Is this how I do a sign analysis table? I’m not sure if I should include the x^2…

The value of sin 3° will be;

⇒ sin 3° = 1/8 (√(3 - √5) (√3 + 1) - √ (5 + √5) (√3- 1)

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The values are,

sin 18° = √(3 - √5) / 2√2

cos 18° = √ (5 + √5) / 2√2

Now,

Find the value of sin 3° as;

⇒ sin 3° = sin (18 - 15)°

   = sin 18° cos 15° - cos 18° sin 15°

   = √(3 - √5) / 2√2 × (√3 + 1) / 2√2  - √(5 + √5) / 2√2 × (√3-1)/2√2

   = 1/8 (√(3 - √5) (√3 + 1) - √ (5 + √5) (√3- 1)

Thus, The value of sin 3° will be;

⇒ sin 3° = 1/8 (√(3 - √5) (√3 + 1) - √ (5 + √5) (√3- 1)

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When the students get reduced to 15 then each student will get 3 pens.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

Total students = 25

Each Student get 2 pens.

So, 25 students get = 25 x 2= 50 pens

Now, number of children reduced = 25 -10= 15

So, each student get = 50/ 15 = 3.333 = 3 pens

Hence, each student will get 3 pens.

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By doing addition and subtraction of integers, the result obtained is

Mohammed had $5290 at the end of the month

What is addition and subtraction of integers?

At first it is important to know about integers

Integers are those numbers which has no fractional part. Integer can be positive, negative and zero is also an integer.

Suppose there are many integers, and we need to find the sum total of all those integers, then the operation used in this case is called addition.

To find how big or small one integer is from the other, then the operation used is called subtraction of integers.

Here we will use addition and subtraction of integers

Bank balance of Mohammed = $8376

Amount of money taken out by Mohammed next month to buy a car = $4595

Amount of money needed to buy new tires for his car = $1200

Amount of salary received by Mohammed next day = $2709

Amount of money Mohammed had at the end of the month =

$(8376 - 4595 - 1200 + 2709)

= $5290

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Answer:

Step-by-step explanation:

Each exponent on the left side is a positive number and therefore their sum is positive too.

But we have a negative value on the right.

This is not possible, hence no solutions.

Answer:

Step-by-step explanation:

Answer:

48 fl oz = 6 c

4 gal = 16 qt

Step-by-step explanation:

4 times 4 is 16

48 divided by 8 is 6

keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above

[tex]y=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{1}{3}}x+7\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

so we're really looking for the equation of a line whose slope is -1/3 and that it passes through (-2 , 5.5)

[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{5.5})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{1}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5.5}=\stackrel{m}{- \cfrac{1}{3}}(x-\stackrel{x_1}{(-2)}) \implies y -5.5= -\cfrac{1}{3} (x +2)[/tex]

[tex]y-5.5=-\cfrac{1}{3}x-\cfrac{2}{3}\implies y=-\cfrac{1}{3}x-\cfrac{2}{3}+5.5\implies y=-\cfrac{1}{3}x-\cfrac{2}{3}+\cfrac{55}{10} \\\\\\ y=-\cfrac{1}{3}x-\cfrac{2}{3}+\cfrac{11}{2}\implies {\Large \begin{array}{llll} y=-\cfrac{1}{3}x+\cfrac{29}{6} \end{array}}[/tex]

Answer:

48 square inches

Step-by-step explanation:

A=1/2 bh

A=(1/2)(8)(12)

A=(4)(12)

A=48 square inches

you can also multiply 8 x 12 then divide by 1/2 or 2 which is still 48. either way is correct but since the formula is half of the base times height that is the step i followed. Also area is always whatever measurement used (in this case inches) squared.

The composite function ( f. g(x)) is x² + 4x + 3

A function can be described mathematically as a rule, law or equation that explains, shows and elaborates the relationship between to variables.

The variables are known as;

From the information given, we have the functions as;

To determine the composite function ( f. g(x)), we have to substitute the value of g(x) as a function in the function f(x) as the variable 'x', we get;

( f. g(x)) = (x + 2)² - 1

Now, let's expand the square

( f. g(x)) = (x + 2) ( x+ 2) - 1

Expand the bracket

( f. g(x)) = x² + 2x + 2x + 4 - 1

Now, let's collect like terms, we get

( f. g(x)) = x² + 4x + 3

Thus, the function is x² + 4x + 3

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The complete question:

Find ( f. g(x)) if f(x)=x^2-1, g(x)=x+2

Answer: no slope

Step-by-step explanation:
m= y2-y1/x2-x1

m= 6-(-6)/4-4

m=12/0

m= no slope

Answer:

y = 0.8x - 0.8

Step-by-step explanation:

Δy ÷ Δx = gradient (x)

4 - -4 = 8

6 - -4 = 10

8 ÷ 10 = 0.8

equation of line; y = mx + c

substitute one of the coordinates into the equation

(6, 4) y  = 4, x = 6

4 = 0.8(6) + c

4 = 4.8 + c

- 4.8 to get the y intercept on it's own

-0.8 = y intercept (c)

confirmation

substitute the new values to get the other y

(-4, -4) y = -4 <-- should be the answer, x = -4

y = mx + c

y = 0.8(-4) - 0.8

y = -3.2 - 0.8

y = -4 the gradient and the y intercept have been proven right

Answer:

[tex]34.8w+5.2x[/tex] cm

Step-by-step explanation:

If the width of a rectangle measures [tex](9.6w+4.7x)[/tex] cm and its length measures [tex](7.8w-2.1x)[/tex] cm, then the perimeter of the rectangle is:

[tex]2(9.6w+4.7x)+2(7.8w-2.1x)[/tex]

[tex](19.2w+9.4x)+(15.6w-4.2x)[/tex]

[tex]19.2w+9.4x+15.6w-4.2x[/tex]

[tex]19.2w+15.6w+9.4x-4.2x[/tex]

[tex]34.8w+5.2x[/tex]

The coordinate of point B is such that M (1,-8) is the midpoint of A(-6,-12) and B will be (5,-2).

A pair of numbers that employ the horizontal and vertical distinctions from the two reference axes to represent a point's placement on a coordinate plane. typically expressed by the x-value and y-value pairs (x,y).

The coordinate of midpoint between two points  (x₁, y₁) and (x₂, y₂) is given by,

( (x₁ + x₂)/2 ,(y₁+ y₂)/2)

Given that, M is the midpoint of A and B.

Let's say the coordinate of point B is B(x,y).

Then,

1 = (-3 + x)/2

x = 2 + 3 = 5

And,

(-6 + y)/2 = -4

y = -8 + 6 = -2

Hence "The coordinate of point B is such that M (1,-8) is the midpoint of A(-6,-12) and B will be (5,-2)".

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The value of v from the given equation v=u+at is 42

An equation is a mathematical expression that contains an equals symbol

From the given equation v=u+at

u=18

a=6

t=4

Substituting for u,a and t in the equation

v=18+6(4)

expanding the bracket

v=18+24

v=42

Hence, the the v in the equation v=u+at is 42

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[tex]x=2.16*10^{11}u-7.2k[/tex].

Side note: This answer could be more precise if made usage of more significant figures. For practicality reasons, in this solution we reduced the amount of significant figures to use.

[tex]150u=0.694(x+7.2K)*10^-9[/tex]

[tex]150u=[(0.694*x)+(0.694*7.2K)]*10^-9\\\\150u=[0.694x+4.9968k]*10^-9\\ \\150u=10^-9*0.694x+10^-9*4.9968k[/tex]

[tex]150u-10^-9*0.694x=10^-9*0.694x-10^-9*0.694x+10^-9*4.9968k\\ \\150u-10^-9*0.694x=10^-9*4.9968k[/tex]

[tex]-150u+150u-10^-9*0.694x=10^-9*4.9968k-150u\\ \\-10^-9*0.694x=10^-9*4.9968k-150u[/tex]

5. Divide both sides by "-10^-9*0.694".

[tex]\frac{-10^-9*0.694x}{-10^-9*0.694} =\frac{10^-9*4.9968k-150u}{-10^-9*0.694} \\ \\\frac{-10^-9*0.694x}{-10^-9*0.694} =\frac{10^-9*4.9968k}{-10^-9*0.694}-\frac{150u}{-10^-9*0.694} \\ \\x=-7.2k-(-2.16*10^{11} u)\\ \\x=-7.2k+2.16*10^{11}u\\ \\x=2.16*10^{11}u-7.2k[/tex]

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The length of one sides of the square Tito's Kitchen is 13 feet.

A square is a quadrilateral with 4 sides equal to each other. The opposite sides of a square is parallel to each other.

The sum of angles in a square is 360 degrees. Each angle is 90 degrees.

The kitchen is a square and has an area of 169 square feet.

The length of one side of the kitchen can be calculated as follows:

area of the square kitchen = l²

where

Therefore,

area of the square kitchen = 169 ft²

169 = l²

square both sides of the equation

√169 = √l²

l = 13 ft

Therefore,

length of the square kitchen = 13 feet.

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Answer: 3274 cookies

Step-by-step explanation:

She sold : 2016 ÷ 8 = 252 ( bags )

The remaining cookies : 12 × 252 = 3024 ( cookies )

She baked : 3024 + 250 = 3274 ( cookies )

Using prime factorization, the LCM and GCF of numbers are

1) For 46 and 4

GCF = 2

LCM = 92

2) For 2 and 34

GCF = 2

LCM = 34

3) For 32 and 4

GCF = 4

LCM = 32

A natural number other than 1 with just the number 1 and itself as factors is known as a prime factor. Actually, 2, 3, 5, 7, 11, and so on are the first few prime numbers. For numbers, we may now also employ what is known as prime factorization, which really involves utilizing factor trees.

When a number is expressed as the product of its prime factors, this is known as prime factorization.

1) The factors of the numbers are

46 = 2 × 23

4 = 2 × 2

GCF = 2

LCM = 2 × 2 × 23

= 92

2) The factors of 34 are

34 = 2 × 17

GCF = 2

LCM = 2 × 17

=34

3) The factors of the numbers are

32 = 2 × 2 × 2 × 2 × 2

4 = 2 × 2

GCF = 2 × 2

= 4

LCM = 2 × 2 × 2 × 2 × 2

= 32

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The co-ordinates of the mid-point of the line PQ are (6,4).

From the question, we have

The point P has co-ordinates (10, 12) and the point Q has co-ordinates (2,-4).

Mid-point of the line PQ =(10+2)/2 , (12-4)/2

= (6,4).

Midpoint:

A location in the middle of a line connecting two points is referred to as the midpoint. The midpoint of a line is located between the two reference points, which are its endpoints. The line that connects these two places is split in half equally at the halfway. In addition, the halfway is reached if a line is drawn to divide the line that connects these two places. When we know the coordinates of two points, we can apply the midpoint formula to get the midpoint between them. If we know the coordinates of the other endpoint and the midpoint, we can use the midpoint formula to obtain the coordinates of the endpoint as well.

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The pattern is that two larger numbers differ by 2 and the smaller is the root of twice the sum of the larger two.

The given formula gives rise to the above observations. it tells you

a = 2x

b = x^2 -1

c = x^2 +1

This is a special case of Euclid's formula ...

a = 2mn

b = m^2 -n^2

c = m^2 +n^2

for n=1.

Since m and n can be any integer values, there are certainly many other. Pythagorean triples that do not match the formula given in the problem. Using n=2, for example, the triples are:

a = 4x

b = x^2 -4

c = x^2 +4

Some triples from this set of formulas are (5, 12, 13), (20, 21, 29), (28, 45, 53), (36, 77, 85).

It should bm be noted that triples from this set of formulas will not match directly those from the formulas in the problem statement, but triples from both lists may reduce to the same primitive triple.

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Complete question

Examine this set of Pythagorean triples from part C. Look for a pattern that is true for each triple regarding the difference between the three values that make up the triple.

Describe this pattern. Then see if you can think of another Pythagorean triple that doesn’t follow the pattern you just described and that can’t be generated using the identity (x2 − 1)2 + (2x)2 = (x2 + 1)2. Explain your findings.

x-value Pythagorean Triple

3 (6,8,10)

4 (8,15,17)

5 (10,24,26)

6 (12,35,37)

The measure of the intercepted arc, [tex]\widehat{XY}[/tex], formed by the secants ZW and ZV is 30°

A secant line is a straight-line which has two points of intersection with a circle.

From a similar question on the internet, the figure consists of an outside angle of 41° formed by two secants and two intercepted consisting of [tex]\widehat{XY}[/tex]and [tex]\widehat{VW}[/tex] which measures 112°

The outside angles of a circle theorem states that the outside angle formed by two secants or two tangent or a combination of a secant and a tangent is the difference of the measure of the difference of the angles of the intercepted arcs divided by two.

