Mathematics, 05.02.2020 09:56 kaileyy06

Calculate ac. round to the nearest hundredth.

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Answer from: historygal

Length of AC is 13.19 cm

Step-by-step explanation:

We have the right triangle ADB with an angle 65° and the length of hypotenuse = 7 cm.

As we know, 'In a right angled triangle, the angles and sides can be written in trigonometric forms'.

That is, $\cos x=\frac{Base}{Hypotenuse}$

i.e. $\cos 65=\frac{AD}{7}$

i.e $AD=7\times \cos 65$

i.e $AD=7\times 0.4226$

i.e. AD = 3 cm

Also, Pythagoras Theorem' states that 'The sum of squares of the length of the sides in a right triangle is equal to the square of the length of the hypotenuse'.

That is, $hypotenuse^{2}=perpendicular^{2}+base^{2}$

i.e. $AB^{2}=BD^{2}+AD^{2}$

i.e. $BD^{2}=AB^{2}-AD^{2}$

i.e. $BD^{2}=7^{2}-3^{2}$

i.e. $BD^{2}=49-9$

i.e. $BD^{2}=40$

i.e. $BD=\pm 6.33$

Since, length of a side cannot be negative.

So, BD = 6.33 cm

Again using Pythagoras Theorem for the right triangle BDC, we have,

$BC^{2}=BD^{2}+DC^{2}$

i.e. $BC^{2}-BD^{2}=DC^{2}$

i.e. $12^{2}-6.33^{2}=DC^{2}$

i.e. $DC^{2}=144-40.07$

i.e. $DC^{2}=103.93$

i.e. $DC=\pm 10.194$

Since, length of a side cannot be negative.

So, DC = 10.194 cm.

Finally, as the side AC is the sum of segments AD and DC, we have,

AC = AD + DC

i.e. AC = 3 + 10.194

i.e. AC = 13.19 cm

Hence, the length of AC is 13.19 cm.

Answer from: Quest

step-by-step explanation:

first, eliminate the parenthesis:

−

second, group like terms:

−

third, combine like terms:

(

−

)

→

−

→

−

Answer from: Quest

$y> \frac{1}{3}x$ and y≤ -x +4 .

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be = $\frac{1-0}{3-0} = \frac{1}{3}$ .

y-intercept of dotted line is y=0 only.

plugging slope m= $\frac{1}{3}$ and b=0 in slope-intercept form y=mx+b, we get

$y=\frac{1}{3}x$ .

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

$y> \frac{1}{3}x$ .

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be = $\frac{4-1}{0-3} = \frac{3}{-3}=-1$ .

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be

y≤ -x +4 .
Write a system of inequalities to represent the shaded portion of the graph.

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Calculate ac. round to the nearest hundredth.
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