Darryl had 5 boxes of books with b books in each box. He decided to give away 1 book from each box. After giving away 1 book from each box, he had 30 total books left.

What is the value of b?

Answer:

(7x+3)

Step-by-step explanation:

The sum of given polynomial is x⁴+x³+4x²-5x-8.

Addition of Algebraic Expressions is the process of collecting like terms and adding them. Identify and add the coefficients of like terms and sum them to find the final expression of given problems.

The given polynomials are x⁴-3x + 1, 4x²-2x+8, and x³-9.

Here, x⁴-3x + 1+4x²-2x+8+x³-9

= x⁴+x³+4x²-3x-2x-9+1

= x⁴+x³+4x²-5x-8

Therefore, the sum of given polynomial is x⁴+x³+4x²-5x-8.

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"Your question is incomplete, probably the complete question/missing part is:"

Add the following polynomials, then place the answer in the proper location on the grid. Write your answer in descending powers of x.

x⁴-3x + 1, 4x²-2x+8, and x³-9

The solution of the system of equations is (8, 11).

We know that one of the equations of the system is:

y = x + 3

And the other line passes through the points (3, 1) and (4, 3), then the slope of that line is:

a = (3 - 1)/(4 - 3) = 2

So the line is something like:

y = 2*x + b

To find the value of b, the y-intercept, we can replace the values of one of the points.

I will use (3, 1)

1 = 2*3 + b

1 = 6 + b

1 - 6 = b

-5 = b

So the other line is y = 2x - 5

Then the system of equations is:

y = x + 3

y = 2x - 5

Now we can solve the system:

x + 3 =2x - 5

3 + 5 = 2x -x

8  =x

The x-value of the solution is 8, then the only option that can be correct is.

(8, 11)

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The operation you would use is multiplication; there is about 0.95 liter in 1 quart. Multiply when converting larger units to smaller units. (option C).

Multiplication is the operation that is used to determine the product of two or more numbers. The sign that is used to denote multiplication is ×. Multiplication is one of the operations in maths. Other operations in mathematics ae addition, division and subtraction.

1 quart = 0.95 liters

In order to convert 100 quart to liters, multiply 100 by 0.95

0.95 x 100 = 95 liters

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The solution for the given equation is 15. Therefore, Nico, Raj and Sandra are correct.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The given equation is 2/5 (5+x)=8

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

Method 1:

Now, 2(5+x)=40

5+x=20

x=15

Method 2:

Multiply 5/2 on both the sides of an equation, we get

2/5 (5+x)×5/2 =8×5/2

5+x=20

x=15

Therefore, Nico, Raj and Sandra are correct.

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"Your question is incomplete, probably the complete question/missing part is:"

Nico, Aditi, Erick, Raj, and Sandra are solving the equation.

Two-fifths (5 + x) = 8

Each student begins to solve the problem as shown.

Nico

Aditi

Erick

Two-fifths (5 + x) = 8. (Five-halves) two-fifths (5 + x) = 8 (five-halves)

Two-fifths (5 + x) = 8. Five-halves (5) + five-halves x = (five-halves) 8

Two-fifths (5 + x) = 8. Two-fifths (5 + x) minus 5 = 8 minus 5

Raj

Sandra

Two-fifths (5 + x) = 8. (one-half) two-fifths (5 + x) = 8 (one-half)

Two-fifths (5 + x) = 8. two-fifths (5) + two-fifths x = 8

Which students are correct in their approach to solving the problem? Select three options.

Nico

Aditi

Erick

Raj

Sandra

Add a phrase to the shape's perimeter to get the side length that is missing.The total length of all of a shape's sides makes up the shape's perimeter.

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The missing side length of perimeter of the figure is 15 feet is 5.

To get the length of the missing side, subtract the perimeter from the total of the known sides. Advice: Consider it. The whole and one component are both known. You deduct the known portion from the total to determine the missing component.

Since there are two of each side length, it is easy to do this by simply adding the length and breadth and multiplying the result by two. The perimeter formula is defined as

perimeter=(length + width)2.

or

add all sides

4 + 3+ 3+ x = 15

10 +x = 15

x = 15 -10 = 5

x = 5

The missing side length of perimeter of the figure is 15 feet is

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The subject pronoun requested would be they and in Spanish would be "ellas".

In the Spanish language, there are two feminine pronouns that are often used as subjects in sentences, these pronouns are:

Ella - This is a singular pronoun equivalent to she

Ellas - This is a plural pronoun equivalent to "they", but again it is exclusively used for feminine nouns such as a group of women.

Based on this, the pronoun you are looking for is the pronoun "ellas", here is an example of how to use it: Ellas son amables.

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The transformation from the function f(x)=1/x to g(x)=1/5x can be achieved by multiplying the input value x by 5.

f(x)=1/x becomes g(x)=1/(5x) after the transformation

A mathematical transformation is a function that maps one set of values (input) to another set of values (output) based on a set of rules or operations. Transformations can be used to manipulate geometric figures, to change coordinate systems, to map one image to another, and more. Common examples of mathematical transformations include translation, rotation, scaling, and reflection.

It could then be concluded that the transformation is achieved by multiplying the input value x by 5.

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The complete question goes thus:

Describe the f(x)=1/x to g(x)=1/5x transformation

The Imaginary part is [tex]& \frac{-5 \sqrt{3}-2}{4}[/tex]

[tex]& \frac{5+2 i}{-1+\sqrt{3} i} \times \frac{-1-\sqrt{3} i}{-1-\sqrt{3} i} \\[/tex]

[tex]& =\frac{-5-5 \sqrt{3} i-2 i+2 \sqrt{3}}{4} \\[/tex]

[tex]& =\frac{-5+2 \sqrt{3}}{4}+i\left(\frac{-5 \sqrt{3}-2}{4}\right) \\[/tex]

Imaginary part

[tex]& \frac{-5 \sqrt{3}-2}{4}[/tex]

The complete question is,

Find the imaginary part of 5+2i/-1+√3i

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The complex number -i5 has -i5 as its imaginary component.

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The area of the square pyramid with the height of the triangular faces of 10 inches and the side length of the square base of 4 inches is 96 square inches. The correct option is therefore;

B. 96 in²

The surface area is the area or extent covered by the outer faces or boundary enclosures of the figure.

The description of the shape in the figure = Square pyramid

Side length of the square base of the square pyramid = 4 inches

Base length of the triangular slant faces = Side length of the square base = 4 inches

Height of the triangular faces = 10 inches

The surface area of the square pyramid is therefore;

Sum of the area of the four triangular faces + Area of the square base

Area of one triangular face = (1/2) × 4 × 10 = 20

Area of the square base = 4 × 4 = 16

The total surface area of the square pyramid is therefore;

A = 4 × 20 in² + 16 in² = 96 in²

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Answer:

2,6,7,8,9 because if doubled it should equal more than ten

Answer:

If AP and DQ are altitudes, AP= 6, DQ = 10, and DE = 12, then AB = 8.

Step-by-step explanation:

The value of a for the given expression will be -3.31.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the expression is 3.6= − a/0.8 − 1.6 − 0.8 a ​ −1.6. The value of a will be calculated as below,

3.6 = − a/0.8 − 1.6 − 0.8 a ​ −1.6

3.6 + 1.6 + 1.6 = -a / 0.8  - 0.8a

6.8 = ( -a - 0.64a ) / 0.8

5.44 = -1.64a

a = -3.31

Therefore, the value of a will be -3.31.

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The option that shows a proportional relationship is selling 94 cars in 1 year (option D)

Two numbers or elements are said to be proportional if they have the same ratio. In this case, the ratio is 24 cars every 3 months, which can be simplified as 8 cars per month.

Based on this ratio, the option that is proportional is selling 96 cars in a year because this will means 96 cars in 12 months and 96/12= 8, which shows the ratio is the same.

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The the vertices of reflected square, Q'R'S'T are Q' = (3, 1), R' = (-8, -2), S' = (-7, -7) and T' = (-2, -6)

A reflection is a mirror image of the shape. An image will reflect through a line, known as the line of reflection. A figure is said to reflect the other figure, and then every point in a figure is equidistant from each corresponding point in another figure.

Given that, a square QRST with vertices Q(-3, 1), R(8, -2), S(7, -7) and T(2, -6)

is reflected across y-axis, to form Q'R'S'T we need to find the vertices of reflected square.

We know that, rule of reflection over y-axis,

(x, y) → (-x, y)

Q' = (3, 1)

R' = (-8, -2)

S' = (-7, -7)

T' = (-2, -6)

Hence, the the vertices of reflected square, Q'R'S'T are Q' = (3, 1), R' = (-8, -2), S' = (-7, -7) and T' = (-2, -6)

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1) In geometry, the coordinate is used as to write the equations of lines as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

2) By showing that the opposite sides of the quadrilateral are congruent.

3) To prove the figure is a rhombus you must verify that all sides are the same length.

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

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

Then, The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = (y₂ - y₁) / (x₂ - x₁) (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

2) We know that;

Opposite angles in a quadrilateral are congruent, and Parallel lines have congruent corresponding angles.

Hence, In coordinate geometry, By showing that the opposite sides of the quadrilateral are congruent.

3) In coordinate geometry, To prove that it is a rhombus, remember that the definition of a rhombus is a quadrilateral with four congruent sides. Therefore, to prove it is a rhombus you must verify that all sides are the same length.

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Answer:

The equation to represent Frederick's account balance after t years is:

A = 1050 * (1 + (0.051/365))^(365t)

Where A is the account balance and t is the number of years.

Option A : The circle represented in the third quadrant has the centre lying at (-3, -1)

The location of a circle in the Cartesian plane is represented by a circle equation. We can construct the equation for a circle if we know the location of the circle's center and how long its radius is. All of the points on the circle's circumference are represented by the circle equation.

The group of points whose separation from a given point has a constant value are represented by a circle. The radius of the circle, abbreviated r, is a constant that describes this fixed point, which is known as the circle's center. The equation (x- x₁)²+(y-y₁)²=r²describes a circle with a center at (x₁,y₁) and a radius of r.

There are different forms to represent the equation of a circle :

The equation of the circle is

(x + 3)² + (y + 1)² = 9

The centre of the circle will be at (-3, -1) from the equation .

Option A :The circle represented in the third quadrant has the centre lying at (-3, -1)

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the equation 4x + 5x^2 -7x in standard form will be 5x² -3x and The value of a, b, and c will be 5, -3, and 0

ax²+bx+c=0, with a not, equals 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated.

Given a quadratic equation  4x + 5x^2 -7x

From the Standard form of a quadratic equation:

ax²+bx+c=0

In our case,

=>  4x + 5x^2 -7x

=> 5x² -3x

Comparing both equations we get the:

z = 5

b = -3

and c = 0

Therefore,  the equation 4x + 5x^2 -7x in standard form will be 5x² -3x and The value of a, b, and c will be 5, -3, and 0.

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Answer:

[tex]3 {x}^{4} - 6 {x}^{3} - 21 {x}^{2} - 2x + 8[/tex]

Step-by-step explanation:

One root being i, an imaginary number is throwing me off.. but I can give it a shot if youd like.

So a coefficient is the number Infront of the X. so for 6X^2, the coefficient is 6.

It says the Leading Coefficient is 3. The one option for that is 3x^4, so that will be the in the first blank.

The exponents now (the little numbers) start with 4 and go down 1 after each block. Which means the last two blocks will have no little numbers since it would be 1 and 0. Those don't need exponents.

For the block after the 21x^2, we have two choices. Either 6x or 2x

For the last block we have two choices also.

8 or 24

To find if it's 6x or 2x...

Its showing roots of -2, i, and 4 with multiplicity of 1, which means

x^2-4x+2x+8

x^2-2x+8

We have 2x and 8

Those must be the other two blocks

Answer:

Step-by-step explanation:

The slope of a line can not be found between two points with the same x-coordinate, as division by zero is undefined. Hence, the line defined by the points (-2,10) and (-2,-15) is a vertical line and has no slope.

The y-intercept of a line is the point at which the line intersects the y-axis, i.e., the value of y when x=0. A vertical line does not intersect the y-axis, hence it has no y-intercept.

Since the line has no slope or y-intercept, its equation can not be written in the standard form of y = mx + b, where m is the slope and b is the y-intercept. Instead, the equation of the line can be written as x = constant, where constant is the x-coordinate of the points on the line, i.e., x = -2.

The function is continuous only if m = 7.

If the function is continue, then the value of the function needs to be the same one in both pieces of the function when we evaluate in x = -2

That means that:

f(-2) = f(-2)  (trivially)

Replacing the two pieces of the function we will get:

m*(-2) - 6 = (-2)^2 + 10*(-2) - 4

now we can solve that equation for m.

