hello, please help me thanks:)​

Answer:

a) -0.7854

b) 2.36

Step-by-step explanation:

Here, we want to find the value of the angles in radians

We proceed as follows;

a) arcsin( - √2/2)

= -0.7854

b) arccos(-√(2)/2

= 2.36

Answer:

The function is:

y = f(-x) -2

Answer:

x<-12 or x>16

Step-by-step explanation:

Answer:

|x - 2| + 3 > 17

|x - 2| > 14

x - 2 < -14 or x - 2 > 14

x < -12 or x > 16

The length of the fence around the enclosure not including the gates is:2l + 2w + 8 m

To find the length of the fence around the enclosure, we need to first find the perimeter of the rectangle and then subtract the combined length of the two gates from it.

Let's assume the length of the rectangle is 'l' and the width is 'w'.

From the given data, we know that each gate is 4 m wide.

Therefore, the width of the rectangle is:

Width = w + (4 m + 4 m) = w + 8 m

The perimeter of the rectangle is:

P = 2l + 2(w + 8 m) = 2l + 2w + 16 m

Now, we need to subtract the combined length of the two gates from the perimeter:

P - 2 × 4 m = 2l + 2w + 16 m - 8 m = 2l + 2w + 8 m

So, the length of the fence around the enclosure not including the gates is:2l + 2w + 8 m

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Answer:

56л

Step-by-step explanation:

area of a pizza of 18 in=  лr²

                                         r=18/2=9

                                          area= л×9²

                                          =81л

area of a pizza of 10in=

                                      r=10/2=5

                                       area=л×5²

                                       =25л

difference=81л-25л

                =56л

Given,

When two angle of the angles are equal then the remaining third angle is also equal.

Beacuase the sum of the interior angle of triangle is 180 degree.

It make the third angle also equal.

Hence, angle A is congurent to angle O.

Statement 1 is true.

In the second statement,

when two triangle all its angles congurent then triangles are similar.

Statement 2 is true.

In the third statement,

If the angles are equal then it can be possible that sides are equal or not equal.

If the sides of the triangle are not congruent then triangle cannot be congruent.

Statement 3 is not true.

In the forth statement,

similar to the third statement, sides of the triangle can be congurent or not.

Statement 4 is false.

In the fifth statement,

The triangle are similar then its perimeter can be equal or half or in other fraction to each other.

Statement 5 is false.

Similarly, statement 6 ia true.As the angles are equal so the traingles can mapped onto.

Statement 7 is true.

The equation is proved.

G\(`tan(x-1)(sin2x-2cos2x)=2(1-2sinxcosx)`\)

We need to prove the given equation. Solution: Using the identity \(`sin2x=2sinxcosx` and `cos2x=1-2sin^2x`\)

in the given equation, we get

\(`tan(x-1)(sin2x-2cos2x)=2(1-2sinxcosx)`⟹ `tan(x-1)(2sinxcosx-2(1-\)

\(2sin^2x))=2(1-2sinxcosx)`⟹ `tan(x-1)(4sin^2x-2)=2-4sinxcosx`⟹ `2sin(x-1)\)

\((2sin^2x-1)=2(1-2sinxcosx)`⟹ `2sin(x-1)(2sin^2x-1)=2(1-2sinxcosx)`⟹\)

\(`2sinxcos(x-1)(4sin^2x-2)=2(1-2sinxcosx)`⟹ `2sinxcos(x-1)(2sin^2x-1)=1-\)

\(sinxcosx`⟹ `2sinxcos(x-1)(2sin^2x-1)=sin^2x+cos^2x-sinxcosx`⟹\)

`\(2sinxcos(x-1)(2sin^2x-1)=(sinx-cosx)^2`⟹ `sinxcos(x-1)(2sin^2x-1)=(sinx-cosx)^2/2`\)

For `LHS`, using identity

\(`sin(90 - x) = cosx`⟹ `sinxcos(x-1)(2sin^2x-1)=(sinx-sin(91-x))^2/2`⟹\)

