Answer:
D
Step-by-step explanation:
BH is perpendicular to AC since an orthocenter is a point at which the three altitudes of a triangle intersect. The altitude of a triangle is that line that passes through its vertex and is perpendicular to the opposite side. Since you know that BH is an altitude due to Point H being an orthocenter, you know that BH is perpedendicular to AC.
Answer:True
Step-by-step explanation:
Total pounds sold:
we know that p pounds of almonds and n pounds of nuts were sold.
The total pounds were 102 pounds.
Therefore:
n + p = 102 ............> equation I
Therefore:
p = 102-n ..............> equation II
For almonds:
1 pound of almonds costs $1, therefore:
p pounds of almonds would cost 1*p = $p
For <span>macadamia:
</span>1 pound of <span>macadamia costs $5.93, therefore:
n pounds of </span><span>macadamia would cost 5.93*n = $5.93n
The total amount paid for both types was </span><span>$452.03, therefore:
$p + $5.93n = </span><span>$452.03 ............> equation III
Substitute with equation II in equation III:
102-n+5.93n = 452.03
4.93n = 350.03
n = 71 pounds
Substitute with the value of n in equation 1 to get p as follows:
n+p = 102
p = 102-n = 102-71 = 31 pounds
Total cost of almonds = $p = $31
Total cost of macadamia = $5.93n = 5.93(71) = $421.03
Therefore, based on the above calculations:
number of pounds of almonds = 31 pounds
cost of almonds = $31
number of pounds of macadamia = 71 pounds
cost of macadamia = </span>$421.03
Answer:
A) -2 - i√3 , -2 + i√3
Step-by-step explanation:
Solve using quadratic formula
x² + 4x + 7 = 0
The Almighty Formula
= -b ± √b² - 4ac/2a
Where ax + bx² + c = 0
From the above question
a = 1, b = 4, c= 7
Hence,
-4 ± √4² - 4 × 1 × 7/2 × 1
-4 ± √16 - 28/2
=( -4 ± √-12)/2
Since
b² - 4ac < 0
We have two complex roots
Simplifying
( -4 ± √-12)/2
= -4/2 ± √-12/2
= -2 ± 2√3i/2
= -2 ± √3i
Therefore,
-2 - √3i , -2 + √3i
or
-2 - i√3 , -2 + i√3
Option A , is the correct answer
Answer:
x=1/2
Step-by-step explanation:
