If two pairs of corresponding sides are ________ and the included angles are ______, then the triangles are similar.

Answer:

It should be D.

Step-by-step explanation:

Answer:

(i) [tex]OE = 0.6\cdot \sin \theta + 1.4\cdot \cos \theta[/tex], (ii) [tex]\theta \approx 33.368^{\circ}[/tex], (iii) The maximum value of OE is approximately 1.523 meters, which is associated with an angle of approximately 23.199º.

Step-by-step explanation:

(i) From Geometry, we get that sum of internal angles of trangle AOD.

[tex]\angle A + \angle O + \angle D = 180^{\circ}[/tex] (1)

If we know that [tex]\angle O = 90^{\circ}[/tex] and [tex]\angle A = \theta[/tex], then the value of [tex]\angle D[/tex] is:

[tex]\angle D = 180^{\circ}-90^{\circ}-\theta[/tex]

[tex]\angle D = 90^{\circ}-\theta[/tex] (2)

But we also have the following identity:

[tex]\angle D +\angle D' +\angle D'' = 180^{\circ}[/tex] (3)

If we know that [tex]\angle D = 90^{\circ}-\theta[/tex] and [tex]\angle D' = 90^{\circ}[/tex], then the value of [tex]\angle D''[/tex] is:

[tex]90^{\circ}-\theta +90^{\circ}+\angle D'' = 180^{\circ}[/tex]

[tex]\angle D'' = \theta[/tex] (4)

By Trigonometry, we derive the following formula:

[tex]OE = OD +DE[/tex]

[tex]OE = AD\cdot \sin A +CD\cdot \cos D''[/tex] (5)

If we know that [tex]AD = 0.6\,m[/tex], [tex]CD = 1.4\,m[/tex], [tex]A = \theta[/tex] and [tex]D'' = \theta[/tex], then the value of OE is:

[tex]OE = 0.6\sin \theta + 1.4\cos \theta[/tex] (6)

(ii) If we know that [tex]OE = 1.1\,m[/tex], then the value of [tex]\theta[/tex]:

[tex]0.6\cdot \sin \theta + 1.4\cdot \cos \theta = 1.1[/tex]

By trial and error, we find that [tex]\theta \approx 33.368^{\circ}[/tex].

(iii) Let [tex]OE = 0.6\cdot \sin \theta + 1.4\cdot \cos \theta[/tex], the first and second derivatives of the function are, respectively:

[tex]OE' = 0.6\cdot \cos \theta -1.4\cdot \sin \theta[/tex] (7)

[tex]OE'' = -0.6\cdot \sin \theta -1.4\cdot \cos \theta[/tex] (8)

We equalize the first derivative of the function to zero and solve for [tex]\theta[/tex]:

[tex]0.6\cdot \cos \theta - 1.4\cdot \sin \theta = 0[/tex]

[tex]1.4\cdot \sin \theta = 0.6\cdot \cos \theta[/tex]

[tex]\tan \theta = \frac{0.6}{1.4}[/tex]

[tex]\theta \approx \tan^{-1} \frac{0.6}{1.4}[/tex]  

[tex]\theta \approx 23.199^{\circ}[/tex]

And we evaluate the second derivative:

[tex]OE'' = -0.6\cdot \sin 23.199^{\circ}-1.4\cdot \cos 23.199^{\circ }[/tex]

[tex]OE'' = -1.523[/tex]

Then, the critical value is associated with an absolute maximum.

The maximum value of OE is:

[tex]OE = 0.6\cdot \sin 23.199^{\circ}+1.4\cdot \cos 23.199^{\circ }[/tex]

[tex]OE \approx 1.523\,m[/tex]

The maximum value of OE is approximately 1.523 meters, which is associated with an angle of approximately 23.199º.

Answer:

The answer is 13

Step-by-step explanation:

Took the test on Edge

Answer:

x=13 :)

I took the quiz

Answer:

hd

Step-by-step explanation:

NO WORK

Answer:

The answer is B.3 because

3*11=33+22=$55

3*9=27+28=$55

Answer:

8) d

9) a

Step-by-step explanation:

8) C = d ·π

36 = d ·π

36 / π = d

9) 4π is the difference, which is 12.56

Answer:

Yes

Step-by-step explanation:

Each input has one output and no input has the same output

Answer:

It will be in the attachment below.

