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3 years ago

Solve the system of linear equations below.

Mathematics

1 answer:

Masja [62]3 years ago

7 0

Answer:

A. x=2 y=7

Step-by-step explanation:

-12x -3 = 3y

6x + 3y = 33

sooo you add them up...

so its

-6x = -12

x=2

and then you plug in the x value into one of the equations

6x + 3y = 33

6(2) + 3y = 33

12 + 3y = 33

3y = 33 - 12

3y = 21

21/3=7

y=7

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Please help ٩(๑òωó๑)۶

otez555 [7]

Answer:

Height of the cliff = 13.66 m

Step-by-step explanation:

Let the height of the cliff is 'x' m and distance between the base of the cliff and the boat is 'y' m.

From right triangle AOC,

tan 30° = $\frac{\text{Opposite triangle}}{\text{Adjacent side}}$

$\frac{1}{\sqrt{3}}=\frac{x}{y}$

y = $x\sqrt{3}$ ------(1)

From right angle triangle BOC,

tan 45° = $\frac{x}{y-10}$

$1=\frac{x}{y-10}$

x = y - 10

y = x + 10 -------(2)

From equations (1) and (2),

$x\sqrt{3}=x+10$

$x(\sqrt{3}-1)=10$

$x=\frac{10}{\sqrt{3}-1 }$

x = 13.66 m

Therefore, height of the cliff is 13.66 m.

7 0

4 years ago

Please help?

Mazyrski [523]

Answer:

$23\sqrt{3}\ un^2$

Step-by-step explanation:

Connect points I and K, K and M, M and I.

1. Find the area of triangles IJK, KLM and MNI:

$A_{\triangle IJK}=\dfrac{1}{2}\cdot IJ\cdot JK\cdot \sin 120^{\circ}=\dfrac{1}{2}\cdot 2\cdot 3\cdot \dfrac{\sqrt{3}}{2}=\dfrac{3\sqrt{3}}{2}\ un^2\\ \\ \\A_{\triangle KLM}=\dfrac{1}{2}\cdot KL\cdot LM\cdot \sin 120^{\circ}=\dfrac{1}{2}\cdot 8\cdot 2\cdot \dfrac{\sqrt{3}}{2}=4\sqrt{3}\ un^2\\ \\ \\A_{\triangle MNI}=\dfrac{1}{2}\cdot MN\cdot NI\cdot \sin 120^{\circ}=\dfrac{1}{2}\cdot 3\cdot 8\cdot \dfrac{\sqrt{3}}{2}=6\sqrt{3}\ un^2\\ \\ \\$

2. Note that

$A_{\triangle IJK}=A_{\triangle IAK}=\dfrac{3\sqrt{3}}{2}\ un^2 \\ \\ \\A_{\triangle KLM}=A_{\triangle KAM}=4\sqrt{3}\ un^2 \\ \\ \\A_{\triangle MNI}=A_{\triangle MAI}=6\sqrt{3}\ un^2$

3. The area of hexagon IJKLMN is the sum of the area of all triangles:

$A_{IJKLMN}=2\cdot \left(\dfrac{3\sqrt{3}}{2}+4\sqrt{3}+6\sqrt{3}\right)=23\sqrt{3}\ un^2$

Another way to solve is to find the area of triangle KIM be Heorn's fomula, where all sides KI, KM and IM can be calculated using cosine theorem.

7 0

3 years ago

-2(x+2)=-12 .............

Dima020 [189]

Answer:

x=4

Step-by-step explanation:

-2(x+2)=-12

x+2=-12/-2

x+2=6

x=6-2

x=4

6 0

3 years ago

choli [55]

Answer: B.x^3+4x^2-19x+14 is correct

Step-by-step explanation:

(x + 7)(x2 – 3x + 2)

Multiplying both

x^3-3x^2+2x+7x^2-21x+14

x^3+4x^2-19x+14

7 0

3 years ago

Miss Blue's gross pay is $903.75. Assuming 7.65% social security withholding, how much should her employer withhold from her che

vesna_86 [32]

Miss Blue's gross pay is 903.75 dollars.
=> the rate of the Social Security is 7.65%.
Now, let's solve for the amount that the employer should withhold from her salary.
=> 903.75 dollars * .0765 = 69.137 dollars will be deducted to her salary.
=> 903.75 dollars - 69.137 dollars = 834.61 dollars is the remaining of her salary.

7 0

4 years ago

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