Which of the following is the maximum value of the function y=–2x2 + 5?

The graph shows a solid line, which crosses the y-axis at 1 and the x-axis at 3, with shading above the line.

The slope-intercept form of a line is represented by y=mx+c where m=slope and c is the y-intercept of the line

Given here: The inequality y≥ -x/3 +1

Now, To graph an inequality, treat the <, ≤, >, or ≥ sign as an = sign, and graph the equation. If the inequality is < or >, graph the equation as a dotted line. If the inequality is ≤ or ≥, graph the equation as a solid line.

Therefore y=-x/3 +1 is a line in slope-intercept form with slope=-1/3 and y-intercept 1

Thus the line should intersect the y-axis  at y=1 and the x-axis at x=3

∴ The graph of this equation is plotted in attached file.

Hence, The graph shows a solid line, which crosses the y-axis at 1 and the x-axis at 3, with shading above the line.

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Answer:

A

Step-by-step explanation:

i took the test xx

I'm no expert at this I looked up some of these so on some that don't feel right, PLS look them up.

Question 1.

A.

Question 2.

A.

Question 3.

B.

Question 4.

C.

Question 5.

A.

Question 6.

D.

Question 7

C.

Question 8

B.

Question 9.

A.

Question 10.

B.

\(\\ \sf\longmapsto \dfrac{2}{3}x=10\)

\(\\ \sf\longmapsto \dfrac{2x}{3}=10\)

\(\\ \sf\longmapsto 2x=3(10)\)

\(\\ \sf\longmapsto 2x=30\)

\(\\ \sf\longmapsto x=\dfrac{30}{2}\)

\(\\ \sf\longmapsto x=15\)

\( \begin{cases}\large\bf{\red{ \implies}} \tt \frac{2}{3} x \: = \: 10 \\ \\ \large\bf{\red{ \implies}} \tt \frac{2x}{3} \: = \: 10 \\ \\ \large\bf{\red{ \implies}} \tt 2x \: = \: 3 \: \times \: 10 \\ \\ \large\bf{\red{ \implies}} \tt 2x \: = \: 30 \\ \\ \large\bf{\red{ \implies}} \tt \: x \: = \:\frac{ \cancel{30} \: \: ^{15} }{ \cancel{2}} \\ \\ \large\bf{\red{ \implies}} \tt \: x \: = \: 15 \end{cases}\)

Answer:

6:12:21

Step-by-step explanation:

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Answer:

Here's an interesting project idea for mathematics that can relate three different topics:

Topic 1: Fractals

Topic 2: Chaos Theory

Topic 3: Differential Equations

Research Question: Can fractals be used to model chaotic systems described by differential equations?

In this project, you can explore the concept of fractals and their applications in modeling complex systems. You can also delve into chaos theory and differential equations to understand how they are used to describe chaotic systems. By combining these three topics, you can investigate whether fractals can provide a better understanding of chaotic systems by modeling them more accurately.

Your research paper can cover the following areas:

Introduction: Provide an overview of fractals, chaos theory, and differential equations, and explain their relevance to the research question.

Fractals: Discuss the properties of fractals and how they can be used to model complex systems. Provide examples of fractals in nature and technology.

Chaos Theory: Explain the concept of chaos and how it is described by differential equations. Discuss the importance of chaos theory in understanding complex systems.

Differential Equations: Provide an overview of differential equations and their applications in physics, engineering, and other fields. Explain how differential equations are used to model chaotic systems.

Combining the three topics: Explain how fractals can be used to model chaotic systems described by differential equations. Provide examples of fractals used in modeling chaotic systems and compare the results to traditional methods.

Conclusion: Summarize the findings of your research and discuss the implications of using fractals to model chaotic systems.

Overall, this project can be a challenging and rewarding exploration of the interplay between three different mathematical topics.

Step-by-step explanation:

The total height of the three jumps is A = 20.744 feet

Given data ,

1st high jump score: 7.016 feet

2nd high jump score: 5.42 feet

3rd high jump score: 8.308 feet

On adding the scores , we get

7.016 + 5.42 + 8.308 = 20.744 feet

On simplifying the equation , we get

A = 20.744 feet

Hence , Oliver jumped a total of 20.744 feet in the three high jumps

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Answer:

B

Step-by-step explanation:

8 can be rewritten as \(2\cdot2\cdot2=2^3\). Therefore, you can rewrite the expression as:

\((2^3)^{\frac{1}{3}}=2^{3\cdot\frac{1}{3}}=2\)

Hope this helps!

Answer:

(1.5, 0.5)

Step-by-step explanation:

(5, 3) and (-2, -2)

5 - 2 / 2 = 1.5

-2 + 3 / 2 = 0.5

The graphs have been correctly dragged to the table to show the image of the triangle after it is reflected over the x-axis, the y-axis, and the line y = x.

