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[tex]\\ \sf\Rrightarrow 2\dfrac{1}{4}-\dfrac{3}{8}[/tex]

[tex]\\ \sf\Rrightarrow \dfrac{9}{4}-\dfrac{3}{8}[/tex]

[tex]\\ \sf\Rrightarrow \dfrac{18-3}{8}[/tex]

[tex]\\ \sf\Rrightarrow \dfrac{15}{8}[/tex]

[tex]\\ \sf\Rrightarrow 1\dfrac{7}{8}[/tex]

Answer:

[tex]\textsf{D)} \quad 1 \dfrac{7}{8}[/tex]

Step-by-step explanation:

Subtract the used volume of punch from the starting volume of punch.

Convert the mixed number to an improper fraction:

[tex]\begin{aligned} \implies 2\frac{1}{4}-\frac{3}{8} & = \dfrac{2 \times 4+1}{4}-\dfrac{3}{8}\\\\ & = \dfrac{9}{4}-\dfrac{3}{8}\end{aligned}[/tex]

Make the denominators of both fractions the same by multiplying the numerator and the denominator of 9/4 by 2:

[tex]\implies \dfrac{9 \times 2}{4 \times 2}-\dfrac{3}{8} = \dfrac{18}{8}-\dfrac{3}{8}[/tex]

[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{c}-\dfrac{b}{c}=\dfrac{a-b}{c}:[/tex]

[tex]\begin{aligned} \implies \dfrac{18}{8}-\dfrac{3}{8} & = \dfrac{18-3}{8}\\\\ & = \dfrac{15}{8}\end{aligned}[/tex]

Convert back into a mixed number:

[tex]\begin{aligned}\implies \dfrac{15}{8} & = \dfrac{8+7}{8}\\\\ & = \dfrac{8}{8}+\dfrac{7}{8}\\\\ & = 1\dfrac{7}{8}\end{aligned}[/tex]

Felicia is a long-distance runner. She is able to run the first 2 hours of a training run at a certain rate. The rate at which she runs after her first 2 hours decreases for the remainder of her training run. On Monday, Felicia runs x hours, where x≥2. The average rate at which Felicia runs for the entire training run is represented by 13+6(x−2)x. What is the meaning of the parts of this rational expression in the context of the situation? Select from the drop-down menus to correctly complete each statement.

Please help I really need help
(40 points)
Match each theorem with its description.
1.
If two angles form a pair of vertical angles, then they are congruent.
2.
The sum of the measures of the interior angles of a triangle is 180°.
3.
If two sides of a triangle are congruent, then the angles opposite those sides are congruent
4.
The midsegment of a triangle is parallel to the third side and its length is one-half the length of the third side.
5.
If two parallel lines are intersected by a transversal, then corresponding angles are congruent.
6.
If two parallel lines are intersected by a transversal, then alternate interior angles are congruent.
7.
If two parallel lines are intersected by a transversal, then the alternate exterior angles are congruent
8.
If two parallel lines are intersected by a transversal, then the same-side interior angles are supplementary.

Match

Triangle Sum Theorem

Alternate Exterior Angles Theorem

Alternate Interior Angles Theorem

Same-Side Interior Angles Theorem

Corresponding Angles Postulate

Isosceles Triangle Theorem

Vertical Angles Theorem

Triangle Midsegment Theorem

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​

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