1/3 : 1/4 ratio as a fraction

Answer:

Step-by-step explanation:

its on satuday

The correct Option is D. 45÷3= 15 . The equation that best shows that 45 is a multiple of 15 is 45 ÷ 3 = 15.

A multiple is a product that results from multiplying two or more numbers.

A common multiple is a multiple that is common to two or more numbers.

A multiple of a number can be expressed as an integer multiple of the number.

If the result is a whole number, the first number is a multiple of the second.

An equation that shows 45 is a multiple of 15 is as follows: 45 ÷ 3 = 15.

A multiple is a number that can be divided by another number without leaving a remainder.

As a result, we divide 45 by 3 to find out whether 45 is a multiple of 15.

If the result is a whole number, 45 is a multiple of 15.

Here is the equation that shows this: 45 ÷ 3 = 15

Thus, we can conclude that the equation that best shows that 45 is a multiple of 15 is  45 ÷ 3 = 15.

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Answer:

The answer is number 3

Y =-3/7X + 3

Step-by-step explanation:

Substitue with the value of the two points in all answers

The value of the left side must equal the value or the right side

For instance,

The two points are (0,3) & (7,0)

Substitue in the first answer with the point (0,3)

3 = - 3 (rejected)

Second answer

3 = 3 works for the point (0,3) then also Substitue with the other point (7,0)

0 = 6 (rejected)

sub. With point (0,3).

Sub. With point (7,0)

Then that's the right one

Answer: [-2,7]

Step-by-step explanation: The range of a graph is just the range of minimum and maximum outputs of the y axis. The minimum y axis value is -2, while the maximum is 7. Putting your answer in brackets means that the endpoints (-2 and 7) are inclusive, which is the case since the dots are filled in. If the dots are hollow, the range does not include those endpoints and you would use parentheses instead.

Answer:

-x + 20(8) = 147 -x + 10(8) = 67

-x + 160 = 147 -x + 80 = 67

x = 13 x = 13

A. The system has exactly one solution. The solution is (13, 8).

B. All three colonies had a population of 8 thousand people in 2013.

Hello!

x² - 5x + 6

= (x² - 2x) + (-3x + 6)

= x(x - 2) - 3(x - 2)

= (x - 2)(x - 3)

The tangent and normal lines of the curve:

Case (i): y = (4 / 5) · x + 13 / 5

Case (ii): (x, y) = (0, 13 / 5)

Case (iii): y = - (5 / 4) · x + 35 / 4

In this problem we have the representation of a curve whose equations for tangent and normal lines must be found. Lines are expressions of the form:

y = m · x + b

Where:

Both tangent and normal lines are perpendicular, the relationship between the slopes of the two perpendicular lines is:

m · m' = - 1

Where:

The slope of the tangent line is found by evaluating the first derivative of the curve at intersection point.

Case (i) - First, determine the slope of the tangent line:

y = √(8 · x + 1)

y' = 4 / √(8 · x + 1)

y' = 4 / √25

y' = 4 / 5

Second, determine the intercept of the tangent line:

b = y - m · x

b = 5 - (4 / 5) · 3

b = 5 - 12 / 5

b = 13 / 5

Third, write the equation of the tangent line:

y = (4 / 5) · x + 13 / 5

Case (ii) - Find the coordinates of the intercept of the tangent line:

(x, y) = (0, 13 / 5)

Case (iii) - First, find the slope of the normal line:

m' = - 1 / (4 / 5)

m' = - 5 / 4

Second, determine the intercept of the normal line:

b = y - m' · x

b = 5 - (- 5 / 4) · 3

b = 5 + 15 / 4

b = 35 / 4

Third, write the equation of the normal line:

y = - (5 / 4) · x + 35 / 4

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The result of the row operation on the matrix is given as follows:

[tex]\left[\begin{array}{cccc}1&0&0&8\\0&8&0&3\\0&0&5&6\end{array}\right][/tex]

The matrix in this problem is defined as follows:

[tex]\left[\begin{array}{cccc}2&0&0&16\\0&8&0&3\\0&0&5&6\end{array}\right][/tex]

The row operation is given as follows:

[tex]R_1 \rightarrow \frac{1}{2}R_1[/tex]

The first row of the matrix is given as follows:

[2 0 0 16]

The meaning of the operation is that every element of the first row of the matrix is divided by two.

Hence the resulting matrix is given as follows:

[tex]\left[\begin{array}{cccc}1&0&0&8\\0&8&0&3\\0&0&5&6\end{array}\right][/tex]

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Answer:

chemical reaction that releases heat energy to the surroundings is known as endothermis reaction

The distance John can ride his bike in 12 minutes is approximately 1.6 miles.

To find out the distance John can ride his bike in 12 minutes, we can use the information given about his rate of riding.

We are told that John can ride his bike 4 miles in 30 minutes. This implies that his rate of riding is 4 miles per 30 minutes.

To calculate the distance John can ride in 12 minutes, we need to determine the proportion of time he is riding compared to the given rate.

We can set up a proportion to solve for the unknown distance:

(4 miles) / (30 minutes) = (x miles) / (12 minutes)

Cross-multiplying, we get:

30 minutes * x miles = 4 miles * 12 minutes

30x = 48

Now, we can solve for x by dividing both sides of the equation by 30:

x = 48 / 30

Simplifying the fraction, we have:

x = 8/5

So, John can ride his bike approximately 1.6 miles in 12 minutes, at his current rate.

Therefore, the distance John can ride his bike in 12 minutes is approximately 1.6 miles.

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The volume of ice cream that can fit within the cone is 84.78 cubic inches.

To determine the volume of ice cream that can fit within the cone, we can consider the cone as a right circular cone with a height of 9 inches and a radius of 3 inches (half of the diameter, which is 6 inches).

The formula for the volume of a right circular cone is given by:

V = (1/3) * π * r^2 * h

where V represents the volume, π is a mathematical constant (approximately 3.14159), r is the radius, and h is the height.

Substituting the given values into the formula, we have:

V = (1/3) * 3.14159 * 3^2 * 9

= (1/3) * 3.14159 * 9 * 9

≈ 84.78 cubic inches

Therefore, the volume of ice cream that can fit within the cone is approximately 84.78 cubic inches.

To provide a visual representation, imagine a cone shape with a height of 9 inches and a diameter of 6 inches. The radius is half of the diameter, so it is 3 inches.

The ice cream fills the cone up to the top, creating a rounded triangular shape. The volume of the ice cream is equivalent to the volume of this cone shape.

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Note the complete question is

Bela's ice cream cone is 9 inches tall and 6 inches across. What volume of ice cream can fit within the cone? Show your work and draw a picture of the scenario.

Type your answer as a number only.

Round your answer to the nearest tenth. Volume = cubic inches

Answer:

f^(-1)(x) = ±√(x - 5).

Step-by-step explanation:

Replace f(x) with y: y = x^2 + 5.

Swap the x and y variables: x = y^2 + 5.

Solve the equation for y. To do this, we'll rearrange the equation:

x - 5 = y^2.

Take the square root of both sides (considering both positive and negative square roots):

±√(x - 5) = y.

Swap y and x again to express the inverse function:

f^(-1)(x) = ±√(x - 5).

Answer:

1

Step-by-step explanation:

The degree of a polynomial is the exponent of the varieble x. So the exponent of x in that function is 1.

Answer:

Step-by-step explanation:

Answer:

29. 59.06°

30. 10.6

Step-by-step explanation:

29.
By using the Tangent angle rule, we can find the angle of elevation,

We know that

Tan Angle = opposite/adjacent

Tan x=AB/BC

Tan x=20/12

Tan x=5/3

[tex]x=Tan^{- }(\frac{5}{3})[/tex]

x=59.06°

30.

The law of sine is a formula that can be used to find the lengths of the sides of a triangle, or to find the angles of a triangle, when two sides and the angle between them are known. The formula is:

a / sin(A) = b / sin(B) = c / sin(C)

Here taking

a / sin(A) = c / sin(C)

here A=75°, C=180-75-50=55° and c -9 and

we need to find a,

substituting value

a/Sin(75°)=9/Sin(55°)

a=9*Sin(75°)/Sin(55°)

a=10.61

Therefore, the value of a is 10.6

Answer:

        tan (θ) = 20/12, and solve for θ

       We then get the equation tan (θ) =  20/12

        θ = arctan(5/3)

        Tan θ  =  opp/adj

        Tan θ  = 20/12

         θ  =  Tan^-1 (20/12)

          θ  =  59.03624346 degrees

           θ = 59.0 degrees

       Hence, the Angle of Elevation is ------->  59.0°

       m < C = 180 degrees - m<A - m<B

       m<C  = 180 degrees - 75 degrees  -  50 degrees

      m<C  =  55 degrees

       a/sin A  =  c/sin C

       a/sin 75 degrees  =  9/sin 55 degrees

        a  =  9 * sin 75 degrees/sin 55 degrees

        a  =  10.3

Therefore, The length of side A in --------> △ABC is approximately 10.3

Hope this helps you!

The correct expression to calculate the area of a triangle with a base of 21 inches and height of 12 inches is (21 × 12) ÷ 2.

The subject of your question is Mathematics, specifically dealing with the topic of how to calculate the area of a triangle. The formula to calculate the area of a triangle is 1/2 multiplied by the base multiplied by the height. So, in your question where the base of the triangle is 21 inches and the height is 12 inches, the correct choice would be D. (21 × 12) ÷ 2 which applies the formula correctly.

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The elliptical ceiling is approximately 30 ft high at the center.

To find the height of the elliptical ceiling at the center, we can use the properties of an ellipse.

In this case, the two foci of the ellipse represent the positions where Juan and his friend are standing.

The distance between the two foci is 80 ft, and Juan is 20 ft away from the nearest wall.

This means that the sum of the distances from any point on the ellipse to the two foci is constant and equal to 80 + 20 = 100 ft.

Since Juan is standing at one focus and the distance to the nearest wall is given, we can determine the distance from Juan to the farthest wall by subtracting the distance to the nearest wall from the sum of the distances.

Distance from Juan to the farthest wall = 100 ft - 20 ft = 80 ft.

The height of the elliptical ceiling at the center is equal to half of the distance between the nearest and farthest walls.

Height of elliptical ceiling = (80 ft - 20 ft) / 2 = 60 ft / 2 = 30 ft.

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The area of the garden is 135 square yards.

Let's imagine you have a rectangular garden measuring 15 yards in length and 9 yards in width.

You want to find the area of this garden, which represents the amount of space inside the garden.

To find the area of a rectangle, you multiply the length by the width.

In this case, the length is 15 yards and the width is 9 yards.

Area = Length × Width

Area = 15 yards × 9 yards

Area = 135 square yards

This means that the garden can hold 135 square yards of grass, flowers, or any other objects you place inside it.

It's worth noting that the unit of measurement for area is always squared, such as square yards in this example.

This is because area is a two-dimensional measurement, representing the space within a flat surface.

By using the formula to calculate the area of a rectangle, you can easily determine the amount of space enclosed by any rectangular area when given the length and width.

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The mean is the measure that gives the most accurate picture of the data's center. It is an essential measure of central tendency that represents the arithmetic average of a dataset.

It is calculated by summing up all the values in the dataset and dividing the sum by the total number of values. The mean is suitable for datasets that have a normal or symmetrical distribution.

The mean is highly sensitive to outliers, which can significantly influence the average value. When outliers are present, it is appropriate to use other measures of central tendency such as the median or mode to obtain an accurate picture of the data's center.

The median is the middle value in a dataset arranged in ascending or descending order. It is not affected by outliers and is suitable for datasets with skewed distributions.

The mode is the most frequent value in the dataset. It is suitable for categorical data but can also be used for continuous data.

In summary, the mean is the most accurate measure of central tendency, but its accuracy can be improved by using the median or mode in datasets with outliers or skewed distributions.

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Answer:

C-351

Step-by-step explanation:

The length of the hypotenuse in the isosceles 90-degree triangle is √(2).

In an isosceles 90-degree triangle, two legs are equal in length, and the third side, known as the hypotenuse, is longer. Let's denote the length of the legs as x and the length of the hypotenuse as 4x.

According to the Pythagorean theorem, in a right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse. In this case, we have:

[tex]x^2 + x^2 = (4x)^2.[/tex]

Simplifying the equation:

[tex]2x^2 = 16x^2.[/tex]

Dividing both sides of the equation by [tex]2x^2[/tex]:

[tex]1 = 8x^2.[/tex]

Dividing both sides of the equation by 8:

[tex]1/8 = x^2[/tex].

Taking the square root of both sides of the equation:

x = √(1/8).

Simplifying the square root:

x = √(1)/√(8),

x = 1/(√(2) * 2),

x = 1/(2√(2)).

Therefore, the length of each leg in the isosceles 90-degree triangle is 1/(2√(2)), and the length of the hypotenuse is 4 times the length of each leg, which is:

4 * (1/(2√(2))),

2/√(2).

To simplify the expression further, we can rationalize the denominator:

(2/√(2)) * (√(2)/√(2)),

2√(2)/2,

√(2).

