If DE = 5x EF = 3x and DF = 32 what is the length of DE?

4.5 Is the answer required

Answer: 2

Step-by-step explanation: got it right :)

Answer:

Probability: 50%

odds: 5:5

Step-by-step explanation:

Answer:

The probability is 50% that ball will be green.

Odds 5:5

Numbers of ways to draw a green marbles: number of ways to draw another marbles.

Step-by-step explanation:

Consider the provided bag of marble.

The bag contains 5 green marble, 3 blue marbles and 2 red marbles.

The total number of marbles are: 5+3+2=10

The probability of getting a green marble is: 5/10=0.5

That means the probability is 50% that ball will be green.

Drawing green marbles means we want marble should be green and ODDs of drawing a green marble means the marble is not green.

There are 5 green marbles, so there are 5 outcomes that we want (out of 10 outcomes total)

There are 10-5 = 5 outcomes that we don't want a green marble.

Number of outcomes we want is 5

Number of outcomes we don't want is 5

Odds in favor = (wanted outcomes):(unwanted outcomes)

Odds in favor = 5:5

Numbers of ways to draw a green marbles: number of ways to draw another marbles.

Answer:

  74 days

Step-by-step explanation:

The proportion left after d days is ...

  p = (1/2)^(d/100)

When that proportion is 60%, we have ...

  .60 = .50^(d/100)

  log(.60) = (d/100)log(.50) . . . . . take logarithms

  100·log(.60)/log(.50) = d ≈ 73.697 ≈ 74 . . . days

The remaining factor of the given polynomial x^3 + 25x^2 + 50x - 1000, knowing that (x-5) and (x+10) are factors, is 'x - 20'. This is calculated by dividing the original polynomial by the known factors.

In the polynomial

x^3 + 25x^2 + 50x - 1000

, you have expressed that (x-5) and (x+10) serve as factors. Thus, to find the remaining factor, we need to divide the polynomial by these two known factors. We'll begin with dividing the original polynomial by (x-5). This yields a quotient of x^2 +  20x - 200. Subsequently, we divide this quotient by the second known factor (x+10), which ultimately gives us the final factor, being

x - 20

. Hence, x - 20 is the remaining factor of the polynomial.

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Answer:

Step-by-step explanation:

Well, there are several  relationships you can describe.  As time increases how does number of pages  react?  Like does it increase or decrease.  Is it always increasing or decreasing by the same amount?  If it's not all the same how do different parts look different.  

There aren't any actual numbers, so you can't say specifically how they relate, like you can't say she read 5 pages a minute or something.

There is no smooth increase or decrease of the graph thus it reperesnts a non linear relationship.

Typically, when a graph increases or decreases abruptly, the data or function it represents is showing some sort of discontinuity or sudden change in behavior.

In other words, there are areas or locations on the graph where values or the slope abruptly shift rather than gradually and constantly changing.

Thus, the slope of the graph is constantly changing and the relationship that is depicted is non linear.

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Answer:

The functions are inverses; f(g(x)) = x ⇒ answer D

[tex]h^{-1}(x)=\sqrt{\frac{x+1}{3}}[/tex] ⇒ answer D

Step-by-step explanation:

* Lets explain how to find the inverse of a function

- Let f(x) = y

- Exchange x and y

- Solve to find the new y

- The new y = [tex]f^{-1}(x)[/tex]

* Lets use these steps to solve the problems

∵ [tex]f(x)=\sqrt{x-3}[/tex]

∵ f(x) = y

∴ [tex]y=\sqrt{x-3}[/tex]

- Exchange x and y

∴ [tex]x=\sqrt{y-3}[/tex]

- Square the two sides

∴ x² = y - 3

- Add 3 to both sides

∴ x² + 3 = y

- Change y by [tex]f^{-1}(x)[/tex]

∴ [tex]f^{-1}(x)=x^{2}+3[/tex]

∵ g(x) = x² + 3

∴ [tex]f^{-1}(x)=g(x)[/tex]

∴ The functions are inverses to each other

* Now lets find f(g(x))

- To find f(g(x)) substitute x in f(x) by g(x)

∵ [tex]f(x)=\sqrt{x-3}[/tex]

∵ g(x) = x² + 3

∴ [tex]f(g(x))=\sqrt{(x^{2}+3)-3}=\sqrt{x^{2}+3-3}=\sqrt{x^{2}}=x[/tex]

∴ f(g(x)) = x

∴ The functions are inverses; f(g(x)) = x

* Lets find the inverse of h(x)

∵ h(x) = 3x² - 1 where x ≥ 0

- Let h(x) = y

∴ y = 3x² - 1

- Exchange x and y

∴ x = 3y² - 1

- Add 1 to both sides

∴ x + 1 = 3y²

- Divide both sides by 3

∴ [tex]\frac{x + 1}{3}=y^{2}[/tex]

- Take √ for both sides

∴ ± [tex]\sqrt{\frac{x+1}{3}}=y[/tex]

∵ x ≥ 0

∴ We will chose the positive value of the square root

∴ [tex]\sqrt{\frac{x+1}{3}}=y[/tex]

- replace y by [tex]h^{-1}(x)[/tex]

∴ [tex]h^{-1}(x)=\sqrt{\frac{x+1}{3}}[/tex]

Answer:

G = (9.4, 9,4)

Step-by-step explanation:

The ratio is applied in the x-distance and the y-distance. The ratio is 2:3 so you have to divide the distances by 5 and 2/5 correspond to FG and 3/5 to GH

x-distance:

x2 - x1 = 16 - 5 = 11

11/5 = 2.2

y-distance:

y2 - y1 = 13 - 7 = 6

6/5 = 1.2

Point G = Point F + (2.2*2, 1.2*2)

Point G = (5, 7) + (4.4, 2.4)

= (9.4, 9.4)

Answer:

The answer to your question is: 95 yards

Step-by-step explanation:

Data

1 inch   ----------------  5 yards

19 inches ------ ? yards

We can solve this problem with a rule of three

              1 inch ------------------ 5 yards

             19 inches --------------   x

             x = (19)(5) / 1 = 95 yards

Answer:

it was wrong!!

Step-by-step explanation:

Answer:

Step-by-step explanation:

Finding the slope is perhaps easiest done by solving for y.

  5x -6 = -3y . . . . subtract 3

  y = -5/3x +2 . . . divide by -3

This is slope-intercept form, so we can see both the slope (the coefficient of x, -5/3) and the y-intercept (the constant, +2).

__

To find the x-intercept, we set y=0 and solve for x. This might be most easily done using the original equation:

  5x -3 = 0 +3 . . . . set y = 0

  5x = 6 . . . . . . . . . add 3 to get the x-term by itself

  x = 6/5 = 1.2 . . . . divide by the coefficient of x. This is the x-intercept.

__

Slope = -5/3

y-intercept = 2

x-intercept = 6/5

Final answer:

The factorization of x² + 3x - 4 is (x + 4)(x - 1), which can be verified using algebra tiles that represent these factors and the product.

Explanation:

The factors of x² + 3x - 4 can be determined by looking for two numbers that multiply to -4 (the constant term) and add up to +3 (the coefficient of the middle term x). Through factor pairs of -4 (e.g., -1 and 4, or 2 and -2), we notice that (+4) and (-1) are the numbers that meet the criteria because 4 × (-1) = -4 and 4 + (-1) = 3. Therefore, the factorization is (x + 4)(x - 1). To use algebra tiles, you would arrange them into a rectangle where the length and width represent the factors of the quadratic expression, and the product area represents the entire expression.

Answer:

Option E.

Step-by-step explanation:

Let the intended length of Rebecca's swimming is = x units

and we assume the length of the pool = l units

Now it is given in the question that " She covers one fifth of her intended distance "

That means distance covered = [tex]\frac{x}{5}[/tex]

" After swimming six more lengths of the pool she had covered one quarter of her intended distance"

So [tex]\frac{x}{5}+6(l)=\frac{x}{4}[/tex]

[tex]6l=\frac{x}{4}-\frac{x}{5}[/tex]

[tex]6l=\frac{x}{20}[/tex]

x = 20×(6l)

x = 120l

Therefore, Rebecca has to complete 120 lengths of the pool.

