Mathematics High School

A mother has 3 kids. Kid A is half the mother's current age. Kid B is 4 years younger than Kid A. In 3 years, Kid C will be 1/5 of his mother's age (not her current age). The sum of all their current ages is the mother's current age.

How old is the mother currently?

How old is each of her kids?

Answers

Answer 1
Let the age of the mother be G.

i)
"Kid A is half the mother's current age."

thus, the age of Kid A is G/2

ii)
"Kid B is 4 years younger than Kid A."

this means, the age of Kid B is the age of Kid A - 4 = G/2 - 4

iii)
"In 3 years, Kid C will be 1/5 of his mother's age (not her current age). "

thus, in 3 years the age of Kid C will be 1/5(G+3)=1/5G+3/5

this means that the current age of Kid C is

1/5G+3/5-3=1/5G+3/5-15/5=1/5G-12/5 = (G-12)/5


The ages of the Kids A, B and C are: 

G/2 , G/2 - 4, (G-12)/5


From the smallest Child's age (G-12)/5 we understand that G-12 is a multiple of 5, 

so G-12 ∈{5, 10, 15, 20, 25, ....}

which means G∈{17, 22, 27, 32, 37, 42, 47, 51, 56, 61... }

From the age of the oldest child G/2, we understand that G must be an even number (so that G/2 is a whole number).

This means that G∈{22, 32, 42, 56,...}

If G was 22, the oldest child would be 11, which makes no sense

If G is 32, the oldest child is 16, which means the woman became a mother at the age of 16, which is rare, but possible.

then G/2=16 , G/2 - 4=12, (G-12)/5=(32-12)/5=20/5=4



If G is 42, her oldest child is 21, no more a "kid", but still, lets consider this case:

the age of the second child is 21-4=17, and the youngest (42-12)/5=6


Answer:

The Plausible cases are :

i) mother: 32, children 16, 12, 4
ii) mother: 42, children : 21, 17, 6 
Answer 2

Final answer:

The mother is currently 40 years old. Kid A is 20 years old, Kid B is 16 years old, and Kid C is 36 years old.

Explanation:

Let's denote the mother's current age as M. Kid A's age is A = M/2. Kid B is 4 years younger than Kid A, so B = A - 4 = M/2 - 4. Kid C will be 1/5 of his mother's age in 3 years, so if we denote Kid C's current age as C, we have C + 3 = 1/5(M + 3). The sum of all their current ages is the mother's current age, so M = A + B + C. With these equations, we can solve for M, A, B, and C.

We substitute A and B into the mother's age equation: M = M/2 + M/2 - 4 + C. Rearranging terms, we get M - 4 = C. Now we have two expressions for C: M - 4 and 1/5(M + 3) - 3. Setting them equal to each other, we get M - 4 = 1/5(M + 3) - 3. Solving for M, we find that M = 40 years old.

Now we can find Kid A, B, and C's ages using the mother's age. Kid A is half the mother's age, A = M/2 = 20 years old. Kid B is 4 years younger than Kid A, B = A - 4 = 16 years old. Kid C's age can be found by the substitution, C = M - 4 = 36 years old. So the mother is 40 years old, Kid A is 20 years old, Kid B is 16 years old, and Kid C is 36 years old.

Related Questions

What's the mean of 0,1,3,2

Answers

Hi Tim! Thanks for asking a question here on Brainly.

☛ To find the mean, we add together all the numbers and then divide it by the amount of numbers there are.

0 + 1 + 3 + 2 
= 6
= 6 / 4 = 1.5

Answer: 1.5

Hope that helps! ★ If you have further questions about this question or need more help, feel free to comment below or leave me a PM. -UnicornFudge aka Nadia

the quadratic equation whose roots are the am and hm between the roots of the equation 2x2 - 3x+5=0

Answers

The first thing to do is to find the roots.

