Sure, let's solve each of the given proportions step-by-step.
Problem 43: [tex]\(\frac{4}{5}=\frac{h}{35}\)[/tex]
To solve for [tex]\(h\)[/tex], use cross-multiplication:
[tex]\[ 4 \times 35 = 5 \times h \][/tex]
[tex]\[ 140 = 5h \][/tex]
[tex]\[ h = \frac{140}{5} \][/tex]
[tex]\[ h = 28 \][/tex]
So, [tex]\(h = 28\)[/tex].
Problem 44: [tex]\(\frac{7}{m}=\frac{21}{30}\)[/tex]
To solve for [tex]\(m\)[/tex], use cross-multiplication:
[tex]\[ 7 \times 30 = 21 \times m \][/tex]
[tex]\[ 210 = 21m \][/tex]
[tex]\[ m = \frac{210}{21} \][/tex]
[tex]\[ m = 10 \][/tex]
So, [tex]\(m = 10\)[/tex].
Problem 45: [tex]\(\frac{n}{2}=\frac{5}{4}\)[/tex]
To solve for [tex]\(n\)[/tex], use cross-multiplication:
[tex]\[ n \times 4 = 5 \times 2 \][/tex]
[tex]\[ 4n = 10 \][/tex]
[tex]\[ n = \frac{10}{4} \][/tex]
[tex]\[ n = 2.5 \][/tex]
So, [tex]\(n = 2.5\)[/tex].
Problem 46: [tex]\(\frac{2}{7}=\frac{5}{7}\)[/tex]
Here, we need to check if the two ratios are equal:
[tex]\[ \frac{2}{7} \neq \frac{5}{7} \][/tex]
The statement [tex]\( \frac{2}{7} = \frac{5}{7} \)[/tex] is false.
So, the proportion is not valid for Problem 46.
In summary:
1. [tex]\(h = 28\)[/tex]
2. [tex]\(m = 10\)[/tex]
3. [tex]\(n = 2.5\)[/tex]
4. The proportion [tex]\(\frac{2}{7}=\frac{5}{7}\)[/tex] is false.
