How tall can each prism be. Please and thank you!!!
2 answers:
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Answer:
see explanation
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Rearrange 3x - 4y = 7 into this form
Subtract 3x from both sides
- 4y = - 3x + 7 ( divide all terms by - 4 )
y = x -
← in slope- intercept form
with slope =
• Parallel lines have equal slopes, hence
y = x + c ← is the partial equation of the parallel line
To find c substitute (- 4, - 2) into the partial equation
- 2 = - 3 + c ⇒ c = - 2 + 3 = 1
y = x + 1 ← in slope- intercept form
Multiply all terms by 4
4y = 3x + 4 ( subtract 4 from both sides )
4y - 4 = 3x ( subtract 4y from both sides )
- 4 = 3x - 4y, that is
3x - 4y = - 4 ← in standard form
Answer:
see explanation
Step-by-step explanation:
A
Given
(x² + 3)² + 21 = 10x² + 30 ← factor out 10 from each term on the right side
(x² + 3)² + 21 = 10(x² + 3) ← subtract 10(x² + 3) from both sides
(x² + 3)² - 10(x² + 3) + 21 = 0
Substituting u = x² + 3 into the equation gives
u² - 10u + 21 = 0 → D
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B
Using u² - 10u + 21 = 0 to solve the equation
Consider the factors of the constant term (+ 21) which sum to give the coefficient of the u- term (- 10)
The factors are - 3 and - 7, since
- 3 × - 7 = 21 and - 3 - 7 = - 10, thus
(u - 3)(u - 7) = 0
Equate each factor to zero and solve for u
u - 3 = 0 ⇒ u = 3
u - 7 = 0 ⇒ u = 7
We now have to use the substitution to convert the solutions into terms of x, that is
x² + 3 = 3 ( subtract 3 from both sides )
x² = 0 ⇒ x = 0 → D
x² + 3 = 7 ( subtract 3 from both sides )
x² = 4 ( take the square root of both sides )
x = ± = ± 2
Thus x = - 2 → C
x = 2 → E