Hi guys

In order to solve the equation −3x + 6 = 5, the first step is to (1 point)

aliya0001 [1]

−3x + 6 = 5 | -6 (first step is: "subtract 6 from both sides" )

-3x = 5-6
-3x = -1 | /(-3) (second step is: "divide by (-3) on both sides" )

 $\displaystyle \\ 
x = \frac{-1}{-3} = \boxed{\frac{1}{3} }$

5 0

2 years ago

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A six-foot-tall person is standing next to a flagpole. The person is casting a shadow 1 1/2 feet in length, while the flagpole i

lara31 [8.8K]

Answer: 20 ft

This problem can be solved by the Thales’s theorem, which states:

Two triangles are similar when they have equal angles and proportional sides

It should be noted that to apply Thales' Theorem, it is necessary to establish the two triangles are similar, that is, that they have the corresponding angles equal or that their sides are proportional to each other.

Now, if we measure the shadow of the flagpole and the shadow of the person, at the same moment, we can use the first Thales' Theorem to calculate the height of the flagpole, knowing the height of the person.

In this case we have two similar triangles (Figure attached) where $H$ is the height of the flagpole, $h=6 ft$ is the height of the person, $A=5 ft$ is the length of the shadow of the flagpole and $a=1\frac{1}{2}=1.5 ft$ is the length of the shadow of the person.

Having this clear, we can write the following relation with both similar triangles:

$\frac{H}{h}=\frac{A}{a}$ (1)

We know all these lengths except $H$ , which is the value we want to to find.

So, in order to approach this problem we have to find $H$ from equation (1):

$H=\frac{A}{a}h$

$H=\frac{5 ft}{1.5 ft}(6 ft)$

Then:

$H=20 ft$ >>>>>This is the height of the flagpole

4 0

3 years ago

Please somebody help me with this please help ASAP

TiliK225 [7]

Step-by-step explanation:

I don't know what your teacher wants to hear here.

can you use and construct certain angles (particularly 90 degrees), can you use compasses ?

for me the best way would be to draw one side as given. then use compasses and draw a half-circle from each end point of the line above the line. both circles have the radius = the given diameter.

then draw the next 2 sides of the square up from the end points of the first line towards the half-circle that was drawn from the other point, so that the end point is exactly on the circle bow. and then connect the engaging endpoints of these 2 sides.

similar for the rectangle.

the only difference is that now for the two sides (which we don't know the length) we need to go up exactly 90 degrees until the lines hit the half-circles.

4 0

3 years ago

Need some help with these problems!

LekaFEV [45]

Answer:

h=12, w=24, t=8

Step-by-step explanation:

System of Linear Equations

We have 3 unknown variables and 3 conditions between them. They form a set of 3 equations with 3 variables.

We have the following data, being

w = price of a sweatshirt

t = price of a T-shirt