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3 years ago

3g-2x=-2135 x=2g+60 Solve for g

Mathematics

1 answer:

jarptica [38.1K]3 years ago

5 0

Answer:

x = -3970, g = 2015

Step-by-step explanation:

Solve this system of linear equations by substitution: substitute 2g + 60 for x in the first equation.

Then we have:

3g - 2(2g + 60) = -2135

Performing the indicated multiplication, we get:

3g - 4g - 120 = -2135, or

-g = -2015

Then g = 2015. Then x = 2(-2015) + 60, or x = -3970

The solution is x = -3970, g = 2015

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Given: △ABC, m∠A=60° m∠C=45°, AB=8 Find: Perimeter of △ABC, Area of △ABC . FIRST CORRECT ANSWER GETS POINTS AND BRAINLIEST!!!! T

Ad libitum [116K]

Answer:

Given : In △ABC, m∠A=60°, m∠C=45°,and AB=8 unit

Firstly, find the angles B

Sum of measures of the three angles of any triangle equal to the straight angle, and also expressed as 180 degree

∴m∠A+ m∠B+m∠C=180 ......[1]

Substitute the values of m∠A=60° and m∠C=45° in [1]

$60^{\circ}+ m\angle B+45^{\circ}=180^{\circ}$

$105^{\circ}+ m\angle B=180^{\circ}$

Simplify:

$m\angle B=75^{\circ}$

Now, find the sides of BC

For this, we can use law of sines,

Law of sine rule is an equation relating the lengths of the sides of a triangle to the sines of its angles.

$\frac{\sin A}{BC} = \frac{\sin C}{AB}$

Substitute the values of ∠A=60°, ∠C=45°,and AB=8 unit to find BC.

$\frac{\sin 60^{\circ}}{BC} =\frac{\sin 45^{\circ}}{8}$

then,

$BC = 8 \cdot \frac{\sin 60^{\circ}}{\sin 45^{\circ}}$

$BC=8 \cdot \frac{0.866025405}{0.707106781} =9.798$ unit

Similarly for AC:

$\frac{\sin B}{AC} = \frac{\sin C}{AB}$

Substitute the values of ∠B=75°, ∠C=45°,and AB=8 unit to find AC.

$\frac{\sin 75^{\circ}}{AC} =\frac{\sin 45^{\circ}}{8}$

then,

$AC = 8 \cdot \frac{\sin 75^{\circ}}{\sin 45^{\circ}}$

$AC=8 \cdot \frac{0.96592582628}{0.707106781} =10.9283$ unit

To find the perimeter of triangle ABC;

Perimeter = Sum of the sides of a triangle

i,e

Perimeter of △ABC = AB+BC+AC = 8 +9.798+10.9283 = 28.726 unit.

To find the area(A) of triangle ABC ;

Use the formula:

$A = \frac{1}{2} \times AB \times AC \times \sin A$

Substitute the values in above formula to get area;

$A=\frac{1}{2} \times 8 \times 10.9283 \times \sin 60^{\circ}$

$A = 4 \times 10.9283 \times 0.86602540378$

Simplify:

Area of triangle ABC = 37.856 (approx) square unit

4 0

3 years ago

Cynthia invests some money in a bank which pays

lidiya [134]

Answer:

£6911 is the smallest amount Cynthia should invest to get £8000 after three years

Step-by-step explanation:

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Amount expected after three years when compounded annually = A = £8000 Formula for Amount of compound interest annually is a follows A = P( 1 + R/100)^n In our case Principal P = x , Amount A = 8000 , R = 5% and n = 3( since compounded annually). On substituting these values in above formula we get 8000 = x ( 1 + 5/100)^3 ⇒8000 = x ( 105/100)^3 ⇒8000 = x ( 21/20 )^3 ⇒(8000 × 20 × 20 × 20)/(21×21×21) = x ⇒x = 6910.70≈6911

Hence £6911 is the smallest amount Cynthia should invest to get £8000 after three years

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Answer:

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Step-by-step explanation:

Let a = Able's score, b = Ben's score, and c = Cal's score.

Since

Able's score was 6 times Ben's score, that means a = 6b.

Cal's score was a third of Able's score, so that means c = a/3. And since a = 6b, that means c = 6b / 3 = 2b.

Thus, the ratio of Able's score to Ben's score to Cal's score, a:b:c, is 6:1:2, because c is twice as much as b and a is 6 times as much as b.

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3 years ago

Rita is hiking along a trail that is 13.7 miles long. So far she has hiked ond tenth of the trail.

lesantik [10]

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Step-by-step explanation:

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3 years ago