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kirill [66]
3 years ago
9

Peggy had three times as many quarters as nickels. She had $1.60 in all. How many nickels and how many quarters did she have? Wh

ich of the following equations could be used to solve the problem?
Mathematics
1 answer:
svlad2 [7]3 years ago
3 0
Let q and n represent the number of quarters and nickels respectively.

q=3n and .05n+.25q=1.6  These are the conditions in mathematical terms.

To solve, use the value of q from the first equation in the second equation to get:

.05n+.25(3n)=1.6  carry out indicated multiplication on left side

.05n+.75n=1.6  combine like terms on left side

.8n=1.6  divide both sides by .8

n=2, since q=3n

q=6

So Peggy had 2 nickels and 6 quarters.
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A bag contains 14 green, 12 orange and 19 purple tennis balls.
Nataliya [291]

Answer:

See explanation

Step-by-step explanation:

There are 14 green, 12 orange and 19 purple tennis balls in the bag,

14+12+19=45 balls in total.

A. The propbabilities that

a randomly chosen ball from the bag is green =\dfrac{14}{45};

a randomly chosen ball from the bag is orange =\dfrac{12}{45}=\dfrac{4}{15};

a randomly chosen ball from the bag is purple =\dfrac{19}{45}.

A probability model for choosing a tennis ball from the bag is

\begin{array}{lccc}\text{Ball}&\text{Green}&\text{Orange}&\text{Purple}\\ \\\text{Probability}&\dfrac{14}{45}&\dfrac{4}{15}&\dfrac{19}{45}\end{array}

B. Suppose a tennis ball is randomly selected and then replaced 75 times. You can expect that orange ball appear

\dfrac{4}{15}\times 75=4\times 5=20 times

5 0
2 years ago
Graph the hyperbola using the transverse axis, vertices, and co-vertices:
Reptile [31]

See attachment for the graph of the hyperbola 12x^2 - 3y^2 - 108 = 0

<h3>How to graph the hyperbola?</h3>

The equation of the hyperbola is given as:

12x^2 - 3y^2 - 108 = 0

Start by calculating the transverse axis

So, we have:

<u>Transverse axis</u>

The vertices of the given hyperbola are (0, 0)

This means that

(h, k) = 0

Where

a = 3 and b = 6

The transverse axis is calculated as:

y = ±b/a(x - h) + k

So, we have:

y = ±6/3(x - 0) + 0

Evaluate the difference and sum

y = ±6/3x

Evaluate the quotient

y = ±2x

This means that the transverse axes are y = 2x and y =-2x

<u>The vertices</u>

In the above section, we have:

The vertices of the given hyperbola are (0, 0)

This means that

(h, k) = 0

<u>The co-vertices</u>

In the above section, we have:

The vertices of the given hyperbola are (0, 0)

This means that

(h, k) = 0

And

a = 3 and b = 6

The co-vertices are

(h - a, k) and (h + a, k)

So, we have:

(0 - 3, 0) and (0 + 3, 0)

Evaluate

(-3,0) and (3, 0)

See attachment for the graph of the hyperbola

Read more about hyperbola at:

brainly.com/question/26250569

#SPJ1

4 0
1 year ago
The function f(x) is represented by this table of values.
Darya [45]
The average slope (s) on the interval [a, b] is given by
  s = (f(b) -f(a))/(b -a)

When there are a lot of computations to do, it is convenient to let a machine do them. The intervals and slopes are ...
  [0, 5] : 5
  [-3, 3] : 0
  [-5, 3] : -2
  [-3, 5] : 2

6 0
3 years ago
3. Find the measure of side DF. See image below.
ad-work [718]

Answer:

d. 5.25

Step-by-step explanation:

make it into two fractions: 6/8 = x/7

solve for x by cross multiplying.

4 0
3 years ago
Please help me with this problem it is for my Geometry class.
makkiz [27]
9/7 or 1 2/7 is the answer. im pretty sure its right.
4 0
3 years ago
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