GH=KL GH=6x+4 KL=10x-8 Solve for GH

ipn [44]

Convert the decimal by multiplying by 100.625%

Convert to a fraction by placing the decimal number over a power of 10.254

5 0

3 years ago

Read 2 more answers

Suppose the population of a certain city is 5416 thousand it is expected to decrease to 4787 thousand in 5 years find the percen

Marta_Voda [28]

Answer:

11.6% decrease (rounded off to the nearest tenth)

Step-by-step explanation:

Population decrease = 5,416,000 - 4,787,000 = 629,000

Percentage decrease = (decrease ÷ original population) × 100

Percentage decrease = $\frac{629,000}{5,416,000}$ × 100 = 11.61373708%

Or 11.6% decrease (rounded off to the nearest tenth)

3 0

3 years ago

Find the area and the circumference of a circle with a radius of 8 cm. Use the value 3.14 for pie and do not round your answer.

Pani-rosa [81]

Well this is pretty simple

for the area we need to use the formula A=3.14*radius*radius

so we just plug it in and we get 3.14*8*8 which is 200.96 centimeters squared

for circumference we need to do C=3.14*diameter

to find the diamter we need to do 8 (radius) x 2 which is 16

plugging it in that would be 3.14 * 16 which is 50.24

So in this case the the area is 200.96 and the circumference is 50.24 :)

4 0

3 years ago

Figure 6 shows a semicircle PTS with center O and radius 8cm. QST is a sector of a circle with center S and R is the midpoint of

sveticcg [70]

(a) <TOR=pi/3 radians

To determine <TOR we use the fact that in the right-angled triangle ORT we know two sides:

|OT|=radius=8cm and |OR|=radius/2=4cm

and can use the sine:

$\sin \angle OTR=\frac{r/2}{r}=\frac{1}{2}\implies \angle OTR =\frac{\pi}{6}$

and since <TRO=pi/2, it must be that

$\angle TOR =\pi-\frac{\pi}{2}-\frac{\pi}{6}=\frac{\pi}{3}$

(b) The arc length is approximately 7.255 cm

In order to calculate the arc length QT, we need to first determine the length |ST| and the angle <OST.

Towards determining angle <OST:

$\angle SOT = \pi - \angle TOR = \pi - \frac{\pi}{3} = \frac{2}{3}\pi$

Next, draw a line connecting P and T. Realize that triangle PTS is right-angled with <PTS=pi/2. This follows from the Thales theorem. Since R is a midpoint between P and O, it follows that the triangles ORT and PRT are congruent. So the angles <PTR and <OTR are congruent. Knowing <PTS we can determine angle <OTS:

$\angle OTR \cong \angle PTR=\frac{\pi}{6}\implies\angle OTS=\angle PTS -\angle PTR -\angle OTR\\\angle OTS = \frac{\pi}{2}-\frac{\pi}{6}-\frac{\pi}{6}=\frac{\pi}{6}$

and so the angle <OST is

$\angle OST = \pi - \angle TOS - \angle OTS = \pi -\frac{2}{3}\pi - \frac{1}{6}\pi=\frac{\pi}{6}$

Towards determining |TS|:

Use cosine:

$\cos \angle OST =\frac{|RS|}{|ST|}\implies |ST|=\frac{\frac{3}{2}r}{\cos \frac{\pi}{6}}=\frac{12\cdot 2}{\sqrt{3}}=8\sqrt{3}cm$

Finally, we can determine the arc length QT:

$QT = {\angle OST}\cdot |ST|=\frac{\pi}{6}\cdot 8 \sqrt{3}=\frac{4\pi}{\sqrt{3}}\approx 7.255cm$

3 0

3 years ago

What type of triangle has an exterior angle that is obtuse at two vertices? Explain your reasoning.

navik [9.2K]

Answer:

A right triangle

Step-by-step explanation:

A right triangle would meet these characteristics. A triangle's inner angles always add up to be 180 degrees. A right triangle has one angle at 90 degrees meaning the other two angles need to be less than 90 degrees and sum up to be 90 degrees. This would indicate that both of these angles' exterior angles would be obtuse because they would be wider than 90 degrees.

5 0

3 years ago