In the same amount of time, James drove twice as far as Roger. Altogether, James and Roger drove 90km. Find the number of kilometres driven by each person.

Answer:

Here is your answer!

Answer:

m<PQR = 18.7°

Step-by-step explanation:

Apply the Law of Sines,

[tex] \frac{Sin A}{a} = \frac{Sin B}{b} [/tex]

Where,

Sin A = Sin 140

a = 100 m

Sin B = Sin R (<PRQ)

b = 50 m

Substitute

[tex] \frac{Sin 140}{100} = \frac{Sin R}{50} [/tex]

Cross multiply

[tex] 100*Sin(R) = 50*Sin(140) [/tex]

Divide both sides by 100

[tex] Sin(R) = \frac{50*Sin(140)}{100} [/tex]

[tex] Sin(R) = 0.32139 [/tex]

[tex] R = Sin^{-1}(0.32139) [/tex]

R ≈ 18.7° (nearest tenth)

m<PQR = 18.7°

The angle PRO is 1.7 degrees.

Given that,

The diagram shows three points P, Q, and R on horizontal ground.

PQ = 50 m, PR = 100 m and angle PQR = 140°.

We have to determine,

The angle PRO.

According to the question,

The value of angle PRO is determined by using the sin rule-following all the steps given below.

[tex]\rm \dfrac{sina}{a} = \dfrac{sinb}{b}[/tex]

Where,  Sin A = Sin 140 , a = 100 m , Sin B = Sin R (<PRQ) , b = 50 m

Substitute all the values in the formula,

[tex]\rm \dfrac{sin140}{100} = \dfrac{sinR}{50}\\\\ \dfrac{0.64}{100} = \dfrac{sinR}{50}\\\\0.0064 = \dfrac{sinR}{50}\\\\0.0064 \times 50 = sinR\\\\0.321 = sinR\\\\R = sin{-1}(0.321)\\\\R = 18.7 \ degree[/tex]

Hence, The angle PRO is 1.7 degrees.

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Answer:

x = 45

Step-by-step explanation:

The angles labeled with the pink x are the same.  Line V and Line X are parallel and alternate interior angles are equal when the lines are parallel.

We know the 3 angles inside the triangle and the sum of the angles of a triangle are 180

x+x+ 2x = 180

4x= 180

4x/4 = 180/4

x = 45

Answer: 8/11

Step-by-step explanation:

This is because there are a total of 22 bulbs. 16 of those bulbs work, giving us the fraction: 16/22. If you simplify 16/22 by dividing the numerator and denominator by 2, you get 8/11.

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

Explanation:

There are 16 working bulbs out of 6+16 = 22 bulbs total.

The probability of randomly selecting a working bulb is 16/22

After that first bulb is selected and not put back, the probability of randomly selecting another working bulb is 15/21. Take note that I subtracted 1 from each part of the original fraction.

So we get the answer of

(16/22)*(15/21) = 240/462 = 40/77 which is choice C.

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Extra info:

[tex]\\ \sf\longmapsto 20°+2p=70[/tex]

[tex]\\ \sf\longmapsto 2p=70-20[/tex]

[tex]\\ \sf\longmapsto 2p=50[/tex]

[tex]\\ \sf\longmapsto p=\dfrac{50}{2}[/tex]

[tex]\\ \sf\longmapsto p=25[/tex]

Answer: 6 Painters

Step-by-step explanation:

Total painters needed to paint 7-room house = 3 painters

Rooms painted by each painter = 3/7

Total painters needed to paint 14-room house = 3/7×14

= 42/7

= 6 painters

Therefore it will require 6 painters to paint 14-room house

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f(x)=3x²+x-3x-1

=x(3x+1)-(3x+1)

=(x-1)(3x+1)

Answer: 83 degrees

Step-by-step explanation:

(16^2 + 8^2 - 17^2)/(2)(16)(8) = 83

2^2 + 2^2 = h^2

8 = h^2

√8 = h

h = 2.82mm

Answered by Gauthmath must click thanks and mark brainliest

Answer:

12

Step-by-step explanation:

bc it is

[tex]x - 12 = 14 \\ x = 14 + 12 \\ x = 26[/tex]

it was help to you ❤︎❤︎❣︎❣︎★★★

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textsf{x - 12 = 14}[/tex]

[tex]\huge\text{ADD 12 to BOTH SIDES}[/tex]

[tex]\huge\textsf{x - 12 + 12 = 14 + 12}[/tex]

[tex]\huge\boxed{\bullet}\huge\text{ CANCEL out: 12 - 12 because it gives}\\\huge\text{you 0}[/tex]

[tex]\huge\boxed{\bullet}\huge\text{ KEEP: 14 + 12 because it gives you}\\\huge\text{the RESULT of the x-value}[/tex]