\(`sinxcos(x-1)(2sin^2x-1)=(-sin(x-1))^2/2`⟹ `sinxcos(x-1)(2sin^2x-1)=sin^2(x-\)

\(1)/2`⟹ `sinxcos(x-1)(4sin^2x-2)=sin^2(x-1)`⟹ `sinxcos(x-1)(2sin^2x-1)=1/2`⟹ `1/2=1/2`.\)

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Answer:

17 players

Step-by-step explanation:

6 people scored 2

8 people scored 3

3 people scored 4

x ≤ 6

which is A

or if not then it's B for

x ≥ 6

Answer:

y= 2x -6

Step-by-step explanation:

The slope-intercept form of a line is given by y= mx +c, where m is the slope and c is the y-intercept.

To find the equation of a line, two information are needed:

Given that the slope is 2, m= 2. Substitute m= 2 into y= mx +c:

y= 2x +c

Let's find the coordinate in which the line intersects the line 2x -3y= 6. Point of intersection refers to the point at which two lines cuts through each other i.e., the point lies on the graph 2x -3y= 6 and the line of interest.

2x -3y= 6

When x= 3,

2(3) -3y= 6

6- 3y= 6

3y= 6 -6

3y= 0

Divide both sides by 3:

y= 0

Coordinate that lies on the graph is (3, 0).

Substitute the point into the equation and solve for c:

y= 2x +c

When x= 3, y= 0,

0= 2(3) +c

0= 6 +c

c= -6

Substitute the value of c back into the equation:

Thus, the equation of the line in slope-intercept form is y= 2x -6.

Additional:

For a similar question on slope-intercept form, do check out the following!

Answer:

the answer is 5/6

Step-by-step explanation:

Answer:

5/16

Step-by-step explanation:

The area of the rectangle will be equal to 11 square units.

Matrix is defined as the arrangement of the numbers variables and expressions in the table as rows and columns.

A matrix is a structured table with columns and rows for arranging numbers, expressions, and even symbols. If the two matrices have equal row and column sizes, they can be added to, subtracted from, and multiplied element by element.

The area of the rectangle is calculated by finding the determinant of the matrix as below,

\(A = \left[\begin{array}{cc}3&-1&\\5&2&\\\end{array}\right]\)

A = ( 6 - ( -5 )

A = 6 + 5

Area = 11 square units

Hence, the value of the area of the rectangle is 11 square units.

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The cost of the molding is given as follows:

$119.30.

The circumference of a circle of radius r is given by the equation presented as follows:

C = 2πr.

The parameters for this problem are given as follows:

d = 9 -> r = 4.5.

(as the radius is half the diameter)

Hence the circumference is given as follows:

C = 2 x π x 4.5

C = 28.27 ft.

The cost is of $4.22 per ft, hence the total cost is given as follows:

4.22 x 28.27 = $119.30.

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Es importante recordar que la velocidad final será negativa, ya que la pelota se está moviendo en dirección contraria al vector de gravedad cuando toca el suelo vel = 0.9 cm/mil*2 * t

La ecuación de velocidad final de los cuerpos en caída libre es:

vel = g x t

Donde "g" es la aceleración debido a la gravedad (en la Tierra, g = -9.8 m/s^2) y "t" es el tiempo que tarda en caer la pelota. Si conocemos la altura "h" desde la que se deja caer la pelota, podemos utilizar la ecuación de cinemática:

h = 1/2 x g x t^2

Despejando "t" de esta ecuación obtenemos:

t = sqrt(2h/g)

Ahora podemos calcular el tiempo que tarda la pelota en caer al suelo:

t = sqrt(2 x altura / (0.0098 km/s^2))

Y utilizando la ecuación de velocidad final de los cuerpos en caída libre, podemos calcular la velocidad final que alcanza la pelota al tocar el piso:

vel = 0.9 cm/mil*2 * t

Es importante recordar que la velocidad final será negativa, ya que la pelota se está moviendo en dirección contraria al vector de gravedad cuando toca el suelo. Espero que esto ayude.

vel = 0.9 cm/mil*2 * t

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Answer:

