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Exact value of the expression cos (2  [tex]tan^-^1 (\frac{4}{3})[/tex]) = -7/25 . which is the cosine of the value of an angle 2 [tex]tan^-^1 (\frac{4}{3})[/tex]) .

let  [tex]tan^-^1 (\frac{4}{3})[/tex] = θ

so tan θ = 4/3

tan θ = p/b

Trignometic angle formula

so  p= 4k and b= 3k where k is a constant value.

h = [tex]\sqrt{p^2+b^2}[/tex]

=> [tex]\sqrt{16k^2+ 9k^2}[/tex]

=> 25k^2

=> 5k

where p is perpendicular , b is base and h is hypotenuse

so h= 5k

sin θ = p/h

=> 4k/5k

=> 4/5

cos  θ =b/h

=> 3k/5k

=> 3/5

and cos (2  [tex]tan^-^1 (\frac{4}{3})[/tex]) = cos (2θ)

cos (2θ) = 2 [tex]cos^2[/tex] θ -1

=> 2 * [tex]\frac{3}{5} ^2[/tex] - 1

=> 18/25 -1

=> -7/25

so value of  cos (2  [tex]tan^-^1 (\frac{4}{3})[/tex]) = -7/25

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Answer:

x=4

y=3

Step-by-step explanation:

work attached here

Answer:

x=4, y=3. (4, 3).

Step-by-step explanation:

-3y=-2x-1

y=x-1

--------------

-3(x-1)=-2x-1

-3x+3=-2x-1

-3x-(-2x)+3=-1

-3x+2x=-1-3

-x=-4

x=4

y=4-1=3

not sure if you need the solution too but if you do it’s (3,-2)

Answer: 45 degrees

Step-by-step explanation:

By the inscribed angle theorem, the measure of an inscribed angle is half the measure of the intercepted arc. The measure of the central angle ∠POR of the intercepted arc ⌢PR is 90°. Therefore, m∠PQR=12m∠POR =12(90°) =45°.

Answer:

(6,3)

Step-by-step explanation:

x+3y=15

6+3×3=15

6+9=15

15=15

again

4x+2y=30

4×6+2×3=30

24+6=30

30=30

Hence the answer is (6,3)

Answer:

C.) 4,3

Step-by-step explanation:

The given system of equations is:

x + 3y = 15

4x + 2y = 30

The first equation can be rewritten as:

y = (15 - x)/3

Substituting this expression for y into the second equation gives:

4x + 2((15 - x)/3) = 30

Solving for x, we get:

x = 4

Substituting this value of x back into the first equation gives:

y = (15 - 4)/3 = 3

Therefore, the solution to the system of equations is (4,3).

Step 2 is the incorrect step and hence d is the correct answer.

The two angles are said to be adjacent angles when they share the common vertex and side. The endpoint of the rays, forming the sides of an angle, is called the vertex of an angle. Adjacent angles can be a complementary angle or supplementary angle when they share the common vertex and side.

Given here: m∠w + m∠z = 90 but this is not true because they are adjacent angles and they lie on a line so they must supplement each other.

m∠w + m∠z = 180

Hence, Step 2 is the incorrect step and hence d is the correct answer.

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The midpoint of a line segment with endpoints A(x1,y1) and B(x2,y2) is the point: M((x₁+x₂)/2,(y₁+y₂)/2)).

The midpoint formula is defined for the points in the coordinate axes. Let (x)1, (y)1, and (x)2, (y)2 be the endpoints of a line segment.

The midpoint is equal to half of the sum of the x-coordinates of the two points, and half of the sum of the y-coordinates of the two points.

The midpoint formula to calculate the midpoint of a line segment joining these points can be given as,

The midpoint is halfway between the two endpoints:

To calculate it:

Add both "x" coordinates, divide by 2

Add both "y" coordinates, divide by 2

M=(xA+xB/2,yA+yB/2)

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Makena deposited $0.70 per day.

In mathematics, the middle value—which is determined by dividing the sum of all the values by the total number of values—is the average value in a set of numbers. To calculate the average of a set of data, add up all the values and divide the result by the total number of values.

Given:

The savings account last month: $6.74, $5.21, $5.53, and $3.52.

Makena deposited $6.74,$5.21,$5.53 and $3.52 in her saving account.

To find the average amount she saves per day.

We add all the deposited savings

= ( 6.74 + 5.21 + 5.53 + 3.52)

= $21.031

Now, Makena Saved per day for the month = $21.031/30

                                                                        =$0.70

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Base e used in exponential functions because base e is the base rate of growth shared by all continually growing processes which lets us take a simple growth rate.

In an exponential function, the base b is a constant. The exponent x is the independent variable in which the domain is the set of real numbers. There are two types of exponential functions, those are exponential growth and exponential decay. In the function f (x) = b^x when b > 1, the function represents exponential growth.

Base e allows us to take a simple growth rate, where all change occurs at the end of the year, and find the influence of compound, continuous growth, where every nanosecond or faster, we are growing slightly.

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According to Pythagoras, the square with the longest side is equal to the total of the squares with two sides. Therefore, the triangle in question has an acute angle of 28.07 degrees.

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

The Pythagorean theorem is satisfied by the triangle's dimension. As a result, the triangle has a right angle.

The acute angle will then be

x = [tex]sin^{-1}8/17[/tex]

x = 28.07 degrees.

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Answer:

y = 1/3 x + 4

Step-by-step explanation:

Answer: 2 and 5.

Step-by-step explanation: We can use algebra to solve for the original numbers. Let's call the smaller number "a" and the larger number "b". From the information given, we know that:

x = b + a^2

y = b - a

The volunteer tells the magician that x = 9 and y = 3. So we can use these values to create a system of equations:

b + a^2 = 9

b - a = 3

To solve for the original numbers, we can first add the two equations together to eliminate b:

a^2 + 2a + 2 = 12

a^2 + 2a = 10

a^2 + 2a - 10 = 0

(a + 5)(a - 2) = 0

This tells us that the two solutions for a are -5 and 2. But since a is a positive integer, we know that it must be 2.

We can now substitute this value of "a" back into the original equations to find "b":

b + a^2 = 9

b + 2^2 = 9

b + 4 = 9

b = 5

So the original numbers are 2 and 5.

The lateral surface area of the cone is:

A = 84.3 in²

We know that for a cone of height H and a radius R, the lateral surface area is given by the formula:

A = pi*R*( √(H² + R²))

Where pi = 3.14

Here the height is 12 inches, and the diameter is 4.4 inches, then the radius is:

R = 4.4i/2 = 2.2 in

Then the lateral surface area is:

A = 3.14*2.2in*( √((12in)² + (2.2in)²))

A = 84.3 in²

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Answer:

25%

Step-by-step explanation:

percent change = (new value - old value)/(old value) × 100%

percent change = (20 - 16)/(16) × 100%

percent change = 25%

Constant of proportionality from side lengths in the original figure to side lengths in the scaled copy = 2/11

Proportion is a mathematical comparison between two numbers.  According to proportion, if two sets of given numbers are increasing or decreasing in the same ratio, then the ratios are said to be directly proportional to each other. Proportions are denoted using the symbol  "::" or "=".

Given,

f is the length of side of original figure

And s be the side of copied figure

f ∝ s

⇒ f = ks       --------(a)

where k is constant of proportionality

Proportion between side of original figure and its copy is such that

s = (11/2)f

f = (2/11)s      -----------(b)

comparing equation (a) and (b)

k = 2/11

Hence, 2/11 is constant of proportionality from side lengths in the original figure to side lengths in the scaled copy.

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Answer:

For example, we know that y = − 1 3 x + 5 y=\frac{-1}{3}x+5 y=3−1x+5 is perpendicular to y = 3 x − 2 y=3x-2 y=3x−2 because 3−1, the new slope, is the opposite reciprocal of 3, the original slope

Step-by-step explanation:

A 2-column table with 4 rows. The first column is labeled x with entries negative 5, 1, 4, 6.  The range is

{9, 0, -7, -1}.

Generally, The range is the difference between the largest and smallest values in a set of data. In statistics, it is a measure of the spread of a dataset, giving an indication of the extent to which values in the data vary. It is calculated by subtracting the minimum value from the maximum value in the dataset.

The range of a function is the set of all possible output values (y-values) of the function.

In this case, the range of the function would be {-1, 0, 7, 9}.

This is determined by looking at the y-values in the second column of the table: {9, 0, -7, -1}.

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the solutions for a system of equations is where the graphs of each equation meet or intersect.

for the picture above with two parallel lines, well, the lines are parallel and apart from each other, that means they never meet or intersect, and since they never intersect, they have no solution.

Answer:

(5x - 3)(x - 3)

Step-by-step explanation:

Yes, the expression "5x^2 - 8x + 9" can be factored.

One way to factor it is to find the two numbers that multiply to give 9 (the constant term) and add to give -8 (the coefficient of x). These two numbers are 3 and -3.

