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Veronika [31]
3 years ago
11

X-5y= -40 18x - 5y = 45 What is the answer to this

Mathematics
1 answer:
baherus [9]3 years ago
4 0

Answer:

(5, 9)

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right

Equality Properties

  • Multiplication Property of Equality
  • Division Property of Equality
  • Addition Property of Equality
  • Subtract Property of Equality

<u>Algebra I</u>

  • Solving systems of equations using substitution/elimination

Step-by-step explanation:

<u>Step 1: Define Systems</u>

x - 5y = -40

18x - 5y = 45

<u>Step 2: Rewrite Systems</u>

18x - 5y = 45

  1. Multiply both sides by -1:                     -18x + 5y = -45

<u>Step 3: Redefine Systems</u>

x - 5y = -40

-18x + 5y = -45

<u>Step 4: Solve for </u><em><u>x</u></em>

<em>Elimination</em>

  1. Combine equations:                    -17x = -85
  2. Divide -17 on both sides:             x = 5

<u>Step 5: Solve for </u><em><u>y</u></em>

  1. Define equation:                    x - 5y = -40
  2. Substitute in <em>x</em>:                       5 - 5y = -40
  3. Isolate <em>y</em> term:                        -5y = -45
  4. Isolate <em>y</em>:                                 y = 9
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How do I solve proportions? Here’s my questions: <br><br> 1. x/8=5/16<br> 2. 5/12=15/x
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Proportions are very simple once you get the hang of them! What you do is cross multiple. :)

1. x/8=5/16

You first start by multiplying x and 16

Then multiply 5 and 8

So now you have 16x=40

Finally divide 16 from each side

You get: x+0.4!

2. 5/12=15/x

Remember to cross-multiply!

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A Venn diagram is shown below: What are the elements of (A n B) ‘ ?
vesna_86 [32]

The elements of (A n B)' are ( 3, 4 , 5 ,6). Option A

<h3>How to determine the set</h3>

The elements of this set (A n B) explains the common elements  of both sets without repetition

Set A = 3, 4

Set B = 5, 6

A n B = 1, 2

(A n B)' = Is the elements both A and B in common but is not found in the universal set

(A n B)'  = ( 3, 4 , 5 ,6)

Thus, the elements of (A n B)' are ( 3, 4 , 5 ,6). Option A

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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,

so

\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,

so

\dfrac{BN}{CN}=\dfrac{\frac{3}{8}BC}{\frac{5}{8}BC}=\dfrac{3}{5}

4 0
3 years ago
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