One large box and two small boxes weigh a total of 100 pounds. One large box and four small boxes weigh a total of 150 pounds. The weight limit of a trailer is 1500 pounds. Write an inequality that represents the numbers of large, x, and small, boxes that can be loaded in the trailer.

Y-axis divides the line segment formed by the points ( -3 ,2) and ( 6,1) in the ratio equals to 1 :2.

As given in the question,

Coordinates of the line segment is given by :

( x₁ , y₁ ) = (-3, 2)

(x₂ , y₂ ) = ( 6,1)

Let the ratio of the given line segment divided by the y -axis that is          ( x, y) = ( 0, y ) be   m : n given by the formula:

( x, y ) = [ ( mx₂ + nx₁) /(m +n) , (my₂ + ny₁ ) / ( m + n ) ]

Substitute the values we get,

( 0 ,y ) =  [ ( 6m -3n) /(m +n) , (1m + 2n ) / ( m + n ) ]

⇒ ( 6m -3n) /(m +n)  = 0

⇒ 6m -3n = 0

⇒ 6m = 3n

⇒m : n = 1 : 2

Therefore, y-axis divides the given line segment into the ratio 1 : 2.

The above question is incomplete, the complete question is :

In what ratio is the line segment joining the points (- 3 2) and (6,1) is divided by Y-axis?

Learn more about ratio here

brainly.com/question/13419413

#SPJ4

The approximate cost per ounce of a container of gochujang at the market is given as follows:

$0.5.

As we have the graph of the linear function, the best way to define it is in slope-intercept form, as follows:

y = mx + b.

For which the parameters are given as follows:

The cost per ounce is represented by the slope.

From the graph, we have that the graph starts at the origin, and when the number of ounces increases by 4, the cost increases by 2, hence the slope representing the cost per ounce is given as follows:

m = 2/4

m = $0.5.

More can be learned about linear functions at https://brainly.com/question/24808124

#SPJ1

The sides given as 16cm , 12cm and 20cm  forms a right triangle because the sides satisfies the condition of Pythagoras Theorem .

What is Pythagoras Theorem ?

The Pythagoras Theorem states that the square of the longest side (hypotnuse) is equal to the sum of the square of the other two sides .

The sides of the triangle are given as ⇒ 16cm , 12cm and 20cm ;

here the hypotnuse (longest side) is = 20 cm ;

According to Pythagoras theorem ,

⇒ [tex]20^{2} =12^{2} +16^{2}[/tex] ;

⇒ [tex]400 =144+256[/tex] ;

⇒ [tex]400=400[/tex] ;

So , The condition of Pythagoras theorem is satisfied .

Therefore , the given sides can form a Right Triangle .

The given question is incomplete , the complete question is

Does the sides 16cm , 12cm and 20cm form a right triangle ?

Learn more about Right Triangle here

https://brainly.com/question/30238309

#SPJ4

Solving the quadratic equation, it is found that the company needs to sell 8 products for the net income to be equal $0.

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

here, we have,

It is given by:

f(x) = 9x² - 54x - 144.

It can be simplified as follows:

f(x) = 9(x² - 6x - 16)

Then:

f(x) = 9[(x + 2)(x - 8)]

It has a net income equals to 0 when:

f(x) = 0,

hence:

x + 2 = 0 -> x = -2.

x - 8 = 0 -> x = 8.

The amount of products sold is positive, hence, the company needs to sell 8 products for the net income to be equal $0.

More can be learned about quadratic equations at brainly.com/question/24737967

#SPJ1

Answer:

real number, in mathematics, a quantity that can be expressed as an infinite decimal expansion. Real numbers are used in measurements of continuously varying quantities such as size and time, in contrast to the natural numbers 1, 2, 3, …, arising from counting

Step-by-step explanation:

The quotient of any two integers is an integer.

A real number is a number that can be measured and represented on a number line; this includes fractions, decimals, irrational numbers, rational numbers, and basically every number you encounter. With that in mind, the quotient of 2 real numbers is not necessary an interger as 2.01/ 1 is not an integer

let's keep in mind that a conjugate is no more than the same "pair" but with a different sign between, so the conjugate of meow + quack is simply meow - quack, and so on, let's also recall that i² = -1.

