is 1 over 3 rational

Answer:

The correct answer is D.

Step-by-step explanation:

Recall that when we make a dilation with center at the origin, the only needed operation is to multiply the coordinates of each point by the factor of dilation. In this particular case the dilation factor is 0.5 so we must do the following operations:

So, the vertices of the triangle after the dilation are those who appear in D.

Answer:

6(4 - 3y)

Step-by-step explanation:

Factor the expression 24−18y

The first thing to check is the common factor to be able to factorize the expression. Take for instance where we have

xa - xb  = x ( a - b)

The common factor is x which is outside the bracket

24−18y

The greatest common factor between 24 and 18 is 6.

Therefore,

24−18y  = 6(4 - 3y)

24−18y  = 6(4) - 6(3y)

Answer:

111/190

Step-by-step explanation:i know you dont want to see explanation so yeah...

Probabilities are used to determine the chances of an event.

The probability that the two selected sweet will not be of the same type is [tex]\frac{111}{190}[/tex]

The given parameters are:

[tex]n = 20[/tex] --- number of sweet

[tex]L = 12[/tex]

[tex]M = 5[/tex]

[tex]H = 3[/tex]

First, we calculate the probability that the two selected sweet will be of the same type.

This is calculated as:

[tex]P(Same) =P(L\ and\ L) + P(M\ and\ M) + P(H\ and\ H)[/tex]

Because the selection is without replacement, the equation becomes

[tex]P(Same) = \frac{12 \times 11}{20 \times 19} +\frac{5 \times 4}{20 \times 19} + \frac{3 \times 2}{20 \times 19}[/tex]

[tex]P(Same) = \frac{132}{380} +\frac{20}{380} + \frac{6}{380}[/tex]

Add fractions

[tex]P(Same) = \frac{132+20+6}{380}[/tex]

[tex]P(Same) = \frac{158}{380}[/tex]

Using the complement rule, the probability that the two selected sweet will not be of the same type is:

[tex]P(Not\ same) = 1 - P(Same)[/tex]

This gives

[tex]P(Not\ same) = 1 - \frac{158}{380}[/tex]

Take LCM

[tex]P(Not\ same) = \frac{380 - 158}{380}[/tex]

[tex]P(Not\ same) = \frac{222}{380}[/tex]

Simplify

[tex]P(Not\ same) = \frac{111}{190}[/tex]

Hence, the required probability is: [tex]\frac{111}{190}[/tex]

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The complete function that models Amare's height above the ground, h(t), as a function of time, t, in minutes is:

h(t) = 25 · sin((π / 3) t) + 4

To model Amare's height above the ground, use the equation of a sinusoidal function.

In this case, since the Ferris wheel has a diameter of 50 meters, the amplitude of the function is half of the diameter, which is 25 meters. The Ferris wheel completes three revolutions in six minutes, so the period of the function is 6 minutes.

The equation for the height function is given by:

h(t) = A · sin((2π / T) t + φ) + h0

Where:

A is the amplitude (25 meters)

T is the period (6 minutes)

φ is the phase shift (0 radians, since Amare enters at the low point)

h0 is the vertical shift (4 meters, since the Ferris wheel sits four meters above the ground)

Substitute the given values into the equation

h(t) = 25 · sin((2π / 6) t + 0) + 4

Simplifying further:

h(t) = 25 · sin((π / 3) t) + 4

Therefore, the complete function that models Amare's height above the ground, h(t), as a function of time, t, in minutes is:

h(t) = 25 · sin((π / 3) t) + 4

Complete question

Amare wants to ride a Ferris wheel that sits four meters above the ground and has a diameter of 50 meters. It takes six minutes to do three revolutions on the Ferris wheel. Complete the function, h(t), which models Amare's height above the ground, in meters, as a function of time, t, in minutes. Assume he enters the ride at the low point when t = 0.

h(t)=--- ·sin----  πt+---- π )+ ----

r² + r - 2 R -4r+8 just got this wrong on quiz so i know this is the right answer now

The simplified expression of  (r⁴ - r² + 4) ÷ (r² - r + 2) is r³ -r+ 4/r ÷ r - 1 + 2/r

An expression is combination of variables, numbers and operators.

The given expression is  (r⁴ - r² + 4) ÷ (r² - r + 2)

r power four minus r square plus four divided by r square minus r plus two.

The expression can not be simplified further as the denominator (r^2 - r + 2) cannot be factored into linear factors

The expression is a rational function and can only be simplified by partial fraction decomposition which involves writing it as a sum of simpler fractional terms.

r (r³ -r+ 4/r) ÷ r(r - 1 + 2/r)

r³ -r+ 4/r ÷ r - 1 + 2/r

Hence, the simplified expression of  (r⁴ - r² + 4) ÷ (r² - r + 2) is r³ -r+ 4/r ÷ r - 1 + 2/r

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The 3rd Image defines a piecewise function because for it to be a function, every input must match to exactly one and only one output. In Images 1, 2, and 4, there are certain inputs that have two outputs or stated otherwise, have two y-values for the same x-value. Only the 3rd Image matches 1 x-value to every 1 y-value. So, that's your answer.

