Mathematics, 23.07.2019 18:00 diamondgdm

An equilateral triangle measuring 8s feet on a side is changed by decreasing the length of one side by 5 feet and increasing the lengths of the other two sides by 3 feet. what is rhe new perimeter?

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We have three sides
a = 8
b = 8
c = 8
The old perimeter is a+b+c = 8+8+8 = 24 feet

Decrease one side, let's say side 'a', by 5 ft
a-5 = 8-5 = 3
Let's call this m, so m = 3

Then increase side b by 3 ft
b+3 = 8+3 = 11
Let's call this n, so n = 11

The same thing will happen to c. The side c will increase to 11, which we'll call p. So p = 11

The old triangle with sides a = 8, b = 8, c = 8 had a perimeter of 24
The new triangle with sides m = 3, n = 11, p = 11 has a perimeter of 25 (because m+n+p = 3+11+11 = 14+11 = 25)

The perimeter has increased by 1 (because 25-24 = 1)

Answer from: Quest

the system of inequity is

$y\leq -x+4$

$3y> x$

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

the solid line passing through the points (0,4) and (4,0).

$y-4=\frac{0-4}{4-0}(x-0)$

$y=-x+4$

the related equation of solid line is $y=-x+4$ .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

$y-0=\frac{0-1}{3-0}(x-0)$

$3y=x$

the related equation of dashed line is $3y=x$

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

$1=-0+4$

$1=4$

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be $\leq$ . the required inequality is

$y\leq -x+4$

similarly, check the second related equation.

$3(1)=0$

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is

$3y> x$

15 points write a system of inequalities to represent the shaded portion of the graph

Answer from: Quest

answer: option a.

step-by-step explanation:

you know that the quadrilateral opqr ( a four sided figure) is inscribed in circle. this means that all its vertices are on the circle.

then, by definition, the opposite angles of the quadrilateral are supplementary, this means that the sum of their measures is 180 degrees.

you can observe in the figure that the angles ∠opq and the angle ∠orq are opposite, therefore:

$m\angle opq+m\angle orq=180\°\\\\m\angle opq+ (2x + 16)\°=180\°$

then, $m\angle opq+ (2x + 16)\°=180\°$ can be used to d to calculate the measure of ∠opq

Quadrilateral opqr is inscribed in circle n, as shown below. which of the following could be used to

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