Jenna had a collection of 206 quarters, nickels, and dimes. She has twice as many nickels as
she does dimes. All of her coins together are worth $31.70. How many of each coin does she
have?

With equational proof

By the analysis of the graph, the constant of proportionality is 2.

By analyzing the graph given we can infer that  If five rooms are reserved, he must provide ten towels.

So x is the number booked and y is the number of towels, Then

x is directly proportional to y,

The given graph is linear in nature, as we increase x, there will be a significant increase increase in y, The constant of proportionality(k) tells us how much y will change when x changes.

The ratio connecting two given numbers in what is known as a proportional relationship is the constant of proportionality. The constant of proportionality may also be referred to as the constant ratio, constant rate, unit rate, constant of variation, or even the rate of change.

Now, 10= k *5

        [tex]k =\frac{10}{5} \\k =2[/tex]

Hence, the constant of proportionality k is 2.

and the equation of the given graph is y = 2x

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The actual distance between city c and city d represented by 2.38 feet on the map as required in the task content is; 700 miles.

It follows from the task content that the actual distance between city c and city d be determined according to the map's scale factor given.

It follows from the task content that the distance between cities a and b which is 500 miles is represented by 1.7 feet on the map;

1.7 feet ===== 500 miles

Hence, let x = the actual distance between the cities c and d represented by 2.38 on the map is; so that we have;

1.7 feet ====== 500 miles

2.38 feet ====== x miles.

x = (500 × 2.38)/1.7

x = 700 miles.

Therefore, the actual distance between the two cities c and d is; 700 miles.

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Seven people sharing the rent would make the cost $120 per person.

When two quantities are inversely proportional, that is, when an increase in one causes a decrease in the other and vice versa, they are said to be inversely proportional.

The general equation for inverse variation is y = k/x, where k is the proportionality constant and x and y are two variables.

Given:

The price paid by Four friends on a ski trip to share the rent of a cabin = $210

The cost per person varies inversely with the number of persons.

Let the cost be C and the number of persons be n,

C ∝ 1/n

So, the equation becomes, k = Cn.

Putting the values in the equation we obtain the value of k,

k = 210×4 = 840

We have to find the number of people sharing the rent that would make the cost $120 per person.

Using the equation,

k = Cn

840 = 120 × n

n = 840/120 = 7

Therefore, seven people sharing the rent would make the cost $120 per person.

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The final term  after following the steps is  ( 42 + 6x ).

We are provided with some steps that we have to follow to reach the final answer or expression. The steps we have to follow to reach the final answer or expression are mentioned below;

Step 1: Add 7 to x

In the first steps we need to add 7 to the x. Mathematically this can be written as,

7 + x

Step 2: Multiply by 6

In the second step we need to multiply the entire term obtained in step 1 by 6 .  Mathematically this can be written as,

( 7 + x ) × 6

= 42 + 6x

Thus, the final term is  ( 42 + 6x ).

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A function with the formula f(x) = ax + b, where a and b are real values, is referred to as a linear function.

The rate of change will be 3/4.

A function with the formula f(x) = ax + b, where a and b are real values, is referred to as a linear function. Here, a stands for the line's gradient, and b for the y-axis intercept (which is sometimes called the vertical intercept).

The rate of change of y with respect to x, can be calculated utilizing any two of the pairs of values of the table, say, (3, -5) and (7, -2).

Rate of change [tex]$=\frac{y_2-y_1}{x_2-x_1}$[/tex]

Let, (3, -5) = (x1, y1) and (7, -2) = (x1, y1).

Rate of change [tex]$=\frac{(-5)-(-2)}{7-3}$[/tex]

Rate of change = 3/4.

Therefore, the correct answer is option c) 3/4.

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An equation for the volume of the prism as a function of the height is Volume = h³ + 2h² - 15h.

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Recall that the ratio 9:8 can be written as follows:

therefore, when 64 is increased in the ratio 9:8 we get:

Answer: 72.

Answer:

72

Step-by-step explanation:

Since X : 64 = 9 : 8

Then we know X/64 = 9/8

Multiplying both sides by 64 cancels on the left64 × (X/64) = (9/8) × 64

X = (9/8) × 64Then solving for X X = 64 × (9/8)X = 72

Therefore 72 : 64 = 9 : 8

Answer:7

Step-by-step explanation:

Answer:

its 7!!!!

Step-by-step explanation: i just got it right im in 8th grade also!

Answer:

f(x) = 0

px^2 + qx - 4p = 0

abc-Formula: x = (-b ± √(b^2 - 4·a·c))/(2·a)

x = (-q ± √(q^2 - 4·p·(-4p)))/(2·p)

x = (-q ± √(q^2 + 4^2·p^2))/(2·p)

Because q^2 + 4^2·p^2 > 0 there are two roots.

