matt is five years older than twice his cousin andy’s age. the sum of their ages is less than 35. let x represent andy's age. which inequality represents andy’s possible age? 0

Answer:

4 or 8, depending on how you interpret the questions

Step-by-step explanation:

In order to break even, they have to sell 4 widgets.  In other words, to make back the $200 they spent on design, they have to sell 4 widgets.  Anything over that is profit.  This assumes the entire $50 selling price goes to profit (no other information was given).

x = number of widgets

50x ≥ 200

x ≥ 4

To make another $200 above the break even, they have to sell 4 more widgets for a total of 8.

Answer:

Third quadrant

Step-by-step explanation:

Look at the attached image. All the points are in the third quadrant.

Answer:

Abc

Step-by-step explanation:

2b + c + 3a = Abc

Answer:

Your answer is x = 24 , y =8√3

Step-by-step explanation:

Sorry for late answer actually I was preparing for my exams. ❤

The required value of the variable is given as x = 24 and y = 8√3. Option C is correct.

Given that,
To determine the value of the variable x and y using trigonometric operators.

These are the equation that contains trigonometric operators such as sin, cos.. etc.. In algebraic operations.



Here,
sin30 = y / 16√3
16√3 / 2 = y
y = 8√3
Now,
cos30 = x / 16√3
√3 / 2 × 16√3 = x
x = 24

Thus, the required value of the variable is given as x = 24 and y = 8√3. Option C is correct.

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Answer:

-8

Step-by-step explanation:

The estimated total number of heartbeats in an average lifetime of 68.4 years is 2.9 billion heartbeats. The maximum number of 91 kg people that can safely occupy an elevator is 10 people.  The diameter of human hair is 0.000056 meters.

(a) To estimate the total number of heartbeats in a lifetime, we multiply the heart rate (69.2 beats/minute) by the number of minutes in a year (60 minutes/hour * 24 hours/day * 365.25 days/year) and then multiply by the number of years in a lifetime (68.4 years). The calculation is: 69.2 beats/minute * 60 minutes/hour * 24 hours/day * 365.25 days/year * 68.4 years ≈ 2,886,699,648 beats. Therefore, the estimated total number of heartbeats in an average lifetime is approximately 2.9 billion heartbeats.

(b) To determine the maximum number of 91 kg people that can occupy the elevator, we divide the maximum mass the elevator can hold (1 metric ton or 1000 kg) by the mass of each person (91 kg). The calculation is: 1000 kg / 91 kg ≈ 10.98. Since we can only have whole numbers of people, the maximum number of people that can safely occupy the elevator is 10.

(c) To express the diameter of a human hair in meters, we convert the given diameter of 56 μm to meters by dividing by 1 million (since 1 μm = 1/1,000,000 meters). Therefore, the diameter of human hair is approximately 0.000056 meters.

(d) To convert 74 miles per hour to meters per second, we multiply the given value by the conversion factor 1609 meters/mile and divide by 3600 seconds/hour. The calculation is 74 miles/hour * 1609 meters/mile / 3600 seconds/hour ≈ 33.12 meters/second. Therefore, 74 miles per hour is approximately equal to 33.12 meters per second.

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Answer:

d = 5.5t

Step-by-step explanation:

Andrew jogs at an average speed of 5.5 miles per hour. He is planning a jog for Saturday morning. How far can Andrew go on his jog? Write an equation for the problem and use the equation to answer the question.

speed = distance / time

speed = 5.5

distance = d

t = time

5.5 = d/t

d = 5.5t

Answer:

d=5.5t

Step-by-step explanation:

Average speed 5.5 per hour

speed= distance/time

speed=5.5

distance=d

T=time

D=5.5t

5.5=d/t

Answer:

Step-by-step explanation:

Given that:

Keiko sold 3 less than three-fourths of his sister's sale.

To find:

Expression that represents what Keiko sold ?

\(1.\ \dfrac{3}{4} x - 3 \\2.\ \dfrac{3}{4} x + 3 \\ 3.\ 3 x + \dfrac{3}{4} \\4.\ 3x - \dfrac{3}{4}\)

Solution:

First of all, let the sales done by Keiko's sister = \(x\)

Now, let us consider the Keiko's sale word by word.

3 less than three-fourths of his sister's sale.

i.e. subtract 3 from the expression obtained in 1st line.

\(\dfrac{3}{4}x-3\)

So, sales done by Keiko = \(\dfrac{3}{4}x-3\)

So, correct answer is:

\(1.\ \dfrac{3}{4}x-3\)

\(\frac{3}{4}x-3\)

An algebraic expression is one that is obtained by performing a finite number of algebraic operations on symbols that represent numbers.

Any of the common arithmetic operations, such as addition, subtraction, multiplication, division, raising to a whole number power, and taking roots, is a basic algebraic operation.

Let \(x\) denotes sale of sister of Keiko.

As Keiko sold \(3\) less than three-fourths of his sister's sales,

Sales of Keiko \(=\frac{3}{4}x-3\)

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To find the distance between the two cruise liners, we can use the Pythagorean theorem. Let's assume Liam is standing at the vertex of a right triangle, with the cliff being the vertical side and the distances to the cruise liners being the diagonal sides.

Let's denote the distance between Liam and the first cruise liner as x, and the distance between Liam and the second cruise liner as y.

For the first cruise liner, we have a right triangle with one leg measuring 2 km (the height of the cliff) and the hypotenuse measuring 5 km. Using the Pythagorean theorem, we can calculate x:

x^2 + 2^2 = 5^2

x^2 + 4 = 25

x^2 = 21

x ≈ √21

Similarly, for the second cruise liner, we have a right triangle with one leg measuring 2 km and the hypotenuse measuring 6.8 km. Using the Pythagorean theorem, we can calculate y:

y^2 + 2^2 = 6.8^2

y^2 + 4 = 46.24

y^2 = 42.24

y ≈ √42.24

Now, to find the distance between the two cruise liners, we subtract the two distances:

Distance between the two cruise liners = y - x ≈ √42.24 - √21

Calculating the approximate values:

Distance between the two cruise liners ≈ 6.5 km

Therefore, the approximate distance between the two cruise liners is 6.5 km.

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Answer:

-2

-1

Step-by-step explanation:

The y-intercept is the point on the y-axis intersected by the graph.

y-intercept is -2

The x-intercept is the point on the x-axis intersected by the graph.

x-intercept is -1

Answer:

see below

Step-by-step explanation:

The x intercept is where it crosses the x axis

It crosses at x = -1

(-1,0)

The y intercept is where it crosses the y axis

It crosses at y = -2

(0,-2)

Answer: 63,343

Step-by-step explanation:

3,649 = 3,000 + 600 + 40 + 9

Now, the multiplication:

( 3,000 + 600 + 40 + 9 ) * 7

21,000 + 42,000 + 280 + 63

Making the sum:

63,343

The expression of the inequality on the graph is;

y ≥ -x+6

y ≥ x - 4

From the graph, we can see that there are 2 lines. Therefore, this is a system of 2 simultaneous inequalities.

The formula for equation of a line in slope intercept form is;

y = mx + c

Let's start with coordinates for the line slanting rightwards.

At x = 0, y = 6

At x = 1, y = 5

Thus;

6 = 0(m) + c

c = 6

Also;

5 = 1(m) + 6

5 - 6 = m

m = -1

Thus, the equation is;

y = -x + 6

We can see the line is a broken line and the shaded portion is above the line. This represents;

y ≥ -x+6

For the second line;

At x = 5, y = 1

At x = 6, y = 2

Thus;

1 = 5m + c

2 = 6m + c

Subtract eq 1 from eq 2 to get;

m = 1

Thus;

1 = 5(1) + c

c = 1 - 5

c = -4

This represents;

y = x - 4

We can see the line is a broken line and the shaded portion is above the line. This represents;

y ≥ x - 4

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Answer:

D. 4a³ + 24ab² - 25b³

Step-by-step explanation:

Simplify the given polynomial expression to find its equivalent as follows:

(2a - 3b)(2a² + 6b²) + (6a²b + 12ab² - 7b³)

2a(2a² + 6b²) -3b(2a² + 6b²) + (6a²b + 12ab² - 7b³)

4a³ + 12ab² - 6a²b - 18b³ + 6a²b + 12ab² - 7b³

Collect like terms

4a³ - 6a²b + 6a²b + 12ab² + 12ab² - 18b³ - 7b³

4a³ + 24ab² - 25b³

Therefore, 4a³ + 24ab² - 25b³ is equivalent to the polynomial expression, (2a - 3b)(2a² + 6b²) + (6a²b + 12ab² - 7b³).

