Which of the following could be the first step to prove the Law of Cosines using the triangle below?

Answer: 14 ounces

Step-by-step explanation:

         To find the mean, we add up all the values and divide by the number of values.

\(\displaystyle \frac{12+14+15+15+14}{5} =\frac{70}{5} =14\;ounces\)

Answer:

The answer is y = -1/3x + 5 !

Step-by-step explanation:

If you observe the line, the y-intercept is 5, from the point in the graph (0,5). From that point, we can see that the rise over run is -1/3. Thus, y = -1/3x + 5.

If x and y have a common prime factor then y and x also have a common prime factor,so x and y are symmetric.

If x-y is divisible by 3 then y-x is also divisible by 3.so it is symmetric and x-y is reflexive as x ∈Z+ ,x-y is a multiple of 3.so it is reflexive.

If x,y and y,z are primes then x,z are also primes.So it is transitive and it is also symmetric If x,y are primes then y,x are also primes.

x and y are symmetric since (a,b)∈ R⇒ a,b are prime and their difference is 2⇒(b,a)∈ R

Step-by-step explanation:

Part a:  x and y have a common prime factor

If x and y have a common prime factor then y and x also have a common prime factor, so x and y are symmetric.

Reflexive: x and y are not reflexive since {1,1}∉ R(1 has no prime factor)

Symmetric: If x and y have a common prime factor then y and x also have a common prime factor , so x and y are symmetric.

Irreflexive: refer point A(above)

Transitive: x and y are not transitive since {2,9}∉ R(has no common prime factor)

Anti symmetric: x and y are not anti symmetric [Refer point B(above)]

If x and y have a common prime factor then y and x also have a common prime factor, so x and y are symmetric.

b) x - y is a multiple of 3

If x-y is divisible by 3 then y-x is also divisible by 3.so it is symmetric and x-y is reflexive as x ∈Z+ ,x-y is a multiple of 3.so it is reflexive.

Symmetric: If x-y is divisible by 3 then y-x is also divisible by 3.so it is symmetric.

Antisymmetric x-y is not anti symmetric (refer above)

Irreflexive refer point D

Reflexive : x-y is reflexive as x ∈Z+ ,x-y is a multiple of 3.

Transitive: if x-y,y-z is multiples of 3 then x-z is also multiples of 3.so it is also transitive.

(c) x and y are both prime

If x,y and y,z are primes then x,z are also primes.So it is transitive and it is also symmetric If x,y are primes then y,x are also primes.

Transitive: If x,y and y,z are primes then x,z are also primes.So it is transitive.

irreflexive Refer It is not reflexive since {4,4}∉ R(4 is not a prime)

Symmetric:  If x,y are primes then y,x are also primes.So it is symmetric..

Reflexive:It is not reflexive since {4,4}∉ R(4 is not a prime)

Antisymmetric: Refer point C

(d) x and y are twin primes (they are primes and their distance is 2)

x and y are symmetric since (a,b)∈ R⇒ a,b are prime and their difference is 2⇒(b,a)∈ R

Symmetric: x and y are symmetric since (a,b)∈ R⇒ a,b are prime and their difference is 2⇒(b,a)∈ R

Irreflexive Refer point D

Antisymmetric Refer point A

Reflexive:  It is not reflexive since {4,4}∉ R

Transitive: It is not transitive because (3,5)∈R and (5,3)∈R but (3,7)∉ R

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The difference of the algebraic expressions is 3x² - 11x + 4

An algebraic expression is an expression that is made up of variables and constants, along with algebraic operations like addition, subtraction, square root, etc.

The difference of two algebraic expressions means the subtraction of the expressions. That is:

(-4x+3) - (7x - 3x² - 1) = -4x+3 -7x+3x²+1

                                 =  3x² - 11x + 4

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Answer:

9.8

Step-by-step explanation:

I checked on google

Answer:

9.8

Step-by-step explanation:

The vertices of the reflected square.

Let's calculate them:

A' = (-0.914, 3.914)

B' = (-2.828, 5.828)

C' = (-0.086, 7.086)

D' = (1.828, 5.172)

The vertices of the image of the square ABCD after reflecting it about the line through (0, 0) and (-2, 2), we can use the following steps:

Find the equation of the reflection line:

The reflection line passes through (0, 0) and (-2, 2).