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The ordered pair that is a solution for both inequalities is (-2, 2).

Here we have the system of inequalities:

y < -x + 1

y > x

And we want to see which one of the given points makes both of them true.

To find that, just replace the values in both inequalities and see if both become true or not.

For example, for the first point:

(-3, 5)

We will get:

5 < -(-3) + 1 = 4

5 > -3

The first one is false, and the second one is true.

The correct option is the second point:

2 < -(-2) +1 = 3

2 > -2

Both are true.

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Answer:

y^10 + (5/8xy^5 - 5/8xy^6) - (25/64x^2)

Step-by-step explanation:

To simplify the given expression, we can expand it using the distributive property:

(5/8x + y^5)(y^5 - 5/8x)

Expanding the expression yields:

= (5/8x * y^5) + (5/8x * -5/8x) + (y^5 * y^5) + (y^5 * -5/8x)

= (5/8xy^5) - (25/64x^2) + y^10 - (5/8xy^6)

Combining like terms, we have:

= y^10 + (5/8xy^5 - 5/8xy^6) - (25/64x^2)

Hope this help! Have a good day!

Answer: 28

Step-by-step explanation:

If [tex]a = 7[/tex] and [tex]b = 2[/tex], then [tex]2ab[/tex] can be worked out as follows:

[tex]\Large 2ab = 2 \times a \times b[/tex]

Substituting the values of [tex]a[/tex] and [tex]b[/tex], we get:

[tex]2 \times 7 \times 2 = 28[/tex]

Therefore, [tex]2ab[/tex] is equal to 28 when [tex]a = 7[/tex] and [tex]b = 2[/tex].

________________________________________________________

The answer is:

Work/explanation:

To evaluate the expression [tex]\sf{2ab}[/tex], I begin by plugging in 7 for a and 2 for b:

[tex]\large\pmb{2(7)(2)}[/tex]

Simplify by multiplying.

[tex]\large\pmb{2*14}[/tex]

[tex]\large\pmb{28}[/tex]

The number we're looking for, which when added to 24/5 results in 9, is 21/5 or 4.2 in decimal form.

Let's solve the equation: 24/5 + x = 9, where x represents the unknown number we're trying to find.

To isolate x, we'll start by subtracting 24/5 from both sides of the equation:

x = 9 - 24/5

To add these two fractions, we need a common denominator. The denominator of 9 is 1, and the denominator of 24/5 is 5. To find a common denominator, we multiply 1 by 5:

x = (9 * 5)/5 - 24/5

This gives us:

x = 45/5 - 24/5

Now we can combine the fractions with the same denominator:

x = (45 - 24)/5

Simplifying the numerator:

x = 21/5

Therefore, the number we're looking for is 21/5. In decimal form, it can be written as 4.2.

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The values in the domain of fᵒg are all real numbers.

Therefore, the correct answer is: x - 6.

To determine the domain of the composite function fᵒg, we need to find the values of x that are valid inputs for the composition.

The composite function fᵒg represents applying the function f to the output of the function g. In this case, g(x) is equal to -9.

So, we substitute -9 into the function f(x) = √6x:

f(g(x)) = f(-9) = √6(-9) = √(-54)

Since the square root of a negative number is not defined in the set of real numbers, the value √(-54) is undefined.

Therefore, -9 is not in the domain of fᵒg.

To find the values in the domain of fᵒg, we need to consider the values of x that make g(x) a valid input for f(x).

Since g(x) is a constant function equal to -9, it does not impose any restrictions on the domain of f(x).

The function f(x) = √6x is defined for all real numbers, as long as the expression inside the square root is non-negative.

So, any value of x would be in the domain of fᵒg.

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The rates of change of the two functions that compare correctly is A. The rate of change of function A is 6, and the rate of change of function B is -10/9.

To compare the rates of change of the two functions, we can calculate the slope of each function. The slope represents the rate of change of a linear function.

For Function A, the equation is y = 6x - 1. The coefficient of x, which is 6, represents the slope. The rate of change of Function A is 6.

For Function B, we are given three points: (13, 0), (4, 10), and (6, 15). We can calculate the slope using the formula: slope = (change in y) / (change in x). Taking the first two points, we have: slope = (10 - 0) / (4 - 13) = 10 / (-9) = -10/9.

Comparing the rates of change, we have:

A. The rate of change of function A is 6.

The rate of change of function B is -10/9.

The correct option is A. The rate of change of function A is 6, and the rate of change of function B is -10/9.

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