Penny uses 3/4 yard fabric for each pillow she makes. How many pillows can she make using 6 yards of fabric. Please show your work

Final answer:

The graph of the inequality y ≥ |x + 2| − 3 is represented by a shaded region above a solid V-shaped boundary line that has its vertex at the point (-2, -3).

Explanation:

To determine which description matches the graph of the inequality y ≥ |x + 2| − 3, it is essential to understand the properties of the inequality and the properties of absolute value functions. The absolute value function |x + 2| creates a V-shaped graph with a vertex at the point (-2, 0). When this is adjusted by subtracting 3, the vertex of the V shape is moved down to (-2, -3).

The inequality sign ≥ indicates that we are looking for the region that includes all y-values that are greater than or equal to the function |x + 2| − 3. Therefore, the region of the graph that we are interested in is above this V-shaped graph. The equal part of the inequality ≥ allows us to use a solid boundary line rather than a dashed line, because the points on the graph of y = |x + 2| − 3 are included in the solutions for the inequality.

So, the correct description is a shaded region above a solid boundary line, which represents all the points (x, y) where y is greater than or equal to the value of |x + 2| minus 3.

Answer:

Just because it is in the interior doesn't mean it is on the bisecting line, and ADB could be an obtuse angle  

Step-by-step explanation:

To find the values of x where f ''(x) equals 0, solve the quadratic equation 12x + 6 = 0 by setting it equal to zero and solving for x: x = -1/2.

To find the values of x where f ''(x) equals 0, we need to solve the quadratic equation 12x + 6 = 0. To do this, we set the equation equal to zero and solve for x:

12x + 6 = 0

12x = -6

x = -6/12

Simplifying, we find that x = -1/2.

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When the slope is undefined, write the equation as x = c, where c is the constant value of the x-coordinate for all points on the vertical line.

When the slope of a line is undefined, it means that the line is vertical. In the slope-intercept form of a linear equation, y = mx + b, m represents the slope of the line. However, when the slope is undefined (infinite), you cannot express it as a finite value m.

For a vertical line passing through a point (a, b), the equation can be written as: x = a.

In this case, there is no slope term, because the line is vertical and does not have a slope in the traditional sense. Instead, the equation simply states that for all points on the line, the x coordinate remains constant at a.

Thus, when the slope is undefined, write the equation as x = c, where c is the constant value of the x-coordinate for all points on the vertical line.

scale of 1:20 means for every 1 inch on the drawing it is 20 inches in real life

5 inches * 20 = 100 inches = 8.33 feet

4 inches *20 = 80 inches = 6.67 feet

8.33 * 6.67 = 55.56 square feet

Answer:

Maximum height achieved by football = 25.5 yards.

Distance traveled by football  51 yards.

Step-by-step explanation:

Path of a football kicked by a field goal kicker can be modeled by the equation y = -0.03x² + 1.53x.

Where x represents horizontal distance and y represents height of the football.

For maximum, height we will find the [tex]\frac{dy}{dx}[/tex] ( derivative ) of the equation and equate it to zero.

[tex]\frac{d(y)}{dx}[/tex] = [tex]\frac{d}{dx}[/tex] (-0.03x² + 1.53x )

[tex]\frac{dy}{dx}[/tex] = -0.03 × 2x + 1.53

By putting [tex]\frac{dy}{dx}[/tex] = 0

-0.06x + 1.53 = 0

0.06x = 1.53

x = [tex]\frac{1.53}{0.06}[/tex] = 25.5 yards

Therefore, maximum height achieved by the ball is  25.5 yards.

Now for horizontal distance covered by ball y should be 0

-0.03x² + 1.53x = 0

x ( 1.53 - 0.03x ) = 0

0.03x = 1.53

x = [tex]\frac{1.53}{0.03}[/tex] = 51 yards.

Football was kicked 51 yards.

Answer:- D shows the triangle pairs which can be mapped to each other using a single translation.

Explanation:-

Translation is a rigid transformation which creates a congruent image as that of the original figure such that the distance between the each point of the original figure and the image is fixed and same.

The translation mapping is given by (x,y)→(x+h,y+k) ,where h is the distance of the x coordinate of the each point of the original figure to the image and  k is the distance of the y coordinate of the each point of the original figure to the image.

In figure D we can see that the distance between each point of ΔCED is equal to the distance between each point of ΔMPN. Thus it shows  the triangle pairs which can be mapped to each other using a single translation.

The Figure 4 is correct as the triangle MNP and CDE can be mapped to each other using a translation.

Further  explanation:

Translation can be defined as to move the function to a certain displacement. If the points of a line or any objects are moved in the same direction it is a translation.

Explanation:

The angle MNP is equal to the angle CDE.

The side PN is equal to the side ED.

The side MN is equal to the side CD.

The translation mapping of a single translation can be expressed as follows,

[tex]\left( {x,y}\right) \Rightarrow \left({x + h,y + k} \right)[/tex]

Here, h represents the distance of translation in x-axis and k represents the distance of translation in y-axis.

In Figure 1 the triangle MNP and CDE cannot be mapped to each other using a single translation.

In Figure 2 the triangle MNP and CDE cannot be mapped to each other using a single translation.

In Figure 3 the triangle MNP and CDE cannot be mapped to each other using a single translation.

In Figure 4 the triangle MNP and CDE can be mapped to each other using a translation.

Hence, the Figure 4 is correct as the triangle MNP and CDE can be mapped to each other using a translation.

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Answer details:

Grade: Middle School

Subject: Mathematics

Chapter: Triangles

Keywords: rotation, translation, triangle, rotation about point A, mapped, triangle pair, mapping, equal angles, sides.

There is an increase in percentage from 48 to 228 is 375%.

Given that, the percent change from 48 to 228.

Percentage change calculator determines the difference in values and the percent change from the original value to the new value.

Here, the difference in values = 228-48 = 180

We know that, percentage increase = Increase ÷ Original Number × 100

Now, 180/48 × 100

= 3.75 × 100

=375%

Therefore, there is an increase in percentage from 48 to 228 is 375%.

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Answer:

The graph of the new equation is shown in figure 2.

Step-by-step explanation:

Consider the provided function.

[tex]y=x[/tex]

The graph of the above function is shown in figure 1.

The slope intercept form is:

[tex]y=mx+c[/tex]

Where m is the slope and c is the y intercept.

Now, compare the slope intercept form with the provided function.

By the comparison it can be conclude that the slope of the provided function is 1 and y intercept is 0. As the coefficient of x is 1.

We need to change the slope from 1 to 4.

So change the coefficient of x from 1 to 4.

Thus, the required function is [tex]y=4x[/tex]

The graph of the new equation is shown in figure 2.

The greatest integer is t/5 + 4 in terms of t.

Integers are numbers which includes the set of natural numbers, o and the negatives of all those natural numbers.

Set of integers are usually denoted as Z.

Let the first even integer be x.

Then the consecutive even integer is x + 2.

Integers are x, x + 2, x + 4, x + 6 and x + 8.

Given, sum of five consecutive even integers is t.

x + x + 2 + x + 4 + x + 6 + x + 8 = t

5x + 20 = t

5 (x + 4) = t

x + 4 = t / 5

Greatest integer is x + 8.

x + 8 = (x + 4) + 4 = t/5 + 4

Hence the greatest integer is t/5 + 4.

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Answer:

=(3g-5)(2g+7)

Step-by-step explanation:

The length of the base is 4  inch.

It is required to find the length of the base.

Triangle is a polygon that has three sides and three angles. The sum of the angle of the triangle is 180 degrees.

Given:

Let b be the length of the base.

h=3  inch.

Area = 6 square inches

a=1/2bh

6=1/2b*3

b=4  inch.

Therefore, the length of the base is 4  inch.

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Answer:

9.29 x 10^-2 it's wrong. It's 9.29 x 10^2 (positive)

Step-by-step explanation:

You can "move" or change the measure of everything using some scales based on specific boards.

There's a way to move from the imperial system (yards, feet, inches) to the metric system ( centimeters, meters, kilometers)

1 square foot = 929.03 square centimetre

929.03 can be written with the scientific notation, taking care of the significant figures like [tex]9.29x10^{2}[/tex]

3 [tex]feet^{2}[/tex] = 2787.09 [tex]cm^{2}[/tex] or [tex]27.87x10^{2}[/tex] [tex]cm^{2}[/tex]

The equation, in slope-intercept form, of the perpendicular bisector is: y = 1/3x.

The slope-intercept form is given as, y = mx + b.

b is y-intercept, and m is the slope.

Slope = change in y/change in x.

The slopes of two lines that are perpendicular to each other are negative reciprocal of each other.

Thus, let's find the slope of the blue line:

Slope = (-2 - 4)/(4 - 2) = -3

Therefore, the slope of the line perpendicular to it would be, 1/3.

Equation of the perpendicular bisector that passes through (3, 1):

Since slope (m) is 1/3, find b by substituting m = 1/3 and (x, y) = (3, 1) into y = mx + b.

Thus:

1 = 1/3(3) + b

1 = 1 + b

1 - 1 = b

b = 0.

Substitute b = 0, and m = 1/3 into y = mx + b:

y = 1/3x + 0

y = 1/3x

Therefore, the equation, in slope-intercept form, of the perpendicular bisector is: y = 1/3x.

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Answer:

Correct answer is 768 tiles.

The Smiths would need 768 tiles to cover the area not occupied by the carpet in their 15 ft by 20 ft room.

To solve this problem, let's first understand the dimensions. The room is 15 ft by 20 ft which gives a total space of 300 ft2. The carpet is 9 ft by 12 ft, so it will cover an area of 108 ft2.

We subtract the area of the carpet from the total area of the room to find the area that needs to be covered with tiles: 300 ft2 - 108 ft2 = 192 ft2.

Each square tile measures 6 inches by 6 inches. We must convert this to feet, as our other measurements are in feet. So, each tile is 0.5 ft by 0.5 ft, giving an area of 0.25 ft2 per tile.

Finally, we divide the total tile area needed (192 ft2) by the area of each tile (0.25 ft2). This gives us: 192 ÷ 0.25 = 768 tiles.

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Given

The equation in the form

[tex]x^{4}+95x^{2}-500 =0[/tex]

Find the factor of the above equation

To proof

factoring the above equation

we get

[tex]x^{4}+100x^{2}-5x^{2}-500 =0\\\\x^{2}(x^{2}+100)-5(x^{2}+100)=0\\\\(x^{2}-5)(x^{2}+100)=0[/tex]

now sloving the equation we get the value

x² = 5

x² = -100

[tex]x =\pm \sqrt{5}\\\\ x=\sqrt{-100}[/tex]

The factor of the equation is

[tex]x=\pm \sqrt{5}\\\\ x= \pm 10i[/tex]

Hence proved

There are a total of 8! different orders in which a skier can finish the race.

What are Permutations and Combinations?

Objects from a set may be chosen in a variety of ways, usually without replacement, to create subsets. These methods are known as permutations and combinations. When the order of selection is a consideration, this process of choosing subsets is known as a permutation; when it is not, it is known as a combination.

In the given question, we have 8 people, who compete in a downhill ski race.

Also, It is also given that there are no ties in the race.

So, There will be only one person among 8 people, who will rank 1,

Similarly, There will be only one person who will rank 2, and so on till rank 8.

So, The total number of orders a skier can finish the race will be:

Total number of ways = [tex]1 \times 2 \times 3 \times 4 \times 5 \times 6 \times7 \times 8[/tex]

The total number of ways is 8!

Hence, The total number of different orders that a skier can finish will be 8!.

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Todd can use the polynomial function [tex]9x^2 - 1[/tex] to calculate his average profit based on the amount of raw materials his furniture company currently has.

The question is asking for a polynomial function that Todd can use to calculate the average profit based on the amount of raw materials the company currently has. To find this, Todd will need to multiply the profit from each piece of furniture (3x + 1) with the amount of furniture he can produce (3x - 1). Thus, the polynomial function will be [tex](3x + 1)(3x - 1)[/tex]. After simplifying we get [tex]9x^2 - 1.[/tex] So this is the polynomial function that Todd can use to predict his average profit.

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