Step-by-step explanation:

Translating a vertex 3 units down and 4 units to the left means that the x coordinate is 4 less than before and the y is 3 less. So, subtract 4 from -5 to get -9; from -2 (twice) to get -6 (twice), and subtract 3 from 5 (twice) to get 2 (twice); from 3 to get 0. So, the new coordinates are (-9, 2), (-6, 2), and (-6, 0). The original shape is in red, and the translated shape is blue.

Answer:

profit is 23 selling price is $483

Step-by-step explanation:

Cp of Camera=Rs.460

profit= 5%

so profit =5% of 460=(5*460)/100=Rs.23

then selling prices of camera= cp of camera + profit Rs=$460+23=483 hope this helps

Answer:

y = 7x + b must have the same slope

2 = 7(2) + b

Answer:

11.5

Step-by-step explanation:

Answer:

11.5

Step-by-step explanation:

0.9(17) - 1.9(2) = and then solve

Answer:

11 minutes

Step-by-step explanation:

I may be missing something. This is too simple.

88 degree change at 8 degrees per minute = 11 minutes.

Answer:

3/4 time left

Step-by-step explanation:

Answer:

Reflection over the X-axis, dilation with a factor of 2

Step-by-step explanation:

Dilation changes the size of the figure, therefore making it not congruent with the original figure.

-6-4=-10

-10/-5=2

so 2 is ur answer

Answer:

You would have to distribute each one or use the box method whinch gives you :

12x^4 − 34x^3 + 20x^2

Answer:

I hope this helps

Step-by-step explanation:

Answer:

A). Yes

B). Yes

C). No

D). Yes

Step-by-step explanation:

Coordinates of the midpoint of a segment joining two points [tex](x_1, y_1)[/tex] and [tex](x_2,y_2)[/tex] are given by [tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex].

A). If the points are A(1, 2) and B(3, 4)

    Coordinates of the midpoint M → [tex](\frac{1+3}{2},\frac{2+4}{2})[/tex]

    M → (2, 3)

    Yes.

B). Extreme points of segment AB are A(0, 8) and B(10, -1)

    Coordinates of the midpoint will be,

    M → [tex](\frac{0+10}{2}, \frac{8-1}{2})[/tex]

    M → (5, 3.5)

    Yes

C). Extreme points of segment AB are A(-7, -5) and B(6, 4)

    Coordinates of the midpoint will be,

     M → [tex](\frac{-7+6}{2}, \frac{-5+4}{2})[/tex]

     M → (-0.5, -0.5)

     NO

D). Extreme points of segment AB are A(4, -2) and B(6, -8)

     Coordinates of the midpoint will be,

     M → [tex](\frac{4+6}{2}, \frac{-2-8}{2})[/tex]

     M → (5, -5)

     Yes

Answer:

So, the prime factors of 6 are written as 2 × 3, where 2 and 3 are prime numbers. It is possible to find the exact number of factors with the help of prime factorisation. The prime factor of the 6 is 2 x 3. The exponent in the prime factorisation is 1 and 1.

:-))

Answer:

Factors of 6: 1, 2, 3, 6. Prime factorization: 2 x 3.

Step-by-step explanation:

Answer:

[tex]y=-3x+10[/tex]

Step-by-step explanation:

Parallel equations have same slope

Therefore slope of 3x + y = -2 is same as slope of other equation.

Slope of 3x + y = -2 is

m=-3

Now we have write equation having slope -3 and passing through point (5, -5)

[tex](y+5)=-3(x-5)[/tex]

[tex]y=-3x+10[/tex]

Answer:

31.5

Step-by-step explanation:

divide 42 by 4 you would get 10.5, then multiple 10.5 by 3 and you would get 31.5 thats the answer

Answer:

the answer is the last one 1 -6 -8 O 1 y =X 1 2 y

Step-by-step explanation:

The feasible region of the result is defined by the system of inequalities.

