The points A, B, C and D lie in order on a straight line.
AB BD = 1:4
AC: CD = 7: 13
Work out AB BC: CD
Give your answer in its simplest form.
Answer:

The equation of the ellipse in vertex form is (x - 1)² / 25 + (y + 2)² / 4 = 1.

In this question we find a representation of an ellipse with a center at point (h, k) = (1, - 2). The vertex form of the equation of the ellipse is introduced below:

(x - h)² / a² + (y - k)² / b² = 1

Where:

Please notice that the major semiaxis is parallel to the x-axis and the minor semiaxis is parallel to the y-axis.

First, write the coordinates of the center of the ellipse:

(h, k) = (1, - 2)

Second, find the lengths of the semiaxes:

Major semiaxis

a = 0.5 · [6 - (- 4)]

a = 5

Minor semiaxis

b = 0.5 · [0 - (- 4)]

b = 2

Third, write the equation of the ellipse:

(x - 1)² / 25 + (y + 2)² / 4 = 1

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The length of ladder is 11.5 m.

What is arithmetic?

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

Main body:

Let the length of ladder = y

And distance of bottom of ladder from the wall = X

According to the given,

Length of ladder y =

√(7² + x²)

Since, the bottom of the ladder is moved 1 meter farther away from the wall, so

Length of ladder y = √(5² +(x+1)²)

as in both equation y is equated

√(7² + x²) = √(5² +(x+1)²)

square root will get cancel on both sides

(7² + x²) = (5² +(x+1)²)

49 + x² = 25 + x² +1+2x

cancelling x² on both sides

49 = 26 +2x

2x = 23

x =11.5 meters

Hence the length of ladder is 11.5 m

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The rate of change in the volume of water will be -6 L/min in the fish tank. which is the correct answer would be an option (A).

The given graph shows the linear relationship between the volume of water in the fish tank in liters and the time in minutes the tank has been draining.

To determine the rate of change in the volume of water in the fish tank

The rate of change in the volume of water is equal to the slope of the given linear function.

As per the given graph, we take two points (0, 60) and (10,0)

The slope of the linear function = (0 - 60) / (10 - 0)

The slope of the linear function = -60/10

The slope of the linear function = -6

Therefore, the rate of change in the volume of water will be -6 L/min in the fish tank.

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The question seems to be incomplete the correct question has been attached below.

a. The function m = 200 - 50v is interpreted as

m = amount left

200 = amount available for buying video games

50 = cost per video game

v = number of video games

b. The domain of the function is 0 < v ≤ 4

the domain is discrete

c. explanation of the graph is below

In the graph, the input values is the number of video games, v while the output value is amount, m(in dollars) left for buying games.

The domain is controlled by the input values. considering the amount set out for games which is 200 we solve for v at zero amount

0 = 200 - 50v

50v = 500

v = 4

The maximum number of video games the amount can buy is 4. For the minimum we can not buy 0 video game but the graph can show amount available before buying the game.

The domain starts from 0, with 0 not inclusive to 4 with 4 included

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The angle a formed at the exterior of the hexagon by a line that goes through a vertex to the center of the hexagon and a second line that touches the adjacent vertex is a = 30°

The properties of a regular hexagon includes;

There are 6 equilateral triangles in a regular hexagon

The triangle ΔOAC formed by the segment that extends into the hexagon is an equilateral triangle.

Therefore;

Triangle ΔABC is an isosceles triangle with segment AC ≅ Segment AB

Therefore;

Angle ∠C is congruent to angle ∠B (base angles of an isosceles triangle

∠C ≅ ∠B

m∠C = m∠B (definition of congruency)

m∠B = a

Therefore;

m∠C = m∠B = a

m∠C = a (substitution property)

From external angle to a triangle, postulate, we get;

m∠OAC = m∠B + m∠C

Therefore;

m∠OAC = a + a

60° = 2·a

a = 60°/2 = 30°

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Answer: 4.16 per pizza

Step-by-step explanation: 54.08 divided by 13 is 4.16

Answer:

y=-6

Step-by-step explanation:

2.3y - 4.2 = -18

       +4.2     +4.2

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

2.3y = -13.8

divide by 2.3 on both sides

y = -6

The value of y for the given equation, 2.3y - 4.2 = -18 will be 6.

