What is the rate of change between the interval x= pi and x= 3pi/2

Answer:

y=6x-2

Step-by-step explanation:

to find the 6 you have to see the difference in the y values and the y values are going up by 6 each time. the -2 comes from the y intercept. to find the y intercept you have to see when x=0 which in this table is -2

hope i helped

y = 6x - 2. The equation that describes how x and y are related is given by y = 6x - 2.

If we look the table of the image, we can see that the graph that describes the relation between x and y is a straight line.

The set of infinite points aligned in the same direction is known as straight line and its main equation has the form y = mx + b, where m is the slope, and b the y-intercept.

In order to solve this problem, we need to find the slope which is [tex]m = \frac{y_{2}-y_{1} }{x_{2}- x_{1}}[/tex]

Solving m for two points of the straight line, Let's take (0, -2) and (1, 4):

[tex]m = \frac{4-(-2)}{1 - (0)}=\frac{6}{1} \\m = 6[/tex]

We can see if we take two points in order from the table always obtain the value m = 6, which means for each unit of x, y increase 6 units.

To find the y- intercept (0, y), from the table of the image we can see when x = 0, y = -2.

Writing the equation y = mx + b, with m = 6 and b = -2:

y = 6x -2

Answer:

  105

Step-by-step explanation:

The numbers that can be used to form triangles are collectively called "triangle numbers." The n-th triangle number is the sum of all numbers less than or equal to n. It is ...

  n(n+1)/2

For n=14, the number is 14(15)/2 = 7·15 = 105.

The clerk used 105 oranges to make the arrangement.

The grocery clerk used 105 oranges to set up a triangular display. This is calculated with the formula for triangular numbers sequence (n*(n+1))/2 where n is the base of the triangle.

To solve the problem, we need to use the approach for calculating the number of items in a triangular number sequence. Triangular numbers are used to form equilateral triangles. The nth term of a triangular number sequence is given by the formula (n*(n+1))/2. In this case, the base of the triangle contains 14 oranges, so n=14.

Using the formula, the total number of oranges used to form triangle by the grocery clerk is (14*(14+1))/2 = 105 oranges. So, the clerk used 105 oranges to set up the display.

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ANSWER

169.1m

EXPLANATION

From the diagram, the horizontal distance traveled is x meters.

This is the side adjacent to the 6° angle.

Since we know the hypotenuse to be 170m, we use the cosine ratio to find the value of x.

[tex]\cos(6 \degree) = \frac{opposite}{hypotenuse} [/tex]

[tex] \cos(6 \degree) = \frac{x}{170} [/tex]

.

This implies that

x=170cos(6°)

x=169.0687222

To the nearest tenth, the horizontal disance travelled is 169.1m

Answer:

x=12.5

Step-by-step explanation:

The given triangle is a right angle triangle.

We cannot use the Pythagoras theorem as the lengths of all sides are not known. We will use triangular ratios here to solve the given problem.  

As it is clear from the diagram that x is the hypotenuse of the triangle and 11 is the length of the base. We will use a ratio in which base and hypotenuse are used.

So,

cos ⁡θ= base/hypotenuse

cos⁡ 28=11/x

x=11/cos⁡28  

x=11/0.8829

x=12.45

Rounding off to nearest 10

x=12.5

In every right triangle, a leg is given by the multiplication between the hypothenuse and the sine of the opposite angle, or the cosine of the adjacent one.

So, in this case, we have

[tex]11 = x\cos(28)[/tex]

Solving for x, we have

[tex]x = \dfrac{11}{\cos(28)}\approx 12.5[/tex]

Answer:

$8/mile

Step-by-step explanation:

Total distance walked was 2  1/4 mi  +  5  1/2 mi = 7  3/4 mi.  Please note: you must use the " / " symbol to indicate division;  "2 1 4" is unclear.

                                           $62

Unit rate = $ per mile = --------------- = $8/mile

                                        7  3/4 mi

Answer:

3 1/4

Step-by-step explanation:

I'll assume you meant 3/4 + (1/3 / 1/6) - (- 1/2) and not 3/4 + (1/3 \ 1/6) - (- 1/2)

So we start with 3/4 + (1/3 / 1/6) - (- 1/2)

The toughest part is (1/3 / 1/6) , but remember that when dividing with a fraction, it's like multiplying by the inverse of that fraction, so...

