What is the value of x in the equation (x + 12) = 165x + 14)

The ratio of the perimeters of two similar triangles is 4:3. What are the areas of these triangles if the sum of their areas is

emmasim [6.3K]

Answer:

the areas of these triangles are 83.2cm² and 46.8cm²

Step-by-step explanation:

1. If the triangles are similar and the ratio of the perimeter ois 4:3, then the areas are in the following ratio:

4²:3²

16:9

2. The sum of their areas is 65 cm², then, you can calculate the area of the larger triangle as following:

130(16/16+9)

130(0.64)

=83.2cm²

3. The area of the smaller triangle is:

130(9/16+9)

130(0.36)

46.8cm²

Hope this helps

6 0

2 years ago

The diagram is not drawn to scale

Firlakuza [10]

Answer:

<h2 /><h3>3x-2 = 25 </h3><h3> 3x = 25+2 </h3><h3> 3x = 27</h3><h3> x =9</h3><h3>the answer is option c</h3>

6 0

2 years ago

The angle of elevation from me to the top of a hill is 51 degrees. The angle of elevation from me to the top of a tree is 57 deg

julia-pushkina [17]

Answer:

Approximately $101\; \rm ft$ (assuming that the height of the base of the hill is the same as that of the observer.)

Step-by-step explanation:

Refer to the diagram attached.

Let $\rm O$ denote the observer.
Let $\rm A$ denote the top of the tree.
Let $\rm R$ denote the base of the tree.
Let $\rm B$ denote the point where line $\rm AR$ (a vertical line) and the horizontal line going through $\rm O$ meets. $\angle \rm B\hat{A}R = 90^\circ$ .

Angles:

Angle of elevation of the base of the tree as it appears to the observer: $\angle \rm B\hat{O}R = 51^\circ$ .
Angle of elevation of the top of the tree as it appears to the observer: $\angle \rm B\hat{O}A = 57^\circ$ .

Let the length of segment $\rm BR$ (vertical distance between the base of the tree and the base of the hill) be $x\; \rm ft$ .

The question is asking for the length of segment $\rm AB$ . Notice that the length of this segment is $\mathrm{AB} = (x + 20)\; \rm ft$ .

The length of segment $\rm OB$ could be represented in two ways:

In right triangle $\rm \triangle OBR$ as the side adjacent to $\angle \rm B\hat{O}R = 51^\circ$ .
In right triangle $\rm \triangle OBA$ as the side adjacent to $\angle \rm B\hat{O}A = 57^\circ$ .

For example, in right triangle $\rm \triangle OBR$ , the length of the side opposite to $\angle \rm B\hat{O}R = 51^\circ$ is segment $\rm BR$ . The length of that segment is $x\; \rm ft$ .

$\begin{aligned}\tan{\left(\angle\mathrm{B\hat{O}R}\right)} = \frac{\,\rm {BR}\,}{\,\rm {OB}\,} \; \genfrac{}{}{0em}{}{\leftarrow \text{opposite}}{\leftarrow \text{adjacent}}\end{aligned}$ .

Rearrange to find an expression for the length of $\rm OB$ (in $\rm ft$ ) in terms of $x$ :

$\begin{aligned}\mathrm{OB} &= \frac{\mathrm{BR}}{\tan{\left(\angle\mathrm{B\hat{O}R}\right)}} \\ &= \frac{x}{\tan\left(51^\circ\right)}\approx 0.810\, x\end{aligned}$ .

Similarly, in right triangle $\rm \triangle OBA$ :

$\begin{aligned}\mathrm{OB} &= \frac{\mathrm{AB}}{\tan{\left(\angle\mathrm{B\hat{O}A}\right)}} \\ &= \frac{x + 20}{\tan\left(57^\circ\right)}\approx 0.649\, (x + 20)\end{aligned}$ .

Equate the right-hand side of these two equations:

$0.810\, x \approx 0.649\, (x + 20)$ .

Solve for $x$ :

$x \approx 81\; \rm ft$ .

Hence, the height of the top of this tree relative to the base of the hill would be $(x + 20)\; {\rm ft}\approx 101\; \rm ft$ .

6 0

2 years ago

Give the following equation in point slopr form, what is the slope of the line?

AVprozaik [17]

Answer:

Slope= 3

Step-by-step explanation:

y - 4= 3(x+6)

y - 4= 3x + 18 distributive property

y - 4(+4) = 3x + 18(+4)

cancel out the 4 with its oposite and apply to both sides.

y = 3x + 22 final answer

Remember the slope intersept equation... y=mx+b

m is slope

b means the y-intersept.

So the final slope of the line is 3. (demostrated by graph below)

Program for graph: Desmos

5 0

2 years ago

Round 715 to the nearest the ten

Mariana [72]

Here's a good rhyming rule to keep in mind.

Zero to four, you get no more.

Five to nine, move up one time.

With this rule you can see that there is a 5 at the end, therefor you should round up. Your number is 720.

8 0

3 years ago

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What is the value of x in the equation (x + 12) = 165x + 14) – 3?