Iris's checking account pays simple interest at 3% per year. She has $185 in
her account. Write a linear function to model the amount of money in her
checking account at any time t.

A. A short word problem about a purchase made to illustrate the equation is that John bought six pens and bought books for $18. The total amount is $72. Find the cost of each pen.

B. The cost of each pen is $9

C. The variable is x.

A. The problem is that John bought six pens and bought books for $18. The

B. The equation to illustrate this will be:

6x + 18 = 72

Collect like terms

6x = 72 - 18

6x = 54

Divide

x = 54 / 6.

x = $9

The cost of each pen is $9.

C. The variable is x = 9. This is the cost of the pen.

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Answer:

4_62

Step-by-step explanation:

its is just leave me

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)

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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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: 34

Step-by-step explanation:

Vertical angles are congruent.

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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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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Using proportions, it is found that the number 523 is 523 units from zero.

A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the context of the problem using arithmetic operations such as multiplication and division with the unit rates of the measures.

One example of application is for the digit values of a number, as:

And so on...

For the number 523 given in this problem, since each unit is worth one, the number of units that it is away from zero is given by:

523/1 = 523 units.

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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!

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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Answer:

0.2

Step-by-step explanation:

Answer:Tes icahd

Step-by-step explanation:

Answer:

p = 55485

Step-by-step explanation:

p =  53600 + 145 n

n = 2022 - 2009 = 13 years

so, p =  53600 + 145(13)

p = 55485

Answer:

$400

Step-by-step explanation:

We see that the discount price is (100-40) = 60% of the original price

If 60% corresponds to $240, than 10% corresponds to 240/6 = $40

Since the original price is 100% = 10*10%, the original price is 10* $40 = 400.

I can't make something with scratch paper right now, i hope you will be able yourself to put the above information is a table :-)

Good luck with it!

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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The graph of the linear inequality can be seen in the image at the end.

Here we have the linear inequality:

y  ≥ 2x + 1

To graph this, we first need to graph the line.

y = 2x + 1

With a solid line, because we have the symbol ≥, which means that the points on the line are solutions.

Once we graphed that line, we look at our inequality:

y  ≥ 2x + 1

It says that y is larger than or equal to the values on the line, so once the line is graphed we need to shade all the region above that line.

The shaded region (and the line itself) represent all the solutions of the linear inequality.

And the graph can be seen below.

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Answer:

By using commutative property, if a = b and b = c, then a = c.

Step-by-step explanation:

Answer:

translative property

Step-by-step explanation:

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

Step-by-step explanation:

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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Answer:

$19.6

Step-by-step explanation:

B=20.50-0.06.x

B=20.50-0.06*15

B=20.50-0.9

B=19.6

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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Given the equation:

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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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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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!

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

Answer: b c

Step-by-step explanation: