Answer:
x = 1
General Formulas and Concepts:
<u>Pre-Algebra</u>
Distributive Property
Equality Properties
- Multiplication Property of Equality
- Division Property of Equality
- Addition Property of Equality
- Subtraction Property of Equality
<u>Algebra I</u>
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify</em>
1/2(8x - 4) = 2x
<u>Step 2: Solve for </u><em><u>x</u></em>
- [Distributive Property] Distribute 1/2: 4x - 2 = 2x
- [Subtraction Property of Equality] Subtract 2x on both sides: 2x - 2 = 0
- [Addition Property of Equality] Add 2 on both sides: 2x = 2
- [Division Property of Equality] Divide 2 on both sides: x = 1
Answer:
a) 301.6 cm³
b) 188.5 cm²
Step-by-step explanation:
The volume and lateral surface area of the cone can be found using the given dimensions with the given formulas. All that is needed is to substitute the appropriate values and do the arithmetic.
__
<h3>a) volume</h3>
The volume is given by the formula ...
V = 1/3πr²h
The dimensions are given on the diagram: r = 6 cm, h = 8 cm. Using these values in the formula, we find the volume to be ...
V = 1/3π(6 cm)²(8 cm) = 96π cm³ ≈ 301.6 cm³
The volume of the cone is about 301.6 cm³.
__
<h3>b) area</h3>
The lateral area of the cone is given by the formula ...
A = πrl
The dimensions are given on the diagram: r = 6 cm, l = 10 cm (the slant height). Using these values in the formula, we find the area to be ...
A = π(6 cm)(10 cm) = 60π cm² ≈ 188.5 cm²
The area of the curved surface is about 188.5 cm².
Answer:
A
Step-by-step explanation:
x=
−b±√b2−4ac
2a
x=
−(2)±√(2)2−4(2)(15)
2(2)
x=
−2±√−116
4
and there is really no solution
Answer:
7 are boys
Step-by-step explanation:
Make a system of equations where g is for girls and b is for boys.
b+g=26
g=3b-2
Substitute "3b-2" in for "g" in the first equation.
b+(3b-2)=26
Rewrite without the parentheses because it's addition and not multiplication.
b+3b-2=26
Combine like terms.
4b-2=26
Add 2 to both sides.
4b=28
Divide by the coefficient of the variable to get it alone.
b=7
Value of x is 11
Step-by-step explanation:
- Step 1: Find x when ΔABC ≅ ΔDEC.
When these two triangles are congruent, their corresponding angles and sides will be equal.
⇒ ∠B = ∠E
⇒ 44° = 4x
∴ x = 44/4 = 11
