Value of both the integers as three times the largest consecutive integer is 15 less than 2/3 the smallest one is -7, -9.
As given,
Let x, x +2 be two consecutive odd integers
Three times largest integer=3( x+2)
15 less than 2/3 smallest integer=(2/3)x -15
Equation :
3(x+2)=(2/ 3)x -15
⇒ 3x +6=(2x -45)/3
⇒ 9x-2x= -18 -45
⇒ 7x=-63
⇒ x =-9
and x+2 =-7
Therefore, value of both the integers as three times the largest consecutive integer is 15 less than the 2/3 the smallest one is -7, -9.
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Answer:
S = £1.28
Step-by-step explanation:
Let the small, medium and large cakes be S, M and L respectively.
Given the following data;
Total profits = £532.48
Total number of cake = 192 cakes
Ratio of S:M:L = 7:6:11
Sum of ratio = 7+6+11 = 24
To find number of each cakes, we would divide the total number of cakes by the sum of ratio;
Number of each cakes = 192/24
Number of each cakes = 8
Next, we determine the exact number of each type of cakes.
Small = 7*8 = 56 cakes.
Medium = 6*8 = 48 cakes.
Large = 11*8 = 88 cakes.
For the profits;
Translating the word problem into an algebraic expression, we have;
M = 2S
L = 3S
56S + 48*(2S) + 88*(3S) = £532.48
56S + 96S + 264S = 532.48
416S = 532.48
S = 532.48/416
S = £1.28
Therefore, the profit for one small cake is £1.28
Answer:
Step-by-step explanation:
7). Since, ∠4 and ∠5 are the linear pair of angles,
m∠4 + m∠5 = 180° [Supplementary angles]
72° + m∠5 = 180°
m∠5 = 180° - 72°
m∠5 = 108°
8). Since, ∠6 and ∠7 are the vertically opposite angles,
Therefore, ∠6 ≅ ∠7
m∠6 = m∠7
3x + 94 = 9x - 38
9x - 3x = 94 + 38
6x = 132
x = 22
m∠6 = 3(22) + 94 = 160°
m∠7 = 9(22) - 38 = 160°
9). Since, ∠2 and ∠3 are the linear pair of angles, both the angles will be supplementary.
m∠2 + m∠3 = 180°
(13x + 54) + (2x + 36) = 180°
15x + 90 = 180°
15x = 90
x = 6
m∠2 = 13(6) + 54 = 132°
m∠3 = 2(6) + 36 = 48°
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
<u>Given vertices of triangle:</u>
- A(1, 2), B(3, 4), C(5, 0)
<u>The centroid is found as the average of x- and y- coordinates of three vertices:</u>
- C = ((x₁ + x₂ + x₃)/3, (y₁ + y₂ + y₃)/3)
<u>Substitute the coordinates into formula:</u>
- C = ((1 + 3 + 5)/3, (2 + 4 + 0)/3) = (3, 2)
Correct choice is B