A plant that manufactures metal plates has a quality control team to check that the plates are the right size. A rectangular plate with dimensions 5 cm by 3 cm must have a length 0.25 cm above or below 5 cm. Use the solution to the equation |x − 5| − 0.25 = 0 to find the minimum and maximum area, in sq. cm, of the plates

Minimum:
Maximum:

Answer:

What are the choices?

Step-by-step explanation:

Answer:

\(\frac{11}{12}\)

Step-by-step explanation:

\(Rule: \frac{x}{y} \pm \frac{a}{b} = \frac{x \pm y}{z}\\\frac{1}{4}+\frac{2}{3} = \frac{3}{12}+\frac{8}{12} (LCM)\\=\frac{3+8}{12}\\=\frac{11}{12}\\\)

The expression (sinx + cosx)^2 + (sinx - cosx)^2 simplifies to

To simplify the expression (sinx + cosx)^2 + (sinx - cosx)^2 using trigonometric identities, we can expand and simplify the expression.

Expanding the squared terms

(sin^2x + 2sinxcosx + cos^2x) + (sin^2x - 2sinxcosx + cos^2x)

Using the trigonometric identity sin^2x + cos^2x = 1, we can simplify further:

(1 + 2sinxcosx + 1) + (1 - 2sinxcosx + 1)

Simplifying the expression, we have:

2 + 2sinxcosx + 2

Combining like terms, we get:

4 + 2sinxcosx

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An image of triangle NOG after a rotation 90° clockwise about the origin is shown below.

In Mathematics and Geometry, a rotation is a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.

Next, we would apply a rotation of 90° clockwise about the origin to the coordinate of this triangle NOG in order to determine the coordinate of its image;

(x, y)                →            (y, -x)

Point N = (-4, -1)          →     Point N' (-1, 4)

Point O = (-4, -3)          →     Point O' (-3, 4)

Point G = (0, -1)          →     Point G' (-1, 0)

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Answer:

4500

Step-by-step explanation:

250 x 18 = 4500

Since the exchange rate cannot be negative, we can discard the second solution. Therefore, the exchange rate in 1964 was $3.5 to £1.

An equation is a statement that shows the equality of two expressions, typically separated by an equal's sign (=). It can be represented using variables, constants, mathematical operations, and sometimes functions. The purpose of an equation is to find the value(s) of the variable(s) that make the equation true. Equations are an essential tool in mathematics and are used in many fields, including physics, engineering, economics, and finance. Some examples of equations are:

\(2x+3=7\)

by the question

that this can be reduced to\(2x^2+3x-25=0\). Solve this equation for x.

Let's start by defining some variables:

Let x be the exchange rate in 1964, in dollars to £1.

Let y be the exchange rate in 1952, in dollars to £1.

Using the information given, we can write:

\(In 1964, $1 / x =£1.\)

\(In 1952, $1.5 + $1 / y = £1.\)

To find the number of pounds he received for $100, we can use the following expressions:

\(In 1964, $100 / x = £(100/x).\)

\(In 1952, $100 / (y + $1.5) = £(100/(y + $1.5)).\)

We are told that in 1952 he received £12 less for his $100 than in 1964, so:

\(£(100/x) - £(100/(y + $1.5)) = 12.\)

Now we can substitute the expressions we found earlier for £1 and simplify:

\((100/x) - (100/(y + $1.5)) = 12\)

\(100(y + $1.5)/xy - 100x/(xy + x$1.5) = 12\)

\(100y + 150 - 100x = 12xy + 18x\)

\(12xy + 18x - 100y + 100x = 150\)

\(2xy + 3x - 25 = 0\)

This is a quadratic equation in x. We can solve it using the quadratic formula:

\(x = (-b ± sqrt(b^2 - 4ac)) / 2a\)

In this case, a = 2, b = 3, and c = -25. Substituting these values, we get:

\(x = (-3 ± sqrt(3^2 - 42(-25))) / 4\)

\(x = (-3 ± sqrt(289)) / 4\)

The two solutions are:

\(x = (-3 + 17) / 4 = 3.5\)

\(x = (-3 - 17) / 4 = -5\)

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Gianna is 90 miles far away in 3 hours of driving.

She drove in total of 180 minutes.

The speed can be defined as the rate at which an object covers some distance. Speed can be measured as the distance traveled by a body in a given period of time. The SI unit of speed is m/s.