The sum of the roots, x1 + x2 = -b / a

x1 + x2 = 3 / 2

The product of the roots, x1 * x2 = c / a

x1 * x2 = 5 / 2

 

The AM means arithmetic mean and is calculated using the formula:

AM = (x1 + x2) / 2

AM = (3 / 2) / 2

AM = 3 / 4 = y1

 

The HM means harmonic mean and is calculated using the formula:

2 / HM = 1 / x1 + 1 / x2

or

2 / HM = (x1 + x2) / x1 * x2

Rewriting in terms of HM alone on the left side:

HM = 2 x1*x2 / (x1 + x2)

HM = 2 (5 / 2) / (3 / 2)

HM = 10 / 3 = y2

 

Creating an equation from y1 and y2:

(y – ¾) (y – 10/3) = 0

y^2 – 10/3 y – ¾ y + 30/12 = 0

y^2 - 49/12 y + 30/12 = 0       (ANSWER)

or

y^2 – 4.083y + 2.5 = 0

Scientists studied two animal populations. Function f(x) = 830(0.8)^x models a bear population in a given region x years after the study began. The table models the cougar population in the same region.
Year after study began: 0, 1, 2, 6, 15
Cougar population: 790, 735, 683, 511, 266
In the year the study began, how many more bears than cougars were in the given region.

Answers

Cougar population was 790 at the beginning
 830-790=40

Answer:

There were 40 more bears than cougars when the study started.

Step-by-step explanation:

Givens:

[tex]f(x)=830(0.8)^{x}[/tex]; where [tex]x[/tex] refers to years after the study began, about bear population.Table given is for cougar population.

So, the problem is asking how many more bears than cougars were in the given region. From the table, we know that there where 790 cougar when the study started.

Now, we have to calculate the initial condition of the function, because it's modelling bear population. Initial condition means when the study started, which is when [tex]x=0[/tex].

So, we have:

[tex]f(0)=830(0.8)^{0}=830(1)=830[/tex]

So, there were 830 bears when the study started.

If we compare, we find that there were 40 more bears than cougars when the study started, because 830-790 = 40.

What's the answer help me out please ?

Answers

Remember that tangent is the opposite leg/adjacent leg. The opposite leg is across from the angle and adjacent leg is next to the angle. So in this case, is 3 across from B and 4 next to B?? If so, it si true; if not, then it is false:)

In addition to the trigonometric ratios, what other methods can be used to solve a right triangle? Give situations for when you might want to use them

Answers

Consider the right triangle shown below.
We shall discuss two methods for solving the right triangle.

Method 1. Use of trigonometric ratios
To use trigonometric ratios requires that either m∠A or m∠B is known and that one of the sides a, b, or c is known.
Example:
Assume that m∠A is known, then m∠B = 90° - m∠A.
Also, assume that b is known.
By definition,
tan A = a/b  => a = b*tan A
cos A = b/c  => c = b/cos A, or
sin A = a/c  =>  c = a/sin A 

Method 2. Algebraic method
When neither m∠A nor m∠B is known, then it is necessary to know the values of two sides: (a and b), (a and c), or (b and c).
The Pythagorean theorem states that
a² + b² = c²
(a) If a and b are known, then
c = √(a² + b²)
(b) If a and c are known, then
b = √(c² - a² )
(c) If b and c are known, then
a = √(c² - b²)

Once all sides are known, trigonometric ratios can be used t determine m∠A and m∠B.
Example:
Because a and c are known,
sin A = a/c
A = sin⁻¹ (a/c), which can be determined from the calculator.

attached below. 20pts will thanks rate and give best answer

Answers

I think the correct answer is A, but please do not be upset with me if it is incorrect.

if a sprinkler waters 1/18 of a lawn in 1/3 hour, how much time will it take to water the entire lawn

Answers

3/3 would be 1 hour

3/18 of the lawn would be done in 1 hour

18/3=6

6*1 = 6

 it would take 6 hours to do the whole lawn


It will take 360 minutes to water the entire lawn

What is cross multiplication?

Cross multiply can be defined as the process of multiplying the numerator of the first fraction on one side of the equals to symbol, with the denominator of the second fraction on the other side of the equals to symbol.

1/18 lawn is watered in 1/3 of hour = 20 min

Whole lawn will be watered in 20 × 18 = 360 min

To learn more about cross multiplication: https://brainly.com/question/26281051?referrer=searchResults

#FPJ2

Given: WA = NO, WS = NT, W = N.
A)SSS
B) SAS
C) ASA
D)AAS

Answers

You have two sides and the included angle congruent between the two triangles, so SAS is the answer.

Answer with explanation:

It is given that ,

  In two triangles, ΔWAS and ΔNOT

1. WA = NO

2. W S = NT

3. ∠W=∠N

≡ΔWAS ≅ ΔNOT

The Angle is included between two sides .

So,these two triangles are congruent by ,SAS.

Option B:→ S AS

The center of a circle is A (-3,3), and B (1,6) is on the circle. Find the area of the circle in terms of pi.

Answers

check the picture below.  so the circle looks like so, and those points, are pretty much endpoints for the radius "r", thus

[tex]\bf \textit{distance between 2 points}\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ -3}}\quad ,&{{ 3}})\quad % (c,d) &({{ 1}}\quad ,&{{ 6}}) \end{array}\qquad % distance value d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2} \\\\\\ r=\sqrt{[1-(-3)]^2+[6-3]^2}\implies r=\sqrt{(1+3)^2+(6-3)^2} \\\\\\ r=\sqrt{4^2+3^2}\implies r=\sqrt{25}\implies \boxed{r=5}\\\\ -------------------------------\\\\ \textit{area of a circle}\\\\ A=\pi r^2\qquad r=5\implies \boxed{A=25\pi }[/tex]

Factor completely then place the answer in the proper location on the grid. Write the answer in descending powers if x

6x^4+15x^3y^2+3x^2y^3

Answers

6x^4 + 15x^3y^2 + 3x^2y^3

3x^2 (2x^2 + 5xy^2 + y^3) <==

Let’s assume the following statements are true: Historically, 75% of the five-star football recruits in the nation go to universities in the three most competitive athletic conferences. Historically, five-star recruits get full football scholarships 93% of the time, regardless of which conference they go to. If this pattern holds true for this year’s recruiting class, answer the following:

a. Based on these numbers, what is the probability that a randomly selected five-star recruit who chooses one of the best three conferences will be offered a full football scholarship?
b. What are the odds a randomly selected five-star recruit will not select a university from one of the three best conferences? Explain.
c. Explain whether these are independent or dependent events. Are they Inclusive or exclusive? Explain.

Answers

The problem above can be shown on a tree diagram as shown below

Question a)

Let C represents the five-star recruit who chooses one of the best three conferences
Let S represents the scholarship offer

P(C∩S) = 0.75×0.93 = 0.6975

Question b)

P(C'∩S) = 0.75×0.07 = 0.0525

Question c)

The two events are independent because it is possible for the events to happen in any order and one event's outcome does not affect the other event's. 

What is the cardinality of the set {ø, {ø}, {ø, {ø}}}?

Answers

[tex]n(\{\emptyset, \{\emptyset\}, \{\emptyset, \{\emptyset\}\}\})=3[/tex]

The next three terms of the sequence 20, 40, 80, 160,… are 320, 640, and 1280.

Answers

correct

Its a geometric sequence with common ratio 2.

In basketball, when monica takes her first free throw, she has a 50% chance of scoring. if she takes an additional throw, she has a 75% chance of scoring on this throw if she scored on the immediately previous throw, but only a 25% chance of scoring on this throw if she didn't score on the immediately previous throw. suppose she has to take a set of three free throws in a row, and she doesn't score on the first one. what is the probability that she scores at least once on one of the subsequent two throws?

Answers

The probability that she scores at least once on one of the subsequent two throws is 37.5%. It is said that on the first row, she has a 50% chance of scoring. If she takes an additional throw, she has a 75% chance of scoring on this throw if she scored on the immediately previous throw, but only a 25% chance of scoring on this throw if she didn't score on the immediately previous throw. You are asked if she has to take a set of three free throws in a row, and she doesn't score on the first one and so multiply 75% by 50% and you will get 37.5%.

Is a triangle with sides of length 7 ft, 24 ft, and 25 ft a right triangle? Explain.

Answers

25^2 = 625
7^2 + 24^2 = 49+576 = 625

625 = 625

ANswer
Yes. It's right triangle

the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse....It's right triangle angle

Find the probability that 3 randomly selected people all have the same birthday. ignore leap years. round to eight decimal places.\

Answers

Final answer:

The probability that 3 randomly selected people all have the same birthday is 1 in 48,627,125.

Explanation:

In order to find the probability that 3 randomly selected people all have the same birthday, we need to consider the total number of possible outcomes and the number of favorable outcomes. There are 365 days in a year (excluding leap years) and each person's birthday is independent of the others. Therefore, the probability of each person having the same birthday as the previous person is 1/365. To calculate the probability that all 3 people have the same birthday, we multiply the probabilities together:

P(3 people have the same birthday) = (1/365) * (1/365) * (1/365) = 1/48,627,125

Thus, the probability that 3 randomly selected people all have the same birthday is approximately 0.0000000206, rounded to eight decimal places.

Learn more about Probability here:

https://brainly.com/question/22962752

#SPJ11

Let f(x) = x + 8 and g(x) = x2 − 6x − 7. find f(g(2)). −7 −3 10 33 open study

Answers

f(g(2))

g(x) = x^2 - 6x - 7
g(2) = 2^2 - 6(2) - 7
g(2) = 4 - 12 - 7
g(2) = -15

f(x) = x + 8
f(g(2) = f(-15) = -15 + 8 = -7 <==

ur answer is -7

Mr. Thompson borrowed $3,000. He repaid the loan with an interest charge of $500 in 36 equal monthly payments. What approximate annual percentage rate did he pay? Find the answer to the nearest tenth of a percent.

Answers

The formula is
APR=(2 × n × I) / [P × (N + 1)]
APR=(2×12×500)÷(3,000×(36+1))
APR=(2×12×500)÷(3,000×37)
APR=0.1081×100
APR=10.81%

Jared bought eighteen doughnuts to share with his coworkers. If each doughnut cost c cents, which expression represents his total cost?

18 + c
18 - c 1
8 ÷ c
18 c

Answers

it would be 18/c. to figure out each cost take the number and divide it by c 

Answer:

i think answer 1

Step-by-step explanation:

tell me i i am wrong

If we multiply every observation in a data set by 2, the mean will

Answers

If the values increase then the mean will as well, but if only the observations increase, the mean will decrease.

If 9a+5b+5c=9 what is -10c-18a-10b?

Answers

9a + 5b + 5c = 9

Multiplying the whole equation by -2.

-18a - 10b - 10c = -18.

Hence, the answer is -18.

What is the solution of \sqrt(2x+4)=16?
x = 6
x = 72
x = 126
no solution

Answers

√(2x+4)=16  square both sides

2x+4=256  subtract 4 from both sides

2x=252  divide both sides by 2

x=126

The solution of the expression will be;

⇒ x = 126

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ √(2x + 4) = 16

Now,

Solve the expression as;

The expression is,

⇒ √(2x + 4) = 16

Square both side, we get;

⇒ 2x + 4 = 16²

⇒ 2x + 4 = 256

⇒ 2x = 256 - 4

⇒ 2x = 252

⇒ x = 126

Thus, The solution of the expression will be;

⇒ x = 126

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ6

how many foci does the graph of a hyperbola have

Answers

They Have 2: Like an ellipse, an hyperbola has two foci and two vertices; unlike an ellipse, the foci in an hyperbola are further from the hyperbola's center than are its vertices: The hyperbola is centered on a point (h, k), which is the "center" of the hyperbola. hope this helps c:

Answer:

A graph of a hyperbola have 2 foci.

Step-by-step explanation:

Foci of a Hyperbola-

The foci of a hyperbola are two fixed points located inside each curve of a hyperbola.

The foci is a plural of the word focus i.e. two focus of a hyperbola are combinely called foci.

Hence, a graph of a hyperbola have 2 foci.

