Answer:
Step-by-step explanation:
A). g(x) = x² - 9x + 14
Since coefficient of highest degree term (x²) is positive, parabola will open upwards.
For any parabola opening upwards,
Right end behavior,
y → ∞ as x → ∞
B). Let the equation of the linear function is,
f(x) = mx + b
Where m = slope of the function
b = y-intercept
From the graph attached,
Slope 'm' =
m = -3
b = -1
Therefore, function 'f' will be,
f(x) = (-3)x - 1
f(x) = -3x - 1
g(x) = x² - 9x + 14
= x² - 7x - 2x + 14
= x(x - 7) - 2(x - 7)
= (x - 2)(x - 7)
If h(x) = f(x)g(x)
h(x) = -(3x + 1)(x -2)(x - 7)
For h(x) ≥ 0
-(3x + 1)(x - 2)(x - 7) ≥ 0
Or 2 ≤ x ≤ 7
Therefore, for 2 ≤ x ≤ 7, h(x) ≥ 0
C). If k(x) =
k(x) =
k(x) = -(3x + 1)(x - 7)
For k(x) = -56
-(3x + 1)(x - 7) = -56
3x² -20x - 7 = 56
3x² - 20x - 63 = 0
3x² - 27x + 7x - 63 = 0
3x(x - 9) + 7(x - 9) = 0
(3x + 7)(x - 9) = 0
dishwasher:
1200*0.15 = 180
1200-180 =$1,020
area:
middle section 6x6 = 36
left triangle 6*6*0.5 = 18
right triangle Area=base x height/2 = 6x6/2 = 18
36 +18 +18 =
72 in^2
4(x + 2) = 96
Divide both sides by 4.
= 24
x + 2 = 24
Subtract 2 from both sides.
(x+2) - 2 = 24 - 2
x = 22
Hence, the value of x is 22.
Answer:
70 mm
Step-by-step explanation:
Use PYTHAGOREAN THEOREM: a^2+b^2=c^2
42^2 + 56^2 = c^2
1764 + 3136 = c^2
4900=c^2
square root of 4900 is 70
so, the final answer is 70 mm
Answer:
Converse: False
Inverse: False
Contrapositive: True
Step-by-step explanation:
Converse: Two angles can be any degree and be congruent, they do not have to both be right angles, which makes this statement false.
Inverse: Same as above. They can be not right angles. If they are the same degree, they are congruent, so they do not have to be right angles, which makes this statement false.
Contrapositive: If angles are congruent, they will not both be right angles, because right angles are the same degree, which makes them congruent. Thus, this statement is true.