The angle of depression from one mountain summit to another is 15.9°. If the two mountains differ in height by 430 metres, find the horizontal distance between the two summits, to the nearest centimetre.

Answer:

Step-by-step explanation:

a)

i)

Time taken at the first part:

ii)

Time taken at the second part:

b)

If time is 3 hours and 15 minutes = 3 1/4 hours = 13/4 hours, the equation is:

c)

Solve the equation:

d)

Answer:

see below

Step-by-step explanation:

Let t = time (in hours)

a) i)  First 105 km of journey

[tex]\mathsf{speed=\dfrac{distance}{time}}[/tex]

[tex]\implies x=\dfrac{105}{t_1}[/tex]

[tex]\implies t_1=\dfrac{105}{x}[/tex]

ii) Rest of journey

distance = 190 - 105 = 85 km

speed = [tex]x+12[/tex] km/h

[tex]\mathsf{speed=\dfrac{distance}{time}}[/tex]

[tex]\implies x+12=\dfrac{85}{t_2}[/tex]

[tex]\implies t_2=\dfrac{85}{x+12}[/tex]

b)  3 hours 15 minutes = 3.25 hours

[tex]\implies[/tex]  total time = [tex]t_1+t_2=3.25[/tex]

[tex]\implies \dfrac{105}{x}+\dfrac{85}{x+12} =3.25[/tex]

[tex]\implies \dfrac{105(x+12)+85x}{x(x+12)} =3.25[/tex]

[tex]\implies 105(x+12)+85x =3.25x(x+12)[/tex]

[tex]\implies 105x+1260+85x =3.25x^2 +39x[/tex]

[tex]\implies 3.25x^2-151x-1260=0[/tex]

multiply by 4:

[tex]\implies 13x^2-604x-5040=0[/tex]

c)

[tex]\textsf{quadratic formula} \ x=\dfrac{-b \pm\sqrt{b^2-4ac} }{2a}}[/tex]

[tex]\implies x=\dfrac{604 \pm\sqrt{(-604)^2-4(13)(-5040)} }{2(13)}}[/tex]

[tex]\implies x=\dfrac{604 \pm\sqrt{626896} }{26}}[/tex]

[tex]\implies x = 53.68, x=-7.22[/tex]

(to 2 decimal places)

d) time ≥ 0, therefore, x = 53.68 only

Substitute x = 53.68 into the expression for [tex]t_1[/tex] and solve for [tex]x[/tex]:

[tex]\implies t_1=\dfrac{105}{53.68}=1.955912... \textsf{hours}=\textsf{1 hr 57 min}[/tex]

Answer:

In y = kx, where k is the constant of proportionality.

Answer:

k is the constant

Step-by-step explanation:

Direct variation is simply explained as when a number is directly proportional to another number. For example, when 8 is directly proportional to 4 then it will result to

=> 8= k4, where k is the constant

=> divide both sides by 4 to get k

=> k= 2

Answer:

24

Step-by-step explanation:

the answer is 24 because the 3 and 12 u divide

Answer: the answer is choice c which is 24 .

Step-by-step explanation: HOPE IT IS CORRECT .THANKS .

Answer:

(125x+8)cm^3

Step-by-step explanation:

Volume= (5x+2)^3 = (125x+8)cm^3

Hey!

Answer:

125x^3+ 150 x^2+ 60x +8.

Formula of the volume of the cube = v=a^3

Substitute:

v=(5x+2)^3

=125x^3+ 150 x^2+ 60x +8.

Answer:

1950

Step-by-step explanation:

i got to this by multiplying 30 and 65

1,950

Step-by-step explanation:

it's 65 x 30 which equals 1,950

Answer:

14 ft²

Step-by-step explanation:

To find the area of a rectangle you multiply the length and width. Sense the length is 10 feet but 3 feet was removed it is now 7 feet. Now you multiply that 7 feet by the width of 2 feet to get

7×2=

Area= 14 ft²

Answer:187

Step-by-explanation: width multiply by height

=11 times 17

=187

Answer:

$13.56 is 80% of $16.95.

Answer:

x = 20, angle B = 92 and angle c = 40

Step-by-step explanation:

3 angles in a triangle adds up to 180, and since A is 48, we have B + C = 132

6x - 28 + 2x = 132
=> 8x - 28 = 132
=> 8x = 160 and x = 20

B = 6 x 20 - 28 = 92
C = 2 x 20 = 40

Answer:

1.0 inch

Step-by-step explanation:

Round the 9 in 0.955, this turns it into 1.0, Since you said an inch, the value will be in inches.

Answer:

1.0in is your answer!

