A water tank an hold 234 cubic meters of water. How many gallons can the water tank hold

2. TU, UV and TV are mid-segments

3. Definition of mid-segment

4. Division property of equality

6. SSS similarity theorem

Solution:

Step 1: Given

T is the midpoint of QR.

U is the midpoint of QS.

V is the midpoint of RS.

Step 2: Mid-segments connects midpoints of opposite sides.

TU, UV and TV are mid-segments.

Step 3: By definition of mid-segment

A triangle mid-segment is parallel to the third side of the triangle and is half of the length of the third side.

and

Step 4: By division property of equality

Divide first segment by RS, second segment by QR and third segment by SQ.

Step 5: By transitive property

Step 6: From the above steps, the sides of the triangle are congruent.

By SSS similarity theorem,

Hence proved.

Answer:

The sales tax is 8%

Explanation:

We are given that:

The price of the rocket is $24 and the sales tax is $1.92

To get the percentage of the sales tax, all we have to do is divide the sales tax by the price of the rocket and then multiply the quotient by 100 (to convert the ratio to percentage)

This is done as follows:

% of sales tax =

% of sales tax = %

Hope this helps :)

Answer:

First three terms = 28, 22, and 16

Step-by-step explanation:

The formula for the nth term of an arithmetic sequence is given by:

an = a1 + (n-1)d, where:

• an is the nth term,
• a1 is the first term,
• n is the term position (e.g., 1st, 4th, etc.),
• and d is the common difference.

Step 1:  Find a1:

We can find a1 by substituting 10 for an, 4 for n, and -6 for d in the nth term formula:

10 = a1 + (4 - 1) * -6

10 = a1 + 3 * -6

(10 = a1 - 18) + 18

28 = a1

Thus, the first term is 28.

Step 2:  Find a2 (the second term):

Now, we can find the second term by substituting 28 for a1, 2 for n, and -6 for d in the nth term formula:

a2 = 28 + (2 - 1) * -6

a2 = 28 + 1 * -6

a2 = 28 - 6

a2 = 22

Thus, the second term is 22.

Step 3:  Find a3 (the third term):

Now, we can find the third term by substituting 28 for a2, 3 for n, and -6 for d in the nth term formula:

a3 = 28 + (3 - 1) * -6

a3 = 28 + 2 * -6

a3 = 28 - 12

a3 = 16

Thus, the third term is 16.

Step 4:  Write the first three terms:

Therefore, the first three terms of the arithmetic series are 28, 22, and 16.

Answer:

  B.  The axis of symmetry is x=1.

  F.  The vertex is (1, 7).

  G. The y-intercept is (0, 10).

Step-by-step explanation:

A graph of the function is helpful sorting this out.

_____

For quadratic ax² +bx +c, the axis of symmetry is x=-b/(2a). Here, that is ...

  x = -(-6)/(2·3)

  x = 1 . . . . axis of symmetry

This is also the x-coordinate of the vertex. The y-coordinate of the vertex can be found by evaluating the expression for this value of x:

  3·1² -6·1 +10 = 7

so the vertex is (1, 7).

__

The y-intercept is the constant, the value of the function when x=0. Here, that is 10, so the coordinates of the y-intercept are (0, 10).

Answer:

domain (0,1,3,5,6) range (-20,-16,-8,0,4) function f(x)=4-4x

domain (-2,-1,0,3,4) range -13,-8,-3,12,17) function f(x)=5x-3

domain (-4,-3,0,2,4) range (-40,-20,0,20,40) function f(x)=10x

domain (-3,-2,-1,2,6) range (0.5,0,-1.5,3,2) function f(x)=3/x+1.5

Step-by-step explanation: