A coin collector has 31 dimes and nickels with a total face value of $2.40. (They are actually worth a lot more.) How many of each coin does she have?

Answer:

9:15

Step-by-step explanation:

[tex]\frac{3*3}{5*3}=\frac{9}{15}=9:15[/tex]

Answer:

[tex]-\sqrt{15}[/tex]

Step-by-step explanation:

we know that

To put factor back into the square root, we have to put squared value

we have

[tex]-5\sqrt{0.6}[/tex]

Remember that

[tex]5=\sqrt{5^2}[/tex]

substitute in the expression above

[tex]-5\sqrt{0.6}=-\sqrt{(5^2)(0.6)}=-\sqrt{25*0.6}=-\sqrt{15}[/tex]

Answer:

Option C. 7.2 units

Step-by-step explanation:

we know that

triangle PAM is similar to triangle RAE by AA Similarity Theorem

Remember that

If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

so

[tex]\frac{PA}{RA}=\frac{AM}{AE}[/tex]

substitute the given values

[tex]\frac{20+x}{20}=\frac{25+9}{25}[/tex]

solve for x

[tex]\frac{20+x}{20}=\frac{34}{25}[/tex]

[tex]20+x=\frac{34}{25}(20)[/tex]

[tex]x=\frac{34}{25}(20)-20[/tex]

[tex]x=7.2\ units[/tex]

The value of 'x' is 7.2 units and this can be determined by using the properties of the triangle and also by using the arithmetic operations.

Given :

According to the given data, the side RE is parallel to side PM therefore it can be said that:

[tex]\rm \dfrac{PA}{RA}=\dfrac{MA}{EA}[/tex]

Now, substitute the values of PA, MA, RA, and EA in the above expression.

[tex]\rm \dfrac{x+20}{20}=\dfrac{9+25}{25}[/tex]

Cross multiply in the above equation.

[tex]25 \times (x + 20) = 20\times (34)[/tex]

25x + 500 = 680

Subtract 680 by 500 in the above equation.

25x = 180

DIvide 180 by 25 in the above equation.

x = 7.2

Therefore, the correct option is C).

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Answer:

Step-by-step explanation:

y=-2x+4

-5x+10y=5

A:Parallel

B:Perpendicular

C: Neither

Tell whether the lines for each pair of equations are parallel, perpendicular, or neither.

y=(-1/5)x+6

-2x+10y=5

A:Parallel

B:Perpendicular

C:Neither

Understanding parallel and perpendicular lines on the coordinate plane is essential in geometry. Here's how you can determine the relationships between lines in this context.
**Parallel Lines:**
Two lines are parallel if they are always the same distance apart (equidistant) and will never meet. In the coordinate plane, parallel lines can be identified by having the same slope.
To show that two lines are parallel, you must find that they have the same slope. For example, if you have two lines described by the equations:
1. \(y = m_1x + b_1\)
2. \(y = m_2x + b_2\)
If \(m_1 = m_2\), then these two lines are parallel.
**Perpendicular Lines:**
Two lines are perpendicular if they intersect at a right angle (90 degrees). On the coordinate plane, two non-vertical lines are perpendicular if the product of their slopes is -1. This means that the slope of one line is the negative reciprocal of the other.
To show that two lines are perpendicular, you would find that the slopes of the two lines multiplied together equal -1. For instance, if you have two lines defined by:
1. \(y = m_1x + b_1\)
2. \(y = m_2x + b_2\)
These lines are perpendicular if \(m_1 \cdot m_2 = -1\), which means \(m_1 = -\frac{1}{m_2}\) or \(m_2 = -\frac{1}{m_1}\).
**Example 1: Check if lines are parallel**
Suppose you are given two lines with equations:
1. \(y = 2x + 3\)
2. \(y = 2x - 4\)
Both lines have a slope of 2 (since the coefficient of \(x\) in both equations is 2). Since the slopes are equal, these lines are parallel.
**Example 2: Check if lines are perpendicular**
Imagine you are given two lines:
1. \(y = \frac{1}{3}x + 2\)
2. \(y = -3x + 1\)
To determine if they're perpendicular, find the product of the slopes: \(\frac{1}{3} \cdot -3 = -1\). Since the product is -1, these lines are perpendicular.
In summary, for parallel lines, check if the slopes are equal. For perpendicular lines, check if the product of the slopes is -1. Of course, these rules presume you're working with non-vertical lines, since vertical lines have undefined slopes and horizontal lines have a slope of 0. Vertical and horizontal lines are also perpendicular to each other.

