For the lengths AB, BC, and AC to equal 7,6, and 13 respectively, what is the
value of x?

a) The equation has a root in the interval (-1,0)

b) The solution of [tex]2x+3cos(x)+e^{x}=0[/tex] by using the Bisection Method is x=0.9977 accurate within [tex]10^{-3}[/tex]

a) The intermediate zero theorem (Bolzano's Theorem) tells us that whenever you have a continuous function in a given interval and the extremes of the functions on this interval have oposite signs, then there must be a zero in between those extreme values.

"If a function f on the closed interval [a,b] is a continuous function and it holds that f(a)>0 and f(b)<0 or f(a)<0 and f(b)>0, then there is at least one x-value such that f(x)=0"

So basically we need to evaluate the given equation for both extremes of the interval x=-1 and x=0, if they return results opposite in sign, then there must be a zero in that interval, so let's evaluate the function for x=-1:

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

[tex]2(-1)+3cos(-1)+e^{-1}=-0.0112[/tex]

Let's now test for x=0

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

[tex]2(0)+3cos(0)+e^{0}=4[/tex]

So notice we ended up with two values -0.0112 and 4. One is positive and the other is negative, therefore there must be a zero in that interval.

b) The zero is located at x=-0.9977

The idea of the bisection method is to find values for x in the middle of two x-values that return opposite sign answers when evaluated on the given function. So we can start with the extremes of the given interval:

x=-1 and x=0

so we find the value in the middle by using the following formula:

[tex]mid-value=\frac{x_{1}+x_{2}}{2}[/tex]

so we get:

[tex]mid-value=\frac{-1+0}{2}[/tex]

mid-value=-0.5

Next, we evaluate the given function for that value:

[tex]2(-0.5)+3cos(-0.5)+e^{-0.5}=2.2393[/tex]

Since we got a positive answer, we now find the midpoint between -0.5 and -1 (which was the last x-value that returned a negative answer) so we get:

[tex]mid-value=\frac{-1-0.5}{2}[/tex]

mid-value=-0.75

Next, we evaluate the given function for that value:

[tex]2(-0.75)+3cos(-0.75)+e^{-0.75}=1.1674[/tex]

and we repeat the process until que get to the desired accuracy. I uploaded a table that has the corresponding iterations and its answers. There were 14 iterations done until we got to the final answer x=-0.9977.

Learn more about the intermediate zero theorem here:

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Answer:

Jeff has 3 watermelons left

Step-by-step explanation:

44-31=13 watermelons

Answer:

13

Step-by-step explanation:

44

-31

13

Answer:

30 ft

Step-by-step explanation:

a² + b² = c²

(15sqrt(2))² + (15sqrt(2))² = c²

225 * 2 + 225 * 2 = c²

c² = 900

c = sqrt(900)

c = 30

Answer: 30 ft

Answer:

30 ft

Step-by-step explanation:

a² + b² = c²

(15sqrt(2))² + (15sqrt(2))² = c²

225 * 2 + 225 * 2 = c²

c² = 900

c = sqrt(900)

c = 30

Answer: 30 ft

Answer:

y = 5x^2-5x-30

Step-by-step explanation:

A parabola with x-intercepts at (-2,0) and (3,0) has the equation

y = a(x+2)(x-3)

where a is to be determined.

We know that it passes through the point (0,-30), so

-30 = a(0+2)(0-3) = -6a

Therefore solve for a to get

a = 5

y = 5(x+2)(x-3)

y = 5(x^2-x+6)

y = 5x^2-5x-30

Step-by-step explanation:

If you like my answer than please mark me brainliest thanks

you just have to expand the trig. functions into their corresponding values and then finish them off.

Answer:

[tex]\boxed{(x+7)^2 =-3x^2-14x}[/tex]

Step-by-step explanation:

[tex]4x^2 + 28x + 49 = 0[/tex]

[tex]\sf Subtract \ 3x^2 \ and \ 14x \ from \ both \ sides.[/tex]

[tex]4x^2 + 28x + 49 -3x^2-14x= 0-3x^2-14x[/tex]

[tex]x^2 + 14x + 49 = -3x^2-14x[/tex]

[tex]\sf Factor \ left \ side \ of \ the \ equation.[/tex]

[tex](x+7)^2 =-3x^2-14x[/tex]

Answer:

(x+7)² = -3x² -14x

Step-by-step explanation:

4x^2 + 28x + 49 = 0

Subtract 3x² and 14x from each sides.

x^2 + 14x + 49 = -3x² -14x

Next step will be factoring.

