Answer:
1655
Step-by-step explanation:
Note the common difference d between consecutive terms of the sequence
d = - 1 - (- 4) = 2 - (- 1) = 5 - 2 = 8 - 5 = 3
This indicates the sequence is arithmetic with sum to n terms
= 
[ 2a₁ + (n - 1)d ]
Here a₁ = - 4, d = 3 and n = 90, thus
= 
[ (2 × - 4) + (89 × 3) ] = 45(- 8 + 267) = 45 × 259 = 1655
Answer:
x = 4 and y = - 5
Step-by-step explanation:
note that the product of a complex number and it's conjugate is real
That is
(a + bi)(a - bi) where a, b are real
= a² - abi + abi - b²i²
= a² + b² ← a real number
For (4 + 5i)(x + yi) to be real
we require (x + yi) to be the conjugate of 4 + 5i , that is 4 - 5i
(4 + 5i)(4 - 5i) ⇒ x = 4 and y = - 5
D) EFGH moved onto E'F'G'H after rotating 180 counterclockwise around the origin and the reflecting across the y-axis.
<h3>How to carry out transformations?</h3>
From online resources gotten about this question, for quadrilateral EFGH and quadrilateral E'F'G'H to be congruent, what we must do first is to rotate 180° counterclockwise around the origin and then move EFGH onto E'F'G'H'.
The last step to get this proof of congruency is to reflect across the y-axis.
Read more about transformations at; brainly.com/question/4289712
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Answer:
$3.98(estimated)
Step-by-step explanation:
3c (cake) + 2(2c - 11) (bread) = 5.87
3c + 4c - 22 = 5.87
7c - 22 = 5.87
7c = 5.87 + 22
7c = 27.87
c = 3.98
