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vampirchik [111]

4 years ago

14

ΔABC has coordinates of A (–5, –7), B (6, –3), and C (2, 7). Find the coordinates of its image after a dilation centered at the

origin with a scale factor of 2.

1 answer:

Alona [7]4 years ago

7 0

Multiply each coordinate by 2 so for example the point C will move to coordinates (4, 14).

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There is a triangle with a perimeter of 63 cm, one side of which is 21 cm. Also, one of the medians is perpendicular to one of t

NemiM [27]

Answer:

21cm; 28cm; 14cm

Step-by-step explanation:

There is no info in the problem/s text which one of the triangle's side is 21 cm. That is why we have to try all possible variants.

Let the triangle is ABC . Let the AK is the angle A bisector and BM is median.

Let O is AK and BM cross point.

Have a look to triangle ABM. AO is the bisector and AOB=AOM=90 degrees (means that AO is as bisector as altitude)

=> triangle ABM is isosceles => AB=AM (1)

1. Let AC=21 So AM=21/2=10.5 cm

So AB=10.5 cm as well. So BC= P-AB-AC=63-21-10.5=31.5 cm

Such triangle doesn' t exist ( is impossible), because the triangle's inequality doesn't fulfill. AB+AC>BC ( We have 21+10.5=31.5 => AB+AC=BC)

2. Let AB=21 So AM=21 and AC=42 .So BC= P-AB-AC=63-21-42=0 cm- such triangle doesn't exist.

3. Finally let BC=21 cm. So AB+AC= 63-21=42 cm

We know (1) that AB=AM so AC=2*AB. So AB+AC=AB+2*AB=3*AB

=>3*AB=42=> AB=14 cm => AC=2*14=28 cm.

Let check if this triangle exists ( if the triangle's inequality fulfills).

BC+AB>AC 21+14>28 - correct=> the triangle with the sides' length 21cm,14 cm, 28cm exists.

This variant is the only possible solution of the given problem.

6 0

3 years ago

What is the domain function y=^4sqrtx-1

Rudik [331]

Answer:

Domain of y= $\sqrt[4]{x-1}$ : is x>=1

Interval notation: [1,∞)

Step-by-step explanation:

We have y= $\sqrt[4]{x-1}$

1) The domain of a function is the set of x values for which the function is real and defined.

2) So, x-1 should be positive means x-1>=0, because fourth root of any negative value would be a complex number and not a real number.

3) Now we solve the inequality x-1>=0

4) Adding 1 to both sides of the inequality we get,

x-1+1 > = 0+1

5) Cancel out -1 and +1 from the left side

6) We get x>=1

It concludes that for the domain of the given function, the x value must be greater than or equal to 1

7 0

3 years ago

(a) Find an angle between 0° and 360° that is coterminal with – 120°.

Novay_Z [31]

Answer:

a) $240\degree$

b) $\frac{15\pi}{4}$

Step-by-step explanation:

<u>Coterminal angles</u> have the same terminal sides in standard position.

a) To find an angle between $0\degree$ and $360\degree$ , that is coterminal with $-120\degree$ , we keep adding multiples of $360\degree$ until we get an angle within the specified range.

$-120\degree \implies -120\degree +360\degree=240\degree$ .

In some cases you would have to subtract in order to get the specified angle. That is when the angle given is positive.

b) This time we want to find an that coterminal with $\frac{15\pi}{4}$ radians.

We keep subtracting multiples of $2\pi$ until we get an angle measure within the specified range.

$\frac{15\pi}{4}=\frac{15\pi}{4}-2\pi=\frac{7\pi}{4}$

4 0

3 years ago

What is the domain of the cubic function f(x)=10x^3 +18x

sweet [91]

ANSWER

(-∞,+∞)

EXPLANATION

The given polynomial function is:

$f(x)=10x^3 +18x$

The domain refers to all values of x that make the function defined.

Polynomial functions are defined for all real values of x

The domain is the set of all real numbers.

This is written in symbolic representation as

(-∞,+∞)

8 0

3 years ago

What is the term to term rule: -41, -38, -35, -32, -29, -26

Firlakuza [10]

Answer:

Here is your formula: A(n) = A(n-1) +3

5 0

3 years ago

Read 2 more answers