(x+7)² = -3x² -14x

Answer:

37.3m**3

Step-by-step explanation:

1/3*7*4*4 = 37.3m**3

Answer:

Pyramid Volume = (area of base * height) / 3

Pyramid Volume = (4 * 4 * 7) / 3

Pyramid Volume = 112 / 3

Pyramid Volume = 37.33333 cubic meters

http://www.1728.org/volpyrmd.htm

Step-by-step explanation:

Answer:

I think it is twenty seven

Answer:

72

Step-by-step explanation:

l = 5w

A = l*w

180 = 5w *w

180 = 5w^2

Divide each side by 5

180/5 = 5w^2 /5

36 = w^2

Taking the square root of each side

sqrt(36) = sqrt(w)^2

6 =w

l = 5w = 5*6 = 30

The perimeter is

P = 2(l+w)

P = 2(6+30) = 2(36) = 72

Answer:

The answer is 1/14w-8

[tex](f+g)(x)=\sqrt{4x+6}+\sqrt{4x-6}[/tex]

Answer:

[tex]\huge\boxed{Option \ 4: (f+g)(x) = \sqrt{4x+6} + \sqrt{4x-6}}[/tex]

Step-by-step explanation:

[tex]f(x) = \sqrt{4x+6}\\ g(x) = \sqrt{4x-6}[/tex]

Adding both

[tex](f+g)(x) = \sqrt{4x+6} + \sqrt{4x-6}[/tex]

Answer:

90 is the answer:)

Step-by-step explanation:

I hope it helps you. Have a marvellous day!

Answer:

90 is the answer

Step-by-step explanation:

Answer:

OD) 16 cubic centimeters

Answer:

Its A

Step-by-step explanation:

The tangent of the given circle is FG hence the correct option will be an option (B).

The tangent of a circle is a line that intersects the circle at the periphery of the circle.

If you draw a line that goes through the center to the tangent touching point then it will give you a 90-degree angle.

Given the circle it's clear that the tangent is only FG hence it will be the correct option  

A circle can have an infinite number of tangents.

In other words, a straight line that only touches a circle twice is said to be tangent to it. The term point of intersection refers to this location

At the tangent line, the tangent to a circle is orthogonal to the radius.

For more information about the tangent of the circle

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Answer:

(MOE) the Margin of Error will decrease by the square root of 2

Step-by-step explanation:

The Margin of Error (MOE) is an inverse function of sample size n ( more precisely of the square root of sample size ). That relation means changes in sample size ( keeping constant other variables of the distribution) will imply opposite changes in the Margin of Error. If we double the sample size increasing it from 200 up to 400,  the Margin of Error will decrease by the square root of 2

Answer:

3 miles

Step-by-step explanation:

5 + m=8

Subtract 5 from each side

5-5 + m=8-5

m = 3

She needs to swim 3 more miles

Answer:

Yelena needs to swim 3 more miles

Step-by-step explanation:

You need to solve for the variable "m", which represents the miles. Based on the information, Yelena swam 5 miles and she needs to swim 8. Solve:

[tex]5+m=8[/tex]

To find the value of m, you need to isolate it on one side of the equation. To do this, you need to get the 8 and 5 on the same side of the equal operation. For this, you need to use reverse operations. This undoes the value from one side and does the same on the other, keeping the equation balanced. Since we have a "positive 5", we take the opposite, which would be a "negative 5". So subtract 5 from both sides of the equation:

[tex]5-5+m=8-5[/tex]

Simplify. The 5's cancel each other out, leaving 0. 8-5 is 3:

[tex]m=3[/tex]

The total miles left that Yelena needs to swim is 3 miles.

