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3 years ago

Solve the simultaneous equations: 4x - y = 22 3x + 4y = 26

1 answer:

6 0

4x - y= 22 /x 4
3x+4y=26

16x - 4y = 88 }+
3x + 4y = 26

16x + 3x - 4y + 4y = 88 + 26
19x = 114 / :19
x = 6

3x + 4y = 26
4y = 26 - 3*6
4y = 8 /: 4
y = 2

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A point H is 20m away from the foot of a tower on the same horizontal ground. From the point H, the angle of elevation of the po

astra-53 [7]

Answer:

a. See Attachment 1

b. $PT = 12.3\ m$

c. $HT = 31.1\ m$

d. $OH = 28.4\ m$

Step-by-step explanation:

Calculating PT

To calculate PT, we need to get distance OT and OP

Calculating OT;

We have to consider angle 50, distance OH and distance OT

The relationship between these parameters is;

$tan50 = \frac{OT}{20}$

Multiply both sides by 20

$20 * tan50 = \frac{OT}{20} * 20$

$20 * tan50 = OT$

$20 * 1.1918 = OT$

$23.836 = OT$

$OT = 23.836$

Calculating OP;

We have to consider angle 30, distance OH and distance OP

The relationship between these parameters is;

$tan30 = \frac{OP}{20}$

Multiply both sides by 20

$20 * tan30 = \frac{OP}{20} * 20$

$20 * tan30 = OP$

$20 * 0.5774= OP$

$11.548 = OP$

$OP = 11.548$

$PT = OT - OP$

$PT = 23.836 - 11.548$

$PT = 12.288$

$PT = 12.3\ m$ (Approximated)

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

Calculating the distance between H and the top of the tower

This is represented by HT

HT can be calculated using Pythagoras theorem

$HT^2 = OT^2 + OH^2$

Substitute 20 for OH and $OT = 23.836$

$HT^2 = 20^2 + 23.836^2$

$HT^2 = 400 + 568.154896$

$HT^2 = 968.154896$

Take Square Root of both sides

$HT = \sqrt{968.154896}$

$HT = 31.1\ m$ (Approximated)

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

Calculating the position of H

This is represented by OH

See Attachment 2

We have to consider angle 50, distance OH and distance OT

The relationship between these parameters is;

$tan50 = \frac{OH}{OT}$

Multiply both sides by OT

$OT * tan50 = \frac{OH}{OT} * OT$

$OT * tan50 = {OH$

$OT * 1.1918 = OH$

Substitute $OT = 23.836$

$23.836 * 1.1918 = OH$

$28.4= OH$

$OH = 28.4\ m$ (Approximated)

5 0

3 years ago

Tyson wrote this expression to describe the total amount of points he won in both rounds of a game.

Rainbow [258]

We know that Tyson wrote this expression to describe the total amount of points he won in both rounds of a game.

The expression is f+15. Let variable f represent points.

The correct answer is B. Tyson doesn't know how many points he earned in the first round. He knows he earned a total of 15 points in the whole game.

7 0

3 years ago

3-4 litros de jugo de frutilla 1 y 1-2 litros de jugo de manzana 1-8 litro de jugo consentrado de limón . 1 y 1-2 litro de agua.

Neko [114]

Answer:

Hay 3,875 litros de jugo multifrutal.

Step-by-step explanation:

(Se asume que el problema fue propuesto en un país distinto a los Estados Unidos, razón por la cual se emplea las reglas del Sistema Internacional.)

La capacidad de jugo multifrutal en el bidón se obtiene con la mezcla de cada jugo frutal y se logra mediante la suma de cada capacidad. A partir del enunciado, tenemos que la capacidad del jugo multifrutal es:

$V = \frac{3}{4}\,L + 1\,\frac{1}{2}\,L + \frac{1}{8}\,L + 1\,\frac{1}{2}\,L$