Answer:
see explanation
Step-by-step explanation:
The sum to n terms of an arithmetic sequence is
= 
[ 2a₁ + (n - 1)d ]
where a₁ is the initial value and d the common difference
Given
= [ 10 + (n - 1)3 ]
Then by comparison
2a₁ = 10 ( divide both sides by 2 )
a₁ = 4 ← initial value
and d = 3 ← common difference
Thus
= 
[ 10 + (7 × 3) ]
= 4(10 + 21)
= 4 × 31
= 124
Almost all correct except two. Please check corrected image.
Answer:
1. -10
2. -11
Step-by-step explanation:
This question boils down to this:
"What is the diagonal of a square with a side length of 90 ft?"
The key to this question is the properties of squares.
All of the angles in a square are right, (90°) but that diagonal is going to bisect two of those into 45° angles.
Now we have two triangles, each with angle measures of 45°, 45°. and 90°.
(an isoceles right triangle)
This 45-45-90 tirnalge is one of two special triangles (the other being the 30-60-90) and here is its special property: the sides opposite these angles can be put as x, x, and x√2 respectively. Why? Well, we know that our triangle is isoceles (the congruent base angles ⇔ congruent sides) and so we call those x...by the Pythagorean theorem...a² + b² = c²...2x² = c²...x√2 = c!
In our case here, that diagonal, being the hypotenuse of our triangle, is going to be 90√2 feet, or approximately 127.3 feet.
Answer:
Step-by-step explanation:
<u>Covert equations in standard form into slope-intercept form of y = mx + b</u>
<h3>#1</h3>
<h3>#2</h3>
- 5x + 3y = 6 ⇒ 3y = -5x + 6 ⇒ y = -5/3x + 2
<h3>#3</h3>
- x - 2y = 2 ⇒ 2y = x - 2 ⇒ y = 1/2x - 1
<h3>#4</h3>
- 3x + 2y = -8 ⇒ 2y = -3x - 8 ⇒ y = -3/2x - 4
