In the figure, polygon ABCD is dilated by a factor of 2 to produce A′B′C′D′ with the origin as the center of dilation.

Point A′ is at
, and point D′ is at
.

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.

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Hi there!

[tex]\large\boxed{x \approx 19.6}[/tex]

We can use right triangle trigonometry to solve.

We are given the angle's adjacent side and are trying to solve for the hypotenuse, so:

Use cosine: cos Ф = A / H

Thus:

cos 30° = 17 / H

Simplify:

0.866 = 17 / H

Isolate for H:

H · 0.866 = 17

H = 17 / 0.866

H = 19.63 ≈ 19.6

Answer:

x = 19.6

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

cos theta = adj / hyp

cos 30 = 17/x

x cos 30 = 17

x = 17/cos 30

x=19.62990

To the nearest tenth

x = 19.6

Answer:

Below.

Step-by-step explanation:

Area = 5(x + 3)

= 5x + 15

Perimeter = 2(x + 3) + 2(5)

= 2x + 6 + 10

= 2x + 16.

Answer:

$9

Step-by-step explanation:

30*(100%-70%)=9

Answer:

9

Step-by-step explanation:

Take the original price

Multiply by the discount percent

30 *70%

30 *.70

21

The discount is 21 percent

Subtract this from the original amount

30-21

9

Answer:

x = -5

Step-by-step explanation:

4-2(x+7) = 3(x+5)

Distribute

4 - 2x-14 = 3x+15

Combine like terms

-2x-10 = 3x+15

Add 2x to each side

-2x-10 +2x =3x+2x+15

-10 = 5x+15

Subtract 15 from each side

-10-15 = 5x+15-15

-25 = 5x

Divide by 5

-25/5 = 5x/5

-5 =x

90/-10

= 9/-1

= -9

So, -9 is the quotient.

Step-by-step explanation:

Hey there!

From the given figure;

Angle FVT = 43°

VT = 53

Taking Angle FVT as reference angle we get;

Perpendicular (p) = FT = ?

Base (b) = VT = 53

Taking the of tan;

[tex] \tan( \alpha ) = \frac{p}{b} [/tex]

Keep all values and simplify it;

[tex] \tan(43) = \frac{ft}{53} [/tex]

0.932515*53 = FT

Therefore, FT= 49.423.

Hope it helps!

Answer:

A. 49.42

Step-by-step explanation:

tan 43 = FT ÷ VT

0.932515086 = FT ÷ 53

49.42 = FT

c.write the fact,organize your thoughts and define your strategy.

Answer:

c

Step-by-step explanation:

because y^3 is raised to the power of two, we will have to multiply the exponents rather than adding them.

By distributing the power of 2, we will get y^2(6).

Because now the exponents are being multiplied, we can just add them to get y^8. The other y has a power of 1, so we'll just add the power of that y as well to get y^9.

summary:

multiply exponents if they are being raised to a power.

add exponents if they are being multiplied, and only add them if they have the same base (in this case, both the bases of the exponents are y, so we can add them)

(-4/9)*3×(-27/20)*4= 7.2

Step-by-step explanation:

here's the answer to your question

Hi,

no need to use discriminant for that.

3(m)^2 = -6

m^2 = -6/3

m^2= -2

in R, there is no

solution as a square can not be negative.

Answer:

x = 1

y = 2

Step-by-step explanation:

5x + 2y = 9

-5x + 4y = 3

==> 6y = 12 ==> y = 12/6 ==> y = 2.

we replace y by its value in the first or the second equation, so will have:

5x + 2×2 = 9

5x + 4 = 9

5x = 5

x = 1

Answer:

y = 4

Step-by-step explanation:

The ratio of the lengths of the sides of a 30-60-90 triangle is

1 : √3 : 2

The sides in this triangle are in the order:

y : 4√3 : x

y/1 = 4√3/√3

y = 4

Answer:

207 tens

Step-by-step explanation:

If you mean

8,000 + 70 = 6000 + X tens

then it should be 207 tens

Step-by-step explanation:

you cannot just put the actual numbers in and calculate ?

and you can't provide the correct problem statement, as it seems.

I assume you mean

an = 3n² - 1

a sequence starts with a1, so, n>=1

a1 = 3×1² - 1 = 3-1 = 2

a2 = 3×2² -1 = 3×4 - 1 = 12 - 1 = 11

a3 = 3×3² - 1 = 3×9 - 1 = 27 - 1 = 26

a4 = 3×4² - 1 = 3×16 - 1 = 48 - 1 = 47

a5 = 3×5² - 1 = 3×25 - 1 = 75 - 1 = 74

there, that is all there is to it. you really needed help with that ?

Answer:

The only limitation is x≠0

The interval notation is (-∞,0)∪(0,∞)

Step-by-step explanation:

Set up the expression.

[tex](x+7)*(\frac{1}{x}-13)[/tex]

Multiply using FOIL.

[tex](x*\frac{1}{x})+(x*-13)+(7*\frac{1}{x})+(7*-13)[/tex]

[tex]1-13x+\frac{7}{x}-91[/tex]

[tex]-13x+\frac{7}{x}-91[/tex]

Find the Domain.

The only limitation is x≠0

The interval notation is (-∞,0)∪(0,∞)

Answer: Let the length of the hypotenuse be x

Applying the Pythagorean theorem we have :

x²=20²+48²

⇒x²=2704

⇒x=52( ∀ x >= 0 )

Step-by-step explanation:

Let assume the hypotenuse(longest side of right triangle) be x

By Pythagoras theorem

[tex] \bf \large \longrightarrow \: {c}^{2} \: = \: {a}^{2} \: + \: {b}^{2} [/tex]

Applying Pythagoras theorem

[tex] \bf \large \implies \: {x}^{2} \: = \: {20}^{2} \: + \: {48}^{2} [/tex]

[tex]\bf \large \implies \: {x}^{2} \: = \:400 \: + \: 2304[/tex]

[tex]\bf \large \implies \: {x}^{2} \: = \:2704[/tex]

[tex]\bf \large \implies \: \sqrt{x} \: = \: \sqrt{2704} [/tex]

[tex]\bf \large \implies \: \: x \: = \: 52[/tex]

Hence , the length of hypotenuse is 52.

Answer:

It is a parallelogram!

Step-by-step explanation:

This is because it has four sides and all the sides have parallel lines if that makes sence.

Answer:

The answer closest to 36.10425. So 36.10 or 36.1

Step-by-step explanation:

x = 44.85 ( 1 - 0.195) = 36.10425

If this helps, it would be nice if 5 stars are given, and a brainliest :)

The amount of the bill before adding the amount of tip is evaluated being of $37.53 approx.

Suppose the value of which a thing is expressed in percentage is "a'

Suppose the percent that considered thing is of "a" is b%

Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).

Thus, that thing in number is

[tex]\dfrac{a}{100} \times b[/tex]

For this case, we can assume the amount of bill without tip being A.

Then, as given, Payton gave 19.5% tip (tip is given assumingly on A), then:

Total price of the bill = Bill amount before tip + Tip

44.85 = A + (19.5 % of A)

(we don't write symbols like of currency generally in equations, and understand it from context(which is dollars here))

44.85 = A + (19.5 % of A)

or

[tex]44.85 = A + \dfrac{A}{100} \times 19.5\\\\\text{Multiplying 100 on both the sides}\\\\4485 = 100A + 19.5A\\4485 = 119.5A\\\\\text{Dividing both the sides by 119.5}\\\\\dfrac{4485}{119.5} = A\\\\37.53 \approx A\\\\A \approx 37.53 \: \rm \text{(in dollars)}[/tex]

Thus, the amount of the bill before adding the amount of tip is evaluated being of $37.53 approx.

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Complementary angles are those whose sum is 90° hence angles 3 and 4 will not be complementary angles but they will have adjacent angles so it will be true.

An angle is a geometry in plane geometry that is created by 2 rays or lines that have an identical terminus.

The identical endpoint of the two rays—known as the vertex—is referenced as an angle's sides.

In another word, the angle is the measurement of the angular distance for example for linear motion we have a meter inch but for angular rotation, we don't have the measurement so the angle is useful to measure the angular rotation.

Given,

Angle 3 and angle 4 are only two angles of a single line

So,

∠3 + ∠4 = 180°

So they will be supplementary angle not complimentary angle.

Angle 3 and 4 are adjacent angle because they are neighbors of each other.

Hence, they will not be complementary angles but will be the adjacent angle.

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Answer:

d the median if the data is 55

You're looking for a number w such that the numbers

{1 + w, 7 + w, 15 + w}

form a geometric sequence, which in turn means there is a constant r for which

7 + w = r (1 + w)

15 + w = r (7 + w)

Solving for r, we get

r = (7 + w) / (1 + w) = (15 + w) / (7 + w)

Solve this for w :

(7 + w)² = (15 + w) (1 + w)

49 + 14w + w ² = 15 + 16w + w ²

2w = 34

w = 17

Then the three terms in the sequence are

{18, 24, 32}

and indeed we have 24/18 = 4/3 and 32/24 = 4/3.

Answer:

brown

Step-by-step explanation:

it might be brown because it compelled

Answer:

b

Step-by-step explanation:

the square root of 8 is 2 and the square root of 18 is 4.5 and both simplified is 4/9.

Aslo did this last week.

Answer:

x = 138

Step-by-step explanation:

A straight line is 180

x+ 42 = 180

X = 180-42

x = 138

Answer:

[tex]1.5,1.2,0.96,0.768[/tex]

Common ratio between successive terms

[tex]=\frac{1.2}{1.5}[/tex]

[tex]=0.8[/tex]

OAmalOHopeO

The value of the common ratio between successive terms in the sequence is,

⇒ 0.8

An sequence has the ratio of every two successive terms is a constant, is called a Geometric sequence.

Given that;

The sequence is,

⇒ 1.5, 1.2, 0.96, 0.768,...

Hence, The value of the common ratio between successive terms in the sequence is,

⇒ 1.2 / 1.5

⇒ 12/15

⇒ 0.8

Thus, The value of the common ratio between successive terms in the sequence is,

⇒ 0.8

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