PLEASE HELP!!! 9. Solve the equation. Check for extraneous solutions. Type your answers in the blanks. Show your work.
|4x + 3| = 9 + 2x

x = _____ or _____

Answers

x=-2 or x=3 are the answers, hope this helps. 
When you have the absolute value of an equation, in order to remove the absolute value signs, you have to set what's inside the signs equal to both the positive and negative of what the solution set is.  By that I mean:
[tex]4x+3=9+2x[/tex] and
[tex]4x+3=-(9+2x)[/tex]
The second one simplifies to
[tex]4x+3=-9-2x[/tex]
Now solve each for x:
[tex]4x+3=9+2x[/tex]
[tex]2x=6[/tex] and x=3
The second one:
[tex]4x+3=-9-2x[/tex]
[tex]6x=-12[/tex] and x=-2
If you check both of these solutions, they both work; neither are extraneous.

On her first stroke, Maria hit a golf ball 140 yards, 2 feet, 9 inch. On her second she hit it 170 yards, 1 foot, 6 inches. How far did the ball go all together

Answers

2 feet 9 inches + 1 foot 6 inches = 3 feet 15 inches

15 inches = 1 foot 3 inches

3 feet + 1 foot = 4 feet

2 ft 9 inches + 1 ft 6 inches = 4 ft 3 inches


1 yard = 3 feet

4feet 3 inches = 1 yard, 1 foot 3 inches

140+170 = 310 yards

310 + 1 = 311

 so it traveled 311 yards 1 foot and 3 inches

Answer:

311 yards and 1 feet and 3 inches

Step-by-step explanation:

Which of the binomials below is a factor of this trinomial?

x² + 2x - 48

A. x + 8
B. x - 3
C. x - 8
D. x + 3

Answers

Hello there!

The complete factor of x² + 2x - 48 is (x-6)(x+8)
So, the correct option is A (x + 8)


I hope that helps!

What do the vertical lines mean?

Answers

The vertical lines are absolute values, the number in between them, if negative turns positive.

Final answer:

In art, vertical lines suggest stability and structure, contrasting with calming horizontal lines and dynamic diagonal lines. These lines help define shapes, indicate motion, and guide the viewer through the composition.

Explanation:

The term vertical lines in the context of art and design, refers to lines that run up and down the canvas or design space, perpendicular to the horizon. These lines can convey a variety of meanings and emotions in visual compositions. According to a description by Oliver Harrison, vertical lines are seen as visually stable and can be associated with structures like tree trunks or classical columns, suggesting strength and stability.

B is between a and c ac=15.8 and ab=9.9. find bc

Answers

Answer:

The value of bc is 5.9 units.

Step-by-step explanation:

Given information: b is between a and c, ac=15.8 and ab=9.9.

We need to find the measure of bc.

Since b is between a and c, therefore the segment ac is the sum of two segments ab and bc.

[tex]ac=ab+bc[/tex]

Substitute ac=15.8 and ab=9.9 in the above equation.

[tex]15.8=9.9+bc[/tex]

Subtract 9.9 from both sides.

[tex]15.8-9.9=9.9+bc-9.9[/tex]

[tex]5.9=bc[/tex]

Therefore the value of bc is 5.9 units.

If assumption of Collinearity is not for granted, then the length of Segment BC is defined by [tex]BC = \sqrt{347.65 -312.84\cdot \cos \beta}[/tex], for [tex]\beta \in [0^{\circ}, 180^{\circ}][/tex].

Reminder - Given that statement seems to be incomplete, we assume that we are talking about Line Segments and that Segments AC and BC may be Collinear.

By Geometry and, being more specific, by definition of Triangles, if we assume that all segment are not necessarily Collinear, then a Triangle may exist and can be modelled by the Law of Cosine:

[tex]BC = \sqrt{AC^{2}+AB^{2}-2\cdot AC\cdot AB\cdot \cos \beta}[/tex] (2)

Where [tex]\beta[/tex] is the angle at point B, in sexagesimal degrees and is between 0° and 180°.

