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marishachu [46]

3 years ago

12

The ratio of the perimeters of two similar triangles is 4:7. What is the area of each of these triangles if the sum of their are

as is 65cm^2.

1 answer:

garri49 [273]3 years ago

3 0

For similar triangles, it is just 4^2 and 7^2

So for the smaller triangle, the area is 16, and for the bigger one, it is 49

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Find the exact values of sin2 θ for cos θ = 3/18 on the interval 0° ≤ θ ≤ 90°

mote1985 [20]

Answer:

$sin(2\theta)=\frac{\sqrt{35} }{18}$

Step-by-step explanation:

Recall the formula for the sine of the double angle:

$sin(2\theta)=2*sin(\theta)*cos(\theta)$

we know that $cos(\theta)=\frac{3}{18}$ , and that $\theta$ is in the interval between 0 and 90 degrees, where both the functions sine and cosine are non-negative numbers. Based on such, we can find using the Pythagorean trigonometric property that relates sine and cosine of the same angle, what $sin(\theta)$ is:

$cos^2(\theta)+sin^2(\theta)=1\\sin^2(\theta)=1-cos^2(\theta)\\sin(\theta)=\sqrt{1-cos^2(\theta)} \\sin(\theta)=\sqrt{1-(\frac{3}{18} )^2}\\sin(\theta)=\sqrt{1-\frac{9}{324} }\\sin(\theta)=\sqrt{\frac{324-9}{324} }\\sin(\theta)=\sqrt{\frac{315}{324} }\\\\sin(\theta)=\frac{3}{18}\sqrt{35 }$

With this information, we can now complete the value of the sine of the double angle requested:

$sin(2\theta)=2*sin(\theta)*cos(\theta)\\sin(2\theta)=2*\frac{3}{18} \,\sqrt{35} \,\frac{3}{18}\\sin(2\theta)=\frac{2*3*3}{18*18}\,\sqrt{35} \\sin(2\theta)=\frac{\sqrt{35} }{18}$

6 0

3 years ago

dirk sold 7 more than 2 times as many gym memberships this month than last month. this month he sold 43 memberships

adelina 88 [10]

Answer:

14.5

Step-by-step explanation:

I am smart

4 0

3 years ago

Read 2 more answers

The bottom one says 13 btw

andriy [413]

Answer:

13

Step-by-step explanation:

8 0

3 years ago

6. AB has coordinates A(-5,9) and B(7,-7). Points P, Q, and T are collinear

MrRissso [65]

Answer:

C) QT

Step-by-step explanation:

We must first find the coordinates of C(x,y) which divides AB in the ration m:n=3:2.

We use the formula

$x=\frac{mx_2+nx_1}{m+n}$

and

$y=\frac{my_2+ny_1}{m+n}$

We plug in the coordinates of A(-5,9) and B(7,-7) and m=3, n=2 to get:

$x=\frac{3*7+2*-5}{3+2}$

$x=\frac{21-10}{5}$

$x=\frac{11}{5}$

and

$y=\frac{3*-7+2*9}{3+2}$

$y=\frac{-21+18}{5}$

$y=-\frac{3}{5}$

C has coordinates $(\frac{11}{5},-\frac{3}{5})$

The line segment that contains C is $QT$

See attachment.

6 0

3 years ago

5.(2) The perimeter of a rectangle is 254cm. Its length is 55cm. Represent the width of the rectangle

alexdok [17]

Answer:

72cm

Step-by-step explanation:

2 (l + w) = 254

2(55) + 2w = 254

2w = 144

w = 72cm

8 0

3 years ago