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2 years ago

9

Match the equation to its solution. 2^2* 2^3 =2^x x = 6 x = 1 x = 5 x = 8

1 answer:

olga_2 [115]2 years ago

5 0

Answer:

x = 5

Step-by-step explanation:

2² x 2³ = 2^x

Laws of indices states that when the base is same the powers can be added when two terms are multiplied,

2^(2+3) = 2^x

2⁵ = 2^x

x = 5

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Vanyuwa [196]

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2 years ago

The endpoints of (MP)are M(2,1) and P(12,6). If point K partitions (MP) in a ratio of MK:KP = 3:2, what are the coordinates of K

GREYUIT [131]

Answer:

K(8, 4)

Step-by-step explanation:

Given:

M(2, 1), P(12, 6)

MK:KP = 3:2

Required:

Coordinates of K

SOLUTION:

Coordinates of K can be determined using the formula below:

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

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

Where,

$M(2, 1) = (x_1, y_1)$

$P(12, 6) = (x_2, y_2)$

$m = 3, n = 2$

Plug in the necessary values to find the coordinates of K:

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

$x = \frac{3(12) + 2(2)}{3 + 2}$

$x = \frac{36 + 4}{5}$

$x = \frac{40}{5}$

$x = 8$

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

$y = \frac{3(6) + 2(1)}{3 + 2}$

$y = \frac{18 + 2}{5}$

$y = \frac{20}{5}$

$y = 4$

The coordinates of K = (8, 4)

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3 years ago

Q 1 PLEASE HELP ME FIGURE THIS OUT 2

dimulka [17.4K]

Answer: $\frac{\pi }{3}$

<u>Step-by-step explanation:</u>

cot is $\frac{cos}{sin}$ on the Unit Circle. When is cos = $\frac{1}{2}$ and sin = $\frac{\sqrt{3}} {2}$ ? In other words, where is the coordinate $(\frac{1}{2},\frac{\sqrt{3}} {2})$ on the Unit Circle?

It occurs at 60° = $\frac{\pi }{3}$ radians

**************************************************************************************

Answer: cot θ

<u>Step-by-step explanation:</u>

sec (90 - θ) * cos θ

= $\frac{1}{cos (90 -\theta)}$ * cos θ

= $\frac{cos\theta}{cos(90 - \theta)}$

= $\frac{cos\theta}{cos90*cos\theta+sin90*sin\theta}$

= $\frac{cos\theta}{0*cos\theta+1*sin\theta}$

= $\frac{cos\theta}{sin\theta}$

= cot θ

**************************************************************************************

Answer: BC = √5, AC = 2√5

<u>Step-by-step explanation:</u>

$\frac{\pi} {3}$ = 60°, which means ΔABC is a 30°-60°-90° triangle so we can use the side length formulas: x - x√3 - 2x.

∠C is the 60°. It matches to side AB so: AB = x√3 = √15 ⇒ x = √5

∠A is the 30°. It matches to side BC so: BC = x = √5

∠B is the 90°. It matches to side AC so: AC = 2x = 2(√5) = 2√5

**************************************************************************************

Answer: k = 4, RS = 12, QS = 28

<u>Step-by-step explanation:</u>

$\frac{QR}{MN} = \frac{RS}{NO}= \frac{QS}{MO}$

$\frac{24}{6} = \frac{RS}{3}= \frac{QS}{7}$

proportionality constant k can be found with $\frac{QR}{MN}$ = $\frac{24}{6}$ = 4

$\frac{QR}{MN} = \frac{RS}{NO}$

→ 4 = $\frac{RS}{3}$

→ 4(3) = RS

→ 12 = RS

$\frac{QR}{MN} = \frac{QS}{MO}$

→ 4 = $\frac{QS}{7}$

→ 4(7) = QS

→ 28 = QS

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3 years ago

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Answer:

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Step-by-step explanation:

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3 years ago

Store owner buys hoodie for 16 dollars and sells it for 72 dollars what is the percent of the markup

ella [17]

Answer:

350% mark up

Step-by-step explanation:

To find the percent markup

Take the new price and subtract the original price

72-16 =56

Then divide by the original amount

56/16

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Change to percent form

350%

6 0

3 years ago

Read 2 more answers