If we know that [tex]AC = 15.8[/tex] and [tex]AB = 9.9[/tex], then the expression for the length of BC is:

[tex]BC = \sqrt{347.65 -312.84\cdot \cos \beta}[/tex]

If assumption of Collinearity is not for granted, then the length of Segment BC is defined by [tex]BC = \sqrt{347.65 -312.84\cdot \cos \beta}[/tex], for [tex]\beta \in [0^{\circ}, 180^{\circ}][/tex].

Please see this question related to Triangles: https://brainly.com/question/24160832

What is 10 1/2 divided 2 1/4

Answers

it should be 4 2/3 you are in highschool you should know this
(10 1/2) / (2 1/4) --- turn them into improper fractions
(21/2) / (9/4) -- when dividing with fractions, flip what u r dividing by, then multiply
21/2 * 4/9 = 
42/9 =
4 2/3 <===

The value of 4 in 943,268

Answers

It is in the 10 thousandths place . So the answer is 40,000

The value of the digit 4 in the number 943,268 is 40,000 because it is in the ten thousand place.

The value of the digit 4 in the number 943,268 depends on its place value in the number.

In 943,268:

- The digit 4 is in the ten-thousands place.

So, the value of the digit 4 in 943,268 is:

4 × 10,000 = 40,000

Therefore, the value of the digit 4 in 943,268 is 40,000.

Other Questions
Bout how many children have become orphaned in the world due to hiv/aids Why did Paine believe that Britain was unworthy of being called a republic? On which number line do the points represent negative seven and one over two and +1? What is the Spanish name of the wooden box used to make percussion sounds in flamenco Write the equivalent decimal and fraction for each percent.Percent: 15%Percent:120%Percent:36%Percent:22%Percent:54%Percent:205%_______________________________________________________________For each fraction or decimal, write the equivalent percent.3/25 =4.06 =0.01 =1/8 =2/5 =0.6%__________________________________________________________90% or 120 is:___3.6 or 5% of:___37 1/2 or 64 is:____39 is __% of 52110% or 55 is____18 is 40% of ____27 is ___ % of 10835 is 25% of ___28 is __% of 2082 is ___% of 40 Do the side lengths of 5, 6, and 8 form a Pythagorean triple?YesNo Transcription of rna from dna in eukaryotes requires: If a person dies at home, what prevents them from donating organs?a.When a person dies at home blood circulation can't be maintained to the organs like it can in a hospital setting.b.The organs are contaminated because death occurred in a non-sterile environment.c.The organs may be damaged on the way to the hospital.d. A person can only have their organs donated if they died in a hospital due to legal reasons. Which is the graph of f(x)=2(3)^x Find the product of 0.094 0.367 During a grade school field trip, ryan and his friends were running down a hill when he stepped on a snake. he was unharmed but shaken by the experience. when one of his friends mentioned the incident months later, ryan could not remember running down the hill that day. freud would say that this is an example of Although they are not glands, these body structures secrete a hormone called B-type natriuretic peptide (BNP). Which of the following was a criticism of laws designed to protect the environment? A. Environmental laws didn't work to clean the environment. B. Too much regulation could hurt businesses. C. Too much regulation would clean the water. D. Too much regulation would attract illegal immigrants. Write a conjecture for the pattern of the sequence Read the sentence. Some families prepare their ancestors ceremonial food. What is the indirect object? How many equations are needed to solve for 1 unknown variable? The surgical suturing of the end of a tendon to a bone is known as __________. A cheetah runs at a speed of 54 miles for every hour. If the distance traveled, in miles, is d and time, in hours, is t, which equation shows the relationship between d and t?A.) d = 54tB.) t = 54dC.) d = 54 + tD.) t = 54 + d The first step in creating a cash flow statement is which of the following?Recording financial goalsRecording expensesRecording incomeRecording tax information How does John DiConsiglio organize the text in "Disease Central," the supplemental text in When Birds Get Flu, to present the central idea? He presents the central idea first. He concludes with the central idea. He presents the central idea in the middle. He summarizes the central idea with a quote. Steam Workshop Downloader