Based on the operation in step 3, the mathematical reasoning that we see is the Associative property.
<h3 /><h3>What is the reasoning in step 3?</h3>
Step 2 was:
= 3/4x (-8x) + (3/4x) (6)
Step 3 then became:
3/4 x (-8) × x × x + 3/4 x 6x
This shows the associative property because the numbers were regrouped but because they are being multiplied by each other, the result will not change.
Find out more on the associative property at brainly.com/question/13181.
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Answer:
You could talk on the phone for 200 minutes at night, or 40 minutes during the day.
For every 5 minutes you reduced your night time talking, you could talk during the day for 1 minute.
Step-by-step explanation:
0.50d + 0.10n < $20
0.50d < $20 --> d < 40 minutes
0.10n < $20 --> n < 200 minutes
Answer:
5.44 cm³
Step-by-step explanation:
The volume of the hexagonal nut can be found by multiplying the area of the end face by the length of the nut. The end face area is the difference between the area of the hexagon and the area of the hole.
The area of a hexagon with side length s is given by ...
A = (3/2)√3·s²
For s=1 cm, the area is ...
A = (3/2)√3(1 cm)² = (3/2)√3 cm²
__
The area of a circle is given by ...
A = πr²
The radius of a circle with diameter 1 cm is 0.5 cm. Then the area of the hole is ...
A = π(0.5 cm)² = 0.25π cm²
__
The volume is the face area multiplied by the length, so is ...
V = Bh = ((3/2)√3 -0.25π)(3) . . . . . cm³
V = (9/2)√3 -0.75π cm³ ≈ 5.44 cm³
The volume of the metal is about 5.44 cm³.
Answer:
OPTION A: 2x + 3y = 5
Step-by-step explanation:
The product of slopes of two perpendicular lines is -1.
We rewrite the given equation as follows:
2y = 3x + 2
⇒ y = 
The general equation of the line is: y = mx + c, where 'm' is the slope of the line.
Here, m = 
.
Therefore, the slope of the line perpendicular to the line given = 
because 
.
To determine the equation of the line passing through the given point and a slope we use the Slope - One - point formula which is:
y - y₁ = m(x - x₁)
The point is: (x₁, y₁) = (-2, 3)
Therefore, the equation is:
y - 3 = (x + 2) $
⇒ 3y - 9 = -2(x + 2)
⇒ 3y - 9 = -2x - 4
⇒ 2x + 3y = 5 is the required equation.
