Pose two problems of everyday life where addition, subtraction, multiplication and division of integers are used

Mathematics

1 answer:

qaws [65]3 years ago

8 0

Answer:

taxes and at work

Step-by-step explanation:

you deal with money at work and you have to calculate numbers doing taxes.

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Solveeee both i neeeeeedddd hellllpppp

SCORPION-xisa [38]

Short answer: C
Remark
Since b is all by itself in equation 2, Substitute it into equation 1.

2a + 3b = 5
b = a - 5 Put this result in equation 1. Be sure and use brackets.
2a + 3(a - 5) = 5 Remove the brackets.
2a + 3a - 15 = 5 Notice the -5 inside the brackets becomes - 15
Combine like terms on the left.
5a - 15 = 5 Add 15 to both sides
5a = 5 + 15
5a = 20 Divide by 5
a = 20/5
a = 4

So far, c is the only possible answer.
b = a - 5
b = 4 - 5
b = - 1

5 0

3 years ago

In the trapezoid ABCD (AB∥CD) point M∈AD, so that AM:MD=3:5. Line L ∥AB and going through point M intersects diagonal AC and leg

siniylev [52]

Answer:

$\dfrac{AP}{PC}=\dfrac{3}{5}$

$\dfrac{BN}{CN}=\dfrac{3}{5}$

Step-by-step explanation:

Consider triangles AMP and ADC. In these triangles,

angle A is the common angle, so $\angle MAP\cong \angle DAC$ by reflexive property;
angles AMP and ADC are congruent as corresponding angles when two parallel lines MP and CD are cut by transversal AD.

Hence, triangles AMP and ADC are similar by AA similarity theorem.

Similar triangles have proportional corresponding sides, thus

$\dfrac{AM}{AD}=\dfrac{AP}{AC}\\ \\\dfrac{3x}{3x+5x}=\dfrac{AP}{AC}\\ \\\dfrac{AP}{AC}=\dfrac{3}{8}\Rightarrow AP=\dfrac{3}{8}AC\\ \\PC=AC-AP=AC-\dfrac{3}{8}AC=\dfrac{5}{8}AC,$

$\dfrac{AP}{PC}=\dfrac{\frac{3}{8}AC}{\frac{5}{8}AC}=\dfrac{3}{5}$

Consider triangles ACB and PCN. In these triangles,

angle C is the common angle, so $\angle ACB\cong \angle PCN$ by reflexive property;
angles ABC and PCN are congruent as corresponding angles when two parallel lines PN and AB are cut by transversal BC.

Hence, triangles ACB and PCN are similar by AA similarity theorem.

Similar triangles have proportional corresponding sides, thus

$\dfrac{CP}{AP}=\dfrac{CN}{CB}\\ \\\dfrac{5x}{3x+5x}=\dfrac{CN}{CB}\\ \\\dfrac{CN}{CB}=\dfrac{5}{8}\Rightarrow CN=\dfrac{5}{8}CB\\ \\BN=BC-CN=BC-\dfrac{5}{8}BC=\dfrac{3}{8}BC,$