27 feet

Step-by-step explanation:

Two walls have same area

Area of first wall(square) = 18*18 = 324

Area of second wall = 12 * x = 324

324/12 = 27

27 feet

Let that be x

Now

Answer:

b

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

Formulas used:

     \(sin^2 \theta + cos^2\theta = 1 => 1-sin^2 \theta = cos^2 \theta\\\\tan^2 \theta + 1 = sec^2 \theta\)

\(Q) \ (1 + tan^2 \theta)(1-sin^2 \theta)\\\\= \ sec^2 \theta \times cos^2 \theta\\\\=\frac{1}{cos^2 \theta} \times cos^2 \theta\\\\= 1\)

Answer:

\((1 + \tan {}^{2} ( \alpha ) )(1 - \sin {}^{2} ( \alpha ) ) \\ = \frac{1}{ \cos {}^{2} ( \alpha ) } \times \cos {}^{2} ( \alpha ) \\ = 1\)

Answer:

5/6 or 0.83 (the 3 is repeated)

Step-by-step explanation:

To reduce this fraction, simply divide the numerator and denominator by 2 (the GCF). So, 1012 = 10÷212÷2 = 5/6. Thus, 1012 is equivalent to 5/6 in the reduced form.

Answer:

D

Step-by-step explanation:

Answer:

3.999 millimeters.

Step-by-step explanation:

To find the height of the cylinder, we can use the formula for the volume of a cylinder:

V = πr²h

Given that the radius (r) of the cylinder is 4 millimeters and the volume (V) is 200.96 cubic millimeters, we can substitute these values into the formula and solve for the height (h).

200.96 = π(4²)h

200.96 = 16πh

To solve for h, we can divide both sides of the equation by 16π:

200.96 / (16π) = h

Using a calculator, we can calculate the approximate value of h:

h ≈ 200.96 / (16 × 3.14159)

h ≈ 3.999

Therefore, the height of the cylinder is approximately 3.999 millimeters.

Answer:

We know that,

Angle E = 123

Angle B = 57

We observe that,

Angle DEB and Angle E form a linear pair and are supplementary.

Angle DEB + Angle E = 180

Angle DEB = 180-123

=57

We know that if two lines are parallel, the corresponding angles are equal.

Conversely, if the corresponding angles are equal, then the two lines are parallel.

Here,

As Angle B and Angle DEB are corresponding angles are equal in measure (Angle B = Angle DEB = 57), we can say that Line AC and Line DF are parallel.

Step-by-step explanation:

ang B = 180 - 57 = 123°

Since the corresponding angles are equal

So AC and DF are parallel to each other.

The sum of the arithmetic series with the parameters  t1 = -2, t3 = 7, and n = 15 is 442.5

The given parameters are:

t1 = -2

t3 = 7

n = 15

Start by calculating the common difference using:

Tn = t1 + (n- 1)d

So, we have:

7 = -2 + (3 - 1) * d

Evaluate

7 = -2 + 2d

Add 2 to both sides

2d = 9

Divide by 2

d = 4.5

The sum  is then calculated using:

\(S_n = \frac n2 * (2a + (n - 1) * d)\)

So, we have:

\(S_{15} = \frac {15}2 * (2*-2 + (15 - 1) * 4.5)\)

Evaluate

\(S_{15} = 442.5\)

Hence, the sum of the arithmetic series is 442.5

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26950 is  the total amount he received at the end of seven years.

What is your interest in simple words?

Interest is the price you pay to borrow money or the cost of borrowing money. Interest is usually given as an annual percentage of the loan amount. This percentage is called the interest rate on the loan.  

given,

pv= 14100

r1-4= 8%

n = 7

r5-7= 12%

A) interest  = FV - PV

                 = PV * ( 1 + r )ⁿ - pv

                  = 14100 * ( 1 + 0.08)⁴ * ( 1 + 0.12)³ - 14100

                   = 26,950.59 - 14100

                     = $12850.59

b)   fv= pv * (1 + r)ⁿ

          = 14100 * ( 1 + 0.08)⁴ * ( 1 +0.12 )³

          = 26950

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Given statement solution is :- None of the given options (a, b, c, or d) match the meaning of the slope. The correct interpretation is that the car travels approximately 0.8 miles every minute.