[tex]\huge\textsf{a = 14 + 12}\\\huge\boxed{\rightarrow}\huge\textsf{ 14 + 12 = a}[/tex]

[tex]\huge\textsf{14 + 12 = \bf 26}[/tex]

[tex]\boxed{\huge\textsf{Therefore, your answer is: a = 26}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]~[tex]\huge\boxed{\frak{Amphitrite1040:)}}[/tex]

5:-c

The 3multiples are 25,50,75

6:-c

[tex]\\ \sf\longmapsto 6\:of\:2+9-5[/tex]

[tex]\\ \sf\longmapsto 6(11-5)[/tex]

[tex]\\ \sf\longmapsto 6(6)[/tex]

[tex]\\ \sf\longmapsto 36[/tex]

7:-a

12,17

8:-c

HCF=2×2×11=44

9:-c

LCM of 9 and 5 is 45 hence its true

10:-c

HCF of two consecutive numbers is 1

Answer:

- 14

Step-by-step explanation:

a = 3

a^2 - 6a - 5

= 3^2 - 6 ( 3 ) - 5

= 9 - 18 - 5

= 9 - 23

= - 14

Answer:

11:35

Step-by-step explanation:

add 13 hour and 45 minutes to 1:50 giving you 4:35 and since the time is 7 hours ahead add another 7 hours and tada

The arrival time in Colombo is 10:35 pm.

The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

Now, First, we need to convert 13 hours and 45 minutes to just hours.

We can do this by dividing the minutes by 60:

45 minutes ÷ 60 = 0.75 hours

So the total flight time is,

13 + 0.75 = 13.75 hours.

Next, we need to add the time difference between London and Colombo. Since Colombo is 7 hours ahead of London, we need to add 7 hours to the total flight time:

13.75 hours + 7 hours = 20.75 hours

Now we need to convert this to a time.

Since the flight left at 01:50, we can add 20 hours and 45 minutes to find the arrival time in Colombo:

01:50 + 20:45 = 22:35

So, the arrival time in Colombo is 10:35 pm.

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Answer:

Hello,

We don't need vw(x) !

[tex]w^{-1}(x)=\dfrac{x-1}{2}[/tex]

Step-by-step explanation:

[tex]w(x)=2x+1=y\\\\2y+1=x \ exchanging \ x\ and\ y\\\\y=\dfrac{x-1}{2} \\\\w^{-1}(x)=\dfrac{x-1}{2}[/tex]

Answer:

y= -2x +8

Step-by-step explanation:

perpendicular lines have a negative reciprocal gradient so

1/2 becomes -2/1 which is the gradient

sub in the values of x and y

2= -2 (3) +C

2= -6 + C

8=C

y=-2x +8

Answer:

y = -2x + 8

Step-by-step explanation:

for me the easiest way is simply to transform the slope and then just determine the y-intersect.

the slope of the original line is 1/2.

it is always the factor of x and represents the y/x ratio of the function (how many units is y changing when x changes a certain number of units).

a perpendicular line (90 degree angle) simply reverses x and y and the sign of the original slope.

so, the slope of the perpendicular line is -2, and the equation is

y = -2x + c

and c we get by using the point coordinates :

2 = -2×3 + c

2 = -6 + c

c = 8

so, we have

y = -2x + 8

For a geometric sequence

a, ar, ar ², ar ³, …

the n-th term in the sequence is ar ⁿ ⁻ ¹.

The first sequence is

1, 3, 9, 27, …

so it's clear that a = 1 and r = 3, and so the n-th term is 3ⁿ ⁻ ¹.

The second sequence is

400, 200, 100, 50, …

so of course a = 400, and you can easily solve for r :

200 = 400r   ==>   r = 200/400 = 1/2

Then the n-th term is 400 (1/2)ⁿ ⁻ ¹.

Similarly, the other sequences are given by

3rd: … 4 × 2ⁿ ⁻ ¹

4th: … 400 (1/4)ⁿ ⁻ ¹

5th: … 5ⁿ ⁻ ¹

6th: … 1000 (1/2)ⁿ ⁻ ¹

7th: … 2 × 5ⁿ ⁻ ¹

Answer:

true

Step-by-step explanation:

Answer:

(i) 7/10

(ii) 3/10

(iii) 1/5

(iv) Rs 40,000

Step-by-step explanation:

The fraction of the salary spent on food = 1/2

The fraction of the salary spent on rented house fee = 1/5

(i) The fraction spent for both food and rental fee = (1/2) + (1/5) = (5 + 2)/10 = 7/10

(ii) The remainder (rest) of the salary = 1 - 7/10 = 3/10

The fraction of the remainder spent for children's education = 1/3

The fraction of the total salary spent for the children's education = (1/3) × (3/10) = 1/10

(iii) The remaining portion deposited in the bank = 1 - (1/10 + 7/10)) = 2/10 = 1/5

(iv) The amount equal to portion of 1/5 of his salary deposited in the bank is Rs 8000

Let x represent his whole salary, we have;

(1/5) × x = Rs 8,000

x = 5 × Rs 8,000 = Rs 40,000

His whole salary is Rs 40,000.

