}\)

Now we can rewrite the expression using the common denominator:

\(3 + \frac{3}{15}+\frac{10}{15}\)

Answer:

Step-by-step explanation:

Volume of cone = \(\frac{1}{3}\pi r^{2}h\\\)

                          \(= \frac{1}{3}*\pi * 4 * 4 * 10\\\\=\frac{160}{3}\pi cm^{3}\)

Answer:

c

Step-by-step explanation:

The approximate solution to the equation 1/x-1 = |x-2| after three iterations of successive approximation is x ≈ 5/2 or x ≈ 2.5.

To solve the equation 1/x-1 = |x-2| using three iterations of successive approximation, we will start with an initial guess and refine it using an iterative process.

Given that the equation involves absolute value, we will consider two cases:

Case 1: x - 2 ≥ 0

In this case, |x-2| simplifies to x-2, and the equation becomes 1/(x-1) = x-2.

Case 2: x - 2 < 0

In this case, |x-2| simplifies to -(x-2), and the equation becomes 1/(x-1) = -(x-2).

Now, let's perform the successive approximation:

Iteration 1:

Let's start with an initial guess, x = 2.

Case 1: When x - 2 ≥ 0,

1/(2-1) = 2-2,

1/1 = 0,

which is not true.

Case 2: When x - 2 < 0,

1/(2-1) = -(2-2),

1/1 = 0,

which is not true.

Since our initial guess did not satisfy the equation in either case, we need to choose a different initial guess.

Iteration 2:

Let's try x = 3.

Case 1: When x - 2 ≥ 0,

1/(3-1) = 3-2,

1/2 = 1,

which is not true.

Case 2: When x - 2 < 0,

1/(3-1) = -(3-2),

1/2 = -1,

which is not true.

Again, our guess did not satisfy the equation in either case.

Iteration 3:

Let's try x = 2.5.

Case 1: When x - 2 ≥ 0,

1/(2.5-1) = 2.5-2,

1/1.5 = 0.5,

which is true.

Case 2: When x - 2 < 0,

1/(2.5-1) = -(2.5-2),

1/1.5 = -0.5,

which is not true.

Our guess of x = 2.5 satisfies the equation in Case 1.

Therefore, the approximate solution to the equation 1/x-1 = |x-2| after three iterations of successive approximation is x ≈ 5/2 or x ≈ 2.5.

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The Greatest Common Divisor (GCD) of 85 and 51 is 17.

The greatest common factor that divides two or more numbers is known as the greatest common divisor (GCD). The highest common factor is another name for it (HCF).

Explanation

Step 1: Divide 85 by 51. The quotient is 1 and the remainder is 34.

Step 2: Divide 51 by 34. The quotient is 1 and the remainder is 17.

Step 3: Divide 34 by 17. The quotient is 2 and the remainder is 0.

Step 4: Since the remainder is 0, the Greatest Common Divisor (GCD) of 85 and 51 is 17.

The GCD of 85 and 51 is 17.

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For the statement "If a polygon lacks right angles, then it is a parallelogram.", the counter example is -

Option A : a right triangle

What is a parallelogram?

A quadrilateral with two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles that are additional to the transversal on the same side.

A counterexample for a conditional statement is an example that satisfies the hypothesis (the first part of the statement) but does not satisfy the conclusion (the second part of the statement).

In this case, the statement is "If a polygon lacks right angles, then it is a parallelogram."

A right triangle is a polygon that lacks right angles, but it is not a parallelogram.

Therefore, a right triangle is a counterexample for this statement.

A square, a regular hexagon, and a rectangle all have right angles, so they are not counterexamples for this statement.

Therefore, the triangle is the counterexample.

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The measure of the interior angle at vertex E can be determined by using the properties of triangles. In a triangle, the sum of all interior angles is always 180 degrees.

Therefore, to find the measure of the interior angle at vertex E, we need to subtract the measures of the other two angles at vertices A and B from 180 degrees. Let's assume that the measures of the angles at vertices A and B are a and b degrees, respectively. Then, the measure of the interior angle at vertex E can be calculated as follows: Interior angle at vertex E = 180 degrees - (measure of angle at vertex A + measure of angle at vertex B) Now, let's refer back to the given answer choices: A. 50 B. 90 C. 30 D. 150 Without additional information or a diagram, it is not possible to determine the exact measures of the angles at vertices A and B. Therefore, we cannot directly calculate the measure of the interior angle at vertex E. In order to solve this problem, we need more information about the triangle or a diagram that shows the relative positions of the vertices.