-2m - 6 = 4 -20 - 4

-2m = -20 + 6 = -14

m = -14/-2 = 7

m = 7

that is the value of m.

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The difference between the area of Figure A and the area of Figure B is 2ft, So correct option is A.

A square grid is a two-dimensional pattern formed by a series of equally spaced horizontal and vertical lines that intersect at right angles, creating a regular array of squares. It can be thought of as a flat, two-dimensional lattice with a consistent spacing between the lines. A square grid can be used to represent many things, such as a map, a game board, a city plan, or a spreadsheet. In mathematics and geometry, a square grid is often used to represent coordinate systems, where each intersection of horizontal and vertical lines corresponds to a specific point with a unique set of coordinates. Square grids are also used in graphic design and art as a foundation for creating patterns, textures, and compositions.

The area of A= 3×4= 12 ft

The area of B= 4×3×1/2×4×2×1/2= 10 ft

12ft - 10 ft= 2ft

Cut down the triangle on the right of figure A, move it to left to form a rectangle, and then calculate the area of A.

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The complete question is:

A line running through the points (2, 0) and (0, 4) has a slope of -2.

The slope of a line is defined as the change in y-axis of the line to the x-axis. Mathematically, it is expressed as:

Slope = Δy/Δx

Using the coordinate points (2, 0) and (0, 4) to determine the required slope:

Slope = 4-0/0-2
Slope= 4/-2
Slope = -2

Hence the slope of the line passing through the point (2, 0) and (0, 4) is -2

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The required inequality is 437 + 36x ≥ 500, where x is the number of miles he should walk each day to meet his goal.

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

Given,

His trip length was 437 miles, and he had 36 days left.

If x is the number of miles covered each day, then the remaining miles to

Then the remained miles to cover = number of days remained × miles  covered in each day

Thus, his trip length = already completed miles + remaining miles

= 437 + 36x

As per the question,

Total miles ≥ 500 miles

⇒ 437 + 36x ≥ 500

Thus, the required inequality is 437 + 36x ≥ 500.

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Answer:

the total number of employees needed is 35 cashiers + 100 floor assistants = 135 employees.

Step-by-step explanation:

Answer: The answer is 12x-3

On a coordinate plane, a vector has origin (0, 0) and terminal point (3, 2). The magnitude of the vector is 5

The magnitude of a vector can be calculated using the distance formula, which is the square root of the sum of the squares of the differences of the x and y components. In this case, the x component is 3 and the y component is 2, so the magnitude can be calculated as follows:

√(3^2 + 2^2) = √(9 + 4) = √(13) = 5

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Answer:

its D

Step-by-step explanation:

on edge

On December 31 of each year, the quick ratio is 1.6. According to the above computation, the quick ratio is improving.

A good fast ratio is often anything greater than 1 or 1:1. If the ratio is 1:1, the company's liquid assets and current liabilities are equal in amount. A greater ratio means the business could more than cover its current liabilities.

For the present year

Current liabilities minus Quick Assets is the Quick Ratio.

= ($1,000 + $1,200 + $800) ÷ $1,875

= $3,000 ÷ $1,875

= 1.6

Current liabilities minus Quick Assets is the Quick Ratio.

=($1,140 + $1,400 + $910) ÷ $2,300

= $3,450 ÷ $2,300

= 1.5

b. according to the above computation, the quick ratio is improving.

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a) The double-declining-balance rate is 0.5 or 50%.

b) The double-declining-balance depreciation for the first year is $53800.

What is depreciation?

Depreciation is an accounting procedure that allows a business to distribute an asset's cost over the course of its useful life. In other words, it keeps track of how an asset's value decreases over time. In order to better align an asset's productivity in use to its operating costs over time, businesses depreciate assets on their financial statements and for tax purposes.

The formula of the double-declining-balance rate is 2 × (1/useful life)

Given that the building acquired at the beginning of the year at a cost of $107,600 has an estimated residual value of $4,300 and an estimated useful life of 4 years.

The double-declining-balance rate is

= 2 × (1/4)

= 0.5

= 50%

The double-declining-balance depreciation for the first year is

$107,600 ×  50%

= $107,600 × (1/2)

= $53800

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