[tex]\textit{difference of squares} \\\\ (a-b)(a+b) = a^2-b^2 \\\\[-0.35em] ~\dotfill\\\\ -1-\sqrt{5}i\hspace{5em}\stackrel{conjugate}{-1+\sqrt{5}i} \\\\\\ (-1-\sqrt{5}i)(-1+\sqrt{5}i)\implies (-1)^2~~ - ~~(\sqrt{5}i)^2\implies (-1)^2~~ - ~~(\sqrt{5})^2 i^2 \\\\\\ 1~~ - ~~(\sqrt{5^2})i^2\implies 1~~ - ~~(5)(-1)\implies 1-(-5)\implies 1+5\implies \text{\LARGE 6}[/tex]

Answer:

4 km wide and 6 km long.

Step-by-step explanation:

Let the width be x, then the length is x+2 km.

Area = width * length

Substituting the given values:

24 = x(x + 2)

24 = x^2 + 2x

x^2 + 2x - 24 = 0

(x + 6)(x - 4) = 0

x = -6, 4

As x must be positive, then x = 4.

So, the dimensions are 4 and 4+2

= 4, 6,

Answer:

width = 3.46 km and length = 6.93 km

Step-by-step explanation:

let the width be : X km

then the length would be: 2X km

as area is length x width

therefore:

2X x X = 24

2X² = 24

X² = 24/2

X² = 12

X = [tex]\sqrt{12}[/tex]

X=  3.46

the width would be 3.46 km while the length would be 2X = (93.46) = 6.93 km

We may apply the simple interest formula to find the due date for repayment from Mikos is 5 months.

I = P*r*t, where I represents interest, P the principal (initial sum), r the interest rate, and t the period of time in years.

The maturity value formula can be used to calculate interest given that the loan's principal is $100,000 and its maturity value is $104,375:

Where MV is the maturity value, P is the principal, and I is the interest, the formula is: MV = P + I.

With the above data, we obtain: 104,375 = 100,000 + I

  I = 4,375.

Now we can use this value of I to find the time t in years:

I = P*r*t

4,375 = 100,000 (0.105) t

t = 4.375 / (100,000 x 0.105)

t = 4.375 / 10,500

t = 0.417 years or approximately 5 months

 So, it takes approximately 5 months to repay the pay back amount .

Therefore, Mike must repay the amount by April 14, which is around five months after the day he took out the loan.

To know more about simple interest at :

brainly.com/question/22621039

#SPJ4

As y varies directly with x, The value of y when x = -4 is 8/5.

Proportional relationships are relationships between two variables where their ratios are equivalent.

Direct variation is expressed as;

y ∝ x

Then, y = k(x)

Where k is the proportionality constant.

Given that y = -8 and x = 20.

First determine the constant of proportionality k.

y = k(x)

-8 = k( 20 )

-8/20 = k

k = -8/20

k = -2/5

Next, we determine the value of y when x = -4.

y = k(x)

Plug in k = -2/5 and x = -4

y = -2/5( -4 )

y = -2/5 × -4

y = 8/5

Therefore, the numerical value of y is 8/5.

Learn more about proportionality here: https://brainly.com/question/27530069

#SPJ1

Therefore , the solution of the given problem of circle comes out to be 100 rotations of the front tire will be made by the back wheel.

Each point in the plane whose distance from that other point is a certain value forms a circle (center). It is therefore a curve composed of vertices that are spaced apart from one another in the plane by a specific amount. Furthermore, it is symmetrical about the center at all angles in terms of rotation. The closed, two-dimensional plane of a circle has all pairs of endpoints equally separated from the "center." When a line is drawn through the circle, a circle symmetry line is created. Furthermore, it rotates equally from all angles about the center.

Here,

The circle of the rear wheel is equal to circle = diameter x π, or 2.5 feet by 12 inches, or 30 inches.

The length of the front axle is 30 x 2 = 60 inches.

The diameter of the front wheel, C, is equal to 60 x Pi, or 60π, in inches.

The diameter of a back wheel is 4 x 2 = 8 inches.

The circumference of back wheel is C = 8 x Pi = 8π in inches.

750 revolutions are equal to

100 × [60Pi/8π] = 6,000π/8π.

100 rotations of the front tire will be made by the back wheel.

Therefore , the solution of the given problem of circle comes out to be 100 rotations of the front tire will be made by the back wheel.

To know more about circle visit:

https://brainly.com/question/29142813

#SPJ4

Answer:

A) 4x4 – 3x3y + 8x2y2 – 7xy3

Step-by-step explanation:

The polynomial written in standard form is: 4x4 + 8x2y2 - 3x3y - 7xy3. Option C

In standard form, a polynomial is written with the highest exponents first and positive numbers in front of each term.

This means that the term with the greatest power comes first, followed by the terms in decreasing order of powers.

The polynomial is organized in option C like this.

Learn more about polynomial

https://brainly.com/question/4142886

#SPJ2

For Sydney with $100 at 5%, monthly, for 10 year we get 229050.

Annual percentage rate (APR) refers to the yearly interest generated by a sum that's charged to borrowers or paid to investors. APR is expressed as a percentage that represents the actual yearly cost of funds over the term of a loan or income earned on an investment.

The interest rate is the amount a lender charges a borrower and is a percentage of the principal—the amount loaned. The interest rate on a loan is typically noted on an annual basis known as the annual percentage rate (APR).

Let the equation be

A = [ p(1 + r/n)nt ] + [ PMT ((( 1 + r/n)nt - 1) / (r / n)) ]

For Sydney with $100 at 5%, monthly, for 10 year

A = [ 100(1 + 0.05/12)(12)(10) ] + 100 (((1 + 0.05/12)(12)(10) - 1) / (0.05 / 12)) ]

= 229050

Therefore, the correct answer is 229050.

To learn more about annual interest rate refer to:

https://brainly.com/question/15728540

#SPJ1

The answer is C) 195/8

First, we can use the fact that A, B, C, D, E, and F are concyclic and that D, E, and F are the midpoints of AB, BC, and AC respectively.

Let r be the radius of the circumcircle of triangle ABC. Then using the Pythagorean theorem, we can find that r = (151413) / (4*K) where K is the area of the triangle.

Now we can use the property that the perpendicular bisectors of any triangle pass through the circumcenter of the triangle. We know that the midpoint of a line segment is the foot of the perpendicular from that point to the other endpoint. Then we can use the property that the radius from the circumcenter of the triangle to the midpoint of a side is half the length of that side.

Therefore, the circumcenter of triangle BDE is located at X = (BD/2, DE/2) = (13/2, 7/2) and the circumcenter of triangle CEF is located at X = (CE/2, EF/2) = (15/2, 7/2).

So the coordinates of X are (13/2, 7/2) and since the circumcenter of a triangle is equidistant from each vertex of the triangle, we can find that XA = XB = XC = r = r = (151413) / (4*K)

Therefore, XA + XB + XC = 3r = 3(151413) / (4*K) = (195/8)

So the answer is c. 195/8.

To learn more about triangles visit: brainly.com/question/2773823

#SPJ4

[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$1230\\ r=rate\to 3.19\%\to \frac{3.19}{100}\dotfill &0.0319\\ t=years\dotfill &3 \end{cases} \\\\\\ A = 1230[1+(0.0319)(3)] \implies \stackrel{balance}{\boxed{A \approx 1347.71}}~\hfill \underset{interest}{\stackrel{1347.71~~ - ~~1230}{\boxed{117.71}}}[/tex]

A. The total number of points of intersection of the graphs of the equations y = 5e^x and xy = 20 is two.

To find the points of intersection, we must solve the two equations for x and y.

For the first equation, y = 5e^x, we can solve for x by taking the natural logarithm of both sides and getting x = ln(y/5).

For the second equation, xy = 20, we can solve for y by dividing both sides by x and getting y = 20/x.

We can then substitute the expression for x in terms of y into the expression for y in terms of x and solve for y to get y = 20/(ln(y/5)). This is a nonlinear equation that must be solved numerically.

By using numerical methods, we can solve the equation and find the two points of intersection, which are (x, y) = (3.68, 4.64) and (x, y) = (0.87, 22.95).

For more questions like Graphs click the link below:

https://brainly.com/question/12657608

#SPJ4

Yes, the set of all real numbers is uncountably infinite but "infinity" is not   a member of the set of real numbers.

