Find the perimeter of a rectangle with a diagonal of 20 inches that make angle measure 30 and 60 using trigonometric function (sine, cosine, tangent)

The range values for the domain of the functions are as follows

x   y

-2  7

0   3

1     1

3    -3

The domain are the input values of the graph the output values are solved using the given functions

The given function 2x-y=3

rearranging gives

y = 3 - 2x

solving for the range values using the domain values: (-2,0,1,3)

= 3 - 2x = 3 - 2 * -2 = 7

= 3 - 2 * 0 = 3

= 3 - 2 * 1 = 1

= 3 - 2 * 3 = -3

The graph is attached

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Answer:

As addition: -13+(-7)=-20

The value of n is A. -1/2

The inequality that does not represent the position of 2 numbers on a number line is A. 4 1/2 > 25/4

A number line is a horizontal representation of number parts with equal intervals

The numbers in a number line is arranged to be increasing from left to right , hence drawing a number line will have the smaller values to the left of the bigger values

n is the negative side of the line and it is half (1/2) way between 0 and -1 hence should be -1/2

for the inequality, 4 1/2 > 25/4

4 1/2 = 4.5

25/4 = 6.25

4.5 should less than 6.25, and hence do not represent the correct position of two numbers

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What is the correct standard form for 400+3+0.07+0.001

403.071

Answer:

=4.03071×10²

Step-by-step explanation:

400+3=403

=403+0.07=403.07

=403.07+0.001=403.071

so 403.071 to standard form is 403.071 divide by 100 is 4.03071 and 10 and and also change to 2 zeros and Chang it to powers so =4.03071×10²

The volume of the cone is 15393.80 cm³

The curved surface area of a cone is 4068.36 cm²

The total surface area of the cone is 7916.81 cm²

Given parameters;

The base radius( r ) of the cone is 35cm

The height( h ) of the cone is 12cm

Case (I): To find the volume of the cone;

The volume of the cone = [tex]\pi r^{2}\frac{h}{3}[/tex]

                                        = π *(35)² * 12/3

                                        = 15393.80 cm³

Case (II): To find the curved surface area of the cone;

The curved surface area of the cone = πrl

We know that;

Slant height l = [tex]\sqrt{(r^2 + h^2)}[/tex]

By substituting the values;

l = [tex]\sqrt{35^2 + 12^2}[/tex]

l = 37

We know that;

The curved surface area of a cone = πrl

                                                          = π * 35 *37

                                                          = 4068.36 cm²

Case (III): The total surface area of the cone;

The total surface area of the cone = πr(l + r)

                                                         = π * 35 * (37 + 35)

                                                         = 7916.81 cm²

Therefore,

The volume of the cone is 15393.80 cm³

The curved surface area of a cone is 4068.36 cm²

The total surface area of the cone is 7916.81 cm²

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Hence, 17-unit percent change is (45/19)×17% = 40.26%

12-unit percent change is (43/16)×12% = 32.25%

18-unit percent change is (-25/20)×18% = -22.5%

8-unit percent change is (-50/5)×8% = -80%

Given, that

The 19-unit percent change is 45 %

Now, 1-unit percent change is 45/19

17-unit percent change is (45/19)×17%

= 40.26%

The 16-unit percent change is 43 %

Now, 1-unit percent change is 43/16

12-unit percent change is (43/16)×12%

= 32.25%

The 20-unit percent change is -25%

Now, 1-unit percent change is -25/20

18-unit percent change is (-25/20)×18%

= -22.5%

The 5-unit percent change is -50 %

Now, 1-unit percent change is -50/5

8-unit percent change is (-50/5)×8%

= -80%

Hence, 17-unit percent change is (45/19)×17% = 40.26%

12-unit percent change is (43/16)×12% = 32.25%

18-unit percent change is (-25/20)×18% = -22.5%

8-unit percent change is (-50/5)×8% = -80%

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Answer:

100% - 80%=20%

Step-by-step explanation:

that's the answer

Answer:

14

Step-by-step explanation:

When the sum M+N is divided by 6 , the remainder is 8

The remainder is the amount "left over" after performing some computation. In arithmetic, the remainder is the integer "left over" after dividing one integer by another to produce an integer quotient (integer division). We always have remainder when the denominator is a factor of numerator.

For example 5/2, diving 5 with 2, 2 is not a factor of 5,

There are 2 2s in 5 with remainder 1.

M/6= x y/6

where is the factor and y is the remainder

therefore m/6= (6x+y)/6

y= 3,. m/6= (6x+3)/6

N/6= (6x+5)/6

therefore dividing both sides by 6

m= 6x+3

n= 6x+5

adding m and n

m+n= 12x+8

dividing m+n by 6

(m+n)/6 = (12x+8)/6

relating (12x+8)/6 with (6x+y)/6

y = 8

Therefore the remainder is 8

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125° is the  angle of CBD

An angle pair that forms a straight line is referred to as a straight angle pair. This pair's sum of any two or more angles is always equal to 180°.