Answer:

C

Step-by-step explanation:

The answer is D. You can't make an equation out of this!

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Answer:

Store A is the better buy.

Step-by-step explanation:

The first thing I did was to find a multiple that 3 and 5 share which is 15. Now, we can figure out how much each store charges for 15 oz. I put the numbers into fraction form to make it easier. 5/1.50 and 3/1.20. To get 5 to 15, I multiplied it by 3, so I also have to do that to 1.50. This leaves me with 4.50. Store A charges 4.50 for 15 oz. Next, we have to go over to the other fraction. To get 3 to 15, I multiplied it by 5. Whatever you do to the numerator, you have to do to the denominator, so you multiply 1.20 by 5. This gets you 6. Store B charges 6 dollars for 15oz, so store A has a better price. I hope this helps.

Triangle angles add to 180 degrees.

25+30=55 degrees, so x=180-55=125 degrees and y=180-x=55 degrees.

Answer:

x = 125

Step-by-step explanation:

y = 25 + 30    { exterior angle equals the sum of opposite interior angles }

y = 55

x + y =180   {   linear pair }

x + 55 = 180

x = 180 -55

x = 125

Answer:

The set has 256 subsets

Step-by-step explanation:

The set is [a,b,c,d,e,f,h,i]

Number of subset can be calculated from the formula

[tex] {2}^{n} [/tex]

where n is the number of element in the set

n=8

This implies that

[tex] {2}^{n} = {2}^{8} =256[/tex]

Two rules come in handy here:

So we have

[tex]

\dfrac{\sqrt[4]{6}}{\sqrt[5]{6}}=\dfrac{6^{\frac{1}{4}}}{6^{\frac{1}{5}}}=6^{1/4-1/5}=\boxed{6^{9/20}}

[/tex]

The answer is B.

Hope this helps.

Answer:

Pamela

Step-by-step explanation:

20*40=800

65*11=715

800>715

Answer:

2 times.

Step-by-step explanation:

Sarah eats squash every 4 days.

Therefore, if Sarah eats squash today then she will eat squash after 4 days, then after 8 days, then after 12 days and so on.

So, if Sarah eats squash today then Sarah eats squash on that day which is multiples of 4 days.  

Again, Sarah eats lima beans every 10 days.

Therefore, if Sarah eats lima beans today then she will eat lima beans after 10 days, then after20 days, then after 30 days and so on.

So, if Sarah eats lima beans today then Sarah eats lima beans on that day which are multiples of 10 days.  

Therefore, if she just eats squash and lima beans yesterday, then she will eat the same after common multiple days of 4 days and 10 days from yesterday.

Now, common multiples of 4 and 10 are 20, 40, 60, etc.

Hence, she will eat both squash and lima beans after yesterday on the 20th day and 40th day from yesterday i.e. twice within 50 days from yesterday. (Answer)

Answer:

x = -2 (multiplicity 2).

Step-by-step explanation:

3x^2+12x+12 = 0

3(x^2 + 4x + 4) = 0

3(x + 2)(x + 2) = 0

x = -2 (multiplicity 2).

2 roots - both equal.

Answer:

3(x+2) (x+2)

Step-by-step explanation:

Given 3x²+12x+12

We expand the equation

That is,

3x²+6x+6x+12

We add parentheses to factor out

(3x²+6x)+(6x+12)

3x(x+2)+6(x+2) > Taking out the

common factors.