Answer:

13 and 39

Step-by-step explanation:

The sum of two numbers = 52

One number is 3 times as large as the other

Equation:

x + 3x = 52

4x = 52

52 / 4 = x

x = 13

13 * 3 = 39

The numbers are 13 and 39

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Answer:

[tex]{26}[/tex]

Step-by-step explanation:

[tex] \sqrt{(0 - ( - 5) ){}^{2} + (0 - 1) {}^{2} } [/tex]

[tex] = \sqrt{ {(5)}^{2} + {( - 1)}^{2} } [/tex]

[tex] = \sqrt{25 + 1} [/tex]

[tex] = \sqrt{26} [/tex]

Answered by GAUTHMATH

Answer:

26

Step-by-step explanation:

(-5, 1) (0, 0)

sqrt(5^2 + (-1^2))

sqrt(25 + 1)

sqrt(26)

So, 26 goes under the radical.

Perimeter:-4a

[tex]\\ \large\sf\longmapsto 4(5)=20in[/tex]

[tex]\boxed{\sf LSA=Height\times Perimeter}[/tex]

[tex]\\ \large\sf\longmapsto LSA=10\times 20[/tex]

[tex]\\ \large\sf\longmapsto LSA=200in^2[/tex]

Answer:

Step-by-step explanation:

(N)0.05 + (17-N)0.1 = M; M = amount of money I have.

Or 1.7-0.05N = M.

An expression two different ways to  the amount of money is equals to

1. 5N + 10 (17 -N)  = Y cents

2. N + 2(17 - N) = Y nickels

" Amount is defined as the total of any given quantity."

According to the question,

Total number of coins = 17

Number of nickels coins = N

Number of dimes coin = 17 - N

'Y' express the amount of money

Represent amount of money in cents

1 dime = 10 cents

1 nickel = 5 cents

Expression to represents amount of money in cents,

5N + 10 (17 -N)  = Y cents

Expression to represents amount of money in nickels,

1 dime = 2 nickel

N + 2(17 - N) = Y nickels

Hence, an expression two different ways to  the amount of money is equals to

1. 5N + 10 (17 -N)  = Y cents

2. N + 2(17 - N) = Y nickels

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Answer:

this looks complicated

Step-by-step explanation:

Answer:

38,250

Step-by-step explanation:

Its a 15% discount so youre only paying 85% of the original 45,000. You then multiply 45,000 by .85 to find what youre paying because the decimal version of 85% is .85. You can find the decimal version of a percentage by dividing the percentage by 100; 85/100=.85. Once you multiply 45,000 by .85 you get 38,250.

Answer:

Option A, 11.7

Step-by-step explanation:

To find height,

tan 68 = 26/h

h = 26/tan(68)

to find x

tan(42) = h/x

x = h/tan(42)

x = 11.7 (rounded to the nearest tenth)

Answered by GAUTHMATH

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

Explanation:

The smaller angles HGE and EGF combine to form the largest angle HGF.

This is an example of the angle addition postulate.

(angle HGE) + (angle EGF) = angle HGF

(3x+11) + (110) = 16x+4

3x+121 = 16x+4

121-4 = 16x-3x

117 = 13x

13x = 117

x = 117/13

x = 9 which is the final answer

We can stop here.

--------------------

Extra info (optional section)

Use this x value to find each angle shown below

Then notice how,

(angle HGE)+(angle EGF) = 38+110 = 148

which is exactly the measure of angle HGF

This confirms that the equation

(angle HGE) + (angle EGF) = angle HGF

is true for that x value of x = 9. Therefore, the answer is confirmed.

9514 1404 393

Answer:

  11) x = 9°

  13) x = -12°

Step-by-step explanation:

11) ∠HGE +∠EGF = ∠HGF

  (3x +11) +(110°) = (16x +4)

  117° = 13x . . . . . . . . . . . . . . . subtract 3x+4, collect terms

  9° = x . . . . . . . . . . . . divide by 13

__

13) ∠BCF +∠FCD = ∠BCD

  (x +78) +(x +41) = 95°

  2x = -24°

  x = -12°

Answer:

The answer is 2x+16=12(1/6x +1/192 )

Step-by-step explanation:

Answer:

264

Step-by-step explanation:

Volume = Area of cross section x height

Area of cross section = 1/2 bh

1/2 (8x6) = 24

24 x 11 = 264 yd^3

Answer:

The answer of this question is 134.83