A publisher needs to send many books to a local book retailer and will send the books in a combination of small and large boxes. Each small box can hold 20 books and each large box can hold 45 books. There were twice as many large boxes sent as small boxes, which altogether can hold 440 books. Write a system of equations that could be used to determine the number of small boxes sent and the number of large boxes sent. Define the variables that you use to write the system.

By using the concept of equation, it can be calculated that-

The equation can be solved by using this system of equations

[tex]3x^5-5x^3+2x^2-10x+4=4x^4+6x^3-11[/tex]

What is equation?

At first it is important to know about algebraic expressions.

Algebraic expression consist of variables and numbers connected with addition, subtraction, multiplication and division.

Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.

Here the system of equation are-

[tex]3x^5-5x^3+2x^2-10x+4=0\\4x^4+6x^3-11=0[/tex]

So the equation can be solved by using this system of equations

[tex]3x^5-5x^3+2x^2-10x+4=4x^4+6x^3-11[/tex]

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Complete Question

Which equation can be solved by using this system of equations?

[tex]3x^5-5x^3+2x^2-10x+4=0\\4x^4+6x^3-11=0[/tex]

Using the concept of asymptote of the function it can be concluded that the number of boxes of cereals sold is 0 after 0 weeks, it will keep falling after reaching the maximum sales and cereals sold is always positive as the cereals introduced so the correct option are A, C and E.

A line that a curve approaches but never touches is an asymptote. The graph of a function converges to a line known as an asymptote, in other words. When graphing functions, asymptotes are usually not necessary to be drawn. The curve must not contact the asymptote when we graph them using dotted lines (imaginary lines). As a result, the asymptotes are merely made-up lines. When either the value of x or y tends to or -, the distance between the asymptote of a function, y = f(x), and its graph is close to zero.

Option A is correct as according to the option A: - B(w)= [tex]\frac{120w}{150+w^{2} }[/tex], w=0.

On putting the value of w=0 in above function implies B(w)=0.

Hence, number of boxes of cereals sold is 0 after 0 weeks.

Option C is correct as function B(w) is decreasing function after reaching its maxima according to graph.

Option E is correct as B(w)= [tex]\frac{120w}{150+w^{2} }[/tex], if w>0

implies that B(w)>0 as numerator>0 and denominator>0.

Based on the asymptote of function the number of boxes of cereals never reach 0 after cereals introduced in the store.

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The slope of the line passes through two points is (y2-y1)/ (x2- x1).

Slope of a line:

The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).

Here we have to find the slope of a line that passes through two points.

Data given:

Point 1 = (x1, y1)

Point 2 = (x2, y2)

The general formula to find the slope of a line:

Slope(m) = (y2 - y1) / (x2 - x1)

Where (x1, y1) and (x2, y2) are two points on the line.

Therefore the slope is (y2-y1)/ (x2 - x1).

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Therefore, the space inside the fence serves as the best indicator of Johnny's home's perimeter.

A perimeter is a closed path that surrounds, encircles, or outlines a two-dimensional shape or a one-dimensional length. The perimeter of a circle or an ellipse is its circumference. Perimeter calculations have many applications in the real world.

Here,

the grassy area = 40' x 100'

He has numerous outbuildings in the forested area as well, and he mows the area surrounding the trees less regularly than the rest of the yard. A fence completely encloses the area that has been described. He maintains his collection of exotic marijuana plants hidden in the long grass in the area outside the fence, which is an area he does not maintain.

Therefore, the space inside the fence serves as the best indicator of Johnny's home's perimeter.

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Answer:

       [tex]\frac{2}{7}[/tex]

Step-by-step explanation:

3.5 = [tex]\frac{7}{2}[/tex]

swap the numerator and denominator (flip the fraction):

reciprocal of [tex]\frac{7}{2}[/tex] is [tex]\frac{2}{7}[/tex]

Answer: something

Step-by-step explanation: you are welcome

Answer: 3.51

Step-by-step explanation:

Answer: The tip was 3.50$

Step-by-step explanation: Since the tip is 20% you would times the given amount by 20 then divide it by 100.

20 x 17.53 / 100 = 3.506

We're rounding to the nearest cent, so that would be 3.50.

Answer:

SA = 124 cm².

V = 72 cm³

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

Based on the given conditions, formulate: 15 × ( 1 - 2/3)

Apply Multiplicative Distribution Law: 15 - 10

Calculate the sum or difference: 5

Answer:

27.72 inches of fabric

Step-by-step explanation:

28+3=31

Fabric used on each player:

559.24÷31=18.04

271.04÷28=9.68

The required  probability that their hospital stay is from 5 to 6 days is 3.31%.

An normal distribution is a sort of ceaseless likelihood dissemination wherein most information guides bunch to the center of the reach, while the rest tighten evenly toward one or the other limit. The center of the reach is otherwise called the mean of the distribution.

