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dezoksy [38]
3 years ago
15

Q5 Q10.) Estimate the age of the paintings.

Mathematics
1 answer:
ludmilkaskok [199]3 years ago
4 0
A=A₀e^{0.000121t}
A/A₀=24%=0.24
0.24=e^{0.000121t}
0.000121t=ln(0.24)
t=ln(0.24)/0.000121
=-11794.35
so painting is 11794 years old
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The diagram shows a rhombus inside a regular hexagon work out the angle x
kvv77 [185]

Answer:

<u>x = 60°</u>

Step-by-step explanation:

The rest of the question is the attached figure.

And it is required to find the angle x.

As shown, a rhombus inside a regular hexagon.

The regular hexagon have 6 congruent angles, and the sum of the interior angles is 720°

So, the measure of one angle of the regular hexagon = 720/6 = 120°

The rhombus have 2 obtuse angles and 2 acute angles.

one of the obtuse angles of the rhombus is the same angle of the regular hexagon.

So, the measure of each acute angle of the rhombus = 180 - 120 = 60°

So, the measure of each acute angle of the rhombus + the measure of angle x = the measure of one angle of the regular hexagon.

So,

60 + x = 120

x = 120 - 60 = 60°

<u>So, the measure of the angle x = 60°</u>

6 0
3 years ago
Find the slant height of a square pyramid with base edges of 12 cm and an altitude of 8 cm?
liberstina [14]
To find the slant height we must take apart the pyramid first. Let us cut it in half. There we can easily see that the slant height is really just the hypotenuse of the triangle formed by half the base and the altitude.

Half the base length would be 6 cm.

Using the Pythagorean therom:

a² + b² = c²
6² + 8² = c²
36 + 64 = c²
100 = c²
c = 10

The slant height should be 10 cm. Hope this helps!
8 0
3 years ago
Read 2 more answers
Luke invited 20 more boys than girls to his birthday party. However, only ¾ of the boys and ⅔ of the girls came. Exactly 19 of L
sveta [45]

Answer:

68

Step-by-step explanation:

Let:

Number of girls invited = x

Number of boys = x +20

3/4 of boy showed up

2/3 of girls showed up

Exactly 19 did not show up

Therefore, we could say:

Fraction of boys that didn't show up = 1 - 3/4 = 1/4

Fraction of girls that didn't show up = 1 - 2/3 = 1/3

That is,

[1/4 *(x + 20)] + [1/3*x] = 19

[(x + 20) / 4] + x /3 = 19

(3(x + 20) + 4x) / 12 = 19

3x + 60 + 4x = 228

7x = 228 - 60

7x = 168

x = 168 / 7

x = 24

Number of girls, x = 24

Number of boys, x + 20 = 24 + 20 = 44

Total friends invited = (24 + 44) = 68

8 0
3 years ago
What is the solution to the equation?
Andru [333]

Answer:

x = 1/8

Step-by-step explanation:

- 24x = - 3

Divide both sides by - 24

x = -3/-24

x = 1/8

4 0
3 years ago
Is anyone here Familiar with Exponent graphing?
Maurinko [17]

Answer:

12. Range = -∞ < x  <+∞; Domain = y > 0

13. Range = -∞ < x  <+∞; Domain = y > 3

Step-by-step explanation:

12. f(x) = ½(6)^x

(a) Create a table containing a few values of x and y

x                                                                                  y

-2     ½(6)⁻² = ½(⅙)² = ½ × ¹/₃₆ = ¹/₇₂ = 0.01

-1     ½(6)⁻¹ = ½(⅙)   = ½ × ¹/₁₂ = ¹/₂₄ = 0.08

0     ½(6)⁰  = ½ ×  0 = ½                  = 0.5

 1     ½(6)¹   = ½ ×  6                         =  3

2     ½(6)²  = ½ × 36                        = 18

(b) Draw your axes

Let the x-axis run from -5 to +5 and the y-axis from 0 to 20

(c) Plot your points

They should look like Fig. 1 below.

(d) Draw the graph

Draw a smooth line through the points.

Extend the line in both directions to the edges of the graph.

Your graph should look like Fig. 2.

(e) Identify the domain and range of the function

The <em>domain</em> is the set of all possible x-values that will give real values for y.

It looks like x can vary from -∞ to +∞ and give a real value for y.

The <em>domain is -∞ < x  <+∞</em>.

The <em>range</em> of a function is the spread of all possible y-values.

It looks like y ⟶ ∞ as x ⟶ ∞, but y ⟶ 0 as x ⟶ -∞.

The x-axis is an <em>asymptote</em>. The function can get as close as possible to the x-axis, but it can never be zero or negative.

The range is y > 0.

12. f(x) = 2^x +3

(a) Create a table containing a few values of x and y

<u> x </u>                                                               <u>  y    </u>

-4     2⁻⁴ + 3 = (½)⁴ + 3 = ¹/₁₆ + 3 = 3¹/₁₆  =    3.1

-2     2⁻² + 3 = (½)² + 3 =   ¼   + 3 = 3¼ =   3.2

0     2⁰ + 3   =  1    + 3                            =   4

2     2² + 3   =  4   + 3                            =   7

4     2⁴ + 3   = 16   + 3                            = 19

(b) Draw your axes

(c) Plot your points

(d) Draw the graph

Your graph should look like Fig. 3.

(e) Identify the domain and range of the function

The domain is -∞ < x  <+∞.

It looks like y ⟶ ∞ as x ⟶ ∞, but y ⟶ 3 as x ⟶ -∞. The line y = 3 is an asymptote.

The range is y > 3.

3 0
3 years ago
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