[tex]\frac{1/3}{1/6} = \frac{1}{3} * \frac{6}{1} = \frac{6}{3} = 2[/tex]

Then we return to the original problem with the new value for the parenthesis:

3/4 + 2 + 1/2 = 3/4 + 8/4 + 2/4 = 13/4 or 3 1/4

Answer:

The correct answer is 3 1/4

Step-by-step explanation:

It is given that,

3/4 + (1/3 \ 1/6) - (- 1/2)

To find the value of given expression

3/4 + (1/3 \ 1/6) - (- 1/2) for finding the answer we have to find the value of

(1/3 / 1/6) = 1/3 * 6/1 = 2

3/4 + (1/3 \ 1/6) - (- 1/2 = 3/4 + 2 + 1/2

 = 3/4 + 8/4 + 2/4 = (3 + 8 + 2)/4 = 13/4 = 3 1/4

The correct answer is 3 1/4

Answer:

No. The ladder is too steep.

Step-by-step explanation:

Length of ladder = 17 feet.  This is the hypotenuse.

Side a of a right triangle = 16.6

To answer this, you need one of the trigonometric functions.  

Opposite = 16.5

hypotenuse = 17

The function you need is the sine function.

Sin(theta) = opposite / hypotenuse

sin(theta) = 16.5 / 17

Sin(theta) = 0.97059

theta = sin-1(0.07059)

theta = 76.07

No the ladder is too steep.

Answer:

The ladder will not be safe.

Step-by-step explanation:

The ladder is 17 ft long

The top of the ladder is 16.5 ft above the ground

The ladder makes a right triangle of height = 16.5 ft and hypotenuse = 17 ft

To find the angle the ladder makes with the ground,

Height ÷ hypotenuse = sin angle

i.e [tex]\frac{16.5}{17}[/tex] = sin angle

[tex]sin^{-1}[/tex] angle = 76.1°

So the ladder is not safe since the angle it makes with the ground is greater than 70°.

Answer:

  see below

Step-by-step explanation:

The functions for these tables are, respectively, ...

  f(x) = 5 - x

  f(x) = 3x

  f(x) = (x -1)² . . . . . a quadratic relation

  f(x) = 4x² . . . . . . a quadratic relation

We assume the intention is that the terminology "quadratic variation" mean "proportional to the square of x". In that case, only the last function has such variation.

Answer:

18

Step-by-step explanation:

The distance is 12 - (-6) = 12 + 6 = 18

-6+x=12 it’s obviously 18 units apart

In any cyclic quadrilateral, angles opposite one another are supplementary, meaning

[tex]m\angle K+m\angle I=m\angle L+m\angle J=180^\circ[/tex]

and given that [tex]\boxed{m\angle K=64^\circ}[/tex], we have [tex]\boxed{m\angle I=116^\circ}[/tex].

By the inscribed angle theorem,

[tex]m\angle JLK=\dfrac12m\widehat{KJ}[/tex]

[tex]m\angle ILJ=\dfrac12m\widehat{IJ}[/tex]

and since

[tex]m\angle L=m\angle JLK+m\angle ILJ[/tex]

we have

[tex]m\angle L=\dfrac{97^\circ+59^\circ}2\implies\boxed{m\angle L=78^\circ}[/tex]

and it follows that

[tex]m\angle J=180^\circ-m\angle L\implies\boxed{m\angle J=102^\circ}[/tex]

hope this answer your question :)

ANSWER

[tex]\cos( \angle \: F) = \frac{5}{13}[/tex]

EXPLANATION

The side length adjacent to <F is 5 units.

The length of the hypotenuse is 13 units.

