Sofia has $1.90 worth of nickels and dimes. She has a total of 25 nickels and dimes altogether. Write a system of equations that could be used to determine the number of nickels and the number of dimes that Sofia has. Define the variables that you use to write the system.

Answer:

The distance between the points ( 5 , - 9 ) and ( - 3 , - 1 ) is 4[tex]\sqrt{8}[/tex]

Step-by-step explanation:

Given points as :

Point A = ( 5 , - 9 )

I.e (x_1 , y_1) = ( 5 , - 9 )

Point B = ( - 3 , - 1 )

I.e( x_2 , y_2) =  ( - 3 , - 1 )

Let The distance between points A and B = AB

So From distance formula

Distance AB = [tex]\sqrt{(y_2 - y_1)^{2} + (x_2 - x_1)^{2}}[/tex]

So, Distance AB = [tex]\sqrt{( - 1 + 9)^{2} + ( - 3 - 5)^{2}}[/tex]

Or, Distance AB = [tex]\sqrt{(8)^{2} + (- 8)^{2}}[/tex]

Or, Distance AB = [tex]\sqrt{64 + 64}[/tex]

Or, Distance AB = [tex]\sqrt{128}[/tex]

∴ Distance AB = 4[tex]\sqrt{8}[/tex]

Hence The distance between the points ( 5 , - 9 ) and ( - 3 , - 1 ) is 4[tex]\sqrt{8}[/tex]  Answer

Answer:

8√2

Step-by-step explanation:

delta math gave me the right answer after I got it wrong

Answer:

15 hours of work would both plumbers  charge the same amount of money for the job.

Step-by-step explanation:

Let us assume the number of hours Richard works = m

Per hour charge = $45

So, the charge for working m hours = m x $45 = 45 m ....... (1)

Let us assume the number of hours Spiro works = m

Per hour charge = $35

So, the charge for working m hours = m x $35 = 35 m

Also, the charge for parts = $150

So, total amount Spiro charges  = Cost for m hours  +  Charge for parts

= 35 m + $150 ......  (2)

Now, for m hours as they charge the SAME AMOUNT.

⇒ From (1) and (2), we get

45 m = 35 m + $150

or, 45 m - 35 m = 150

or, 10 m = 150

⇒ m = 150/10 = 15

or, m = 15

Hence, 15 hours of work would both plumbers  charge the same amount of money for the job.

Answer:

See explanation

Step-by-step explanation:

A sixth grade silence club needs 180$ to pay for the tickets to a science museum.

1. Suppose there 15 students in the club, then each of them needs to pay

[tex]\dfrac{\$180}{15}=\$12[/tex]

This means each ticket costs $12.

2. Suppose each ticket cost $15, then there are

[tex]\dfrac{\$180}{\$15}=12[/tex] students in the club.

Final answer:

Explains the meaning and interpretations of 180 divided by 15 in the context of purchasing museum tickets for a silence club in a clear manner.

Explanation:

180 divided by 15 in this context means dividing the total amount needed for tickets by the number of equal cost tickets being purchased. Let's interpret this:

Hence, the quotient of 180 divided by 15 is 12, which means either 15 tickets are bought or 12 tickets with the total amount.

Answer:

4x

Step-by-step explanation:

5x+2x=7x

7x-3x=4x

Answer: 6

Step-by-step explanation: 5-2+3

Answer:

11) x = 11

12) x = 11

Step-by-step explanation:

11) Δ RQP and Δ RLK are similar.

Hence, the ratios of the corresponding sides of the two triangles will be constant.

So, [tex]\frac{RK}{PR} = \frac{RL}{QR}[/tex]

⇒ [tex]\frac{x - 4}{49} = \frac{11}{77}[/tex]

⇒ [tex]\frac{x - 4}{49} = \frac{1}{7}[/tex]

⇒ x - 4 = 7

⇒ x = 11 (Answer)

12) Δ QRS and Δ QDC are similar.

So, [tex]\frac{QD}{QR} = \frac{QC}{QS}[/tex]

⇒ [tex]\frac{2x - 14}{32} = \frac{6}{24}[/tex]

⇒ 2x - 14 = 8

⇒ 2x = 22

⇒ x = 11 (Answer)

Answer:

72

Step-by-step explanation:

3(20+4)=a0

60+12=a0

72=a0

im not quite sure what you want. I solved for a0. Plz tell me if this is correct. If its not, tell me what u need, then I will solve it for you.

Answer:

72

Step-by-step explanation:

3 * 20 = 60

3 * 4 = 12

60 + 12 = 72

Answer:

1.4 times k

Step-by-step explanation:

If k feet is the distance from home plate to third base, and the distance from first base to third base is 1.4 times the previous value, then

distance from first base to third base = 1.4 * k or 1.4 times k

If, for example, k=90 feet, then from first to third base there are

1.4*90=126 feet

Answer:

1.415 gram of the element will be left.

Step-by-step explanation:

The decay of radioactive element Krypton-91 can be formulated as  

[tex]A_{t} = A_{0} e^{-kt}[/tex] ............ (1)

where, [tex]A_{0}[/tex] is the initial amount of the element.

[tex]A_{t}[/tex] is the amount of element left after t seconds.

And k is a rate constant.

Now, given that the half-life of the element is 10 seconds.

So, from equation (1) we get

[tex]0.5 = e^{- k \times 10}[/tex]

taking ln on both sides, we get.

ln 0.5 = -10k

⇒ k = 0.0693

So, the equation (1) becomes [tex]A_{t} = A_{0} e^{-0.0693t}[/tex] ........ (2)

Now, if 16 gram of the element are initially present, then we asked to determine the amount of the element left after 35 seconds.

So, from equation (2) we have [tex]A_{t} = 16 e^{- 0.0693 \times 35} = 1.415[/tex] gm.

So, 1.415 gram of the element will be left. (Answer)

After 35 seconds, approximately 1.414 grams of krypton-91 would remain, based on its half-life of 10 seconds and the nature of radioactive decay.

The question pertains to the concept of radioactive half-life, which is the time it takes for half the atoms in a radioactive sample to decay. For krypton-91 with a half-life of 10 seconds, after 35 seconds, we can calculate the remaining amount using the concept of half-lives. We know that after each half-life, the remaining amount of the radioactive substance is halved.

To find out how many half-lives have passed in 35 seconds for krypton-91, we divide the elapsed time by the half-life:

Number of half-lives = Total time elapsed / Half-life duration = 35 seconds / 10 seconds = 3.5 half-lives.

After each half-life, the quantity remaining is halved. This gives us:

Amount after 1st half-life = 16 g / 2 = 8 g

Amount after 2nd half-life = 8 g / 2 = 4 g

Amount after 3rd half-life = 4 g / 2 = 2 g

However, since we have 3.5 half-lives, we must halve the amount one more time, but only halfway (since we have half of a half-life), giving us:

Amount after 3.5 half-lives = 2 g / √2 ≈ 2 g / 1.414 = 1.414 g

Therefore, approximately 1.414 grams of krypton-91 would remain after 35 seconds.

Answer:

10n -11 =3 + 4n + 6n​

10n - 10n -11 =3-3 + 4n + 6n​

-11 - 3 = -10n + 4n + 6n

-14= -10n + 10n

-14 = n

Step-by-step explanation:

10n -11 =3 + 4n + 6n​

10n - 10n -11 =3-3 + 4n + 6n​

-11 - 3 = -10n + 4n + 6n

-14= -10n + 10n

-14 = n

Answer:

The number of soda can that are in the pack is 6 .

Step-by-step explanation:

Given as :

The volume of soda pack = 113.04 inches³

The height of cylinder shaped can = H = 6 inches

The diameter of cylinder shaped can = 2 inches

So, the radius R = [tex]\frac{Diameter}{2}[/tex] =  [tex]\fr{2}{2}[/tex]

Or, R = 1 inches

Now, The volume of cylinder = [tex]\pi[/tex] × R² × H

Or , The volume of cylinder = 3.14 × 1² × 6

Or , The volume of cylinder = 3.14 × 6 = 18.84 inches³

So, The number of soda cans packed = [tex]\dfrac{\textrm volume of soda pack}{\textrm volume of cylinder}[/tex]

or,  The number of soda cans packed = [tex]\frac{113.04}{18.84}[/tex]

∴ The number of soda cans packed = 6

Hence The number of soda can that are in the pack is 6 .  Answer

Answer:

(0,-7/5)

Step-by-step explanation:

2x^2+8x=x-3x^2

2x^2+3x^2=x-8x

5x^2=-7x

5x^2+7x=0

x(5x+7)=0

x=0 or x=-7/5

solution set is (0,-7/5)

Answer:

x=0,x=-1.4

Step-by-step explanation:

[tex]2 {x}^{2} + 8x - x + 3 {x}^{2} = 0 \\ 5 {x}^{2} + 7x = 0 \\ x(5x + 7) = 0 \\ x = 0 \\ \\ 5x + 7 = 0 \\ x = - \frac{7}{5} = -\frac{140}{100} = -1.4[/tex]

Answer:

5 1/12

Step-by-step explanation:

What you should do is find the common denominator for all of these numbers, which is 12.

Now you have to multiply the fraction part so the denominator equals 12.

1*6/2*6= 6/12

3*3/4*3= 9/12

5*2/6*2= 10/12

Now you have to add up all of these numbers

2+6/12+1+9/12+10/12= 3 25/12, which simplified would equal 5 1/12.

Answer:

7C

Step-by-step explanation:

[tex]14c^2=2*7*c*c\\35 c=5*7*c\\G.C.F.=7C[/tex]

Answer:

The total amount of the mortgage is $ 871879.4

Step-by-step explanation:

Given as :

The cost of house = $ 175,000

The first 80% of mortgage amount = 80% of $ 175,000 = 140,000

The second 20 % of mortgage amount =  20% of $ 175,000 = 35,000

The rate of interest for 80 % mortgage = 4.75 %

The rate of interest for 20 % mortgage = 7.525 %

The time period for both mortgage is 30 years

Let The amount at 80 % mortgage = [tex]A_1[/tex]

And The amount at 20 % mortgage = [tex]A_2[/tex]

So, From compounded method

[tex]A_1[/tex] = principal × [tex](1+\dfrac{\textrm rate}{100})^{\textrm time}[/tex]

or, [tex]A_1[/tex] = 140,000 × [tex](1+\dfrac{\textrm 4.75}{100})^{\textrm 30}[/tex]

Or,  [tex]A_1[/tex] = 140,000 × [tex](1.0475)^{30}[/tex]

Or,  [tex]A_1[/tex] = 140,000 × 4.02365

Or, [tex]A_1[/tex] = $ 563311

Again

[tex]A_2[/tex] = principal × [tex](1+\dfrac{\textrm rate}{100})^{\textrm time}[/tex]

or, [tex]A_2[/tex] = 35,000 × [tex](1+\dfrac{\textrm 7.525}{100})^{\textrm 30}[/tex]

Or,  [tex]A_2[/tex] = 35,000 × [tex](1.07525)^{30}[/tex]

Or,  [tex]A_2[/tex] = 35,000 × 8.81624

Or, [tex]A_2[/tex] = $ 308568.4

∴ Total amount A =  [tex]A_1[/tex] +  [tex]A_2[/tex]

I.e A = $ 563311 + $ 308568.4 = $ 871879.4

Hence The total amount of the mortgage is $ 871879.4  answer

Answer:351,226.80

Step-by-step explanation:

Answer:

5.555.5 im pretty sure

I think it is 5.555.5

A consistent , independent system of equation is one that has at least one solution.It is independent because it has a single solution.

Step-by-step explanation:

The three types of systems of linear equations in two variables and three types of solutions.

An independent  system has exactly one solution pair (x,y). The point of intersection presents the single solution.

An inconsistent system has no solution.such equations will produce two parallel lines with no solution.

A dependent system has infinitely many solution.Such lines are coincident.

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Keyword : consistent, independent , equations

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A consistent, independent system of equations is a system where the equations have a unique solution.

A consistent, independent system of equations is a system where the equations have a unique solution. This means that there is exactly one set of values for the variables that satisfy all of the equations simultaneously.

For example, consider the following system of equations:

In this system, there is a unique solution: x = 2 and y = 3. Therefore, it is a consistent, independent system of equations.

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Answer:

Shaneeka live from Phil 7/33 mile far.

Step-by-step explanation:

Given:

Ben lives 6/11 mile north of Phil, and 1/3 mile north of Shaneeka.

Now, to get how far does Shaneeka live from Phil.

So, by subtracting the distance from  6/11 mile north where Ben lives from Phil to  1/3 mile north where Ben lives from Shaneeka:

[tex]\frac{6}{11} -\frac{1}{3}[/tex]

[tex]=\frac{6\times 3 -1\times 11}{33}[/tex]

[tex]=\frac{18-11}{33}[/tex]

[tex]=\frac{7}{33}[/tex]

Therefore, Shaneeka live from Phil 7/33 mile far.

The value of x is 2/3.Distributive property states that multiplying the total of two or more addends by a number will produce the same result as multiplying each addend by the number separately and then adding the results together.

Distinguish distributive property?

This property states that multiplying the total of two or more addends by a number will produce the same result as multiplying each addend by the number separately and then adding the results together.

Mathematically, the distributive law, also known as the distributive property, is the rule relating the operations of multiplication and addition. It is denoted by the symbol a(b + c) = ab + ac, which means that the monomial factor an is distributed, or separately applied, to each term of the binomial factor b + c, resulting in the product ab +...