Answer: C! The 3rd graph

Step-by-step explanation: Why does your equations have f(x)= and g(x)= ? Mine is only y= for every graph shown. All same numbers though.

The radius of the cone with a height of 3 in and a volume of 12 in is 1.95 in.

Radius is the line that connects any point of the circumference of a circle to the center of that circle.

Given:

Where:

Make r the subject of the equation

From the question,

Given:

Substitute these values into equation 2

Hence, the radius of the cone with a height of 3 in and a volume of 12 in is 1.95 in.

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Final answer:

The radius to the nearest hundredth is 1.38

Explanation:

To find the radius of a cone with a given height and volume, use the formula [tex]V = 1/3 * \pi * r^2 * h[/tex], where V is the volume, r is the radius, and h is the height.

In this case, the volume is given as 12 in^3 and the height is given as 3 in.

Substituting these values into the formula:

[tex]12 = 1/3 * \pi * r^2 * 3[/tex]

Multiply both sides of the equation by 3:

[tex]36 = \pi * r^2 * 3[/tex]

Divide both sides of the equation by 3π:

[tex]12/\pi = r^2[/tex]

Take the square root of both sides of the equation:

[tex]r = \sqrt{(12/\pi )[/tex]

Approximating it to nearest hundredth -

r ≈ 1.38

Answer:

The area added to the office according to the new blueprint

Step-by-step explanation:

you're welcome

Answer:

Sample response: Julio divided 6 whole parts into groups of 2 instead of dividing them into groups of  

1

2

which would make the quotient 12, not 3.

Step-by-step explanation:

Given is a composite figure where we have a semicircle and a triangle.

To find the area of the semicircle, we need diameter of the circle which is the distance between two given points (2,4) and (2,-3). So the diameter is 4-(-3) = 7 and radius would be 3.5 units.

Area of circle = π·r² = 3.14 × (3.5)² = 38.465 squared units.

So, area of semicircle = 38.465 ÷ 2 = 19.2325 squared units.

To find the area of the triangle, we need base and height of the triangle. The base is same as diameter = 7 and the height would be distance between given point (5,0) and (2,0), so height is 5-2 = 3.

Area of triangle [tex] =\frac{1}{2} bh = \frac{1}{2} (7)(3) = 10.5 [/tex] 1/2 * 7 * 3 = 10.5 squared units.

Total area = Area of triangle + Area of semicircle = 10.5 + 19.2325 = 29.7325 squared units.

So, final answer is 29.7325 squared units.

The x value for point C is not one of the given options.

To find the x value for point C such that AC and BC form a 2:3 ratio, we first need to find the coordinates of point C. The given components are Cx = -2/3, Cy = -4/3, and C₂ = 7/3. Substituting these values into Equation 2.21, we get:

C = sqrt((-2/3)² + (-4/3)² + (7/3)²) = sqrt(23/3)

Therefore, the x value for point C is not one of the options given. None of the options (A) 6, (B) -0.6, (C) 4, or (D) -2.4 are correct.

Final answer:

To find the x value for point C such that AC and BC form a 2:3 ratio, substitute the coordinates of point C into the equation and solve for C.

Explanation:

To find the x value for point C such that AC and BC form a 2:3 ratio, we can use the coordinates of points A, B, and C. We have Cx = -2/3, Cy = -4/3, and C₂ = 7/3. Substituting these values into Equation 2.21 gives:

C = √((-2/3)² + (-4/3)² + (7/3)²) = √(4/9 + 16/9 + 49/9) = √(69/9).

So the x value for point C is √(69/9).

The total distance of the trail is 100/7 km, which simplifies to approximately 14.29 km.

To find the total distance of the trail, let's break down the information provided step by step.

First day: They hiked 1/8 of the trail.

Second day: They hiked 4/7 of the remaining trail after the first day. So, on the second day, they covered (1 - 1/8) × (4/7) of the total trail.

Third day: They hiked 1/3 of the remaining trail after the second day, plus the last 8 km.

Now, we can set up an equation to solve for the total distance:

1/8 + (1 - 1/8)× (4/7) + (1 - 1/8 - (1 - 1/8)× (4/7)) × (1/3) + 8 = Total Distance.

Let's calculate each part:

First day: 1/8 of the total trail.

Second day: (1 - 1/8)× (4/7) = 28/56 - 7/56 = 21/56 of the total trail.

Third day: (1 - 1/8 - 21/56)× (1/3) = (56/56 - 7/56 - 21/56) × (1/3) = 28/56× (1/3) = 28/168 = 1/6 of the total trail.

