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3 years ago

Consider this figure of a hexagon.

2 answers:

6 0

A)
It looks like the [irregular] hexagon has 3 rectangles and 2 triangles within it.
So let's exclude the triangular corners on bottom left and top right for now.
First we have a large rectangle covering most of the upper left of the polygon. 20 ft × 7 ft = 140 sq.ft.
Now we have a rectangle on the bottom right. The width is 11 ft, so take the 7 away from that, 4 ft. × 14 ft. on bottom. 4 ft × 14 ft = 56 sq.ft.
The last small rectangle fits on the right between the 2 other rectangles. It is 24-20 on top/bottom × 7-6 right/left. 4 ft × 1 ft = 4 sq.ft.
Now for the triangles: bottom left is 11-7 × 24-14 = 4 ft × 10 ft. 1/2bh = 1/2×10×4 = 20 sq.ft.
Top right is 24-20 × 11-5 = 4 ft × 6 ft. 1/2bh = 1/2×4×6 = 12 sq.ft.

B)
Add them all together for the total area (A):
A = 140 + 56 + 4 + 20 + 12 = 140+60+32
= 232 sq.ft.

Hope that explains it well enough! ;)

just olya [345]3 years ago

3 0

Answer:

Step-by-step explanation:

(A)

1 big rectangle-2 corner triangles

(B)

24 * 11 = 264 square feet the triangles

11-7

= 4

24 -14

=10

1/2 * 4 * 10

= 20

24-20 by 11-6

=1/2 * 4 * 5 =10

=264 - (20+10)

= 264 - 30

=234 square feet

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what is the equation in point-slope form of the line that passes through the point ( -1,,-4) has a slop of a -3

Vesnalui [34]

The answer has to resemble y=Mx+b so to find your y intercept plug in your coordinates into that equation so put your slope in for m and your x intercept in for x and the y intercept in for y so -4= -3(-1)+b now get b alone -1=b so your equation would be y=-3x-1

6 0

4 years ago

Rewrite the indicated real nth root(s) of a in radical form

notsponge [240]

Answer:

$\sqrt[n]{a}$

1. $\sqrt[3]{27}$ = $\sqrt[3]{3^3}$ = 3

2. $\sqrt[4]{16}$ = $\sqrt[4]{2^4}$ = 2

3. $\sqrt[6]{64}$ = $\sqrt[6]{2^6}$ = 2

4. $\sqrt[5]{243}$ = $\sqrt[5]{3^5}$ =3

Hope that helps!

7 0

3 years ago

Examine this system of equations. Which number can be multiplied by each equation so that when the two equations are

andreyandreev [35.5K]

Answer:

15 times the first equation and -12 times the second equation

Step-by-step explanation:

we have

$\frac{3}{4}x+\frac{2}{3}y=6$ ------> first equation

$\frac{5}{8}x+\frac{5}{6}y=12$ ------> second equation

Multiply the first equation by 15 both sides

$(15)\frac{3}{4}x+(15)\frac{2}{3}y=6(15)$

$\frac{45}{4}x+10y=90$ -----> new first equation

Multiply the second equation by -12 both sides

$(-12)\frac{5}{8}x+(-12)\frac{5}{6}y=12(-12)$

$-\frac{60}{8}x-10y=-144$ -----> new second equation

Adds the two new equations

$\frac{45}{4}x+10y=90\\-\frac{60}{8}x-10y=-144\\-----------\\\frac{45}{4}x-\frac{60}{8}x=90-144$

The y-term was eliminated

5 0

3 years ago

in triangle PQR the measure of angle R=90, QP=73, RQ=55, and PR=48. what is the value of the sine of angle P to the nearest Hund

alexandr402 [8]

Answer:

P ≈ 48.89°(nearest hundredth)

Step-by-step explanation:

The triangle PQR forms a right angle triangle since angle R is 90°. The triangle has an hypotenuse , adjacent and opposite side.

Using the SOHCAHTOA principle one can find the sine ratio of angle P. Let us designate where each side represent.

opposite side(QR) = 55

adjacent side(PR) = 48

hypotenuse(PQ) = 73

sin P = opposite/hypotenuse

sin P = 55/73

P = sin⁻¹ 55/73

P = sin⁻¹ 0.75342465753

P = 48.8879095605

P ≈ 48.89°(nearest hundredth)

5 0

3 years ago

A researcher is concerned that graduate students get less than the recommended 8 hours of sleep a night. She selects a random sa

dsp73

Answer:

H0 : μ = 8

H1 : μ < 8

Test statistic = - 7.51

conclude that there is statistical significance that student at the school get less than 8 hours of sleep on average.

Step-by-step explanation:

The hypothesis :

H0 : μ = 8

H1 : μ < 8

The test statistic :

(xbar - μ) ÷ (s/√(n))

Sample data :

1.75, 2, 2.25, 2.25, 2.5, 3, 3.5, 3.5, 3.5, 3.75, 4, 4.25, 4.5, 4.5, 4.5, 4.75, 5.25, 5.5, 5.75, 5.75, 5.75, 6, 6, 6, 6.25, 6.25, 6.25, 6.5, 6.5, 6.5, 6.75, 7, 7, 7, 7.5, 7.5, 7.75, 8, 8.25, 8.25, 8.25, 8.5, 8.75, 9, 9

Using calculator :

Sample mean, xbar = 5.71666

Sample standard deviation, s = 2.04

The test statistic :

(5.7166 - 8) ÷ (2.04/√(45))

-2.28 / 0.3041052

= - 7.5085

= - 7.51

Degree of freedom = 45 - 1 = 44

Pvalue(-7.51, 44) = 0.00001

α = 1% = 0.01

Since Pvalue < α ; we reject H0 and conclude that there is statistical significance that student at the school get less than 8 hours of sleep on average.

4 0

3 years ago