Answer:
see explanation
Step-by-step explanation:
(1)
given
4x² = 81 ( divide both sides by 4 )
x² = ( take the square root of both sides )
x = ± = ±
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(2)
subtract 7 from both sides
(4x - 3)² = 32 ( take the square root of both sides )
4x - 3 = ± = ± 4
Add 3 to both sides
4x = 3 ± 4 ( divide both sides by 4 )
x = ±
Answer:
The value of x is 7 ⇒ 1st answer
Step-by-step explanation:
* Lets revise a fact in the circle
- The two tangents drawn from a point out side the circle are equal
∵ RSTUV is circumscribed about a circle
∴ Each side of the pentagon is a tangent to the circle
- Look to the attached figure to know how we will solve the problem
- Each tangent divided into two parts
# RS = x + y
∵ RS = 8
∴ x + y = 8 ⇒ (1)
# RV = x + n
∵ RV = 12
∴ x + n = 12 ⇒ (2)
- Subtract (2) from (1)
∴ y - n = -4 ⇒ (3)
# ST = y + z
∵ ST = 12
∴ y + z = 12 ⇒ (4)
# TU = z + m
∵ TU = 15
∴ z + m = 15 ⇒ (5)
- Subtract (5) from (4)
∴ y - m = -3 ⇒ (6)
# UV = m + n
∵ UV = 9
∴ m + n = 9 ⇒ (7)
- Add (6) and (7)
∴ y + n = 6 ⇒ (8)
- Lets solve equation (3) and equation (8) to find y
∵ y - n = -4 ⇒ (3)
∵ y + n = 6 ⇒ (8)
- Add (3) and (8)
∴ 2y = 2 ⇒ divide two sises by 2
∴ y = 1
- Lets substitute the value of y in equation (1)
∵ x + y = 8 ⇒ (1)
∵ y = 1
∴ x + 1 = 8 ⇒ subtract (1) from both sides
∴ x = 7
* The value of x is 7
Answer:
80, 70 and 87
Step-by-step explanation:
-Range is mathematically defined as the difference between the largest and smallest data point in a data set.
-Given the mean=79, median=80 and the range is 17.
#let a be the largest score and b be the smallest score:
The sum of the 3 scores is equivalent to the 237.
#we subtract the given median and equate using range to solve for a and b;
Hence, the test scores are 80, 70 and 87