By applying a reflection over the x-axis to the coordinates of this triangle, we have the following coordinates of the image triangle;

(x, y)                →      (x, -y)

(1, -3)             →      (1, -(-3)) = (1, 3)

(3, -2)             →      (3, -(-2)) = (3, 2)

(4, -5)             →      (4, -(-5)) = (4, 5)

By applying a reflection over the y-axis to the coordinates of this triangle, we have the following coordinates of the image triangle;

(x, y)                →      (-x, y)

(1, -3)             →        (-1, -3)

(3, -2)             →      (-3, -2)

(4, -5)             →      (-4, -5)

By applying a reflection over the line y = x to the coordinates of this triangle, we have the following coordinates of the image triangle;

(x, y)                →      (y, x)

(1, -3)             →        (-3, 1)

(3, -2)             →      (-2, 3)

(4, -5)             →      (-5, 4)

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width of the rectangle = b = x

length of the rectangle = l = 8 + 2x

Perimeter of the rectangle = 70cm

Also, perimeter of the rectangle = 2(l + b)

70 = 2[x + (8 + 2x)]

70 = 2(x + 8 + 2x)

70 = 2(3x + 8)

70 = 6x + 16

70 - 16 = 6x

54 = 6x

54/6 = x

9 = x

Therefore, b = x

b = 9cm

l = 8 + 2x

I = 8 + 2×9

I = 8 + 18

I = 26cm

Answer:

4

Step-by-step explanation:

Answer:

  (b)  3 units

Step-by-step explanation:

You want to know the length of OB' when OB = 3/4 and ∆ABC is dilated about point O by a factor of 4.

The dilation factor multiplies every length.

If OB is 3/4, then OB' is 4(3/4) = 3.

The length of OB' is 3 units.

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Answer:

May I ask why you are you doing this math in college?

Step-by-step explanation:

Answer:

42 folds. This fact is mentioned in search results [1], [2], [3], [4], [5], and [7]. It is also noted in search result [6] that the answer may be 45 folds instead of 42, but this is in the context of a discussion on exponential growth and is not a commonly accepted answer to the question. Finally, search result [10] poses a similar question but provides the same answer of 42 folds to reach the moon.

Step-by-step explanation:

Triangle FBT is similar to triangle ADQ with a scale factor of 5/3. AD = 9; BF = 15, DQ = 6; BT = 10, FT = 21; AQ = 12.6

∠F = ∠A = 40°, ∠Q = ∠T = 55°, ∠B = ∠D = 85°

Similar triangles are triangles that have the same shape and the ratio of their corresponding sides are in the same proportion. Corresponding angles are equal.

triangle FBT is similar to triangle ADQ with a scale factor of 5/3.

AD = 9; BF = 9 * 5/3 = 15

DQ = 6; BT = 6 * 5/3 = 10

FT = 21; AQ = 21 * 3/5 = 12.6

∠F = ∠A = 40°, ∠Q = ∠T = 55°, ∠B = ∠D = 85°

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Answer:

P= 3200 cm

Step-by-step explanation:

Perimeter = 2(l+w)

In this case since the perimeter has to be in centimeters, we have to change the length of the rectangle to centimeter.

12 meter to centimer = 12 x 100 = 1200 cm

2( 1200 +400)

2 (1600)

=  3200 cm

Hence the value of c = 4 in [3,5] for Rolles theorem.

Rolle's Principle

If a function f is defined in the closed interval [a, b] in a manner that meets the requirements listed below.

The interval [a, b] is closed and the function f is continuous.

ii) On the open interval, the function f can be differentiated (a, b)

iii) If f (a) = f (b), then at least one value of x exists; in this case, let's assume that this value is c, which is situated between a and b, i.e. (a c b), in such a way that f'(c) = 0.

There exists a point x = c in (a, b) such that f'(c) = 0 if a function is continuous on the closed interval [a, b] and differentiable on the open interval (a, b).

let f(x)=x²-8x+12 in [3,5]

i) f(x) is continuous in closed interval [3,5] because f(x) is algebraic function.

ii) f(x) is differentiable in the open interval (3,5) since the algebraic function is differentiable.

now f(3)=3²-8*3+12

f(3)= 9-24+12

f(3)= -3

f(5) = 25-40+12

f(5)= - 3

f(3) = f(5)

f'(x)= 2x-8

x=c ,c in [3,5]

f'(c)= 2c-8

2c-8=0

c=4

Hence the value of c = 4 in [3,5] for Rolles theorem.

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The shape that can tessellate without leaving gaps is the hexagon (option A).

The shapes that can tessellate without leaving gaps are shapes that can be repeated to completely cover a flat surface without any overlaps or gaps. Among the options provided, the shape that will tessellate without leaving gaps is the hexagon (option A).

A hexagon is a six-sided polygon with equal sides and angles. It is a regular polygon, which means all of its sides and angles are equal. A regular hexagon can be arranged and repeated in a pattern to fill a plane without any gaps or overlaps. Bees' honeycombs are a real-world example of hexagonal tessellation.