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The degree of the polynomial is the largest of these three values, which is 75

Algebraic expressions called polynomials include constants and indeterminates. Polynomials can be thought of as a type of mathematics. Nearly all branches of mathematics employ them to express numbers, and calculus is one of those branches where they play a crucial role.

Simply locate the highest exponent in the formula to determine the degree of the polynomial. The degree of the polynomial is seven because it is the highest exponent above.

There are multiple variables in the polynomial. The biggest sum of ALL of the exponents for ALL of the variables in a term is the polynomial's degree.

Given that := 105\(y^{75} + 125^{5} - 100x^{10}\)

= 105\(y^{75} + 125^{5} - 100x^{10}\)

To find the degree of a polynomial, simply find the highest exponent in the expression.  As seven is the highest exponent above, it is also the degree of the polynomial.

The polynomial has more than one variable. The degree of the polynomial is the largest sum of the exponents of ALL variables in a term.

The first term is 105\(y^{75}\)

The degree of this term is 75

The second term is 125\(x^{5}\)

The degree of this term is 5.

The third term is 100\(x^{10}\)

The degree of this term is 10.

The degree of the polynomial is the largest of these three values, which is 75

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The  work required to pump the water out of the spout is 70.9 * 10⁶ joules which is 71 M Joules approx.

Let the spherical tank be divided into a series of horizontal disks.

Let x be the height of each disk, g = gravity and p = density

Volume of each disk = πr2dx

Where r is the radius of each disk and dx is the thickness

By Pythagoras r² = 6² - x²= 36 -x²

Therefore Volume = π*(36-x²)*dx cubic metres

The distance each disk has to be lifted to escape the top of the spout = 2 + 6-x meters = (8-x)

Work needed to lift each disk to outlet = distance * mass where

mass = volume * density * gravity

        = pi(36-x²)*p*g = 9800pi(36-x²)dx

dW =  (8-x)* 9800pi(36-x²)dx

Since we have already accounted for the height of the spout, the work required is obtained by integrating the above expression from the bottom of the tank to the top. In other words, - 6 to + 6.

W = ⌠(8-x)*9800pi(36-x2)dx = 9800pi⌠[288 - 36x - 8x² +x³]dx

The odd terms evaluate to zero and we can rewrite the above as 2* I from 0 to 6.

W = 9800pi*2 [288x - 8x³/3] at x = 6 = 1152*19600π Joules = 22579200π joules = 70963200j

Total work required = 70.9 * 10⁶ joules

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The given expression is

If we use the distributive property, we solve as follows

Step-by-step explanation:

y = 3x_______equation1

3x + 2y = 12_____equation2

sub y into equation 2

3x+2(3x)=12

3x+6x=12

9x=12

x=3/4

sub X into equation 1

y=3x

y=3(3/4)

y=9/4

y=9/4 x=3/4

I hope this helps

The set Y^X can be defined as the set of all possible mappings between the elements of X and Y.

In mathematics, the set of all functions from a set X to a set Y is denoted by Y^X, and is defined as the set of all possible mappings from X to Y. The set Y^X consists of all possible functions that can be constructed from the set X to the set Y.

Here, the function is a mapping between two sets in which each element of the first set is mapped to one and only one element of the second set.

An example of the set of all functions from X to Y is as follows: Consider the sets X = {1,2,3} and Y = {a,b,c}. Then the set of all functions from X to Y is denoted by Y^X. It is represented as follows:

Y^X = {f | f: X → Y}

Therefore, the set of all functions from X to Y is given by:

Y^X = { (1,a), (1,b), (1,c), (2,a), (2,b), (2,c), (3,a), (3,b), (3,c) }

where each element in Y^X is a function that maps each element of X to an element of Y.

The set of all functions from X to Y is an important concept in mathematics as it is widely used in many areas such as graph theory, topology, and calculus.

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The correct answer is that the data set {3, 7, 4} is represented in the given histogram.(option-a)

The given histogram represents the number of children in each age group who need to travel to school. Since the histogram has only three bars, we can conclude that there are only three age groups.