:Done

Answer:

(-5, 0)

(-1, 0)

Step-by-step explanation:

x-intercepts are points where the graph intersects the x-axis (or when y = 0)

Step 1: Write out function

f(x) = x² + 6x + 5

Step 2: Factor

f(x) = (x + 5)(x + 1)

Step 3: Find binomial roots

x + 5 = 0

x = -5

x + 1 = 0

x = -1

Alternatively, you can graph the function and analyze the graph for x-intercepts:

Step-by-step explanation:

What is the equation of the parabola that has a vertex at

(

−

4

,

2

)

and passes through point

(

−

7

,

−

34

)

?

To solve this you need to use the vertex form of the equation of a parabola which is

y

=

a

(

x

−

h

)

2

+

k

, where

(

h

,

k

)

are the coordinates of the vertex.

Explanation:

The first step is to define your variables

h

=

−

4

k

=

2

And we know one set of points on the graph, so

x

=

−

7

y

=

−

34

Next solve the formula for

a

y

=

a

(

x

−

h

)

2

+

k

−

34

=

a

(

−

7

+

4

)

2

+

2

−

34

=

a

(

−

3

)

2

+

2

−

34

=

9

a

+

2

−

36

=

9

a

−

4

=

a

To create a general formula for the parabola you would put in the values for

a

,

h

, and

k

and then simplify.

y

=

a

(

x

−

h

)

2

+

k

y

=

−

4

(

x

+

4

)

2

+

2

y

=

−

4

(

x

2

+

8

x

+

16

)

+

2

y

=

−

4

x

2

−

32

x

−

64

+

2

So the equation of a parabola that has a vertex at

(

−

4

,

2

)

and passes through point

(

−

7

,

−

34

)

is:

y

=

−

4

x

2

−

32

x

−

62

The domain is the input values, which are the x values.

The x values in the given pairs are: 8, 0,4,-3

The domain set is (-3, 0, 4, 8)

The required domain of the set of ordered pairs is [8, 0, 4, -3]

Given that,

Set of ordered pair; (8, -13); ( 0,-5); (4, -9); (-3,2).

We have to determine,

The domain of the set of ordered pair.

According to the question,

The domain refers to the set of possible input values.

The domain of a graph consists of all the input values shown on the x-axis.

A relation is a set of ordered pairs.

The domain is the set of all the first components of the ordered pairs.

Then,

Set of ordered pair; (8, -13); ( 0,-5); (4, -9); (-3,2).

Here, Set of all the input values on the x-axis.

Therefore,

The set of values of x is { 8,0,4,-3 }

Hence, The required domain of the set of ordered pairs is [8, 0, 4, -3]

To know more about Domain click the link given below.

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Answer: a) 0.003

b) 0.125

c) 0.047

Step-by-step explanation:

We have a set of 8 numbers {1,2,...,8}

Let's analyze each case:

a) 5 and 8 are picked. The probability here is:

In the first selection, we have two possible picks (we can pick 5 or 8), so we have two possible outcomes out of 8 total outcomes,  the probability for the first selection is:

P = 2/8 = 1/4.

Now, if one of those numbers was picked in the first selection, only one outcome is possible in this second selection, (if before we picked a 5, here we only can pick an 8, or if in the first selection we picked an 8, here we only can pick a 5.)

the probability is:

P = 1/8

The joint probability is equal to the product of the individual probabilities, so here we have:

P = (1/4)*(1/8) = 1/32 = 0.003

b) The numbers match (we draw two sixes, for example) :

In the first selection, we can have any outcome (the only requirement is that in the second selection we pick the same outcome), so the probability is:

P = 8/8 = 1

in the second selection, we can have only one outcome, so here the probability is:

P = 1/8

The joint probability is p = 1/8  = 0.125

c) The sum is smaller than 4:

The combinations are:

1 - 1  , 1 - 2  and 2 - 1

We have 3 combinations, and the total number of possible combinations is:

8 options for the first number and 8 options for the second selection:

8*8  = 64

The probability is equal to the number of outcomes that satisfy the sentence (3) divided by the total number of outcomes (64):

P = 3/64 = 0.047

9514 1404 393

Answer:

Step-by-step explanation:

1. de Moivre's theorem (or identity) states that ...

  [tex](\cos(\theta)+i\sin(\theta))^n=\cos(n\theta)+i\sin(n\theta)[/tex]

It is a statement about powers of complex numbers, so is related to the complex plane.

__

2. To graph a parametric equation, you need to know the relationship between the parameter and the coordinates you want to graph.