Option E is the answer.

[tex]\bf (\stackrel{x_1}{-3}~,~\stackrel{y_1}{-4})~\hspace{10em} \stackrel{slope}{m}\implies 0 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-4)}=\stackrel{m}{0}[x-\stackrel{x_1}{(-3)}]\implies y+4=0(x+3) \\\\\\ y+4=0\implies y=-4[/tex]

Answer:

3x+5y-16=0

Step-by-step explanation:

See it in the pic.

Equation of tangent line to the curve is

[tex]y=-\frac{3}{5}x+\frac{16}{5}[/tex]

Equation of tangent line is in the form of y=mx+b

where m is the slope and b is the y intercept

Derivative of a given function is the slope. To find slope at the given point , we find out f'(2)

we are given with function

[tex]f(x)= \frac{5x}{1+x^2} \\Apply \; quotient \; rule \\5\frac{\frac{d}{dx}\left(x\right)\left(1+x^2\right)-\frac{d}{dx}\left(1+x^2\right)x}{\left(1+x^2\right)^2}\\5\cdot \frac{1\cdot \left(1+x^2\right)-2xx}{\left(1+x^2\right)^2}\\\frac{5\left(1-x^2\right)}{\left(1+x^2\right)^2}\\[/tex]

Now we find f'(2) by replacing 2 for x

[tex]f'(x)=\frac{5\left(1-x^2\right)}{\left(1+x^2\right)^2}\\f'(2)=\frac{5\left(1-2^2\right)}{\left(1+2^2\right)^2}\\f'(2)=\frac{-15}{25} \\f'(2)=-\frac{3}{5}[/tex]

Now we use the given point and the  slope to get the equation of tangent line

[tex]m=-\frac{3}{5} and (2,2)\\y-y_1=m(x-x_1)\\y-2=-\frac{3}{5}(x-2)\\y-2=-\frac{3}{5}x+\frac{6}{5}\\y=-\frac{3}{5}x+\frac{6}{5}+2\\y=-\frac{3}{5}x+\frac{16}{5}[/tex]

Equation of tangent line to the curve is

[tex]y=-\frac{3}{5}x+\frac{16}{5}[/tex]

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Answer:

quotient = 4x + 3 + (3/x+6)

Step-by-step explanation:

To solve this, we conduct polynomial division. We divide the first term of the divisor into the first term of the polynomial.

Step 1: Divide the first term of the polynomial, 4x^2, by the first term in the divisor, x, to obtain 4x. This is the first term of our quotient.

Step 2: Keep the divisor, x+6, as it is and multiply it by the first term of the quotient, 4x.  We obtain 4x^2 + 24x.

Step 3: Subtract this result from the original polynomial. The difference is 3x+22.

Step 4: The divisor x+6 is then divided into the first term of the new polynomial, 3x, to obtain 3.  Add this to the quotient, making the quotient 4x+3.

Step 5: Multiply the divisor, x+6, by the new term in the quotient, +3, obtaining 3x+18.

Step 6: Subtract this result from the last polynomial, 3x+22, to get the remainder, 4

So when we divide 4x^2 +27x+22 by x+6, we get the quotient is 4x+3 and the remainder is 4.

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Answer:

The answer is c. $48,000

Step-by-step explanation:

To find the free cash flow, we need to take into account the money that is entering the company and the money that is being used.  Money that we are earning is possitive, and money being spend goes with a minus.

The net cash, the $50,000 is our sales column. And is money entering the company.

The Investment would be our CAPEX or directly we can use it as investment. And this money is being spended.

The dividends, are the payments that we are doing to the board of directors or the share holders. Since we are paying others, we know this money is being used.

