A shipping box has to have specific dimensions to hold an item. The volume must be 10240 cubic inches. The height must be `1/5` of the length and `1/4` of the the width. Give the dimensions of the box below. Give your answers as whole numbers or decimals rounded to 1 decimal place.

The constant of variation k for the direct variation in 4x = –6y will be 1.5.

It should be noted that a direct variation simply means the mathematical relationship that exists between two variables which can be expressed by an equation such that a variable is equal to another one.

Therefore, the constant of variation k for the direct variation in 4x = –6y will be:

4x = –6y

Divide through by 4

4x / 4 = -6y / 4

x = -1.5y

Therefore, the constant of variation is 1.5.

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Answer: DG and EF are parallel. DE=13

Step-by-step explanation:

DG and EF are parallel. They are both right angled triangles.
EF/DG=DE/CD

5/1.25=DE/3.25

4=DE/3.25

4*3.25=DE

13=DE

The algebraic expression of the mathematical statement three more than a number, multiplied by five more than the number is (3 + x) * (5 + x)

The mathematical statement is given as

Three more than a number, multiplied by five more than the number.

Let the number be represented with x.

So, we have the following illustration

Three more than a number, multiplied by five more than the number ⇒ Three more than x, multiplied by five more than x

More than means +

So, we have the following illustration

Three more than a number, multiplied by five more than the number ⇒ 3 + x, multiplied by 5 + x

Multiplied by means *

So, we have the following illustration

Three more than a number, multiplied by five more than the number ⇒ (3 + x) * (5 + x)

Hence, the algebraic expression of the mathematical statement three more than a number, multiplied by five more than the number is (3 + x) * (5 + x)

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Answer:

Step-by-step explanation:

Answer:

I believe its cubic polynomial because it has 3 degrees

Step-by-step explanation:

Answer:

quartic

Step-by-step explanation:

The degree of a polynomial is the highest exponent in the expression. Polynomials are classified by their degree

This polynomial has its highest exponent 4

Therefore the degree of this polynomial is 4

A polynomial with degree 4 is known as a quartic polynomial

According to the given statement

Quadratic equation for x2+8x−5=0 is x=-4± √21

Second-degree algebraic expressions of the type ax2 + bx + c = 0 are known as quadratic equations.

There are a maximum of two solutions for x in the second-degree quadratic equations. These two solutions for x are denoted as (, ) and are also known as the roots of the quadratic equations.

According to the given value;

For this equation: a=1, b=8, c=-5

1x2+8x+−5=0

Step 1: Use quadratic formula with a=1, b=8, c=-5.

x=

−b±√b2−4ac

2a

x=

−(8)±√(8)2−4(1)(−5)

2(1)

x=

−8±√84

2

x=−4+√21 or x=−4−√21

Hence,quadratic equation for x2+8x−5=0 is x=-4± √21

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The weight of each baby based on the information will be:

Martin = 2.9 kg

Daniel = 3.5kg

Kevin = 3.9 kg

Martin = x

Daniel = x + 0.6

Kevin = x + 1

Total weight = 10.3 kg

Therefore, this will be solved as:

x + x + 0.6 + x + 1 = 10.3

3x + 1.6 = 10.3

3x = 10.3 - 1.6

3x = 8.7

Divide

x = 8.7 / 4

x = 2.9

Therefore, the weights will be:

Martin = x = 2.9 kg

Daniel = x + 0.6 = 2.9 + 0.6 = 3.5kg

Kevin = x + 1 = 2.9 + 1 = 3.9 kg

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Answer:

8a^5 - 28a^4 + 2a^3 +29a^2 + 6a - 9

Step-by-step explanation:

(4a3-5a-3) × (2a2-7a+3)

= 4a^3 × 2a^2 + 4a^3(-7a) + 4a^3 × 3 - 5a × 2a^2 - 5a(-7a) - 5a × 3 - 3 × 2a^2 - 3(-7a) - 3 × 3

= 8a^5 - 28a^4 + 2a^3 +29a^2 + 6a - 9

Answer:

32

Step-by-step explanation:

1-295/2

Answer:

x>22/3 or x<-32/3

Step-by-step explanation:

Step 1 - add 6 to both side

Step 2 - divide both sides by two

Step 3 - Solve Absolute Value

We know either x+ 5/3 >9 or x+5/3<-9

Subtract 5/3 from both sides

Answer:

-1

Step-by-step explanation:

Answer:

-1 is the answer

Step-by-step explanation:

Another name for a zero sum pair is additive inverse.

