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3 years ago

Given -8(x-3)=-32 prove x=7

Mathematics

1 answer:

AleksAgata [21]3 years ago

7 0

Step-by-step explanation:

Plug x in :

-8(7-3) = -32

Distribute :

-56 - (-24) = -32

Subtract :

-32 = -32

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Given: PS=RT, PQ=ST Prove: QS=RS

ivanzaharov [21]

Answer:

I) Eq(1) reason: sum of segments of a straight line

II) Eq(2) reason: Given PQ = ST & PS = RT

III) Eq(3) reason: sum of segments of a straight line

IV) Eq(4) reason: Same value on right hand sides of eq(2) and eq(3) demands that we must equate their respective left hand sides

V) Eq(5) reason: Usage of collection of like terms and subtraction provided this equation.

Step-by-step explanation:

We are given that;

PS = RT and that PQ = ST

Now, we want to prove that QS = RS.

From the diagram, we can see that from concept of sum of segments of a straight line we can deduce that;

PQ + QS = PS - - - - (eq 1)

Now, from earlier we saw that PQ = ST & PS = RT

Thus putting ST for PQ & PS for RT in eq 1,we have;

ST + QS = RT - - - - (eq 2)

Again, from the line diagram, we can see that from concept of sum of segments of a straight line we can deduce that;

RS + ST = RT - - - - -(eq 3)

From eq(2) & eq(3) we can see that both left hand sides is equal to RT.

Thus, we can equate both left hand sides with each other to give;

ST + QS = RS + ST - - - (eq 4)

Subtracting ST from both sides gives;

ST - ST + QS = RS + ST - ST

This gives;

QS = RS - - - - (eq 5)

Thus;

QS = RS

Proved

5 0

3 years ago

HELP FAST PLEASE 10 POINTS

NeX [460]

Answer:

56% and B

Step-by-step explanation:

To calculate her percentage score, create the fraction of her score out of the total and multiply by 100%

percent score = $\frac{112}{200}$ × 100% = 56%

Her percent score is in the interval 50% - 64%

Thus her result is a B

3 0

3 years ago

Read 2 more answers

Witch number is 164,501,423

kykrilka [37]

What are the choices?

5 0

3 years ago

A basketball coach keeps track of the points scored per game for all of the players . She gives a trophy to the player with the

Verdich [7]

Your Question was incomplete so I will solve a similar question that will help you to tackle this kind of questions.

Q)Two university female basketball players are being considered for an award to be given to the most consistent player with the highest scoring average for the season. The number of points scored per game for all games played during the season is given by the following table. ( Table Attached)

a) Calculate the population mean and population standard deviation of the number of points scored per game for each player.

(b) Using the results of part (a) which player should receive the award.

Answer:

<h3>Player B should receive the award.</h3><h3>Step-by-step explanation:</h3>

Points of player A:- 5,32,45,25,8,10,35,12,37,21

First we will calculate the mean for player A

∑x = 5 + 32 + 45 + 25 + 8 + 10 + 35 + 12 + 37 + 21

∑x = 230

N = 10

Mean = µ= ∑x/N = 230/10 = 23

Now we will calculate the standard deviation for Player A

x - µ = -18 , 9, 22, 2, -15, -13, 12, 11, 14, -2

(x - µ)^2 = 324, 81, 484, 4, 225, 169, 144, 121, 196, 4

∑(x - µ)^2 = 1752

σ = sqrt( ∑((x - µ)^2/N) )

σ = sqrt(1752/10)

σ = 13.236

Calculating mean for player B:

Points of player B = 18, 20, 22, 15, 35, 24, 29, 19, 25, 23

∑x = 18 + 20 + 22 + 15 + 35 + 24 + 29 + 19 + 25 + 23

N =10

µ = 230/10

µ = 23

Calculating standard deviation for player B:

(x - µ ) = -5, -3, -1, -8, 12, 1, 6, -4, 2, 0

(x -µ )^2 = 25, 9, 1, 64, 144, 1, 36, 16, 4, 0

∑(x - µ)^2 = 300

σ = sqrt(300/10)

σ = 5.48

Since both Player A and Player B have same mean we will calculated the coefficient of variation for both the players.

For player A:

σa/µa *100 = 13.24/23 *100 = 57.56

For Player B:

σb/µb *100 = 5.48/23 * 100 = 23.82

Since the coefficient of variation of Player B is less than Player A hence Player B should receive the award.

3 0

3 years ago

Read 2 more answers

How far will a cyclist travel in 1/4 hour if he cycles at 18 kilometres per hour

Zinaida [17]

In one hour he would cycle 18Km, therefore in a 1/4 hour the cyclist would ride a 1/4 of 18 = 4.5Km.

3 0

3 years ago