(3x+6) (x+2)

= 3(x+2) (x+2)

Answer:

24.4 feet

Explanation:

Let x be the length of the wooden board as shown in the diagram.

Using trigonometry ratio, we can write

[tex] \cos(35)=\frac{20}{x}[/tex]

[tex] \implies0.819= \frac{20}{x} [/tex]

cross multiplying we get:

[tex]0.819 \times x = 20[/tex]

Diving through by 0.819, we obtain

[tex]x = 24.42[/tex]

To the nearest tenth, x=24.4 feet.

Answer:

yes it is!

Step-by-step explanation:

if you add 8+10=18

11+10+21

8+11=19

if the numbers do not repeat or add up to one of the numbers you've got as an option it is a right triangle.

Answer:

Step-by-step explanation:

-4x-8=8x+16

-8=12x+16

-24=12x

-2=x

x = -2

Answer:

He used 55% protein 500 pounds and 25% protein 1000 pounds

Step-by-step explanation:

x pounds of 55% contains x * 0.55 pounds of pure protein

y pounds of 25% contains x * 0.25 pounds of pure protein

1500 pounds of 35% contains 1500 * 0.35 = 525 pounds of pure protein

x + y = 1500  ... (1)

0.55 x + 0.25 y = 525   ...(2)

0.25 times both sides of (1)    

0.25 x + 0.25 y = 1500 * 0.25 = 375   ... (3)

(2) - (3)  0.3 x = 150  ....  divide 0.3 on both sides

x = 500

y = 1500 - 500 = 1000

Answer:

The answer to this question would be $10.31

Step-by-step explanation:

To answer this question, you would first need to add the first two numbers which are $2.15 and $5.08 which results in $7.23 and then you would need to add the last number to the amount which then gives you the answer as $10.31.

Answer:$10.31

Step-by-step explanation:

$2.15+ $5.08+ $3.08=$10.31

Answer:

OA there is not enough information

Step-by-step explanation:

only the angles are congruent in both squares

Answer:

OA there is not enough information to determine whether the squares are congruent.

Step-by-step explanation:

Answer:

5x9=45

9×5=45

3×15=45

So the third answer is the correct choice.

Step-by-step explanation:

The best thing you can do with these types of problems is work out each multiplication fact untill you see which ones equal the number you are looking for.

The store manager wants to display 45 cans of soup in an array. The three possible ways to display the cans are 1 X 9, 9 X 5, and 3 X 15.

The store manager wants to display 45 cans of soup in an array. An array is a rectangular arrangement of objects. There are three possible ways the cans could be displayed: 1 X 9, 9 X 5, and 3 X 15.

For example, if the cans are displayed in a 1 X 9 array, there would be 1 row and 9 columns, making a total of 9 cans.

The other two options can be understood in a similar way, with the number before 'X' representing the number of rows and the number after 'X' representing the number of columns.

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Answer:

75 grams

Step-by-step explanation:

Crossmultiply to find x (grams of cereal)

12/100 = 9/x

x(12) = (100)(9)

x12 = 900

x = 75

The 75 grams of tasty oats cereal will give you 9 grams of protein.

Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.

We are given that there are 12 grams of protein in 100 grams of cereal .

Let x be the grams of cereal.

Therefore, 12/100 = 9/x

Now Crossmultiply to find x (grams of cereal);

x(12) = (100)(9)

x12 = 900

x = 75

The 75 grams of tasty oats cereal will give you 9 grams of protein.

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Answer:

The greatest number of pairs of skis and snowboards the group can rent are 21 pairs of skis and 9 pairs of snowboards.

Step-by-step explanation:

Given:

A group can rent pairs of skis and snowboards by the week. They get a reduced rate if they rent 7 pairs of skis for every 3 snowboards rented. The reduced ski rate is $45.50 per pair of skis per week, and the reduced snowboard rate is $110 per snowboard per week.

The sales tax on each rental is 16%.

The group has $2,500 available to spend on ski and snowboard rentals.

If the ratio of pairs of skis to snowboards is 7:3.

