A shop window is 6 meters long and has an area of 18m².What is the height of the window

Answer:

x = 8

Step-by-step explanation:

According to trigonometry identity

sin x = Cos (90-x)

Hence if we have;

Sin (4x + 10) º = Cos (6x)

Sin (4x + 10) º = Sin(90- 6x)

4x + 10 = 90 - 6x

4x+6x = 90 - 10

10x = 80

x = 80/10

x = 8

Hence the value of x is 8

Answer:

The answer is below

Step-by-step explanation:

The equation for a linear function is given as:

y = mx + b

where m is the slope of the function (that is the rate of change), b is the initial value of y when x is 0.

Given that the function where x represent the number of years since 1960 and y is the cost in dollar as:

[tex]f(x)=\frac{2.14}{55}x+0.31[/tex]

a) In the year 1960, that is x = 0, the cost of a gallon of gas is given as:

[tex]f(0)=\frac{2.14}{55}(0)+0.31\\\\f(0)=\$0.31[/tex]

b) From the function [tex]f(x)=\frac{2.14}{55}x+0.31[/tex], we can see that the rate of change is 2.14/55. Therefore, the cost increase each year by 4 cents per year.

The equation for the given circle is:

[tex]x^2 + y^2 + 4x + 6y - 3 = 0[/tex]

Remember that for a circle whose center is (a, b) and has a radius r, the equation is:

[tex](x - a)^2 + (y - b)^2 = r^2[/tex]

In this case, the center is (-2, -3) and the diameter is 8 units, so the radius is r = 4.

Then the equation is:

[tex](x + 2)^2 + (y + 3)^2 = 4^2[/tex]

Expanding the squares we get:

[tex](x^2 + 2*2*x + 4) + (y^2 + 2*3*y + 3^2) = 16\\\\x^2 + y^2 + 4x + 6y + 4 + 9 - 16 = 0\\\\x^2 + y^2 + 4x + 6y - 3 = 0[/tex]

So the correct option is the third one.

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2/26  that is the answer ok now peace

Answer:

a. 25.98i - 15j mi/h

b. 1.71i + 4.7j mi/h

c. 27.69i -10.3j mi/h

Step-by-step explanation:

a. Identify the ship's vector

Since the ship moves through water at 30 miles per hour at an angle of 30° south of east, which is in the fourth quadrant. So, the x-component of the ship's velocity is v₁ = 30cos30° = 25.98 mi/h and the y-component of the ship's velocity is v₂ = -30sin30° = -15 mi/h

Thus the ship's velocity vector as ship moves through the water v = v₁i + v₂j = 25.98i + (-15)j = 25.98i - 15j mi/h

b. Identify the water current's vector

Also, since the water is moving at 5 miles per hour at an angle of 20° south of east, this implies that it is moving at an angle 90° - 20° = 70° east of north, which is in the first quadrant. So, the x-component of the water's velocity is v₃ = 5cos70° = 1.71 mi/h and the y-component of the water's velocity is v₄ = 5sin70° = 4.7 mi/h

Thus the ship's velocity vector v' = v₃i + v₄j = 1.71i + 4.7j mi/h

c. Identify the vector representing the ship's actual motion.

The velocity vector representing the ship's actual motion is V = velocity vector of ship as ship moves through water + velocity vector of water current.

V = v + v'

= 25.98i - 15j mi/h + 1.71i + 4.7j mi/h

= (25.98i + 1.71i + 4.7j - 15j )mi/h

= 27.68i -10.3j mi/h

Answer:  I believe it's (x-1) 2+(y-1) 2=13

Answer:

a) C = 75n +60

b) see graph

c) 210

Step-by-step explanation:

75 n -C + 60 = 0

Add C to each side

75 n -C + 60  + C = 0+C

75 n  + 60 = C

Rewritng

C = 75n +60

This is in slope intercept form where y = mx+b

75 = m and 60 =b

See the graph

The slope is 75 and the y intercept is (0,60)

The scale is 1 on the n axis  ( time) and 100 on the C axis (cost)

Let n be two hours

Cost = 75(2) +60

        =150 +60

          =210

Answer:

C. 49

Step-by-step explanation:

Start by filling in your values.

[tex]7^{2} + 99 / 11 - 9[/tex]

Solve using PEMDAS.

49 + 99 / 11 - 9

49 + 9 - 9

58 - 9

49

Answer:

[tex]c .\: \: 49[/tex]

Step-by-step explanation:

[tex] {y}^{2} + 99 \div x - 9[/tex]

[tex] {7}^{2} + 99 \div 11 - 9[/tex]

[tex] 49 +99÷11-9[/tex]

[tex]49+9-9[/tex]

[tex]58-9[/tex]

[tex]49[/tex]

Answer:

59

Step-by-step explanation:

Answer:

The mean of this data set is 10.6

Step-by-step explanation:

To find the Mean of a data set, you add up all the values and then divide by the number of values.

3 + 4 + 6 + 7 + 10 + 15 + 19 + 21 = 85

This data set has 8 values.

85 ÷ 8 = 10.6

Answer: keith

Step-by-step explanation:

The system of equations to represent the number of pages read per day by Keith and Tameka, using d for days and p for pages are,

p = 6d

p = 5d + 15

Since we know that,

A system of equations is the set of equations in which the finite set of equations is present for which the common solution is sought.

Two students are reading a book.  Keith reads 6 pages a day.

The equation for Keith, where d for days and p for pages can be given as,

p = 6xd

p = 6d

Tameka reads 5 pages a day, but he starts sooner and has already read 15 pages. The equation for Tameka, where d for days and p for pages, can be given as,

p = 5xd + 15

p = 5d + 15

Hence, the system of equations to represent the number of pages read per day by Keith and Tameka, using d for days and p for pages are,

p = 6d

p = 5d + 15

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Answer:

y = 1/2x - 3/2

Step-by-step explanation:

y = 1/2x + b

1 = 1/2(5) + b

1 = 5/2 + b

-3/2 = b

Answer:

y=1/2x-3/2

Step-by-step explanation:

y-y1=m(x-x1)

y-1=1/2(x-5)

y-1=1/2x-5/2

y=1/2x-5/2+1

y=1/2x-5/2+2/2

y=1/2x-3/2

Answer: square root property

Step-by-step explanation:trust me

Answer:

77 feet above the ground.

Step-by-step explanation:

After going up 11 flights, (5 +6), he goes down 8, which brings you to 3 and then back up to 7 (3 +4). Since each story is 11 feet high, you multiply 7 and 11, to get a total of 77.

ANSWER:

A is number 3

B is number 2

Step-by-step explanation:

The left side is A and B (order)

the right side is 1,2,3,4 (order)

explanation: A is number 3 because as said in A the tram already has 5 people which is what we start with a1 = 5 and we add 11 at each stop as shown in the equation.

B is number 2 for the same reason as it started with 2 but added 4 inches of rain each time.

Given:

The scale factor of the actual sports utility vehicle to the toy model is 50:1.

Actual length = 7 feet

Actual width = 5 feet

To find:

The length and width of the toy model.

Solution:

a. Let l be the length of the toy model, then

[tex]\dfrac{\text{Actual length}}{\text{Length of the toy model}}=\dfrac{50}{1}[/tex]

[tex]\dfrac{7}{l}=\dfrac{50}{1}[/tex]

[tex]7=50l[/tex]

[tex]\dfrac{7}{50}=l[/tex]

[tex]0.14=l[/tex]

Therefore, the length of the toy model is 0.14 feet.

b. Let w be the width of the toy model, then

[tex]\dfrac{\text{Actual width}}{\text{Width of the toy model}}=\dfrac{50}{1}[/tex]

[tex]\dfrac{5}{w}=\dfrac{50}{1}[/tex]

[tex]5=50w[/tex]

[tex]\dfrac{5}{50}=w[/tex]

[tex]0.10=w[/tex]

Therefore, the width of the toy model is 0.10 feet.

Answer:

Hello! answer: 1/6

Step-by-step explanation:

The probability of landing on D is 1/6 because there are 6 spots on the spinner you can land on A, B, C, D, E, and F and there is only 1 section labelled "D" therefore the probability of landing on D is 1/6 hope that helps!

Answer:

The answer is A

Step-by-step explanation:

This I because the area of a square is =

(length of on side)² = l²

The options there are not perfect squarss except A

which is 64 in²

And we know that 8² will give you 64

so then it means one side is 8 in

So the area =

8² = 8 in × 8 in = 64 in²

Answer:

452 m

Step-by-step explanation:

Answer:

Step-by-step explanation:

Distribute the Negative Sign:

=−9x+32+−1(15x+41)

=−9x+32+−1(15x)+(−1)(41)

=−9x+32+−15x+−41

Combine Like Terms:

=−9x+32+−15x+−41

=(−9x+−15x)+(32+−41)

=−24x+−9

Answer:

-24x - 9

Step-by-step explanation:

Combine like terms.

Answer:

20.5 mpg

Step-by-step explanation:

Here we're looking to calculate the car's fuel economy, expressed in miles per gallon, or mpg:

 164 miles

------------------ = 20.5 mpg

  8 gallons

Answer:

the question in the parenthesis

Step-by-step explanation:

because thats how the order of operations work

Answer:

To solve this problem you must apply the procedure shown below:

1. You have that ladder measures 10 foot and forms and angle of 70 degrees with the ground.

2. Therefore, you have:

Sinα=opposite/hypotenuse

α=70°

opposite=x

hypotenuse=10

3. When you substitute the values, you obtain:

Sin(70°)=x/10

4. Now, solve for x, as following:

x=(10)(Sin(70°)

x=9.39 feet

Therefore, the answer is: 9.39 feet.

Step-by-step explanation:

Answer:

Ok so the probability  would be 16%(can be round to)

Step-by-step explanation:

Answer:

Last option

Step-by-step explanation:

First method :

Red Line:

Take 2 coordinates through which the line passes. Let it be (0, 7) and (14, 0).

[tex]slope, m=\frac{ 0-7}{14-0} = -\frac{7}{14} = -\frac{1}{2}[/tex]

[tex]Equation : (y - 7) = -\frac{1}{2}(x)[/tex]

                [tex]2y - 14 = -x\\2y + x = 14\\4y + 2x = 28[/tex]                  [tex][ multiply \ by \ 2 \ on \ both \ sides][/tex]

Blue Line:

Take coordinates through which the line passes.

Let it be (-4, -12) and (-10, -9).

[tex]slope, m = \frac{-9 + 14}{-10} = \frac{5}{-10} = -\frac{1}{2}[/tex]

[tex]equation : (y + 12) = -\frac{1}{2} (x+4)\\[/tex]

              [tex]y = -\frac{1}{2}x - 2 - 12\\\\y = -\frac{1}{2}x -14\\\\2y = -x - 28\\\\-2y = x +28[/tex]

Second Method:

From the graph it is clear the lines are parallel. The slopes of line parallel to each other are equal. So convert each equation into standard line equation form :y = mx + b

And check for set of equation whose slope are same.

First set :

[tex]y = 10x - 15 \\\\=> slope = 10\\\\-9x + 2y = 10\\2y = 9x + 10\\\\y = \frac{9}{2}x + 5 => slope = \frac{9}{2}[/tex]

Slopes are not equal.

Second set :

[tex]2y = 2x + 5\\y = x + \frac{5}{2}\\slope = 1\\\\\\3x -4y = -5\\4y = 3x + 5\\\\\y = \frac{3}{4}x + \frac{5}{4}\\\\slope = \frac{3}{4}[/tex]

Slopes are not equal.

Third set :

[tex]y = 3x +10 \\slope = 3\\\\\\2x - 3y = -6\\3y = 2x +6\\\\y = \frac{2}{3}x + 2\\\\slope = \frac{2}{3}[/tex]

Slopes are not equal.

Fourth set :

[tex]2x + 4y = 28\\4y = -2x +28\\\\y = -\frac{1}{2}x + 7\\\\slope = -\frac{1}{2}\\\\\\-2y = x + 28\\\\y = -\frac{1}{2}x - 14\\\\slope = -\frac{1}{2}[/tex]

Slopes are same.

Answer:

The answer is 136 .

Answer:

Step-by-step explanation:

According to problem description, we have two triangles

The first one:   the fish pond and feet and eyes of Kendra

The second one the fish  pond and the side wall of the apartment

These two triangles have angle  α  as common angle and its tan

tan α  =  1.5/ 2   =  x/ 40     then         note  :  150 cm  =  1.5 m

1.5/ 2   =  x/ 40

x  =  40 * 1.5 / 2

x  =  30 m

Answer:

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