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

It is given that, the equation is 2.3y - 4.2 = -18.

We have to simplify the equation in order to find the value of y as,

2.3y - 4.2 = -18.

Rearrange the equation as

2.3y= -18+4.2

2.3y= -13.8

y= -13.8/2.3

y= 6

Thus, the value of y for the given equation, 2.3y - 4.2 = -18 will be 6.

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After simplification,  the factor of the expression [tex]x^{-1/2}+x^{-3/2}+x^{-5/2}[/tex] is [tex]\frac{x^2+x+1}{x^{5/2}}[/tex].

In the given question,

We have to factor the expression [tex]x^{-1/2}+x^{-3/2}+x^{-5/2}[/tex].

The given expression is [tex]x^{-1/2}+x^{-3/2}+x^{-5/2}[/tex].

The given all term having negative power. So make the term in positive we can write it as

[tex]x^{-1/2}+x^{-3/2}+x^{-5/2}=\frac{1}{x^{1/2}}+\frac{1}{x^{3/2}}+\frac{1}{x^{5/2}}[/tex]

Taking 1/[tex]x^{1/2}[/tex] from the left side

[tex]x^{-1/2}+x^{-3/2}+x^{-5/2}=\frac{1}{x^{1/2}}(1+\frac{1}{x}+\frac{1}{x^2})[/tex]

Now solving the bracket by multiply and divide [tex]x^2[/tex] in each term.

[tex]x^{-1/2}+x^{-3/2}+x^{-5/2}=\frac{1}{x^{1/2}}(1\times\frac{x^2}{x^2}+\frac{1}{x}\times\frac{x^2}{x^2}+\frac{1}{x^2}\times\frac{x^2}{x^2})[/tex]

[tex]x^{-1/2}+x^{-3/2}+x^{-5/2}=\frac{1}{x^{1/2}}(\frac{x^2}{x^2}+\frac{x}{x^2}+\frac{1}{x^2})[/tex]

Simplifying the bracket

[tex]x^{-1/2}+x^{-3/2}+x^{-5/2}=\frac{1}{x^{1/2}}(\frac{x^2+x+1}{x^2})[/tex]

[tex]x^{-1/2}+x^{-3/2}+x^{-5/2}=\frac{x^2+x+1}{x^{5/2}}[/tex]

Hence, the factor of the expression [tex]x^{-1/2}+x^{-3/2}+x^{-5/2}[/tex] is [tex]\frac{x^2+x+1}{x^{5/2}}[/tex].

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Answer:

b

Step-by-step explanation:

Answer: 54, if there are 9 pages with 6 photos each, then you would do 6 x 9 = 54.

Answer:

54 pictures

Step-by-step explanation:

9 pages, 6 pictures in each page, 9*6=54

The value of addition for the equation (f + g) (-2) is 15 and the value of subtraction for the equation (f + g) (-2) is 39.

A function is a relationship that assigns exactly one output value to each input value. Like numbers and polynomials, functions can be added, subtracted, multiplied, and divided to create new functions. Here are the rules for performing these operations on functions.

Let f(x) and g(x) be two functions:

Addition:

We can add two functions:

(f + g)(x) = f(x) + g (x) ...... (1)

Given that:

f(x) = 5x^2 + 7

g(x) = 3x - 6

Putting the value of f(x) and g(x) in equation (1).

(f + g)(x) = 5x^2 + 7 + 3x - 6

(f + g)(x) = 5x^2 + 3x + 1 .......(2)

We have to evaluate the value of (f + g) (-2). Therefore, put the value of x = -2 in equation (2). We get,

(f + g) (-2) = 5 (-2)^2 + 3 x -2 + 1

(f + g) (-2) = 20 - 6 +1

(f + g) (-2) = 15

Hence, for the addition of the equation (f + g) (-2) the value is equal to 15.

Subtraction:

We can add two functions:

(f - g)(x) = f(x) - g (x) ...... (3)

Given that:

f(x) = 5x^2 + 7

g(x) = 3x - 6

Putting the value of f(x) and g(x) in equation (3).

