To solve the given problems, let's break it down step-by-step.
### 1. Find the value of the letter that makes these equations true
a) [tex]\(13 + 16 = 29\)[/tex]
This equation is true. The sum of 13 and 16 is indeed 29.
b) [tex]\(17 + 1 = -2\)[/tex]
This equation is false. The sum of 17 and 1 is not -2.
c) [tex]\(m - 8 = (1, d)\)[/tex]
This equation is unclear and appears to be missing information. It cannot be verified as is.
1) [tex]\(+14 = -1\)[/tex]
This equation is false. The value 14 does not equal -1.
### 2. Solve these equations
a) [tex]\(2t = -18\)[/tex]
To solve for [tex]\(t\)[/tex], divide both sides by 2:
[tex]\[ t = \frac{-18}{2} = -9.0 \][/tex]
b) [tex]\(\frac{m}{12} = -2\)[/tex]
To solve for [tex]\(m\)[/tex], multiply both sides by 12:
[tex]\[ m = -2 \times 12 = -24 \][/tex]
c) [tex]\(48 = -6b\)[/tex]
To solve for [tex]\(b\)[/tex], divide both sides by -6:
[tex]\[ b = \frac{48}{-6} = -8.0 \][/tex]
(1) [tex]\(\frac{1}{4} = 15\)[/tex]
This equation is false. The fraction [tex]\(\frac{1}{4}\)[/tex] does not equal 15.
### 3. Write an equation for each of these problems and solve for the unknown number
a) When I add 2 to the cube of a number, the answer is 10.
Let [tex]\(x\)[/tex] be the unknown number. We can write the equation:
[tex]\[ x^3 + 2 = 10 \][/tex]
To solve for [tex]\(x\)[/tex], subtract 2 from both sides and take the cube root:
[tex]\[ x^3 = 10 - 2 \][/tex]
[tex]\[ x^3 = 8 \][/tex]
[tex]\[ x = \sqrt[3]{8} = 2.0 \][/tex]
b) If I subtract 98 from a number, I get 12.
Let [tex]\(y\)[/tex] be the unknown number. We can write the equation:
[tex]\[ y - 98 = 12 \][/tex]
To solve for [tex]\(y\)[/tex], add 98 to both sides:
[tex]\[ y = 12 + 98 = 110 \][/tex]
c) Multiply the square of a positive number by 2 and the answer is 72.
Let [tex]\(z\)[/tex] be the unknown number. We can write the equation:
[tex]\[ 2z^2 = 72 \][/tex]
To solve for [tex]\(z\)[/tex], divide both sides by 2 and take the square root:
[tex]\[ z^2 = \frac{72}{2} \][/tex]
[tex]\[ z^2 = 36 \][/tex]
[tex]\[ z = \sqrt{36} = 6.0 \][/tex]
So, the values are:
- [tex]\(t = -9.0\)[/tex]
- [tex]\(m = -24\)[/tex]
- [tex]\(b = -8.0\)[/tex]
- [tex]\(x = 2.0\)[/tex]
- [tex]\(y = 110\)[/tex]
- [tex]\(z = 6.0\)[/tex]