To determine the meaning of the slope of the linear model for the given data, let's analyze the information provided. The table represents the distance traveled by a car at different time intervals.

Minutes | Distance Traveled (in miles)

50 | 20

20 | f

40 | 60

100 | a

125 | 80

100 | 100

To find the slope of the linear model, we need to calculate the change in distance divided by the change in time. Let's consider the intervals where the time changes by a fixed amount:

Between 50 minutes and 20 minutes: The distance changes from 20 miles to 'f' miles. We don't have the exact value of 'f', so we can't calculate the slope for this interval.

Between 20 minutes and 40 minutes: The distance changes from 'f' miles to 60 miles. Again, without knowing the value of 'f', we can't calculate the slope for this interval.

Between 40 minutes and 100 minutes: The distance changes from 60 miles to 'a' miles. We don't have the exact value of 'a', so we can't calculate the slope for this interval.

Between 100 minutes and 125 minutes: The distance changes from 'a' miles to 80 miles. Since we still don't have the exact value of 'a', we can't calculate the slope for this interval.

Between 125 minutes and 100 minutes: The distance changes from 80 miles to 100 miles. The time interval is 25 minutes, and the distance change is 100 - 80 = 20 miles.

Therefore, based on the given data, we can conclude that the car travels 20 miles in 25 minutes. To determine the meaning of the slope, we divide the distance change by the time change:

Slope = Distance Change / Time Change

= 20 miles / 25 minutes

= 0.8 miles per minute

So, none of the given options (a, b, c, or d) match the meaning of the slope. The correct interpretation is that the car travels approximately 0.8 miles every minute.

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Answer:

\(\displaystyle \frac{cd^6}{a^4b^2}\)

Step-by-step explanation:

\(\displaystyle \frac{a^{-4}b^{-2}cd^6}{e^{-7}}\\\\=a^{-4}b^{-2}cd^6e^7\\\\=\frac{cd^6}{a^4b^2}\)

Notice that the variables with negative exponent that were originally in the denominator went to the numerator (like with \(e^{-7}\)) and became positive, and vice versa with those originally in the numerator went in the denominator (like with \(a^{-4}b^{-2}\)) and also became positive.

Step-by-step explanation:

a‐⁴b‐²cd⁶

_______

e‐⁷

cd⁶e⁷

_____

a⁴b²

Answer:

48

Step-by-step explanation:

To solve this we need to do the operations in the brackets first. We should start with the innermost brackets. Then, we work our way outwards. To show my working out I will use an asterisk (*) for multiplication to not confuse X as a variable.

8*{[(7 + 4) * 2] - [(11 - 7) * 4]}  

= 8*{[(11) X 2] - [(4) X 4]}

= 8*{[22] - [16]}

= 8*{6}

= 48

Answer:

Step-by-step explanation:

(2x + 7)(x + 1)

answer is A

Jasica should invest $878.84 per month in a sinking fund with 3% interest compounded monthly to accumulate $83,000 in 7 years.

To determine how much Jasica should make in a sinking fund, we can use the formula for the future value of an annuity due:

FV = PMT x \((((1 + r/n)^nt\) - 1) / (r/n))

Where:

FV = future value

PMT = monthly payment

r = interest rate (as a decimal)

n = number of compounding periods per year

t = number of years

In this issue, we are solving for PMT.

Given:

FV = $83,000,

r = 0.03 (3% expressed as a decimal),

n = 12 (monthly compounding),

t = 7 years.

Plugging in the values, we have:

$83,000 = PMT x \((((1 + 0.03/12)^(12*7)\) - 1) / (0.03/12))

Simplifying:

$83,000 = PMT x (94.4523)

PMT = $83,000 / 94.4523

PMT = $878.84 (rounded to the nearest cent)

Therefore, Jasica should invest $878.84 per month in a sinking fund with 3% interest compounded monthly.

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