The first bar represents children aged 5-10, of which there are 3. The second bar represents children aged 11-13, of which there are 7. The third bar represents children aged 14-18, of which there are 4.

Therefore, the data set that is represented in the histogram is:

{3, 7, 4}

None of the other data sets given match the values in the histogram. The first data set has duplicate values and is not sorted by age group. The second data set includes ages that are not represented in the histogram. The third data set has values for ages 6, 11, 12, 13, 14, 15, 17, and 18, but the histogram does not have bars for all those ages. (option-a)

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m_6 + m_8 = 180º because they form a straight line.

So, (2x-5) + (x+5) = 180

    3x = 180

      x = 60

So, m_115º    (2•60 - 5 = 115)

Also, because the two lines are parallel m_6 = m_3 by alternate interior angles.

So, m_3 = 115º

1) The way we transform the simultaneous equation in system A to system B is;

1 * Equation [A1] → Equation [B1]

2 * Equation [A1] + Equation [B1] → Equation [B2]

2) The way we transform the simultaneous equation in system Bto system C is;

1 * Equation [B1] → Equation [C1]

-1/11 * Equation [B2] → Equation [C2]

We are given the system of simultaneous equations as;

System A;

-7x + 2y = 5   ----A1

3x - 4y = 23  ------A2

System B;

-7x + 2y = 5   -----B1

-11x = 33  ------B2

System C;

-7x + 2y = 5   ----A1

x = -3  ------A2

1) To find out the operation that transforms system A into system B, we need to analyze both equations and by careful observation, we see that;

When we multiply A1 by 2 and add to A2, the result will give us B2.

Let us check;

A1 * 2 = 2(-7x + 2y) = 2(5)

-14x + 4y = 10

Add to A2 to get;

-11x = 33

2)  To find out the operation that transforms system B into system C, we need to analyze both equations and by careful observation, we see that;

When we multiply B2 by -1/11 and the result will give us C2.

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Answer:

160 more stickers

Step-by-step explanation:

640 divided by 4 is 160

160 times 5 is 800

800 minus 640 is 160

you need 160 more stickers

Answer:

15

Step-by-step explanation:

Answer:15

Step-by-step explanation:

Step-by-step explanation:

the constant k of proportionality is defined by

y = kx

or in our case

b = ka

so, let's see

14 = k×2

k = 14/2 = 7

this also works for the other data pairs :

7×5 = 35

7×9 = 63

7 × 1/3 = 7/3

perfect.

so, the constant of proportionality is 7.

Answer: A:Yes

Step-by-step explanation:

This table shows a proportional relationship between the variables x and y.

Answer:

Your answer would be Yes

Step-by-step explanation:

Khan Academy

\(\huge\bold\purple{2/3:}\)

Answer:

The answer is 11.8

Step-by-step explanation:

The value of x and y is 12.2 and 11.8 respectively.

The tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side.

The sine (sin) of an acute angle in a right angled triangle is the ratio between the side opposite the angle and the hypotenuse of the triangle.

According to the given question.

We have a right angled triangle.

In which one angle is 44 degrees and hypotenuse is 17 units.

Here,

With respect to angle 44 degrees the adjacent side is x and the opposite side is y.

Therefore,

Sine of 44 degrees is given by

\(sin44^{o} = \frac{opposite\ side }{Hypotenuse}\)

\(\implies sin44^{o} = \frac{y }{17}\)

\(\implies 0.6946 = \frac{y}{17}\)

\(\implies 0.6946 \times 17 = y\)

\(\implies y = 11.80\)

\(\implies y = 11.8\)

And, tangent of 44 degrees is give by

\(tan 44^{o} = \frac{opposite \ side }{adjacent \ side }\)

\(\implies tan44^{o} = \frac{y}{x}\)

\(\implies tan44^{o} = \frac{11.8}{x}\)

\(\implies 0.9657 = \frac{11.8}{x}\)

\(\implies x = \frac{11.8}{0.9657}\)

\(\implies x = 12.22\)

\(\implies x = 12.2\)

Therefore, the value of x and y is 12.2 and 11.8 respectively.

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The vertex of point A' in the dilated triangle A'B'C' is (6, 4.5).

