To factor <span>54x+81 using the greatest common factor, find the GCF of 54 and 81 by listing all factors and finding the biggest.
54 - 1, 2, 3, 6, 9, 18, 27, 54
81 - 1, 3, 9, 17, 81
9 is the gcf, so factor it out.
</span><span>54x+81 = <u>9</u>(6x + 9)</span><span>
</span>
Answer:
<u>Option A. 11.15 in³ </u>
Step-by-step explanation:
The question is as following:
A snow cone is a tasty treat with flavored ice and a spherical bubble gum ball at the bottom. The radius of the cone is 1.75 inches, and its height is 3.5 inches. If the diameter of the bubble gum ball is 0.5 inches, what is the closest approximation of the volume of the cone that can be filled with flavored ice?
A.) 11.15 in³
B.) 11.22 in³
C.) 0.07 in³
D.) 33.67 in³
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<u>Solution:</u>
Volume of the cone = π r² h/3
Vcone = 3.14 * (1.75in)² * 3.5in/3
Vcone = 3.14 * 3.0625 in² * 1.167
Vcone = 11.22 in³
Volume of the gum ball = 4/3 * π * r³
Vball = 4/3 * 3.14 * (0.5in/2)³
Vball = 4/3 * 3.14 * (0.25in)³
Vball = 4/3 * 3.14 * 0.015625 in³
Vball = 0.065 in³
11.22 in³ - 0.065 in³ = 11.155 in³
<u>The answer is option A. 11.15 in³ </u>
Answer:
5
Step-by-step explanation:
x^2-7x=30
x^2-7x-30=0
a = 1, b = -7, c = -30
sqrt(b^2-4ac)
sqrt(49+120)
sqrt(169)
13
-b +/- 13
7 + 13 = 20
7 - 13 = -6
2a = 2
20/2 = 10
-6/2 = -3
we know x>0, so it cant be -3. so now its just 10 - 5
Answer:
17.6 m²
Step-by-step explanation:
Given the ratio of similar shapes = a : b, then
area of shapes = a ² : b²
Δ PTQ and Δ PRS are similar and so the ratio of corresponding sides are equal, that is
PT : PR = 6 : 9 = 2 : 3, thus
ratio of areas = 2² : 3² = 4 : 9
let the area of Δ PQT be x, then using proportion
= ( cross- multiply )
9x = 4(x + 22) ← distribute
9x = 4x + 88 ( subtract 4x from both sides )
5x = 88 ( divide both sides by 5 )
x = 17.6
Thus area of Δ PQT = 17.6 m²
Answer:
C = 36 pi or approximately 113.04
Step-by-step explanation:
The circumference of a circle is given by
C = 2*pi*r
C = 2*pi*18
C = 36 pi
We can approximate pi by 3.14
C = 36*3.14
C =113.04