The perpendicular distance of (2, -4) from x axis is

Answer:

b=4

Step-by-step explanation:

So, we have the function [tex]f(x)=1/x[/tex]. We need to find b such that the average rate of change or the slope is -1/8 between the intervel [2, b]. First, let's find f(2).

f(2) = 1/(2) = 1/2

So, we have the point (2, 1/2)

At point b, f(b) = 1/b.

Let's plug this into the slope formula:

[tex]\frac{y_2-y_1}{x_2-x_1}=\frac{.5-\frac{1}{b} }{2-b} =-1/8[/tex]

Now, we just need to solve for b. First, let's multiply both the numerator and denominator by b (to get rid of the annoying fraction in the numerator).

[tex]\frac{.5b-1}{2b-b^2} =\frac{-1}{8}[/tex]

Now, cross multiply.

[tex]4b-8=b^2-2b[/tex]

[tex]b^2-6b+8=0[/tex]

Solve for b. Factor using the numbers -4 and -2.

[tex]=(b-4)(b-2)=0[/tex]

Thus, b=4 or b=2.

However, b=2 is not a possible solution since the interval [2,2] means nothing. Thus, b=4.

We want to find an interval such that the given equation, f(x) = 1/x, has an average rate of change of -1/8 in that interval.

We will see that the interval is [2, 4]

-------------------------------

For a function f(x), the average rate of change in the interval [a, b] is given by:

[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]

Here we have:

[tex]f(x) = 1/x[/tex]

And the interval is [2, b] such that r in that interval is -1/8, so we need to solve:

[tex]r = -1/8 = \frac{f(b) - f(2)}{b - 2} = \frac{1/b - 1/2}{b - 2}[/tex]

We can rewrite it to:

[tex]-1/8 *(b - 2)= 1/b - 1/2\\\\-1/8 *(b - 2)= 2/2b - b/2b = (2 - b)/2b = -(b - 2)/2b[/tex]

Now we can remove the term (b - 2) because it appears on both sides, so we get:

[tex]-1/8 = -1/2b\\1/8 = 1/2b\\2/8 = 1/b\\1/4 = 1/b\\b = 4[/tex]

Then we found that b must be equal to 4, so the interval is [2, 4]

If you want to learn more, you can read:

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Answer:

True

Step-by-step explanation:

All equiangular triangles are similar.

Answer:

Step-by-step explanation:

Hello!

Y varies directly with X, meaning that every time X increases/ decreases, the value of Y is modified.

If Y=12 when X=4 then you can say that Y varies 3 times every time X varies 1 unit

12= 4*z

z=12/4= 3

So Y= 3x

With this in mind:

1) x= 8

Y= 3*8= 24

2) x= 3

Y= 3*3= 9

3) Y= 6

Y= 3x

x=Y/3= 6/3= 1

I hope this helps!

Answer:

23

Step-by-step explanation:

Raise 3 to the power of 3

27 - 4

Subtract 4 from 27

23

Hope this was correct

Answer:

23

Explanation:

step 1 - rewrite the expression with the value of x

[tex]x^3 - 4[/tex]

[tex](3)^3 - 4[/tex]

step 2 - solve the exponent

[tex](3)^3 - 4[/tex]

[tex]27 - 4[/tex]

step 3 - subtract

[tex]27 - 4[/tex]

[tex]23[/tex]

therefore, the value of the expression is 23.

Given: A water bottle cost 4 dollars and a hat cost 6 dollars.

Let x = Number of water bottles

y = Number of hats

The club wants to raise $1200.

i.e. Required equation : 4x+6y=1200

At x=0,

[tex]0+6y=1200\Rightarrow\ y=\dfrac{1200}{6}\Rightarrow\ y=200[/tex]

At x= 300

[tex]4(300)+6y=1200\\\Rightarrow\ 1200+6y=1200\Rightarrow\ 6y=0\Rightarrow y=0[/tex]

At x= 240

[tex]4(240)+6y=1200\\\Rightarrow\ 960+6y=1200\Rightarrow\ 6y=240\Rightarrow y=40[/tex]

So,three ordered pairs(x,y) that exist on the line : (0,200), (300,0) and (240,40)

Plot these point on graph and join them.

