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3 years ago

Inez has 20 coins consisting of dimes and quarters. How many of each type does she have if all together she has $4.10

1 answer:

6 0

X = # dimes
y = # quarters

x+y = 20 so x = 20 - y
0.1x + 0.25y = 4.1

substitute x = 20 - y into 0.1x + 0.25y = 4.1

0.1x + 0.25y = 4.1
0.1(20 - y) + 0.25y = 4.1
2 - 0.1y + 0.25y = 4.1
0.15y = 2.1
y = 2.1 / 0.15
y = 14

x = 20 - 14 = 6

answer
Dimes: 6 coins
Quarters: 14 coins

Double check
6 + 14 = 20 coins total
6(0.1) + 14(0.25) = 0.6 + 3.5 = $4.10

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Sophia‘s favorite homemade cookie recipe requires one cup of chocolate chips for 10 servings if the number of cups required for

weqwewe [10]

Answer:

3 cups

Step-by-step explanation:

We can use a proportion to find how many cups of chocolate chips she needs for 30 servings. Assuming c = cups of chocolate chips and b = batches

$\frac{c}{b}$

$\frac{1}{10} = \frac{c}{30}$

We can now multiply the diagonal values that don't include the missing variable (30 and 1) and then divide it by the value that is diagonal to the variable (10)

$30 \cdot 1 = 30\\30 \div 10 = 3$

Therefore, she needs 3 cups of chocolate chips to make 30 servings.

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3 years ago

Read 2 more answers

Solve for x in equation x-c/2=d

lana66690 [7]

X-c/2 = d
Multiply by 2 on both sides. Leaves us with:
x-c = 2d
Add 2 to both sides. Leaves us with:
x = 2d + c
Unless you have values to substitute into the variables, this is your answer:
x = 2d + c

4 0

3 years ago

What is the 9th term of the geometric sequence 4, −20, 100, …?

sveta [45]

First, we are going to find the common ratio of our geometric sequence using the formula: $r= \frac{a_{n}}{a_{n-1}}$ . For our sequence, we can infer that $a_{n}=-20$ and $a_{n-1}=4$ . So lets replace those values in our formula:
$r= \frac{-20}{4}$
$r=-5$

Now that we have the common ratio, lets find the explicit formula of our sequence. To do that we are going to use the formula: $a_{n}=a_{1}*r^{n-1}$ . We know that $a_{1}=4$ ; we also know for our previous calculation that $r=-5$ . So lets replace those values in our formula:
$a_{n}=4*(-5)^{n-1}$

Finally, to find the 9th therm in our sequence, we just need to replace $n$ with 9 in our explicit formula:
$a_{9}=4*(-5)^{9-1}$
$a_{9}=4*(-5)^{8}$
$a_{9}=1562500$

We can conclude that the 9th term in our geometric sequence is 1,562,500

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2 years ago

What does it mean by type of angles and relationship between the angles if the line are parallel ?

valkas [14]

Where two lines cross, four (4) angles are formed. Two adjacent angles that share a vertex can be called a "linear pair." Two non-adjacent angles that have the same vertex and the same lines for sides, are called "vertical angles."

Where a transversal crosses two parallel lines, eight (8) angles are formed, four (4) at each intersection. In addition to the above angle types, there are other relationships that can be described.

Angles can be called corresponding, if they are in the same location relative to the intersection point (both on the north-east corner, for example). Angles are interior if they are between the parallel lines; exterior of they are not. They get the additional descriptor of opposite, if they are on opposite sides of the transversal.

If the angles are not opposite, and share a side but not a vertex, they can be called adjacent. (Only interior angles can be adjacent, one pair on either side of the transversal.)

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With the above definitions in mind, several relationships arise where a transversal crosses parallel lines. (Types of angles are italicized.) Two examples of each type are listed by angle numbers. Angles 1 and 2 are a linear pair, for example.

Angles of a linear pair are supplementary. (1, 2), (5, 7)

Vertical angles are congruent. (1, 4), (6, 7)

Adjacent angles are supplementary. (3, 5), (4, 6)

Corresponding angles are congruent. (1, 5), (4, 8)

Opposite interior angles are congruent. (3, 6), (4, 5)

Opposite exterior angles are congruent. (1, 8), (2, 7)

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3 years ago

a jeweler makes a necklace using red and blue beads. The jeweler has 24 red beads and 36 blue beads. What is the greatest number

aleksley [76]

Answer:

Step-by-step explanation:

24+36

20+30=50

4+6=10

50+10=60

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2 years ago