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3 years ago

Solve the equation for x 3x+9x = 6x + 42

Mathematics

1 answer:

podryga [215]3 years ago

3 0

= 3x + 9x = 6x + 42

= 3x + 9x - 6x = 42 ( transposing +6x from LHS to RHS changes +6x to -6x )

= 12x - 6x = 42

= 6x = 42

= x = 42 ÷ 6 ( transposing ×6 from LHS to RHS changes ×6 to ÷6 )

= x = 7

Let us check whether we have found out the correct value of x or not by placing 7 in the place of x :

= ( 3 × 7 ) + ( 9 × 7 ) = 6 × 7 + 42

= 21 + 63 = 42 + 42

= 84 = 84

= LHS = RHS

Hence proved we have derived the correct value of x .

Therefore , the value of x = 7 .

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Natalee wanted to demonstrate the volume of a square pyramid. To do this, she took a hollowed out pyramid that has a base of 25

swat32

Answer:

The answer is below

Step-by-step explanation:

Natalee transferred water from a square pyramid to a cube. To calculate how many times she will need to dump the water from the pyramid into the cube to completely fill the cube, we divide the volume of the cube by the volume of the square pyramid. Hence:

Number of times = volume of cube / volume of pyramid

The perimeter of the pyramid base = 25 in, hence the length of one side of the bae = 25 / 4 = 6.25 in

Volume of square pyramid = base² × (height / 3) = (6.25 in)² * (5 in / 3) = 65.1 in³

Volume of cube = 125 in³

Number of times = 125 in³ / 65.1 in³ = 1.92

3 0

3 years ago

The bigger of two numbers is four more

Otrada [13]

Answer:

X=the smaller

y=the larger

The bigger of two numbers is four more than the smaller, then:

y=x+4

one more than twice the smaller is the same as the larger, then

1+2x=y

We have the following system of equations:

y=x+4

y=2x+1

We solve this system by equal values method:

x+4=2x+1

x-2x=1-4

-x=-3

x=3

We find the value of "y"now:

y=x+4

y=3+4

y=7

the values of x and y are:

x=3

y=7

Step-by-step explanation:

7 0

3 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 $\rm \triangle OBA$ :

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