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3 years ago

14

Simplify fully, does anyone know ?

2 answers:

Misha Larkins [42]3 years ago

7 0

Answer:

see explanation

Step-by-step explanation:

Using the rule of exponents

$\frac{a^{m} }{a^{n} }$ = $a^{(m - n)}$ , then

(a)

$\frac{x^{7} }{x^{3} }$ = $x^{(7-3)}$ = $x^{4}$

(b)

$\frac{y^{5} }{y^{4} }$ = $y^{(5-4)}$ = $y^{1}$ = y

Julli [10]3 years ago

6 0

Here's an explanation! :)

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Jada is standing 10 feet away from the base of the tree and spots a nest sitting on a branch. The angle of elevation from the gr

expeople1 [14]

Answer:

14.3 feet

Step-by-step explanation:

Let the height of the tree = x feet.

It is given that the horizontal distance from the base of tree = 10 feet and the angle of elevation to the nest is 55°.

So, we get the following figure.

As, we are obtaining a right angled triangle.

Using the trigonometric form for the angles of a right angled triangle, we get,

$\tan x=\frac{opposite}{adjacent}$

i.e. $\tan 55=\frac{x}{10}$

i.e. $x=10\times \tan 55$

i.e. $x=10\times 1.43$

i.e. $x=14.3$

Hence, the height of the tree is 14.3 feet.

4 0

4 years ago

Bhaskar went for hiking with scouts’ team and there the scouts were given a task to build tents with the help of bamboos, ropes

dimulka [17.4K]

The triangles on Bhaskar's tent are similar triangles.

<em>The length of IJ is 4.5 m </em>
<em>The applicable theorem is the mid-point theorem </em>
<em>The appropriate formula for area is the Heron's formula </em>
<em>The ratio of ABC to DEF is 1 : 9</em>

<u>(a) The length of IJ</u>

The given parameter are:

$\mathbf{EF = 9m}$

I and J are at the midpoint of DE and DF

The above highlight means that

$\mathbf{IJ= \frac 12 \times EF}$ --- midpoint theorem

Substitute 9 for EF

$\mathbf{IJ= \frac 12 \times 9m}$

$\mathbf{IJ= 4.5\ m}$

<u>(b) The property used to find GH and IJ</u>

In (a), the midpoint theorem is used to calculate IJ

GH and IJ are corresponding sides of similar triangles,

So the midpoint theorem can also be used to calculate the length of GH

<u>(c) The area of the triangle</u>

For the given triangles, the lengths of the sides are known.

When side lengths are known, the formula to use for finding the triangle's area is the Heron's formula.

The Heron's formula is:

$\mathbf{Area = \sqrt{s \times (s -a) \times (s - b) \times (s - c)}}$

Where:

$\mathbf{s = a + b + c}\\\mathbf{a,b,c \to sides\ of\ the\ triangle}$

<u>(d): The ratio of the areas:</u>

For the small triangle, we have:

$\mathbf{a= 3.8,\ b = 4,\ c = 3}$

So, we have:

$\mathbf{s = 3.8 + 4 + 3 = 10.8}$

So, the area is:

$\mathbf{Area = \sqrt{s \times (s -a) \times (s - b) \times (s - c)}}$

$\mathbf{A_{small} = \sqrt{10.8 \times (10.8 -3.8) \times (10.8 - 4) \times (10.8 - 3)}}$

$\mathbf{A_{small} = \sqrt{4009.824}}$

For the big triangle, we have:

$\mathbf{a= 11.4,\ b = 12,\ c = 9}$

So, we have:

$\mathbf{s = 11.4 + 12 + 9 = 32.4}$

So, the area is:

$\mathbf{Area = \sqrt{s \times (s -a) \times (s - b) \times (s - c)}}$

$\mathbf{A_{big} = \sqrt{32.4 \times (32.4 -11.4) \times (32.4 - 12) \times (32.4 - 9)}}$

$\mathbf{A_{big} = \sqrt{324795.744}}$

The ratio of the small triangle to the big triangle is:

$\mathbf{Ratio = A_{small} : A_{big}}$

$\mathbf{Ratio = \sqrt{4009.824}:\sqrt{324795.744}}$

Divide by 4009.824

$\mathbf{Ratio = \sqrt{1}:\sqrt{81}}$

Take square roots

$\mathbf{Ratio = 1 : 9}$

Hence, the ratio of ABC to DEF is 1 : 9

Read more about similar triangles at:

brainly.com/question/24874611

7 0

3 years ago

Whats the answer can someone answer please

butalik [34]

Answer:

b and c

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

Solve the equation graphically in the given interval. State each answer rounded to two decimals. (Enter your answers as a comma-

andreyandreev [35.5K]

Answer:

kjmalopiuajkm;l'aojsdnkjdfla

Step-by-step explanation:

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3 years ago

Given that ƒ(x) = x² + 5x, evaluate ƒ(-2).<br><br> -6<br> -14<br> 7

Iteru [2.4K]

f(-2) means replace x in the equation with -2, then solve:

-2^2 +5(-2)

Simplify:

4 + -10

Add:

-6

3 0

3 years ago