A number's cumulative is its inverse number. When a number is multiplied by its cumulative , the sum of both figures equals zero. The straightforward approach is to convert a positive number to a negative number and vice versa. We formerly know that 7(- 7) Equals 0. Accordingly,-7 is the cumulative of 7, and 7 is the cumulative  of-7.

Inverse cumulative Property

When the sum of two real figures is zero, each is said to be the cumulative  of the other.

Inverse Complement of Real figures

A whole number, a natural number, an integer, a bit, a numeric, or any real number can be specified.

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If [tex]x[/tex] is positive, then [tex]\tan^{-1}(x)[/tex] is between 0 and π/2, which means [tex]\cos(\tan^{-1}(x))[/tex] is between 1 and 0.

Let [tex]\theta = \tan^{-1}(x)[/tex]. Then [tex]\tan(\theta) = x[/tex], and it follows from the Pythagorean identity that

[tex]\sin^2(\theta) + \cos^2(\theta) = 1 \implies \tan^2(\theta) + 1 = \sec^2(\theta) \\\\ ~~~~ \implies \sec(\theta) = \sqrt{1 + \tan^2(\theta)} \\\\ ~~~~ \implies \cos(\theta) = \dfrac1{\sqrt{1+\tan^2(\theta)}} \\\\ ~~~~ \implies \cos(\tan^{-1}(x)) = \boxed{\dfrac1{\sqrt{1+x^2}}}[/tex]

We took the positive square root when solving for [tex]\sec(\theta)[/tex] because we know [tex]\cos(\theta)[/tex] is non-negative, between 0 and 1.

Answer:

Choice C; degree is 3

Step-by-step explanation:

The degree of the polynomial is the greatest of the exponents (powers) of its various terms.

So the degree of this polynomial is 3  which is choice C

Charles is correct as the solution of the mathematical operation (6 + 6) × 6 is also 72 as 12 × 6 = 72.

So, 12 × 6 = 72

Now, let's do what Charles say as follows:
Break 12 as 6 + 6.

Therefore, Charles is correct as the solution of mathematical operation (6 + 6) × 6 is also 72 as 12 × 6 = 72.

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Answer:

Step-by-step explanation:

Round each number individually,

276.93 Rounded up -> 277

69.24 Rounded Down -> 69

102.56 Rounded up -> 103

73.69 Rounded up -> 74

Total = 523

Anything 0.50 to 0.99 gets rounded up

Anything 0.01 to 0.49 gets rounded down

When to the nearest dollar

In simplest radical form, the values are,

(1) The missing length = 48

(2) The missing length = 48

(3) The missing length = 140

(4) The missing length = 25

(1) : In triangle,

ΔADB ≅ ΔABC

∠A = ∠A

∠ABC = ∠ABD

So, ΔADB ≅ ΔABC

AD/AB = AB/AC

AD = 64 AND AC = 100 substitute in this equation,

64/AB = AB/100

AB * AB = 64*100

[tex]AB^{2}[/tex] = 6400

AB = [tex]\sqrt{6400}[/tex]

AB = 80

Because,

∠ADB = 90°

So,

[tex]AD^{2} +BD^{2} =AB^{2}[/tex]

[tex]BD^{2} = AB^{2} -AD^{2}[/tex]

BD = [tex]\sqrt{BD^{2}-AD^{2} }[/tex]

BD = [tex]\sqrt{6400-4096}[/tex]

BD = [tex]\sqrt{2304}[/tex]

BD = 48

Therefore,

The missing length is BD = 48

(2) : In triangle,

ΔADB ≅ ΔABC

∠A = ∠A

∠ABC = ∠ABD

So, ΔADB ≅ ΔABC

AD/AB = AB/AC

AD = 64 AND AC = 100 substitute in this equation,

64/AB = AB/100

AB * AB = 64*100

[tex]AB^{2}[/tex] = 6400

AB = [tex]\sqrt{6400}[/tex]

AB = 80

Because,

∠ADB = 90°

So,

[tex]AD^{2} +BD^{2} =AB^{2}[/tex]