Basically, The real numbers R is the set of "all the numbers" on the number line that  includes the rationals and irrationals together.

The real numbers are an uncountably infinite set – there actually are far more real numbers than there are natural numbers, and there is no way to line up the reals and the naturals so that we are assigning exactly one real number to each natural number. Hence there is no possible way of counting the number it can be considered in the category of uncountably infinite. If the domain of a function is all real numbers, you can represent this using interval notation as (−∞,∞), however "infinity" is not a member of the set of real numbers.

Learn more about Real numbers here:

https://brainly.com/question/551408

#SPJ4

7 girls own 7 dresses, and each dress has 7 different hats to go with it then the total number of hats are 49.

Calculating the sum of two or more numbers is the process of multiplication. It is stated as "a multiplied by b" when two numbers, let's say "a" and "b," are multiplied.

Multiplication in mathematics is essentially just adding a number repeatedly in relation to another number.

A word problem is a type of mathematics exercise where the majority of the problem's context is supplied in spoken language as opposed to mathematical notation. Most word problems incorporate some type of narrative, hence they are sometimes called "story problems," and the quantity of technical jargon they employ can vary.

Given that 7 girls own 7 dresses, and each dress has 7 different hats to go with it then the total number of hats are:

Hats = (7)(7) = 49.

Hence, there are a total of 49 hats.

Learn more about multiplication here:

https://brainly.com/question/1292482

#SPJ1

The required system of equation is given as y = 3x + 12 and y=x³+4x²+3x+12.

The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.

Given equation,
y=x³+4x²+3x+12

To determine the x-intercept put equation y = 0

0 = x³+4x²+3x+12

Factorize the above equation

0=(x²+3)(x+4)

One of the factors from above is given as

x+4=0  

x = -4

The x-intercept is (-4,0)

For the y-intercepts, x=0 and solve.

y = 12

y = 12

The y-intercept is (0,12)

Now equation of the line passing these points is given as.

m = (y₂ - y₁) /  (x₂ - x₁)
m = 12/3
m = 3

C, we already have C=12

So the equation of the line is
y = mx + c
y=3x+12

Thus, the required system of equation is given as y = 3x + 12 and y=x³+4x²+3x+12.

Learn more about equations here:

brainly.com/question/10413253

#SPJ1

Answer:

a. Leslie must pay the first $500 of the repair costs, as that is her comprehensive insurance policy's deductible.

b. The insurance company must pay the remaining $1,266 of the repair costs, as that is the total cost of the repairs ($1,766) minus Leslie's portion of the cost (the $500 deductible).

Therefore , the solution of the given problem of combination comes out to be  479001.6.

Combinations are mathematical procedures that count the number of possible configurations from a set of items, where the selection direction is immaterial. You can select any arrangement of the parts in any combination. It's possible to mix together combinations and permutations.

Here,

Given : four ambassadors and one advisor for each of them are to be seated at a round table with 12 chairs numbered in order 1 to 12..

and n ways for seating 8 people.

Thus , to find this permutation- combination arrangement .

So,

nPr => 6 P 6 and * 12P6

nPr =>  665280 * 720

nPr = > 47,90,01,600

and divide it by 1000 .

So ,

=> 479001600/1000

=> 479001.6

Therefore , the solution of the given problem of combination comes out to be  479001.6.

To know more about combination , visit

https://brainly.com/question/20211959

#SPJ4

The solution is,  D: A package that weighs 5 pounds will cost $15 for both options.

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

here, we have,

The customer can send a package for $5, plus an additional $2 per pound.

The cost, y, can be represented by the equation y = 5 + 2x,

where x represents the amount of pounds of the package.

Another option is that the customer can pay a one-time fee of $15 to send the box, represented by the equation y = 15.

so, we get,

2x + 5 = 15

x = 5

Hence, The solution is,  D: A package that weighs 5 pounds will cost $15 for both options.

To learn more on equation click:

brainly.com/question/24169758

#SPJ1

Answer:

D: A package that weighs 5 pounds will cost $15 for both options.

Step-by-step explanation:

2x + 5 = 15

x = 5

Thus, the person above me is correct :)

Answer: 15/2

Step-by-step explanation: -5/2 + 1/4W = -5/8

-    1/4W = -5/8 + 5/2

-    1/4W = 15/8

-     W = 15/8 × 4

-      W = 15/2

Answer:

B

Step-by-step explanation:

the 4 is how far along you go on the x-axis (horizontal line).

the -2 is saying it needs to be 2 boxes below 0 on the y-axis (vertical line).

therefore the answer is b

The surface area is approximately 100.5m².

Surface Area = πrl + πr²

Where r is the radius of the base and l is the slant height.

Surface Area = π(2m)(4m) + π(4m)²

Surface Area = 100.5m²

The surface area of a right circular cone can be calculated by using the formula surface area = πrl + πr². In this particular case, the height of the cone is 4m and the radius of the base is 2m. Therefore the surface area of the cone is calculated as follows: π(2m)(4m) + π(4m)² = 100.5m². This surface area includes both the base and sides of the cone.

learn more about area here

https://brainly.com/question/27683633

#SPJ4

Answer:

1) 33.422

2) 0.37

3) 34.034567

4) 19.501

5) 38.07

6) 51.02

7) 65.38

8) 0.072

Cheers

The best estimate of the average change in rent each year include the following: C. $40.

Mathematically, the rate of change is also referred to as slope or gradient and it can be calculated by using this formula;

Rate of change, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Rate of change, m = (y₂ - y₁)/(x₂ - x₁)

Next, we would determine the rate of change of the value of y with respect to the value of x on the scatter plot, which represents a line that is passing through the points (0, 800) and (10, 1200):

Rate of change, m = (1200 - 800)/(10 - 0)

Rate of change, m = 400/10

Rate of change, m = 40.

Based on the scatter plot, we can reasonably infer and logically deduce that the average rate of change in rent each year is equal to 40 dollars.

Read more on scatterplot here: brainly.com/question/28605735

#SPJ1

Complete Question:

The scatter plot below shows the average rent (in dollars per month) for a 1-bedroom apartment in New York City each year between 2000 and 2013.

Which of the following is the best estimate of the average change in rent each year?

answer choices

$0.5

$1

$40

$400

Answer:

38

Step-by-step explanation:

4/2+33-2+5=2+33-2+5=35-2+5=33+5=38

A degree 3 polynomial has either 1 real root, 2 real roots, or 3 real roots. It is possible for the polynomial to have imaginary roots as well, but these are not counted.

A polynomial of degree 3 is a equation in the form of ax3 + bx2 + cx + d = 0. For a polynomial of degree 3, the number of roots it has depends on the value of the discriminant, which is calculated using the formula b2 - 4ac.  If the discriminant is positive, the polynomial has three real roots. If the discriminant is equal to zero, the polynomial has two real roots. If the discriminant is negative, the equation has one real root and two imaginary roots. In the case of one real root, the polynomial can be factored into (x - r) (ax2 + bx + c). In the case of two real roots, the polynomial can be factored into (x - r1) (x - r2). In the case of three real roots, the polynomial can be factored into (x - r1) (x - r2) (x - r3).

Learn more about polynomial here

https://brainly.com/question/11536910

#SPJ4

Answer:

500 > 40 + 5t

Step-by-step explanation:

At least 500

40 intro = initial, constant

t = time in seconds

5 words per second

Please mark as brainliest

A type I error, also known as a false positive, is when a test incorrectly rejects the null hypothesis. In this context, a type I error would mean that the test incorrectly concludes that the proportion of water bottles that are recycled is more than 23% after the program, when in reality it is still 23%.

1. Calculate the means of the two samples.

2. Calculate the standard deviation of the two samples.

3. Calculate the degrees of freedom (df) by subtracting 1 from the total

number of samples.

4. Calculate the t-statistic by subtracting the means of the two samples, dividing the result by the standard deviation, and then dividing that result by the square root of the degrees of freedom.

5. Calculate the critical value of t from the t-distribution table for the degrees of freedom and the chosen level of significance.

6. Compare the calculated t-statistic with the critical value of t.

7. Make a decision – accept or reject the null hypothesis.

Learn more about null hypothesis here

https://brainly.com/question/28920252

#SPJ4