Mathematically;

[tex]m\angle z = \dfrac{\widehat{VW} - \widehat{XY}}{2}[/tex]

Where;

The outside angle formed by the secant ZW and ZV, m∠z = 41°

[tex]\widehat{VW}[/tex] = 112°

Which gives;

[tex]41^{\circ}= \dfrac{112^{\circ}- \widehat{XY}}{2}[/tex]

2 × 41° = 112° - [tex]\widehat{XY}[/tex]

82° = 112° - [tex]\widehat{XY}[/tex]

[tex]\widehat{XY}[/tex] = 112° - 82° = 30°

[tex]\widehat{XY}[/tex] = 30°

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The equations in order from least to greatest unit rate are y = 13/6x,y = 11/5x, y = 21/9x and y = 19/8x

On a graph, the unit rate is obtained by calculating the slope of the line. The slope is the change in y divided by the change in x:

Slope = y2-y1 / x2-x1  

Thus, we can any two convenient points on the graph and use it calculate the slope:

Let's pick points (5, 10) and (12, 25)

This implies x1 = 5, y1 = 10 and  x2 = 12, y2 = 25

Slope = y2-y1 / x2-x1

Slope = 25-10 / 12-5 = 15/7

Thus,  the unit rate of the graph is 15/7 = 2.143

Find the equations with unit rates greater than the unit rate of the graph:

y = 19/8x: unit rate = 19/8 =  2.375

y = 27/13x: unit rate = 27/13 = 2.077

y = 21/9x: unit rate = 21/9 = 2.333

y = 11/5x: unit rate = 11/5 = 2.200

y = 15/17x: unit rate = 15/17 = 0.882

y = 31/15x: unit rate = 31/15 = 2.067

y = 13/6x: unit rate = 13/6 = 2.167

The equations with unit rates greater than the unit rate of the graph are y = 19/8x, y = 21/9x, y = 11/5x and y = 13/6x

Therefore, the equations in order from least to greatest unit rate are y = 13/6x,y = 11/5x, y = 21/9x and y = 19/8x. Drag each tile to the correct box accordingly

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The time that the three buses will next arrive at the station, given the time between their individual arrivals is 10 am.

Service A arrives every 15 minutes. Service B arrives every 20 minutes. Service C arrives every 30 minutes.

The goal is to find the time when all services arrive at the same time. This can be found by finding the LCM of all three times. This will show the shortest time till all services arrive.

The LCM of 15 minutes, 20 minutes, and 30 minutes is 60 minutes.

The three bus services will arrive at the same time in 60 minutes which is:

= 9 am + 60 minutes

= 10 am

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The statement that is most likely correct for the negatively skewed data distribution given is B. The mean is less than the median.

What is a Negatively Skewed Data Distribution?

A negatively skewed data distribution has the tail to the left of the number line, and therefore its median is usually greater than its mean.

The dot plot shows a data distribution that is negatively skewed. Therefore, the statement that is most likely to be true is B. The mean is less than the median.

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The standard form of the equation, 3y = 9x -12, is -5x + y = 0.5. The correct option is the third option -5x+y=0.5

From the question, we are to write the given equation is standard form.

The given equation is

y = 5x + 0.5.

The standard form of a linear equation is

Ax + By = C

Where A, B, and C are constants

x and y are variables

Now, we will write the given equation is the standard form of a linear equation.

y = 5x + 0.5

Subtract 5x from both sides of the equation

y - 5x = 5x - 5x + 0.5

y - 5x = 0.5

Rewrite the equation, so that it would correspond to the standard form of a linear equation

-5x + y = 0.5

Hence, the standard form is -5x + y = 0.5

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The critical values of the chi statistic are; χ²R = 8.643 and χ²L = 42.796

The confidence interval estimate of σ is; 0.20 < σ < 0.45

We are given the following data;

Sample size; n = 23

Degree of freedom; df = n - 1 = 23 - 1 = 22

Confidence level; α - level = 99%

Sample standard deviation; s = 0.25 mg

For χ²R;

The significance level is; 1 - (1 - 0.99)/2= 0.995

The degree of freedom is; df = 22

From critical value tables, we know that; χ²R = 8.643

For χ²L ;

The significance level is; (1 - 0.99)/2 = 0.005

The degree of freedom is; df = 22

From critical value tables, we know that; χ²L = 42.796

The confidence interval estimate of σ is;

s * √[(n-1)/χ²L] < σ < s * √[(n-1)/χ²R)]

Plugging in the relevant values gives;

0.28 * √(22/42.796) < σ < 0.28 * √(22/8.643)

0.2008 < σ < 0.4467

0.20 < σ < 0.45

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The answer will be the graph of the straight line.

What is the equation straight line?

Y = mx + c is the general equation for a straight line, where m denotes the line's slope and c the y-intercept. It is the version of the equation for a straight line that is used most frequently in geometry. There are numerous ways to express the equation of a straight line, including point-slope form, slope-intercept form, general form, standard form, etc. A straight line is a geometric object with two dimensions and infinite lengths at both ends. The formulas for the equation of a straight line that are most frequently employed are y = mx + c and axe + by = c. Other versions include point-slope, slope-intercept, standard, general, and others.

Using the equation we can plot the graph in 2D.

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