A straight angle has a 180° angle.

The two angles are from a straight line, and they sum to 180 degrees.

A + B + C = 180

8x -41+ 9x+17 = 180

Conjoin similar terms

17x -24 = 180

24 more on each side

17x -24+24 = 180 +24

17x = 204

multiply by 17

17x/17 = 204/17

x =12

We desire CBD angled.

CBD = 9x+17

= 9*12+17=108+17

= 125

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Answer:

[tex]\frac{4+\sqrt{11} }{5}[/tex]

Step-by-step explanation:

to rationalise the denominator, multiply the numerator and denominator by the conjugate of the denominator.

the conjugate of 4 - [tex]\sqrt{11}[/tex] is 4 + [tex]\sqrt{11}[/tex] , then

[tex]\frac{1(4+\sqrt{11}) }{(4-\sqrt{11})(4+\sqrt{11}) }[/tex] ← expand denominator using FOIL

= [tex]\frac{4+\sqrt{11} }{16-11}[/tex]

= [tex]\frac{4+\sqrt{11} }{5}[/tex]

The equation 6(x + 5) = 6x + 5 has NS (No Solution) and the equation -4x = 7x - 33 has IM (Infinite Many solutions).

Let us take the given equation

6(x + 5) = 6x + 5

⇒ 6x + 30 = 6x + 5

⇒ 6x - 6x = 5 - 30

⇒ 0 = -25

Hence, the given equation has No Solution (NS)

Let us take the given equation

-4x = 7x - 33

-4x - 7x = -33

-11x = -33

x = 3

Hence, the given equations has Infinite Many solutions (IM)

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The maximum and minimum measurements are 5 and -3 respectively.

f ( x ) = -x^3 +3x^2+ 45 x + 10

f' l x ) = 0

0 = - 3x^2 +6x +45

x = 5,- 3.

f ( 4 ) = - ( 4 )^3+ 3( 4 )^ 2 + 45 ( 4 ) + 10 = 174

f ( - 4 ) = - ( - 4 )^3 + 3( - 4 )^2 + 45(- 4) + 10 = - 58

f ( - 3 ) = -(- 3 )^3 + 3 ( - 3)^2 + 45 (- 3) + 10 = - 7 1

+ ( 5 ) = -(5)^3 + 3(5 )^2 +45(5)+ 10 = 185

Absolute maximum = maxis{ f(4 ),f(5),f(-4),f( - 3 )}

                        = 185 at x=5

Absolute mininum=minis{f(4 ),f(5),f(-4),f( - 3 )}

                      = - 71 at x= -3

In light of this, the maximum and minimum values are 5 and -3, respectively.

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The rational number is equivalent to 0.36 is 9/25

From the question, we have the following decimal number that can be used in our computation:

Decimal number = 0.36

To start with, we need to express the decimal number as a fraction

This is represented as follows:

So, we have the following representation

Decimal number = 36/100

Change the label of the above representation to rational number

Rational number = 36/100

Simplify the rational number (divide the numerator and the denominator by 2)

Rational number = 18/50

Simplify the rational number (divide the numerator and the denominator by 2)

Rational number = 9/25

Hence, the equivalent rational number is 9/25

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Answer:

76

Step-by-step explanation:

Proportionately, it would take the restaurant 22.75 avocadoes to make 14 orders of guacamole since it takes 6.5 avocados to make 4 orders.

Proportion refers to the quantity of a value or variable contained in another value.

Proportion is a fractional value like a ratio that shows the numerical relationship between two or more values.

Proportions are depicted using fractions, decimals, or percentages.

The number of avocados required for 4 orders of guacamole = 6.5

The total number of orders of guacamole required = 14

The number of avocados to make 1 order = 6.5/4

The number of avocadoes required to fill 14 orders = 22.75 (6.5/4 x 14)

Thus, in proportion, it would take 22.75 avocados to make 14 orders of guacamole.

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The value of b of the equation is -9/5

Given that: line JK passes through points J(-4,-5) and K(-6,3) and if the equation of the line is written in slope-intercept form, y=mx+b

The equation of line is an algebraic form of representing the set of points, which together form a line in a coordinate system

Using the y-y₁/y₂-y₁ = x-x₁/x₂-x₁

where (x₁, y₁) = (-4,-5) and (x₂, y₂) = (-6,3), the equation is:

y-(-5) / 3-(-5) = x-(-4)/-6-(-4)

y+5 / 3+5 = x+4 /6+4

(y+5)/8 =  (x+4)/10       cross multiply:

10(y+5) = 8(x+4)

10y + 50 = 8x + 32

10y = 8x +32 - 50

10y = 8x - 18

y = 8x/10 - 18/10

y = 4x/5 - 9/5

Comparing y = 4x/5 - 9/5 with y=mx+b

b = -9/5

Therefore, the value of b is -9/5

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Answer:

  shifted down 4 units

Step-by-step explanation:

You want to know the effect on the graph of changing y=2x+2 to y=2x-2.