Step-by-step explanation:

the person above me explained it good enough

Answer:

Step-by-step explanation:

We know that sine and cosine are equal when angles are complementary.

sin and cos are equal when their sum is 90°

So

Answer:

60 boys

Step-by-step explanation:

To find how many boys, you need to find how many times more than 75 is than five. To do that, divide 75 by 5 and you'll get 15. Multiply 4 by 15 and you get 60 boys. (i'm guessing bc im in middle school lol)

1. 3*3 + 3*8 = 9+24=33

2. 4*4+.5*2*4+5*5= 16+4+25=45

3. 5*10+4*10= 90

4. 24+.5*4*4 = 32

Answer:

64

Step-by-step explanation:

so each day you times the amount of money by two

1=2

2=4

3=8

4=16

5=32

6=64

7=128

Answer:

(6,2)

Step-by-step explanation:

Graph is below

Answer:

  Plant B grows 3 times as fast as Plant A

Step-by-step explanation:

Both plants start at 0 height on Day 1 and grow the same amount each day. Plant A grows 2 cm each day; Plant B grows 6 cm each day. The growth rate of Plant B is 3 times the growth rate of Plant A.

Answer:

what event there is no picture or words to tell me please explain

Step-by-step explanation:

The principal of a loan is the amount of money they took out as a loan.

Principal = $35,000

The number of hours it takes Elisabeth to read 3/4 of the book is;  5³/₅ hours

We are told that she reads 15 of her books in 112 hours.

Thus, number of hours to read one book is;

112/15 hours per book

Therefore, number of hours to read ³/₄ of the book is;

³/₄ * ¹¹²/₁₅ = 28/5

As a mixed number is 5³/₅ hours per book

Read more on mixed numbers at; https://brainly.com/question/10225

Answer:

5 5/8 h

Step-by-step explanation:

took the test and got it right :)

Answer:

22

Step-by-step explanation:

180-90-68=22

Answer:

180 - (90+68) = 22

B =22

Hope this helps!

Answer:

8.23 cm

Step-by-step explanation:

A circle is given to us and we need to find out the length of the bolded arc . The arc subtends an angle of 118° at the centre . And the radius of the circle is 4cm .As we know that , length of the arc is given by ,

[tex]\longrightarrow Length_{arc}= \dfrac{\theta}{360}\times 2\pi r [/tex]

Here ,

On substituting the respective values,

[tex]\longrightarrow Length_{arc}=\dfrac{118^o}{360^o}\times 2(3.14)(4cm) [/tex]

Simplify ,

[tex]\longrightarrow Length_{arc}= 0.3277 \times 25.18 \ cm [/tex]

Multiply ,

[tex]\longrightarrow \underline{\underline{Length _{arc}= 8.23 \ cm}} [/tex]

This is the required answer!

Answer:

7.7.7.7 and 7^4 and seven to the fourth power

Step-by-step explanation:

They all equal 2401.

They are all the same but in different forms:

(7.7.7.7- expression)

(7^4 - exponential form)

(seven to the fourth power-word form of exponent)

Answer:

I think 15

Step-by-step explanation:

15+16+17+18+19+20=105

if it was 14 it would equal to 99

Answer:

A ,D , F

Step-by-step explanation:

A) x-3=0 , x=3

B 1+x=2 , x=2-1=1 , x=1

C 9-x=3 , x=9-3=6 , x=6

D) 6=2x , x=6/2=3 , x=3

E (1/5)x=3 , x=3*5=15 , x=15

F) x^2=9 x=√9 , x=3

Answer:

4 - 12x

Step-by-step explanation:

-6(-2/3 + 2x)

we can distribute by multiplying -6 by whats inside of the parenthesis ( -2/3 and 2x )

-6 * -2/3 = 4

-6 * 2x = -12x

4 - 12x would be the equivalent expression

Given expression to us is ,

→ -6( -2/3 +2x)

Simplify by multiplying each terms inside the brackets by -6 .

→ -6*-2/3 + 2x*(-6)

Simplify,

→ 4 -12x

Hence option 3 is correct .

I hope this helps .

Answer:

African American and women

Step-by-step explanation:

Mary Eliza Mahoney was eager to encourage greater equality for African Americans and women

hope this helps!

Problem 13

If we want to multiply (x^3-3x^2+2x) with (x^3-2x^2+x), then we can set up a diagram shown below. The terms are along the outside. The stuff inside is the result of multiplying each pair of outer terms.

This is known as the box method to keep track of all the terms multiplied.

Once the table is filled out, we add up each term inside the boxes. Combine like terms if possible. Notice that I color-coded the like terms (eg: the x^3 terms are in green boxes).

The final answer is x^6 - 5x^5 + 9x^4 - 7x^3 + 2x^2