K+3 3/4=5 2/3-1 1/3
k+3 3/4=4 1/3
lets find the lcm first then multiply both sides by it but first change it to improper fraction
LCM is 12
[k+15/4]=[13/3]12
12k+45=52
12k=7
k=7/12
Answer: concentration = 15.58%
Step-by-step explanation:
Given: mass of sugar = 24 g = 24 ml [ ∵ 1 g = 1 ml]
Volume of solution = Quantity of water + quantity of solute
= 130 +24 ml
= 154 ml
Concentration = 
Hence, the concentration =15.58%
a³ + b³ + c³ + 3abc = ( a + b + c)(a² + b² + c² + ab + bc + ca)
if a + b + c = 0. then a³ + b³ + c³ = 3abc
here a + b + c = 15 + (-9) + (-6)
a + b + c = 15 - 15
a + b + c = 0
so a³ + b³ + c³ = 3abc
15³ + (-9)³ + (-6)³ = 3(15)(-9)(-6)
= 2430
so the answer is 2430
Answer
The vertex is at point (-3, -1)
The axis of symmetry is x = -3
Explanation
We are asked to find the vertex and axis of symmetry of the equation given.
f(x) = x² + 6x + 8
The vertex of a quadratic equation is the point where the graph of the quadratic equation changes from sloping negatively to sloping positively and vice-versa.
The axis of symmetry represents the straight line that divides the graph of the quadratic equation into two mirror parts that are similar to and are mirror images of each other. This axis of symmetry usually passes through the vertex.
To find the vertex, it is usually at the turning point where the first derivative of the quadratic equation is equal to 0.
(df/dx) = 0
f(x) = x² + 6x + 8
(df/dx) = 2x + 6
At the vertex
(df/dx) = 2x + 6 = 0
2x = -6
Divide both sides by 2
(2x/2) = (-6/2)
x = -3
We then insert this into the equation to get the corresponding f(x) value.
f(x) = x² + 6x + 8
f(-3) = (-3)² + 6(-3) + 8
= 9 - 18 + 8
= -1
Hence, the vertex is at point (-3, -1)
And since the axis of symmetry has to pass through the vertex,
The axis of symmetry is x = -3
Hope this Helps!!!
Answer:
ABC is an isosceles triangle.
Because it consists of two congruent triangles created by CD, side AC = CB, making it an isosceles triangle.
Step-by-step explanation:
I can conclude that triangle ABC is an isosceles triangle.
Perpendicular means intersecting at 90°. Bisector means intersecting at the midpoint, halfway between the two ends.
Since CD is dropped from vertex C and is a perpendicular bisector of AB, angle C is also bisected.
Therefore angle C for both triangles CDA and CDB is of equal measure.
We know angle D for both triangle CDA and CDB is of equal measure, 90°, because CD is a <em>perpendicular </em>bisector of AB.
The two triangles also share the same side CD.
Triangles CDA and CDB are congruent for having 2 equal angles and 1 equal side (ASA property).
Since they are congruent, AD = AB and AC = CB. Therefore triangle ABC is an isosceles triangle.