Answer: your answer in in the screenshot

Step-by-step explanation:

The unit rate per inch on the map is 5/4 , and the length of road B is 18.75 miles.

in the question ,

it is given that ,

On the map  [tex]1\frac{1}{2}[/tex]  miles is equal to  [tex]1\frac{7}{8}[/tex] inches  .

we first convert the mixed fraction to normal fractions ,

we get

[tex]1\frac{1}{2}[/tex]  miles = (1*2+1)/2 = 3/2 miles

and

[tex]1\frac{7}{8}[/tex] inches = (8+7)/8 = 15/8 inches

So, the statement becomes

On the map  3/2  miles is equal to  15/8 inches .

So  1 mile = (15/8)/(3/2) = (15*2)/(8*3) = 30/24 = 5/4

so , the unite rate is 5/4 inches per mile .

given the road B is 15 miles long .

and the unit rate is 5/4 .

so 15 miles = 15 *(5/4) = 75/4 = 18.75 inches

Therefore , The unit rate per inch on the map is 5/4 , and the length of road B is 18.75 miles.

The given question is incomplete , the complete question is

A certain map shows two roads. Road A is [tex]1\frac{1}{2}[/tex] miles long but is [tex]1\frac{7}{8}[/tex] inches long on the map. What is the unit rate for inches per mile on this map​? If road B is 8 miles ​long, how long is road B on the map​?

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Answer:

The answer is -18

Step-by-step explanation:

- [tex](-3)^{2}[/tex] + 3(-3)

-9 + -9 = -18

The approximate value of the expression given will be equal to -6.3.

An approximation may be defined bringing the value of a certain entity which is almost similar, but not exactly equal to the correct value. The expression can be written as −12 + √32. The value of √32 can be written as 5.656. Since, after decimal 6 to the right of 5 is greater than 5 so to the nearest tenth, we can write as 5.66. Therefore, √32 = 5.66

For the required value of the expression we can write,

−12 + √32

Putting the value of √32 = 5.66 in the expression we get

-12 + √32 = -12 + 5.66

After solving we get

⇒ -12 + √32 = -6.34

To the nearest tenth it will be -6.3.

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Answer: a) [tex]y = \frac{2}5x} - \frac{4}{5}[/tex]  b) y = -2x + 4

Step-by-step explanation:

2x - 5y = 4

2x - 4 = 5y

[tex]y = \frac{2}5x} - \frac{4}{5}[/tex]

6x + 3y = 12

3y = -6x + 12

y = -2x + 4

Answer:

8.9 is larger

Step-by-step explanation:

7/8 is 0.875 in decimal form

8/9 is 0.88 or 0.89 if you round up.

7/8 < 8/9

Hope this helps! Please have a great day :)

The amount of money Landon will make in 1 hour is $12 and he needs to work for 13 hours to make $156.

The amount of money he will make in 1 hour can be calculated by using division.

It can be determined by dividing the total amount earned by him by the total number of hours he worked yesterday. Therefore;

money earned in 1 hour = total amount earned ÷ total number of hours

money earned in 1 hour = 48 ÷ 4

money earned in 1 hour = $12

Now we can calculate the number of hours he needs to work at the movie theater to make $156 by dividing the desired amount by the amount earned in one hour. Therefore;

number of hours required = 156 / 12

number of hours required = 13

Hence, Landon will make $12 in one hour and he will need to work 13 hours to make $156

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1. Common ratio of the G.P is 50

2. First term of the G.P is -100

3. Sum of the 8th term is 250.

Given,

In a Geometric progression,

7th term is 16 times the 3rd term

Sum of 2nd and 6th term is 102

Common ratio is positive.

Now,

Take a as first term.

r as common ratio

Then,

2nd term = a + r

6th term = a + 5r

So,

a + r + a + 5r = 102

Then,

2a + 6r = 102

2a = 102 - 6r

a = (102 - 6r) / 2

Now,

1. Common ratio:

Consider any term,

Here, 3rd term = a + 2r

Substitute a here.

a + 2r =  (102 - 6r) / 2 + 2r

102 - 6r + 4r = 2

102 - 2 = 6r - 4r

100 = 2r

r = 100/2 = 50

That is,

The common ratio of the G.P is 50.

2. First term:

Consider,

7th term is 16 times the 3rd term

That is,

3rd term = a + 2r

7th term = 16(a + 2r)

r = 50

Then,

a + 50 × 2 = 16(a + 50 × 2)

a + 100 = 16(a + 100)

a + 100 = 16a + 1600

100 - 1600 = 16a - a

15a = -1500

a = -1500/15

a = -100

Therefore,

The first term of the G.P is -100

3. Sum of the 8th term.

8th term = a + 7r = -100 + 7 × 50 = -100 + 350 = 250

That is,

The sum of the 8th term is 250.

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Okay, here we have this:

Considering the provided information, we are going to calculate the requested probability, so we obtain the following:

Let us remember that in a 6-sided dice, the numbers it contains are (1,2,3,4,5,6), and of those 3 are odd, then we are going to substitute in the following formula of the simple probability of an event :

Probability of an event=Favorable Cases/Possible Cases

Probability of tossing an odd number with 6 sided number cube =3/6

Probability of tossing an odd number with 6 sided number cube =1/2

Finally we obtain that the probability of tossing an odd number with 6 sided number cube is 1/2.

Answer:

Explanation:

The standard form of an equation is expressed as y = mx+b

m is the slope

Given the equation x - y = 6

Rewrite in standard form;

-y = -x + 6

Multiply through by -1

-(-y) = -(-x) - 6

y = x - 6

Compare with the standard equation

mx = 1x

mx+b

m is the slope

Given

We are given a trapezoid and we are asked to determine one of its angles. To do that we need to have into account that the following angles are equal:

Also, the sum of two different angles must be equal to 180, therefore, we have the following relationship:

Replacing the value of angle W:

Subtracting 112 to both sides:

Therefore, the measure of angle Z is 68.

Answer:

13

Step-by-step explanation:

y^2 = 169

y = [tex]\sqrt{169}[/tex]

y = 13

Answer:

A goes to K. C goes to M. B goes to L.

Step-by-step explanation:

:)

Given:

Because the dividend is the same for all three expressions the larger the divisor the__the quotient

the answer will be: smaller or least

It is to be noted that Saturn is 1.29 *x 10⁹ km further from the sun than Venus.

Recall that we are given:
approximate distance from the sun for a few different planets.  

Hence, to detect how much farther (in km) from the sun Saturn is than Venus we initiate a series of subtractions.

Recall that
Planet             approximate distance from the sun ( km)

Mercury          5.8 x 10⁷

Venus             1.1 x 10⁸

Earth               1.5 x 10⁸

Saturn             1.4 x 10⁹

The distance of Saturn form the sun and Venus is given as

= Distance of Saturn from Sun - Distance of Venus from Sun

= 1.4 x 10⁹  - 1.1 * 10⁸  [Multiply 1.4 x 10 and we've got]

= 14 x 10⁸  - 1.1 * 10⁸  

= (14 - 1.1) * 10⁸ [ Collect like terms and consolidate]

= 12.9  x 10⁸  [Revert back to the power of 9 and we have]

=  1.29 x 10⁹ km

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Full Question:

The table shown below gives the approximate distance from the sun for a few different planets. How much farther (in km) from the sun is Saturn than Venus?  Express your answer in scientific notation.

Planet                                  Approximate distance from the Sun (in km)

Mercury                                        5.8 x 10⁷

Venus                                           1.1 x 10⁸

Earth                                             1.5 x 10⁸

Saturn                                           1.4 x 10⁹

It is found that Saturn is 1.29 x 10⁹ km further from the sun than Venus.

The number is written in the form  [tex]a \times 10^b[/tex] where we have  [tex]1 \leq a < 10[/tex]

We have been given that the approximate distance from the sun for a few different planets.  

Hence, to determine the farthest distance (in km) from the sun Saturn is than Venus, we get;

Planet             the approximate distance from the sun ( km)

Mercury          5.8 x 10⁷

Venus             1.1 x 10⁸

Earth               1.5 x 10⁸

Saturn             1.4 x 10⁹

The distance between Saturn from the sun and Venus can be calculated as;

= Distance of Saturn from Sun - Distance of Venus from Sun

= 1.4 x 10⁹  - 1.1 x 10⁸

= 14 x 10⁸  - 1.1 x 10⁸  

= (14 - 1.1) x 10⁸

= 12.9  x 10⁸

=  1.29 x 10⁹ km

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If the equation be 125000 = 45000( 1 + 0.021/365[tex]$) ^{365t[/tex] then simplifying we get the value of t exists 7.61 x [tex]10^{-6}[/tex].

Solving a math problem is the same thing as simplifying an expression. You basically strive to write an expression as simply as you can when you simplify it. At the conclusion, there shouldn't be any more multiplying, dividing, adding, or removing to do.

Let the equation be 125000 = 45000( 1 + 0.021/365[tex]$) ^{365t[/tex]

simplifying the above equation, we get

t = [tex]$\frac{125000}{ 45000( 1+ \frac{0.021}{365} ) 365}[/tex]

t = 7.61 x [tex]10^{-6}[/tex].

Therefore, the value of t exists 7.61 x [tex]10^{-6}[/tex].

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The determined value of the number of nickels and the number of dimes that Grayson has is

This is further explained below.

Generally, The following phrase represents Jayden's complete financial worth:

Nickels are worth $0.05 each.

The dime value is equal to $0.10

The total value is equal to the sum of the values of the nickels and dimes.

where;

[tex]1.20= (0.05*2 x) +(0.1*x)[/tex]

0.1 x+0.1 x=1.2

0.2 x=1.2

[tex]x=\frac{1.2}{0.2}[/tex]

x=6

y=2

In conclusion, the Total number of dimes=6

Total number of nickels=12

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Answer:

3A+B+2a+4b

Step-by-step explanation:

Answer:

short piece = 20

Longer piece = 40

Step-by-step explanation:

Comment

Let the shorter piece be x

Then the longer piece is 2x

Givens

The rope is 60 meters long

Equation

x + 2x = 60 meters               Combine like terms

Solution

3x = 60                                  Divide by 3

3x/3=60/3

x = 20