(f - g)(x) = 5x^2 + 7 - (3x - 6)

(f - g)(x) = 5x^2 + 7 - 3x + 6

(f - g)(x) = 5x^2 - 3x + 13 ....... (4)

We have to evaluate the value of (f - g) (-2). Therefore, put the value of x = -2 in equation (4). We get,

(f - g)(-2) = 5(-2)^2 - 3(-2) + 13

(f - g)(-2) = 5 x 4 + 6 + 13

(f - g)(-2) = 20 + 6 + 13

(f - g)(-2) = 39

Hence, for the subtraction of the equation (f - g) (-2) the value is equal to 39.

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Answer:

D

Step-by-step explanation:

x³ + 3x² ← factor out x² from each term

= x²(x + 3)

Using the formula of volume of cone, the height of the cone is 3/8.

In the given question,

We have to find the missing dimension of the cone.

Volume of cone is 1/18 pi, radius is 2/3 ft.

As we know that volume of cone is one third of the product of pi, square of radius and height.

The formula of cone is

[tex]V=\frac{1}{3}\pi r^2h[/tex]

where V=Volume of cone

r=radius of cone

h=height of the cone

We know V=1/18 π, r=2/3 ft.

We don't know the value of h. So we find the value of h.

putting the value in formula

[tex]\frac{1}{18}\pi=\frac{1}{3}\pi\times\frac{4}{9}\times h[/tex]

Simplifying

[tex]\frac{1}{18}\pi=\frac{4}{27}\pi\times h[/tex]

[tex]\frac{\pi}{18}=\frac{4\pi}{27}\times h[/tex]

Multiply by 4/27π on both side

[tex]\frac{\pi}{18}\times\frac{27}{4\pi}=\frac{4\pi}{27}\times\frac{27}{4\pi}\times h[/tex]

Simplifying

[tex]\frac{1}{2}\times\frac{3}{4}=h[/tex]

Simplifying

h = 3/8

Hence, the height of the cone is 3/8.

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Answer:

Step-by-step explanation:

Answer:

y = [tex]\frac{1}{4}[/tex] x + [tex]\frac{5}{2}[/tex]

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given

y - 3 = [tex]\frac{1}{4}[/tex] (x - 2 ) ← distribute parenthesis

y - 3 = [tex]\frac{1}{4}[/tex] x - [tex]\frac{1}{2}[/tex] ( add 3 to both sides )

y = [tex]\frac{1}{4}[/tex] x + [tex]\frac{5}{2}[/tex] ← in slope- intercept form

Answer:

1 1/4

Step-by-step explanation:

2 divided by 2 is 1.

1/2 or 0.5 divided by 2 is 0.25. this is equal to 1/4.

Answer: 1 [tex]\frac{1}{4}[/tex]

Step-by-step explanation:

First of all, we need to multiply 2 [tex]\frac{1}{2}[/tex] by 1/2.

But to do that, we need to turn 2 [tex]\frac{1}{2}[/tex]  into an improper fraction.

First of all, we need to multiply the whole number by the denominator, which is 2 x 2, to get 4.

Now, we need to add the numerator to our product, which is 4 + 1.

This gives us the improper fraction of 5/2.

Now, we need to multiply 5/2 by 1/2.

To do this, we need to multiply across.

5 x 1 = 5

2 x 2 = 4

This gives us 5/4.

Now, we turn it into a mixed number.

5/4 is 1 [tex]\frac{1}{4}[/tex].

This gives us our final answer of 1 [tex]\frac{1}{4}[/tex]

Answer:

B

Step-by-step explanation:

because im smart :) give me brainliest or else

Answer:

Step-by-step explanation:

The intersection consists of the elements that are contained in all of the intervals.

(-2, 2) (-1, 4) (0, 6)

Correct me if im wrong

The value of 6 is equal to 3.

Given that:

If 1=3, 2=3, 3=5, 4=4, 5=4.

So, we have to find the value of 6.

To calculate the value of 6 we have to think logically.

Looking at this question logically,

1 is written as ONE, so it contains three alphabets.

2 is written TWO, so it contains three alphabets.

