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Given ƒ(x) = 4x² – 4x – 20, find ƒ(10)

The value of x is 9 would make line segment fg is parallel to line segment bc.

It is given that FG || BC.

From the diagram,

If a transversal line intersect two parallel lines then the corresponding angles are same. There in triangle ACB and AGF.

If a transversal intersects two parallel lines, then each pair of interior angles on the same side of the transversal is supplementary, i.e. they add up to 180°. When two lines intersect each other, then the opposite angles, formed due to intersection, are called vertical angles or vertically opposite angles.

∠GFA=∠CBA

∠AGF=∠ACB

If two parallel lines are intersected by a transversal, then the interior angles on the same side of the transversal are equal.

Angle A is common is both triangles.

[tex]$$\begin{aligned}& \frac{F A}{B A}=\frac{G A}{C A} \\\\& \frac{x+1}{(x+1)+(x+6)}=\frac{x-1}{(x-1)+(x+3)} \\& \frac{x+1}{(2 x+7}=\frac{x-1}{(2 x+2)} \\& (x+1)(2 x+2)=(x-1)(2 x+7) \\& 2 x^2+4 x+2=2 x^2+5 x-7 \\& 4 x+2=5 x-7 \\& x=9\end{aligned}$$[/tex]

Therefore, the value of x is 9.

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Answer: Yes, answer is 15

Step-by-step explanation:

Another way to look at this is 50% of 30, or just 1/2 of 30.

To calculate the distance between two places, we can apply the distance formula d=((x2 - x1)² + (y2 - y1)²).

The distance of an object is its overall motion, regardless of direction.

Distance is the amount of space that an object has covered, regardless of where it began or concluded.

By understanding how far an object is from us, we may calculate its actual size.

It is possible to calculate the area that an object takes up in the sky.

The actual size of an object can then be determined by taking into account its distance.

The further away something is, the smaller it appears.

The distance between two locations on a plane is the length of the line segment connecting them.

The formula d=((x2 - x1)2 + (y2 - y1)2) is frequently used to calculate the separation between two points.

Therefore, to calculate the distance between two places, we can apply the distance formula d=((x2 - x1)² + (y2 - y1)²).

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No, you will not reach your goal. At 16.6 miles per hour, it would take you 6.74 hours to complete the bike portion of the Ironman Triathlon. This is more than the 6.4 hours you want to complete it in.

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The function of graph x is v shaped.

What is the function of graph?

The collection of all points in the plane with the form (x, f(x)) that make up a function f's graph. We may alternatively say that the graph of f is the graph of y = f. (x). Consequently, a special case of an equation's graph is the graph of a function.

The relation depicted by the graph is not a function if any vertical line touches it more than once.

The given graph is non functional graph the right graph need is :

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To determine the time the power came back on, we need to determine how much time has passed since the power went out and the alarm clock reset where the power came back on at 17.79 hours or 17 hours and 47 minutes (17:47).

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The slope is 0 when 0/(-5) and it means, the line with this slope must be coincident or parallel to the x-axis

We know that the slope of a line is nothing but the change in y coordinate with respect to the change in x coordinate.

The slope of the line describes the steepness of a line.

Also,  if a line makes an angle θ with the positive direction of the x-axis, then the slope of the line will be tangent of angle θ

m = tan θ

Here we have been given a slope 0/(-5)

As we know 0/(-5) = 0

So, the slope is 0.

The slope is 0 when 0/(-5)

Let m be the slope of the line, m = 0

From definition of slope of line,

0 = tan θ

θ = arctan(0)

θ = (nπ)                where n = 0, 1, 2, . . .

This means, the slope 0/(-5) represents that for every fiveunits of horizontal distance crosses there is no change of vertical distance.

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Answer:

no, the origin is located at 0,0

Answer: Lola is incorrect. The two expressions have different values.

Expression A is (a/b)^(-4)^0 which is equal to 1, since any non-zero number raised to the power of 0 is 1.

Expression B is (a/b)^0^(-4) which is (a/b)^(-4) which is the reciprocal of (a/b)^4. They are different values.

In general, it's important to be careful with the order of operations when working with exponents and to be aware of the difference between a^b^c and (a^b)^c or a^(b*c) depending on the context.

Step-by-step explanation:

The next two varieties of field daisy have 55 and 89 petals.

We know that the Fibonacci Sequence is the series of numbers such that:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ...

Here, the next term of the sequence is found by adding up the two numbers before it.

For exa., the fourth term 2 is the sum of (1+1),

the fifth term 3 is the sum of (1+2)

In this question the numbers of petals of field daisies follow a Fibonacci sequence.

The three varieties have 13, 21, and 34 petals.

The next variety of field daisy would be the sum of 21 and 34

21 + 34 = 55

And the fifth variety of field daisy would be the sum of 34 and 55

34 + 55 = 89

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a. The value of a is 5500. b. The value of r is 0.92. c. There are 2022 trees still alive till 1st October 2023.

The percentage is defined as a ratio expressed as a fraction of 100.

a) The value of a is 5500.

b) To find the value of r, we can use the equation N = ar where N is the number of trees still alive t years after 1st October 2018. We know that N = 5060 on 1 October 2019, so we can substitute these values into the equation:

5060 = 5500 r

r = 5060/5500

r = 0.92

c) To find the predicted percentage decrease in trees still alive between 1 October 2018 and 1 October 2030, we can use the equation:

[tex]N = ar^t[/tex]

Here a = 5500, r = 0.92 and t = 12

We can now substitute the values, then we get

N = 5500 × (0.92)¹² ≈ 2021.67

N = 2022

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A table of equivalent ratios for the number of miles and hours that Alexander drove is as follows:

Miles        Hours

46                 1

184                4

414                9

The data points are plotted on the coordinate axes of the graph shown in the image attached below.

In Mathematics, a proportional relationship can be represented by the following mathematical expression:

x = ky

Where:

In order to have a proportional relationship and equivalent ratios, the variables x and y must have the same constant of proportionality. Therefore, we would determine the constant of proportionality (k) as follows:

Constant of proportionality (k) = x/y

Constant of proportionality (k) = 184/4

Constant of proportionality (k) = 46.

When hours y = 1, the number of miles x is given by:

x = ky

x = 46 × 1

x = 46 miles.

When miles x = 414, the number of hours y is given by:

y = x/k

y = 414/46

y = 9 hours.

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-112°  =  1.95 units clockwise. This can be solved using the concept of central angle.

Correct option is: d

A circle's central angle is the angle formed by two of its radii. The circle's two places of intersection (Note: The opposite end of the radii meets at the circle's centre) together make up a section known as the arc Length.

A central angle is an angle whose legs (sides) are radii intersecting the circle at two different places, A and B, and whose apex (vertex) is the center O of a circle. The central angle is the angle created by the two radii of the circle. A 360° angle is completed by the circle. A circle's central angle has a value between 0 and 360°.

For the given central angle,

-112°  = d 1.95 units clockwise

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The missing values of the angles x and y of the given diagram are; x = 32.5° and y = 22°

From the attached image, we can see that angle 12 and 13 are corresponding angles and as such;

m∠12 = m∠13

Similarly, angles 6 and 2 are corresponding angles and we can say that;

m∠6 = m2

We know that sum of angles on a straight line is 180 degrees and as such since m<9 = 2x - 5, then we have;

m<9 = 180 - m<12

= 180 - 120

= 60°

Therefore,

2x - 5 = 60

2x = 65

x = 65/2

x = 32.5°

m<8 = m<6 = 98° because they are vertically opposite angles

Thus;

y + m<9 + m<8 = 180 ( sum of angles of a triangle is 180 degrees)

y + 60 + 98=180

y + 158 = 180

y = 22°

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Therefore , the solution of the given problem of function comes out to be  $33 will be the price of haircut in 1997.

Mathematics is a science that investigates numbers, their variations, mathematics and the local tissues, shapes, and the both their actual and potential placements. Function describes the connection between a collection of inputs, each of which has an associated output. A function is an association domain of inputs that results in a single, distinctive output for each input. Each function is given a city or municipality or a scope, often known as a realm.

Here,

Given : c = 2y + 29

where c is the typical cost of the a haircut and

y is the number of years since 1995.

For the model, the slope is 2.

It implies that starting in 1995,

the average price of a haircut will rise by 2 each year.

=>1995 has y=0 and a cost of 29.

=> 1996's y=1 results in a cost of 29+2=31.

=>When y=2 in 1997, the price is 29+4 = 33, and so forth.

Therefore , the solution of the given problem of function comes out to be  $33 will be the price of haircut in 1997.

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Answer:

2

Step-by-step explanation:

functions mean that each input can only have one output.

if we do 2 as the input it will have both 7 and -5 a the output making it not a function

hopes this helps

Answer: B

Step-by-step explanation:

Answer:

Hey there!

Arithmetic sequences are made up of terms that are added or subtracted, and geometric sequences are made up of terms that are multiplied or divided.

Given this info, we can see that we go from 10 to -5. Because we know that this is geometric, we see that we must divide by -2 in our sequence.

We can see that this is true because -5/-2=5/2.

Now, we could simply continue dividing by negative two to get our answer, which is -5/16.

You could easily do that with a calculator, but if you had to find a term that was farther from the first term, that would take forever to do with a calculator, so there is an equation that you can use and plug in your numbers to find the answer quickly.

, where  is the number of term in the sequence (6 in this problem), a is the first term of the sequence (10), and r is the common ratio (-1/2).

I hope this helps!

Step-by-step explanation:

The unit vector that lies in the xy plane at an angle of 155 degrees from the x axis with a positive y component is (0.4237, 0.9055).

A unit vector is a vector with a magnitude of 1. To find the unit vector that lies in the xy plane at an angle of 155 degrees from the x axis with a positive y component, we can use the formula for a two-dimensional vector in polar coordinates:

r = (cos(θ), sin(θ))

where r is the unit vector, θ is the angle in radians, and cos(θ) and sin(θ) are the x and y components, respectively.

First, we need to convert the angle from degrees to radians:

θ = 155° * (π / 180°) = 2.68 radians

Next, we can plug in the values into the formula:

r = (cos(2.68), sin(2.68)) = (0.4237, 0.9055)

So, the unit vector that lies in the xy plane at an angle of 155 degrees from the x axis with a positive y component is (0.4237, 0.9055).

To summarize, the process for finding a unit vector in the xy plane at an angle from the x axis is:

Convert the angle from degrees to radians

Use the formula for a two-dimensional vector in polar coordinates: r = (cos(θ), sin(θ))

Plug in the values into the formula to find the unit vector

Note: Keep in mind that the angle of a unit vector is relative to the positive x axis, with positive angles going counterclockwise and negative angles going clockwise.

Therefore, The unit vector that lies in the xy plane at an angle of 155 degrees from the x axis with a positive y component is (0.4237, 0.9055).

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The unit vector that lies in the xy plane at an angle of 155 degrees from the x axis with a positive y component is (0.4237, 0.9055).

A unit vector is a vector with a magnitude of 1. To find the unit vector that lies in the xy plane at an angle of 155 degrees from the x axis with a positive y component, we can use the formula for a two-dimensional vector in polar coordinates:

r = (cos(θ), sin(θ))

where r is the unit vector, θ is the angle in radians, and cos(θ) and sin(θ) are the x and y components, respectively.

First, we need to convert the angle from degrees to radians:

θ = 155° * (π / 180°) = 2.68 radians

Next, we can plug in the values into the formula:

r = (cos(2.68), sin(2.68)) = (0.4237, 0.9055)

So, the unit vector that lies in the xy plane at an angle of 155 degrees from the x axis with a positive y component is (0.4237, 0.9055).

To summarize, the process for finding a unit vector in the xy plane at an angle from the x axis is:

Convert the angle from degrees to radians

Use the formula for a two-dimensional vector in polar coordinates: r = (cos(θ), sin(θ))

Plug in the values into the formula to find the unit vector

Note: Keep in mind that the angle of a unit vector is relative to the positive x axis, with positive angles going counterclockwise and negative angles going clockwise.

Therefore, The unit vector that lies in the xy plane at an angle of 155 degrees from the x axis with a positive y component is (0.4237, 0.9055).

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Answer: 8x^3yz^4(3xy^2-4z)

Step-by-step explanation:

Factor out the greatest common factor: [tex]8[/tex]

8 x 3 = 24
8 x 4 = 32

Factor out the smallest powers from both sides: [tex]x^3 yz^4[/tex]

Leave the remaining x, y, and z values

[tex]8x^3yz^4(3xy^2-4z)[/tex]

There are  [tex]8^5\\[/tex] cubes in the Container.

Exponents and powers are ways used to represent very large numbers or very small numbers in a simplified manner.

For example, if we have to show 3 x 3 x 3 x 3 in a simple way, then we can write it as [tex]3^4[/tex], where 4 is the exponent and 3 is the base.

Given:

Volume of Container = [tex]8^7[/tex] cm³

Volume of Each cube = 8² cm³

So, the number of cubes in the container

= Volume of Container / Volume of Each cube

=  [tex]8^7[/tex] cm³ / 8² cm³

Now, using Exponents property

[tex]a^m / a^n= a^{m-n[/tex]

Then, number of cubes in the container

=  [tex]8^7[/tex] cm³ / 8² cm³

= [tex]8^{7-2[/tex]

= [tex]8^5\\[/tex]

Hence, the number of cubes are  [tex]8^5\\[/tex].

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An equation of the line that passes through the points (- 4, 7) and (2, 8) is 6y = x + 31.

In the given question, we have to find an equation of the line that passes through the points (- 4, 7) and (2, 8).

The point-slope approach is typically used when two points that sit on a specific line are specified.

A line's equation is written as y - y(1) = m(x - x(1)), where y(1) is the Y-axis coordinate, m is the slope, and x(1) is the X-axis coordinate.

Firstly we find the value of m using the formula

m = [tex]\frac{y(2)-y(1)}{x(2)-x(1)}[/tex]

From the given points x(1) = -4, y(1) = 7, x(2) = 2, y(2) = 8.

Now putting the value

m = [tex]\frac{8-7}{2-(-4)}[/tex]

Now solving

m = [tex]\frac{1}{2+4}[/tex]

m = [tex]\frac{1}{6}[/tex]

Now we finding the equation of line. We can use any one point in the given points.

Now taking the points (2, 8), x(1) = 2 and y(1) = 8

Now putting the value in equation y - y(1) = m(x - x(1)).

y - 2 = [tex]\frac{1}{6}[/tex](x - 8)

Multiply by 6 on both side, we get

6(y - 6) = x - 5

6y - 36 = x - 5

Add 36 on both side, we get

6y = x + 31

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The complete question is:

What is an equation of the line that passes through the points (- 4, 7) and (2, 8)?

If we multiply monomial and binomial, then it is become polynomial.

Perfect Squares: The Square of a Difference Squaring a binomial every time results in a trinomial.

In other words, if we find the product of 6 and 3 by simply calculating 6 times 3 which equals 18.

A monomial is a statement of the form k⋅xⁿ, where k is a real number and n is a positive integer. It is essentially a polynomial with a single term.

When we are multiplying two monomials, we can rewrite the product as a single monomial using properties of multiplication and exponents.

A polynomial equation with two terms normally joined by a plus or minus sign is called a binomial.

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Answer:

67.75

Step-by-step explanation:

[tex]84.95 - 2.15 \cdot (3.91 - 1.91)^3[/tex]

[tex]3.91-1.91=2[/tex]

[tex]2^3=8[/tex]

[tex]2.15\cdot8=17.2[/tex]

[tex]84.95 -17.2=67.75[/tex]

So, the final answer is 67.75

Answer:2350 million

Step-by-step explanation:

hope this helps

To find the roots of a quadratic equation by the factorization method, you can use the following steps:

Write the equation in standard form (ax^2 + bx + c = 0)

Factor the equation completely by setting it equal to zero and factoring out the greatest common factor.

Set each factor equal to zero and solve for the roots.

For example, to find the roots of the equation x^2 + 5x + 6 = 0, we can factor it as (x+3)(x+2) = 0.

To find the roots, we set each factor equal to zero and solve for x:

x + 3 = 0, x = -3

x + 2 = 0, x = -2

So the roots of the equation x^2 + 5x + 6 = 0 are -3 and -2.

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Therefore , the solution of the question is given by the theorem of

constant proportionality comes out to be 1.5 .

The proportion between any directly proportional quantities is the proportionality constant. If the growth and decline of two quantities occur at the same rates, they are directly proportional. When two quantities, y and x, are approximately equal to one another, the proportionality constant, k, is equal to their product, y/x.

Here,

Given :

=> original price : $15 ,$25,$35

=> sale price: $10,$20,$30

To find the proportional relationship :

=> 15/10 =1.5

=> 25/20 = 5/4 = 1.25

=> 35/30 = 7/6 = 1.16

Therefore , the solution of the given problem of constant proportionality comes out to be 1.5 .

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The value of B+U+S+T+E+D is 20. B represents the number 2, U represents the number 3, S represents the number 19, T represents the number 20, E represents the number 5, and D represents the number 4. When these numbers are added together, they equal 20.

BUSTED is an acronym for 'Believing Uncovering Solving Troubles Everywhere Dynamicly'. It is a popular phrase used by the characters in the Scooby-Doo cartoons. It is a phrase used to express the moment when the mystery is solved and the bad guy is caught.

BUSTED is an important part of the Scooby-Doo cartoon series. It expresses the moment when the mystery is solved and the bad guy is caught. It is also a great way to encourage children to believe in themselves and to use their own detective skills to solve a mystery. The value of B+U+S+T+E+D is 20, and it is a fun way to teach kids math and problem solving skills.

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For horizontal asymptote, for the graph function y=f(x) where the straight line equation is y=b, which is the asymptote of a function x → + ∞, if the following limit is finite.

what is the equation for the horizontal asymptoms?

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