Create an equation with one solution of x = −7
All help is appreciated :)

2.5 inches will be the volume of the box if he cuts a square with 2 inch sides.

What is volume ?

Let each side of  he square that's cut-off from each corner be represented by x.

This means that the base of the box will be of dimension of the side 15−2x while the height of the box will be x.

Thus;

Volume of box is:

V = (15 − 2x)(15 − 2x)x

V = (15 − 2x)²x

V = (4x² - 60x + 225)x

V = 4x³ - 60x² + 225x

Let's differentiate with respect to x to get;

dV/dx = 12x² - 120x + 225

Maximum value of x is at dV/dx = 0

12x² - 120x + 225 = 0

Using quadratic formula, we arrive at;

x = 2.5 or 7.5

Now, let's find the second derivative of the volume;

d²V/dx² = 24x - 120

Putting x = 2.5 gives;

d²V/dx² = 24(2.5) - 120

d²V/dx² = -60Thus, V is maximum at x = 2.5, since d²V/dx² is negative

At x = 7.5;

d²V/dx² = 24(7.5) - 120

d²V/dx² = 60

Thus, V is minimum at x = 7.5, since d²V/dx² is negative

Thus,we will use x = 2.5

Maximum volume; V = (15 − 2(2.5))(15 − 2(2.5))(2.5)

V = 10 × 10 × 2.5

V = 250 Sq.inches

Dimensions are;

(15 − 2x) = 15 - 2(2.5) = 10 inches

(15 − 2x) = 15 - 2(2.5) = 10 inches

x = 2.5 inches

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Explanation:

The LCM of 5 and 9 is 5*9 = 45

This is the LCD of the two fractions.

So,

3/5 + 2/9 = 27/45 + 10/45 = 37/45

ax^2 + bx + c = 0

a=1

b=4

c=-8

x^2 + 4x - 8 = 0

(I thought I was wrong but I might be correct lol)

The expression 400 + 0.1s represents her total weekly earnings.

An expression is written in the form of variables and constants separated by the operation of addition and subtraction. There are many types of expressions some of them are algebraic expression, trigonometric expression, logarithmic expressions, and many more.

Given Tasha earns $400 per week plus a commission of 10% on her weekly sales.

She also saves one-fourth of her earnings.

Assuming the amount she makes on sales is s.

∴ The expression that represents her total weekly earnings is,

= 400 + 0.1s.

As 10% in decimal can be written as (10/100) = 0.1.

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Answer:

0.2

Step-by-step explanation:

The scale factor from the ΔABC to ΔDEF is 3/2 cm.

Given that, in triangle ABC, side AB measures 12 cm and is the longest side and in triangle DEF, side DE measures 8 cm and is the longest side.

To adjust the size of a figure without altering its shape, a scale factor is a number or conversion factor that is utilized.

The fundamental equation to determine a figure's scale factor is written as, Scale factor is equal to the difference between the dimensions of the new and old shapes.

The scale factor from the triangle ABC to triangle DEF is 12/8 = 3/2 cm

The scale factor from the triangle DEF to triangle ABC is 8/12 = 2/3 cm

Therefore, the scale factor from the ΔABC to ΔDEF is 3/2 cm.

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The formula in terms of x and y for dy/dx is y/ -2x

The value of dy/dx at the point (1,1) is -0.5

The question is incomplete, the full question is given below:

200 cars  can produced  when x dollars is spent on labor and y dollars is spent on capital. the equation that relates x and y is 45 x^1/3 y^2/3= 200

a. Find a formula in terms of x and y for dy/dx

b. Find the value of  dy/dx at the point (1,1). Round your answer to 4 decimal places

Part a

A formula in terms of x and y for dy/dx

We differentiate equation that relates x and y with respect to x by implicit differentiation:

=d/dx(45 x^1/3 y^2/3) =d/dx( 200)

=> 45 *(1/3) x^-2/3 y^2/3 + 45 x^1/3 2/3 y^ -1/3 dy/dx=0

=>  x^-2/3y^2/3+ 2 x^1/3 y^-1/3 dy/dx=0

=> y/x= -2dy/dx

=> log y = -2 log x +log c

=> y= x^ -2 +c

putting x=y=1

c=0

then y= 1/x^2

b) y/x= -2dy/dx

put x=y=1 we get

-1/2 = dy/dx

dy/dx =-0.5

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Answer:

Answer down below!

