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3 years ago

The sum of two numbers is 31. The sum of the smaller and 3 times the larger is 85

Mathematics

1 answer:

In-s [12.5K]3 years ago

6 0

X+y=31 So, x=31-y
x+3y=85

31-y+3y=85
31+2y=85
2y=54
y=27
x+3×27=85
x+81=85
x=4

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What is the x-and y-intercept of the graph 4x -5y =40??

umka21 [38]

Answer:

x-intercept = 10

y-intercept = -8

Step-by-step explanation:

$4x-5y=40$

To identify the y-intercept, we will need to format the equation in the form $y=mx+b$ . We can start by subtracting $4x$ from both sides of the equation:

$-5y=-4x+40$

Divide both sides of the equation by the coefficient of $y$ , which is $-5$ :

$y=\frac{-4}{-5} x - 8$

The $b$ is representative of the y-intercept in $y=mx+b$ .

Identify $b$ in the equation $y=\frac{-4}{-5} x - 8$ :

$b=-8$

Therefore, our y-intercept is -8.

To solve for the x-intercept, replace the $y$ in the equation $y=\frac{-4}{-5} x - 8$ with a zero:

$0=\frac{-4}{-5} x - 8$

Add $8$ to both sides of the equation:

$8=\frac{-4}{-5} x$

You can go ahead and divide $-4$ by $-5$ to get rid of the fraction:

$8=0.8x$

Divide both sides of the equation by the coefficient of $x$ , which is $0.8$ :

$10=x$

Therefore, our x-intercept is 10.

8 0

3 years ago

The figures below are based on semicircles and squares. Find the perimeter and the area of each shape. Give your answer as a com

irina1246 [14]

Answer:

Part 1) The area of the figure is $A=48\ cm^2$

Part 2) The perimeter of the figure is $P=4(2+3\pi)\ cm$

Step-by-step explanation:

Part 1) Find the area of the figure

we know that

The area of the figure is equal to the area of three squares

$A=3[4^2]=48\ cm^2$

Part 2) Find the perimeter of the figure

we know that

The perimeter of the figure is equal to two times the length side of the square, plus the circumference of six semicircles ( or the circumference of three circles)

Remember that

The circumference of a circle is equal to

$C=\pi D$