Answer:
a = - 3, a = 4
Step-by-step explanation:
Given f(x) = x² + 2 and g(x) = x + 14 , then
f(a) = a² + 2 and g(a) = a + 14
For f(a) = g(a) , then equate the right sides
a² + 2 = a + 14 ( subtract a + 14 from both sides )
a² - a - 12 = 0 ← in standard form
(a - 4)(a + 3) = 0 ← in factored form
Equate each factor to zero and solve for a
a + 3 = 0 ⇒ a = - 3
a - 4 = 0 ⇒ a = 4
Answer:
5x - 4 = 56
2x + 3 = 27
Step-by-step explanation:
2(5x - 4 + 2x + 3) = 166
10x - 8 + 4x + 6 = 166
14x - 2 = 166
+ 2 +2
14x = 168
divide both sides of the equal sign by 14
12
5(12) - 4 = 60 - 4 = 56
2(12) + 3 = 24 + 3 = 27
The gradient of the straight line is -3.
<h3>How to find the gradient of a line?</h3>
The gradient of a straight line is the rate at which the line rises (or falls) vertically for every unit across to the right.
The gradient of a line is the slope of the line.
The gradient of the line is the change in the dependent variable with respect to the change in the independent variable.
Therefore, using (0, 4) and (1, 1) let's find the gradient.
gradient = y₂ - y₁ / x₂ - x₁
x₁ = 0
x₂ = 1
y₁ = 4
y₂ = 1
gradient = 1 - 4 / 1 - 0
gradient = - 3 / 1
gradient = - 3
learn more on gradient here: brainly.com/question/1852598
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Answer:
AB = 2*sqrt(5) or
AB = 4.47
Step-by-step explanation:
AB is the hypotenuse of a right triangle A and B and the corner where 2 and 4 meet.
The length of AB is governed by the Pythagorean Theorem.
AB^2 = x^2 + y^2 Substitute 2 and 4 for x and y
AB^2 = 2^2 + 4^2 Expand the right side
AB^2 = 4 + 16 Add the right side
AB^2 = 20 Take the square root of both sides
sqrt(AB^2) = sqrt(20)
Factor 20 = 2*2 *5
Rule: when taking the square root of a number the pairs can take 1 member of the pair outside the root sign and throw the other one a way.
AB = 2 * sqrt(5) One of the roots has been thrown away.
Answer:
Every 30 hours
Step-by-step explanation:
Train A arrives at central station on the hour and every 12 minutes, you mean with that on every 72 minutes
Train B arrives at central station on the hour and every 15 minutes, you mean with that on every 75 minutes
In accordance with the given, the smallest number containing numbers 72 and 75 is 1800 minutes.
When we convert this number of minutes in hours we get:
1800 / 60 = 30 hours
God with you!!!