The cosine ratio is

[tex] \cos( \angle \: F) = \frac{adjacent}{hypotenuse} [/tex]

This implies that:

[tex] \cos( \angle \: F) = \frac{5}{13}[/tex]

The fourth choice is correct.

use pythagorean theorem

Answer:

x = 3.6

Step-by-step explanation:

Using the tangent ratio in the right triangle

tan20° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{x}{10}[/tex]

Multiply both sides by 10

10 × tan20° = x, hence

x ≈ 3.6

Answer:

The smallest box dimensions are 4 x 4 cm.

Find the diagonal and this would be the diameter of the smallest circle.

Using the Pythagorean theorem:

4^2 + 4^2 = c^2

16 + 16 = c^2

c^2 = 32

c = √32

c = 5.658 cm ( Round answer as needed.)

I hope it’s correct

Answer:

65 men

91 women

Step-by-step explanation:

the ratio is 5 to 7 and there are 156 total

5+7 is 12

so this gives us

5/12*156=65 men

7/12*156=91 women

65 + 91 = 156

Answer:

To eliminate x multiply the first equation by 3 and the second equation by 4

To eliminate y multiply the first equation by 3 and the second equation by 2

Step-by-step explanation:

We are given a system of linear equations;

4x-2y=7

3x-3y=15

solving by elimination means that we shall be getting rid of one of the variables in order to determine the other. In this case we can either eliminate x or y. In order to eliminate any of these variables, we first must make their coefficients equal in both equations. To eliminate x;

Multiply the first equation by 3 and the second equation by 4.

To eliminate y;

Multiply the first equation by 3 and the second equation by 2.

The polynomial f(x)=x^4+3x^2+7 has four roots over the complex numbers according to the fundamental theorem of algebra, counting roots with multiplicity greater than one as distinct. This is consistent with the theorem's stipulation that a polynomial of degree n has exactly n roots.

The subject of this question is the fundamental theorem of algebra which belongs to the domain of Mathematics, specifically the study of polynomials. As indicated in the question, we have a function, f(x), which represents a polynomial of degree 4 as shown by the highest exponent. According to the fundamental theorem of algebra, a polynomial of degree n has exactly n roots, counting multiplicity. This means a function f(x)=x4+3x2+7, which is a fourth degree polynomial, will have four roots over the complex numbers.

This is also true per the theorem when roots with multiplicity greater than one are considered distinct. For example, f(x)=x2 is a polynomial of degree 2; it has two roots, both are zero, hence the two roots are counted as two distinct roots.

While the quadratic formula is used for finding roots of second degree polynomials, it is not directly applicable here since we are dealing with a fourth degree polynomial.

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Answer:

Step-by-step explanation:

This is right triangle trig.  The reference angle is 12 in one case and 60 in the other, but the horizontal distance doesn't change in either one, and neither does what you are looking for, which is the height of the balloon in both cases of the angle differences.  And if you're looking for the difference in the height, you'll find both and subtract the smaller from the larger.  

The height is across from the reference angle and the horizontal distance is adjacent to the reference angle, so the trig identity you want is tangent.  Set up according to the angle measure of 12 degrees:

[tex]tan(12)=\frac{x}{280}[/tex] and

280 tan(12) = x

x = 59.5 ft

Now for the angle measuring 60 degrees:

[tex]tan(60)=\frac{x}{280}[/tex] and

280 tan(60) = x

x = 484.9

The difference between the two heights is 425.5 feet.

Answer:

Step-by-step explanation:

x² + 5x – 104 = 0

Factor using the AC method.  Here, a = 1 and c = -104.  Multiplied together, ac = -104.  Factors of -104 that add up to +5 are +13 and -8.

(x + 13) (x - 8) = 0

x = -13, 8

A negative width doesn't make sense, so x = 8.  Therefore, the width is 8 inches and the length is 5 more than that, or 13 inches.

Answer:

width = 8

length = 13

Step-by-step explanation:

All that is left to do is factor the results that you have

x^2 + 5x - 104 = 0

You need two numbers that are fairly close together (ignore the sign differ by 5) and multiply to 104.

The two numbers are 8 and 13

More formally stated, the quadratic can be factored to

(x + 13)(x - 8) = 0

x - 8 =0

x - 8 + 8 = 8 + 0

x = 8

x + 13 = 0 has no meaning.

That means that the width ( a positive number ) = 8

The length is 5 more = 13

Answer:

You take the repeating group of digits and divide it by the same number of digits but formed only by 9s.

Step-by-step explanation:

Let's say you have 0.111111111111...., your repeating pattern is 1, that consists of one digit (1).  You take that digit and you divide it by 9:

1/9 is the fraction equivalent to 0.111111111111111...

Let's say you have 0.12121212121212...., the repeating pattern is 12, that consists of 2 digits (12).  You take those 2 digits and divide them by 99:

12/99 is the fraction equivalent to 0.12121212121212...

which can be reduced to 4/33

If you have 0.363363363363..., your repeating pattern is 363, which is 3 digits, so you divide 363by 999:

363/999 is the fraction equivalent to  0.363363363363...

which can be simplified to 121/333

To write a repeating decimal as a fraction, multiply the decimal by a suitable power of 10 to eliminate the repeating part, subtract the original equation from the new equation, solve for the variable, and simplify the fraction if possible.

To write a repeating decimal as a fraction, you can use a trick that involves using a variable to represent the repeating part of the decimal. Let's take an example of the repeating decimal 0.3333...

Therefore, the repeating decimal 0.3333... can be written as the fraction 1/3. This method can be applied to any repeating decimal to convert it into a fraction.

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Answer:

A

Step-by-step explanation:

(x−2) means the graph is shifted 2 units to the right.

+3 means the graph is shifted 3 units up.

So the graph of g(x) is shifted 2 units right and 3 units up.

The correct graph of the circle [tex]\rm x^2+y^2=9[/tex] is graph D, the corrcet option is D.

A circle can be represented as;

[tex]\rm (x-h)^2+(y-k)^2=r^2[/tex]

Where h and k are the centers of the circle and r is the radius of the circle.

The given equation of the circle is;

[tex]\rm x^2+y^2=9[/tex]

Here the center of the circle h = 0 and k = 0 so the circle passes through the origin.

The radius of the circle is;

[tex]\rm r^2=9\\\\r^2=3^2\\\\r=3[/tex]

Hence, the correct graph of the circle [tex]\rm x^2+y^2=9[/tex] is graph D, the correct option is D.

Learn more about circle here;

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Starting from the Pythagorean identity, we deduce

[tex]\sin^2(x)+\cos^2(x) = 1 \iff \cos^2(x) = 1-\sin^2(x) \iff \cos(x) = \pm\sqrt{1-\sin^2(x)}[/tex]

If we plug in the value 7/10 for sin(x), we have

[tex]\cos(x) = \pm\sqrt{1-\dfrac{49}{100}} = \pm\sqrt{\dfrac{51}{100}}=\pm\dfrac{\sqrt{51}}{10}[/tex]

Answer:

https://socratic.org/questions/how-do-you-write-the-equation-of-the-quadratic-function-with-roots-6-and-10-and-

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

Given the roots are x = 6 and x = 10, then

the factors are (x - 6) and (x - 10)

The quadratic is then the product of the roots

y = a(x - 6)(x - 10) ← a is a multiplier

To find a substitute (8, 2) into the equation

2 = a(2)(- 2) = - 4a ( divide both sides by - 4 )

a = - [tex]\frac{1}{2}[/tex]

Hence

y = - [tex]\frac{1}{2}[/tex](x - 6)(x - 10) ← expand factors

y = - [tex]\frac{1}{2}[/tex](x² - 16x + 60) ← distribute

y = - [tex]\frac{1}{2}[/tex] x² + 8x - 30

Answer:

7x

Step-by-step explanation:

Sorry this is the best way I could show the work as the equation maker on this site does not support doing something in this format

To divide the expression (14x^2 - 21x) by (2x - 3), you can use long division to get the answer 7x.

To divide the expression (14x^2 - 21x) by (2x - 3), we can use long division. Here are the steps:

Therefore, the answer is 7x.