The equation here is:

Sales - Investment - Dividends = Free Cash Flow

So it $50,000 - $1,000 - $1,000 = $48,000

Answer:

The answer to your question is:    Y = (13, -14)

Step-by-step explanation:

Data

midpoint = mp = (6, -3)

one endpoint = X = (-1, 8)

second endpoint = Y = (x, y)

Formula

Xmp = (x1 + x2) / 2

Ymp = (y1 + y2) / 2

Process

                    x2 = 2xmp - x1

                    y2 = 2ymp - y1

                   x2 = 2(6) - (-1)                     y2 = 2(-3) - 8

                   x2 = 12 + 1                          y2 = -6 - 8

                   x2 = 13                               y2 = - 14

                   Y = (13, -14)

Answer

The first one

Step-by-step explanation:

The product of a number and 3 is 6 more than the number

The product of a number = n x 3

6 more than the number = n + 6

Put them together and its =

n x 3 = n + 6

I hope this helps :)

Sorry if its wrong

The product of a number and 3 is 6 more than the number is n.3 = n + 6.

A numerical expression is of the form of numbers and their operations.

According to the question given we have to model a numerical expression from the statement given which is The product of a number and 3 is 6 more than the number.

Let the number be 'n'.

∴ Product of a number and 3 which is 3×n is 6 more than the number n + 6.

So, 3n = n + 6.

3n - n = 6.

2n = 6.

n = 6/3.

n = 2.

This can also be written as n.3 = n + 6.

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Final answer:

The x-component of vector A is 4.00 units east, and the y-component of vector A is -3.00 units south, calculated using the cosine and sine functions respectively.

Explanation:

The student has asked for the components of vector A which has a magnitude of 5.00 units and is at an angle of 36.9° south of east. To find the components of a vector, we use trigonometric functions. The component along the x-axis (east-west direction) is found using the cosine function, and the component along the y-axis (north-south direction) is found using the sine function. Since the angle is south of east, the x-component will be positive and the y-component will be negative in our coordinate system.

The x-component of vector A (Ax) is calculated as:

Ax = A * cos(θ) = 5.00 * cos(36.9°) = 5.00 * 0.800 = 4.00 units

The y-component of vector A (Ay) is calculated as:

Ay = A * sin(θ) = 5.00 * sin(36.9°) = 5.00 * 0.600 = 3.00 units

Therefore, the components of vector A are 4.00 units east and -3.00 units south.

Answer:

The girls had a higher average in the reading test than the boys.

Step-by-step explanation:

To find the solution, you need to find the mean (average) of the group of boys and group of girls each. The mean of numbers can be found by dividing the sum of all numbers by the amount of numbers there are.

Lets start by finding the mean of the boys group. Find the sum of all numbers:

[tex]2.0 + 3.9 + 4.3 + 4.9 + 6.0 = 21.1[/tex]

Now divide the sum by how many numbers, or in this case, how many boys did the test:

[tex]21.1 \div 5 = 4.22[/tex]

The mean, average, of the tests conducted by the group of boys is 4.22.

Repeat the same for the girls group:

[tex]2.8 + 3.8 + 4.5 + 5.2 + 5.9 = 22.2 \\ 22.2 \div 5 = 4.44[/tex]

The mean, average, of the tests conducted by the group of girls is 4.44.

Compared to 4.22, 4.44 is bigger than 4.22.

Answer:

$1.91

Step-by-step explanation:

This means the cost of the item to you is $1.91. You will pay $1.91 for a item with original price of $2.25 when discounted 15%. In this example, if you buy an item at $2.25 with 15% discount, you will pay 2.25 - 0.3375 = 1.91 dollars.

Answer:

1.91

Step-by-step explanation:

1- 2.25

2- 2.25÷100= 0.0225 find 1 percent

3- 0.0225×15=0.3375 find the 15 percent

4- 2.25-0.3375=1.9125 subtract the discount of the original price

5- 1.91 round off to two decimals

Answer:

The answer to your question is:   x > - 32/9

Step-by-step explanation:

                                            -5/2(3x+4)<6-3x

Multiply by 2                      -5(3x + 4) < 12 - 6x

Simplify                             -15x - 20 < 12 - 6x

Add +6x                            -15x + 6x -20 < 12 - 6x + 6x

Simplify                            - 9x - 20 < 12

Add + 20                          -9x -20 + 20 < 12 + 20

Simplify                            -9x  <  32

Divide by -9                     -9/-9 x > 32/-9

Simplify                             x > - 32/9

Answer:

y+1.4=1.9 (x-4.5)

Step-by-step explanation:

The slope is the number in front of the brackets, which must be positive 1.9. This eliminates the last option. It is y+1.4 because the formula is y-y1=m (x-x1)

So once you substitute values

y--4.5=1.9 (x-4.5)

y+4.5=1.9 (x-4.5)

An equation of the line in point-slope form is: B. y + 1.4 = 1.9(x - 4.5)

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

At data point (4.5, -1.4) and a slope of 1.9, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - (-1.4) = 1.9(x - 4.5)  

y + 1.4 = 1.9(x - 4.5)

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Answer:

mixture a because there's not so much purple.the more purple the darker it is

Answer:

The mixture B is a lighter shade of purple.

Step-by-step explanation:

In order to answer the question, we first need to calculate the proportion of purple in both mixtures. The mixture that has the lowest proportion of purple will be the lighter one.

For mixture A :

5 cups of purple

2 cups of white paint

⇒ Mixture A is made with 5 + 2 = 7 cups of paint in which 5 are cups of purple. Therefore, we can calculate the proportion of purple as :

[tex]\frac{5CupsOfPurple}{7CupsInTheMixture}=\frac{5}{7}=0.7143[/tex]

This means that approximately 71.43% of the mixture A is made of purple paint.

For mixture B :

15 cups of purple paint

8 cups of white paint

⇒ Mixture B is made with 15 + 8 = 23 cups of paint in which 15 are cups of purple. Therefore, we can calculate the proportion of purple as :

[tex]\frac{15CupsOfPurple}{23CupsInTheMixture}=\frac{15}{23}=0.6522[/tex]

This means that approximately 65.22% of the mixture B is made of purple paint.

If we compare the proportions :

[tex]0.7143>0.6522[/tex] ⇒ [tex]Proportion_{A}>Proportion_{B}[/tex]

We conclude that the mixture B is a lighter shade of purple because it has the lowest proportion of purple (we can also think that mixture B has the highest proportion of white)

Answer:

  [1] = 6

  x = -3/2 is the root

Step-by-step explanation:

A perfect square trinomial is of the form ...

  (a + b)² = a² +2ab +b²

You have ...

Then the factorization is ...

  16w² +48w +36 = (4w +6)²

This will be zero when x = -6/4 = -3/2.

Answer:

MN = sqrt(34)

Step-by-step explanation:

First, draw the segment FN. The diagonal, MN, of the prism is the hypotenuse of triangle NFM. Triangle NFM is a right triangle with legs FN and FM and hypotenuse MN.

Leg FM of triangle NFM has length 4 cm.

We need to find the length of leg FN.

Look at the base of the prism which is square UNAF. FN is a diagonal of that square. Now think of right triangle FUN with legs UN and UF, each of length 3 cm. We can find FN with the Pythagorean theorem.

(UF)^2 + (UN)^2 = (FN)^2

3^2 + 3^2 = (FN)^2

(FN)^2 = 18

FN = sqrt(18)

Now we know FN. We use FN and FM as legs and find MN, the hypotenuse of triangle NFM.

(FN)^2 + (FM)^2 = (MN)^2

18 + 4^2 = (MN)^2

18 + 16 = (MN)^2

(MN)^2 = 34

MN = sqrt(34)

Answer:

12 1/2

1/2

6 1/4

Step-by-step explanation:

hope this helps ya

To estimate Martin's friend's purchase of grapes, convert 12 3/5 to an improper fraction and multiply it by 3/8. The estimate is 9/40 pounds of grapes.

To estimate how many pounds of grapes Martin's friend bought, we can use compatible fractions. Martin bought 12 3/5 pounds of grapes. His friend bought 3/8 of that amount.

Step 1: Convert 12 3/5 to an improper fraction.

12 3/5 = (5 * 12 + 3)/5 = 63/5

Step 2: Multiply the improper fraction by 3/8.

(63/5) * (3/8) = (63 * 3)/(5 * 8) = 9/40

Therefore, Martin's friend estimated about 9/40 pounds of grapes.

Answer:

  ray

Step-by-step explanation:

A ray is a line that extends in one direction from its end point.

Answer: Hi, first lets give our variables some names.

Lets call Ks to Karen's salary and Js to Jason's salary.

then, in 1995:

Ks₁ - Js₁ = 2000$

in 1998:

Ks₂ - Js₂ = 2440$

now, we know that  Ks₂ = (1 +p)*Ks₁ and   Js₂ = (1+p)*Js₁

so we can write the second equation as:

p*(Ks₁ - Js₁ ) = 2440$

replacing the parentesis with the first equiation

(1+p)*(2000$) = 2440$

(1+p)= 2440/2000 = 1.22

so p = 0.22, or a 22%

Answer:

-1, 2, 5, 8, 11

Step-by-step explanation:

There is an easy and fast way to solve this. A linear function means that the steps on y and x are constant.

On the x axis you are walking 5 steps each column, so you start from 5, plus 5 steps is 10, plus 5 steps is 15, plus 5 steps is 20, plus 5 steps is 25.

Now you have to do the same for the y axis, but you have to use your brain.

You start from -1, and you have to reach 11, using the same number of steps for each column, just like before the necessarily with the same number.

You start from -1, plus 3 steps is 2, plus 3 steps is 5, plus 3 steps is 8, plus 3 steps is 11. Done.

You can use maths also, but it will take time.

You need to find that function. A linear function can be written as:

[tex]y = mx + q[/tex]

You have two points of the line, (5, -1) and (25, 11), but you need to find the y coordinate of other three points.

Let's find the line by substituting those points in the general function of the line:

[tex] - 1 = 5m + q \\ 11 = 25m + q[/tex]

This is a system of two equations with two variables, m and q. You can solve it. From the first equation you have that:

[tex]q = - 1 - 5m[/tex]

Put this in the second equation to know the value of m:

[tex]11 = 25m + ( - 1 - 5m)[/tex]

[tex]11 = 25m - 1 - 5m \\ 20m = 12 \\ m = \frac{12}{20} = \frac{3}{5} [/tex]

Now you can use this in the first equation to know the value of q:

[tex]q = - 1 - 5( \frac{3}{5} ) \\ q = - 1 - 3 \\ q = - 4[/tex]

So your line is:

[tex]y = \frac{3}{5} x - 4[/tex]

If you want to know the y coordinates that you are missing, you just need to put the corresponding x coordinate in this function and you will find the same results as before.

To fill in a table for a linear function, you need to understand the relationship between x and y in a linear function (y = mx + b), calculate y values for given x values using this relationship, and arrange these pairs in the table.

To fill in a table that represents a linear function, we need to understand that in a linear function, the change in the output (y) is constant for every unit change in the input (x). The relationship between x and y can be written as y = mx + b, where m is the slope and b is the y-intercept.

Here's a simple example. For a linear function y = 2x + 1, if your x values are 1, 2, and 3, the y values would be y(1) = 2*1+1 = 3, y(2) = 2*2+1 = 5, y(3) = 2*3+1 = 7. So the table would look like:

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Answer:

The answer to your question is: 30 boxes

Step-by-step explanation:

Data:

A packing crate measures 0.40 m 0.40 m 0.25 m.

boxes of cookies measure 22.0 cm 12.0 cm 5.0 cm

Formula

Volume of a rectangular prism: l x w x h

Volume of the bigger prism = 40 cm x 40 x 25 cm = 40 000 cm3

Volume of the smaller prism = 22 x 12 x 5 = 1320 cm3

Then we divide the volumes = 40000 / 1320 = 30.3 boxes