What is the leading coefficient of this polynomial?

[tex]f(x)=3x^2-0.2x^5+7x^3[/tex]

Answer:

Option C.

Step-by-step explanation:

Option C. A parabola is a set of all points that are the same distance from a point called focus and a line called vertex.

The correct option is option C.

A parabola is a set of all points that are the same distance from a point called focus and a line called vertex.

The parabola is symmetric about its axis.

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Answer: Last Option

[tex]Y =\frac{1}{2}cosx + 3[/tex]

Step-by-step explanation:

If the graph of the function [tex]y=kf(x) +d[/tex]  represents the transformations made to the graph of [tex]y= f(x)[/tex]  then, by definition:

If  [tex]0 <k <1[/tex] then the graph is compressed vertically by a factor k.

If  [tex]|k| > 1[/tex] then the graph is stretched vertically by a factor k

If [tex]k <0[/tex]  then the graph is reflected on the x axis.

If [tex]d> 0[/tex] the graph moves vertically upwards d units.

If [tex]d <0[/tex] the graph moves vertically down  d units.

In this problem we have the function [tex]y = cos⁡x[/tex]

And we know that The graph of [tex]y = cos⁡x[/tex] is transformed with  a vertical compression by a factor of 1/2 and a translation 3 units up

therefore it is true that [tex]0 <k <1[/tex] and [tex]k=\frac{1}{2}[/tex] and  [tex]d =3> 0[/tex]

Therefore the  new equation is:

[tex]Y =\frac{1}{2}cosx + 3[/tex]

ANSWER

[tex] \sum_{n=1} ^{32} (4n + 1) = 2144[/tex]

EXPLANATION

The given series is

[tex] \sum_{n=1} ^{32} (4n + 1) [/tex]

The first term in this series is

[tex]a_1=4(1) + 1 = 5[/tex]

The last term is

[tex]l = 4(32) + 1 = 129[/tex]

The sum of the first n terms is

[tex]S_n= \frac{n}{2} (a + l)[/tex]

The sum of the first 32 terms is

[tex]S_ {32} = \frac{32}{2} (5 + 129)[/tex]

[tex]S_ {32} =16 \times 134[/tex]

[tex]S_ {32} =2144[/tex]

Therefore,

[tex] \sum_{n=1} ^{32} (4n + 1) = 2144[/tex]

ANSWER

d. The amplitude is 2

period:

[tex]\frac{2\pi}{3} [/tex]

EXPLANATION

The given function is

[tex]f(t) = - 2 \cos(3t) [/tex]

This function is of the form,

f(t) = a cos(bt)

The amplitude of this function is |a|

where a=-2

[tex] | - 2| = 2[/tex]

The period of this function is given by,

[tex]T= \frac{2\pi}{b} [/tex]

But b=3,

[tex]T= \frac{2\pi}{3} [/tex]

Option D is correct.

Answer:

Are there any options for an answer?

Step-by-step explanation:

Answer:

because women are still commonly looked down upon, and men more superior. It is not fair due to the fact that women get paid less and men get hired for more jobs.

Step-by-step explanation:

Answer:

the answer is D.126

Step-by-step explanation:

Use the formula A=2(wl+hl+hw)

Answer:

C) r3 < r2 < r1

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

To create an equation for a graph where y depends on x, identify the type of relationship presented by the graph. For a linear relationship, use the formula y = mx + b, where 'm' is the slope and 'b' is the y-intercept. Determine the slope using two points on the line and then solve for 'b' using the slope and one of the points.

Creating an equation for a graph where y depends on x is a common task in algebra. It's essential to identify the type of relation presented by the graph, which may include linear, quadratic, exponential, or logarithmic relationships. Let's assume, for example, that the graph represents a simple linear relationship.

In this case, you would use the formula for a line, which is y = mx + b. 'm' represents the slope of the line, and 'b' stands for the y-intercept.

To find the slope 'm', you can choose two points on the line and calculate the change in y divided by the change in x. Once the slope is determined, plug one of the points' coordinates into the equation and solve for 'b', the y-intercept. This will give you the equation for the line.

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The equation for that graph, where y depends on x can be expressed in slope-intercept form as: y = -2x + 6.

To find the equation of the line, you can use the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. First, find the slope (m) using any two given points on the graph, i.e. (0, 6) and (4, -2):

[tex]\[ m = \frac{{\text{{change in }} y}}{{\text{{change in }} x}} = \frac{{-2 - 6}}{{4 - 0}} = \frac{{-8}}{{4}} = -2 \][/tex]

Now, substitute one of the points (e.g., (0, 6)) and the slope into the equation:

y = mx + b

6 = -2(0) + b

b = 6

So, the equation of the line is y = -2x + 6.

