If x = 45, y = 63, and the measure of AC = 4 units, what is the difference in length between segments AB and AD? Round your answer to the nearest hundredth.

Answer:

L

Step-by-step explanation:

Answer:

Given :

length offshore = CS=√(1+X^2)

Cable charged = 5000√(1+X^2)

onshore length = 4-X

laying cost = 3000(4-X)

total cost:

C=5000√(1+X^2) +3000(4-X)

DC/DX

= [5000*(0.5)*2X/{√(1+X^2)}]-3000=0... for optimum

5000X=3000√(1+X^2)

25X^2=3+3X^2

22X^2=3

X=√(3/22)

= 0.3693 miles

So, it would be laid offshore to S in a manner that

BS=X=0.3693 miles

Onshore=4-0.3693

=3.6307 miles

Answer: -3y + 8z

Step-by-step explanation:

2x -2x = 0

-2y + - y= -3y

5z + 3z= 8z

-3y + 8z

The expression 2x − 2y + 5z − 2x − y + 3z is simplified as − 3y + 8z.

Making anything easier to accomplish or comprehend, as well as making it less difficult, is the definition of simplification.

PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.

The expression is given below.

⇒ 2x − 2y + 5z − 2x − y + 3z

Simplify the expression, then we have

⇒ 2x − 2y + 5z − 2x − y + 3z

⇒ 2x − 2x − 2y − y + 5z + 3z

⇒ 0 − 3y + 8z

⇒ − 3y + 8z

The expression 2x − 2y + 5z − 2x − y + 3z is simplified as − 3y + 8z.

More about the simplification link is given below.

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Answer:

See below.

Step-by-step explanation:

When x has a value between 0 and 90 the values of sin x ranges from 0, if x = 0 and 1 , if x = 90 degrees.

The cosine of x  has the reverse  value: cos x is 1 for x = 0 and 0 for x = 90 degrees.

At x = 45 the sine and cosine are equal in value.

So for sin x < cos x the value of x must be between 0 and 45  degrees.

So a possible value of x  is 30 degrees.

When x = 30 sin x = 0.5 and cos x = 0.866.

Answer:

45 degrees

Step-by-step explanation:

Because the shape is a square, all of the sides are equal and all of the angles are 90 degrees. From there you simply divide  90 by 2.

Answer:

∠ ABE = 45°

Step-by-step explanation:

The diagonals of a square bisect the angles, thus

∠ ABC = 90°, so

∠ ABE = 0.5 × 90° = 45°

Answer:

probability that Stu buys a sandwich and gets the bus = 0.35

Step-by-step explanation:

Probability of success of two independent events is the product of the respective probabilities, i.e. the multiplication rule.

P(Sandwich) = P(S) = 0.5

P(Bus) = P(B) = 0.7

Assuming the events are independent,

probability that Stu buys a sandwich and gets the bus

= P(SB) = P(S)*P(B) = 0.5*0.7 = 0.35

Answer: 0.35

Step-by-step explanation:

First there is a 50% chance, or a 0.5 chance that Stu gets a sandwich.  Then, ignoring the other .5, there is a .7 chance that he makes the bus.  Thus, 1/2 of .7 is 0.35.

Hope it helps <3

======================================================

Work Shown:

Segments AB, BC, CD, DA, and DN are all the same length (4 units)

The semicircle has area of

A = (1/2)*pi*(radius)^2

A = 0.5*pi*2^2

A = 2pi

The square has area of

B = (side length)^2

B = 4^2

B = 16

The trapezoid has area of

C = (height)*(base1+base2)/2

C = (DN)*(CD+MK)/2

C = (4)*(4+8)/2

C = 24

Add up the results of A, B and C to get the total area

A+B+C = 2pi+16+24 = 2pi+40

The total area is 2pi+40 square mm

The area of the figure will be 2π + 40 mm². Then the correct option is C.

The area of a two - dimensional figure is the area that its perimeter encloses. The quantity of unit squares that occupy a closed figure's surface is its region.

The figure is made by semicircle, square, and trapezium. Then the area is given as,

A = Area of a semicircle + Area of square + Area of trapezium

A = (π / 2) x r² + (AB)² + 1/2 x (CD + MK) x DN

A = (π / 2) x 2² + (2 x 2)² + 1/2 x (4 + 8) x 4

A = 2π + 16 + 24

A = 2π + 40 mm²

The area of the figure will be 2π + 40 mm². Then the correct option is C.

More about the area link is given below.

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Answer:

-5.7

Step-by-step explanation:

OUR EQUATION IS A QUADRATIC EQUATION

Let Δ be our dicriminant :

Answer:

The coordinates of r' are x = 10 and y = 12.

Step-by-step explanation:

The vertex experiments two operations: Dilation and translation, whose definitions are presented herein:

Dilation with respect to origin

[tex](x',y') = (0,0) + 3\cdot (x,y)[/tex], [tex]\forall \,x,y \in \mathbb{R}[/tex]

Translation

[tex](x',y') =(x+4,y)[/tex], [tex]\forall\,x,y\in \mathbb{R}[/tex]

If [tex]x = 2[/tex] and [tex]y = 4[/tex], then:

1) [tex](2,4)[/tex] Given.

2) [tex](0,0) + 3\cdot (2,4)[/tex] Dilation with respect to origin.

3) [tex](6,12)[/tex] Vectorial sum and scalar multiplication.

4) [tex](6+4,12)[/tex] Translation.

5) [tex](10,12)[/tex] Vectorial sum. Result.

The coordinates of r' are x = 10 and y = 12.

Answer:

10,12 is the answer

Step-by-step explanation:

I just did it on a p e x

Answer:

311.36

Step-by-step explanation:

For  a geometric series sum of first n terms is [tex]a(1-r^n)/(1-r)[/tex]

if r is less than 1.

where a is the first term and r is the common ratio.

____________________________\

given

a = 108

r = [tex]\frac{2}{3}.[/tex]

n = 8

thus , sum of n term is

[tex]a(1-r^n)/(1-r)\\=>108(1-(2/3)^8)/(1-2/3)\\=> 108 (1 - 256/6561)/1/3\\=> 108(6561-256)/ 6561/1/3\\=> 108(6305)/2187\\=>311.36[/tex]

Thus sum of first 8 terms is 311.36

Answer:

[tex]-2[/tex]

Step-by-step explanation:

[tex]( ++)2 + ( -+)2 + ( +-)2[/tex]

[tex]++ = +[/tex]

[tex]-+ = -[/tex]

[tex]+- = -[/tex]

[tex]( +)2 + ( -)2 + ( -)2[/tex]

[tex]2-2-2[/tex]

[tex]=-2[/tex]

Answer:

3

Step-by-step explanation:

We use Order of Operations BPEMDAS.

Step 1: Multiply

12 - 15/3(2) + 1

Step 2: Divide

12 - 5(2) + 1

Step 3: Multiply

12 - 10 + 1

Step 4: Subtract

2 + 1

Step 5: Add

3

Answer: 3

Step-by-step explanation:

PEMDAS

P: No parenthesis

E: No exponents

M and D: 4x3 = 12(12-15÷3×2+1), 15÷3 = 5(12-5×2+1), 5*2 = 10(12-10+1)

A and S: 12-10 = 2(2+1), 2+1=3(3)

Answer:

R$ 27,00

Step-by-step explanation:

R $ 72,00 = Um bolo de morango + dois quilos de bolo de chocalate

Um bolo de morango = R$ 18,00

R $ 72,00 = R$ 18,00 + Dois quilos de bolo de chocalate

Dois quilos de bolo de chocalate = R$72,00 - R$18,00

= R$54,00

Dois (2) quilos de bolo de chocalate = R$54,00

Um (1) quilo de bolo de chocalate = x

2x = R$ 54,00

x = R$ 54,00/2

x = R$ 27,00

Um quilo do bolo de chocolate = R$27,00

Answer:

17

Step-by-step explanation:

3(5) + 2 = 15 + 2

= 17

Therefore x= 17

Answer:

[tex]\huge\boxed{f(5)=17}[/tex]

Step-by-step explanation:

[tex]f(x)=3x+2\\\\f(5)=?\\\\\text{substitute}\ x=5\ \text{to}\ f(x):\\\\f(5)=3(5)+2=15+2=17[/tex]

Answer:

[tex]\boxed{\sf \ \ \ -2(x+4)(x-3)^3 \ \ \ }[/tex]

Step-by-step explanation:

Hello,

let's note k a real, we can write the polynomial as

[tex]k(x-(-4))^1(x-3)^3=k(x+4)(x-3)^3[/tex]

and we know that f(0)=216 so

[tex]216=k(0+4)(0-3)^3=k*4*(-1)^3*3^3=-27*4*k=-108k\\\\<=> k=-\dfrac{216}{108}=-2[/tex]

So the solution is

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

hope this helps

Answer:

see below

Step-by-step explanation:

sqrt(20)

sqrt(4*5)

We know that sqrt(ab) = sqrt(a) sqrt(b)

sqrt(4) sqrt(5)

2 sqrt(5)

Answer:

We can factor down 20 with it's greatest prime GCF, which is 5. We get a 4. When we factor that down the same way, we get 2. If we repeat that process, we get 5, 2, and 2, which turns into [tex]2\sqrt{5}[/tex].