3 is written as THREE, so there are 5 alphabets.

4 is written as FOUR, so it contains four alphabets.

5 is written as FIVE, so it contains four alphabets.

6 is written as SIX, so it contains three alphabets.

So, in this way, 6 can be written as 3.

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The total amount after merging their account will be $34.34.The sum of $75 + $156.56 will make $231.56.

A summation, also abbreviated as a sum, is the outcome of adding two or more numbers or quantities. Here are always an integer number of terms in a summation. There could be only two terms, but there could be one hundred, a thousand, or a million. There are summations with an infinite set of parameters.

As per the given,

Mohan has 2 current accounts, the first has a balance of $101.46.

The second has -$21.21.

Total amount of Mohan = 101.46 - 21.21 = $80.25

Eve's balance = -$45.91

Combined balance = $80.25 - $45.91 = $80.25

As per the given,

Eve has a savings account with $231.56 in it. She wants to buy a new coat for $75.00. She calculates that she will have $156.56

$231.56 = $156.56 - $75

$231.56 + $75 = $156.56

Hence "The total amount after merging their account will be $34.34.The sum of $75 + $156.56 will make $231.56".

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Product of the given expression (3 x 10⁹) and (2 x 10⁹) in the scientific notation is given by 6 x 10¹⁸.

As given in the question,

Given expression is equal to :

(3 x 10⁹) and (2 x 10⁹)

Apply law of indices of multiplication to get the product of the given expression

mᵃ × mᵇ = mᵃ⁺ᵇ

Product of the given expression (3 x 10⁹) and (2 x 10⁹) in the scientific notation is equal to

(3 x 10⁹) and (2 x 10⁹)

= ( 3 × 2 ) × ( 10⁹ × 10⁹ )

= 6 × 10⁹ ⁺ ⁹

= 6 × 10¹⁸

Therefore, product of the given expression (3 x 10⁹) and (2 x 10⁹) in the scientific notation is given by 6 x 10¹⁸.

The complete question is:

Find the product of (3 x 10⁹) and (2 x 10⁹). Write the final answer in scientific notation.

6 x 10⁸¹

6 x 100¹⁸

6 x 10¹⁸

6 x 10⁹

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Answer: 56.70 g

Step-by-step explanation:

Answer:

f(x)=5(x^2)

Step-by-step explanation:

Answer:

u need a chart image

Step-by-step explanation:

The solution to the equation are as follows.

y = c₁[tex]e^{\sqrt{-3 -sin²(x)x} }[/tex] + c₂                [tex]e^{\sqrt{-3 -sin²(x)x} }[/tex]

What is differential equation?

In arithmetic, a equation is associate equation that relates one or a lot of unknown functions and their derivatives.

Main body:

Find the first derivative.

dy/dx=r[tex]e^{rx}[/tex]

Find the second derivative.

d²y/dx² =r² [tex]e^{rx}[/tex]

Substitute into the differential equation.

r²[tex]e^{rx}[/tex]+4[tex]e^{rx}[/tex]=cos ²x

Factor [tex]e^{rx}[/tex]out of r²[tex]e^{rx}[/tex].

[tex]e^{rx}[/tex]r²+4[tex]e^{rx}[/tex]=cos²x

Factor [tex]e^{rx}[/tex] out of 4[tex]e^{rx}[/tex].

[tex]e^{rx}[/tex]r²+[tex]e^{rx}[/tex]⋅4=cos²x

Factor out of [tex]e^{rx}[/tex]r²+4[tex]e^{rx}[/tex]

[tex]e^{rx}[/tex](r²+4)=cos²x

Since exponentials can never be zero, divide both sides by

[tex]e^{rx}[/tex]r²+4=cos²x

Use the double-angle identity to transform

cos²x to 1−sin²(x).

r² +4=1−sin²(x)

Subtract 4 from both sides of the equation.

r²=1−sin²(x)−4

Simplify the right side.

r² = -3 -sin²x

r = √-3 -sin²x

By the principle of superposition, the general solution is a linear combination of the two solutions for a second order homogeneous linear differential equation.

y = c₁[tex]e^{\sqrt{-3 -sin²(x)x} }[/tex] + c₂

Hence the differential solution is as follows.

