5m + 6n; m = 2 and n = 4

Let's say that the money that each person has is equal to a letter:

A=Debbie, B=John, C=David.

Now we can write some equations.

"John has four times as much money as his sister Debbie who has half as much as their friend David."

B = 4A

A = 0.5C

"Together the three children have $105"

A+B+C=105

This is now a system of equations problem. Substitute to solve.

A + (4A) + C = 105

(0.5C) + 4(0.5C) + C = 105

3.5C = 105, so C = 30.

Plug this into the previous equations to get A=15 and B=60

So Debbie has $15, John has $60, and David has $30

The conditions or surroundings in which we all live is called the environment. The main elements of the environment are air, water, temperature, weather conditions and more.

The environment is the base of the life cycle. It is the most precious gift of nature. But now our environment is in danger. Saving the environment is very important for living a comfortable life. It is the biggest challenge for humans to revert the environment to its real state. But nothing is impossible.

We need to take some steps immediately in order to save the environment and revert it back to its original form. Using natural resources efficiently is a powerful way to save our environment.

☆...hope this helps...☆

_♡_mashi_♡_

Step-by-step explanation:

we are missing the inequality sign in step 3.

step 1 and step 2 are correct.

step 4 is wrong.

the correct step 3 looks like

3x <= -3

if your original step 3 says the same, then the first wrong step is step 4.

if your original step 3 does not say the same, then the first wrong step is step 3.

Answer:

180 degrees

Step-by-step explanation:

Because 360 is i full turn around and you can divide 360 by 2 and you will get 180  

Hope This Helped

Answer:

126

Step-by-step explanation:

Answer:

2:3, 2 to 3

Step-by-step explanation:

9 and 6 are both factors of three, so you have to reduce. 3 goes into 9 tree times, and 3 goes into 6 twice. Since it is circles to squares, the 2 comes first then 3.

Hope this helps!

Answer:

I believe it should be rounded to 11, if not decimal would be 10.88

Step-by-step explanation:

49 divided by 9 equals 5.44 which is the amount times the 49cm^2 triangle is compared to the 9cm^2. So then the side is 2cm, multiply by the amount times bigger the other triangle is which would be 10.88. Hopefully I'm not wrong:)

Answer:

The answer is 4 and 2/3 cm²

Step-by-step explanation:

Take the square root of 49 and 9 and you'll get 7 and 3 since the scale factor is the large area over the small area.

The large area would be √49 cm²

The small area would be √9 cm²

  7          x cm

------ =  ----------, cross multiply

  3         2 cm

7 × 2 = 3 × x

14 = 3x

x = 14/3, x = 4 and 2/3

Answer:

135 ft^3

Step-by-step explanation:

The volume of a cone is [tex]\frac{1}{3} \pi r^{2}h[/tex]. The radius is 4 and the height is 8, so these values can be plugged in:

[tex]V = \frac{1}{3} \pi \times 4^{2} \times 8[/tex]

[tex]V = \frac{128\pi }{3}[/tex]

This is about 134.041286553 which rounds to 135 ft^3.

The sum of the first n terms of sequence 85 +85(.9) +85(.9)² + ... would be 348.08.

Let's suppose its initial term is a , multiplication factor is  r and let it has total n terms,

then, its sum is given as:

[tex]S_n = \dfra[/tex][tex]\dfrac{a(r^n-1)}{r-1}[/tex]

(sum till nth term)

Given geometric sequence;

85 +85(.9) +85(.9)² + ...

a = 85

r = 0.9

its sum is given as:

[tex]S_n = \dfra[/tex][tex]\dfrac{a(r^n-1)}{r-1}[/tex]

[tex]S_n = \dfrac{85(0.9^5-1)}{0.9-1}\\\\S_n = \dfrac{85(0.5904-1)}{-0.1}\\\\\\S_n = \dfrac{85(-0.4095)}{-0.1}\\\\S_n = 348.08[/tex]

Thus,

The sum of the first n terms of sequence 85 +85(.9) +85(.9)² + ... would be 348.08.

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The simplified form of this expression is 28 + 10i

Imaginary numbers are numbers that are composed of a real number and an imaginary part.

< To resolve this issue, let's remove the first parenthesis:

(3i + 4) - i + 4(6 + 2i)

3i + 4 - i + 4(6 + 2i)

< In the second parentheses, let's apply the distributive property:

3i + 4 - i + 4(6 + 2i)

3i + 4 - i + 4 . 6 + 4 . 2i

3i + 4 - i + 24 + 8i

< Finally, let's just sum the like terms, along with the real terms:

3i + 4 - i + 24 + 8i

10i + 4 + 24

10i + 28

28 + 10i

Therefore, the correct value will be 28 + 10i

Step-by-step explanation:

Yes it is .

7x+9 _> 7•3

7x+9_> 21

7x_> 21 - 9

7x _> 12 divide both side with 7 to find x

then x _> 1.4

which mean x can be any number that is greater than or equal to 1.4 so 2 is correct .

Hi Student!

Looking at the problem statement, we can see that they are asking for us to determine whether x = 2 is a solution of the expression provided or not.  The first step that we take is plugging in all the values which means that we take 2 and plug it into all of the x's that we have in the expression that we provided.  Then we simplify that expression down on both sides.  If the expression in the end results to true then x = 2 is a solution of the expression but if it defaults to false than x = 2 isn't a solution.

Plug in the values

Simplify both sides

The final expression states that 23 is greater than or equal to 21 which is true. Therefore, x = 2 is a solution of the expression that was provided in the problem statement.

Answer:

Step-by-step explanation:

follow the formula in the picture

Area = b * h

Area = 15 * 8

Area = 120 in²

Answer: 384.85

Step-by-step explanation

Setting up and equation from the word problem, Orlando has 24 apps on his phone, and Maria has 10 apps on her phone.

Let's assume that Orlando has x number of apps on his phone. According to the given information, Maria has 14 fewer apps, so the number of apps on Maria's phone would be (x - 14).

The total number of apps on both phones is 34, so we can set up the equation:

x + (x - 14) = 34

Simplifying the equation:

2x - 14 = 34

Adding 14 to both sides:

2x = 48

Dividing both sides by 2:

x = 24

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Answer:

x= 3/2

Step-by-step explanation:

3/x=2

Multiply x both sides so,

3 =2x

Divide 2 to get the value of x so,

x= 3/2

In order to save money, the person should buy Toilet paper B.

In order to determine the unit price of each option, divide the total cost by the number of rolls. The option that would save money is the cheaper option.

Unit cost = total cost / number of rolls

$4.59 / 6 = $0.77

$9.02 / 12 = $0.75

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Answer:

https://www.calculator.net/triangle-calculator.html?vc=&vx=16&vy=9&va=&vz=12&vb=&angleunits=d&x=54&y=24

Step-by-step explanation:

I went to this website

https://www.calculator.net/triangle-calculator.html

put in what I knew of the triangle and got all the information you may need.

Based on this construction, the value of m∠ABC is 64°.

From the point, E and D, two arcs are made which are intersecting each other at point P.

It means, that line BP is the bisector of angle ABC. ABC will be:

= 2 * 32=64

Therefore, based on this construction, the value of m∠ABC is 64°.

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Hi Student!

Let's go through each of the options that were provided to the question stating what part of the circle was highlighted in red and talk about what they mean.

First off, radius is the distance from the outer line to the middle which perfectly incapsulates what the red line is.  Therefore, the correct answer would be option A, Radius.

However, if you want to understand the rest of the definitions you can follow with the bullets provided.

The highest possible number of inhabitants in that little town are 743.

A person or animal that lives in a place is called as the inhabitant.

Suppose there is this little town with a finite number of people: (1) No two inhabitants have exactly the same number of hairs. (2) No inhabitant has exactly 743 hairs or no hairs at all. (3) There are more inhabitants than there are hairs on the head of any inhabitant.

Let say there are 519 people in the town. and make them stand in a line with increasing number of hairs on their heads. This way, there will be a person on the last, who has no hair.

There are more number of people than the hairs. From bald to 742 hairs, 743 is the limit.

Thus, the highest possible number of inhabitants in that little town are 743.

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Answer: x=15, y=3

Step-by-step explanation:

Subtracting the two equations, we get -3y=-9, meaning y=3.

Substituting this into the first equation, we get that x-3=12, and thus, x=15.

[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$8000\\ P=\textit{original amount deposited}\dotfill & \$5000\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &2 \end{cases} \\\\\\ 8000=5000[1+(\frac{r}{100})(2)]\implies \cfrac{8000}{5000}=1+\cfrac{r}{50}\implies \cfrac{8}{5}=1+\cfrac{r}{50} \\\\\\ \cfrac{8}{5}-1=\cfrac{r}{50}\implies \cfrac{3}{5}=\cfrac{r}{50}\implies \cfrac{3(50)}{5}=r\implies 30=r[/tex]

The equation which is used to find the value of c will be c = 5/Cos 35

The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.

We are given the following

m<ACB = 90degrees

m<ABC = 35degrees

The side opposite to m<ABC is AC

BA = hypotenuse

CB = adjacent = 5inches

Required

The equation to solve BA which is c

Using the Pythagoras theorem;

Cos Ф = Adjacent/Hypotenuse

Cos m<ABC = CB/BA

Cos m<ABC = 5/c

c = 5/cosm<ABC

c = 5/Cos 35

Hence the equation that can be used to solve for c is c = 5/Cos 35

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The nature of the research is called Observational Study while the target Population is American Students.

1) In study, we survey members of a sample without trying to affect them while in experiment, we assign people or things to groups and apply some treatment to one of the groups, while the other group does not receive treatment. Thus, this is an observational study.

2) The sample is the 100 students made up of 50 boys and 50 girls.

3) The target Population are American College Students

4) The sampling method is; Simple random Sampling

5) The data is qualitative because it deals with description of feelings rather than dealing with numbers and figures.

6) It is unlikely that the results would be invalid because of sampling bias as it was only done in a private university.

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Answer:

  14 visits

Step-by-step explanation:

The total number of points on Blake's card will be the sum of the initial number and the number earned for visits. The number earned for visits is the product of the number of visits and the the points earned per visit.

__

The number of points on Blake's card will be ...

  p = 35 +11.5x . . . . . when Blake makes x visits to the theater

We want to find x when p=196, so we have ...

  196 = 35 +11.5x

This 2-step equation is solved in the usual way.

  161 = 11.5x . . . . step 1, isolate the variable term by subtracting the constant

  14 = x . . . . . . . . step 2, divide by the variable coefficient

Blake must make 14 visits to earn a free movie ticket.

Answer:

A

tyler has a points card for a movie theater.

he receives 75 rewards points just for signing up.

• he earns 10.5 points for each visit to the movie theater.

he needs 180 points for a free movie ticket.

.

a

how many visits must tyler make to earn a free movie ticket?

Step-by-step explanation:

Answer:

4 8 1 4 0,683 the (783)-213=509

Answer:

8

Step-by-step explanation:

Intersecting Chords Formula:

(segment piece) x (segment piece) = (segment piece) x (segment piece)

5*x = 4*10

5x = 40

Divide by 5

5x/5 = 40/5

x = 8

Answer:

c.

Step-by-step explanation:

we estimate by rounding the factors to "easy numbers". that means numbers we can easily calculate even in our heads, and we get at just a ballpark number as result for orientation.

59 is much closer to 60 than to 50.

42 is much closer to 40 than to 50.

of course, we round to the closest "round numbers", so that the loss of precision through the rounding is as little as possible, so that the estimation still gives a much value as possible.

and the sum of the differences of the factors should be as close to 0 as possible.

so, 60×40 is the closest and therefore best estimation.

the sum of the factor differences is (+1 - 2) = -1.

compare to the real result :

59×42 = 2,478

answer a and b are by the way not correct :

50×40 = 2000 (and not 2500)

60×50 = 3000 (and not 3500)

FYI - in this case 50×50 = 2500 would be the closest estimation.

and the sum of the factor differences would be (-9 + 8) = -1.

normally, this wide "jumping" (-9 to +8) would make it only second choice.

[tex]\bold{Q:}[/tex]

[tex]\bold{Ans:}[/tex]

A balance or scale is an instrument used to measure mass.

Hope it helps.

[tex]\bold{Feel \: free \: to \: correct \: me}[/tex]~