Now, let's add all these parts together:

1/8 + 21/56 + 1/6 + 8 = Total Distance.

To simplify, let's find a common denominator:

1/8 + 3/8 + 14/56 + 8/8 = Total Distance.

Now, add the fractions:

16/56 + 14/56 + 14/56 + 56/56 = Total Distance.

Combine:

100/56 = Total Distance.

Now, simplify:

Total Distance = 100/56×8/8 = 800/56 km.

Divide both numerator and denominator by the greatest common divisor, which is 8:

Total Distance = 100/7 km.

So, the whole trail is approximately 14.29 km.

Answer:

15

Step-by-step explanation:

To rewrite[tex]\(2x^2 - 7x + 5\) by completing the square, first factor out the coefficient of \(x^2\), then add and subtract \(\frac{49}{16}\) inside the parentheses, rewrite as a perfect square trinomial, and simplify. The result is \(2\left(x - \frac{7}{4}\right)^2 - \frac{9}{8}\).[/tex]

To rewrite the quadratic function[tex]\(2x^2 - 7x + 5\)[/tex]by completing the square, follow these steps:

1. Factor out the coefficient of[tex]\(x^2\):\[2x^2 - 7x + 5 = 2(x^2 - \frac{7}{2}x) + 5\][/tex]

2. Take half of the coefficient of [tex]\(x\)[/tex]and square it:

[tex]\[\left(\frac{-7}{2} \div 2\right)^2 = \left(\frac{-7}{4}\right)^2 = \frac{49}{16}\][/tex]

3. Add and subtract this value inside the parentheses:

[tex]\[2\left(x^2 - \frac{7}{2}x + \frac{49}{16} - \frac{49}{16}\right) + 5\][/tex]

4. Rewrite the expression inside the parentheses as a perfect square trinomial:

[tex]\[2\left[\left(x - \frac{7}{4}\right)^2 - \frac{49}{16}\right] + 5\][/tex]

5. Distribute and simplify:

[tex]\[2\left(x - \frac{7}{4}\right)^2 - 2 \times \frac{49}{16} + 5\]\[= 2\left(x - \frac{7}{4}\right)^2 - \frac{49}{8} + 5\]\[= 2\left(x - \frac{7}{4}\right)^2 - \frac{49}{8} + \frac{40}{8}\]\[= 2\left(x - \frac{7}{4}\right)^2 - \frac{9}{8}\]So, the quadratic function \(2x^2 - 7x + 5\) rewritten by completing the square is \(\boxed{2\left(x - \frac{7}{4}\right)^2 - \frac{9}{8}}\).[/tex]

Law of cosines :

The law of cosines establishes:

[tex] c ^ 2 = a ^ 2 + b ^ 2 - 2*a*b*cosC.
[/tex]

general guidelines:

The law of cosines is used to find the missing parts of an oblique triangle (not rectangle) when either the two-sided measurements and the included angle measure are known (SAS) or the lengths of the three sides (SSS) are known.

Law of the sines:

In ΔABC is an oblique triangle with sides a, b, and c, then:

[tex] \frac{a}{sinA} =\frac{b}{sinB} =\frac{c}{sinC} [/tex]

The law of the sines is the relation between the sides and angles of triangles not rectangles (obliques). It simply states that the ratio of the length of one side of a triangle to the sine of the angle opposite to that side is equal for all sides and angles in a given triangle.

General guidelines:

To use the law of the sines you need to know either two angles and one side of the triangle (AAS or ASA) or two sides and an opposite angle of one of them (SSA).

The ambiguous case :

If two sides and an angle opposite one of them is given, three possibilities may occur.

(1) The triangle does not exist.

(2) Two different triangles exist.

(3) Exactly a triangle exists.

If we are given two sides and an included angle of a triangle or if we are given 3 sides of a triangle, we can not use the law of the sines because we can not establish any proportion where sufficient information is known. In these two cases we must use the law of cosines

The Law of Sines, Law of Cosines, and the Ambiguous Case are used to solve triangles depending on the given information. The Law of Sines is used when you have angles and sides but no right angle, the Law of Cosines is used when you have at least one side and angles, and the Ambiguous Case is used when you have one angle and two sides with two possible triangles. General guidelines are provided for each law.

The Law of Sines:

The law of sines is used to solve triangles when you have information about the measures of angles and sides, but do not have a right angle. It relates the ratios of the lengths of the sides of a triangle to the sines of its angles.

The Law of Cosines:

The law of cosines is used to solve triangles when you have information about the measures of angles and sides, and at least one side is known. It relates the lengths of the sides of a triangle to the cosine of one of its angles.

The Ambiguous Case:

The ambiguous case, also known as the law of sines with the ambiguous case, is used to solve triangles when you have information about the measures of angles and sides, and want to find all possible solutions. It occurs when you have one angle and two sides given, but there are two possible triangles that can be formed.

General Guidelines:

Answer:

maybe 2,800,000