Caleb has 5x² yellow pens and 4x green
pens.
He has twice as many pink pens as yellow
pens.
He also has 3 fewer black pens than green
pens.
Write an expression in terms of x for the total
number of yellow, green, pink and black pens
that Caleb has.
Give your answer in its simplest form.

The decimal point is to be placed three places to the left.

What are decimal numbers?

When we divide a whole number into smaller parts, we get decimals. Then, there are two parts to a decimal number: a whole number part and a fractional part. The whole component of a decimal number has the same decimal place value system as the complete number. After the decimal point, however, when we proceed to the right, we obtain the fractional portion of the decimal number.

Given that, in the question, the product of a decimal number between 350 and 400 and 0.48 results in the numbers 182136. As 0.48 is just 48/100, let's take a decimal number between 350 and 400.

If the number is 370.1, for example, we can write it as 3701/10 because it has one decimal point.

Our denominator will be 1000, because both the denominators are 100 and 10, which is equivalent three decimal places to the left of the result when we multiply 48/100 by 3701/10.

The result provided to us should therefore be written as 182.136, with the decimal point moved three spaces to the left.

The decimal point is to be placed three places to the left.

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1) The two column proof for ΔLMN ≅ ΔLON is as developed below.

2) The  two column proof for ΔGHJ ≅ ΔKLM is as developed below

A two-column proof is defined as a geometric proof that consists of a list of statements, and then the reasons that we know those statements are deemed to be true.

1) The two column proof showing that ΔLMN ≅ ΔLON is;

Statement 1: LN bisects ∠MLO and LM ≅ LO

Reason 1: Given

Statement 2: MN ≅ ON

Reason 2: Line segment bisector

Statement 3: ∠MLN ≅ ∠OLN

Reason 3: def. of angle bisector

Statement 4: LN ≅ LN

Reason 4: Reflexive property of congruence

Statement 5: ΔLMN ≅ ΔLON

Reason 5: SSS Congruency postulate

2) The two column proof is as follows;

Statement 1: ∠G ≅ ∠K, ∠J ≅ ∠M

Reason 1: Given

Statement 2: ∠H ≅ ∠L

Reason 2: 3rd angle theorem

Statement 4: ΔGHJ ≅ ΔKLM

Reason 4: ASA Congruency Postulate

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One of the alternatives isc=d because when a line meets two parallel lines, matching angles are created and the identical corners are congruent.

Coplanar, straight lines that don't intersect anywhere are considered parallel lines in geometry. Planes in the same three-dimensional space that never cross each other are said to be parallel. Curves that are parallel to one another and maintain a set minimum distance do not touch or intersect. Lines in a plane that consistently have the same separation are said to be parallel. Nothing can cross a parallel line. Lines that cross at a straight angle of 90 degrees are called perpendicular lines.

A = d is also a solution due to vertical angles. Finally, b+d=180 since b+c=180 and c=d, and b+d=180 as a result. The solution is therefore B,C,E, where a=d, c=d, and b+d=180.

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Answer:

Well, nothing because you didn't say how much money you make a day, a week, or a month.

Step-by-step explanation:

You tried to trick me haha <3

Answer: 1, 2, 3, 4 are the consecutive perfect cubes which are added to obtain a sum of 100.

Step-by-step explanation:

Perfect cubes are the numbers that are triple product of same number.

1^3 = 1

2^3 = 8

3^3 = 27

4^3 = 64

1+8+27+64 = 100

Answer: 1, 2, 3, 4 are the consecutive perfect cubes which are added to obtain a sum of 100.

Explanation:

Perfect cubes are the numbers that are triple product of same number.

1^3 = 1

2^3 = 8

3^3 = 27

4^3 = 64

1+8+27+64 = 100

The graph of g(x) is shifted vertically by 5 units below the graph of f(x). The graph of g(x) is shifted horizontally by 5 units to the left of the graph of f(x)

Given: f(x) = 2x and g(x) = f(x + k). If k = -5

Subtituting k = -5, we have:

g(x) = f(x -5) = 2(x-5)

The graph of g(x) is shifted vertically by 5 units below the graph of f(x)

The graph of g(x) is shifted horizontally by 5 units to the left of the graph of f(x)

To see this, we can consider the value of x = 0 for both functions. For f(x), f(0) = 20 = 0. For g(x), g(0) = f(-5) = 2(-5) = -10. Thus, the value of g(0) is 5 units below the value of f(0).

Similarly, the value of x = 5 for f(x) is f(5) = 25 = 10, while the value of x = 0 for g(x) is g(0) = f(-5) = 2(-5) = -10. Thus, the value of x = 5 for f(x) is 5 units to the right of the value of x = 0 for g(x).

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The diagram that shows the rotation of rectangle ABCD by -90 degrees is; Option A

When we rotate positive 90 degrees, the rotation is said to be counterclockwise but when we rotate negative 90 degrees, the rotation is said to be clockwise.

Now, we want to find the rotation that correctly describes rotation of the rectangle ABCD by negative 90 degrees.

Thus, looking at the options, the only one that has the negative 90 degrees rotation that is clockwise will be option A because we see that when we rotate to the right which is clockwise, the first point is A which is exactly what is in option A.

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Answer:

yx6-5= greater than or equal to 8

Step-by-step explanation:

math brain

The probability that a person has colon cancer given that they have a positive test result is approximately 0.98. The answer lies in the range [0.95, 1.00].

Let's call the probability that a person has colon cancer given that they have a positive test result "p". We can use Bayes' Theorem to find this probability.

Bayes' Theorem is: p(A|B) = (p(B|A) * p(A)) / p(B)

In this case, A is the event that the person has colon cancer, and B is the event that the person has a positive test result.

We are given that:

p(B|A) = 1 (all people who have colon cancer will have a positive test result)

p(B|~A) = 0.02 (2% of people who do not have colon cancer will have a positive test result).

We are also given that p(A) = 2/102 (2 out of 102 people who undergo routine screening have colon cancer) and p(~A) = 100/102 (100 out of 102 people who undergo routine screening do not have colon cancer).

Substituting these values into Bayes' Theorem, we get:

p(A|B) = (1 * (2/102)) / (1 * (2/102) + 0.02 * (100/102))

Simplifying, we get:

p(A|B) = 0.98

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switch the variables

x = -y + 6

x - 6 = -y

-x + 6 = y

Answer:

whats the question?

Step-by-step explanation:

The amount of margarine needed in Kg for making biscuits is  0.6kg

In general, the term "proportion" refers to a part, share, or amount that is compared to a whole.

According to the definition of proportion, two ratios are in proportion when they are equal. Two ratios or fractions are equal when an equation or a declaration to that effect is utilized.

The amount of margarine needed in Kg is calculated using proportions

If 225 ml or soup requires 150 g of margarine then 0.9 liters of soup will require

0.225 l  = 0.15 kg

0.9 l = ?

cross multiplying

0.225 * ? = 0.9 * 0.15

? = 0.135 / 0.225

? = 0.6

Angela will require 0.6 kg of margarine

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the derivative of the expression will be f'(x)*(1-f(x)) -( f(x)*-f(x)) / (f(x))².

What is derivative?

A function's varied rate of change with respect to an independent variable is referred to as a derivative. When there is a variable quantity and the rate of change is irregular, the derivative is most frequently utilised. The derivative is used to assess how sensitive a dependent variable is to an independent variable (independent variable). In mathematics, a quantity's instantaneous rate of change with respect to another is referred to as its derivative. Investigating the fluctuating nature of an amount is beneficial.

given expression p(x)= f(x)/1-f(x)

The derivative of the given expression will be

p'(x) = f'(x)*(1-f(x)) -( f(x)*-f(x)) / (f(x))²

Hence the derivative of the expression will be f'(x)*(1-f(x)) -( f(x)*-f(x)) / (f(x))².

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The required original price of the coat is given as £95.

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

here,
let the original price of the coat be x,
According to the question
x - 17% of x = 78.85
x - 0.17x = 78.85
0.83x = 78.85
x = 78.85 / 0.83
x = £95

Hence, the cost of the coat before the sale is £95.

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The fractions 1/12 and 1/4 are equivalent to 2/6.

A fraction is a numeral that represents a rational number.

Let a and b be two numbers, then their fraction can be represented as a/b.

Given that,

Two fractions are equivalent to 2/6.

There can be many fractions which are equal to 2/6.

Let one fraction is 1/12,

And other fraction is x,

So, according to given condition,

x + 1/12 = 2/6

x = 2/6 - 1/12

x = 3/12

x = 1/4

The required fractions are 1/12 and 1/4.

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Answer:

the coordinates of the other corner are (-10/3, -1 3/4).

The four ordered pairs that represent the corners of Maya's rectangular driveway are (-1, 1), (1 1/2, -8 1/2), (-10/3, -1 3/4), and (1 1/2, -1 3/4).