Answer: the other guy is correct. Got it right on my test. Have a nice day. :|

Step-by-step explanation:

Answer:

x = 10 units, y = 5 units

Step-by-step explanation:

Given triangle ABC is a 30-60-90 triangle,

m∠C = 60°

By applying Sine rule in the given triangle,

Sin(60)°= [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]

Sin(60)° [tex]=\frac{\text{AB}}{\text{AC}}[/tex]

[tex]\frac{\sqrt{3}}{2}=\frac{\text{AB}}{\text{AC}}[/tex]

[tex]\frac{\sqrt{3}}{2}=\frac{5\sqrt{3}}{x}[/tex]

x = 10 units

Similarly, by applying Cosine rule in the given triangle,

Cos(60)° = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]

Cos(60)° = [tex]=\frac{\text{BC}}{\text{AC}}[/tex]

[tex]\frac{1}{2}=\frac{y}{x}[/tex]

y = [tex]\frac{x}{2}[/tex]

y = 5 units

Therefore, x = 10 units and y = 5 units will be the answer.

Answer:

Step-by-step explanation:

Given the system of equations;

a) x+3y=9

-4x+12y=12

This equation is a linear simultaneous equation with 2 equations and two unknown values. When the number of equations given is equal to the number of unknown variables, this means that the solution sets of the equations are unique and real and will provide us with just one solution.

b) For the system of linear equation

2x-y-4=0 .... *3

6x=3y+12  ... *1

First lets multiply equation 1 by 3, om multiplying by 3 we will have;

6x-3y-12 = 0

6x-3y = 0+12

6x-3y = 12

Rearranging equation 2 will give;

6x - 3y = 12

It is seen that both equation ate the same. This means that what we have is one equation with two unknowns. For a system of equation with one equation and two unknowns, there will be infinite number of solutions after solving the equation. Hence, the number of solutions for this system of equation is INFINITE

Answer:

Megan hired the canoe for 2 hours

Step-by-step explanation:

Given:

Cost(h) = 6h+15 = 27

Solution

6h+15 = 27

6h = 27-15 = 12

h = 2

Answer:

[tex]x=0\\y=2[/tex]

Step-by-step explanation:

El método de reducción también llamado Suma y Resta, consiste en multiplicar una o ambas ecuaciones de tal manera que los coeficientes de una de las incógnitas sean iguales y de signo contrario, de tal forma que se eliminen al sumar las ecuaciones.

Nuestras ecuaciones son:

[tex]-x+3y=6\\x+y=2[/tex]

En este caso podemos observar que x y -x son iguales y de signo contrario así que no tendremos que multiplicar y podemos sumar ambas ecuaciones.

Al sumarlas tenemos que:

[tex]4y=8\\y=2[/tex]

Ahora sustituímos el valor que encontramos de y en la segunda ecuación para poder obtener el valor de x.

[tex]x+y=2\\x+2=2\\x=2-2\\x=0[/tex]

Por lo tanto, x = 0 y y = 2

Answer:

See my explanation

Step-by-step explanation:

-2x + (x - 4) = 18

-x - 4 = 18

-x = 22          <- this is wrong in question writing as x = 22

so, x = -22

Answer:

The correct answer is D.

Step-by-step explanation:

A function is when an input value has only one output value.

It cannot be A, because -7 produces both 2 and -4.

It cannot be B, because -9 produces both 9 and 7.

It cannot be C, because -4 produces both -6 and -7.

Therefore, it has to be D.

Answer:

An example of a prism could be a an amazon box to represent a rectangular prism.  As the height, length, or width of the box increases, the volume increases allowing more items to fit within the box.

An example of a cone would be an ice cream cone.  As the height or the radius of the cone increases, the more volume the cone can hold, meaning more ice cream for you.

An example of a cylinder could be a cup.  As the height or the radius of the cup increases, the larger the volume.  More drink for you.

An example of a sphere would be a soccer ball.  As the radius increases, the volume of the ball increases.  Hence, larger soccer balls have a bigger radius than smaller soccer balls.  This allows for different varients of the ball to be created (i.e., youth, highschool, college, pro).

Note, the volume can also be decreased by simply shrinking the measurements instead of increasing them.

Step-by-step explanation:

Let's simply look at the equations of each shape.

