Answer:
First one: x = all real numbers
Second one: x = 0
Step-by-step explanation:
for the first one
given 8x+10=2(4x+5) we need to isolate the variable (x) using inverse operations
step 1 distribute the 2 to what is in the parenthesis ( 4x and 5 )
2 * 4x = 8x
5 * 2 = 10
now we have 8x + 10 = 8x + 10
step 2 subtract 8x from each side
8x - 8x = 0
8x - 8x = 0
now we have 10 = 10
subtract 10 from each side
10 - 10 = 0
10 - 10 = 0
we're left with 0 = 0 meaning that all real numbers are solutions
For the second one
given 3x-8=2(x-4) once again we need to isolate the variable using inverse operations
step 1 distribute the 2 to what is in the parenthesis (x - 4)
2 *x = 2x
2 * -4 = -8
now we have 3x - 8 = 2x - 8
step 2 add 8 to each side
-8 + 8 = 0
-8 + 8 = 0
now we have 2x = 3x
step 3 subtract 2x from each side
3x - 2x = x
2x - 2x = 0
we're left with x = 0
Answer:
Step-by-step explanation:
24/9 would be 8:3
Hope this helps :)
Step-by-step explanation:
1) i will asume x2 and z2 are squares here.
ok, here we only have restrictions to x and z, so y can take all the values in R.
is a circle of radius 6, you can see this if for example we set z = 0, then x goes from -6 to 6, the same if we set x = 0 then z goes from -6 to 6.
and the equation
describes a circle.
So here, the region is the solid cylinder of radius 6, where the Y axis is also the axis of the cylinder.
2) you tipped the same inequality but different numbers in the right side, here i think you are saying that the inequalities describes the set of all points whose distance from the y-axis is equal or less tan 6.
From the diagram above,
XZ = 10 in and OX = 10 in
we are to find length of OY
XZ is a chord and line OY divides the chord into equal length
Hence, ZY=YX= 5 in
Now we solve the traingle OXY
To find OY we solve using pythagoras theorem

applying values from the triangle above
![\begin{gathered} OX^2=XY^2+OY^2 \\ 10^2=5^2+OY^2 \\ 100=25+OY^2 \\ OY^2\text{ = 100 -25} \\ OY^2\text{ = 75} \\ OY\text{ = }\sqrt[]{75} \\ OY\text{ = }\sqrt[]{25\text{ }\times\text{ 3}} \\ OY\text{ = 5}\sqrt[]{3\text{ }}in \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20OX%5E2%3DXY%5E2%2BOY%5E2%20%5C%5C%2010%5E2%3D5%5E2%2BOY%5E2%20%5C%5C%20100%3D25%2BOY%5E2%20%5C%5C%20OY%5E2%5Ctext%7B%20%3D%20100%20-25%7D%20%5C%5C%20OY%5E2%5Ctext%7B%20%3D%2075%7D%20%5C%5C%20OY%5Ctext%7B%20%3D%20%7D%5Csqrt%5B%5D%7B75%7D%20%5C%5C%20OY%5Ctext%7B%20%3D%20%7D%5Csqrt%5B%5D%7B25%5Ctext%7B%20%7D%5Ctimes%5Ctext%7B%203%7D%7D%20%5C%5C%20OY%5Ctext%7B%20%3D%205%7D%5Csqrt%5B%5D%7B3%5Ctext%7B%20%7D%7Din%20%5Cend%7Bgathered%7D)
Therefore,
Length of OY =
Answer:
Part A) Option A. QR= 3 cm
Part B) Option B. SV=6.5 cm
Step-by-step explanation:
step 1
<u>Find the length of segment QR</u>
we know that
If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent
so
In this problem Triangle QRW and Triangle QSV are similar by AA Similarity Theorem
so

we have
---> because S is the midpoint QT (QS=TS)
--->because V is the midpoint QU (QW+WV=VU)
--->because V is the midpoint QU (QV=VU)
substitute the given values

solve for QR

step 2
Find the length side SV
we know that
The <u><em>Mid-segment Theorem</em></u> states that the mid-segment connecting the midpoints of two sides of a triangle is parallel to the third side of the triangle, and the length of this mid-segment is half the length of the third side
so
In this problem
S is the mid-point side QT and V is the mid-point side QU
therefore
SV is parallel to TU
and

so