We have,

mean(a) = 7.37, standard deviation(S) = 2

Using formula

[tex]Z = \frac{x-a}{S}[/tex]

Then,

P( hospital stay is from 5 to 6 days)

P(5[tex]\leq[/tex]x[tex]\leq[/tex]6) = P[tex](\frac{5-7.37}{2}\leq z\leq \frac{6-7.37}{2})[/tex] = P(-3.16 ≤ z ≤-1.827 )

⇒P(z≤-1.827) - P(z≤-3.16)

⇒ 0.034 - 0.001 = 0.331 = 3.31%

Theus, probability is  3.31%

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[tex]\tan 64^{\circ}=\frac{x}{11} \implies x=11 \tan 64^{\circ}[/tex]

The two equations of a line are 1) Two point form

2)Slope-intercept form

Two-point form: The equation of a line passing through the two points [tex](x_{1} ,y_{1} )[/tex] and [tex](x_{2} ,y_{2} )[/tex]. The slope of the two-point form is [tex]m=\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]

The equation is [tex]y-x_{1}=\frac{y_{2} -y_{1} }{x_{2} -x_{1} } (x-x_{1})[/tex]

Slope-intercept form: The slope-intercept form is [tex]y=mx+c[/tex]. Here m represents the slope of the line and c represents the y-intercept of the line.

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The sampling method that is the most appropriate in studying the opinions of stay-at-home mothers in all towns across the country is A. Simple random sampling, because the people in the sample are accessible and available

Sampling is the process of selecting the group from which you will collect data for your research. For example, if you want to know what students think at your university, you could survey 100 of them. In statistics, sampling allows you to test a hypothesis about a population's characteristics.

Simple random sampling is a type of probability sampling in which a subset of participants is chosen at random from a population. Each person in the population has an equal chance of being chosen. The data is then collected from as large a percentage of this random subset as possible.

Based on the information illustrated, the correct option is A.

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Answer: D) Cluster sampling, because the studied population is spread across a wide area such that simple random sampling would be difficult to implement

Step-by-step explanation: Just took the test and got this right, also simple random sampling one small town wouldn't be an accurate sample for the entire country, and cluster sampling is better since the question inquired about the entire country... If that makes any sense lol.

Safia can fit 4 cakes on the oven tray at one time

Firstly, We need to change the measurements from mm to cm

600mm x 0.1cm/1mm = 60cm

500mm x 0.1cm/1mm = 50cm

Area of the Tray (rectangular) = 60cm * 50cm = 3,000cm²

Area of the cake tin (circular) = π r²

r = d/2 = 25/2 = 12.5cm

Area of the cake tin = 3.14 * (12.5cm)²

Area of the cake tin = 3.14 * 156.25cm²

Area of the cake tin = 490.625cm²

Area of the tray ÷ Area of the cake tin = number of cake tins that fit

3,000cm² ÷ 490.625cm² = 6.11 or 6 cake tins.

thus, We can conclude that she can fit 6 cakes in the oven at once.

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(complete question)

Safia bakes cakes. The dimensions of the oven tray are 600mm x 500mm. A cake tin is 25 cm in diameter. How many cake tins can Safia fit on the oven tray at one time?

The equation used to find the answer is 26 -14 -6 =

An equation is a mathematical statement that is made up of two expressions connected by an equal sign. For example, 3x – 5 = 16 is an equation.

number of flowers picked by the girl = 14

number of flowers already with her = 6

number of flowers picked by her grand mother = 26

so her grandmother picked 26 - 14 - 6 flowers more than her. so then equation becomes 26 -14 -6 = ?

In conclusion, the equation that best describes the above is 26 -14 -6 = ?

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Answer: 5

Step-by-step explanation:

Because 5x5=25

house flipping is the buying of a house for a low price with the intention of reselling it for a profit after a short period of time.

Buyers that acquire distressed houses, patch them up, and then resell them for a profit are included. These properties are often found through foreclosures, bank short sales, or property auctions.

To be successful at real estate flipping, you must be able to manage your money properly and invest in inexpensive homes. These are generally properties that need a lot of attention.

Following that, you'll need to spend on modifications that will boost the resale value of the house and draw the attention of a possible buyer. When the improvements are finished, you must list and advertise the home.

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The required measure of the angle x is given as 117.38°.

A triangle is given with a measure of.
a = 50, b = 55 and c = 90ft

The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°

Here,
Apply cosine formula,
c² = a² + b² -2abcosx
Substitute the value in the above expression,
90² = 50² + 55² - 2×50×55×cosx
cosx = -0.46
x = cos⁻¹[-0.46]
x = 117.38°

Hence, as a result, the measure of the angle x is 117.38°.

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Answer:

The isosceles triangle altitude bisects the angle of the vertex and bisects the base. It should be noted that an isosceles triangle is a triangle with two congruent sides and so, the altitude bisects the base and vertex.

