Find sin D, sin E, cos D, and cos E. Write each answer as a fraction in simplest form

Answer:

B (0, 285 ) , C (380, 0 )

Step-by-step explanation:

the first step is to obtain the equation of the line in slope- intercept form

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = A(- 260, 480 ) and (x₂, y₂ ) = D (620, - 180 )

m = [tex]\frac{-180-480}{620-(-260)}[/tex] = [tex]\frac{-660}{620+260}[/tex] = [tex]\frac{-660}{880}[/tex] = - [tex]\frac{66}{88}[/tex] = - 0.75 , then

y = - 0.75x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equatio

using (620, - 180 ) , then

- 180 = - 465 + c ⇒ c = - 180 + 465 = 285

So y- intercept is B (0, 285 )

y = - 0.75x + 285 ← equation of line

to find the x- intercept , let y = 0 in the equation and solve for x

0 = - 0.75 + 285 ( subtract 285 from both sides )

- 285 = - 0.75x ( divide both sides by - 0.75 )

380 = x

x- intercept is C (380, 0 )

Difference:

x values

260 + 620 = 880

y values

480 + 180 = 660

Gradient = change in y/ change in x

Or

gradient = rise/run

= 660/880

= 3/4

= 0.75

We've got a negative slope - gradient must be negative

y = mx + c

y = - 0.75x + c

To find the y-intercept (c), which on the diagram is point B - you substitute one of the coordinates into the equation y = - 0.75x + c.

You use - point A or D - it don't matter which

I'll pick D - (620,−180)

y= -0.75x + c

-180 = - 0.75 x 620 + c

-180 = - 465 + c

+465

285= c

Thus, the equation is:

y = - 0.75x + 285

or

y = - 3/4x + 285

Where point B is (0,285) and C is (380,0)

To find:

B substitute x = 0 into the equation

(y= - 3/4 x 0 + 285)

C substitute y = 0 in the equation

0 = - 3/4x + 285

-285

- 285 = - 0.75x

÷ - 0.75

380 = x

( I converted 3/4 to 0.75 to make things clearer)

Hope this helps!

Answer:

10

Step-by-step explanation:

the formula y = mx +c

the y is obviously, y.

m, also means the gradient has a value of -4

c is the y-intercept, so the value of c is 10.

Answer: See below

Step-by-step explanation:

Let us write the equation of the given line in standard form:

[tex]6 x-3 y=5 \quad \Rightarrow \quad y=2 x-\frac{5}{3}[/tex]

A. The line moves away from the origin by a scale factor of 6, but its inclination still remains the same. Therefore, after any dilation, the slope of that line never changes.

Thus, the slope of the given line after dilation will be the same as the original slope, which is m = 2.

B. The x-intercept of the line before dilation will be given by substituting x = 0 in the given equation as shown below:

[tex]y=2(0)-\frac{5}{3}=-\frac{5}{3}[/tex]

Now, the y-intercept of the line after the dilation will be given by:

[tex]6\left(-\frac{5}{3}\right)=-10[/tex]

The shortest length of the fence used by the rancher in a rectangular field of 1000000 square feet is 4899 ft.

The area of a rectangle is a region enclosed in four corners where two opposite sides are equal. The area of the rectangle is mathematically expressed as:

Area of a rectangle = length(x) × breath(y)

1000000 sq.ft = (x) × (y) ---- (1)

However, to determine the fencing, we have:

Length of fencing = 2x + 2y  

Suppose we use the x-direction to estimate the region where the fencing is located, we have:

Length of fencing = 2x + 2y + x

Length of fencing = 3x + 2y ---- (2)

From equation (1), make (y) the subject of the formula and replace the value of y with equation (2)

The Length of fencing is:

[tex]\mathbf{L = 3x - 2( \dfrac{1000000}{x})}[/tex]

[tex]\mathbf{\dfrac{dL}{dx} = 3 - \dfrac{2000000}{x^2} = 0}[/tex]

[tex]\mathbf{ x^2= \dfrac{2000000}{3} }[/tex]

[tex]\mathbf{ x= \dfrac{1000\sqrt{2}}{\sqrt{3}} }[/tex]

[tex]\mathbf{x = \dfrac{1000 \sqrt{6}}{3}}[/tex]

Now, if we replace the value with equation (1), then y will be:

