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Shkiper50 [21]
3 years ago
10

Francois earns a weekly salary of $475 plus a 5.5% commission one sales at a gift shop. How much would be earn in a week if he s

old $700 in goods? Round to nearest cent.
Mathematics
1 answer:
andriy [413]3 years ago
4 0
475 + .055(700)=513.50
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Translate into algebraic equation - a number plus 15 exceeds twice that number by 3​
bija089 [108]

Answer:

n + 15 > (2n)/3

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3 0
2 years ago
The sum of thrice a number and 5 is greater than or equal to the sum of twice a number and 1. Write down the inequality and solv
sertanlavr [38]

Answer:

May be helpful.

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7 0
1 year ago
The domain of both f(x) = x - 6 and g(x) = x + 6 is all real numbers. What is the domain of h(x) = f(x)/g(x)?
arlik [135]
This is a quotient (division) of two functions we must be concerned with the fact that division by zero is undefined.

Since g(x) is in the divisor position, it cannot equal 0.
x+6 \neq 0
x \neq -6 Subtract 6 from both sides to solve.
So the domain is all real numbers except -6
Set notation {x | x ∈ R, x ≠ -6}
Interval notation (-∞,-6)∪(-6,∞)
6 0
3 years ago
Which series of transformations will not map figure H onto itself
7nadin3 [17]

Answer:

D

Step-by-step explanation:

Given a square with vertices at points (2,1), (1,2), (2,3) and (3,2).

Consider option A.

1st transformation (x+0,y-2) will map vertices of the square into points

  • (2,1)\rightarrow (2,-1);
  • (1,2)\rightarrow (1,0);
  • (2,3)\rightarrow (2,1);
  • (3,2)\rightarrow (3,0).

2nd transformation = reflection over y = 1 has the rule (x,2-y). So,

  • (2,-1)\rightarrow (2,3);
  • (1,0)\rightarrow (1,2);
  • (2,1)\rightarrow (2,1);
  • (3,0)\rightarrow (3,2)

These points are exactly the vertices of the initial square.

Consider option B.

1st transformation (x+2,y-0) will map vertices of the square into points

  • (2,1)\rightarrow (4,1);
  • (1,2)\rightarrow (3,2);
  • (2,3)\rightarrow (4,3);
  • (3,2)\rightarrow (5,2).

2nd transformation = reflection over x = 3 has the rule (6-x,y). So,

  • (4,1)\rightarrow (2,1);
  • (3,2)\rightarrow (3,2);
  • (4,3)\rightarrow (2,3);
  • (5,2)\rightarrow (1,2)

These points are exactly the vertices of the initial square.

Consider option C.

1st transformation (x+3,y+3) will map vertices of the square into points

  • (2,1)\rightarrow (5,4);
  • (1,2)\rightarrow (4,5);
  • (2,3)\rightarrow (5,6);
  • (3,2)\rightarrow (6,5).

2nd transformation = reflection over y = -x + 7 will map vertices into points

  • (5,4)\rightarrow (3,2);
  • (4,5)\rightarrow (2,3);
  • (5,6)\rightarrow (1,2);
  • (6,5)\rightarrow (2,1)

These points are exactly the vertices of the initial square.

Consider option D.

1st transformation (x-3,y-3) will map vertices of the square into points

  • (2,1)\rightarrow (-1,-2);
  • (1,2)\rightarrow (-2,-1);
  • (2,3)\rightarrow (-1,0);
  • (3,2)\rightarrow (0,-1).

2nd transformation = reflection over y = -x + 2 will map vertices into points

  • (-1,-2)\rightarrow (4,3);
  • (-2,-1)\rightarrow (3,4);
  • (-1,0)\rightarrow (2,3);
  • (0,-1)\rightarrow (3,2)

These points are not the vertices of the initial square.

5 0
3 years ago
A boat travels 12 km upstream and back in 1 hour 45 minutes. If the speed of the current is 3 km/h throughout, find the speed of
Elza [17]

Answer:

14.3 km/h   to 3 significant figures

Step-by-step explanation:

Let time travelling upstream be t1 hours and downstream = t2 hours.

t1 + t2 = 1.75..........................(1)

Let v  be the speed of the boat in still water.

12 / t1 = v - 3.........................(2)

12 /  t2 = v + 3........................(3)

From (1) and (3) , substituting for t2:-

12 / (1.75 - t1) = v + 3 ..................(4)

Subtract:-   (2) - (4):-

12 / t1 - 12 / (1.75 - t1) = -6

12(1 .75 - t1) - 12t1 = -6t1(1.75 -  t1)

21 - 12t1 - 12t1 = -10.5t1 + 6t^2

6t1^2 + 13.5t1 - 21 = 0

Solving this gives t1 = 1.058 hours

Therefore the speed in still water (v)  = 12/1.058 + 3 = 14.3 to 3 sig figs

3 0
3 years ago
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