We can calculate the slope (m) of the line using the formula (y2 - y1) / (x2 - x1):

m = (2 - 0) / (-2 - 0) = 2 / -2 = -1.

Using the point-slope form of a line (y - y1) = m(x - x1), we can use either of the given points to write the equation of the line:

y - 0 = -1(x - 0)

y = -x.

Find the midpoint of each side of the square:

The midpoints of the sides of a square are also the midpoints of its diagonals.

The midpoint of AB is ((4+6)/2, (3+4)/2) = (5, 3.5).

The midpoint of BC is ((6+5)/2, (4+6)/2) = (5.5, 5).

The midpoint of CD is ((5+3)/2, (6+5)/2) = (4, 5.5).

The midpoint of DA is ((3+4)/2, (5+3)/2) = (3.5, 4).

Reflect the midpoints about the line:

To reflect a point (x, y) about the line y = -x, we can find the perpendicular distance (d) from the point to the line and use it to determine the reflected point.

The perpendicular distance d from the line y = -x to a point (x, y) is given by the formula:

d = (y + x) / √(2).

The coordinates of the reflected points can be found using the formula for reflection across a line:

x' = x - 2d / √(2)

y' = y - 2d / √(2).

Calculate the reflected vertices:

The coordinates of the reflected vertices are as follows:

A' = (4 - 2(3.5 + 5) / √(2), 3 - 2(3.5 - 5) / √(2))

B' = (6 - 2(5 + 5) / √(2), 4 - 2(5 - 5) / √(2))

C' = (5 - 2(5.5 + 5) / √(2), 6 - 2(5.5 - 5) / √(2))

D' = (3 - 2(4 + 5) / √(2), 5 - 2(4 - 5) / √(2))

Now we can plot the original square ABCD and its image A'B'C'D' on the same graph to visualize the reflection.

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━━━━━━━☆☆━━━━━━━

▹ Answer

$1.30

▹ Step-by-Step Explanation

To find the price per pound, you have to divide the total amount of money by the amount of pounds:

$7.80/6 lbs = $1.30

Hope this helps!

CloutAnswers ❁

━━━━━━━☆☆━━━━━━━

Answer:

(a) - 3/2

(b) - 78/25

Step-by-step explanation:

According to the trigonometry, the tangent of any angle is the ratio of rise to the run of the right angle triangle .

The sine of an angle is the ratio of rise to the hypotenuse of the right angle triangle.

The cosine of an angle is the ratio of run to the hypotenuse of the right angle triangle.

(a)

\(tan\beta = \frac{3}{-2} = \frac{-3}{2}\)

(b)

\(13 sin\beta cos \beta = 13\times \frac{3}{\sqrt{3^2+2^2}}\times\frac{-2}{\sqrt{3^2+2^2}}\\\\13 sin\beta cos\beta = \frac{- 78}{25}\)

The correct answer is D. No because 23 and 25 are not supplementary.

In the given diagram, it is stated that the measures of angles 23 and 27 are 45°, and the measure of angle 25 is 135°. To determine if lines C and D are parallel, we need to analyze the angles formed by these lines.

If the alternate interior angles or corresponding angles are congruent, then the lines are parallel. However, in this case, we don't have enough information about the angles formed by lines C and D to make that determination.

The fact that angle 23 and angle 27 are congruent (both measuring 45°) doesn't provide any information about the relationship between lines C and D. Similarly, the measure of angle 25 being 135° doesn't give us any insight into the parallelism of lines C and D. Therefore, we cannot conclude that lines C and D are parallel based on the given information, and the correct answer is D.

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Answer:

quotient is undefied

Step-by-step explanation:

The surface area of the complex solid is 530 square yards.

In this problem we need to determine the surface area of the complex solid, that is, the sum of the area of all faces of the solid. The area formulas required to find the surface area is:

A = w · h

Where:

The surface area of the complex solid is:

A = 2 · (11 yd) · (3 yd) + 2 · (4 yd)² + (12 yd) · (11 yd) + (12 yd) · (3 yd) + (12 yd) · (7 yd) + 2 · (4 yd) · (12 yd) + (12 yd) · (7 yd)

A = 66 yd² + 32 yd² + 132 yd² + 36 yd² + 84 yd² + 96 yd² + 84 yd²

A = 530 yd²

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Answer:

...

Step-by-step explanation:

...

Answer:

12/log3

Step-by-step explanation:

Hope it helps you

Answer:

y ≈ 2.262

Step-by-step explanation:

Using the rule of logarithms

log\(x^{n}\) = nlogx

Given

\(3^{y}\) = 12 ( take log of both sides )

log\(3^{y}\) = log12 , then

ylog3 = log12 ( divide both sides by log3 )

y = \(\frac{log12}{log3}\) ≈ 2.262 ( to 3 dec. places )

Answer:

130 will be correct answer

Step-by-step explanation:

The three angles are

34° 70° and 126°

we have to find fourth angle

let us consider fourth angle as X

The sum of quadrilateral is 360°.

So

34°+70°+126°+ x = 360°

130+X =360°

X = 360°-130°

X = 230°

Here we got the fourth angle

The solution to the given system of equation is -3

Given the system of equation below;

-4x+3y= = -21

-2x -3y = 3

Add both equation to have;

-4x - 2x = -21 + 3

-6x = -18

x =. 3

Substitute x = 3 into any of the equation to have;

-2(3) - 3y = 3

-6 - 3y = 3

-3y = 3 + 6

-3y = 9

y = -3

Hence the solution to the given system of equation is -3

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Answer:

Perry's claim is correct while Karina is incorrect

Step-by-step explanation:

Question is incomplete (See Attachment)

First, we need to determine the area covered by Karina and Perry

For Karina, there are 9 square boxes each of which has an area of 1 unit sq

So:

\(Karina = 9 * 1\ unit^2\)

\(Karina = 9\ unit^2\)

For Perry:

There are 18 square boxes, each of which has an area of 1 unit sq.

So:

\(Perry = 18 * 1\ unit^2\)

\(Perry = 18\ unit^2\)

Comparing both areas, we can conclude that Perry's claim is correct while Karina is incorrect

Answer:

9 squares

Step-by-step explanation:

Anne bought a piece of ribbon = 7 over 9 m long = 63 m²

she used = 3 over 18 m = 54 m²

left = 9 m²

maximum number of squares she could form of 1 m = 9

The following area tagged expression or sentence as;

1. Expression

2. Expression

3. Sentence

4. Sentence

5. Expression

Algebraic expressions are described as expressions that are composed of variables, terms, coefficients, factors and constants.

These expressions are also identified with various mathematical or arithmetic operations, such as;

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The completely factoring form of 6a^2 - 15a + 6 is 3(2a - 1)(a - 2).

To completely factor the expression 6a^2 - 15a + 6, the first step is to check if there is a common factor among the coefficients (6, -15, and 6) and the terms (a^2, a, and 1).

In this case, we can see that the common factor among the coefficients is 3, so we can factor out 3:

3(2a^2 - 5a + 2)

Now we need to factor the quadratic expression inside the parentheses further. We are looking for two binomials that, when multiplied, give us 2a^2 - 5a + 2. The factors of 2a^2 are 2a and a, and the factors of 2 are 2 and 1. We need to find two numbers that multiply to give 2 and add up to -5.

The numbers -2 and -1 fit this criteria, so we can rewrite the expression as:

3(2a - 1)(a - 2)

Therefore, the completely factored form of 6a^2 - 15a + 6 is 3(2a - 1)(a - 2).

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The equation y(x,t)=0.8[(4x+5t)2+5] , represents a moving pulse where x and y are in meter and t is in second.

i) Direction of wave propagation is negative x-axis.

ii) The wave speed is 1.25m/s.

iii)The maximum displacement from the mean position (i.e., the amplitude of the wave) is 0.16 m.

iv)The wave pulse is symmetric.

We compare the given wave equation from the standard wave equation. On comparing, direction and wave speed is found out. The Remaining two parts are found by maxima concept and changing x by −x at t=0 to get a wave is symmetric.

Moving pulse is given by

⇒y(x,t)=0.8[(4x+5t)2+5]

Comparing (4x+5t) with (ax+bt) then we get,

⇒a=4 and b=5 ⋯⋯⋯(1)

(i) When coefficients of x and t are positive then the wave pulse is moving negative x-direction. So, given an equation with coefficients a = 4 and b= 5 are positive. Therefore, the direction of the given equation will be negative x axis.

(ii) After getting the coefficient a and b, we can calculate the speed by determining the value of b/a. And we have value of a =4 and b =5 from the equation (1) .Then speed of the wave will be

=> b/a=5/4

=> speed of the wave =1.25m/s

(iii) To get the maximum displacement from the mean position we put (4x+5t)=0. As the denominator is minimum, the fraction will be maximum. Therefore displacement will be

=> y=0.85, putting the (4x+5t) is equal to zero.

After simplify we get,

=> y=0.16 m

Hence maximum displacement is 0.16m from the mean position,

(iv) We replace x by −x and also put t= 0 in the given equation. If the equation does not change, replacing the x by −x, it will be symmetric otherwise not.

Putting t=0 in the given equation y(x,t) we get,

=> y=0.8(4x)2+5

Now replace x by −x on the above equation we get, y=0.8(4x)2+5

there will not be any change. Therefore, the given equation is symmetric.

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Complete question:

If y(x,t)=0.8[(4x+5t)2+5] , represents a moving pulse where x and y are in meter and t is in second. Find

(i) Direction of wave propagation.

(ii) The wave speed.

(iii) The maximum displacement from the mean position (i.e., the amplitude of the wave)

(iv) Whether the wave pulse is symmetric or not.

Answer:

\(2\frac{3}{4}\)

Step-by-step explanation:

Let's bring them to the same denominator: 4

\(2\frac{1}{4} = 2 + \frac{1}{4} = \frac{2\cdot 4}{4} + \frac{1}{4} = \frac{8}{4} + \frac{1}{4} = \frac{9}{4}\\~\\5 = \frac{5\cdot 4}{4} = \frac{20}{4}\\~\\5 - 2\frac{1}{4} = \frac{20}{4} - \frac{9}{4} = \frac{11}{4} = \frac{8}{4} + \frac{3}{4} = \frac{2\cdot 4}{4} + \frac{3}{4} = 2 + \frac{3}{4} = 2\frac{3}{4}\)

Answer:

6 times x

Step-by-step explanation:

6x can be written as (6)(x) which can be written as 6 *x, or 6 times x.

[] When you have two numbers next to each other like this, and one of them is a variable, you multiply them together.

[] While 6x can be written as 6 x x you can see it gets confusing as the multiplication sign looks a lot like the variable, so 6 x x can be written as 6x for this reason as well

Have a nice day!

     I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

Answer:

"6 times x"

Step-by-step explanation:

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

In many algebraic equations and expressions, the multiplication sign is usually omitted, especially when there is a coefficient getting multiplied by a variable.

For example, if we were to write the expression '3 times y' we would write it as '\(3y\)' and not '\(3 \times y\)' for efficiency.

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

Hope this helps.

Given:

A circle with a center at C.

Required:

We need to find the names of the given parts.

Explanation:

Recall that radius is a line segment extending from the center of a circle to the circumference.

Line segment AC extends from the center C of a circle to the circumference.

Recall that the arc of a circle is defined as the part of the circumference of a circle.

AE is the part of the circumference of a circle.

Recall that a straight line segment joins and is included between two points on a circle.

D and E are two points on a circle.

A straight line DE line segment joins and is included between two points D and E on a circle.

Recall that meeting a curve or surface in a single point if a sufficiently small interval is considered a straight line tangent to a curve.

AB is tangent.

Recall that an inscribed angle is an angle with its vertex "on" the circle, formed by two intersecting chords.

Recall that a central angle is an angle formed by two radii with the vertex at the center of the circle.

Recall that an angle formed by an intersecting tangent and chord has its vertex "on" the circle.

Final answer:

Answer:

x = 9.9 in.

Step-by-step explanation:

area of triangle = base * height /2

49 = x*x /2

49*2 = x^2

98 = x^2

\(\sqrt{98}\) = x

\(7\sqrt{2}\) = x

9.9 = x