On the other hand, octagons (option B) and pentagons (option C) do not tessellate by themselves without gaps. While they can be used in combination with other shapes to create tessellations, they cannot tessellate on their own.

A circle (option D) cannot tessellate without leaving gaps. A circle is a curved shape, and it cannot form a repeating pattern that completely covers a flat surface without overlaps or gaps.

In summary, the shape that can tessellate without leaving gaps is the hexagon (option A).

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Inverse of function f(x) = 7x + 6 is

Given,

f(x) = 7x + 6

Now,

Put y in place of f(x)

y = 7x + 6

Now interchange the variables,

x = 7y + 6

Solve for variable y,

y = x/7 - 6/7

Replace y with f-¹(x),

f-¹(x) = x/7 - 6/7

Thus the inverse of the function is obtained to be x/7 - 6/7 .

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To find all points on the x-axis that are 16 units away from the point (5, -8), we can use the distance formula. The distance between two points (x₁, y₁) and (x₂, y₂) is given by the formula:

d = √((x₂ - x₁)² + (y₂ - y₁)²)

In this case, the y-coordinate of the point (5, -8) is -8, which lies on the x-axis. So, any point on the x-axis will have a y-coordinate of 0. Let's substitute the given values and solve for the x-coordinate.

d = √((x - 5)² + (0 - (-8))²)

Simplifying:

d = √((x - 5)² + 64)

Now, we want the distance d to be equal to 16 units. So, we set up the equation:

16 = √((x - 5)² + 64)

Squaring both sides of the equation to eliminate the square root:

16² = (x - 5)² + 64

256 = (x - 5)² + 64

Subtracting 64 from both sides:

192 = (x - 5)²

Taking the square root of both sides

√192 = x - 5

±√192 = x - 5

x = 5 ± √192

Therefore, the two points on the x-axis that are 16 units away from the point (5, -8) are:

Point 1: (5 + √192, 0)

Point 2: (5 - √192, 0)

In summary, the points on the x-axis that are 16 units away from the point (5, -8) are (5 + √192, 0) and (5 - √192, 0).

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The smallest number of students who go to one of these clubs is 21.

A stem-and-leaf diagram is a quantitative assessment of a collection of data in which the data values are divided into a "stem" (the first digit of the number) and a "leaf" (the remainder of the number) (the last digit of the number).

Based on the given stem and leaf diagram, the smallest number of students who go to one of these clubs is represented by the leaf value "1" in the stem "2."

Therefore, the smallest number of students who go to one of these clubs is 21.

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Answer: Any cake being baked in an oven is an endothermic reaction

Step-by-step explanation: Endothermic reactions in a closed system are when heat is transferred from the external environment into the system.

The group of individuals fitting a description is called option D: Population, this is because, in statistics, a population is seen as am entire group of individuals, items, or elements that tends to have or share a common characteristics.

The term "population" describes the complete group of people or things that you are interested in investigating. It is the group of individuals or thing(s) about which you are attempting to draw conclusions.

There are infinite and finite populations. A population with a set quantity of people or things is said to be finite. An endless population is one that has an infinite amount of people or things.

Therefore, the correct option is D

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See full text below

A group of individuals fitting a description is the _____

Which of the term below fit the description above.

A.census

B.sample

C.parameter

D.population

Answer:

5(n+7)=8

Step-by-step explanation:

Answer:

The area of the entire rectangle is \(20x^2-10x-30\)

Step-by-step explanation:

Area of a Rectangle

The area of a rectangle of height H and width W is:

A=H.W

The rectangle has a height of H=5 and a width of \(W=4x^2-2x-6\). Calculate the area:

\(A=5*(4x^2-2x-6)\)

Expand the product:

\(A=20x^2-10x-30\)

The area of the entire rectangle is \(20x^2-10x-30\)

The algebric expression -1/4 + 3/5 is equal to 7/20 when simplified.

To solve the expression -1/4 + 3/5, we need to find a common denominator for the fractions and then perform the addition.

The common denominator for 4 and 5 is 20. We can rewrite the fractions with this denominator:

-1/4 = -5/20

3/5 = 12/20

Now that the fractions have the same denominator, we can add them:

-5/20 + 12/20 = (-5 + 12)/20 = 7/20

Therefore, -1/4 + 3/5 is equal to 7/20.

To further simplify the fraction, we can check if there is a common factor between the numerator and denominator. In this case, 7 and 20 have no common factors other than 1, so the fraction is already in its simplest form.

Thus, the final answer is 7/20.

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Answer:

$83,781.90

Step-by-step explanation:

Dividend received each year is $83781.9

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Given;

Number of shares= 5715

Yearly dividend of each share= $14.66

Now,

Total dividend of all shares

=5715*14.66

=83781.9

Therefore, by algebra the dividend will be $83781.9

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Answer:

2,100.000

Step-by-step explanation:

Answer:

2000+100.000=2100

Its simple just calculate it in a calculator...

Answer:

Plot B

Step-by-step explanation:

Plot B has a negative slope.

Answer:

10

Step-by-step explanation: