Exercise 4.1 Identify critical numbers and find the absolute maximum value and absolute minimum value for each of the given functions on the given interval. 1 f(x) = x³; [-2, 1] 2 f(x)=x²- 2x² + 3; [−1, 2] 3 5 (5 - 2x); [-1,2] f(x) = f(x)=x²-3x²; [-1, 3] 4 6 f(x)=2cosx+x; [0,2 ] f(x) = 3x³ - 20x³; [-2, 2]​

Tom earns $100 in 5 days if he makes $5622 in 281.10 day, in the given arithmetic problem.

A branch of mathematics that deals with the properties of numbers is known as arithmetic, which uses the four operations. A branch of mathematics that deals with the properties of numbers is known as arithmetic, which uses the four operations.

The four operations are addition, subtraction, multiplication, and division. The guidelines for each procedure are very specific.

One of the fundamental principles of addition and subtraction is that while addition increases a number's overall value, subtraction decreases it.

Given that he earn $5622 in 281.10 day

In 1 day he earns = 5622/281.10

                             = $20

So in 5 days he earns = 5 × $20

                                     = $100

Thus, Tom earn $100 in 5 days if he makes $5622 in 281.10 day, in the given arithmetic problem.

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Full question:

Tom makes ​$5622 in 281.10 days. How much does he make in 5 ​days?

Answer:

1.72 inches

Step-by-step explanation:

= P=2s×b

= 32.7=2s×9.5

= 32.7=19s

= 32.7/19=19s/19

= s=1.72

The expression a³ - b³ is not a feasible mathematical operation.

The index form of a number is described as that number that is written in the form of an exponential expression, or single number having another number or variable as its power.

It is a mathematical method of writing numbers that are too large or too small in a more convenient form.

Other names for index forms are standard forms and scientific notation.

Some of the rules for the addition, subtraction or multiplication of index forms are;

From the information given, we have that;

a³ - b³

From the rules given, this is not mathematically feasible as the bases are not similar.

Hence, the expression is non-feasible

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In the given graph, expression of function f(x)  in following interval of values of x is,

1. In interval -6 ≤ x ≤ -3; F(x) =  (3x-1)/2

2. In interval 2 ≤ x ≤ 6; F(x) = -2x+7

The equation of a straight line is a relationship between x and y coordinates, The general equation of a straight line is y = mx + c, where m is the slope of the line and c is the y-intercept.

In the given graph,

In interval -6 ≤ x ≤ -3

we can make equation of line by using two point form of straight line,

y-y₁ =  y₂-y₁/x₂-x₁(x-x₁)

points are (-6, 0.5) and (-3, 5)

After putting both the points in the equation

⇒ 2y = 3x-1

Similarly, in the interval 2 ≤ x ≤ 6

for the points (3,2) and (6, -5)

⇒ 2x + y =7

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Answer: To calculate the % confidence interval for the proportion of US adults who spend less than three hours watching TV on an average day, we can use the following formula:

p +/- z*(sqrt(p(1-p)/n))

Where:

p = proportion of US adults who spend less than three hours watching TV on an average day (0.42)

z = standard normal score for a given level of confidence (e.g. for a 95% confidence level, z = 1.96)

n = sample size (1031)

Plugging in the given values, we get:

0.42 +/- 1.96*(sqrt(0.42*(1-0.42)/1031))

Simplifying, we get:

0.42 +/- 0.0156

So the 95% confidence interval for the proportion of US adults who spend less than three hours watching TV on an average day is approximately (0.40,0.44)

So the answer is (0.40,0.44)

Step-by-step explanation:

Answer:

145

Step-by-step explanation:

We have the equation 5x+20 for the line of best fit

Let x = 25

y = 5*25+20

  = 125 + 20

  = 145

The score should be 145 when he plays for 25 minutes

Answer:

Angle A is 66°

Step-by-step explanation:

< b  is equal to 57 because the opposite side lengths are equal.

The sum of the interior angles of a triangle is 180

180 - 57 - 57 = 66

Ratio of concentrate and water in 1:1 would be most reliable for this situation. Thus, A is the correct option.

A ratio is a way to compare two or more comparable quantities by writing the numbers with a colon in between each one. The figures must be whole numbers without any units.

You must practise the techniques described here repeatedly until they are automatic in order to master them. After reading this text and/or watching the related video tutorial, you should be able to:

• calculate the ratio of two or more similar quantities, regardless of whether they are expressed in the same units;

• divide a quantity into a number of parts in given ratios;

• use ratios to scale up or scale down a list of ingredients.

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Correct answer:

A customer wants to make screen wash from concentrate and water.

The diagram shows the amount of concentrate she puts into a container.

ml

1000

800

600

400

200

The customer adds water into the container up to the 1000 ml division. Which Ratio of concentrate and water would be most reliable.

A.  1:1

B. 4:5

C. 2:5

D. 1:5

Answer:

Step-by-step explanation:

4(x-2)+11=3(x+3)

Use distributive property to get rid of the parentheses

4x-8+11=3x+9

Simplify the addition and subtraction

4x+3=3x+9

subtract 3 on both sides and 3x on both sides to isolate x

x=6

Answer: The equation for the translation of x2 + y2 = 64 three units to the left and two units down is:

(x − 3)2 + (y − 2)2 = 64

Step-by-step explanation:

This is known as the standard equation of a circle centered at (3, 2) with a radius of 8.

When translating a shape, we need to change the center point of the shape. If we want to translate 3 units to the left and 2 units down, it means that we need to change the center point of the shape from the origin to (3, 2). This can be achieved by subtracting 3 from x and subtracting 2 from y in the equation of the circle. This results in (x - 3)2 + (y - 2)2 = 64, which is the equation for the translated circle.

Answer: (x - 3)^2 + (y - 2)^2 = 64.

Step-by-step explanation:

This is because to translate a point or a function in the x-axis by a certain value we need to add or subtract the value from the x variable. To translate in the y-axis we need to add or subtract the value from the y variable. In this case, we are translating it three units to the left, so we subtract 3 from x, and two units down so we subtract 2 from y.

Answer:

Step-by-step explanation:

The triangle on the right side fits into the missing part of the left side.

So what I did is (5+4) and times 10 = 90m.

P.s:If I'm wrong I'm sorry.

Step-by-step explanation:

well, it is a rectangle, where an isoceles right-angled triangle is cut off in the top left corner, but that triangle is added to the top right corner.

so, the area is the same as the regular rectangle.

we know, the area of a rectangle is

length × width

now, we know the length for sure (10 m).

what is the width ?

we know the part of the width until the triangle is 5 m.

and we know the leg length of the triangle is 4 m.

the width is simply the sum of the basic part and the leg length

5 + 4 = 9 m

so the area of all this is

10 × 9 = 90 m²

Step-by-step explanation:

Add

1/5+3/10=5/10

Find common denominator

1/5+3/10=1*2/5*3+3*1/10*1=2/10+3/10

10 is the least common multiple of denominators 5 and 10. Use it to convert to equivalent fractions with this common denominator.

Add

2/10+3/10=2+3/10=5/10

Simplify

5/10=1/2

5 is the greatest common divisor of 5 and 10. Reduce by dividing both the numerator and denominator by 5.

The type of relationship shown on the graph that depicts Edward's exam scripts is a Linear relationship.

A straight-line link between two variables is referred to statistically as a linear relationship (or linear association). Both a graphical representation of a linear relationship, in which the variable and constant are connected by a straight line, and a mathematical representation, in which the dependent variable is determined by multiplying the independent variable by the slope coefficient and a constant.

Linear relationships can be represented graphically or mathematically as the equation y = mx + b.

Edward's cost per math paper 1 or math paper 2 script marked will change depending on the type of paper and the number of papers. This simply means that Edward's charges are increasing per paper marked which is shown a linear relationship in the attached graph.

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The y intercept of the data collected is 42°C

An equation is an expression composed of variables and numbers linked together by mathematical operations.

The slope intercept form of a linear equation is:

y = mx + b

Where m is the slope (rate of change) and b is the y intercept.

Let y represent the average temperature and x represent the month. x = 0 represent the month January.

From the table, at January, the average temperature is 42°C. Hence the y intercept is 42°C.

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The length of actual kitchen floor is 18 ft and the width of actual kitchen floor is 13.5 ft.

What is scale?

The ratio that describes the relationship between the actual figure and its model is called the scale. It serves as a representation of the actual figures in smaller units on maps. A scale of 1:5, for instance, means that 1 on the map is equivalent to the size of 5 in the real world.

A scale is a group of levels or numbers that are applied to a specific system of measurement or comparison.

Given:

Julio is using Scale models to help remodel his kitchen.

Julio makes a Scale drawing of the kitchen floor to determine how many square feet of flooring he needs to buy.

The Scale of his drawing is 1 inch: 4 feet.

we know that

scale ---------->  inch / 4 feet = 0.25 in/ft

[scale] = [scale drawing] / [actual]

[actual] = [scale drawing] / [scale]

for length --------> 4 1/2 in ---------> 4.5 in  (scale drawing)

[actual] = [4.5] / [0.25] =18 ft

for width ---------> 3 3/8 in ---> (3*8+3)/8 ---> 27/8 in  (scale drawing)

[actual] = [27/8] / [0.25] = 13.5 ft

Hence,  the length of actual kitchen floor is 18 ft and the width of actual kitchen floor is 13.5 ft.

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Complete question:

Julio makes a scale drawing of the kitchen floor to determine how many square feet of flooring he needs to buy . The scale of his drawing is 1 inch:4 feet. (The length is 4 1/2 and the width is 3 3/8)

What is the actual are of Julio's kitchen floor?

The ratio of the radius of Circle A to the radius of Circle B is given as follows:

0.6.

The radius of a circle represents the distance between the circle of the center to any point on the circumference of the circle.

From the circles given on the image presented at the end of the answer, the radius of each circle is given as follows:

Hence the ratio of the radius of circle A to the radius of circle B is calculated as follows:

rA/rB

Replacing the numeric values for each radius, the ratio is calculated as follows:

3/5 = 0.6.

The circles are given by the image presented at the end of the answer.

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Integer multiplication and division are two fundamental operations on integers. Integer multiplication is the same as repeated addition, which involves adding an integer a particular number of times.

4 3 means to multiply 4 three times, i.e. 4 + 4 + 4 Equals 12. Integer division denotes the equal grouping or division of an integer into a certain number of groups. For example, -6 2 denotes splitting -6 into two equal halves, yielding -3. In this topic, we will study more about integer multiplication and division. Integer multiplication is the process of repetitive addition of positive and negative numbers, or simply integers. When it comes to integer multiplication, the following situations must be considered:

2 positive numbers multiplied

2 negative numbers multiplied

1 positive and 1 negative number multiplied

Integer division entails grouping of objects. It contains both positive and negative numbers. Division of numbers, like multiplication, involves the same instances.

2 positive numbers divided

2 negative numbers divided

1 positive and 1 negative number divided

When you divide numbers by two positive signs, Positive = Positive 16 8 = 2.

When two negative signs are used to divide integers, Negative Negative = Positive -16 -8 = 2.

Negative Positive = Negative -16 8 = -2 when you divide numbers with one negative sign and one positive sign.

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The fraction compares BC to BD is 2/3. Therefore, option A is the correct answer.

The distance formula which is used to find the distance between two points in a two-dimensional plane is also known as the Euclidean distance formula. On 2D plane the distance between two points (x₁, y₁) and (x₂, y₂) is Distance = √[(x₂-x₁)²+(y₂-y₁)²].

Given that, the coordinate points are B(0,1), D(3 ,1) and C(2, 1).

Here, BC is

BC=√[(2-0)²+(1-1)²]

BC=2 units

BD is

BD= √[(3-0)²+(1-1)²]

BD= 3 units

The fraction compares BC to BD is 2/3

Therefore, option A is the correct answer.

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

Which of the following fractions compares BC to BD? coordinate plane with segment BD at B(0,1) and D(3 ,1); point C is on segment BD and (2, 1).

Answer choices:

A) 2/3

B) 5/2

C) 2/5

D) 3/2

Answer:

2/5

Step-by-step explanation:

d = √[(x2 - x1)² + (y2 - y1)²]

For segment BD:

BD = √[(5 - 0)² + (1 - 1)²]

= √[5² + 0²]

= √25

= 5

For segment BC:

BC = √[(2 - 0)² + (1 - 1)²]

= √[2² + 0²]

= √4

= 2

The ratio of the areas of two similar polygons can be found by using the ratio of their perimeters or the ratio of similarity and squaring it which is true.

The polygon is a 2D geometry that has a finite number of sides. And all the sides of the polygon are straight lines connected to each other side by side.

Similar polygons are those whose perimeter ratios are identical to their respective scale factors. The common fraction of the sizes of two matching sides of two identical polygons is known as a scale factor.

The given statement is true.

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Answer:

The formula for the volume of a cylinder is V = πr^2h, where r is the radius and h is the height.

So, using the given measurements, we can substitute in the values and solve for the volume:

V = π(1.9 cm)^2(8.9 cm) = 301.958 cm^3

Rounded to the nearest tenth, the volume of the can is 301.9 cm^3.

Step-by-step explanation:

Answer:

23.75483

Step-by-step explanation:

I used a calculator lol

Answer:

-4

Step-by-step explanation:

[tex] 6^5 \times 6^n = 6^1 [/tex]

When you multiply powers with the same bases, add the exponents.

[tex] 6^{5 + n} = 6^1 [/tex]

[tex] 5 + n = 1 [/tex]

[tex] n = -4 [/tex]

Answer: -4

The area of the shape in the figure is calculated to be 180 m²

The area of the shape in the figure can be solved by breaking the shape into three rectangles, calculating the area of each rectangle and adding up

Area of rectangle is calculated by the formula

= length *  width

Area of the first rectangle

= 4 * 16

= 64

Area of the second rectangle

= (16 - 4) * (12 - 4 - 5)

= 12 * 3

= 36

Area of the third rectangle

= 16 * 5

= 80

Adding up

= 80 * 36 * 64

= 180 m²

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Figures with more than 3 sides but with no pairs of parallel sides:

Figures with more than 3 sides and with one or more pairs of parallel sides, almost all even sided polygons:

Figures with one or more pairs of parallel sides:

Figures with less than 4 sides:

Figures with less than 4 sides and with at least two sides of equal length:

Figures with at least two sides of equal length:

Figures with at least one curved side:

Figures with at least one curved side and with at least one obtuse angle:

Figures with at least one obtuse angle (polygons with more than 4 sides will have obtuse angles)

Answer:

91 degrees

angles on a straight line add up to 180

x = 180-89 = 91

therefore angle 5 is 91

The coordinates of the remaining vertices exists (2√(13),1) and (-2, 4√(13)).

A group of values that exhibit precise positioning The first number on a graph represents the distance along, while the second number represents the distance up or down.

To find the coordinates of the remaining vertices of square ABCD, we can use the information given about diagonal AC and the properties of a square. Since a square has equal side lengths and right angles, we know that the distance between opposite vertices on a diagonal must be equal to the side length of the square.

Given the coordinates of vertex A and C, we can use the distance formula to find the length of AC:

Let the equation be Distance [tex]d=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}[/tex]

substitute the values in the above equation, we get

AC = [tex]\sqrt{((2 - (-2))^2 + (4 - 1)^2)}[/tex]

simplifying the equation, we get

AC = √(4 + 9) = √(13)

We can utilize the knowledge of the square's side length to determine the locations of the remaining vertices. Vertex B is known to have the same y-coordinate as vertex A, while vertex C is two units to the left in terms of the x-coordinate. Therefore, the coordinates of vertex B exists (-2 + 2√(13), 1).

Similar to vertex A, vertex D is known to have an identical x-coordinate, but its y-coordinate is four units below vertex C. Therefore, the coordinates of vertex D exists (-2, 4√(13))

Therefore, the coordinates of the remaining vertices exists (2√(13),1) and (-2, 4√(13)) respectively.

The complete question is:

Square ABCD has a diagonal AC with vertices A(-2, 1) and C(2, 4). Find the coordinates of the remaining vertices. Express your answers as decimals, if necessary.

The coordinates are and D.

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The quadratic equation with the given zeros is:

y = 2.5*x^2 - 5x - 7.5

For a quadratic equation with the zeros h and k, and a leading coefficient a is:

y = a*(x - h)*(x - k)

Here we know that the zeros are 3 and -1, replacing these values we will get:

y = a*(x - 3)*(x + 1)

Finally, we also know that the quadratic goes through (1, -10)

Replacing these values we will get:

-10 = a*(1 - 3)*(1 + 1)

-10 = a*(-2)*2

-10 = -4a

10/4 = a

5/2 = a = 2.5

Then the quadratic equation is:

y = 2.5(x - 3)*(x + 1)

Expanding that we will get:

y = 2.5*(x^2 - 3x + x - 3)

y = 2.5*x^2 - 5x - 7.5

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Answer:

Step-by-step explanation:

Do you mean "isn't complete or not in final form?"

If it does, it is because the equation is not yet simplified. You can still change its structure by distributing the negative sign to the right parenthsis to make it a whole polynomial.

[tex](2x^{2} + 5) - (4x-1)\\2x^{2} + 5 - 4x + 1\\2x^{2} - 4x + 6\\[/tex]or

[tex]2 (x^{2} - 2x + 3)[/tex]

Answer: y = 0

Step-by-step explanation:

A midline of a sinusoidal function is the horizontal center line about which the function oscillates above and below. For y = sin x, the midline is y = 0 (the x-axis). The midline is parallel to the x-axis and is located halfway between the graph's maximum and minimum values.

Answer: -81a^2 + 27a + 10

Step-by-step explanation: We can do this question by using FOIL (first, outer, inner, last)

(-9a-2)(9a-5)

First, multiply the first two terms in the parentheses

-9a times 9a is -81a^2

Second, multiply the outer terms

-9a times -5 is 45a

Third, multiply the inner terms

-2 times 9a is -18a

And lastly, multiply the last terms

-2 times -5 is 10

After doing this we end up with -81a^2 + 45a - 18a + 10 = -81a^2 + 27a + 10