[tex]BD^{2} = AB^{2} -AD^{2}[/tex]

BD = [tex]\sqrt{BD^{2}-AD^{2} }[/tex]

BD = [tex]\sqrt{6400-4096}[/tex]

BD = [tex]\sqrt{2304}[/tex]

BD = 48

Therefore,

The missing length is BD = 48

(3): In triangle BDC

tanθ = BC/DC

tanθ = 60/36

θ  = [tex]tan^{-1}[/tex](60/36)

θ  = [tex]tan^{-1}[/tex](1.66)

θ = 53.16

And,

[tex]BD^{2} =BC^{2} +CD^{2}[/tex]

[tex](BD)^{2}[/tex] = 60*60 + 36*36

[tex](BD)^{2}[/tex] = 3600+1296

[tex](BD)^{2}[/tex] = 4896

BD = 69.97

In big triangle, ABC

cosθ = BC/AC

cosθ = 60/(36+u)

cos69.97 = 60/(36+u)

0.342 = 60/(36+u)

36+u = 60/0.342

36+u = 195.4

u = 195.4 - 36

u = 139.4

u = 140

Therefore,

The maximum length u = 140

(4) : In ΔABC and  ΔDAB

∠B = ∠B   (Common)

∠A = ∠D = 90°

Hence, ΔBAC ≅ ΔBDA

AB/BC = BD/AB

15/x = 9/15

x = (15*15)/9

x = 225/9

x = 25

Therefore,

The missing length x = 25

Hence,

(1) The missing length = 48

(2) The missing length = 48

(3) The missing length = 140

(4) The missing length = 25

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Answer:

m = 0

Step-by-step explanation:

- 10 = - 10 + 7m ( add 10 to both sides )

0 = 7m ( divide both sides by 7 )

0 = m

Answer: x∈[-4,3)     y∈(-5,5)

Step-by-step explanation:

[tex]Domain:x\in[-4,3)\\Range\ of\ y:\ y\in(-5,5)[/tex]

Answer:

m = 2

Step-by-step explanation:

Find LCM.

[tex]7,\:14\\14=7\cdot \:2\\=2\cdot \:7\\=7\cdot \:2\\=14\\[/tex]

Multiply

[tex]\frac{2m}{7}\cdot \:14+\frac{3m}{14}\cdot \:14=1\cdot \:14[/tex]

Simplify(AA)

[tex]\frac{2m}{7}\cdot \:14\\=\frac{2m\cdot \:14}{7}\\=\frac{28m}{7}\\=4m[/tex]

Simplify(AB)

[tex]\frac{3m}{14}\cdot \:14\\=\frac{3m\cdot \:14}{14}\\=3m[/tex]

Simplify(AC)

[tex]1\cdot \:14\\= 14[/tex]

Divide

[tex]=7m = 14\\\frac{7m}{7}=\boxed{\frac{14}{7}}\\= 2[/tex]

Answer:

[tex]\frac{-5}{12}[/tex]

Step-by-step explanation:

[tex]\frac{-3}{4}[/tex] - [tex]\frac{-1}{3}[/tex]  Subtracting a negative number is the same as adding a positive

[tex]\frac{-3}{4}[/tex] + [tex]\frac{1}{3}[/tex]  Rewrite each fraction with a common denominator.  Let's use 12 as our new denominator.

[tex]\frac{-3}{4}[/tex] = [tex]\frac{-9}{12}[/tex]  multiple the top and the bottom of the first fraction by 3 to get the equivalent fraction [tex]\frac{-9}{12}[/tex]

[tex]\frac{1}{3}[/tex] = [tex]\frac{4}{12}[/tex]  Multiple the top and bottom of the first fraction by 4 to get the equivalent fraction [tex]\frac{4}{12}[/tex].

Now, add the two fractions

[tex]\frac{-9}{12}[/tex] + [tex]\frac{4}{12}[/tex] = [tex]\frac{-5}{12}[/tex]  The denominator stays the same and you add the numerators.

A baseball stadium has 45,000 seats. If tickets have been bought for 5/8 of the seats for the next game, then 45000−(5/8⋅45000)=16875 seats left.

We will subtract (5/8⋅45000) from 45000.

To subtract in mathematics is to take something away from a group or a number of things. The group's total number of items decreases or becomes lower when we subtract from it. The components of a subtraction problem are the minuend, subtrahend, and difference.

Subtraction is therefore the antithesis of addition. Thus, addition and subtraction are the polar opposites of each other. We could say that subtraction is the opposite of addition.

A subtraction number sentence is an equation that displays the result of subtracting one number from another. The first number is the minuend, the second number is the subtrahend, and the answer is the difference in a subtraction number sentence.

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Answer:

[tex]\sf A. \quad -3.5 < -\dfrac{10}{3}[/tex]

Step-by-step explanation:

Convert -3.5 into a fraction:

[tex]\implies \sf -3.5=-\dfrac{35}{10}=-\dfrac{\diagup\!\!\!\!5 \times 7}{\diagup\!\!\!\!5 \times 2}=-\dfrac{7}{2}[/tex]

Rewrite both fractions so that they have the same denominator:

[tex]\implies \sf -\dfrac{7}{2}=-\dfrac{7 \times 3}{2 \times 3}=-\dfrac{21}{6}[/tex]

[tex]\implies \sf -\dfrac{10}{3}=-\dfrac{10 \times 2}{3 \times 2}=-\dfrac{20}{6}[/tex]

[tex]\textsf{As }\: -\dfrac{21}{6} < -\dfrac{20}{6} \textsf{ then}:[/tex]

[tex]\sf \implies -3.5 < -\dfrac{10}{3}[/tex]

The value of x is 74

Surekha Washburn has scores of 61, 65, 77, and 81 on her algebra tests.

a. Use an inequality to find the scores she must make on the final exam to pass the course with an average of 72 or higher, given that the final exam

counts as two tests.

let score on final exam is x

two test are 2x

then we get the value of x

[tex]\frac{61 + 65 + 77 + 81 + 2x}{6}[/tex] = 72

[tex]\frac{284 + 2x}{6}[/tex]  = 72

284 + 2x =432

2x = 432 - 284

x = [tex]\frac{148}{2}[/tex]

x = 74

The average is defined as the mean value which is equal to the ratio of the sum of the number of a given set of values to the total number of values present in the set.

Average Formula in Maths

The formula to find the average of given numbers or values is very easy. We just have to add all the numbers and then divide the result by the number of values given. Hence, the average formula in Maths is given as follows:

Average = Sum of Values/ Number of values

Suppose, we have given with n number of values such as x1, x2, x3 ,….., x n. The average or the mean of the given data will be equal to:

Average = (x1+x2+x3+…+x n)/n

How to Calculate Average?

We can easily calculate the average for a given set of values. We just have to add all the values and divide the outcome by the number of given values.

Average can be calculated using three simple steps. They are:

Step 1: Sum of Numbers:

The first step in finding the average of numbers is to find the sum of all the given numbers.

Step 2: Number of Observations:

Next, we have to count how many numbers are in the given dataset.

Step 3: Average Calculation:

The final step in calculating the average is to divide the sum by the number of observations.

Now, let us consider an example to calculate the average.

If there are a group of numbers say, 20, 21, 23, 22, 21, 20, 23. Then find the average of these values.

By average formula, we know,

Average = (Sum of values)/No. of values

= (20+21+23+22+21+20+23)/7

= 150/7

=21.42

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We have the identity

[tex](a + b)^2 = a^2 + 2ab + b^2 = a^2 + ab + b (a + b) \\\\ ~~~~ \implies a + b = \sqrt{a^2 + ab + b (a + b)} \\\\ ~~~~ \implies a + b = \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b \sqrt{\cdots}}}}[/tex]

assuming [tex]a+b\ge0[/tex].

For the numerator, let [tex]b=1[/tex], so [tex]a\ge-1[/tex], which means

[tex]a^2 + a = x \implies a = \dfrac{-1 + \sqrt{1 + 4x}}2[/tex]

and so

[tex]\sqrt{x + \sqrt{x + \sqrt{x + \sqrt{\cdots}}}} = \dfrac{-1 + \sqrt{1 + 4x}}2 + 1 = \dfrac{1 + \sqrt{1 + 4x}}2[/tex]

For the denominator, let [tex]b=-1[/tex] so that [tex]a\ge1[/tex]. Now

[tex]a^2 - a = x \implies a = \dfrac{1 + \sqrt{1 + 4x}}2[/tex]

so that

[tex]\sqrt{x - \sqrt{x - \sqrt{x - \sqrt{\cdots}}}} = \dfrac{1 + \sqrt{1 + 4x}}2 - 1 = \dfrac{-1 + \sqrt{1 + 4x}}2[/tex]

So, in the integral we can simplify and evaluate it to

[tex]\displaystyle \int_0^{2021} \frac{\sqrt{x + \sqrt{x + \sqrt{x + \sqrt{\cdots}}}}}{1 + \sqrt{x - \sqrt{x - \sqrt{x - \sqrt{\cdots}}}}} \, dx \\\\ ~~~~~~~~ = \int_0^{2021} \frac{\frac{1 + \sqrt{1 + 4x}}2}{1 - \frac{1 - \sqrt{1+4x}}2} \, dx \\\\ ~~~~~~~~ = \int_0^{2021} \frac{1 + \sqrt{1 + 4x}}{1 + \sqrt{1 + 4x}} \, dx \\\\ ~~~~~~~~ = \int_0^{2021} dx = \boxed{2021}[/tex]

Answer:

1/2

Step-by-step explanation:

If there are 13 men, then the ratio of men to the total is 13:26. If you simplify that, it would just be 1:2, so for every 2 students in the class, 1 of those students is a man. This would just be half.

Answer:

Step-by-step explanation: just mutiply 7x3 you get 21

Considering the definition of perpendicular line, the equation of of perpendicular line is y= -3/4x + 5/2.

A linear equation o line can be expressed in the form y = mx + b

where

Perpendicular lines are lines that intersect at right angles or 90° angles. If you multiply the slopes of two perpendicular lines, you get –1.

In this case, the line is 3y= 4x +7. Expressed in the form y = mx + b, you get:

y= (4x +7)÷ 3

y= 4/3x -+7/3

The line has a slope of  4/3. If you multiply the slopes of two perpendicular lines, you get –1, then:

4/3× slope perpendicular line= -1

slope perpendicular line= (-1)÷ 4/3

slope perpendicular line= -3/4

So, the perpendicular line has a form of: y= -3/4x + b

The line passes through the point (6, -2). Replacing in the expression for parallel line:

-2= (-3/4)×6 + b

-2= -9/2 + b

-2+ 9/2= b

5/2= b

Finally, the equation of of perpendicular line is y= -3/4x + 5/2.

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Increase in the length is 3.64 ft.

What is area of square?

The area of square is the product of side of the square.

i.e., Area of square =  side * side

Given that;

Yossi has garage whose area =262 ft²

And, 50% area is incremented.

Now, the New Area is calculated as;

Area = 262 × 150%

       = 393 ft²

As we know that;

Area of Square = (Length) × (Length)

Length = √393 = 19.82 ft

Also,

Length of garage = √262 = 16.18 ft

Hence, Increase in the length = 19.82 - 16.18 = 3.64 ft.

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Using proportions, the person who earned the most commission is given by:

B. Bridget.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.

The commission is given by:

Rate(as a decimal) x Number of Items x Cost of Each Item.

Hence, for Bridget, the commission is given by:

B = 0.045 x 18 x 50 = $40.5.

For Curtis, the commission is given by:

C = 0.0375 x 11 x 80 = $33.

For Gloria, the commission is given by:

G = 0.0475 x 5 x 140 = $33.25.

For Hugo, the commission is given by:

H = 0.0425 x 13 x 60 = $33.15.

Hence Bridget earned the most commission and option B is correct.

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Approximately 733395 babies were born in the UK in 2018.

Given,

In the UK in 2018 a baby was born every 43 seconds.

We have to find the total number of babies in the UK in 2018.

A baby in every 43 seconds.

There is 3600 seconds in an hour.

There is 24 hours in a day.

In 2018 there were 365 days.

So, the total number of babies born in 2018 in the UK:

= (Seconds in an hour × hours in a day × total days in 2018) ÷ 43

= (3600 × 24 × 365) ÷ 43

= 31536000 ÷ 43

= 733395.3488

≈ 733395

That is, in the UK in 2018 approximately 733395 babies were born.

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