Step-by-step explanation:

Let's try and find a point that we can easily start on (a point that lands perfectly on the graph)

The point that we will use is (2,2)

So, starting from there we use rise/run to get our answer

We go up 1 and over -2

So, our slope will be (since we cannot simply it...)

-1/2

Hello!

To find the slope:

 ==> need to pick two points on the line

   (x₁, y₁): (0,3)

   (x₂,y₂): (4,1)

   [tex]Slope = \dfrac{y_2-y_1}{x_2-x_1} =\dfrac{1-3}{4-0} =\dfrac{-2}{4} =-\dfrac{1}{2}[/tex]    <== Answer

Hope that helps!

[tex]g(f(\text{x})) = -3\text{x}^2+3[/tex]

[tex]g(f(2)) = -9[/tex]

=======================================================

Explanation:

Let's compute g(f(x))

We do this by starting with the outer function g(x). Then replace every x with f(x). Then plug in the definition of f(x) as shown below.

[tex]g(\text{x}) = \text{x}-1\\\\g(f(\text{x})) = f(\text{x})-1\\\\g(f(\text{x})) = 4-3\text{x}^2-1\\\\g(f(\text{x})) = -3\text{x}^2+3\\\\[/tex]

At this point, we then plug in x = 2 so we can find that...

[tex]g(f(\text{x})) = -3\text{x}^2+3\\\\g(f(2)) = -3(2)^2+3\\\\g(f(2)) = -3(4)+3\\\\g(f(2)) = -12+3\\\\g(f(2)) = -9\\\\[/tex]

Given the equation:

Answer:Tes icahd

Step-by-step explanation:

For the given rectangle RSTW, the condition satisfies the criteria of rectangles is equal to m ∠SRZ = 40°.

As given in the question,

In the given figure of rectangle RSTW,

Conditions satisfies the criteria of the rectangles are as follow:

a. m ∠SRZ = 40°

Line segment SR is parallel to TW. TR is the transversal.

m ∠SRT = m ∠WTR ( Alternate interior angles)

T -Z - R

m ∠SRZ = m ∠WTZ = 40°

Given criteria is satisfies the criteria of rectangles.

b. m ∠STZ = 40°

All the interior angles of rectangle are of measure 90°

m ∠STW = 90°

m ∠WTZ = 40° (given)

m ∠STZ + m ∠WTZ = 90°

⇒ m ∠STZ = 50°

Given option does not satisfies the criteria of rectangles.

c. m ∠SRW = 80°

All the interior angles of rectangle are of measure 90°

Given option does not satisfies the criteria of rectangles.

d. m ∠TWR = 80°

All the interior angles of rectangle are of measure 90°

Given option does not satisfies the criteria of rectangles.

Therefore, for the given rectangle RSTW, the condition satisfies the criteria of rectangles is equal to  m ∠SRZ = 40°.

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Answer:

It goes

1.) C

2.) A

3.) B

we need to verify for each equation if x=3 is a solution. If we replace x by 3 in the first equation we get

so the answer is letter A

The most appropriate choice for area of rectangle will be given by-

Difference between area of rectangle 2 and area of rectangle 3 is the largest.

Difference is 25.92 [tex]cm^2[/tex]

What is area of rectangle?

Area of rectangle is the total space taken by the rectangle.

If l is the length of the rectangle and b is the breadth of the rectangle, then area of rectangle is given by

Area of rectangle = [tex]l \times b[/tex]

Here,

Area of rectangle 1 = 60.81 [tex]cm^2[/tex]

Area of rectangle 2 = 61.44 [tex]cm^2[/tex]

Area of rectangle 3 = 35.52 [tex]cm^2[/tex]

Area of rectangle 4 = 47.88 [tex]cm^2[/tex]

Difference between Area of rectangle 1 and rectangle 2 =

                                                                                             (61.44 - 60.81)[tex]cm^2[/tex]

                                                                                            = 0.63 [tex]cm^2[/tex]

Difference between Area of rectangle 1 and rectangle 3 =

                                                                                            (60.81 - 35.52)[tex]cm^2[/tex]