Explanation in detail:

25-(3x+5)=2(x+8)+x \s 25-3x-5=2x+16+x

20-3x=3x+16

20-3x-3x=16

20-6x=16

6x=20-16

6x=4

x=4/6

simplify is x = 2/3 .

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Answer:

$3,750

Step-by-step explanation:

In english:

First we need to calculate the area of the garden. As it is a triangle we calculate the area as:

area = (base*height)/2

The base is 25m and the height 15m, so the area is:

area = 25*15/2 = 187.5 m2

As each m2 costs $20, for the whole cost we need to calculate the product between 187.5 m2 and $20:

cost = 187.5 * $20 = $3,750

Total cost: $3,750

In spanish (en espanol):

Primero necesitamos calcular el área del jardín. Como es un triángulo calculamos el área como:

área = (base * altura) / 2

La base mide 25 my la altura 15 m, por lo que el área es:

área = 25 * 15/2 = 187.5 m2

Como cada m2 cuesta $ 20, para el costo total necesitamos calcular el producto entre 187.5 m2 y $ 20:

costo = 187.5 * $ 20 = $ 3,750

Costo total: $3,750

Answer:

Tory=14 Quentin=14

Step-by-step explanation:

Sister and brother same age

s=sister    b= brother

 s=b

Tory=s+3    Quentin =2b-8 = 2s-8

EQUATION

s+3 = 2s-8

3=s-8

11=s

sister=11   brother = 11

Tory=11+3=14           quentin=2(11)-8 = 22-8=14

By creating equations based on the ages of Tory and Quentin relative to their siblings, we find that both Tory and Quentin are 14 years old.

Let's denote Tory's age as T and her sister's age as S. Given that Tory is 3 years older than her sister, we can write the first equation as:

T = S + 3

Similarly, let's denote Quentin's age as Q and his brother's age as B. It's given that Quentin's age is 8 years less than twice his brother's age, which gives us the second equation:

Q = 2B - 8

Since Tory and Quentin are the same age, we also know that T = Q, and their siblings are the same age, so S = B. Combining these equations:

T = S + 3
T = 2S - 8

Setting the two expressions for T equal to each other gives us:

S + 3 = 2S - 8

Solving this equation:

Tory and Quentin are both 14 years old.

The correct answer is: D. (A u B)

Step-by-step explanation:

The operations on sets are of two types

1. Union

2. Intersection

In union, the elements of both sets are combined in one set while in intersection only common elements of both sets are considered.

Here,

"all of the elements which are in set A or  B"

This statement means the elements of both sets have to be considered. The word "Or" points to the combination of both sets as an elements belonging to any of the set will be considered. So union operation will be used.

Hence,

The correct answer is: D. (A u B)

Keywords: Sets, Union

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Answer:

$10 per hour. It takes 0.1 hours to earn $1

Step-by-step explanation:

E=10h

E=10 x 1

E=10

Carys earns $10 per hour.

E=10h

1=10h

1/10=10h/10

0.1=h

It takes Carys 0.1 hours to earn a dollar.

Answer:

3

Step-by-step explanation:

3+11t-9u

3+11(9)-9(11)

3+99-99

3+0

3

Answer:

Step-by-step explanation:

3+11(9)-9(11)

3+99-99

3

Answer:

hope it helps :):):)

Step-by-step explanation:

you need to find the common number for both numerator and denominator to multiply to  

the answer will be 72/27

where by multiplying 8 and 3 by 9 gives us 72/27

To find a ratio that forms a proportion with 8/3, a common multiplier needs to be applied. Examples or cross-multiplication can be used to confirm whether two ratios are proportional by comparing products or multipliers.

To determine which ratio forms a proportion with the ratio 8/3, we need to find a common multiplier that can be applied to 8/3 to get the other ratio. A proportion occurs when two ratios are equal to each other after a certain multiplier is applied. To demonstrate this with an example, if we have a ratio of x/y that we want to be proportional to 8/3, we are looking for a multiplier 'k' so that x/y = k*(8/3).

Let's use a concrete example.

If we take the ratio 16/6, we might suspect that this forms a proportion with 8/3.

By finding a common multiplier, we can show this by dividing each part of the second ratio by the corresponding part of the first ratio (16/8 and 6/3) to see if they equal the same number.

In this example, both 16/8 and 6/3 result in the multiplier 2, confirming that 16/6 is proportional to 8/3.

Another way to approach this is to form a cross-multiplication.

If we cross-multiply 8/3 and x/y and both x times 3 and y times 8 yield the same product, then the ratios form a proportion.

For example, 8/3 and 16/6 would form a cross-multiplication of 8*6 and 3*16, both of which are equal to 48, thus confirming the proportionality.

