LEARNING TASK 1

A shape is shown on the centimetre grid below.

krok68 [10]

Answer:

The area of the shape after it has been enlarged by

scale factor 2 will be: 10 cm²

Step-by-step explanation:

The Area is basically a measure of how much space in square units there is inside an object.

As the shape is shown on the centimeter grid.

The shape clearly occupies the space of 5-centimeter squares.

We also know that If the scale factor > 1, the image is enlarged.

As we know to determine the area of the shape after it has been enlarged by scale factor 2, all we need to do is to multiply the area of the original shape by 2.

The area of original shape = 5 cm²

The area of the shape after the dilation by a scale factor 2 = 5 × 2 = 10 cm²

Thus, the area of the shape after it has been enlarged by

scale factor 2 will be: 10 cm²

4 0

2 years ago

Read 2 more answers

Alexis wants to make a paperweight at pottery class. He designs a pyramid-like mode l with a base area of 100 square centimeters

olga55 [171]

Answer:

$\frac{3}{2}$ g/cm²

Step-by-step explanation:

First, we need to find the volume of the prism. The volume of a square pyramid is V = Bh/3

B = 100 cm²

h = 6 cm

V = 100 cm² * 6 cm /3

V = 600 cm³ /3

V = 200 cm³

Next, we need to solve for the density based on the desired volume and mass.

m = mass = 300 g

V = volume

density = m/V

density = 300 g / 200 cm³

density = 3/2 g/cm³

The lowest possible density of the material to make the paperweight would be $\frac{3}{2}$ g/cm²

4 0

2 years ago

What is the linear function equation represented by the graph? f (x) = ?

Alex Ar [27]

The equation is :
y = -.5/1 + 1

5 0

2 years ago

Read 2 more answers

The diagonal of a side of rhombus are of equal length. Find the measures of angles of the rhombus.

sergij07 [2.7K]

Explanation:

Consider ABCD is a rhombus

We know that

All sides are equal in rhombus i.e,

⇛AB=BC=CD=DA

and AC and BD are digonals

Given that

Diagonal and the side of the rhombus are equal.

⇛AB = BC = CD = DA = AC

Diagonal AC divides the rhombus into two triangles .

They are ∆ BAC and ∆ DAC

In triangle BAC

BA=BC=AC,(Given)

⇛∠ BAC=∠ABC= ∠ACB =60°→→→Eqn(i)

Similarly in ∆DAC ,

DA=DC=AC

⇛∠DAC=∠ACD=∠ADC=60°→→→Eqn(ii)

From eqn(i) and eqn(ii)

∠A=∠BAC+∠DAC=60°+60°=120°

and

∠B= ∠ABC = 60°.

and

∠C=∠ACB+∠ACD=60°+60°=120°

and

∠D =∠ADC=60°

∴ ∠A = 120° , ∠B = 60° ,∠C = 120° & ∠D = 60°

Answer:-The measures of the all angles in the rhombus are 120° , 60° ,120° and 60°.

Note: [Figure refers in the attached file.

7 0

2 years ago

The promising alternative energy sources currently under development are fuel cell technology and large-scale solar energy power

Mumz [18]

Answer:

Step-by-step explanation:

a) Denote the event of commercially availability of f_uel cell technology as F_, commercial availability of solar power technology as S

Write the probability of energy supplied by these energy sources in the next 10 years

P(energy supplied) = P(S ∪ F) -----(1)

Rewrite eqn (1)

P(energy supplied) = P(S) + P(F) - P(F) P(S) ----(2)

substitute 0.85 for P(S) and 0,7 for P(F) in eqn (2) to find the probability of energy supplied by these energy sources

P(energy supplied) = 0.85 + 0.7 - (0.7 * 0.85)

= 0.85 + 0.7 - (0.595)

= 1.55 - 0.595

= 0.955

Therefore, the probability that there will be energy supplied by these two alternative sources in the next 10 years is 0.955

B) write the probability of only one source of energy available

P(only one source of energy available) = $P(\bar F S)$ ∪ $P( \bar S F)$ ---(3)

Rewrite the equation (3)

P(only one source of energy available) =

$=P(\bar F S)+P(\bar S F)\\\\=\{[1-P(F)]P(S)+[1-P(S)]P(F)\}---(4)$

$=\{[1-0.7]0.85+[1-0.85]0.7\}\\\\=0.255+0.105\\\\=0.36$

Therefore,The probability that only one of the two alternative energy sources will be commercially viable in the next 10 years is 0.36

4 0

2 years ago