Mathematics, 24.11.2020 06:10 shanice13

In ΔWXY, y = 88 cm, x = 85 cm and ∠X=70°. Find all possible values of ∠Y, to the nearest 10th of a degree.

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Answer from: raiindrxp

All possible values of ∠Y are 76.6° and 103.4°

Step-by-step explanation:

In Δ WXY

∵ x is the opposite side of ∠X

∵ y is the opposite side of ∠Y

→ By using the sine rule

∴ $\frac{x}{sin(X)}$ = $\frac{y}{sin(Y)}$

∵ x = 85 and y = 88

∴ m∠X = 70°

→ Substitute them in the rule above

∴ $\frac{85}{sin(70)}$ = $\frac{88}{sin(Y)}$

→ By using the cross multiplication

∴ 85 × sin(Y) = 88 × sin(70)

→ Divide both sides by 85

∴ sin(Y) = 0.9728582427

∴ m∠Y = $sin^{-1}$ (0.9728582427)

∴ m∠Y = 76.62037845

→ Round it to the nearest tenth

∴ m∠Y = 76.6°

→ The other value of ∠Y is the obtuse angle supplement of ∠Y

∴ m∠Y = 180 - 76.6

∴ m∠Y = 103.4°

∴ All possible values of ∠Y are 76.6° and 103.4°

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

step-by-step explanation:

i think something is missing in your question because y-1=(x-12) would not pass through the point (-4,-3). because if you replace x by -4 your are supposed to find y=-3 which is not the case her. if you replace x by -4 you find =-15.

i assume the right equation is y-1=1/4*(x-12) because this one is passing through both your points (if you are interested to know how i found that out i can tell you).

in this equation if i replace x by -4 i find y=-3 and if i replace x by 12, i find y=1 so the line representing this equation is passing through those 2 points.

then the standard form of the equation is finding an expression of y in function of x

y-1=1/4*(x-12)

y=x/4-3+1

y=x/4-2

hope that .

do you confirm there was a mistake in the question?

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In ΔWXY, y = 88 cm, x = 85 cm and ∠X=70°. Find all possible values of ∠Y, to the nearest 10th of a d...

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