Answer:

Because it is a rectangle, the area is expressed as A = xy, or length times width.

Because it is next to the river, he only needs to fence three sides, so F = x + 2y.

Knowing the amount of fencing available is 7500m, we get:

7500 = x + 2y        solve for x

x = 7500 - 2y         substitute into the area equation

A = (7500 - 2y)y     distribute

A = -2y2 +7500y

You can see that this is a parabola which opens down, meaning that the point of maximum area will be at the vertex, y = -b/2a = -7500/[2(-2)] = 1875

x = 7500 - 2(1875) = 3750

A = 3750(1875)  = 7,031,250 m2

Step-by-step explanation:

The largest area that can be enclosed is  781250 m²

where

l = length

w = width

The farmer wants to enclose a rectangular plot that borders a river. He is not fencing the side along the river. Therefore,

perimeter = l + 2w

l = 2500 - 2w

Therefore,

area = (2500 - 2w)w

(2500 - 2w)w = 0

w = 0 or 1250

average = 1250 / 2 = 625 meters

Hence, the max area is at w = 625 meters

Therefore,

l = 2500 - 2(625) = 1250

length = 1250 meters

width = 625 meter

Therefore,

area = 1250 × 625 = 781250 m²

Therefore, the largest area that can be enclosed is  781250 m²

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Answer:

24.(24)

Step-by-step explanation:

(x+x/10)+x/5=x*24.(24)%

Answer:

$10

Step-by-step explanation:

Interest rate of 6% means ,She had to pay 6 percent of $400 in a year as Interest

Which is 6×[tex]\frac{400}{100}[/tex] = $ 24 (In 12 months)

So, In one month she had to pay $2.

Thus,

In 5 months she had to pay $10 as Interest

Answer: $10

Step-by-step explanation:

Formula for calculating interest= PRT ÷ 100 where,

P = Principal

R = Rate

T = Time

P= $400

R= 6%

T = 5 months

Note that there are 12 months in a year.

Simple Interest= PRT/100

= (400 × 6 × 5) ÷ (12 × 100)

= 12000 ÷ 1200

= 10

The simple interest is $10

Answer:

[tex]a=0.5[/tex]

[tex]b=-2[/tex]

Step-by-step explanation:

we have

[tex]y=ax^{2}+bx+3[/tex]

For x=2, y=1

substitute

[tex]1=a(2)^{2}+b(2)+3[/tex]

[tex]4a+2b=-2[/tex] -----> equation A

Remember that

If the function has a relative minimum in (2,1), then the first derivative of the function must be equal to zero when x=2

The first derivative is equal to

[tex]\frac{dy}{dx}=2ax+b[/tex]

so

[tex]0=2a(2)+b[/tex]

[tex]b=-4a[/tex] ----> equation B

Solve the system of equations A and B by substitution

Substitute equation B in equation A

[tex]4a+2(-4a)=-2[/tex]

solve for b

[tex]4a-8a=-2[/tex]

[tex]-4a=-2[/tex]

[tex]a=0.5[/tex]

Find the value of b

[tex]b=-4a[/tex] ----> [tex]b=-4(0.5)=-2[/tex]

The quadratic equation is

[tex]y=0.5x^{2}-2x+3[/tex]

Answer:

Multiply i and 8

Multiply i and 1

The i just gets copied along.

The answer is i

i

8*i evaluates to 8i

12+8*i evaluates to 12+8i

The final answer (almost!) is

12+8i

Now, let's simplify the i's to get our final answer:

The i in 8i cannot be simplified, so just leave it as is.

The final answer is

12+8i

Step-by-step explanation:

Answer:

Gerry will need to knit 135 stitches wide and 351 rows long for make a scarf that is 18 inches wide and 36 inches long.

Step-by-step explanation:

1. Let's review the data given to us for solving the question:

Measures of the gauge swatch = 4 inches * 4 inches

Number of stitches wide of the gauge swatch = 30

Number of rows long of the gauge swatch = 39

2. How many stitches wide will she need to knit in order to make a scarf that is 18 inches wide and 36 inches long?

Using Rule of Three Simple we can found that value, this way;

Number of stitches wide for 18 inches wide = (18 * 30)/4

Number of stitches wide for 18 inches wide = 540/4 = 135

Gerry will need to knit 135 stitches wide for make a scarf that is 18 inches wide.

We can found the same way, the rows long:

Number of rows long for 36 inches long = (36 * 39)/4

Number of rows long for 36 inches long = 1,404/4 = 351

Gerry will need to knit 351 rows long for make a scarf that is 36 inches long.