1. Start by calculating the distance between the vertices of the original triangle ABC:

  - Distance between A(4, 3) and B(3, -2):

    Δx = 3 - 4 = -1

    Δy = -2 - 3 = -5

    Distance = √((-\(1)^2\) + (-\(5)^2\)) = √26

  - Distance between B(3, -2) and C(-3, 1):

    Δx = -3 - 3 = -6

    Δy = 1 - (-2) = 3

    Distance = √((-6)² + 3²) = √45 = 3√5

  - Distance between C(-3, 1) and A(4, 3):

    Δx = 4 - (-3) = 7

    Δy = 3 - 1 = 2

    Distance = √(7² + 2²) = √53

2. Apply the scale factor of 1.5 to the distances calculated above:

  - Distance between A' and B' = 1.5 * √26

  - Distance between B' and C' = 1.5 * 3√5

  - Distance between C' and A' = 1.5 * √53

3. Determine the coordinates of A' by using the distance formula and the given coordinates of A(4, 3):

  - A' is located Δx units horizontally and Δy units vertically from A.

  - Δx = 1.5 * (-1) = -1.5

  - Δy = 1.5 * (-5) = -7.5

  - Coordinates of A':

    x-coordinate: 4 + (-1.5) = 2.5

    y-coordinate: 3 + (-7.5) = -4.5

4. Thus, the vertex of point A' in the dilated triangle A'B'C' is (2.5, -4.5).

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Answer:

The slope is

\( - \frac{4}{3} \)

Step-by-step explanation:

To find the slope given two points we use the formula

\(m = \frac{y2 - y1}{x2 - x1} \)

where

m is the slope

(x1 , y1) and (x2 , y2) are the points

From the question

The points are (3,14) and (6,10)

The slope of the line (3,14) and (6,10) is

\(m = \frac{10 - 14}{6 - 3} = \frac{ - 4}{ 3} \)

\(m = - \frac{4}{3} \)

Hope this helps you

Question 24 :

P594.65 : 35 days

P594.65/7 : 35/7 days

P84.95 : 5 days

⇒ A. P84.95

Question 25 :

88.75 + 85.5 + 90.5 + 87.25 / 4

352/4

88

⇒ B. 88

Question 26 :

I = P × r × t

I = 580.00 × 0.065 × 1

I = P37.70

⇒ B. P37.70

At the given point,

\(f(5,0) = \dfrac1{\sqrt{5^2 + 0^2 - 9}} = \dfrac1{\sqrt{16}} = \dfrac14\)

Then the level curve is

\(\dfrac1{\sqrt{x^2 + y^2 - 9}} = \dfrac14 \\\\ \implies \sqrt{x^2 + y^2 - 9} = 4 \\\\ \implies x^2 + y^2 - 9 = 4^2 \\\\ \implies x^2 + y^2 = 25 = 5^2\)

which is a circle centered at the origin with radius 5 - quite easy to sketch.

The system, it is standard form is

meaning

and

With the value of y an z in hand, we now solve for x in the first equation

Hence, the solution is

x = 65, y = 8, and z = 3.

Answer:

30+(2x+7)+63=180(sum of angles of triangle )

30+2x+7+63=180

2x+100=180

2x=180-100

x=80/2

x=40

Answer:

\(\boxed {\boxed {\sf (2x+7)+30+63= 180}}\)

\(\boxed {\boxed {\sf x=40}}\)

Step-by-step explanation:

We are asked to write an equation to solve for x and use the equation to find x.

We know that the angles in a triangle must add to 180 degrees. Therefore, the sum of the three angles in this triangle: 30, 63, and (2x+7) must equal 180. We can set up an equation.

\((2x+7)+ 30 +63= 180\)

Now we can use the equation to solve for x. First, we combine like terms on the left side of the equation. The 3 terms without variables or constants can be added.

\(2x+ (7+30+63)= 180\)

\(2x+ (100)= 180\)

We are solving for x, so we must isolate the variable. 100 is being added to 2x. The inverse operation of addition is subtraction. Subtract 100 from both sides of the equation.

\(2x+100-100= 180-100 \\2x=180 -100 \\2x=80\)

x is being multiplied by 2. The inverse operation of multiplication is division. Divide both sides of the equation by 2.

\(\frac {2x}{2}= \frac{80}{2}\)

\(x= \frac {80}{2} \ \\\)

\(x=40\)

The equation is (2x+7)+ 30+63= 180 and x is equal to 40.