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steposvetlana [31]
3 years ago
10

Question 3

Mathematics
1 answer:
igor_vitrenko [27]3 years ago
7 0

Answer:

The system has exactly one solution where x = 0 and y = -3.

Step-by-step explanation:

-6x + y = -3

7x - y = 3

(7x - 6x) + (y - y) = 3 - 3

x + 0 = 0

x = 0

7(0) - y = 3

0 - y = 3

-y = 3

y = -3

-6(0) + y = -3

0 + y = -3

y = -3

So, the system has exactly one solution where x = 0 and y = -3.

Hope this helps!

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Square root of -19 in terms of i​
yulyashka [42]

Answer:

i√19

Step-by-step explanation:

Because √(-19) = √(-1)√19, and because √(-1) = i, we get i√19

7 0
3 years ago
If ABCD is an A4 sheet and BCPO is the square, prove that △OCD is an isosceles triangle. And find the angles marked as 1 to 8 wi
Dmitry [639]

Answer:

The diagram for the question is missing, but I found an appropriate diagram fo the question:

Proof:

since OC = CD = 297mm Therefore, Δ OCD is an isoscless triangle

∠BCO = 45°

∠BOC = 45°

∠PCO = 45°

∠POC = 45°

∠DOP = 22.5°

∠PDO = 67.5°

∠ADO = 22.5°

∠AOD = 67.5°

Step-by-step explanation:

Given:

AB = CD = 297 mm

AD = BC = 210 mm

BCPO is a square

∴ BC = OP = CP = OB = 210mm

Solving for OC

OCB is a right anlgled triangle

using Pythagoras theorem

(Hypotenuse)² = Sum of square of the other two sides

(OC)² = (OB)² + (BC)²

(OC)² = 210² + 210²

(OC)² = 44100 + 44100

OC = √(88200

OC = 296.98 = 297

OC = 297mm

An isosceless tringle is a triangle that has two equal sides

Therefore for △OCD

CD = OC = 297mm; Hence, △OCD is an isosceless triangle.

The marked angles are not given in the diagram, but I am assuming it is all the angles other than the 90° angles

Since BC = OB = 210mm

∠BCO = ∠BOC

since sum of angles in a triangle = 180°

∠BCO + ∠BOC + 90 = 180

(∠BCO + ∠BOC) = 180 - 90

(∠BCO + ∠BOC) = 90°

since ∠BCO = ∠BOC

∴  ∠BCO = ∠BOC = 90/2 = 45

∴ ∠BCO = 45°

∠BOC = 45°

∠PCO = 45°

∠POC = 45°

For ΔOPD

Tan\ \theta = \frac{opposite}{adjacent}\\ Tan\ (\angle DOP) = \frac{87}{210} \\(\angle DOP) = Tan^-1(0.414)\\(\angle DOP) = 22.5 ^{\circ}

Note that DP = 297 - 210 = 87mm

∠PDO + ∠DOP + 90 = 180

∠PDO + 22.5 + 90 = 180

∠PDO = 180 - 90 - 22.5

∠PDO = 67.5°

∠ADO = 22.5° (alternate to ∠DOP)

∠AOD = 67.5° (Alternate to ∠PDO)

3 0
3 years ago
Solve the system using elimination.<br><br> 2x-4y=-22<br> 7x+5y=18<br><br> what are the coordinates
user100 [1]

Answer:

The coordinates are (22, 18)

Step-by-step explanation: hope this helps its a bit easy if ur in middle school

6 0
3 years ago
Sakura speaks 150 words per minute on average in Hungarian, and 190 words per minute on average in Polish. She once gave cooking
marusya05 [52]

Answer:3 minute

Step-by-step explanation:

Sakura speaks hungarian =150 words per minute

Sakura speaks polish =190 words per minute

and it is given she speaks 270 more words in polish than in hungarian

She speaks for a total of 5 minutes

let she speaks hungarian for t mins

therefore 150\times t+270=190\left ( 5-t\right )

t=2 mins

therefore sakura speaks hungarian for 2 mins and polish for 3 mins

6 0
3 years ago
Find the measure of the indicated angle. Round to the nearest degree.
slava [35]

Answer:

Step-by-step explanation:

Use SOH CAH TOA to recall how the trig functions fit on a triangle

SOH: Sin(Ф)= Opp / Hyp

CAH: Cos(Ф)= Adj / Hyp

TOA: Tan(Ф) = Opp / Adj

5)

Adj = 14

Hyp = 26

∠X

so use

CAH

Cos(X) = 14/26

X = arcCos(14/26)

X = 57.421°

X = 57.4 ° ( rounded to nearest 10th )

6)

∠X

Hyp = 46

Opp = 12

use SOH

Sin(x) = 12/46

X = arcSin(12/46)

X = 15.121°

X = 15.1 ° ( rounded to nearest 10th )

7)

∠X

Adj = 29

Opp = 24

use TOA

Tan(x) = 29 / 24

X = arcTan( 29 /24)

X = 50.389

X = 50.4 °  ( rounded to nearest 10th )

8)

∠X

Adj = 22

Opp = 6

use TOA agian

Tan(x) = 6 / 22

X = arcTan(6/22)

X = 5.194

X = 5.2 °  ( rounded to the nearest 10th )

:)

8 0
3 years ago
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