Answer:
Each side of the Rhombus is 5 units
Step-by-step explanation:
Since the sides of a rhombus area all equal in length;
Then, the length of a side is enough to get the lengths of the other sides
Mathematically, finding the distance between two points out of what we are given will be enough to get the measure of one of the side of the rhombus
We apply the distance formula appropriately to get the distance between the side of the Rhombus
D = √(x2-x1)^2 + (y2-y1)^2
let us use the points (-1,0) and (4,0)
D = √(4 + 1)^2 + (0-0)^2
D = √25
D = 5
Answer:40
Step-by-step explanation:
40 beacause you have to round to the nearset 10
Answer:
a) A-B = { 1 , 3, 5 }
b) The remainder is 50
c) f + g)(x) = x⁴+ 5x³
d) 
Step-by-step explanation:
Step(I):-
1) a)
Let A = { 1, 3, 5, 7 } and B = { 7 , 14 , 21 }
A - B = {1,3,5,7} - { 7,14,21}
A - B = { 1 , 3, 5}
b)
Given f (x)=3x³−11x−48
x-1 ) 3 x³ - 11x -48 (- 3x²-3x -2
-3<u>x³ +3x</u>²
3x²-11x-48
<u> -3x²+9x</u>
<u> </u> 2x -48
-2x +2
<u> </u>
50
The remainder is 50
c) Given f(x) = x³ and g(x) = x + 5
(f. g)(x) = f(x) .g(x) = x³ . (x+5) = x³(x) + 5 x³ = x⁴+ 5x³
d)
Given function y = 3 + x²+x³y³ ...(I)
By using derivative formulas
y = xⁿ

Apply d/dx ( UV) = U V¹ + V U¹
Differentiating equation (I) with respective to 'x' , we get


Answer:
The graph in the attached figure
Step-by-step explanation:
Let
x -----> the number of solved puzzles
y -----> the number of solved riddles
we know that

The solution of the inequality is the shaded area above the solid line 
The slope of the solid line is negative 
The y-intercept of the solid line is the point (0,4)
The x-intercept of the solid line is the point (2,0)
therefore
The graph in the attached figure
Answer:
You should make 250 quarts of Creamy Vanilla and 200 of Continental Mocha to use up all the eggs and cream.
Step-by-step explanation:
This problem can be solved by a first order equation
I am going to call x the number of quarts of Creamy Vanilla and y the number of quarts of Continental Mocha.
The problem states that each quart of Creamy Vanilla uses 2 eggs and each quart of Continental Mocha uses 1 egg. There are 700 eggs in stock, so:
2x + y = 700.
The problem also states that each quart of Creamy Vanilla uses 3 cups of cream and that each quart of Continental Mocha uses 3 cups of cream. There are 1350 cups of cream in stock, so:
3x + 3y = 1350
Now we have to solve the following system of equations
1) 2x + y = 700
2) 3x + 3y = 1350
I am going to write y as function of x in 1) and replace it in 2)
y = 700 - 2x
3x + 3(700 - 2x) = 1350
3x + 2100 - 6x = 1350
-3x = -750 *(-1)
3x = 750
x = 250
You should make 250 quarts of Creamy Vanilla
Now, replace it in 1)
y = 700 - 2x
y = 700 - 2(250)
y = 700 - 500
y = 200.
You should make 200 quarts of Continental Mocha