__

3. Here are the relationships:

  (x, y) = (r·cos(θ), r·sin(θ))

  (r, θ) = (√(x² +y²), arctan(y/x)) . . . with attention to quadrant

Answer:

Base area (B) should not be added.

Step-by-step explanation:

Base area should not be added as cone is not solid. Only Lateral surface area is sufficient in order to find the required paper.

Answer:

51.

Step-by-step explanation:

f(x) = x^2 + 2x + 3 and g(x) = x + 4.

f(g(x)) = (x + 4)^2 + 2(x + 4) + 3

= x^2 + 4x + 4x + 16 + 2x + 8 + 3

= x^2 + 8x + 16 + 2x + 11

= x^2 + 10x + 27.

x = 2.

f(g(2)) = 2^2 + 10 * 2 + 27

= 4 + 20 + 27

= 31 + 20

= 51.

Hope this helps!

Answer:

1st:

[tex] {x}^{3} - 3 { x}^{2} - 3[/tex]

2nd:

[tex] {x}^{2} - 5x + 4[/tex]

3rd:

[tex] - 4x - 8[/tex]

Step-by-step explanation:

Graph all of them and see which ones cross the x- axis at the same points.

186|2

93|3

31|31

1

310|2

155|5

31|31

1

434|2

217|7

31|31

1

[tex]186=2\cdot3\cdot31\\310=2\cdot5\cdot31\\434=2\cdot7\cdot31\\\\\text{hcf}(186,310,434)=2\cdot31=62[/tex]

Answer:

1. C. The researcher must compute an estimated standard error for the mean difference score to compute a t statistics.

2. B. 10

3. A. 12

Step-by-step explanation:

The degrees of freedom is number of independent variable factors that affect the range of parameters. The degrees of freedom is the calculation of number values that are free to vary. The degrees of freedom is calculated by N-1. Standard error is the estimated deviation of standard deviation from its sample mean distribution.

Answer:

Step-by-step explanation:

Considering the polynomial 2x⁵ + 4x³ - 3x⁸. The polynomial is not yet in standard form. For a polynomial to be in standard form, the power of the variables must decrease as we progress to the right of the expression.

A) The polynomial in standard form is therefore   - 3x⁸ + 2x⁵ + 4x³. We can see that the power are reducing as we move through each terms i.e from 8 to 5 then to 3.

B) The degree of a polynomial is the maximum degree among all the terms of the polynomial. The term that has the maximum degree is -3x⁸. Hence, the degree of the polynomial is 8

C) There are only 3 terms in the polynomial given. The terms are separated by mathematical signs. The terms if the polynomial are 2x⁵,  4x³ and - 3x⁸.

D) The leading term of the polynomial is the term that comes first after rewriting the polynomial in standard format. Given the standard from of the polynomial given as  -3x⁸ + 2x⁵ + 4x³, the leading term will be  - 3x⁸

E) Given the leading term to be  - 3x⁸, the leading coefficient of the polynomial will be the coefficient of the leading term. The coefficient of -3x⁸ is -3

The answer is the population grew over the hundred-year span by [tex]6.481*(10)^6[/tex]

Given that in 2014, the population of people in Ohio = [tex]11.59[/tex] million

Also given that One-hundred years earlier of the year 1914, the population =  [tex]5.109[/tex] million people

One-hundred years earlier in the year 2014 = 2014 [tex]- 100[/tex] years

One-hundred years earlier in the year 2014 = Year 1914

The scientific notation of the year 2014 population is [tex]11.59*(10)^6[/tex]

The scientific notation of the year 1914 population is [tex]5.109*(10)^6[/tex]

How much did the population grow over the hundred-year span?

Growth of the population from 1914-2014 = [tex]11.59*(10)^6 - 5.109*(10)^6[/tex]

Growth of the population from 1914-2014 = [tex]6.481*(10)^6[/tex]

Conclusion: The population grew over the hundred-year span by [tex]6.481*(10)^6[/tex]

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Answer:

476 workers

Step-by-step explanation:

Men: women : total

3          4           3+4 = 7

We want 204 men

204/3 =68

Multiply each by 68

Men: women : total

3*68    4*68      7*68

204        272      476

Answer:

There are 476 workers

Step-by-step explanation: