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2 years ago

Regular pentagon RSTUV has sides that are half the length of regular pentagon JKLMN.

Mathematics

1 answer:

Andrew [12]2 years ago

7 0

Answer:

Step-by-step explanation:

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Maths functions question

yarga [219]

Answer:

a) OA = 1 unit

b) OB = 3 units

c) AB = √10 units

Step-by-step explanation:

<u>Given function</u>:

$g(x)=2^x$

Point A is the y-intercept of the exponential curve (so when x = 0).

To find the y-value of Point A, substitute x = 0 into the function:

$\implies g(0)=2^0=1$

Therefore, A (0, 1) so OA = 1 unit.

If BC = 8 units then the y-value of Point C is 8.

The find the x-value of Point C, set the function to 8 and solve for x:

$\begin{aligned}f(x) & = 8 \\\implies 2^x & = 8\\2^x & = 2^3\\\implies x &= 3\end{aligned}$

Therefore, C (3, 8) so Point B is (3, 0). Therefore, OB = 3 units.

From parts (a) and (b):

A = (0, 1)
B = (3, 0)

To find the length of AB, use the distance between two points formula:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$\textsf{where }(x_1,y_1) \textsf{ and }(x_2,y_2)\:\textsf{are the two points.}$

Therefore:

$\implies \sf AB=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}$

$\implies \sf AB=\sqrt{(3-0)^2+(0-1)^2}$

$\implies \sf AB=\sqrt{(3)^2+(-1)^2}$

$\implies \sf AB=\sqrt{9+1}$

$\implies \sf AB=\sqrt{10}\:\:units$

5 0

1 year ago

A cooler contains 6 3/4 liters of water. A team drinks 2/3 of water in the cooler. How many liters of water does the team drink?

andriy [413]

Answer:

4 1/2

Step-by-step explanation:

2/3 of 6 3/4 = 4 1/2

because "of" in math means multiply

so 2/3 x 6 3/4 = 4 1/2

4 0

2 years ago

Read 2 more answers

Find the measure of the missing angles

vekshin1

Answer:

H: 119 degrees.

G: 61 degrees.

M: 54 degrees.

K: 126 degrees.

Step-by-step explanation:

6 0

1 year ago

The North Colony Trail at Royal Gorge, Colorado, is 18 miles long. Stacey has hiked eight miles to a resting spot. She hikes the

Kruka [31]

Answer:

4 h

Step-by-step explanation:

The resting spot was at the 8 mi mark.

When Stacey reached the 16th mile, they had covered

16 mi - 8 mi = 8 mi

They took 2 h for every 1 h, so

$\text{Time required} = \text{8 mi} \times \dfrac{\text{1 h}}{\text{2 mi}} = \textbf{4h}$

It may be easier to do this calculation on a number line. Each jump of 2 mi represents 1 h, and there are four jumps, so they took four hours.

7 0

2 years ago

A multiplication expression without exponents that is equivalent to (3ª)(3)

stealth61 [152]

(3)3 is 9 and (3)4 is 12

8 0

2 years ago