Volume of a prism = base * height

Volume of a cone = Pi * r^2 * (height/3)

Volume of a cylinder = Pi * r^2 * height

Volume of a sphere = (4/3) Pi r^3

Notice that the volumes of prisms, cones, and cylinders directly correlate to height.  As height increases, the volume increases.  The sphere is unique in that the height is 2 * radius; however, the volume is related to the cube of the radius.  Consider if you expanded the radius of the sphere, the volume will increase.

Answer:

Increase or decrease the dimensions of objects. See below for an explanation!

Step-by-step explanation:

An amazon box, which is a rectangular prism, is an example of a prism. If you increase the height, length, or width of the box, you can fit more stuff inside.

A cup is an example of a cylinder; by increasing the height or radius of the cup, you can fit more of a drink inside.

An icecream cone is an example of a cone; if the height or radius were increased, you might fit more ice cream inside.

A soccer ball is an example of a sphere; increasing the radius makes it larger, and various sizes are available for different levels.

You may also shrink the dimensions for each of these objects to make them smaller.

Hope this helps!

Answer:

17) x = 11, -8

18) exact form: x = + 2 sqaure root 6/ 3 + 2

I hope this helps :)

Answer:

[tex]\frac{7}{12}[/tex] of the cake

Step-by-step explanation:

add [tex]\frac{1}{8}[/tex] and [tex]\frac{1}{6}[/tex] to see the total amount of cake eaten.

a. find the common denominator: 8 x 3 = 24 and 6 x 4 = 24

b. multiply accordingly to get the correct numerator: [tex]\frac{3}{24}[/tex] + [tex]\frac{4}{24}[/tex]

c. add: [tex]\frac{3}{24}[/tex] + [tex]\frac{4}{24}[/tex] = [tex]\frac{7}{24}[/tex]

subtract found value from total to find left over cake.

a. 24 - 7 = 14

simplify.

a. [tex]\frac{14}{24}[/tex] = [tex]\frac{7}{12}[/tex]

You are left with [tex]\frac{7}{12}[/tex] of the cake.

Answer:

y = [tex]-\frac{1}{3}x+5[/tex]

Step-by-step explanation:

Let the equation of the given line is,

y = mx + b

where 'm' = slope of the line

b = y-intercept of the line

Since slope of a line passing through two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is represented by,

m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

If the points are (0, 5) and (-3, 6),

Slope of the line 'm' = [tex]\frac{6-5}{-3-0}[/tex]

                                 = [tex]-\frac{1}{3}[/tex]

y-intercept of the line 'b' = 5

Therefore, equation of the given line will be,

y = [tex]-\frac{1}{3}x+5[/tex]

Answer:

$24 will be the cost of tennis racquet with weight 25 oz.

Step-by-step explanation:

Given that Price of racquet is inversely proportional to its weight.

i.e.

[tex]Price \propto \dfrac{1}{Weight}[/tex]

We can replace the proportional sign with a constant of proportionality.

[tex]Price = \dfrac{C}{Weight}[/tex]

Where C is a constant named as constant of proportionality.

Given that cost of 20 oz. racquet is $30.00

Putting both the values :

[tex]30 = \dfrac{C}{20}\\\Rightarrow C = 600[/tex]

So, the equation becomes:

[tex]Price = \dfrac{600}{Weight}[/tex]

Now, we have to find the price of 25 oz. racquet.

Putting Weight = 25 oz and finding Price:

[tex]Price = \dfrac{600}{25}\\\Rightarrow Price = \$24[/tex]

So, $24 will be the cost of tennis racquet with weight 25 oz.

Answer:

y = [tex]\frac{1}{2} x - 3[/tex]

x + y = 18

Step-by-step explanation:

Let the kitten's weight be y and the cat's weight be x

Condition # 1:

y = [tex]\frac{1}{2} x - 3[/tex]

Condition # 2:

x + y = 18

Answer:

Statement 3: A cone is one-third the size of a cylinder with the same height and radius.

Statement 4: A cone has a circular base.

Step-by-step explanation:

Statement 3: A cone is one-third the size of a cylinder with the same height and radius.

Statement 4: A cone has a circular base.

The true statement is:

Statement 3: A cone is one-third the size of a cylinder with the same height and radius.

Statement 4: A cone has a circular base.

A cone is a three-dimensional solid geometric shape having a circular base and a pointed edge at the top . A cone has one face . There are no edges for a cone.