Now, to find the greatest number of pairs of skis and snowboards rentals.

So, the rent of 7 pairs of skis = [tex]7\times 45.50=\$318.50.[/tex]

And the rent of 3 pairs of snowboards = [tex]3\times 110=\$330.[/tex]

So, total rental amount of 7 pairs of skis and 3 pairs of snowboards:

[tex]318.50 + 330 = 648.50.[/tex]

Now, to get the rental amount after sales tax:

648.50 + 16% of $648.50.

[tex]=648.50 +\frac{16}{100}\times 648.50.[/tex]

[tex]=648.50+103.76[/tex]

[tex]=\$752.26.[/tex]

The total rental amount after sales tax = $752.26.

As the group has available $2,500.

So, the sets according to the given ratio:

[tex]2500\div 752.26 = 3.32.[/tex]

[tex]=3\ sets.[/tex]

Thus, there are 3 sets of the ratio 7:3.

So, the rental price according to sets are:

The rent of Skis:

[tex]7\times 3 = 21[/tex] 

[tex]21\times 45.50= 955.50[/tex]

The rent of snowboards:

[tex]3\times 3 = 9[/tex]

[tex]9\times 110 = 990[/tex]

So. the total rental amount of skis and snowboards according to sets are:

[tex]955.50 + 990 = 1,945.50[/tex]

Now, the amount of rent after sales tax:

$1945.50 + 16% of $1945.50.

[tex]=1945.50+\frac{16}{100}\times 1945.50[/tex]

[tex]=1945.50+311.28=\$2256.78.[/tex]

Thus, the total cost = $2256.78.

Now, to get the greatest number of pairs of skis to snowboards that can be rent:

[tex]2,500 - 2,256.78 = 243.22[/tex]

The cost of 21 pair of skis and 9 pairs of snowboards is $2256.78 and the group has available only $2500 to spend.

Thus, they can rent only 21 pairs of skis and 9 pairs of snowboards.

Therefore, the greatest number of pairs of skis and snowboards the group can rent are 21 pairs of skis and 9 pairs of snowboards.

Area of sector is 17.584 meters

Solution:

Given that we have to find the approximate area of a sector given O= 56 degrees with a diameter of 12m

Diameter = 12 m

Radius = Diameter / 2 = 6 m

An angle of  56 degrees is the fraction [tex]\frac{56}{360}[/tex] of the whole rotation

A sector of a circle with a sector angle of 56 degrees is therefore also the fraction [tex]\frac{56}{360}[/tex] of the circle

The area of the sector will therefore also be  [tex]\frac{56}{360}[/tex] of the area

[tex]\text{ sector area } = \frac{56}{360} \times \pi r^2\\\\\text{ sector area } = \frac{56}{360} \times 3.14 \times 6^2\\\\\text{ sector area } = 17.584[/tex]

Thus area of sector is 17.584 meters

Answer:

Carbon dioxide and water.

Answer:

it is carbon dioxide and water

Step-by-step explanation:

Answer:

Answer is in explanation.

Step-by-step explanation:

Part A:

The [tex]x[/tex]-coordinate of the intersection of the curves for the equations [tex]y=4^{-x}[/tex] and [tex]y=2^{x+3}[/tex] is the same as the solution to [tex]4^{-x}=2^{x+3}[/tex] because the equation [tex]4^{-x}=2^{x+3}[/tex] is the result of finding when (for what [tex]x[/tex]'s) the [tex]y[/tex]'s are the same for the the equations [tex]y=4^{-x}[/tex] and [tex]y=2^{x+3}[/tex].