Given,

Gianna drives 5 miles in 10 minutes

Speed per minute = 5/10 = 0.5 miles/minute

Gianna drove in total for 3 hours

1 hour = 60 minutes

3 hours = 60 × 3 = 180 minutes

Distance Gianna drove in 180 minutes = speed per minute × time

                                                                = 0.5 × 180

                                                                = 90 miles

Hence, Gianna drove 90 miles in 3 hours, 180 minutes is total time she drove.

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Answer:

Step-by-step explanation:To solve this problem, we need to work backwards from the final price that Gina paid and determine the discounted price before tax was added.

Let x be the original price of the laptop. After a 25% discount, the discounted price is:

Discounted price = x - 0.25x = 0.75x

Next, we add 7% tax to the discounted price:

Final price = (0.75x) + 0.07(0.75x) = 0.8025x

We know that the final price that Gina paid was $963, so we can set up an equation:

0.8025x = 963

Solving for x, we get:

x = 1200

Therefore, the original price of the laptop was $1200, and the discounted price before tax was:

Discounted price = 0.75x = 0.75(1200) = $900

To check, we can add the 7% tax to the discounted price:

Final price = $900 + 0.07($900) = $963

This matches the price that Gina paid, so we can be confident in our answer.

The graph of the relation can be seen in the image at the end, there we can see that the relation is a function.

A function is a relation where each input is mapped into a single output, where the notation is (input, output).

The inputs go on the horizontal axis and the outputs on the vertical axis.

Here we have the following relation:

(-5,-1), (-4,1), (-3,3), (-1,5), (1,7)

The graph of these points can be seen on the image below. There you can see that there are no two points on the same vertical line, that means that the relation is a function.

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Answer:

The standard form of the equation of a circle with center at (h, k) and radius r is:

(x - h)^2 + (y - k)^2 = r^2

We are given that the center of the circle is (4, -1), so h = 4 and k = -1. We also know that the circle passes through the point (-4, 1), which means that the distance from the center of the circle to (-4, 1) is the radius of the circle.

The distance between two points (x1, y1) and (x2, y2) is given by the distance formula:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

So the radius of the circle is:

r = sqrt((-4 - 4)^2 + (1 - (-1))^2) = sqrt(100) = 10

Now we can substitute the values of h, k, and r into the standard form equation of a circle:

(x - 4)^2 + (y + 1)^2 = 10^2

Expanding the equation gives:

x^2 - 8x + 16 + y^2 + 2y + 1 = 100

Simplifying and putting the equation in standard form, we get:

x^2 + y^2 - 8x + 2y - 83 = 0

Therefore, the equation in standard form of the circle with center at (4, −1) and that passes through the point (−4, 1) is:

x^2 + y^2 - 8x + 2y - 83 = 0

Answer:

Step-by-step explanation:

Given: cos θ = -4/5 , sin x = -12/13, θ is in the third quadrant, and x is in the fourth quadrant; evaluate tan x.

-12/5

-13/5

-5/12

The required maximum value is 6

And Y intercept is 5.

The given function is

f(x) = √(x+9) + 2

Now to find the maxima and minima at the given interval,

The appropriate method is to plot the graph of the given function,

Now put values of x from the interval  [-9, 7] and get the corresponding values of function and mark them on the graph paper.

Now after plotting figure we get

In the given interval [-9, 7]

The function attains maximum value at 7  = 6

And the Y intercept of function is at 5

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The bakery should use the range to determine whether or not the equipment changes have worked. The correct answer is C.

To determine whether the equipment changes made by the bakery have resulted in more uniform-sized muffins, they should use the measure of variability. The most suitable measure, in this case, would be the range.

The range is calculated by finding the difference between the maximum and minimum values in a data set. In this scenario, the bakery made 25 muffins and measured each one. By finding the range of the measurements, they can assess the spread of sizes among the muffins.

Here's how they can use the range to evaluate the effectiveness of the equipment changes:

Collect the measurements of all 25 muffins.

Determine the maximum and minimum measurements.

Calculate the range by subtracting the minimum measurement from the maximum measurement.

If the range of the muffin sizes is smaller compared to the range before the equipment changes, it suggests that the modifications have resulted in more uniform-sized muffins. Conversely, if the range remains similar or larger, it indicates that the changes might not have effectively improved the uniformity of muffin sizes.

