frank weighs 160 lbs gains 2 lbs a week, john weighs 208 lbs and loses 3 lbs a week


A. when will they weigh the same, and how much will they weigh

B. Explain clearly

Answer:

Let's mark Pat's age is x. Then Mattie's age is 2x and Jon's age is 4x.

So (x + 4) + (2x + 4) + (4x + 4) = 61.

7x + 12 = 61 => 7x = 49 => x = 7.

So the answer is

Pat = 7

Mattie = 14

Jon = 28

The ages of Pat, Mattie, and Jon are as follows: 7 years, 14 years & 28 years.  

If we take Pat's age as = 'x' years,

so, Mattie's age will be = '2x' years.

and then, Jon would be = 2(2x)

                                        = '4x' years.

Now, the sum of their ages after 4 years =

 => (x+4) + (2x+4) + (4x+4) = 61

 => 7x+12 = 61

 => 7x= 61-12

 => 7x= 49

 => x= 49/7

 => x = 7

Therefore, Pat's age is  = 7 years.

              Mattie's age is = 14 years (2×7).

                  Jon's age is = 28 years (4×7).

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Answer:

5/3

Step-by-step explanation:

4 4/9 * 3/8 = 40/9 * 3/8 = 120/72 = 10/6 = 5/3

With an accuracy of within $0.01, the student will be able to recognize

and determine the total worth of a given assortment of coins and bills, including pennies, nickels, dimes, quarters, half-dollars, and dollar bills.

TEKS stands for Texas Essential Knowledge and Skills. It is a set of state standards for public schools in Texas, that outline what students should know and be able to do in each grade level and subject area. The standards cover subjects such as English language arts, mathematics, science, social studies, and languages other than English.

The TEKS are used to guide the development of curriculum and instruction in Texas schools.

The clear learning goal for the Texas Essential Knowledge and Skills (TEKS) skill of determining the value of a collection of coins and bills could be: "The student will be able to accurately identify and calculate the total value of a given collection of coins and bills, including pennies, nickels, dimes, quarters, half-dollars, and dollar bills, to within $0.01."

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The circle's radius is equal to 3.659 or 3.7.

A circle's or a sphere's radius is the length of the line between the center and the edge.

From the center of the circle or sphere to any point on its perimeter, the radius' length is constant.

Its diameter is halved by its length.

A line segment from a circle's or sphere's center to its perimeter or boundary is known as the radius in geometry. I

t is a crucial component of spheres and circles and is frequently abbreviated as "r."

When discussing multiple radiuses at once, the plural form of radius is "radii." the longest line connecting any points on the opposite side of a circle or sphere.

Hence, The circle's radius is equal to 3.659 or 3.7.

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Answer:

  18 tickets at $7

Step-by-step explanation:

You want a "Singapore Math" model solution to the number of $7 tickets Mrs. Hana bought if she got $14 change from $200, and she received a total of 30 tickets, some of which cost $5 each.

The attachment shows the model we decided upon. Starting from $200, we subtract $14 in change, then divide the remainder into tickets costing $7 each and tickets costing $5 each. The point where the total number of tickets is 30 is the point that identifies the solution.

Mrs. Hana bought 12 tickets at $5 each, and 18 tickets at $7 each.

__

Additional comment

Most illustrations of Singapore Math models are solving for a single variable. Here, we must choose values for two variables (the numbers of $5 and $7 tickets) so the intended model isn't clear.

The model we have used is adequate for the purpose, but tedious to construct. It requires us to identify the point at which the count of $7 tickets (top bar) and the count of $5 tickets (bottom bar) has a sum of 30.

The integer number that represents the submarine's depth is given as follows:

-460.

Integer number are numbers that can have either positive or negative signal, but are whole numbers, meaning that they have no decimal part.

The concepts of height and depth are given as follows:

A submarine in the middle of the ocean at a depth of 115 feet, hence the integer that represents the initial depth is given as follows:

-115.

The submarine dived to a depth that is four times the initial depth, hence the integer that represents the final depth is given as follows:

4 x -115 = -460.

(meaning that the final depth of the submarine is of 460 feet).

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On solving the provided proportionality question we got that, U = 7.72, is rounded off nearest to tenth digit.

When two quantities or variables are linearly related in mathematics, the term "proportional" is used. Both quantities increase by two times when one increases by two. Each variable decreases in proportion to the other when it falls to 1/100th of its previous value.We must determine the ratio of the two quantities for each value supplied in order to determine if two quantities are proportionate. The proportionate link between them is evident if their proportions are equal. Their connection is not proportionate if all the ratios are out of balance.

Here,

U/5 = 17/11

U = 17/11 X 5

U = 7.72

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The linear function in the option is − x / 3 + y / 7 = 11.

A linear function is a function that represents a straight line on the coordinate plane.

Linear function can be represented in slope intercept form as follows:

y = mx + b

where

Therefore, let's select the linear function from the options:

− 3 / x + y / 7 = 11

-3x⁻¹ + 1 / 7 y = 11 (Not a linear function)

− x / 3 + 7 / y = 11

- 1 / 3 x + 7y⁻¹ = 11 (Not a linear function)

− x / 3 + y / 7 = xy (Not a linear function)

− x / 3 + y / 7 = 11

- 1 / 3 x + 1 / 7 y = 11 (This is the linear function)

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The unit rate of change of the proportional relationship is given as follows:

2.25.

The graph of the proportional relationship is given by the image presented at the end of the answer.

A proportional relationship is a linear function with an intercept of zero modeled as follows:

y = kx.

In which k is the constant of proportionality.

The input and output variables for this problem are given as follows:

The constant k, representing the unit rate, is obtained by the division of the output of the input from the table, hence:

k = 4.5/2 = 6.73/3 = 9/4 = 2.25.

Meaning that the function is defined as follows:

y = 2.25x.

The function is graphed for a domain of x ≥ 0, as the number of cups of sugar must be a countable, non-negative amount.

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Answer:

Intial money=Rs 3300

final money=3300-(70×5)-(2×125)-2500

=3300-350-250-2500

=3300-3100=RS 200

Now,

share of each of them= 200/2=Rs100

*mark me brainliest

A triangular number succession is the representation of numbers as just an ordered set of equilateral triangles. The order of these numbers is 1, 3, and 6.

A triangular number is one that may be written as the sum of a initial n positive integers.

The first 3 triangular numbers are therefore 1, 3, and 6.

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Answer:

SaS

Step-by-step explanation:

Answer:

[tex]x = \sqrt{87}[/tex]

Step-by-step explanation:

So, we need to use a bit of an unorthodox method here. We will use the Pythagorean theorem to find x. We will first start by finding out what all of our sides are. In the theorem, it's  [tex]a^{2} + b^{2} = c^{2}[/tex] . We know that the b is x, and the c is 16, but we need to know what a is. a is not 18. We need to find the distance starting at the right triangle. To do that, we must subtract 5 from 18, giving us 13. So, we have:

[tex]13^{2} + x^{2} = 16^{2}[/tex]

Now, we will simplify the equations:

[tex]169 + x^{2} = 256[/tex]

Then, we will subtract 169 from both sides, giving us:

[tex]x^{2} = 87[/tex]

Square rooting both sides gives us:

[tex]x = \sqrt{87}[/tex]

And we cannot simplify further because 87's prime factorization doesn't let it have any ways to get out of the square root.  

Hope this helped

The university accepts 6000 students out of the 10000 that applied.

Enrolled, in the context of education, is the process of registering a student with a school. The process typically requires a student to complete an application form and submit it to the school, along with any other required documents or fees. Once the student has been accepted and enrolled, they will be given a student ID number and will be able to access all the school's resources, such as classes and activities. In addition, the school may assign an advisor to the student to help them adjust to the school and plan out their academic path.

Of those 6000 accepted students, 45% will actually enroll, which is 2700 students. Therefore, of the 10000 students that applied, 2700 will actually enroll into the university.

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As per the given probability, the flipped coin is Coin A.

Probability in math is know as the entire possible set of outcomes of a random experiment is the sample space or the individual space of that experiment.

Here we have given that you have two biased coins. Coin A comes up heads with probability 0. 1 and Coin B comes up heads with probability 0. 6.

Here we know that you are not sure which is which, so you choose a coin randomly and flip it.

As per the given situation here we have to know that if the flip is heads, then you guess that the flipped coin is B.  

Which is defined that if the the flip is tails, then you guess that the flipped coin is A.  

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Answer:

Step-by-step explanation: You can add all of these numbers with a calculator. but be sure what are the numbers telling you what to do. So always focus on the words that are going to mention about the numbers.

Therefore, 60 different combinations can be made wearing one of each type

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Answer:

Hope the picture helps you draw.

Step-by-step explanation:

The measures of the angles of the triangles are

The measure of ∠B = 80.3°

The measure of ∠C = 59.7°

The length of side AB = 20.2 units

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

if a² + b² = c² , it is a right triangle

if a² + b² < c² , it is an obtuse triangle

if a² + b² > c² , it is an acute triangle

Given data ,

Let the triangle be represented as ΔABC

Now , the measure of side AC = 23

The measure of side BC = 15

The measure of ∠A = 40°

From the law of sines , we get

( sin A ) / a = ( sin B ) / b = ( sin C ) / c

Substitute the value of A and a in the equation , we get

sin ( 40 )° / 15 = sin B / 23

On simplifying the equation , we get

sin B = ( 23/15 ) x sin ( 40 )°

Now , m∠B = 80.27°

So , the measure of angle ∠B = 80.3°

And ,

The interior angles of a triangle is 180°

So , The measure of angle ∠C = 180° - ( 80.3° + 40° )

On simplifying the equation , we get

The measure of angle ∠C = 59.7°

Now ,

From the law of cosines , c² = a² + b² - 2ab ( cos C )

Substitute the value of a , b and cos C in the equation , we get

c² = 15² + 23² - 2 ( 15 ) ( 23 ) cos ( 59.7 )°

On simplifying the equation , we get

c² = 225 + 529 - 348.12363

c² = 405.87

Taking square roots on both sides of the equation , we get

c = 20.156

c = 20.2 units

Therefore, the measure of side AB = 20.2 units

Hence , the measures angles of triangle is solved

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Answer:

A directed segment is a segment that has distance (length) and direction. Hope this helps.

We can plot in the coordinate plane if an ordered pair is known to us.

The space or plane in where location of points is represented by a pair of numerical terms with respect to some reference lines or reference direction is called coordinate plane.

let we have some pair of numerical terms such as A (4, 9) and B (6, 10)

that is needed to plot in the coordinate plane.

At first, we will plot the point A (4, 9)

we will start from the origin and move horizontally along the direction of X axis up to 4 unit. In the next, start again and move up vertically in the direction of y axis up to 9 unit. And we will draw a point at the final location.

By the same way, we can plot the point B.

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The equation y = 5x - 8 and y = 9x - 8 have one solution at

(0, -8)

The equation is solved simultaneously by elimination method as follows

y = 5x - 8

y = 9x - 8

subtraction the equations

0 = -4x - 0

-4x = 0

x = 0

substituting x = 0 into y = 5x - 8

y = 5x - 8

y = 5 * 0 - 8

y =0 - 8

y = -8

The solution of the equation is at the point (0, -8)

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Answer: Trapezoid

Step-by-step explanation:

Answer:

Step-by-step explanation:

Trapezoid square and the down right all the way

When a polynomial has four or more terms, the easiest way to factor it is to use grouping.

Grouping can be understand more better with an example:

for eg:  factor x^3 + x^2 – x – 1 by using grouping. Just follow these steps:

However, x^2 – 1 is a difference of squares and factors again as (x+1)(x-1). This gives you a final factorization of: (x + 1)(x + 1)(x – 1), or (x + 1)2(x – 1).

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Answer:

144

I wish you luck in your assignments.

Answer: 144 articles

Step-by-step explanation:

If it makes 12 in half-hour, then 24 in an hour because 12*2 is 24.

then 24*6=144.

Christopher sold 20 cups of large 20-ounce cups of lemonade

outside his house.

A straight line on the coordinate plane is represented by a linear function. As an illustration, the equation y = 3x – 2 depicts a linear function because it is a straight line in the coordinate plane.

Any function whose graph is not a straight line is said to be nonlinear. Any curve other than a straight line can be a graph of it.

An example of a non-linear function is a quadratic function.

Given, Christopher has set up a lemonade stand outside his house and sells small cups and large cups of lemonade.

Small cups sold is x and the number of large cups sold is y.

Each small cup holds 10 ounces of lemonade and each large cup holds 20 ounces of lemonade and he sold 800 ounces.

Therefore,

10x + 20y = 800...(i)

He also sold twice as many small cups as large cups.

Therefore,

2y = x...(ii)

10(2y) + 20y = 800.

20y + 20y = 800.

40y = 800.

y = 20.

So, He sold 20 cups of large lemonade.

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Answer:

ED = AB = 25√3

Step-by-step explanation:

Let ED = AB = X

DC = 100 - BC

Tan 60 = [tex]\frac{\sqrt{3} }{1} = \frac{ED}{DC}[/tex] = [tex]\frac{X}{100-BC}[/tex]

[tex]\sqrt{3} (100-BC) = X[/tex]

Tan 30 = [tex]\frac{1}{\sqrt{3} } = \frac{AB}{BC} = \frac{X}{BC}[/tex]

[tex]\frac{BC}{\sqrt{3} } = X[/tex]

[tex]\sqrt{3} (100-BC) = \frac{BC}{\sqrt{3} } \\3(100-BC) = BC\\300 - 3BC = BC\\300 = BC + 3BC\\300 = 4BC \\75 = BC[/tex]

X = [tex]\frac{BC}{\sqrt{3} } = \frac{75}{\sqrt{3} }\\[/tex]

X = 25√3