Properties of Cone

As, from the properties of cone we can say that.

A cone is one-third the size of a cylinder with the same height and radius. and, : A cone has a circular base..

Learn more about cone here:

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Answer:

45°

Step-by-step explanation:

[tex]tan^{-1}(1)[/tex] = 45°

Answer:

[tex]\huge\boxed{\theta=45^o\ \vee\ \theta=225^o}[/tex]

Step-by-step explanation:

[tex]\tan\theta=1[/tex]

[tex]\bold{METHOD\ 1}\\\\\text{Use the table in the attachment}\\\\\tan45^o=1\to\theta=45^o\ \vee\ \theta=45^o+180^o=225^o\\\\\bold{METHOD\ 2}\\\\\tan\theta=1\to\tan^{-1}1=\theta\to\theta=45^o\ \vee\ \theta=225^o[/tex]

Answer:

Step-by-step explanation:

Let the unknown number = x

[tex]x *\frac{-5}{27}=\frac{-10}{9}[/tex]

x = [tex]\frac{-10}{9}[/tex] ÷ [tex]\frac{-5}{27}[/tex]

[tex]x=\frac{-10}{9}*\frac{-27}{5}\\\\\\x=-2* - 3\\x = 6[/tex]

Answer:

73cm²

Step-by-step explanation:

Area of rectangle=½ length×width

=½×18×7

=63cm²

Area of triangle=½b×h

base=18-13= 5cm

height=11-7 =4cm

½×b×h

½×5×4

=10cm²

Area of total=63+10

73cm²

Answer: 73c2

Step-by-step explanation:

Answer:

32.8 cm

Step-by-step explanation:

decagons have 10 sides, so 328/10=32.8

Answer:

32.8 cm

Step-by-step explanation:

A regular decagon has 10 equal sides.

The perimeter of the decagon is 328 centimeters. The perimeter is the measure of all 10 sides added together. Since this is a regular decagon, all 10 sides are equal. Therefore, we can divide 328 by 10.

328 / 10

32.8

Add units, in this case, centimeters or cm.

32.8 cm

Each side of the decagon is 32.8 centimeters.

Answer:

x = 8

or

x = -4

Step-by-step explanation:

3x² - 12x = 96

Divide both sides by 3

x² - 4x = 32

Add 4 to both sides

x² - 4x + 4 = 32 + 4

(x - 2)² = 6²

Find the square root of both sides

√(x - 2)² = √6²

x - 2 = +/- 6

x - 2 = +6 or -6

x - 2=+6

x=6+2

x=8

x - 2=-6

x=-6+2

x=-4

x = 8

or

x = -4

Answer:

Step-by-step explanation:

Initial balance of Marta Fuentes  = $1200.50

Charge made by her bank;

Credit of $505 and Charge on new checks is $12.

Total charge incurred = $505+$12

Total charge incurred = $517

Since there will be no outstanding checks or deposit, her checkbook balance will be the difference between the initial balance and amount charged by the bank.

Checkbook balance = $1200.50 - $517

Checkbook balance = $683.50

Hence her checkbook balance should be $683.50

Answer:

The correct option is;

A dilation by a scale factor of Two-fifths and then a translation of 3 units up

Step-by-step explanation:

Given that the coordinates of the vertices of square S are

(0, 0), (5, 0), (5, -5), (0, -5)

Given that the coordinates of the vertices of square S' are

(0, 1), (0, 3), (2, 3), (2, 1)

We have;

Length of side, s, for square S is s = √((y₂ - y₁)² + (x₂ - x₁)²)

Where;

(x₁, y₁) and (x₂, y₂) are the coordinates of two consecutive vertices

When (x₁, y₁) = (0, 0) and (x₂, y₂) = (5, 0), we have;

s = √((y₂ - y₁)² + (x₂ - x₁)²) = s₁ = √((0 - 0)² + (5 - 0)²) = √(5)² = 5

For square S', where (x₁, y₁) = (0, 1) and (x₂, y₂) = (0, 3)

Length of side, s₂, for square S' is s₂ = √((3 - 1)² + (0 - 0)²) = √(2)² = 2

Therefore;

The transformation of square S to S' involves a dilation of s₂/s₁ = 2/5

The after the dilation (about the origin),  the coordinates of S becomes;