Answer:A- 4a³+24ab²-25b³

Step-by-step explanation:

Answer:

(5 , -6)

Step-by-step explanation:

When you are going to rotate something to 180 degrees, either in the clockwise or counterclockwise direction, each point of x and y will be changed from (x, y) to (-x, -y).

Before rotation, x = -5 and y = 6

After rotation, x = 5 and y = -6

Answer:

(5 , -6) when rotated 180 degrees

It would take 5040 cubic inches of water to completely fill the aquarium.

We know that the formula for the volume of cuboid :

V = length × width × height

Let us assume that l represents the length of the aquarium, w represent the width and h represents the height.

Here, l = 20 inches

w = 14 inches

and h = 18 inches

Using the formula for the volume of cuboid, the volume of aquarium would be,

V = l × w × h

V = 20 × 14 × 18

V = 5040 cu.in.

Therefore, it would take 5040 cu.in. of water.

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To write a polynomial in standard form, simplify and then arrange the terms in descending order.

\(\alpha x^2+bx+c\)

The standard form is \(4x^2+8x+5\)

\(4x^2+8x+5\)

Therefore, the standard form is \(4x^2+8x+5\)

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Yolanda is buying school supplies. She buys n packages of pencils at 1.40 per package and m pads of paper at 1.20 each. The expression 1.4 represents the cost of one package of pencils while the expression 1.2 represents the cost of one pad of paper.

The given expressions represent the cost of one package of pencils and one pad of paper. Hence,1.4 represents the cost of one package of pencils.1.2 represents the cost of one pad of paper.Yolanda buys n packages of pencils.

Therefore, the total cost of pencils will be n × 1.4

Similarly, Yolanda buys m pads of paper.

Therefore, the total cost of pads will be m × 1.2

Therefore, the total cost of buying n packages of pencils at 1.40 per package and m pads of paper at 1.20 each will be,1.4n + 1.2m

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Answer:(x+3)=2x

Step-by-step explanation:

Answer:

- 12x² + 9x + 9

Step-by-step explanation:

(- 10x² + 2) + (- 2x² + 9x + 7 ) ← remove parenthesis

= - 10x² + 2 - 2x² + 9x + 7 ← collect like terms

= - 12x² + 9x + 9

A quadrilateral whose diagonals do not always bisect each other is a rectangle.

A rectangle is a quadrilateral with four right angles. The diagonals of a rectangle are perpendicular to each other and bisect each other, but not all quadrilaterals with perpendicular diagonals and diagonals that bisect each other are rectangles. For example, a square is a type of quadrilateral with perpendicular diagonals and diagonals that bisect each other, but it has four congruent sides and four right angles, unlike a rectangle.

The word "rectangle" comes from the Latin words "rectus," meaning "right," and "angulus," meaning "angle." This reflects the fact that a rectangle has four right angles.

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The length of Stan's movie is 2 hours 25 minutes

The length of Talia's movie is 2 hours 55 minutes.

In order to determine the length of the movies, subtract the end time of the movie from the time the movie started.

Subtraction is the mathematical operation that is used to calculate the difference between two or more numbers. The sign that is used to represent subtraction is -.

Length of the movie = time the movie ended - time the movie started

Length of Stan's movie = 9:40 - 7:15 = 2 : 25 hours

Length of the Talia's movie = 10 : 10 - 7 : 15 = 2 : 55 hours

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Answer: I believe he could wear 768 outfits

Step-by-step explanation: I had a similar question consisting of the same numbers.

Treat the matrices on the right side of each equation like you would a constant.

Let 2X + Y = A and 3X - 4Y = B.

Then you can eliminate Y by taking the sum

4A + B = 4 (2X + Y) + (3X - 4Y) = 11X

==>   X = (4A + B)/11

Similarly, you can eliminate X by using

-3A + 2B = -3 (2X + Y) + 2 (3X - 4Y) = -11Y

==>   Y = (3A - 2B)/11

It follows that

\(X=\dfrac4{11}\begin{bmatrix}12&-3\\10&22\end{bmatrix}+\dfrac1{11}\begin{bmatrix}7&-10\\-7&11\end{bmatrix} \\\\ X=\dfrac1{11}\left(4\begin{bmatrix}12&-3\\10&22\end{bmatrix}+\begin{bmatrix}7&-10\\-7&11\end{bmatrix}\right) \\\\ X=\dfrac1{11}\left(\begin{bmatrix}48&-12\\40&88\end{bmatrix}+\begin{bmatrix}7&-10\\-7&11\end{bmatrix}\right) \\\\ X=\dfrac1{11}\begin{bmatrix}55&-22\\33&99\end{bmatrix} \\\\ X=\begin{bmatrix}5&-2\\3&9\end{bmatrix}\)

Similarly, you would find

\(Y=\begin{bmatrix}2&1\\4&4\end{bmatrix}\)

You can solve the second system in the same fashion. You would end up with

\(P=\begin{bmatrix}2&-3\\0&1\end{bmatrix} \text{ and } Q=\begin{bmatrix}1&2\\3&-1\end{bmatrix}\)

Step-by-step explanation:

hence it has been done . check the file .

hope this helped you

any problem then comment it .

Answer:B

Step-by-step explanation:

The equation y = 8x has a constant of proportionality of 8. Option B is correct.

Types of proportion

Given equation is \(y = 8x\).

On comparing above equation and y =kx

\(k = 8\).

Hence, option B is correct.

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Answer:

1/12 of a mile

Step-by-step explanation:

Total distance of 10 members of the Balin's soccer club =5/6 of a mile

To find the distance that each member ran, Balin wrote the expression:

5/6 ÷ 10

Which expression is equivalent to Balin's expression?

5/6 ÷ 10

= 5/6 × 1/10

= 5/60

= 1/12 of a mile

Each member of the Balin's soccer club ran 1/12 of a mile

e

Step-by-step explanation:

Considering that it has a higher coefficient of variation, the distribution of cell phone bills at Smithtown South High School is more spread out.

The coefficient of variation for a distribution is given by the standard deviation of the distribution divided by the mean of the distribution. The higher the coefficient, the more spread out the distribution is.

For the distributions in this problem, the coefficients are given as follows:

Due to the higher coefficient of variation, the distribution of cell phone bills at Smithtown South High School is more spread out.

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The R9,000 loan offer can be analyzed as follows;

A loan is a financial agreement that is made between a lender and a borrower, such that the borrower accepts a certain amount of money provided by the lender, which is to be paid back after a specified period of time, with an interest.

The total amount which has to be paid as repayment for the loan can be obtained by finding the product of the monthly installment and the total number of months to repay the loan:

Total amount Theo pays = R318.92 × 48 = R15308.16

The reasons banks and other financial institutions offer loans to people that did not apply for loans includes;

Theo's investment options can be analyzed as follows;

Option 1: Investment with simple interest calculation

Interest earned = R9,000 × 8% × 4 years = R2,880

The total value of the investment after 4 years = R9,000 + R2,880 = R11,880

Option 2: Investment with compound interest calculation

The total value of the investment after 4 years = R9,000 × (1 + 7%)⁴ = R11,797.16409

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The change to the rental agreement made by Larry Landlord without informing Telly is considered a breach of contract, specifically a material breach, which allows Telly to be discharged from the contract.

When a party to a contract makes a significant change to the terms of the agreement without the consent or knowledge of the other party, it is generally considered a breach of contract. In this case, Larry Landlord altered the rental agreement by doubling the monthly rent payment without informing Telly. Such a change is considered a material breach, as it substantially affects the terms of the contract and the obligations of both parties.

As a result, Telly is entitled to be discharged from the contract, meaning she is no longer bound by its terms and obligations. She may seek legal remedies or negotiate a resolution based on the breach.

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