The constant in the equation y=2x+2 is the y-intercept. The line described by this equation crosses the y-axis at y=2.

When the equation is changed to y=2x-2, the y-intercept changes from +2 to -2, a shift down of 4 units. The shifted line has the same slope as the original, so is parallel to it.

The effect on the graph is to move it down 4 units.

Answer:

The area of the dount is about 35.325 in²

Step-by-step explanation:

In order to find the area of a donut with a hole on the center we need to find the area of the center and the area of the circle of the donut (as if the donut was whole)

*The radius is half of the diameter or r = d/2

The area of a circle is A = n(3.14) r² or pi(3.14)× radius

Answer:

$1053

Step-by-step explanation:

If we have that £1 = $1.62, then we can multiply both sides by 650 in order to get £650 on the left side of the equality. We must multiply the right side also by 650, and so we get £650=$1.62 * 650.

To do this multiplication, we can break 1.62 down  simply into $1.00 +$0.6+$0.02

650*$1.00=$650, 650*$0.6=650*6/10=65*6=$390, and 650*$0.02=650*2/100=6.5*2=$13.

When we add these three products together, we get $650+$390+$13=$1053. And so, £650=$1053

Graph for the equation ( y = -300x +  1200 ) below

y-intercept = ( 0, 1200 )

x-intercept = ( 4, 0 )

Hope this helps! :)

The y-intercept is ( 0, 1200 ) and the x-intercept is ( 4, 0 ).

The graph is simply a structured representation of the data. It aids in our comprehension of the data. The numerical information gathered through observation is referred to as data.

In a line graph, the information or data is represented as a series of markers, or dots, and is then connected to one another by a straight line.

Given:

y=-300x+ 1200

Now, for y- intercept put x=0

y= 1200

and, for x- intercept put y= 0

0 = -300x +1200

x= 4

Hence, the y-intercept is ( 0, 1200 ) and the x-intercept is ( 4, 0 ).

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The correct statement regarding the proportional relationships is given as follows:

Boat A travels at a faster rate than Boat B.

A proportional relationship is a special case of a linear function with intercept zero in which the output variable is given by the multiplication of the input variable and the constant of proportionality, in the case of a direct relationship, as follows:

y = kx

The function for boat A is:

d = 10.5t.

Hence the rate is:

10.5 miles per hour.

From the graph, the rate for boat B is obtained as follows:

k = 90/10 = 9 miles per hour.

A higher constant means a faster rate, 10.5 is greater than 9, hence boat A travels faster.

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

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Using the trigonometry ratio, the value of angle x is 66.42°.

In the given question,

One of the support wires for a radio tower is 100 feet long.

One end of the wire is 40 feet from the base of the tower.

We have to find the angle (x), in degrees, that the support wire make with the ground.

To find the angle of x we use trigonometry ratio.

According to the ratio cosine is the ratio between base and hypotenuse.

So the formula is Cos x= B/H

where H = Hypotenuse

B = Base

From the given figure we know that, H=100 feet, B=40 feet

Now putting the value

Cos x= 40/100

Simplifying

Cos x = 2/5

Cos x = 0.4

So x = arccos(0.4)

x = 66.42

Hence, the value of angle x is 66.42°.

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Answer:

Divide by Three Trick

This is a fun trick. If the sum of the digits in a number can be divided by three, then the number can as well.

Examples:

1) The number 12. The digits 1+2=3 and 12 ÷ 3 = 4.

2) The number 15. The digits 1+5 = 6, which is divisible by 3. It turns out that 15 ÷ 3 = 5

Answer:

7+2/8+5

Step-by-step explanation:

The measures of the each angle of the triangle is 84, 28 and 68 degrees.

A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees.  

The triangle has the sum of the measures of the angles as 180°.

Angle A is three times as large as angle B and also 16° larger than C.

Therefore,

let

angle A = x

Angle B = x / 3

Angle C = x - 16

Therefore,

x + x - 16 + x  /3  = 180

7 / 3 x - 16 = 180

7 / 3 x = 180 + 16

7 / 3 x = 196

cross multiply

7x = 196 × 3

7x = 588

divide both sides by 7

x = 588 / 7

x = 84

Therefore,

A = 84 degrees

B = 84 / 3 = 28 degrees

C = 84 - 16 = 68 degrees

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Step-by-step explanation:

so, we have 2 cost functions. each consisting of 1 large centerpiece, and x smaller arrangements.

cost1(x) = 19x + 50

cost2(x) = 23x + 42

to get the value for x we know that the cost is the same either way.

that means

cost1(x) = cost2(x) = 19x + 50 = 23x + 42

19x + 50 = 23x + 42

50 = 4x + 42

8 = 4x

x = 2

so, she orders 2 small arrangements.

the total cost is

19×2 + 50 = 38 + 50 = $88

cross check with the other function :

23×2 + 42 = 46 + 42 = $88

correct