How long does it take light to reach us from the sun, 1.50 ×108km away??

The volumes of two similar figures are 343 mm3 and 512 mm3. If the surface area of the larger figure is 192 mm2, what is the sur

Kobotan [32]

In geometry, similar figures are those whose ratios of the corresponding sides are equal and the corresponding angles are congruent. In relation to the volume, we determine first the cube roots of the given and find the ratio as shown below.

s1 / s2 = cube root of (512/343)
= 8/7
The square of this ratio is the ratio of the areas of the figure. If we let x be the area of the smaller figure then,
(8/7)^2 = 192 mm²/ x
The value of x from the equation is 147 mm².

The area therefore of the smaller figure is 147 mm².

3 0

2 years ago

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Alexa buys 27 stamps, each stamp is of 1 square unit of area. She exchanges them for 8 sugar cubes, whose total volume is numeri

Vikentia [17]

The answer is 8 sugar cubes

8 0

2 years ago

Mixed numbers between 0 and 2 with an interval of 1/3 between each pair of mixed numbers

Marysya12 [62]

A mixed number is a whole number plus a fraction.The smallest whole number is 1.So no mixed number can be less than 1.
Mixed numbers that are 1/3 apart and are between 0 and 2
could be (1-1/3) and (1-2/3).
They could also be (1-1/6), (1-1/2), and (1-5/6) .

3 0

2 years ago

Which properties are present in a table that represents an exponential function in the form y-b* when b > 1?

Oksana_A [137]

Answer:

<u>Properties that are present are </u>

Property I

Property IV

Step-by-step explanation:

The function given is $y=b^x$ where b > 1

Let's take a function, for example, $y=2^x$

Let's check the conditions:

I. As the x-values increase, the y-values increase.

Let's put some values:

y = 2 ^ 1

y = 2

and

y = 2 ^ 2

y = 4

So this is TRUE.

II. The point (1,0) exists in the table.

Let's put 1 into x and see if it gives us 0

y = 2 ^ 1

y = 2

So this is FALSE.

III. As the x-value increase, the y-value decrease.

We have already seen that as x increase, y also increase in part I.

So this is FALSE.

IV. as the x value decrease the y values decrease approaching a singular value.

THe exponential function of this form NEVER goes to 0 and is NEVER negative. So as x decreases, y also decrease and approached a value (that is 0) but never becomes 0.

This is TRUE.

Option I and Option IV are true.

7 0

2 years ago

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Seth is using the figure shown below to prove the Pythagorean Theorem using triangle similarity: In the given triangle PQR, angl

Naily [24]

Answer:

Part A: $\triangle RPQ \sim \triangle RSP$

Part B. All angles are same, so the triangles are similar.

Part C. RP = 8

Step-by-step explanation:

We are given a right angled triangle $\triangle RPQ$ with $\angle P = 90^\circ$ .

PS is perpendicular to the hypotenuse RQ of $\triangle RPQ$ and S lies on RQ.

Part A:

To identify the pair of similar triangles.

$\triangle RPQ \sim \triangle RSP$ .

Part B:

To identify the type of similarity.

Kindly refer to the image attached in the answer area.

Let us consider the triangles $\triangle RPQ \ and\ \triangle RSP$ .

$\angle RSP =\angle RPQ =90^\circ$

Also, $\angle R$ is common to both the triangles under consideration.

Now, we can see that two angles of two triangles are equal.

So, third angle of the two triangles will also be same.

i.e. All three angles of two triangles $\triangle RPQ \ and\ \triangle RSP$ are equal to each other.

So, by A-A-A (Angle - Angle - Angle) similarity, we can say that $\triangle RPQ \sim \triangle RSP$ .

Part C:

RS = 4

RQ = 16, Find RP.

There is one property of similar triangles that:

The ratio of corresponding sides of two similar triangles is equal.

i.e.

$\dfrac{RS}{RP} = \dfrac{RP}{RQ}\\\Rightarrow RP ^2 = RS \times RQ\\\Rightarrow RP ^2 = 4 \times 16\\\Rightarrow RP ^2 = 64\\\Rightarrow \bold{RP = 8\ units}$

5 0

2 years ago