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3 years ago

Twice the sum of a number and 3 times a second number is 4. The difference of ten times the seco

1 answer:

34kurt3 years ago

4 0

Two numbers that gives twice the sum of a number and 3 times a second number is 4. The difference of ten times the second number and five times the first is 90 are -10 and 4

Given :

Twice the sum of a number and 3 times a second number is 4. The difference of ten times the second number and five times the first is 90.

Let a and b be the two unknown numbers

Lets frame equation using the given statements

Twice the sum of a number and 3 times a second number is 4.

$2(a+3b)=4\\a+3b=2$

the difference of ten times the second number and five times the first is 90

$10b -5a=90\\Divide \; by \;5 \\2b-a=18$

Now use these two equations to solve a and b

$a+3b=2\\-a+2b=18$

Add both the equations

$a+3b=2\\-a+2b=18\\--------------------------\\5b=20\\b=4$

Now find out 'a'

$a+3b=2\\a+3(4)=2\\a+12=2\\a=2-12\\a=-10$

The two numbers are -10 and 4

Learn more : brainly.com/question/13856304

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3 years ago

(High points) please solve with explanation

AysviL [449]

Answer:

The area and the perimeter of the picture are:

Area = 160 cm^2
Perimeter = 67.31 cm

Step-by-step explanation:

To find the area of that figure, you can find the area how if it was a rectangle and next subtract the area of the triangle in the upper part. The area of a rectangle could be found by the next formula:

Area of a rectangle = base * height

As you can see in the picture, the base is 16 cm and the height is 12 cm, then we replace in the formula:

Area of a rectangle = 16 cm * 12 cm
Area of a rectangle = 192 cm^2

Now, we calculate the area of the triangle to subtract to the area we found and obtain the real area, the formula to obtain the area of a triangle is:

Area of a triangle = (base * height) / 2

The height of the triangle is 8 cm, and the base is 8 cm too, because you subtract to the base of the rectangle (16 cm) the measurements in the upper part (16 - 4 - 4 = 8), Now, we replace in the formula:

Area of a triangle = (8 cm * 8 cm) / 2
Area of a triangle = (64 cm^2) / 2
Area of a triangle = 32 cm^2

We subtract to the found area:

Area of the picture = 192 cm^2 - 32 cm^2
Area of the picture = 160 cm^2

To find the perimeter, you must add all the sides of the picture, but, as you can see, there is a side that doesn't have the measurent, this is the hypotenuse of the triangle used before, but how we know the other sides, we can use Pythagorean theorem:

$a^{2}+b^{2}=c^{2}$

Where:

a = Opposite leg (8 cm)
b = Adjacent leg (8 cm)

So, we replace in the theorem:

$a^{2}+b^{2}=c^{2}$

$(8 cm)^{2}+(8cm)^{2}=c^{2}$ (and we clear c)
$\sqrt{(8 cm)^{2}+(8cm)^{2}} =c$
$\sqrt{64 cm^{2}+64cm^{2}} =c$
$\sqrt{128cm^{2}} =c$
c = 11.3137085 cm
c ≅ 11.31 cm

At last, we add all the sides of the picture begining by the base and going by the left side:

Perimeter of the picture = 16 cm + 12 cm + 4 cm + 11.31 cm + 8 cm + 4 cm + 12 cm
Perimeter of the picture = 67.31 cm approximately.

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