The distance between the two points is ten.
Answer:
b. Miguel ends up with $35 less than he started with
Step-by-step explanation:
He spends $35 × 4 = $140.
He earns $21 × 5 = $105.
His net increase is $105 -140 = -$35.
Miguel ends up with $35 less than he started with.
The correct answer choice is:
______________________________________________ [C]: "<span>
Multiply each side by −8, subtract 35 from each side" .
_______________________________________________Explanation:_______________________________________________Given: "</span>

(x + 35) = -7 " ;
We can START by multiply each side of the equation by "-8" to completely get rid of the "

" fraction on the "left-hand-side" of the equation:
since: "

* -8 = 1 ; and: "1" , multiplied by any given value, is equal to that given value; so in effect, the "1" becomes eliminated.
"

* -8 =

*

=

=

= 1 .
____________________________________________________So, given: "

(x + 35) = -7 " ; ;
We multiply each side of the equation by "-8" ;
→ -8 * {

(x + 35) } = -7 * {-8) " ;
→ 1 (x + 35) = 56 ;
→ x + 35 = 56 ;
Then, we SUBTRACT "35" (FROM EACH SIDE OF THE EQUATION) ; to isolate "x" on ONE SIDE OF THE EQUATION; and to solve for "x" ;
→ x + 35 − 35 = 56 <span>− 35 ;
</span>→
x = 21 .
______________________________________________________
So, as explained, the correct answer is:
______________________________________________________
Answer choice: [C]:
______________________________________________________
"<span>
Multiply each side by −8, subtract 35 from each side" .
______________________________________________________</span><span>
</span>
2.943 × 10-²
= <span>2.943
----------
10²</span>
1) For each of these, keep in mind vertex form: f(x)=a(x-h)^2+k. With vertex form, a is the direction and width, h is the horizontal placement of the vertex, and k is the vertical placement. For the first one, notice that "a" is positive 1, so it faces up. This means that D, the one facing down, cannot be the answer. "h" is 1, so we will move the vertex to the right one unit (keep in mind (x-h), so if it were to be (h+3) you would move it to the left, not the right). "k" is -3, so we would move the vertex down 3 units. That said, the vertex should be at (1,-3) so the answer is C, or the one right below the first one.
2) The graph of f(x)=|2x| translated 5 units to the left means that h is equal to -5. When we plug -5 into vertex form, it should look like: g(x)=|2(x+5)|. The answer to this is A.
3) The equation for reflection on the x axis is f(x)=-a(x-h)+k. So, if the parent function f(x)=4|x| were to be reflected on the x axis, the function would look like this: g(x)=-4|x|. The answer to this should be B.
4) Since h=1 and k=0 in the function f(x)=-3|x-1|, the vertex will be (1,0).
5) This can also be written as g(x)=|x|-3. This means that k=-3, and will be a vertical translation of 3 units down.