Part B:

Table for [tex]y=4^{-x}[/tex]:

[tex]x[/tex]  |          [tex]y=4^{-x}[/tex]                     |  [tex](x,y=4^{-x})[/tex] |

-3                |          [tex]y=4^{-(-3)}=4^{3}=64[/tex] | [tex](-3,64)[/tex] |

-2                |          [tex]y=4^{-(-2)}=4^{2}=16[/tex]  | [tex](-2,16)[/tex] |

-1                 |          [tex]y=4^{-(-1)}=4^{1}=4[/tex]     | [tex](-1,4)[/tex]

0                 |          [tex]y=4^{-(0)}=4^{0}=1[/tex]     | [tex](0,1)[/tex]

1                  |          [tex]y=4^{-(1)}=4^{-1}=\frac{1}{4}[/tex] | [tex](1,\frac{1}{4})[/tex]

2                 |          [tex]y=4^{-(2)}=4^{-2}=\frac{1}{16}[/tex] | [tex](2,\frac{1}{16})[/tex]

3                 |          [tex]y=4^{-(3)}=4^{-3}=\frac{1}{64}[/tex] | [tex](3,\frac{1}{64})[/tex]

Table for [tex]y=2^{x+3}[/tex]:

[tex]x[/tex]  |        [tex]y=2^{x+3}[/tex]                   | [tex](x,y=2^{x+3})[/tex] |

-3                |        [tex]y=2^{-3+3}=2^{0}=1[/tex]    | [tex](-3,1)[/tex]

-2                |        [tex]y=2^{-2+3}=2^{1}=2[/tex]    | [tex](-2,2)[/tex]

-1                |        [tex]y=2^{-1+3}=2^{2}=4[/tex]    | [tex](-1,4)[/tex]

0                |        [tex]y=2^{0+3}=2^{3}=8[/tex]    | [tex](0,8)[/tex]

1                |        [tex]y=2^{1+3}=2^{4}=16[/tex]    | [tex](1,16)[/tex]

2                |        [tex]y=2^{2+3}=2^{5}=32[/tex]    | [tex](2,32)[/tex]

3               |        [tex]y=2^{3+3}=2^{6}=64[/tex]    | [tex](3,64)[/tex]

You can see in the two tables the y-coordinates are the same value of [tex]4[/tex] when [tex]x=-1[/tex]. So basically the common point in both tables is [tex](-1,4)[/tex] so [tex](-1,4)[/tex] is a solution.

Part C:

I'm going to graph both [tex]y=4^{-x}[/tex] and [tex]y=2^{x+3}[/tex] on the same coordinate plane. I will then find where they will intersect.

I'm going to graph my points from the table to [tex]y=4^{-x}[/tex] and [tex]y=2^{x+3}[/tex].

This can be seen in my drawing.

I graphed [tex]y=4^{-x}[/tex] in blue.

I graphed [tex]y=2^{x+3}[/tex] in red.

Another way:

An algebraic approach:

[tex]4^{-x}=2^{x+3}[/tex]

[tex](2^2)^{-x}=2^{x+3}[/tex] (since [tex]4=2^2[/tex] and now the bases on both side are the same)

[tex]2^{-2x}=2^{x+3}[/tex]

[tex]-2x=x+3[/tex] (since [tex]2^{a}=2^{b}[/tex] then [tex]a=b[/tex])

[tex]-3x=3[/tex] (subtracted [tex]x[/tex] on both sides)

[tex]x=-1[/tex] (divided both sides by [tex]-3[/tex])

The solution is [tex]x=-1[/tex].

Answer:

D)

Step-by-step explanation:

Answer:

40x - 320

Step-by-step explanation:

5x - 40

Something equivalent is...

40x - 320

Still the same.

Infinitely many equations are equivalent to 5x-40.

Example 10x-80 ≡5x-40.

" Equivalent equation are such set of equations which same set of solutions."

According to the question,

Given equation,

5x - 40

Equivalent equation  to 5x - 40 are as follows,

10x -80

20x - 160

30x - 240........so on

Hence, Infinitely many equations are equivalent to 5x-40.

Example 10x-80 ≡5x-40.

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Answer:

Table C represents an exponential function.

Answer:

18

Step-by-step explanation:

18x9/0-12.6 x 14 x 13.2 = 18

f(x)=x2+7

f(4)=4*2+7

4*2=8

8+7=15