Therefore, the bakery should use the range to determine whether or not the equipment changes have worked. The correct answer is C.

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Answer:

Step-by-step explanation:

In the Intermediate Phase of mathematics education, one topic that demonstrates a hierarchical and logical progression in patterns, functions, and algebra is the concept of "Linear Equations."

The topic of Linear Equations in the Intermediate Phase builds upon the foundation laid in earlier grades and serves as a stepping stone towards more advanced algebraic concepts. Here is an overview of the topic sequence and content area spread for Linear Equations:

Introduction to Variables and Expressions:

Students are introduced to the concept of variables and expressions, learning to represent unknown quantities using letters or symbols. They understand the difference between constants and variables and learn to evaluate expressions.

Solving One-Step Equations:

Students learn how to solve simple one-step equations involving addition, subtraction, multiplication, and division. They develop the skills to isolate the variable and find its value.

Solving Two-Step Equations:

Building upon the previous knowledge, students progress to solving two-step equations. They learn to perform multiple operations to isolate the variable and find its value.

Writing and Graphing Linear Equations:

Students explore the relationship between variables and learn to write linear equations in slope-intercept form (y = mx + b). They understand the meaning of slope and y-intercept and how they relate to the graph of a line.

Systems of Linear Equations:

Students are introduced to the concept of systems of linear equations, where multiple equations are solved simultaneously. They learn various methods such as substitution, elimination, and graphing to find the solution to the system.

Word Problems and Applications:

Students apply their understanding of linear equations to solve real-life word problems and situations. They learn to translate verbal descriptions into algebraic equations and solve them to find the unknown quantities.

The content area spread for Linear Equations includes concepts such as variables, expressions, equations, operations, graphing, slope, y-intercept, systems, and real-world applications. The progression from simple one-step equations to more complex systems of equations reflects a logical sequence that builds upon prior knowledge and skills.

By following this hierarchical progression, students develop a solid foundation in algebraic thinking and problem-solving skills. They learn to apply mathematical concepts and procedures in a systematic and logical manner, paving the way for further exploration of patterns, functions, and advanced algebraic topics in later phases of mathematics education.

Answer:

24

Step-by-step explanation:

6*8x:2

48x:2

x:48/2

x:24

The value of is -26

First, to determine the value of x, we need to know that index forms are described as mathematical forms that are used to represent numbers of values that are too small or large in more convenient forms

From the information given, we have that;

5⁷ˣ⁺⁵ = 125²ˣ⁻⁷

Now,  make that the bases are like terms, we have that;

125 = 5³

Substitute the value and we have;

5⁷ˣ⁺⁵ = 5³⁽²ˣ⁻⁷⁾

Take the exponents, we get;

7x + 5 = 6x - 21

collect the like terms, we have;

7x - 6x = -21 - 5

x = - 26

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So the quotient of the division is 9a² - 72a + 573, and the remainder is -1856.

A polynomial is a mathematical expression consisting of variables and coefficients, combined using arithmetic operations such as addition, subtraction, multiplication, and exponentiation. The variables in a polynomial can only have non-negative integer exponents, and the coefficients can be any real number. Polynomials can have one or more variables and can be of different degrees, which is determined by the highest exponent of the variable in the expression.

Here,

First, let's simplify the expression by combining like terms:

(9a³ + 64a - 67a - 16) + (a + 8) = 9a³ - 3a + 8

Now we can use synthetic division to divide 9a³ - 3a + 8 by (a + 8).

The coefficients of the terms in 9a³ - 3a + 8, written in descending order of degree, are 9, 0, -3, and 8. To use synthetic division, we will need to include a placeholder coefficient of 0 for the missing term of degree 1:

-8 |   9   0  -3   8

    |___  -72 576 -1864

    |  9 -72 573 -1856

The last number in the bottom row, -1856, is the remainder. Therefore, we have:

9a³ - 3a + 8 = (a + 8)(9a²2 - 72a + 573) - 1856

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Complete question:

Solve the following using synthetic division:  (9a³ - 3a + 8)/(a + 8)

Answer:(15,0)

Step-by-step explanation:

It is always true an equation in slope-intercept form represents a direct variation.

For example, the amount of money you earn by hours.

Let:

x = Number of hours

y = Amount of money

a = Money per hour = $5

The equation will be:

Answer:

Step-by-step explanation:

44+9x+18+5x+20=180

14x+82=180

14x=180-82=98

x=98/14=7

other angles are

9x+18=9×7+18=81°

and 5x+20=5×7+20=55°

so angles are 44°,55°,81°

so smallest angle=44°

easy claps!!

Answer: 30=2x+4 and there are 17 girls in the class.

Step-by-step explanation: if x+4=[total girls] and x=[total boys] and 30=[total kids], then x+4+x = 2x+4 = [total kids], since total kids id 30 then our equation is 30 = 2x + 4 and x= 13boys so 30-13= 17girls.

It's BASIC prealgebra so you should probably practice bit more with linear equations!

Answer:

Step-by-step explanation:

p + n + d + q = 25

Put everything into quarters.

p and q are equally likely to be drawn

q + n + d + q = 25

There are 3 times as many nickels as quarters

n = 3q

q + 3q + d + q = 25

There is 25% more dimes than quarters.

d = 1.25 q

q + 3q + 1.25q + q = 25

6.25 q = 25

q = 25/6,25

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

q = 4

p = 4

d = 1.25 * 4 = 5

n = 12

Answer: Estimated the standard deviation α  = 5.35

Step-by-step explanation:

According to Empirical rule, the largest value is approximately:

ц + 3α

And the smallest value is approximately:

ц + 3α

Based on the given figures in the question, we can say

ц + 3α = 140.6

ц - 3α = 108.5

Now subtracting these two; we have

ц + 3α - ( ц - 3α  ) = 140.6 - 108.5

ц + 3α - ц + 3α = 32.1

6α = 32.1

α = 32.1 / 6

α = 5.35

Estimated the standard deviation α  = 5.35

Susan has 875 grams of grapes left.

1. Susan bought a 1 kilogram bag of grapes, which is equivalent to 1000 grams (since there are 1000 grams in a kilogram).

2. Susan ate 125 grams of the grapes on her way home.

3. To find out how many grams of grapes Susan has left, we need to subtract the amount she ate from the initial weight of the bag. Therefore, we subtract 125 grams from 1000 grams.

  1000 grams - 125 grams = 875 grams

4. Thus, Susan has 875 grams of grapes left.

measurement units:

In this problem, we used grams as the measurement unit. Grams are commonly used to measure the weight of small objects like grapes. Since the problem stated that Susan bought a 1 kilogram bag of grapes, it was necessary to convert the kilogram measurement to grams.

This conversion was done by multiplying the kilogram value by 1000 (1 kilogram = 1000 grams). By using the correct measurement units, we were able to accurately calculate the amount of grapes Susan had left after eating a portion.

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9. The value of x is 7

10. In the figure  x = 10

11. The relationship is that their sum is 180 degrees

This relationship is known as the Same-Side Interior Angles Theorem.

12. The statement is true.

Supporting statement: If the two lines are parallel, then the alternate exterior angles created by the transversal line are equal

14 < 3 = 94 degrees

9. The value of x is solved using the knowledge of corresponding angles are equal

< A = < B

4x = 3x + 7

x = 7

10. In the figure < 3 and < 6 are alternate internal angles which is equal

7x - 10 = 5x + 10

7x - 5x = 10 + 10

2x = 20

x = 10

11. The relationship between the interior angles on the same side is that their sum is 180 degrees

This relationship is known as the Same-Side Interior Angles Theorem. It is a fundamental concept in geometry and is used to solve problems involving parallel lines and transversals.

12. The statement is true.

Supporting statement: If the two lines are parallel, then the alternate exterior angles created by the transversal line are equal

13. The measure of w is solved using the idea of vertical angels

w + 85 = 148

w = 148 - 85

w = 63

14. The mistake is that < 5 is not corresponding angle to < 2

The correct solution is < 3 = < 5 alternate internal angles

< 3 + 86 = 180 supplementary angles

< 3 = 180 - 86

< 3 = 94 degrees

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Answer:

8000 inv^3

Step-by-step explanation:

Answer:

The formula for density (ρ) is:

Density (ρ) = Mass (m) / Volume (V)

Step-by-step explanation:

Where:

Answer:

Multiplied, Group Addition

Step-by-step explanation:

Again, all I know of.