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A linear regression equation that represents the data set is y = 39.7x + 1127.8. Also, the number of new cases for 2011 is equal to 1525 cases.

In this scenario, the Year since 2002 (x) would be plotted on the x-axis of the scatter plot while the New cases (y) would be plotted on the x-axis of the scatter plot.

From the Excel sheet, you should right click on a data point on the graph (scatter plot), select format trend line and then tick the box to display an equation for the linear regression (line of best fit) on the graph.

By critically observing the scatter plot (see attachment) which models and shows the relationship given in the table, an equation for the linear regression is given by:

y = 39.7x + 1127.8

For 2011, the value of x is given by:

x = 2011 - 2002 = 9 + 1 = 10 years.

Now, we can determine the new cases for 2011:

y = 39.7(10) + 1127.8

y = 397 + 1127.8

y = 1524.8 ≈ 1525 cases.

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Answer:

1. [tex]\frac{6}{11}[/tex] × [tex]\frac{1}{4}[/tex] = [tex]\frac{3}{22}[/tex]

2. [tex]4\frac{1}{3}[/tex] × [tex]\frac{9}{14}[/tex] = [tex]\frac{13}{3}[/tex] × [tex]\frac{9}{14}[/tex]

               = [tex]\frac{39}{14}[/tex]

               = [tex]2\frac{11}{14}[/tex]

3. [tex]3\frac{3}{6}[/tex] × [tex]\frac{2}{3}[/tex] = [tex]\frac{21}{6}[/tex] × [tex]\frac{2}{3}[/tex]

             = [tex]\frac{7}{3}[/tex]

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

4. [tex]\frac{6}{15}[/tex] ÷ [tex]\frac{2}{5}[/tex] = [tex]\frac{6}{15}[/tex] × [tex]\frac{5}{2}[/tex]

            = 1

5. [tex]1\frac{4}{5}[/tex] ÷ [tex]\frac{3}{25}[/tex] = [tex]\frac{9}{5}[/tex] × [tex]\frac{25}{3}[/tex]

               = [tex]\frac{45}{3}[/tex]

               = 15

The roller coaster has a deceleration of 3 meters per second.

In this problem we need to calculate the magnitude of the deceleration experimented by the roller coster, which is under uniform accelerated motion. This can be easily found by means of the following formula:

a = (v' - v) / t

Where:

If we know that v = 20 m / s, v' = 2 m / s and t = 6 s, then the magnitude of the deceleration of the roller coster is:

a = [(2 m / s) - (20 m / s)] / 6 s

a = - 18 m / s / 6 s

a = - 3 m / s²

The magnitude of deceleration is 3 meters per square second.

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Find the negative reciprocal of the original line and use point slope formula y-y1=m(x-x1)  to find the perpendicular line.

y= -x+3

a) The ratio system that models this situation which has an equation.

0.20 m + 1 (5 m) = 0.60 x (5)

0.80 m + 0 (5 m) = 0.40 x (5)

b) The system solution is:

m = 2.5 lb

p = 5-m = 2.5 lb

This is a mixing issue.

Mixture A of 20% peanuts + 80% almonds

Let's call the 100% peanut mixture B and the mixture C of 60% peanuts + 40% almonds

Adding mixture A and mixture B together gives mixture C, so we know that the pounds of mixture A and mixture B is 5 lb.

Let m be the amount in pounds of the 20% peanut and 80% almond mixture or mixture A

When 5-m = p is the amount of mixture B in pounds.

The system of equations that models this situation is, therefore:

0.20 m + 1 (5 m) = 0.60 x (5) ...... (1)

0.80 m + 0 (5 m) = 0.40 x (5) ...... (2)

Solving any of the above equations we find the value of m = 2.5 lb

Amount of mixture A in pounds = 2.5 lb

Amount of mixture B in pounds = 5-2.5 = 2.5 lb

The system solution is:

m = 2.5

p = 2.5

So, we can make 5 lbs of mixture C (60% peanuts + 40% almonds) from 2.5 lbs of mixture A (20% peanuts + 80% almonds) and 2.5 lbs of mixture B (100% peanuts).

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