(0, 0) transformed to (remains at) (0, 0) ....center of dilation

(5, 0) transformed to (5×2/5, 0) = (2, 0)

(5, -5) transformed to (2, -2)

(0, -5) transformed to (0, -2)

Comparison of (0, 0), (2, 0), (2, -2), (0, -2) and (0, 1), (0, 3), (2, 3), (2, 1) shows that the orientation is the same;

For (0, 0), (2, 0), (2, -2), (0, -2) we have;

(0, 0), (2, 0) the same y-values, (∴parallel to the x-axis)

(2, -2), (0, -2) the same y-values, (∴parallel to the x-axis)

For (0, 1), (0, 3), (2, 3), (2, 1) we have;

(0, 3), (2, 3) the same y-values, (∴parallel to the x-axis)

(0, 1), (2, 1) the same y-values, (∴parallel to the x-axis)

Therefore, the lowermost point closest to the y-axis in (0, 0), (2, 0), (2, -2), (0, -2) which is (0, -2) is translated to the lowermost point closest to the y-axis in (0, 1), (0, 3), (2, 3), (2, 1) which is (0, 1)

That is (0, -2) is translated to (0, 1) which shows that the translation is T((0 - 0), (1 - (-2)) = T(0, 3) or 3 units up

The correct option is therefore a dilation by a scale factor of Two-fifths and then a translation of 3 units up.

Answer:

a

Step-by-step explanation:

Answer:

Devi's present age = 15 years

Devi's Mother's present age = 45 years

Step-by-step explanation:

Let the present age of Devi be x years.

Therefore, mother's present age = 3x

Five years ago:

Devi's age = (x - 5) years

Mother's age =( 3x - 5) years

According to the given condition:

Five years ago:

Devi's mother's age = 4 times Devi's age

3x - 5 = 4( x - 5)

3x - 5 = 4x - 20

20 - 5 = 4x - 3x

15 = x

x = 15 years

3x = 3* 15 = 45 years

Hence,

Devi's present age = 15 years

Devi's Mother's present age = 45 years

r = radius

h = r+12 = height, 12 more than the radius

[tex]V = \text{Volume of cone (oblique or not)}\\\\V = \frac{1}{3}\pi*r^2*h\\\\V = \frac{1}{3}\pi*r^2*(r+12)\\\\V = \frac{1}{3}\pi*r^2*r+\frac{1}{3}\pi*r^2*12\\\\V = \frac{1}{3}\pi*r^3+\frac{1}{3}*12\pi*r^2\\\\V = \frac{1}{3}\pi r^3+4\pi r^2\\\\[/tex]

ANSWER: SECOND OPTION

Answer:

[tex]Depth = 100m[/tex]

Step-by-step explanation:

Given

Initial Level = 340 m

Number of stages = 4

Difference in each stage = 60 m

Required

Determine the depth of the submarine after 4 stages

First, we have to calculate the total distance moved towards the surface of the sea;

This is calculated as

[tex]Total\ Distance = Number\ of\ Stages * Difference\ in\ each\ stage[/tex]

[tex]Total\ Distance = 4 * 60m[/tex]

[tex]Total\ Distance = 240m[/tex]

This implies that the submarine moved a total distance of 240 metres;

It;'s new depth is calculated as follows;

[tex]Depth = Initial\ Depth - Total\ Distance[/tex]

[tex]Depth = 340m - 240m[/tex]

[tex]Depth = 100m[/tex]

Hence, its new depth after 4 stages of rising is 100m

Answer:

The 8 square meters represent the product of the height by the width of the wall and therefore, its area.

Step-by-step explanation:

Ginnie is going to paint a wall and measures the height and the width, the walls are usually in the form of a rectangle or square. To find the area of both we need to multiply the height by the width (in the case of the square both are the same) and this will give us the total amount of paint that we need to paint the wall.

In this example, Ginnie finds that she needs enough paint to cover 8 square meters, therefore, these 8 square meters represent the product of the height by the width (that we don't know but it doesn't matter) of the wall and therefore, its area.

Answer:

A

Step-by-step explanation:

Using ZPP we get x = 0, 2x + 4 = 0, x + 5 = 0. Solving these, we get x = 0, x = -2, x = -5.