A pure acid measuring x liters is added to 300 liters of a 20% acidic solution. The concentration of acid, f(x), in the new substance is equal to the liters of pure acid divided by the liters of the new substance, or f(x)=x+60/x+300. Which statement describes the meaning of the horizontal asymptote?

A The greater the amount of acid added to the new substance, the more rapid the increase in acid concentration.
B The greater the amount of acid added to the new substance, the closer the acid concentration is to one-fifth.
C As more pure acid is added, the concentration of acid approaches 0.
D As more pure acid is added, the concentration of acid approaches 1.

Answer:

(1, 3 )

Step-by-step explanation:

Given the 2 equations

y = 3x → (1)

x + y = 4 → (2)

Substitute y = 3x into (2)

x + 3x = 4, that is

4x = 4 ( divide both sides by 4 )

x = 1

Substitute x = 1 into (1) for corresponding value of y

y = 3 × 1 = 3

Solution is (1, 3 )

Answer:

x = 1 & y = 3

Step-by-step explanation:

y = 3x -----(1)

x + y = 4 -------(2)

sub(1)into(2)

x + 3x = 4

4x = 4

x = 1

sub x=1 into(1)

y = 3(1)

y = 3

Answer:

For 2.5 x - 1.75 = 5 (7 - 0 5 x) ,   x  = 1.47/1.1

Step-by-step explanation:

Here, the given equation is :  2.5 x - 1.75 = 5 (7 - 0 5x)

By DISTRIBUTIVE PROPERTY:

A(B -  C) =  AB - AC

Solving for the value of x , we get:

2.5 x - 1.75 = 5 (7 - 0 5 x)

⇒ 2.5 x - 1.75 = 5 (7)  - 5 (05 x)

⇒ 2. 5 x - 1. 75 = 35 - 25 x

or, 2. 5 x + 25 x = 35 + 1. 75

or, 27 . 5 x = 36.75

⇒ x =  36.75/ 27.5  =  7.35/ 5.5 = 1.47/1.1

or, x  = 1.47/1.1

Hence, for 2.5 x - 1.75 = 5 (7 - 0 5 x) ,   x  = 1.47/1.1

The explicit formula for the sequence 1/2, -4, 32, -256 is an = 1/2 * (-8)^(n-1), where n represents the position of each term in the sequence.

To find an explicit formula for the sequence 1/2, -4, 32, -256, we need to look for a pattern in the sequence. Upon examination, we notice that each term is obtained by multiplying the previous term by -8.

The first term, a1, is 1/2. The second term, a2, is 1/2 times -8, which is -4. If we continue this pattern, the nth term of the sequence can be described by the formula an = 1/2 * (-8)^(n-1).

Therefore, the explicit formula for the nth term of this sequence is an = 1/2 * (-8)^(n-1).

Final answer:

The explicit formula for the sequence 1/2, -4, 32, -256 is an = 1/2 × (-8)(n-1), where n represents the nth term. This is derived from the pattern that each term is -8 times the previous term, indicating a geometric sequence.

Explanation:

To find an explicit formula for the sequence 1/2, -4, 32, -256, we need to look for a pattern in the terms of the sequence. Upon inspection, we see that each term is -8 times the previous term. This is a geometric sequence with a common ratio of -8.

The formula for the nth term of a geometric sequence is given by an = a1 × r(n-1), where a1 is the first term and 'r' is the common ratio.

Applying this to the given sequence with a1 = 1/2 and r = -8, the explicit formula for the nth term (an) is:

A graph of a right-angled triangle, ΔABC with side lengths of 3, 4, and 5 units is shown in the picture below.

In Mathematics and Euclidean Geometry, a triangle is a two-dimensional geometric shape that comprises three side lengths, three vertices and three angles only.

Generally speaking, there are five major types of triangle based on the length of their side lengths and angles, and these include the following;

In this scenario, the lengths of three of the sides of the triangle and the measure of the included angle are;

AB = 3 units with vertices A (0, 3)

BC = 4 units with vertices B (0, 0).

AC = 5 units with vertices C (4, 0)

m∠B = 90 degrees.

In conclusion, we would use an online graphing tool to plot this right-angled triangle as shown in the image attached below.

Complete Question:

Drag the vertices of the triangle below to draw a right triangle with side lengths 3, 4, and 5.

Answer:

see explanation

Step-by-step explanation:

All angles of a square are right angles by definition, thus

∠ACD = 90°

The diagonals bisect each other at right angles, thus

∠1 = 90°

The diagonals bisect the angles at the vertices, thus

∠2 - 45°

Answer:

True

Step-by-step explanation:

Horizontal lines with equation y = c where c is the value of the y- coordinates the line passes through are parallel to the x- axis and have a slope of zero.

Vertical lines with equation x = c where c is the value of the x- coordinates the line passes through are parallel to the y- axis and have an undefined slope.

Answer:

10

Step-by-step explanation:

To solve this, we have to do 4 divided by 2/5, because there are stops every 2/5 mile of a 4-mile track.

To make dividing easier, you can write 4 as a fraction, which would be 4/1

Now, divide:

4/1 ÷ 2/5

Remember that when you divide a fraction by another fraction, you can multiply the first fraction by the reciprocal of the second fraction and get the same fraction.

The reciprocal of 2/5 is 5/2.

So 4/1 x 5/2 = 20/2, which can be simplified as 10.

So there are 10 stops. ^-^

Answer:

[tex]y=0.95x+2.5[/tex]

Step-by-step explanation:

we know that

The linear equation in slope intercept form is equal to

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

where

m is the slope

b is the y-intercept

Find the slope

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

take the points

(0,2.5) and (100,97.5)

substitute in the formula

[tex]m=\frac{97.5-2.5}{100-0}[/tex]

[tex]m=\frac{95}{100}[/tex]

[tex]m=0.95[/tex]

Find the y-intercept b

we have

[tex]m=0.95[/tex]

[tex]point\ (0,2.5)[/tex]

substitute i the linear equation  [tex]y=mx+b[/tex]

[tex]2.5=0.95(0)+b[/tex]

solve for b

[tex]b=2.5[/tex]

Note It was not necessary to calculate the value of b because the value is given in the table

Remember that the y-intercept is the value of y when the value of x is equal to zero (the y-intercept is the point (0,2.5))

The linear equation is

[tex]y=0.95x+2.5[/tex]

To write the equation of a linear relationship in slope-intercept form, find the slope and y-intercept. Use the formula y = mx + b, where m is the slope and b is the y-intercept. Calculate the slope using the formula m = (y2 - y1) / (x2 - x1). Substitute the slope and one set of coordinates into the slope-intercept form equation and solve for b.

To write the equation of the linear relationship in slope-intercept form, we need to find the slope (m) and the y-intercept (b). We can use the formula y = mx + b, where m is the slope and b is the y-intercept.

To find the slope, we can use the formula: m = (y2 - y1) / (x2 - x1). Choosing any two points from the given data, we can calculate the slope.

Let's use the points (0, 2.5) and (100, 97.5):
m = (97.5 - 2.5) / (100 - 0) = 95 / 100 = 0.95

Next, we can substitute the slope and one set of coordinates into the slope-intercept form equation and solve for b:

2.5 = 0.95(0) + b
b = 2.5

Therefore, the equation of the linear relationship is: y = 0.95x + 2.5

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Answer:

Below.

Step-by-step explanation:

Let the distance in miles be d and the time taken = t hours.

Then the direct proportion is d = kt  where k is some constant.

In this case k = d/t = 18.

d = 18t is the equation relating  distance and time.

In this case the 18 represents Milo's speed in  miles per hour.

Answer:

[tex]y=8\cos \left(\dfrac{1}{2}x+\pi\right)+2[/tex]

Step-by-step explanation:

The equation of cosine function will be

[tex]y=a\cos (kx+b)+c[/tex]

Find [tex]a:[/tex]

The minimum y is [tex]y_{min}=-6,[/tex] the maximum  y is [tex]y_{max}=10,[/tex] so

[tex]a=\dfrac{1}{2}\cdot |-6-10|=\dfrac{1}{2}\cdot 16=8[/tex]

Find [tex]k:[/tex]

The period of the function is [tex]T=4\pi,[/tex] so

[tex]T=\dfrac{2\pi }{k}\Rightarrow k=\dfrac{2\pi }{4\pi }=\dfrac{1}{2}[/tex]

Find [tex]b:[/tex]

At [tex]x=0,\ y=y_{min}=-6[/tex]

Function [tex]y=\cos x[/tex] at [tex]x=0[/tex] has the value [tex]y=y_{max}=1,[/tex] so [tex]b=\pi[/tex] [translate by one-fourth of the period]

Find [tex]c:[/tex]

The graph has the midline [tex]y=\dfrac{10-6}{2}=2,[/tex] so [tex]c=2.[/tex]

Hence,

[tex]y=8\cos \left(\dfrac{1}{2}x+\pi\right)+2[/tex]

Answer:

x = 6

Step-by-step explanation:

The formula of slope of a straight line passing through two given points ([tex]x_{1},y_{1}[/tex]), and ([tex]x_{2},y_{2}[/tex]) is given by  

[tex]m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex].

As, the straight line passes through the points (x,-4) and (2,8) and has slope - 3.

So, we can write [tex]\frac{8 - (- 4)}{2 - x} = - 3[/tex]

⇒ 12 = 3x - 6

⇒ 3x = 18

⇒ x = 6 (Answer)

Answer:

1400 cm squared

Step-by-step explanation:

40*35=1400cm squared

Answer:

The answer is 30 I just did this

Step-by-step explanation:

Follow me and thank me plz

Answer:

a. 4 represents the amount of pounds of strawberries each friend got.

b. 4 represents the number of friends who were sharing the strawberries.

Step-by-step explanation:

You need to analize the information given in the exercise.

You know that the total amount of pounds of strawberries that are shared equally is:

[tex]Total=20\ lb[/tex]

a. Then if the group of people is formed by 5 friends, you need to divide the total pounds of strawberries that by 5 in order to calculate the amount of pounds of strawberries each one of them got.

If in the equation [tex]20\div5=4[/tex], 5 represents the number of people, then 4 represents the amount of pounds of strawberries each friend got.

b. If each person got 5 pounds of strawberries, you can calculate the number of friends who was sharing them by dividing the total pounds of strawberries by 5.

So, if in the equation [tex]20\div5=4[/tex],  5 represents the pounds of strawberries per person, then 4 represents the number of friends who were sharing the strawberries.

The mathematics problem given, namely 20 divided by 5 equals 4, represents the principle of equally distributing 20 strawberries among 5 friends. Each friend gets 4 strawberries.

The subject of your question is mathematics. The equation 20 divided by 5 equals 4 represents how twenty pounds of strawberries can be equally divided among a group of five friends. This is a division problem, an essential operation in arithmetic.

The principle it is demonstrating is how to distribute something equally among a group. In this case, if we have 20 strawberries and need to distribute them evenly among 5 friends, each friend will receive 4 strawberries. This is represented mathematically as 20 (total strawberries) divided by 5 (number of friends) equals 4 (strawberries per friend). So, your equation is correct.

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Answer:

10 weeks

Step-by-step explanation:

so 14 pieces in 7 weeks is 2 a week

so using that rate in 10 weeks you would get 20 pieces

Answer:

The answer is 148 degrees

Step-by-step explanation:

I'm pretty sure it is 148°... In my notes it says "if a tangent to a circle & a chord intersect at a point on the circle, then the measure of each angle they form is one-half the measure of its intercepted arc." Hope this helps...

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The measure of arc QPN is 148° if the measure of angle QNT is 74°.

Given a circle with center O.

TS is the tangent of the circle at point N.

From the figure, we have, ∠ONT = 90°, since the angle formed at the tangent by the diameter is always the right angle.

Now,

m∠ONT = m∠QNT + m∠ONQ

Substitute the values.

90° = 74° + m∠ONQ

m∠ONQ = 90 - 74 = 16°

Now, from triangle QNO, OQ = ON, since, both are radii of the same circle.

The angle which lies opposite to these sides will be also equal.

So, m∠ONQ = m∠OQN =  16°.

Now, by the angle sum property of a triangle, the sum of the interior angles of a triangle is 180°.

So,

m∠ONQ + m∠OQN + m∠QON = 180°

16° + 16° + m∠QON = 180°

m∠QON = 180° - (16° + 16°)

m∠QON = 148°

The measure of arc QPN is equal to the central angle = 148°

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The complete question is given below:

Answer:

She should sell 20 band posters from total 80 to keep the maintain the same ratio.

Step-by-step explanation:

The total number of movie posters collector has  = 120

The total number of band posters collector has  = 80

The current ratio of movie poster : band poster  = 120 : 100

or, reducing the ratio further, we get

ratio of movie poster : band poster  = 6 : 5   ......  (1)

Now, the number of posters she wants to sell = 24

So, the remaining movie poster left = 120 - 24  = 96

Let us assume she sells m band posters to keep the ratio equal.

So, the number of band posters she is left with = 100 - m

⇒The ratio of movie poster left  : band poster  left = 96 : 100 - m  .. (2)

Now here as the ratio remains same after selling m band posters, so

[tex]\frac{6}{5}  = \frac{96}{100 - m} \\\implies 100 - m = 96 \times\frac{5}{6} =  80\\or, 100 - 80 = m\\\implies  m= 20[/tex]

or, m = 20

Hence, she should sell 20 band posters from total 80 to keep the maintain the same ratio.

Answer:

Let l be the length and w the width of the rectangle.

P as the perimeter and A as the area.

length of a rectangle is four times the width:

w = w

l = 4w

System of equation : 2l + 2w = P

Substitute:

2(4w) + 2w = 45

8w + 2w

10w = 45

w = 45 / 10

w = 4.5

Solve for l:

l = 4w

l = 4(4.5)

l = 18

Area:

A = lw

A = 18(4.5)

A = 81 in²

Answer:

area =81  square inches

Step-by-step explanation:

width =w

lenght= 4w

2w + 2(4w)=45

10w=45

w=4.5

l= 4.5(4) = 18

4.5+4.5 +18+18 = 45

Area = l*w

4.5*18 = 81

Area= 81 square inches

These rates are not in proportion. Juan walked faster.

Explanation:

First, we want to make these ratios to have the same denominator so we can compare the numerators. To do this, do 3x5 and 8x5 to get 40:15. Then, we do 5x3 and 14x3 to get 42:15. Now we can just compare the numbers 40 and 42, and since 42 < 40, we know Juan walked faster.

The rates of 8/3 miles per hour and 14/5 miles per hour are not in proportion.

To determine whether the rates of Anna and Juan are in proportion, we can compare the rates of their walking speeds by forming a ratio and seeing if the ratios are equivalent. Anna walked 8 miles in 3 hours, which gives us a rate of 8/3 miles per hour. Juan walked 14 miles in 5 hours, resulting in a rate of 14/5 miles per hour.

To check the proportion, we set up a ratio of Anna's speed to Juan's speed: (8/3) / (14/5). If these rates are proportional, the cross-products of the ratios will be equal. However, when you cross-multiply, you get 8 * 5 = 40 and 3 * 14 = 42. Since 40 is not equal to 42, the rates are not in proportion.

Answer:

B. -x + 8

Step-by-step explanation:

Given expression

[tex]\dfrac{8-4(x-6)}{4}[/tex]

Consider the numerator [tex]8-4(x-6).[/tex]

First, use distributive property:

[tex]8-4(x-6)=8-(4x-24)[/tex]

Open the brackets:

[tex]8-(4x-24)=8-4x+24[/tex]

Combine the like terms:

[tex]8-4x+24=(8+24)-4x=32-4x[/tex]

Again use distributive property:

[tex]32-4x=4\cdot 8-4x=4(8-x)[/tex]

Now, the expression is

[tex]\dfrac{4(8-x)}{4}=8-x\ \text{or}\ -x+8[/tex]

Answer:

4 weeks

Explanation:

Length of Lavita’s painting = [tex]1 \frac{2}{3} m=\frac{5}{3} m[/tex]

Length she was able to finish each week= [tex]\frac{3}{8}m[/tex]

Now,

If she is able to finish[tex]\frac{3}{8}m[/tex] in 1 week

Then

[tex]\frac{3}{8}m[/tex] = 1 week

1 m = [tex]\frac{8}{3}m[/tex] week

Therefore

[tex]\frac{5}{3} m=\frac{8}{3} \times \frac{5}{3} \text { week }[/tex]

= [tex]\frac{40}{9}[/tex]week

=4.44 week

= 4 weeks (approx.)

Answer:

Step-by-step explanation:

he whole assignment seems to deal only with one simple concept, a direct variation

Sometimes text or your notes have definitions that are difficult to understand.

Here is the definition that is easy to understand:

A direct variation gives you an equation that contains no constants, and there are no exponents on the two variables.

e.g. y = 8x is a direct variation,

but y = 8x + 4 is NOT, since I see a constant of 4

a direct variation can be written in the form

y = kx , where k is the constant of variation

#1, not a variation, I see a +1 sitting there as a constant

#2, yes it is a direct variation:

-12x = 6y

6y = -12x

y = -2x

so the constant of variation is -2 , if y varies directly with x

or

-12x = 6y

x = -(1/2)x

now the constant of variation is -1/2 , if x varies directly as y

so it depends how you express the equation, either in terms of x or in terms of y

#3,

.7x - 1.4y = 0

.7x = 1.4y

1.4y = .7x

y = (.7/1.4)x = (1/2)x

so , yes it is, and the constant of variation is 1/2

From #4 on, you have to first find the equation.

I will do #4, you try the remaining.

#4, they tell us it is a direct variation, so it must look like

y = kx

They give us x=2 when y = -10

let's plug in those values:

-10 = k(2)

2k = -10

k = -5

aaahhhh, so y = -5x is our equation

#6, same way, just some fractions to deal with

#7, to graph, pick any x, and find the y to get ordered pairs,

e.g. let x = 3, then y = (1/3)(3) = 1, --> point(3,1)

let x = 9, then y = (1/3)(9) = 3 ---> point (9,3)

plot those two points, and join with a straight line

Notice how I picked multiple of 3's for my x's so I could take 1/3 of the x without ending up with fractions?

#8 , same as #7, pick multiples of 2 for your x's

#9 and #10 are the same type

#9

assume it is a direct variation, then its equation must be

y = kx

use the first given data: x = 3, y = 5.4

then 5.4 = k(3)

3k = 4.5

k = 1.5

equation is y = 1.5x

do the other points satisfy our equation?

for (7, 12.6)

is 12.6 = 1.5(7) ?

12.6 = 10.5 ??? NO, so the given data is NOT a direct variation

#10 same way

Answer:1. 2y=5x+1 answer is A Not a direct variation

2. -12x=6y answer is D Direct variation, constant of variation is -2

3. 0.7x-1.4y=0 answer is B Direct variation, constant is 1/2

4. y=-10 when x=2 answer is A y=-5x

5. y=7 1/2 when x=3 answer is C y=5/2 x

6. y=10.4 when x=4 answer is D y=2.6x

7. y=1/3 x answer is A the graph that reads (6, 2) where the green arrow is on the top right portion and on the bottom left is (-6, -2)

8 y=-1/2 x answer is C graph

9. the table x is first 3, 7, 12 y is next 5.4, 12.6, 21.6 answer is B Direct variation, y=1.8x

10. the table x is first -2, 3, 8 y is next 1, 6, 11 answer is A not a direct variation

p.s. this is for the direct variation practice

hope i helped

Step-by-step explanation:

Answer:

10 pages per technician per day is the unit metric for the production work.

Step-by-step explanation:

Consider the provided information.

Stiviko's approved work plan included 4 technicians to create 200 web pages  over 5 days.

They can create 200 web pages over 5 days.

[tex]\frac{200}{5}=40[/tex]

That means in one day they can create 40 pages.

There are 4 technicians who work, therefore the unit metric for the production work is: [tex]\frac{40}{4}=10[/tex]

Hence, 10 pages per technician per day is the unit metric for the production work.

Answer:

10 pages per technician per day

Step-by-step explanation:

Answer:

A) -4

Step-by-step explanation:

f(x)=10-2x

f(7)=10-2(7)

f(7)=10-14

f(7)=-4

fx)= 10-2x

f(7)=10-2(7)

do the bracket first

-2(7)=-14

f(7)=10-14

f(7)=-4

answer:

-4

Answer:

Pretty sure the answer is 20 :)

Answer:

20 inches

Step-by-step explanation:

From the question, diagonal of the television screen is given to be 25 inch and the  width of the television set is given to be 15 inches and we are asked to find the height of the screen.

We can solve this question using the Pythagoras theorem.

The Pythagoras theorem states that in a right-angle triangle;

opposite²  +  adjacent²  = hypotenuse²

From the question, the width is given to be 15 inches, the with is  our adjacent. Also the diagonal is given to be 25 inches, the diagonal is  our hypotenuse. And we were ask to find the height, the height is our opposite.

so;

opposite = ?  

adjacent = 15

hypotenuse = 25

Let opposite = x

we can now substitute into our theorem;

opposite²  +  adjacent²  = hypotenuse²

x²     +    15²  = 25²

x²   =   25²  -   15²

x²    =  625  -  225

x²   = 400

x    =  √400

x     =  20

opposite  =  20 inches

Since opposite is the height of the screen, then the height of the screen is 20 inches.

Therefore the height of the screen is 20 inches.  

Answer:

900 minutes

Step-by-step explanation:

Plan A: 700 free minutes + 15 cents per minute over 700 ($40)

Plan B: 500 free minutes + 5 cents per minute over 500 ($50)

The charges for x minutes (assumed x>700) for plan A will be

40+0.15(x-700)

The charges for x minutes (assumed x>500) for plan B will be

50+0.05(x-500)

To find the value of x where both charges are the same, we equate

40+0.15(x-700)=50+0.05(x-500)

Operating

40+0.15x-105=50+0.05x-25

Simplifying

0.10x=90

x=900 minutes

Both plans would charge the same amount when 900 minutes per month are used

Answer:

C) Multiplicative Inverse Property

Step-by-step explanation:

Because 1/10 is the inverse of 10.

For example, 15*(1/15)=1.

Answer:

C

Step-by-step explanation:

Answer:

multiply 35(26)

Step-by-step explanation:

35(26)=910

and 910/26=35 ,

so w=910

Answer:

910

Step-by-step explanation:

Your equation is w ÷ 26 = 35

To solve for 'w,' you have to get 'w' alone on one side. To do that, you multiply both sides by 26, getting rid of the '÷ 26' on the left side of the equation.

w ÷ 26 = 35

w = 910

So your answer is 910  ^-^