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3 years ago

Solve the simultaneous equations 3x + 2y = 30 3x - y = 21

Mathematics

1 answer:

Mrac [35]3 years ago

3 0

Answer:

x = 8 , y = 3

Step-by-step explanation:

3x + 2y = 30

3x - y = 21 -> y = 3x - 21

3x + 2 (3x - 21) = 30

3x + 6x - 42 = 30

3x + 6x = 30 + 42

9x = 72

x = 72/9 = 8

y = 3*8 - 21 = 24 - 21 = 3

∴ x = 8 & y = 3

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Evaluate the expression9!/3!

Ne4ueva [31]

The answer to 9!/3! Is 60480

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3 years ago

What is the perimeter of parallelogram HIJK? Round to the nearest hundredth.

bixtya [17]

Answer:

Perimeter of the parallelogram = 26.64 units

Step-by-step explanation:

The perimeter of parallelogram = 2(a + b)

Here a = KJ = 7 units.

b = HK

We need to find the HK using the distance formula.

Distance formula = $\sqrt{(x2 - x1)^2 + (y2 - y1)^2}$

H = (-4, 3) and k = (-2, -3)

Now plug in x1 = -4, y1 =3, x2 = -2, y2 = -3 in the distance formula

HK = $\sqrt{(-2 -(-4))^2 + (-3 - 3)^2}$

= $\sqrt{(-2 +4)^2 + (-6)^2}$

= $\sqrt{4 + 36}$

= $\sqrt{40}$

HK = b = 6.32 units

Now plug in a = 7 and b = 6.32 in the perimeter formula, we get

Perimeter = 2(7 + 6.32)

= 2(13.32)

= 26.64 units

Thank you.

6 0

3 years ago

Please help me I need the answer

VMariaS [17]

Check the picture below.

well, since the triangle is an isosceles, with twin sides and twin angles at the "base", let's check what the angle at R is, 15(7) - 31 = 74, and her twin sister at T is also 74, that means that the angle at S is 180 - 74 - 74 = 32.

4 0

2 years ago

Can anyone explain to me how to do this question ? ty !!

julia-pushkina [17]

Step-by-step explanation:

use a little imagination.

the whole thing is a combination of churches and half- circles.

and you know the formula for the area of a circle ?

A = pi×r²

so, the only difficulty is to find the circles and then the radius of each involved circle.

when you look at the picture, the shaded area is almost identical to the lower half of the main circle.

2 bumps "look" over into the other side, but one equally sized bump is removed from this lower half.

so, as a first step we will calculate the area of the lower half of the main circle.

the diameter is 24 m, so the radius is half of that : 12m

the area of the large circle is therefore

pi×12² = 144×pi m²

since we only need the (lower) half, we divide this by 2 :

144×pi / 2 = 72×pi m²

the bumps up and down are actually half-circles too. just of smaller circles.

since AB = BC = CD, we know each of these lines are 1/3 of the main diameter AD.

so, the diameter of the smaller circles is 24/3 = 8 m

and their radius is half of that = 8/2 = 4m

the area of such a small circle is therefore

As = pi×4² = 16×pi m²

and a small half-circle area is then

16×pi / 2 = 8×pi m²

so, for the full shaded area I need to take the large half-circle and add 2 small half-circles, and then subtract 1 small half-circle.

so, in total I only need to add 1 small half-circle.

Ashaded = 72×pi + 8×pi = 80×pi m²

5 0

3 years ago

A deposit of $4,500 at 5% for 3 years:

tekilochka [14]

I = 4500 × 0.05 × 3
<span>I = $ 675.00</span>

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3 years ago