                                                                                             = 25.29 [tex]cm^2[/tex]

Difference between Area of rectangle 1 and rectangle 4 =

                                                                                             (60.81 - 47.88)[tex]cm^2[/tex]

                                                                                            = 12.93 [tex]cm^2[/tex]

Difference between Area of rectangle 2 and rectangle 3 =

                                                                                             (61.44 - 35.52)[tex]cm^2[/tex]

                                                                                            = 25.92 [tex]cm^2[/tex]

Difference between Area of rectangle 2 and rectangle 4 =

                                                                                            (61.44 - 47.88) [tex]cm^2[/tex]

                                                                                            = 13.56 [tex]cm^2[/tex]

Difference between Area of rectangle 3 and rectangle 4 =

                                                                                           (47.88 - 35.52) [tex]cm^2[/tex]

                                                                                            = 12.36 [tex]cm^2[/tex]

Difference between area of rectangle 2 and area of rectangle 3 is the largest.

Difference is 25.92 [tex]cm^2[/tex]

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Answer:

Parallelograms are shapes with 2 pairs of parallel sides, like a square or a rhombus. Parallel means lines on a shape that never touches.

Step-by-step explanation:

Hope this helps!

P.S, brainliest? Thanks!

Answer: 34

Step-by-step explanation:

Vertical angles are congruent.

Answer:

8

Step-by-step explanation:

To solve this problem you multiply 4 by 100 and then divide the total by 50 as follows: (4 x 100) / 50

The proofreading rate will be ( 7.5 pages/ hour) and the cost per hour will be $20.

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 Karyn proofreads 15 pages in 2 hours for $40. The rate will be calculated as:-

Rate of reading = ( 15 / 2 )

Rate of reading = ( 7.5 ) pages per hour

The cost will be calculated as:-

For 2 hours = $40

For 1 hour = ( 40 / 2 )

For 1 hour = $20

Therefore, the proofreading rate will be ( 7.5 pages/ hour) and the cost per hour will be $20.

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Answer:

x = 20

Step-by-step explanation:

4x + 1 and 2x + 41 are alternate exterior angles and are congruent , then

4x + 1 = 2x + 41 ( subtract 2x from both sides )

2x + 1 = 41 ( subtract 1 from both sides )

2x = 40 ( divide both sides by 2 )

x = 20

Answer: 6w^3-3+18u^2

Step-by-step explanation:

Answer: b c

Step-by-step explanation:

Answer:

7 soloists

Step-by-step explanation:

10%   is  .1 in decimal form

70  x  0.1 = 7 soloists

Answer:

Step-by-step explanation:

not that bad

goodluck tho :)

Answer:

p = 55485

Step-by-step explanation:

p =  53600 + 145 n

n = 2022 - 2009 = 13 years

so, p =  53600 + 145(13)

p = 55485

The equation that can be solved to determine the number of days when both jobs would have the same cost is 120d + 1,500 = 110d + 2,500.

The equations that would be formed would be linear equations. A linear equation is an equation that has a single variable that is raised to the power of one. A linear equation is a straight line when it is drawn on a graph.

The equation that represents the total bonus of the first job is: fixed pay + total variable pay

1,500 +( $120 x d)

1,500 + 120d

The equation that represents the total bonus of the second job is: fixed pay + total variable pay

$2,500 + ($110 x d)

$2,500 + $110d

When the amount at both jobs are equal, the two above linear functions would be equal

$2,500 + $110d = 1,500 + 120d

Combine similar terms together:

$2,500 - $1,500 = $120d - $110d

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1. The given sequence 28, 14 ..... will be either arithmetic or geometric sequence.

2. The common difference of the sequence 28, 14 ..... will be;

d = - 14

And, Next three terms of the arithmetic sequence are;

0, -14, -28

What is Geometric sequence?

An sequence has the ratio of every two successive terms is a constant, is called a Geometric sequence.

Given that;

The first two terms of the sequence,

28, 14 .....

Now,

Let the sequence is in arithmetic sequence, then;

28, 14 ......

The common difference of the sequence is;

d = 14 - 28

d = - 14

And, Let the sequence is in geometric sequence, then;

28, 14 ......

The common difference of the sequence is;

d = 14/28

d = 1/2

Thus, The given sequence 28, 14 ..... will be either arithmetic or geometric sequence.

2. If the given sequence is in arithmetic sequence, then;

28, 14 ......

The common difference of the sequence is;

d = 14 - 28

d = - 14

And, The nth term of the arithmetic sequence is;

⇒ [tex]a_{n} = a + (n - 1)d[/tex]

Where, 'a' is the first term and 'd' is the common difference of the sequence.

So, The 3rd term of the arithmetic sequence is,

⇒ [tex]a_{n} = a + (n - 1)d[/tex]

[tex]a_{3} = 28 + (3-1)(-14)\\ \\a_{3} = 28 - 2 * 14\\\\a_{3} = 28 - 28\\\\a_{3} = 0[/tex]

And, The 4th term of the arithmetic sequence is,

[tex]a_{4} = 28 + (4-1)(-14)\\ \\a_{4} = 28 - 3 * 14\\\\a_{4} = 28 - 42\\\\a_{4} = -14[/tex]

And,  The 5th term of the arithmetic sequence is,

[tex]a_{5} = 28 + (5-1)(-14)\\ \\a_{5} = 28 - 4 * 14\\\\a_{4} = 28 - 56\\\\a_{5} = -28[/tex]

Therefore,  Next three terms of the arithmetic sequence are;

⇒ 0, -14, -28

Thus,

1. The given sequence 28, 14 ..... will be either arithmetic or geometric sequence.

2. The common difference of the sequence 28, 14 ..... will be;

d = - 14

And, Next three terms of the arithmetic sequence are;

0, -14, -28

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A literal equation is one that is mostly made up of letters. Examples of literal equations include formulas.  

A literal equation is one that is mostly made up of letters. Examples of literal equations include formulas. Every variable in the equation "literally" represents a crucial aspect of the overall relationship that the equation expresses. Multiple letters or variables make up a literal equation. Examples include the formula for calculating speed (v=Dt) and the area of a circle (A=r2). In this part, we resolve straightforward one-variable equations.

Alternatively,

Ax +By = C

Any sign that crosses over equal(=) signs always change

In this case, Ax crosses over to C

By = C - Ax

To eliminate y from By, then

By/y = (C - Ax) /y

y cancel out y on the left side

B  = (C - Ax) /y

The complete question is,

Solve for B in the literal equation Ax+By=C

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The angle ∠1=62° ,∠2=71° ,∠3=109° ,∠4=35° ,∠5=109° ,∠6=29° ,∠7=47° and ∠8=62° for the given quadrilateral by using different laws for angle and lines.

A polygon with four sides, four angles, and four vertices is called a quadrilateral. The Latin words quadri, which means four, and latus, which means side, were combined to create the English word quadrilateral. 

A polygon is a two-dimensional, closed shape that is flat or plane and is bounded by straight sides. Its sides are not curved. A polygon's edges are another name for its sides. The vertices (or corners) of a polygon are the places where two sides converge.

∠1=62° by parallel line properties.

∠2=71° by alternate angles.

∠3=109° by alternate angles

∠4=35° by triangle properties

∠5=109° by alternate angles

∠6=29° by triangle properties

∠7=47° by parallel line properties.

∠8=62° by parallel line properties.

for the given quadrilateral by using different laws for angle and lines, The angles are ∠1=62° ,∠2=71° ,∠3=109° ,∠4=35° ,∠5=109° ,∠6=29° ,∠7=47° and ∠8=62°.

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The tax amount to the nearest cent:$6.478

What is Tax?

Tax is the sum of money that citizens hand up to the government in exchange for goods and services. A taxpayer and a tax collector are both partners in any tax transaction. An entity that pays taxes to the government is referred to as a taxpayer. Any middleman that collects taxes on the government's behalf, including the government, is a tax collector.

Given,

The price of Rare gem = $82.00

The  sales tax = 7.9%

Converting percent into decimal

7.9 / 100 = 0.079

The amount of sales tax = 82 x 0.079

                                        = $6.478

The Total amount of the gem before the sales tax:

82 - 6.478 = $75.522

Hence, The tax amount to the nearest cent is $6.478

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