Step-by-step explanation:

To plot the other two corners of Maya's rectangular driveway, we need to determine the coordinates of the points that are diagonally opposite to the points (-1, 1) and (1 1/2, -8 1/2).

Since the points (-1, 1) and (1 1/2, -8 1/2) are diagonally opposite, we can draw a line through the center of the rectangle that is perpendicular to the line connecting these two points. The center of the rectangle can be found by averaging the x-coordinates and the y-coordinates of the two points. The x-coordinate of the center is (-1 + 1 1/2)/2 = 1/4 and the y-coordinate of the center is (1 + -8 1/2)/2 = -3 3/4.

We can then use the center of the rectangle and the slope of the line connecting (-1, 1) and (1 1/2, -8 1/2) to find the coordinates of the other two corners. The slope of the line is (-8 1/2 - 1)/(1 1/2 - (-1)) = -17/3, so the slope of the line perpendicular to it is -3/17.

We can use this slope and the center of the rectangle to find one of the remaining corners by moving a fixed distance in the y-direction from the center. For example, if we move 2 units in the positive y-direction from the center, we will reach the point (1/4, -3 3/4 + 2) = (1/4, -1 3/4). We can then use the slope of the line to find the x-coordinate of the other corner by solving the equation y = mx + b for x, where m is the slope, x is the x-coordinate of the corner, y is the y-coordinate of the corner, and b is the y-intercept. The y-intercept is the y-coordinate of the center, so we can solve the equation as follows:

y = -3/17 * x + (-3 3/4)

x = (y - (-3 3/4))/(-3/17)

Substituting the coordinates of the corner we found earlier, we get:

x = (-1 3/4 - (-3 3/4))/(-3/17) = (2)/(-3/17) = -10/3

So, the coordinates of the other corner are (-10/3, -1 3/4).

The four ordered pairs that represent the corners of Maya's rectangular driveway are (-1, 1), (1 1/2, -8 1/2), (-10/3, -1 3/4), and (1 1/2, -1 3/4).

The average rate of change, in simplest form, is -2/5.

What is average rate ?

Divide the change in y-values by the change in x-values to determine the average rate of change. Identifying changes in quantifiable parameters like average speed or average velocity calls for the knowledge of the average rate of change.

The rate of change of the function is its gradient or slope.

The formula for calculating the gradient of a function is expressed as:

[tex]m=\frac{d y}{d x}=\frac{y_2-y_1}{x_2-x_1}$$[/tex]

Using the coordinate points from the table (0,41) and (15,35)

Substitute the coordinate into the expression:

[tex]$$\begin{aligned}& m=\frac{35-41}{15-0} \\& m=\frac{-6}{15} \\& m=\frac{-2}{5}\end{aligned}$$[/tex]

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The vertex of the function f(x) = 10.25 |x - 0.75| will be at (0.75, 0).

The absolute function is also known as the mode function. The value of the absolute function is always positive.

If the vertex of the absolute function is at (h, k). Then the absolute function is given as

f(x) = | x - h| + k

The absolute function is given as,

f(x) = 10.25 |x - 0.75|

Compare the function f(x) with standard equation, then we have

h = 0.75

k = 0

The vertex of the capability f(x) = 10.25 |x - 0.75| will be at (0.75, 0).

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The equation of the line that is parallel to given line is y = 4x + 12

Parallel lines have an equal slope. The slope of parallel lines is identical because they are all equally inclined with respect to the positive x-axis.

If m₁ and m₂ are slopes of parallel lines then => m₁ = m₂

Here we have  

A line is parallel to y = 4x + 11 ---- (1)

The given line is in form of y = mx + c  [ where slope of line = m ]

On comparing both lines, Slope given line = 4

Let the required line with slope m₁ is y = m₁x + c --- (2)

As we know slope of parallel lines are equal or same  

=> Slope of line (2), m₁ 4

Line (2) => y = 4x + c

Given that the line passes through (-2, 4)

=> 4 = 4(-2) + c

=> 4 = -8 + c

=> c = 12

Therefore,

The equation of the line that is parallel to given line is y = 4x + 12

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The trigonometric ratio, cos E of the right triangle is 5 / 13.

A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees.

A right triangle is a triangle that has one of its angles as 90 degrees.

The sides and angles of a right triangle can be found using trigonometric ratios. The sides of a right triangle base on its sides are as follows;

Therefore,

cos E = adjacent / hypotenuse

Hence,

let's find the hypotenuse side using Pythagoras theorem,

24² + 10² = c²

c = √576 + 100

c = √676

c = 26

cos E = 10 / 26

Therefore,

cos E = 5 / 13

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Average rate of growth over this period is 0.4%.

Average rate of growth over a period is given by:

A=P[tex]e^{rT}[/tex] where,

A- Population at time T

P- Initial population

r-average rate of growth

T-Time period

Now, P=250,000, A=310,000 and T=21 (2000-1980+1)

therefore, putting values in the equation, we get:

310,000=250,000[tex]e^{21r}[/tex]

⇒ [tex]e^{21r}[/tex] = 1.24

⇒ 21r = log(1.24)

⇒ r = 0.0044 or 0.4%.

so, the average rate of growth over this time period is 0.4%.

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The square root of a negative number is not a real number, this system of equations has no solution.

What is the system of equations?

A system of linear equations is a set of two or more equations that includes common variables. To solve a system of equations, we must find the value of the unknown variables used in the equations that must satisfy both equations.

To solve for x and y, we can start by solving one of the equations for one of the variables. Let's solve the second equation for y:

2x + y = 5

y = 5 - 2x

Now we can substitute this expression for y in the first equation to get an equation in terms of x:

x² + 3x + (5 - 2x) = 0

x² + 3x + 5 - 2x = 0

x² - x + 5 = 0

We can then solve this equation for x using the quadratic formula:

x = (-3 ± √(9 - 20))/2

x = (-3 ± √(-11))/2

Hence, the square root of a negative number is not a real number, this system of equations has no solution.

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The proof for the Base Angles Theorem is explained below:

A triangle's opposite angles are congruent if its two sides are congruent. We shall build the angle bisector through the vertex angle of an isosceles triangle in order to demonstrate the Base Angles Theorem. We created two congruent triangles by building the angle bisector, and then we utilized CPCTC to prove that the base angles are congruent. Base angles: The angles that include the base of an isosceles triangle are known as the "base angles."

Any triangle with at least two congruent sides is said to be isosceles. Legs are the isosceles triangle's congruent sides. The base is the other side. Base angles are the angles formed between the base and the legs.

Given: [tex]\bar{ LM}[/tex]≅ [tex]\bar{LN}[/tex]

Prove: ∠M≅∠N

According to the figure,

Given,

[tex]\bar{ LM}[/tex]≅ [tex]\bar{LN}[/tex]

By the definition of mid-point,

O is the mid-point of [tex]\bar{MN}[/tex]

Now, by joining the two points determine and draw a line of [tex]\bar{LO}[/tex]

Now, Again by the definition of mid-point

[tex]\bar{MO}[/tex]≅[tex]\bar{NO}[/tex]

Now, by using reflexive property,

[tex]\bar{LO}[/tex]≅ [tex]\bar{LO}[/tex]

By SSS rule,

ΔLMO≅ΔLNO

By CPCTC rule,

∠M≅∠N

Hence proved.

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it's B. 3,406 that the answer I now bye bye

Answer:

it's b

Step-by-step explanation:

Answer:

Step-by-step explanation:

The initial height of the rocket before it is launched can be found by evaluating the function h(t) at t=0. To do this, you can substitute 0 for t in the function:

h(0) = -5(0)² + 42(0) + 54

h(0) = 0 + 0 + 54

h(0) = 54

Therefore, the initial height of the rocket before it is launched is 54 meters.

Answer: 54 meters.

Step-by-step explanation: The initial height of the rocket before it is launched is represented by the constant term in the quadratic function, which is 54. This means that the rocket's height at time t = 0 (before it is launched) is 54 meters.

To confirm this, you can plug in t = 0 into the quadratic function to get:

h(0) = -5(0)² + 42(0) + 54 = 54 meters

This means that the initial height of the rocket before it is launched is 54 meters.

Answer:

B. $4

Step-by-step explanation:

The table shows the cost for different numbers of baseballs. Number of Baseballs Cost 3 $12 6 $24 9 $36 12 $48 Question What is the cost per baseball?

A. $3

B. $4

C. $7

D. $9

E. $12

12/3 = 4

24/6 = 4

36/9 = 4

48/12 = 4

Answer: B $4

Step-by-step explanation:

The table shows the cost for different numbers of baseballs. Number of Baseballs Cost 3 $12 6 $24 9 $36 12 $48 Question What is the cost per baseball?

A. $3

B. $4

C. $7

D. $9

E. $12

[tex]\frac{12}{3} = 4\\\\\frac{24}{6} = 4\\ \\\frac{36}{9} =4\\\\\frac{48}{12} = 4[/tex]

Hence, the right answer is B, $4