Answer: 99

Step-by-step explanation:

substitute 6 in to the x in the equation

[tex]6^{2} +10(6)+3[/tex]

36+60+3

96+3

99

Answer:

99

Step-by-step explanation:

(6)^2 +10(6)+3

6^2=6*6=36

10*6=60

36+60+3

99

The angular radius θ of the first dark ring for a point source being imaged by this telescope is 4.00 × 10^-5 degrees

The value of λ = 550 nanometer

The value of D = 0.96 m

We have to find the angular radius theta

The equation will be

sin θ = 1.22λ / D

Substitute the values in the equation

sin θ = 1.22 × (550 × 10^-9) / 0.96

Multiply the term in the numerator

sin θ = 6.71 × 10^-7 / 0.96

Divide the numbers

sin θ = 6.98 × 10^-7

θ = sin^-1 (6.98 × 10^-7)

θ = 4.00 × 10^-5

Therefore, the value of θ is 4.00 × 10^-5 degrees

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The theorem to shows triangle ATC is congruent to triangle BTD will be ''SAS'' theorem.

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

The triangle ATC is congruent to triangle BTD.

Now,

In the figure, we get;

⇒ AT = TB   (Side)

⇒ AC = BD  (Side)

⇒ ∠ATC = ∠DTB = 90°  (Vertically opposite angle)

Thus, By using SAS theorem the triangle ATC is congruent to triangle BTD.

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Answer:

140 Miles

$70.2

Step-by-step explanation:

1. Set up an equation

    In this case, the equation would be [tex]59 +0.08x=52+0.13x[/tex]

    In this equation, x = miles

2. Simplify

    You need to subtract 0.08x from the left side and 52 from the right   side.  

    This will give you a number that is equal to an x value.

    [tex]7=0.05x[/tex]

3. Divide

    Divide 0.05 from both sides. This will give you X=140. Since x=miles,                

    You would need to drive 140 miles to make the two sides equal.

4. Find the cost.

    Plug the 140 in for the x on one side. You only need to do this to one  

    side because both of the sides are equal.

    59 + (0.08 x 140) = $70.2

The length and width of the rectangular field is 316 ft and 133 ft respectively.

An algebraic equation is a mathematical statement that equalises two expressions. A variable, coefficients, and constants are common components of an algebraic equation. Also look into Algebraic Expressions. Equality is represented by equations or the equal sign.

It is balanced because both sides are equal in value. To avoid making an error that throws the equation out of balance, ensure that any change on one side is reciprocated on the other.

Given,

perimeter of rectangular field = 898 ft

let width be 'x'

then,

length = x+183

The perimeter of a rectangle is,

[tex]P = 2(length + width)\\\\898 = 2( ( x + 183 ) + x )\\\\898 = 2(2x+183)\\\\898 = 4x + 366\\\\4x = 898 - 366\\\\4x = 532\\\\x=\frac{532}{4}\\\\x=133[/tex]

Thus, the width is 133 ft and length is (133+183)=316 ft.

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Your question is incomplete, here is the complete question.

A certain field is a rectangle with a perimeter of 898 ft. The length is 183 ft more then the width. Find the width and length of the rectangular field?

Gerund can be used in place of infinitive depends on the sentence as this is a subjective.

Explanation:

Gerund can be used in place of infinitive in the sentence.

Therefore, gerund and infinitive are interchangeable or not depends on the sentence.

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It will take 2 years for the value of the car to be 5300 dollars based on the car depreciation rate.

A = [tex] {P (1-r)}^{nt} [/tex], where A is amount, P is principal, r is rate, t is time period and n is number of iterations in a year.

Keep the values in formula -

5300 = 21900 (1 - 12.25)t

Performing division on Left Hand Side of the equation

5300/21900 = (0.1225)t

Performing division on Left Hand Side of the equation and subtraction on Right Hand Side of the equation

0.24 = 0.1225t

Performing division

t = 0.24/0.1225

t = 1.96 or 2

Hence, it will take 2 years.

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The number of solutions over the complex number system to the given polynomial is 5 .

The complex  number is fundamentally the mix of a real number and a nonexistent/imaginary number. The complex number is given by  a+ib, where a is defined as the real number  and ib = imaginary number. Additionally, a,b has a place with real numbers and i = √-1.

Consequently, a complex number is a straightforward portrayal of expansion of two numbers, i.e., real number and a imaginary number. One piece of it is simply genuine and the other part is absolutely nonexistent.

Now, the given polynomial is 7x⁵ - 33x⁴ -4x²+3x+52=0.

We know very well that for complex number, its number of solution is decided by the degree of the polynomial. Degree is defined as the highest exponent of variables present in polynomial. Highest exponent present in polynomial is 5.

Hence, number of solutions are 5.

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Both sides of an equation must contain the same number of atoms in order for it to be properly balanced.

An element is balanced if it has the same amount of atoms on both sides of the equation. The equation is balanced if all the components are in balance. Equal numbers and types of each atom appear on both sides of balanced chemical equations. A balanced equation must have coefficients that are the simplest whole number ratio. Chemical reactions always conserve mass.

When the quantity of each type of atom is the same on both sides of the reaction, a chemical equation is considered to be balanced. A chemical equation should have the same number of atoms on both sides. The number of atoms for each element is conserved during a chemical reaction, despite the possibility that reactant molecules may change during the process (producing distinct molecules of product).

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Correct Question:

If an equation is balanced properly both sides of the equation must have the same number of _________________.