Correct response:

The system of inequalities shown in the graph is given by the option B.

B. y ≤ x + 1

y ≤ x² - 3·x

An inequality is a relation which makes a non-equal comparison between two numbers or mathematical expressions.

here, we have,

Methods used to find the system of inequalities

Please find attached the possible graph of the inequality

The possible graph obtained from a similar question has a straight line portion and a quadratic portion.

Points on the straight line are; (0, 1), (3, 4), and (5, 6)

Therefore;

Equation of the line is; y - 1 = 1 × x

Therefore;

y = x + 1

The shaded region is below the line which gives;

y ≤ x + 1

Points on the quadratic graph are; (0, 0), (4, 4), and (2, -2).

The general form of a quadratic equation is; y = a·x² + b·x + c

Therefore, we have;

0 = a × 0 + b × 0 + c

Which gives;

c = 0

4 = a × 4² + b × 4 = 16·a + 4·b

-2 = a × 2² + b × 2 = 4·a + 2·b

4 = 16·a + 4·b...(1)

-2 = 4·a + 2·b...(2)

Multiplying equation (2) by 2 and subtracting from equation (1) gives;

2 × -2 = 2 × (4·a + 2·b) = 8·a + 4·b

-4 = 8·a + 4·b

4 - (-4) = 16·a + 4·b - (8·a + 4·b) = 8·a

8 = 8·a

a = 1

-2 = 4 × 1 + 2·b

2·b = -2 - 4 = -6

Which gives;

y = 1·x² - 3·x = x² - 3·x

The line is a solid line and shaded region is the region under the graph which gives;

y ≤ x² - 3·x

Therefore;

The inequalities in the graph are given by option B.

B. y ≤ x + 1

y ≤ x² - 3·x

Learn more about graph of inequalities here:

brainly.com/question/6749279

#SPJ7

Answer:

let the numbet of formal attires with Clara be X

Clara lended susan 1/2 = X/2

Clara buys 4 = X/2 +4

Answer = X/2 + 4

( as the number of formal attires originakly with Clara is not specified)

Step-by-step explanation:

Since the zeroes of f(x) are -2 and 6,

(x + 2) and (x - 6) are factors of f(x).

=> f(x) = (x + 2)(x - 6) = x² - 4x - 12.

Answer:

The function f(x) is a quadratic function and the zeros of f(x) are -2 and 6. Assume the leading coefficient of f(x) is 1.

(x+2) and (x-6) are the factors of f(x)

[tex]f(x) = (x + 2)(x - 6) \\ = {x}^{2} - 6x + 2x - 12 \\ = \boxed{{x}^{2} - 4x - 12}[/tex]

Answer:

4 more students

Step-by-step explanation:

To find how many more students Mrs. K has, subtract 19 from 23:

23 - 19

= 4

So, Mrs. K has 4 more students than Mr. Curran

Answer:

B Im pretty sure

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

just going by the trend this makes the most sense

Answer:

the best number is 17 cuz the sequence is to add 2 sooo it's 17 then 19

Answer:

2n+5

Step-by-step explanation:

Sequence = 7,9,11,13,15 ....

tn = a + (n-1)d  where a is first number, and d is common difference

tn = 7 + (n-1)2

= 7 + 2n - 2

= 2n+5

therefore tn (or nth term rule) = 2n+5

Answer:

The system of equations represent the same line ⇒ B

Step-by-step explanation:

In the system of equations ax + by = c and dx + ey = f, if

∵ The one line represented by the equation 25y - 20x = 100

→ Divide the terms of the equation by 5 to simplify it

∴ 5y - 4x = 20 ⇒ (1)

∴ a = 5, b = -4, c = 20

∵ The other line represented by the equation 5y - 4x = 20 ⇒ (2)

∴ d = 5, e = -4, f = 20

→ Compare the two equations

∵ a = d, b = e, c = f

→ By using the 1st case above

∴ The system of equations represent the same line