[tex]\mathbf{y = \dfrac{1000000}{\dfrac{1000 \sqrt{6}}{3}} }\\ \\ \\ \\ \mathbf{y = \dfrac{3000 }{\sqrt{6}}}[/tex]

[tex]\mathbf{x =500\sqrt{6}}[/tex]

Now, the shortest length of the fencing can be computed by using the equation (2):

L = 3x + 2y

[tex]\mathbf{L = 3( \dfrac{1000 \sqrt{6}}{3}) + 2(500 \sqrt{6})}[/tex]

[tex]\mathbf{L =1000 \sqrt{6} + 1000 \sqrt{6}}[/tex]

[tex]\mathbf{L =2000 \sqrt{6} }[/tex]

[tex]\mathbf{L \simeq 4899 \ ft}[/tex]

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Answer:

7525 milliliters

Step-by-step explanation:

because if you multiply 2150 by 3.5 you will get that number

Diameter be d

Radius be r

Diameter=2r=46.4(2)=92.8cm

The rise/run of AC and CE in the similar triangles are the same, the true statement is: B. slope of AC = slope of CE.

On a coordinate plane, the corresponding sides of two triangles are always the same because the ratio of the rise over run is always the same.

Triangles ABC and CDE are similar triangles, therefore the rise over run of AC and CE, which is the slope, will be the same.

Thus, slope of AC = slope of CE.

Learn more about slope on:

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Answer:

13. 360 14. 1080 15. x=53 16. x=135

Step-by-step explanation:

Equation: (n-2)*180

For 13. all angles in a a quadrilateral add up to 360

For 14. 8 sides-2=6. 180*6=1080 degrees

For 15. 15+155+137=307. 360-307=53. x=53 degrees

For 16. 6 sides-2=4. 4*180=720. 90*2=180. 720-180=540. 540/4=135.

x=135

Cos(angle) = adjacent leg/ hypotenuse

cos(angle) = 21/36

angle = arccos(21/36

Angle = 54.31

Angle = 54 degrees

Step-by-step explanation:

1. 3=5x-12

3+12=5x

15/5=x

3 = X

2. -3x + 5 = -13

-3x= -13 -5

x = -18/-3

x= 6

3. -x+6=4

-x =4-6

x=-2/-1

×=2

4.-4y=48

y =48/-4

y = -12

5. m/2=10

m=10×2

m=20

6.-2.5b=20.5

b = 20.5/-2.5

b = -4.2

7. ×/7+15=8

×/7 = 8-15

× = -7×7

× =-49

8. ⅓d-6=0

⅓d=6

d =6×3

d =18

9.(g-13)/4=9

g-13=9×4

g =36+13

g =49

10. (1-k)/5=5

1-k =5×5

-k =25-1

k =24/-1

k=-24

Answer:

r = 9 meters

Step-by-step explanation:

2r + 8 = 26 <== subtract 8 from both sides

    - 8     - 8

2r = 18 <== divide both sides by 2 to isolate the variable

/2    /2

r = 9 meters

Hope this helps!

Answer:

Step-by-step explanation:

To find the value of r, isolate it on one side of the equation.

[tex]\sf{2r+8=26}[/tex]

First, you have to subtract by 8 from both sides.

[tex]\sf{2r+8-8=26-8}[/tex]

Solve.

Subtract the numbers from left to right.

26-8=18

2r=18

Divide by 2 from both sides.

[tex]\sf{\dfrac{2r}{2}=\dfrac{18}{2} }[/tex]

Solve.

Divide the numbers from left to right.

18/2=9

r=9

I hope this helps. Let me know if you have any questions.

Answer:

1st,15

2nd, 40

3rd, 36

Step-by-step explanation:

Answer:

the answer to this question. is quadratic trinomial

Answer:

The answer is quadratic trinomial because it is to the power of 2, and has 3 terms.

Answer:

81

Step-by-step explanation:

double digit numbers begin at 10 and end at 99

10 → 19 has 10 double digits

20 → 29 has 10 double digits

and so on up to 90 → 99

that is there are 90 double digits from 10 → 99

double digits with same value are 11, 22, 33, 44, 55, 66, 77, 88, 99

that is 9 double digits with the same value

Then double digits with different values = 90 - 9 = 81

Answer:

81 double digits numbers.

Step-by-step explanation:

From 1 to 99, first 9 numbers are single digit numbers

Double digit numbers = 99 - 9 =90

In this 90 numbers, 11,22,33,44,55,66,77,88,99 have same digits.

90 - 9 = 81

Answer:

Here is a diagram I made that shows all of the angles of the letters. (By to the way, letters I, C, and S don't have any angles, so I didn't include them.)

Step-by-step explanation:

Answer:

5\beta ???

Step-by-step explanation:

please recheck the question ..

Answer:

see explanation

Step-by-step explanation:

the sequence is linear, that is arithmetic with nth term

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

given a₈ = 18 and a₁₂ = 26 , then

a₁ + 7d = 18 → (1)

a₁ + 11d = 26 → (2)

subtract (1) from (2) term by term to eliminate a₁

4d = 8 ( divide both sides by 4 )

d = 2

substitute d = 2 into (1) and solve for a₁

a₁ + 7(2) = 18

a₁ + 14 = 18 ( subtract 14 from both sides )

a₁ = 4

then

a₂₀ = 4 + (19 × 2) = 4 + 38 = 42

Answer:

Step-by-step explanation:

For two triangles to be similar, they need to have the same radius.

So, to make them similar, we can simply :

This would give Circle A and B the same radius, and they will be similar.

Answer:

9.33π

Step-by-step explanation:

the formula to solve for the volume of a cone is V=πr^2 * h/3

r = radius of base (2mi)

h = height (7mi)

plug in the numbers

V=π2^2 * 7/3

V=π4*2.33333333

V=9.33π

Answer:

B & C

Step-by-step explanation:

Acute angles are sharp-like angle - they are measured between 1° up to 89°. That means acute angles have measurement starting from 1 to 89.

The shape of acute angles, as said, they are namely sharp angles because their vertex and lines form sharp shape.

So what you have to do is to find angles that look like a sharp pencil/pen, probably something that can be understandable:

Sharp-looking measurements are:

Keep in mind that ∠GFE is really an acute angle, but ∠HFE is a right angle.

Let’s look into more types of angles as shown in choices:

Hence, acute angles are ∠GFE and ∠DBA

The angles which are acute are ∠GFE and ∠DBA.

Angles are the figure formed by the intersection of two lines or rays by sharing a common point. This point is called the vertex of the angle.

Angles are usually measured in degrees or radians.

Given three figures and corresponding angles.

We have to find the acute angles.

Acute angles are angles which measures less than 90 degrees.

An angle which measure 90 degrees is the right angle which stands vertically.

Acute angles are less than this.

From the figure and options, acute angles are ∠GFE and ∠DBA.

Hence the acute angles are ∠GFE and ∠DBA.

Learn more about Acute Angles here :

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Answer:

C

Step-by-step explanation:

It cannot be D and A and B are the same

Answer:

90 degrees around the origin

Step-by-step explanation:

When you rotate the first time it is 90 degrees

When you rotate two times it is 180 degrees

When you rotate three times it is 270 degrees

Hope it helps:)

Answer: a. 24:600

b. 53

Step-by-step explanation:

First simplify:

24:600

6:150

2:30

1:15

Answer:

1/3n-5

Step-by-step explanation:

n=1/3n

subtract 5

so the expression is 1/3n-5

Answer:

[tex]n\frac{1}{3}-5[/tex]

Step-by-step explanation:

Hey there!

This is the equation for your answer because you said that he finds 1/3 of n and then subtracts 5

Answer:

x = 0, y = 5

Step-by-step explanation:

y = 7x + 5

=> x = (y-5) / 7

y = 2x + 5 = 2 *(y-5) /7 + 5

=> (y - 5) / 2 = ( y - 5) / 7

=> y =5 since only 0 / 2 = 0 / 7

=> x = (y -5) / 7 = 0 / 7  = 0

Answer:

b.

Step-by-step explanation:

We have been given a number 8¼. We are asked to find the opposite of the opposite of our given expression.

Since our given number in positive, so opposite of our given number will be:

–8¼

The opposite of new number will be:

–(–8¼)

Therefore, the expression –(–8¼) represents the opposite of the opposite of 8¼ and option 'b' is the correct

Answer:

The answer would be 47/99

Step-by-step explanation:

Answer:

srat

Step-by-step explanation:hehe i really dont know