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2 years ago

ABC is a triangle and PQ is parallel to BC.BC=12.6cm, PQ=8.4 cm and AQ= 7.2 cm.Find AC

Mathematics

1 answer:

nlexa [21]2 years ago

6 0

With a line parallel to a side through a triangle we get similar triangles so a proportion.

AC : BC = AQ : PQ

AC = BC AQ / PQ

AC = 12.6 (7.2) / 8.4

AC = 10.8 cm

Answer: 10.8 cm

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After 8 years a loan grows to $75 210. If the interest was compounded annually at a rate of 8.5%, find the size of the initial l

stealth61 [152]

Given:
Future Value = $75,210
term = 8 years
rate = 8.5%
Initial loan = ?

In this case, we need to find the present value of the loan. Compounded means that even the interest has an interest.

PV = FV / (1 + i)^n

PV = 75,210 / (1 + 0.085)⁸

PV = 75,210 / (1.085)⁸

PV = 75,210 / 1.9206

PV = 39,159.64

Initial loan is $39,159.64
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2 years ago

The product of sin 30 degrees and sin 60 degrees is the same as the product of

zysi [14]

Answer:

$sin(30\°)*sin(60\°)=cos(60\°)*cos(30\°)$

Step-by-step explanation:

we know that

$sin(\alpha)=cos(\beta)$

when

$\alpha+\beta=90\°$ -------> complementary angles

$sin(30\°)=cos(60\°)$

$sin(60\°)=cos(30\°)$

Because

$30\°+60\°=90\°$ -------> complementary angles

In this problem the product of

$sin(30\°)*sin(60\°)$

is equal to

$cos(60\°)*cos(30\°)$

therefore

$sin(30\°)*sin(60\°)=cos(60\°)*cos(30\°)$

3 0

2 years ago

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Which statements are true about circle Q? Select three options. The ratio of the measure of central angle PQR to the measure of

kkurt [141]

Answer:

<h3>- The ratio of the measure of central angle PQR to the measure of the entire circle is One-eighth. </h3><h3>- The area of the shaded sector depends on the length of the radius. </h3><h3>- The area of the shaded sector depends on the area of the circle</h3>

Step-by-step explanation:

Given central angle PQR = 45°

Total angle in a circle = 360°

Ratio of the measure of central angle PQR to the measure of the entire circle is $\frac{45}{360} = \frac{1}{8}$ . This shows ratio that <u>the measure of central angle PQR to the measure of the entire circle is one-eighth</u>.

Area of a sector = $\frac{\theta}{360}*\pi r^{2}$

$\theta$ = central angle (in degree) = 45°

r = radius of the circle = 6

Area of the sector

$= \frac{45}{360}*\pi (6)^{2}\\ = \frac{1}{8}*36 \pi\\ = 4.5\pi units^{2}$

<u>The ratio of the shaded sector is 4.5πunits² not 4units²</u>

From the formula, it can be seen that the ratio of the central angle to that of the circle is multiplied by area of the circle, this shows <u>that area of the shaded sector depends on the length of the radius and the area of the circle.</u>

Since Area of the circle = πr²

Area of the circle = 36πunits²

The ratio of the area of the shaded sector to the area of the circle = $\frac{4.5\pi }{36 \pi } = \frac{1}{8}$

For length of an arc

$= \frac{45}{360}*2\pi r\\= \frac{45}{360}*2\pi (6)\\= \frac{45}{360}*12 \pi \\= \frac{12\pi }{8} \\= \frac{3\pi }{2} units$

ratio of the length of the arc to the area of the circle = $\frac{\frac{3\pi}{2} }{36\pi} = \frac{3}{72} =\frac{1}{24}$

It is therefore seen that the ratio of the area of the shaded sector to the area of the circle IS NOT equal to the ratio of the length of the arc to the area of the circle

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2 years ago

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Alexis has a rectangular piece of red paper that is 4 centimeters wide. It’s length is twice it’s width. She glued a rectangular

Montano1993 [528]

for the rectangular red paper :

w₁ = width of the red paper = 4 cm

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A₁ = area of the red paper = L₁ w₁ = 8 x 4 = 32 cm²

for the rectangular blue paper :

w₂ = width of the blue paper = 3 cm

L₂ = length of blue paper = 7 cm

A₂ = area of the blue paper = L₂ w₂ = 7 x 3 = 21 cm²

area visible is given as

A = A₁ - A₂ = 32 cm² - 21 cm² = 11 cm²

so 11 square units of red paper will be visible on top

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2 years ago

The graph represents the function where electricity usage in kilowatts per hour of a clock radio varies directly with the number

geniusboy [140]

Answer:

Reasonable estimation for constant of variation is 0.25 kWh per day.

Step-by-step explanation:

We are given the following information in the question:

The graph represents the function where electricity usage.

Electricity usage in kilowatts per hour of a clock radio varies directly with the number of days.
The x-axis shows the number of days and usage in kilo-watt per hour is showed on the y-axis.
Some coordinates of the graph are: (0,0), (2,0.5) and (6,1.5)

Formula for constant of variation:

$\displaystyle\frac{y_2-y_1}{x_2-x_1}$

Putting the values from the coordinates (2,0.5) and (6,1.5), we get:

$\displaystyle\frac{1.5-0.5}{6-2} = \frac{1}{4} = 0.25\text{ kilowatt-hours per day}$

Hence, reasonable estimation for constant of variation is 0.25 kWh per day.

7 0

2 years ago

Read 2 more answers

ABC is a triangle and PQ is parallel to BC.BC=12.6cm, PQ=8.4 cm and AQ= 7.2 cm.Find AC​

ABC is a triangle and PQ is parallel to BC.BC=12.6cm, PQ=8.4 cm and AQ= 7.2 cm.Find AC