For this case we have that by definition, the volume of a parallelepiped is given by:

[tex]V = l * w * h[/tex]

Where:

l: It's the long

w: It is the width

h: It's the height

From the figure we have the following data:

[tex]V = 975 \ ft ^ 3\\h = 9 \ ft\\w = 4ft\\x =?[/tex]

We must find the value of the length of the parallelepiped:

[tex]975 = x * 4 * 9\\975 = 36x\\x = \frac {975} {36}\\x = 27.083[/tex]

Answer:

[tex]x = 27.1 \ ft[/tex]

Answer:

you mulitple the two bottomz by the other number

example 3/4 and 2/8

8 is a common mulitple so 3/4 becomes 6/8 and now they have common denominators

Step-by-step explanation:

example 3/4 and 2/8

8 is a common mulitple so 3/4 becomes 6/8 and now they have common denominators

and the numerator gets multipled with the same number as the denominator

Answer:

$179.17

Step-by-step explanation:

You already know the formula but you have it typed incorrectly.  The rt is raised as a power to the e.  Just in case you didn't know that.  Filling in our formula with what we have gives us:

[tex]A(t)=125e^{(.18)(2)[/tex]

Simplify that power to .36 and we have

[tex]A(t)=125e^{.36}[/tex]

Now raise e to the power of .36 on your calculator and get

A(t)= 125(1.433329415)  and

A(t) = $179.17

Answer:

C 179 is the answer.

Step-by-step explanation:

Answer:

Option B is correct.

Step-by-step explanation:

A city has population = 10000

Population increase each year = 4%

So, Population increase after 1 year = 10000 * 4%

                                                           = 10000*4/100

                                                           = 400

Adding in the current population:

10000+400 = 10,400

Population increase after 2 year = 10,400*4%

                                                     = 10400*4/100

                                                      = 416

Adding in the current population:

10400+416 = 10816

Population increase after 3 year = 10,816*4%

                                                     = 10816*4/100

                                                      = 433

Adding in the current population:

10816+433 = 11,249

Population increase after 4 year = 11,249*4%

                                                     = 11249*4/100

                                                      = 450

Adding in the current population:

11249+450 = 11,699

Population increase after 5 year = 11,699*4%

                                                     = 11699*4/100

                                                      = 468

Adding in the current population:

11699+468 = 12167

So, the population after 5 yeras will be 12167.

Option B is correct.

The population of the city will be approximately 12,167 people after 5 years, calculated by using the formula for exponential growth with a 4% annual increase from the initial population of 10,000.

The question involves calculating the future population of a city that is experiencing exponential growth over a period of time. To find the population of a city 5 years later when the population increases by 4% per year, we use the formula for exponential growth, which is:

P = [tex]P0 * (1 + r)^t[/tex]

Where:

P is the future population

P0 is the initial population (which is 10,000)

r is the annual growth rate (which is 4% or 0.04)

t is the number of years (which is 5)

Using the formula, we calculate:

P = 10,000 × (1 + 0.04)⁵

P = 10,000 × (1.04)⁵

P = 10,000 × 1.2166529

P = 12,166.529

So, the population will be approximately 12,167 people 5 years later.

Answer:

Option a) x = −1, 5.4

Step-by-step explanation:

we have

[tex]f(x)=x^{2} -x-12[/tex]

[tex]g(x)=3.4x-6.6[/tex]

equate f(x) and g(x)

[tex]x^{2} -x-12=3.4x-6.6[/tex]

Solve the quadratic equation by graphing

The solutions are x=-1 and x=5.4

see the attached figure

Answer:

x= -1, 5.4

Step-by-step explanation:

[tex]f(x)= x^2-x-12[/tex]

[tex]g(x)= 3.4x -6.6[/tex]

f(x) is a quadratic equation and g(x) is a linear equation

To find f(x)= g(x) we need to find the point where the graph  of f(x) and g(x) intersects.

The quadratic equation f(x) and linear equation g(X) intersects at two points

from the graph f(x)= g(x) at x= -1 and x=5.4

Answer:

x=6

Step-by-step explanation:

15 = 5x + 45

     /5     /5

15 = x + 9

-9        -9

6 = x

The value of x = 6