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For this case we have to:

Wednesday:

[tex]6 \frac {2} {3} = \frac {3 * 6 + 2} {3} = \frac {20} {3}[/tex]

Saturday:

He ran [tex]2 \frac {1} {4}[/tex] times more than on Wednesday, that is:

[tex]\frac {20} {3} + \frac {4 * 2 + 1} {4} =\\\frac {20} {3} + \frac {9} {4} =\\\frac {20 * 4 + 9 * 3} {12} =\\\frac {107} {12} =\\8 \frac {11} {12}[/tex]

Thus, on Saturday, he ran [tex]8 \frac {11} {12}[/tex]miles

Answer:

[tex]8 \frac {11} {12}[/tex]

Answer:

  a = 20; b = 2√101

Step-by-step explanation:

The triangle at upper left and the one at lower right are similar. Ratios of corresponding sides are equal, so ...

  200/a = a/2

  400 = a^2

  √400 = 20 = a

Then, by the Pythagorean theorem, the value of b can be found:

  b = √(a^2 + 2^2) = √(400 +4) = √4·√101

  b = 2√101

Answer:

D

Step-by-step explanation:

The following steps describes the correct order of steps for constructinf an angle bisector of angle DEF.

(1). Draw a circle with a radius less then the arms of angle.

(2). Draw a line from point of intersections of arc (circle) and arms of the angle.

(3). Draw two circles with radius = distance between point of intersection of circle and arms of angle, center taken as point of intersection of circle and arms. than draw an equilateral triangle.

(4). Use a straightedge to connect the vertex of angle and the right  most vertex of the equilateral triangle.

Hence option D is correct.

Answer:

it's a geometric sequence. the explicit formula is: 8 times 1/2^n-1

Answer:

B. Geometric. [tex]f(n) =16\cdot \left(\frac{1}{2}\right)^{n}[/tex], [tex]\forall n \in \mathbb{N}_{O}[/tex]

Step-by-step explanation:

The problems shows a geometric sequence, since the statement describes succesive halves that are consumed by Achilles. The formula is:

[tex]f(n) =\Sigma_{i=1}^{n} 16\cdot \left(\frac{1}{2}\right)^{i}[/tex], [tex]\forall n \in \mathbb{N}[/tex]

Answer:

The volume of the ball is 256 cm³

Step-by-step explanation:

we know that

The density is equal to the ratio of the mass by the volume

D=m/V

Solve for V

The volume is equal to the ratio of the mass by the density

V=m/D

In this problem we have

m=128 g

D=0.5 g/cm³

substitute

V=128/0.5=256 cm³

Answer:

(-2,-5)

Step-by-step explanation:

y=1/2x-4 and y=-2x-9

Just substitute one into the other and then solve for x. Then go back to get y.

1/2x-4=-2x-9

Add 4 on both sides

1/2x =-2x-5

Add 2x on both sides

2.5x=-5

Divide both sides by 2.5

x=-5/(2.5)=-2

Plug into y=-2x-9 to find y.

y=-2(-2)-9=4-9=-5.

Answer (-2,-5)

Answer:

A)  (-2,-5)

Step-by-step explanation:

ANSWER

The correct choice is D.

EXPLANATION

See the attachment for explanation;

[tex]S=15\times15+4(7.5\times15)=\boxed{675}[/tex]

Answer:

Option C is correct.

Step-by-step explanation:

Given:

Length of the base rectangle = 15 unit

Width of the  base rectangle = 15 unit

Height of triangle on the side of pyramid = 15 unit

Length of the base of the triangle = 15 unit

Surface are of the rectangular pyramid = Area of Base + 4 × Area of triangle on side.

Area of base = length × width = 15 × 15 = 225 unit²

Area of the triangle = 1/2 × base  × height = 1/2 × 15 × 15 = 112.5 unit²

Surface Area = 225 + 4 × 112.5  = 225 + 450 = 675 unit²

Therefore, Option C is correct.

Supplementary angles, totaling 180 degrees, are demonstrated by ∠2 and ∠4, as well as ∠3 and ∠5, in the context of lines b and c, as depicted in the diagram.

Supplementary angles are pairs of angles whose measures add up to 180 degrees. In the context of lines b and c, the identified supplementary angle pairs are ∠2 and ∠4, as well as ∠3 and ∠5. These pairs satisfy the condition that the sum of their measures equals 180 degrees. Visually, this relationship is evident in the provided diagram, reinforcing the concept of supplementary angles. Specifically, the equation ∠2 + ∠4 = 180° and ∠3 + ∠5 = 180° illustrates the supplementary nature of these angle pairs. Understanding supplementary angles is crucial in geometry, as it provides a fundamental principle for evaluating the relationships between angles formed by intersecting lines. In the given scenario, the angles ∠2, ∠4, ∠3, and ∠5 exhibit supplementary properties, emphasizing their collective role in forming a straight line and contributing to the overall understanding of geometric configurations.

The correct question maybe :-

Given in the attachment

Answer:

y =8

Step-by-step explanation:

[tex]y^{2} = 16*4[/tex]

Answer:

D

Step-by-step explanation:

The equation given gives y in terms of x, where y is Shaun's savings and x is the number of months.

We want to know the amount he will save in 25 months, so we can plug in x = 25 into the equation and get a value of y, that is the amount he will save. So:

[tex]y = 6x^2 + 75x+200\\y = 6(25)^2 + 75(25)+200\\y=5825[/tex]

D is the correct answer.

Answer:

well since there are infinite numbers the probability is hard to solve. is there like a:

what is the probability of selecting a number that is a multiple of 15 in a hat that has paper with numbers from 1- 100

kind of thing?

Step-by-step explanation:

The desired equation relating the variables is;

Also, a large bag of dog food that contains 210 cups of food will last 140 days according to the equation.

According to the question;

The small dog gets fed 3/4 cups of dog food twice a day.

In essence; The dog is fed twice a day with 3/4 cups of dog food each time.

Therefore; The dog gets fed 2× (3/4) cups of dog food per day

a) The equation is therefore;

b) To determine the number of days a large bag of dog food will last if it contains 210 cups of food;

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Answer:

Option Z

The graph in the attached figure

Step-by-step explanation:

Let

x----> the number of chickens sandwiches

y----> the number of hamburgers

we know that

[tex]x+y\leq 40[/tex] ----> inequality A

[tex]4x+2y\geq 100[/tex] ----> inequality B

using a graphing tool

The solution is the triangular shaded area

see the attached figure

ANSWER

[tex]W''(2, - 3)[/tex]

EXPLANATION

The given point bas coordinates

W(-2,3).

The mapping for reflection over the x-axis is

[tex](x,y)\to(x, - y)[/tex]

[tex]W(-2,3)\to \: W'(-2, - 3)[/tex]

This point W'(-2,-3) is then reflected over the y-axis.

The mapping for reflection over the y-axis is

[tex](x,y)\to (-x, y)[/tex]

[tex]W'(-2,-3)\to \: W''(2, - 3)[/tex]

Point W is initially transformed by reflecting it over the x-axis, which inverses the sign of the y-coordinate, followed by a reflection over the y-axis, which inverses the sign of the x-coordinate. The final position of point W" on the coordinate plane is therefore (2, -3).

To answer this mathematics question involving coordinate geometry and reflections, one must understand how reflections in the x-axis and y-axis affect the coordinates of a point.

A reflection of a point across the x-axis changes the sign of the y-coordinate, and a reflection across the y-axis changes the sign of the x-coordinate. Thus, if we start with point W at (-2,3), a reflection over the x-axis to create point W' changes the y-coordinate's sign, yielding point W' at (-2,-3). Then, reflecting W' over the y-axis changes the x-coordinate's sign, yielding our final point W" at (2,-3).

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Answer:

86

Step-by-step explanation:

Angles in a triangle add up to 180 degrees

add 74 with 20 to get 94

subtract 94 from 180 to get the value of x

180-94=86

The value of x in the triangle whose two interior angle values are given as 74 degrees and 20 degrees is 86 degrees.

A triangle is a closed 2-dimensional polygon with three angles and three straight sides.

According to the Triangle Angle Sum Theorem, the sum of the three interior angles in a triangle is always 180°.

Hence,

angleA + angleB + angleC = 180°

Given the data in the question;

We substitute our given values into the expression above.

angleA + angleB + angleC = 180°

74° + 20° + x = 180°

94° + x = 180°

x = 180° - 94°

x = 86°

Hence, the value of x in the triangle whose two interior angle values are given as 74 degrees and 20 degrees is 86 degrees.

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Answer:

Answer choice B

Step-by-step explanation:

A 45-45-90 triangle is half a square. So, the hypotenuse is the diagonal of the square.

The diagonal of the square is [tex]d\sqrt{2}[/tex], where d is the side of the square.

In your case, we have

[tex]d\sqrt{2}=110\sqrt{2}\approx 155.56[/tex]

Answer:

88.39

Step-by-step explanation:

ANSWER

Phase shift = right 30°, period = 60°

EXPLANATION

See attachment.

the probability is 1/18

Answer:

0.382

0.4

option (a)

Step-by-step explanation:

Formula to calculate probability

a)

probability = number of times event occur  / total number of trials

Experimental probability of landing on white = 191/500 = 0.382

b)

probability = favourable outcome / total outcome

Theoretical probability of landing on white = 2/5 = 0.4

c)

As more trials are conducted, the experimental probability generally gets closer to the theoretical probability.

The student must calculate frequencies, relative frequencies, and probabilities based on the results from spinning a dial. The frequencies are the counts of outcomes, relative frequencies are these counts divided by total spins, and probabilities are based on the assumption of a fair spinner.

The question is about filling in a table with the results from spinning a dial 500 times. This tasks involves calculating frequencies, relative frequencies, and probabilities which are fundamental concepts in probability and statistics. Since we do not have the actual results, I will explain the process of completing the table:

If an outcome occurred 100 times in 500 spins, the frequency is 100. To calculate the relative frequency, divide 100 by 500, which equals 0.2. Round this to the nearest thousandth to get 0.200.

Remember to round all your final calculated values appropriately as per the instructions given in the question.