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olganol [36]
3 years ago
14

A total of 22 dimes and nickels have a value of $1.90. If d represents the number of dimes and n represents the number of nickel

s, which system of equations models this situation?
theres an image

Mathematics
1 answer:
Eva8 [605]3 years ago
7 0

Answer:

d + n = 22 and 0.1d + 0.05n = 1.9

Step-by-step explanation:

Let d represents the number of dimes and n represents the number of nickel.

Total of dimes and nickels = 22

Therefore, d + n = 22

1 dime = 10 cents = 0.1

1 nickel = 5 cents = 0.05

Value of 22 dimes and nickel = $1.90

So, 0.1d + 0.05n = 1.9

Hence, d + n = 22 and 0.1d + 0.05n = 1.9 models the given situation.

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1. Assume O P || NM.
ipn [44]

1. Assuming OP || NM, considering the triangle proportionality theorem possible measurements for the segments are: ON = 3 units, LO = 1 unit, PM = 6 units, LP = 2 units

2. The possible values are decided by assuming  \frac{ON}{LO} = \frac{PM}{LP} = 3 using the triangle proportionality theorem.

3. Another method is applying the AA Similarity Theorem to compare corresponding side lengths of the triangles that are proportional to each other.

<h3>What is the Triangle Proportionality Theorem?</h3>

Triangle proportionality theorem states that if a line is parallel to one of the sides of a triangle intersects two of the other two sides, it divides the two sides into proportional corresponding segments.

1. Assuming that OP || NM, we would apply the triangle proportionality theorem to have the following ratio:

\frac{ON}{LO} = \frac{PM}{LP}

Using the above ratio, we can choose the following possible lengths for the segments:

ON = 3 units

LO = 1 unit

PM = 6 units

LP = 2 units

2. The values are decided assuming that the ratio, \frac{ON}{LO} = \frac{PM}{LP} = 3

This means that the ratio of the proportional segments, irrespective of the their measurement should give you an assumed equal ratio of 3:1.

Therefore, since:

\frac{3}{1} = 3\\\\\frac{6}{2} = 3

The measurements, ON = 3 units, LO = 1 unit, PM = 6 units, LP = 2 units are therefore possible measurements.

3. Using the AA Similarity Theorem to prove that ΔLPO ≅ ΔLMN, the corresponding sides of both triangles will be proportional.

LP/LM = LO/LN = PO/MN

We can use this to choose possible measurements while assuming a ratio between the proportional sides of both triangles.

Let's assume that: LP/LM = LO/LN = PO/MN = 1/4

Let,

LO = 1 unit

LN = 4 units

Therefore, ON = LN - LO = 4 - 1 = 3 units.

Same way the other possible measures can be gotten provided a ratio is assumed.

Learn more about triangle proportionality theorem on:

brainly.com/question/24804474

4 0
3 years ago
What is the name of this chord
Anon25 [30]
Link provided in other answer is a SCAM !!! Don’t click on it.
6 0
3 years ago
Is y= -9/5x + 1/5 perpendicular to y= 5/9x + 2/9
Lana71 [14]

The given lines are perpendicular to each other.

Further explanation:

Given lines are:

Line 1: y= -9/5x + 1/5

Line 2:  y= 5/9x + 2/9

As the lines are in slope=intercept form, the co-efficient of x are their slopes

Let m1 be the slope of line 1 and m2 be the slope of line 2

Then

m_1=-\frac{9}{5}\\m_2=\frac{5}{9}\\m_1.m_2=-\frac{9}{5}*\frac{5}{9}\\m_1.m_2=-1

As we can see that the product of slopes of both lines is -1. The product of slopes of perpendicular lines is -1.

The given lines are perpendicular to each other.

Keywords: Slope, slope-intercept form

Learn more about equation of lines at:

  • brainly.com/question/4703807
  • brainly.com/question/4710621

#LearnwithBrainly

7 0
3 years ago
Please help will get branliest if right
zaharov [31]

Answer:

A

Step-by-step explanation:

\dfrac{1}{3}+\dfrac{3}{5}+\dfrac{2}{3}= \left[ \dfrac{1}{3}+\dfrac{2}{3} \right]+\dfrac{3}{5}\\\\\\=\dfrac{3}{3}+\dfrac{3}{5}\\\\\\=1+\dfrac{3}{5}\\\\\\=\dfrac{5}{5}+\dfrac{3}{5}\\\\\\=\dfrac{8}{5}\\\\\\=1\dfrac{3}{5}

7 0
3 years ago
Read 2 more answers
What is the slope intercept form in equation form or this graph?
Snowcat [4.5K]
Y=2x+0
the y intercept is 0 and the slope is 2/1
6 0
3 years ago
Read 2 more answers
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