The domain and the range of the function are all set of real numbers
<h3>How to determine the domain and the range?</h3>
The function is given as:
f(x) = 4x + 3
The above function is a linear function
Linear functions have a domain and a range of all set of real numbers
Hence, the domain and the range of the function are all set of real numbers
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The length of the unknown sides of the triangles are as follows:
CD = 10√2
AC = 10√2
BC = 10
AB = 10
<h3>Triangle ACD</h3>
ΔACD is a right angle triangle. Therefore, Pythagoras theorem can be used to find the sides of the triangle.
where
c = hypotenuse side = AD = 20
a and b are the other 2 legs
lets use trigonometric ratio to find CD,
cos 45 = adjacent / hypotenuse
cos 45 = CD / 20
CD = 1 / √2 × 20
CD = 20 / √2 = 20√2 / 2 = 10√2
20² - (10√2)² = AC²
400 - 100(2) = AC²
AC² = 200
AC = √200 = 10√2
<h3>
Triangle ABC</h3>
ΔABC is a right angle triangle too. Therefore,
Using trigonometric ratio,
cos 45 = BC / 10√2
BC = 10√2 × cos 45
BC = 10√2 × 1 / √2
BC = 10√2 / √2 = 10
(10√2)² - 10² = AB²
200 - 100 = AB²
AB² = 100
AB = 10
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Répondre:
r <27
Explication étape par étape:
Compte tenu de l'inégalité 5r + 9> 10r - 126
Nous devons trouver l'ensemble de solutions
5r + 9> 10r - 126
Ajouter 126 des deux côtés
5r + 9 + 126> 10r - 126 + 126
5r + 135> 10r
5r-10r> -135
-5r> -135
Divisez les deux côtés par -5 (notez que le signe changera)
-5r / -6 <-135 / -5
r <27
Par conséquent, les ensembles de solutions sont des valeurs inférieures à 27
Answer: y=4x-23
Step-by-step explanation:
First multiply the 4 on the right side to make it y+3=4x-20. Then subtract 3 on both sides to get y=4x-23
The domain for which the function is defined is given by:
D.
.
<h3>What is the domain of a function?</h3>
The domain of a function is the set that contains all possible input values for the function.
A square root is only defined for non-negative values, hence:
.
.
The intersection of these two domains is
, hence option D is correct.
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