We can use these two numbers to factor out the common factor (x - 3) from the expression:

5x^2 - 8x + 9 = (5x^2 - 8x) + 9

= (5x^2 - 8x + 9) - 9 + 9

= (5x^2 - 8x + 9) - (3x - 3x)

= (5x - 3)(x - 3)

So the fully factored form of the expression is (5x - 3)(x - 3)

So, (5x - 3) and (x - 3) are the factors of the expression "5x^2 - 8x + 9"

Answer:

$3

Step-by-step explanation:

$13.99 is for one hour and one hour is for 3 children. This means they paid a total of 3 hours.

$13.99 * 3 = $41.97 for admission alone

Now our total is $50.97

Let's subtract that from admission to find sock price in total

$50.97-$41.97 = $9

Again, 3 children and each for a pair, so lets divide that $9 by 3 for each child.

$9/3 = $3

Triangle abc is congruent to triangle edf. So, priya knows that there is a sequence of rigid motions that takes abc to edf. From the rigid transformation that takes ABC to EDF, the coinciding parts based on congruency; are matched below.

Triangle congruence is when two triangles are said to be congruent to one another, it signifies that their corresponding sides and angles are equal.

Consequently, we can state that if triangle ABC and triangle EDF are congruent;

Angle A ≅ Angle E

Angle B ≅ Angle D

Angle C ≅ Angle F

Segment AB ≅ Segment ED

Segment AC ≅ Segment EF

Segment BC ≅ Segment DF

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The value of the equation is P ( 4 , 4 ) , where P is the point of intersection of the equations

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the first equation be represented as A

Now , the value of A is

4x - 2y = 8  

Adding 2y on both sides of the equation , we get

2y + 8 = 4x

Subtracting 8 on both sides of the equation , we get

2y = 4x - 8   be equation (1)

Now , let the second equation be represented as B

Now , the value of B is

y = ( 3/2 )x - 2

On simplifying the equation , we get

2y = 3x - 4   be equation (2)

Now , subtracting equation (2) from equation (1) , we get

4x - 8 - ( 3x - 4 ) = 0

4x - 8 - 3x + 4 = 0

x - 4 = 0

Adding 4 on both sides of the equation , we get

x = 4

Substitute the value of x = 4 in equation ( 1 ) , we get

2y = 8

y = 4

So , the value of x = 4 and y = 4

The equations are plotted on the graph and the point of intersection is the solution to the equation , P ( 4 , 4 )

Hence , the equations are solved

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Answer:

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p is inversely proportional to the square of q:

p is 20 when q is 7, substitute:

Find the value of k:

Determine p when q is equal to 2:

The derived units answers are 379 mg, 787 × 10^3 mg and 0.0743 kg.

What do you mean by units?

Unit is a quantity of constant magnitude which is used to measure the magnitudes of other quantities of the same manner

0.379 g = ? mg

as we know, 1 gram is equal to 1000 milligrams. i.e. 1 g = 1000 mg

∴ 0.379 × 1 g

= 0.379 × 1000 mg

= 379 mg

787 g = ? mg

as we know, 1 gram is equal to 1000 milligrams. i.e. 1 g = 1000 mg

∴ 787 × 1 g

= 787 × 1000 mg

= 787000 mg

= 787 × 10^3 mg

74.3 g = ? kg

as we know, 1 gram is equal to 1 / 1000 kilograms. i.e. 1 g = 1 / 1000 kg

∴ 74.3 × 1 g

= 74.3 × 1 / 1000 kg

= 74.3 / 1000 kg

= 0.0743 kg

Therefore, the derived units answers are 379 mg, 787 × 10^3 mg and 0.0743 kg.

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The probability of spinning an odd number, flipping heads, then spinning a yellow is of 1/9.

A probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

The probabilities for each case in this problem are given as follows:

The events are independent, hence the probability is obtained multiplying each probability as follows:

p = 2/3 x 1/2 x 1/3 = 1/9.

The complete problem is given by the image shown at the end of the answer.

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The value of the upper quartile is 24.

This method is used to divide a data set into four equal parts and find the values of the quartiles.

To calculate the upper quartile, we first need to find the median (the middle value) of the data set.

This question involves the use of the quartile calculation method.

This can be done by arranging the data in numerical order and finding the middle value.

In this case, the median value is 20.

The upper quartile is then calculated by finding the median of the values above the median.

In this case, the values above the median are 22, 24, 28, and 30.

To find the upper quartile, we need to calculate the median of these values.

This is done by arranging the values in numerical order and finding the middle value, which is 24. Therefore, the upper quartile is 24.

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