Answer:
1.) k = 5
2.) n = -20
3.) p = -13
4.) m = -450
5.) b = -38
6.) n = -24
7.) x = 21
8.) x = 12
9.) b = -2
10.) b = 5
Step-by-step explanation:
To solve all equations, do the reciprocal, or opposite of what is being done. For example, if a number and a variable are being multiplied, you would divide by the number to solve.
1.) 55 = 11k
(11 and k are being multiplied, so you would divide)
Divide by 11 on both sides:
55 = 11k
/11 /11
5 = k
2.) Add 15 on both sides:
n - 15 = -35
+15 +15
n = -20
3.) Divide by -6 on both sides:
78 = -6p
/-6 /-6
-13 = p
4.) Multiply by 18 on both sides:
m/18 = -25
18(m/18) = (-25)18
m = -450
5.) Add 20 on both sides:
18 = -20 - b
+20 +20
38 = -b
Divide by -1 on both sides:
38 = -b
/-1 /-1
-38 = b
6.) Subtract 12 on both sides:
12 + n/4 = 6
-12 -12
n/4 = -6
Multiply by 4 on both sides:
4(n/4) = (-6)4
n = -24
7.) Multiply by 2 on both sides:
2(-7 + x/2) = (7)2
-7 + x = 14
Add 7 on both sides:
-7 + x = 14
+7 +7
x = 21
8.) Subtract 2 on both sides:
-4x + 2 = -22
-2 -2
-4x = -24
Divide by -4 on both sides:
-4x = -24
/-4 /-4
x = 12
9.) Add 9 on both sides:
7 = -8b - 9
+9 +9
16 = -8b
Divide by -8 on both sides:
16 = -8b
/-8 /-8
-2 = b
10.) Multiply by -3 on both sides:
-3(b - 14/-3) = (3)-3
b - 14 = -9
Add 14 on both sides:
b - 14 = -9
+14 +14
b = 5
To efficiently double the volume of a square pyramid, you need to double the height of the pyramid.
<span>V = (1/3)Ah where A is the area of the base. If you double the height and leave A unchanged, the volume will also be doubled (replace h with 2h in the formula).</span>
Let Joy be x years old
<span>Joy's brother's age is 3 years older than twice joy's age.
</span>Joy's Brother = 2x + 3
<span>The sum of Joy's age and her brother's age is 24.
x + 2x + 3 = 24
3x + 3 = 24
3x = 24 - 3
3x = 21
x = 21 </span>÷ 3
x = 7
Joy:
x = 7
Brother:
2x + 3 = 2(7) + 3 = 17
Difference in their age = 17 - 7 = 10 years
They are 10 years apart.
Answer:
37
Step-by-step explanation:
Right Scalene Triangle
Side a = 37
Side b = 12
Side c = 35
Angle ∠A = 90° = 1.5708 rad = π/2
Angle ∠B = 18.925° = 18°55'29" = 0.3303 rad
Angle ∠C = 71.075° = 71°4'31" = 1.2405 rad
C=71.075°B=18.925°A=90°b=12a=37c=35
Area = 210
Perimeter p = 84
Semiperimeter s = 42
Height ha = 11.35135
Height hb = 35
Height hc = 12
Median ma = 18.5
Median mb = 35.51056
Median mc = 21.2191
Inradius r = 5
Circumradius R = 18.5
Vertex coordinates: A[0, 0] B[35, 0] C[0, 12]
Centroid: [11.66667, 4]
Inscribed Circle Center: [5, 5]
Circumscribed Circle Center: [17.5, 6]
Answer:
1.6238 × 10^8
Step-by-step explanation:
