If AD/DB =AE/EC, then line segment blank is parallel to line segment blank

Answer:

n = 14

Step-by-step explanation:

Write the equation in algebraic (numbers and symbols) form

[tex]\frac{238}{n}[/tex] = n + 3              Rearrange the equation

[tex]n\frac{238}{n}[/tex] = n(n + 3)           Multiply both sides by 'n'

238 = n(n + 3)          On the left, multiplying and dividing by 'n' cancels out

238 = n² + 3n           Distributed right side

0 = n² + 3n - 238        Rearranged to standard form for quadratic equations

Remember standard form for quadratic equations is: ax² + bx + c = 0

State the variables a, b and c:

a = 1; b = 3; c = -238

When a quadratic equation is in standard form, you can use the quadratic formula to solve for 'n'. (Usually, you see the variable 'x', but the quadratic formula can solve for 'n' as if it is 'x', as long as it's in standard form.)

[tex]n = \frac{-b±\sqrt{b^{2}-4ac}}{2a}[/tex]  (ignore the Â, it's a formatting error)

[tex]n = \frac{-(3)±\sqrt{(3)^{2}-4(1)(-238)}}{2(1)}[/tex]  Substitute the values for 'a', 'b' and 'c' from the equation

[tex]n = \frac{-3±\sqrt{9-(-952)}}{2}[/tex]     In the root, two negatives make a positive

[tex]n = \frac{-3±\sqrt{9+952}}{2}[/tex]     Add inside the root

[tex]n = \frac{-3±\sqrt{961}}{2}[/tex]       Find the square root of 961

[tex]n = \frac{-3±{31}{2}[/tex]     Split the equation at the ±

Split for adding:

[tex]n = \frac{-3+31}{2}[/tex]    Simplify

n = 14

Split for subtracting:

[tex]n = \frac{-3-31}{2}[/tex]      Simplify

n = -17

You get the answers 14 and -17 for 'n'. Decide which one is 'inadmissible', meaning it can't be right even if it solves the equation.

The problem says 'n' is a natural number. Natural numbers are all non-partial numbers count up from 1. (Non-partial means as a fraction, they are reduced to a number over 1). Since -17 is less than 1, it is inadmissible because it is not a natural number.

Therefore, 'n' is 14.

Answer:

$45

Step-by-step explanation:

We are given the following information;

We need to determine the amount of interest the money will earn after three years.

Therefore, in this case;

Simple interest = ($300 × 5 × 3) ÷ 100

                         = $45

Thus, the money invested earned a simple interest of $45

Using the formula for simple interest, we find out that Edin will earn £45 as interest on his savings of £300 over a period of 3 years at a simple interest rate of 5% per annum.

The subject of this question is simple interest. The formula for simple interest is: Principal * Rate * Time. Let's plug in the given values into the formula. Here, the principal amount is £300, the rate of interest is 5% per annum (or 0.05 in decimal form), and the time is 3 years. So, the calculation will be: £300 * 0.05 * 3.

After performing the calculation, we find that the interest Edin will earn after 3 years is £45.

https://brainly.com/question/22621039

#SPJ3

Answer:

4 hours = 14400 seconds.

Step-by-step explanation:

i) In 1 hour there are 60 minutes

ii) in 1 minute there are 60 seconds

iii) therefore 1 hour = 60 minutes

                               = 60 [tex]\times[/tex] 60 seconds

                               = 3600 seconds

iv) therefore to convert 4 hours to seconds we have to multiply the number of hours by 3600 seconds

      therefore 4 hours = 4 [tex]\times[/tex] 3600 seconds = 14400 seconds.

Answer:

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

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 )

y = [tex]\frac{2}{3}[/tex] x + 2 ← is in slope- intercept form

with slope m = [tex]\frac{2}{3}[/tex]

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{2}{3} }[/tex] = - [tex]\frac{3}{2}[/tex], thus

y = - [tex]\frac{3}{2}[/tex] x + c ← is the partial equation

To find c substitute (2, - 4) into the partial equation

- 4 = - 3 + c ⇒ c = - 4 + 3 = - 1

y = - [tex]\frac{3}{2}[/tex] x - 1 ← equation of perpendicular line

Answer:

  $10,000

Step-by-step explanation:

Let x represent the amount invested in the 5.5% bond.

For an annual income of $1800, we want ...

  (5.5%)x + (6.25%)(30,000-x) = 1800

  (-0.75%)x + 1875 = 1800

  -0.0075x = -75 . . . . . . . . . subtract 1875

  x = 10,000 . . . . . . . . . . . . . divide by -0.0075

At most $10,000 should be invested at 5.5% to obtain at least $1800 in interest.

Answer:

The true statement is: A. The range for Week 1 equals the range for Week 2.

Step-by-step explanation:

Let's recall that the range of a data set is the difference between the largest number and the smallest number.

As we can confirm in the plot for week 1, the range is:

Range for week 1 = Largest number - smallest number

Range for week 1 = 89 - 62 = 27

In the same way, we can confirm in the plot for week 2 that the range is:

Range for week 2 = Largest number - smallest number

Range for week 2 = 89 - 62 = 27

Ranges for week 1 and 2 are equal, thus,

The true statement is: A. The range for Week 1 equals the range for Week 2.

Answer:

1/5 3/8 1/2

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

You would start by dividing

3 by 4. Then multiply 3/4 and 4. The 4s would cancel out leaving you with 3.  3/ 4×4=3

hope this helps

Final answer:

To answer the student's question, first find the quotient of 3 and 4, which is ¾, and then multiply that result by 4 to get the final answer of 3.

Explanation:

The student is asking for the result of multiplying 4 with the quotient of 3 and 4. To solve this, first calculate the quotient of 3 and 4, which is ¾. Then, multiply this result by 4.

Step 1: Quotient of 3 and 4 = 3 ÷ 4 = ¾

Step 2: Multiply the quotient by 4 = ¾ × 4

When you calculate step 2, you get:

¾ × 4 = (3 × 4) / 4 = 3

So, 4 times the quotient of 3 and 4 is 3.

Answer:

36x + 12y + 24 = T

Step-by-step explanation:

If Sahil has 36 packs of x pencils, then x would equal the number of pencils in each pack. Same thing goes for y. 12 packs of y pencils and y will be the number of crayons in each pack.

36(x) = Total number of pencils.

12(y) = Total number of crayons.

24 = The numbers of erasers which is given.

36x + 12y + 24 = Total numbers of items.

15/60+12/60+10/60= 37/60

Answer:

[tex]\large\boxed{x=\dfrac{17}{7}}[/tex]

Step-by-step explanation:

[tex]\text{A geometric mean of}\ x\ \text{and}\ y:\\\\\sqrt{xy}\\\\\text{Let}\ x-\text{the number}.\\\\\text{Substitute:}\\\\\sqrt{17}=\sqrt{(7)(x)}\iff17=7x\qquad\text{divide both sides by 7}\\\\\dfrac{17}{7}=\dfrac{7x}{7}\to x=\dfrac{17}{7}[/tex]

Greater Than!

First make the denominator (the bottom number) the same for both fractions. So you can multiply the 1/2 by 5 and the 4/5 by 2.

This will make them 5/10 and 8/10.

Then, you see that 8/10 (4/5) is greater than 5/10 (1/2)

Hope that’s makes sense! :)

The fraction 4/5 is greater than 1/2. This conclusion can be reached by converting the fractions to decimal form, where 4/5 becomes 0.8 and 1/2 becomes 0.5, highlighting that 0.8 is indeed greater than 0.5.

The question is whether the fractional value of 4/5 is greater than, less than, or equal to 1/2. To compare these fractions, it may be helpful to first convert them to decimal form, as this is often easier to understand than comparing fractions directly. 4/5 as a decimal is 0.8 and 1/2 as a decimal is 0.5. Hence, 0.8 is greater than 0.5. Therefore, 4/5 is greater than 1/2.

https://brainly.com/question/34222181

#SPJ2

Answer:

20; 500

Step-by-step explanation:

1.5 is what percent of 7.5. 7.5 is 5 times 1.5, so 1.5 is 1/5 of 7.5. 1/5=20%. Inversely, 7.5 is 5 times 1.5, 5=500%.

[tex]1 \frac{1}{2} \text{ is } \underline{20\%} \text{ of } 7 \frac{1}{2}[/tex];  [tex]7 \frac{1}{2} \text{ is } \underline{500\%} \text{ of } 1 \frac{1}{2}[/tex]

[tex]1 \frac{1}{2}[/tex] becomes [tex]\frac{3}{2}[/tex].

[tex]7 \frac{1}{2}[/tex] becomes [tex]\frac{15}{2}[/tex].

[tex]\text{Percentage} = \frac{\text{part}}{\text{whiole}} \times 100\%[/tex]

[tex]\frac{\frac{3}{2}} {\frac{15}{2}} \times 100\% = \frac{3}{15}\times 100\% = \frac{1}{5}\times 100\% = 20\%.[/tex]

Thus,

[tex]1 \frac{1}{2} \text{ is } \underline{20\%} \text{ of } 7 \frac{1}{2}.[/tex]

[tex]\frac{\frac{15}{2}} {\frac{3}{2}} \times 100\% = \frac{15}{3}\times 100\% = 5\times 100\% = 500\%.[/tex]

Thus,

[tex]7 \frac{1}{2} \text{ is } \underline{500\%} \text{ of } 1 \frac{1}{2}.[/tex]

Complete question:

fill in the blanks:

[tex]1 \frac{1}{2}[/tex] is ____ % of [tex]7 \frac{1}{2}.[/tex] ;            [tex]7 \frac{1}{2}[/tex] is ____ % of [tex]1 \frac{1}{2}.[/tex]  

3 copies of 1/6 makes it 1 copy 1/2 because 3 times of 1/6 is 3/6 which is 1/2

Step-by-step explanation:

3 times 1/6 = 3/6

which is 1/2.

Hence it takes 3 copies of 1/6 to show the amount as 1 copy of 1/2

Alternatively,

1/6+1/6+1/6= 1/2

3/6=1/2

1/2=1/2

Answer:

0.36 or [tex]\frac{9}{25}[/tex]

Step-by-step explanation:

9/20=.45

4/5=.8

Answer: .36

The labor fee is $13.55 and each quart of oil is $2.25

Step-by-step explanation:

Let,

x be the amount of each quart of oil

y be the amount of labor fee

According to given statement;

5x+y=24.80        Eqn 1

7x+y=29.30        Eqn 2

Subtracting Eqn 1 from Eqn 2

[tex](7x+y)-(5x+y)=29.30-24.80\\7x+y-5x-y=4.50\\2x=4.50[/tex]

Dividing both sides by 2

[tex]\frac{2x}{2}=\frac{4.50}{2}\\x=2.25[/tex]

Putting x=2.25 in Eqn 1

[tex]5(2.25)+y=24.80\\11.25+y=24.80\\y=24.80-11.25\\y=13.55[/tex]

The labor fee is $13.55 and each quart of oil is $2.25

Keywords: linear equation, subtraction

Learn more about subtraction at:

#LearnwithBrainly

The answer to this one would be 2.

Answer: 2

Step-by-step explanation:

1 1/2 divided 3/4

First make all a fraction

3/2 divided 3/4

3/2*4/3 inverted

2

Answer:

In order for it to benefit his father to buy the pass Seth have to attend the movies for 11 times.

Step-by-step explanation:

Given:

Cost of movie pass = $40

Cost per matinees with pass = $1.00

Cost per matinees without pass = $3.50

To Find:

Number of times must Seth attend in order for it to benefit his father to buy the pass = ?

Solution:

Let x be the number of times he wants to visit

To profit his father

The number of visits without pass =  the number of visits with passin the cost  of $3.50

Then, without pass if he visits for x times then the cost will be  = 3.50x

Also with pass, the number of times he can visit the pass  =  [tex]\frac{40}{3.50}[/tex]

then

[tex]\frac{350 x}{3.50} = \frac{40}{3.50}[/tex]

[tex]3.50x = 40[/tex]

[tex]x = \frac{40}{3.50}[/tex]

x =  11.42

x = 11 (approx)

Answer:

Step-by-step explanation:

5) D  2000/200 = 10

6) C 90/9 = 10

7) B 80/8 = 10

8) A)   10 times 2 =10*2 = 20

Answer: [tex]0.8[/tex] pages per hour.

Step-by-step explanation:

For this exercise it is important to know that, by definition, Direct variation equations have the following form:

[tex]y=kx[/tex]

Where "k" is the constant of variation.

Therefore, it is a straight line that passes through the origin.

In this case, given the graph attached in the exercise, you can follow these steps in order to find the constant of variation:

Step 1: You need to choose any point on the line. Let's choose the point (5,4).

Step 2: Now you must ubstitute the coordinates of that point into  [tex]y=kx[/tex]. Then:

[tex]4=k(5)[/tex]

Step 3: Finally, you must solve for the Constant of variation "k", in order to find its value. Therefore, you get that this is:

[tex]k=\frac{4}{5}\\\\k=0.8[/tex]

Answer:

the first loan is cheaper

Step-by-step explanation:

convert percent values to decimals

8.5/100=.085

7.75/100=.0775

find the value for the first loan

1550*.085*4=527

find the value for the first loan

1550*.0775*5=600.625

compare

Belle would pay $5100 in interest for the 4-year loan at 8.5% and $5812.50 for the 5-year loan at 7.75%. Therefore, less interest would be paid with the 4-year loan.

To calculate the simple interest, we use the formula I = P*R*T, where P is the principal amount, R is the interest rate, and T is the time in years.

For the 4-year loan at 8.5%, interest would be: I = $15,000 * 8.5/100 * 4 = $5100

For the 5-year loan at 7.75%, interest would be: I = $15,000 * 7.75/100 * 5 = $5,812.50.

So, the 4-year loan at 8.5% will require less interest payment.

https://brainly.com/question/40405117

#SPJ2

Answer:

The AP is, 1 , 6, 11, 16, 21, 26, 31, .....................

Step-by-step explanation:

From the question;

We are required to find the AP;

nth term = a + (n-1) d , where a is the first term and d is the common difference

5th term = a + 4d

7th term = a + 6d

5th term + 7th term = 2a + 10d = 52  ..........eqn 1

10th term = a + 9d

2a + 10d = 52

a + 9d = 46

Multiplying the second equation by 2, we get;

2a + 10d = 52

2a + 18d = 92

Eliminating a by subtracting the two equations; we get;

-8d = -40

   d = 5

Solving for a

a + 9d = 46

   a = 46 - 9d

      = 46 - 9(5)

      = 46 - 45

   a  = 1

Thus, the first term, a= 1 and the common difference, d= 5

Therefore;

First term = a = 1

Second term = a + d = 1 + 5 = 6

Third term = a + 2d = 1 + 2(5) = 11

Fourth term = a + 3d = 1 + 3(5) =16

Fifth term = a + 4d = 1 + 4(5) = 21

Sixth term = 1 + 5d = 1 + 5(5) = 26

Seventh term = 1 + 6d = 1 + 6(5) = 31

Thus,

The AP is, 1 , 6, 11, 16, 21, 26, 31, .....................

Answer:

Step-by-step explanation:

a vertical line has an undefined slope....(8,6).....its equation is x = 8 because no matter what y is, x will always be 8.

but u need it in standard form Ax + By = C

so it is written as : x + 0y = 8 <===

A = 1

B = 0

C = 8

Ax + By = C will be a vertical line passing through point (8,6) for values of A = 1 , B = 0 and C = 8.

What is a vertical line ?

In a coordinate plane, a line parallel to the Y-axis is called vertical Line. Any point in this line will have the same value for the x-coordinate.

We know that the x-axis has lines that run vertical then if you have a point use your x-ordinate.  

The equation of a vertical line is :

x = C

here : C is the value of the x- coordinates the line passes through.

In the given question we have to find out the values of A , B and C for which Ax + By = C be a vertical line passing through point (8,6).

Here , the coordinate of point (x , y) is (8 , 6).

So , the equation of vertical line will be x = 8.

So , if we compare it with the general form of line , Ax + By = C, then we get :

8A + By = 8

So , values of A , B and C :

A = 1, B = 0, C = 8

Therefore , Ax + By = C will be a vertical line through point (8,6) for values of A = 1 , B = 0 and C = 8.

Learn more about vertical lines here :

https://brainly.com/question/16583313

#SPJ2

The correct answer is C; Dependent variable.

Further explanation:

Researchers are very interested in the dependent variable. This variable is what is being tested and measured during the research in progress. In this case, it is the new energy drink.

The researchers are looking for an effect to occur while changing the independent variable of the case study. There are three main different types of variables used in research studies, they are;

With the athletes doing exercises after consuming the test product, they are seeing if the product does give more energy than if they hadn't of consumed the energy drink.

Learn more about dependent variables at https://brainly.com/question/383055

#LearnwithBrainly

Answer:

a is the answer or 320 ft

Step-by-step explanation:

95*65=6175 ft^ for area

95+95+65+65=320 ft

Answer:

8

x

2

+

22

x

y

+

15

y

2

Step-by-step explanation:

yeet

Answer:

Step-by-step explanation:

Answer:

$56?

Step-by-step explanation:

I think you get 100%-30%=70%.

70%=0.70

0.70*$80= $56

Answer:

see explanation

Step-by-step explanation:

sinA = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{BC}{AB}[/tex] = [tex]\frac{20}{29}[/tex]

cosA = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{AC}{AB}[/tex] = [tex]\frac{21}{29}[/tex]

tanA = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{20}{21}[/tex]

The functions sin, cos, and tan for a given angle in a right triangle are defined in terms of ratios of the side lengths. They are respectively the ratios of the opposite side to the hypotenuse, the adjacent side to the hypotenuse, and the opposite side to the adjacent side.

In a right triangle, sin(A) is defined as the ratio of the side opposite to angle A (opposite side) to the hypotenuse, cos(A) as the ratio of the adjacent side to the hypotenuse, and tan(A) as the ratio of the opposite side to the adjacent side.

Suppose the lengths of the sides of the given right triangle are a, b, and c (where c is the length of the hypotenuse).

Then, sin(A) = a/c, cos(A) = b/c, and tan(A) = a/b. These ratios must be put in reduced form by simplifying the fractions if necessary.

https://brainly.com/question/31675053

#SPJ11