Answer:

Drag it untill you get a right triangle . this is where you get the height

Answer:

Step-by-step explanation:

The direction of movement of Jordan on his birthday forms a right angle triangle. His movement from his house to his parents due south represents the opposite side of the right angle triangle. His movement due west represents the adjacent side and the movement back home along the straight line, d represents the hypotenuse. To determine d, we would apply the Pythagorean theorem. Thus

d² = 6² + 4² = 52

d = √52 = 7.2 km

The total distance that he drove on his birthday is

6 + 4 + 7.2 = 17.2 km

Answer: 1/4

Step-by-step explanation: Here, we have 1/3 ÷ 4/3.

Dividing by a fraction is the same

as multiplying by its reciprocal.

In other words, we can change the division sign

to multiplication and flip the second fraction.

So here, 1/3 ÷ 4/3 can be rewritten as 1/3 × 3/4.

Now we're simply multiplying fractions.

Before multiplying however, always try to cross-cancel.

Notice that we can cross-cancel 3 and 3 to 1 and 1.

So we now have 1/1 × 1/4.

Multiplying across the numerators

and denominators, we have 1/4.

Answer:

Solution,

Summation FX= 5+10+6+12+X

=33+x

N(total no.of items)=5

Now,

Mean= summation FX/N

or 9=33+X/5

or 9*5=33+X ( cross multiplication)

or 45=33+X

or -x=33-45

or -x=-12

X=12

Hope this helps...

Good luck on your assignment..

Answer:

x = 12

Step-by-step explanation:

The mean calculated by adding all the numbers of a set and dividing it by the total number of numbers. In this case, we have five numbers, but we do not know what the sum of all the numbers is because one of the numbers in under the pronumeral x. The find this out we need to work backwards. We know that when all the five numbers are added we should get 45 (it is 9 time 5 as there are five numbers in the set). The next step is to subtract 45 from the number that we known (i.e. 45 - 5 - 10 - 6 - 12). This comes to 12.

To double-check if you got the right answer you could add all five numbers include the 12 and divide it by 5 to see if the answer is 9.

Answer:

B. f^-1(x) = x+3

Step-by-step explanation:

Given the function f(x) = x-3, to get its inverse, the following steps mist be followed.

First we will make y = f(x)

y = x-3

Then we will make x the subject of the formula to have:

y+3 = x-3+3

y+3 = x

x = y+3

Finally, we will replace back y with x to have:

y = x + 3

f^-1(x) = x+3

This gives the inverse of the function.

Answer:

C. 4c+20

Step-by-step explanation:

If 4 buses are filled with kids, to get how many kids there are in total you would have to multiply the number 4, to represent the buses, times the number of kids in 1 bus, represented by C in this case. Then you would add 20 kids to represent the number of kids traveling in cars.

With that you have 4c+20.

Answer:

60° and 30°

Step-by-step explanation:

Since they are complementary, the 2 equations add up to 90°

5x + 4x - 18 = 90

9x - 18 = 90

9x = 108

x = 12

Simply plug in x to find our angles:

5(12) = 60°

4(12) - 18 = 48 - 18 = 30°

Answer:

5x = 60°, 4x - 18 = 30°

Step-by-step explanation:

Sum of complementary angles is 90°.

5x + 4x - 18 = 90

9x = 90+18

9x = 108

x = 12

5x = 5* 12= 60°

4x - 18 = 4*12 - 18 = 30°

Answer:

D. Congruent - SAS

Step-by-step explanation:

Two sides and the included angle of a triangle are congruent to the corresponding parts of another triangle.

The triangles are congruent by SAS.

Answer:

5

Step-by-step explanation:

Perimeter of the rectangle: 3+7+3+7=20

Square perimeter is same as rectangle, so square perimeter is also 20.

Side length is 20/4, which is 5

Answer:

- 3 and 5

Step-by-step explanation:

The equation of a line in slope- intercept form is

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

y = - 3x + 5 ← is in slope- intercept form

with slope m = - 3 and y- intercept c = 5

Answer:

the slope (gradient) is -3, and the y-intercept is +5

Step-by-step explanation:

A line in the slope-intercept form

   y = mx + b

has a slope of m and a y-intercept of b

Therefore for the line

  y=-3x + 5

the slope (gradient) is -3, and the y-intercept is +5

Answer:

-8.

Step-by-step explanation:

You can get the y-intercept when you find the y-value when x = 0.

y = x^2 - 8

y = 0^2 - 8

y = 0 - 8

y = -8

So, the y-intercept is -8.

Hope this helps!

Answer:

y = -8, if x2 mean 2 times x.

y = -7, if x2 mean X^2

Step-by-step explanation:

Y-intercept mean x = 0.

Plug x = 0, into the parabola, you get the answer.

Answer:

2x^-4  or 2/x^4.

Step-by-step explanation:

We replace the x in f(x) by g(x).

f(g(x)) =  2 (x^-2)^2

= 2 x^(-2*2)

= 2x^-4

= 2/x^4.