Alda is measuring the growth of a plant. Its initial height was 14 centimeters (cm), and the plant has consistently grown 32 cm each day.

Which linear equation represents the plant height, (y), after a given number of days, (x)?
Responses

y=32x+14y is equal to 3 halves x plus 14

x=32y+14x is equal to 3 halves y plus 14

y=14x+32y is equal to 14 x plus 3 halves

y=32x−14

Answer: The items cost as follows;

(a) Brush = $3.50, (b) Sketchbook = $21 and (c) Paint set = $28

Step-by-step explanation: First of all we shall assign letters to the unknown variables, hence we shall call the brush x, the sketchbook y, and the paint set we shall call z.

The total amount spent by Corey was $52.50 because after buying all he needed, he had $2.00 left out of a total of $54.50. This means his transaction can be expressed as follows;

x + y + z = 52.50

However, we know that the brush was 1/6 as much as the sketchbook, that is, if the sketchbook is y, then the brush which is x shall be 1/6 of y. Simply put, x = 1/6y or x = y/6.

Similarly, the sketchbook cost 3/4 of the paint set. If the paint set is z, that means y = 3/4z or y = 3z/4.

Note however that, if y = 3z/4, then by cross multiplication,

4y = 3z

4y/3 = z

Having derived that x = y/6 and z = 4y/3, we can substitute for the values of x and z into the original equation

x + y + z = 52.50

y/6 + y + 4y/3 = 52.5

using a common denominator which is 6, you now have;

(y + 6y + 8y)/6 = 52.5

By cross multiplication, you now have

15y = 52.5*6

15y = 315

Divide both sides of the equation by 15

y = 21

Therefore, if the sketchbook is y, then the sketchbook costs $21.

Also if the brush is x, then the brush costs

x = y/6

x = 21/6

x = 3.50 (The brush costs $3.50)

Also if the sketchbook costs 3/4 of the paint set, then

y = 3z/4

21 = 3z/4

21*4 = 3z

84 = 3z

Divide both sides of the equation by 3

28 = z (The paint set costs $28)

there is no common factor between 23 and 12, since 23 is a prime number. Therefore, we cannot simplify 23/1 to get an equivalent fraction with a denominator of 12.

It is not possible to create a fraction with a denominator of 12 that is equivalent to 23.

To understand why, we can look at the definition of equivalent fractions. Two fractions are equivalent if they represent the same value. This means that if we can simplify one fraction to get the other, then they are equivalent.

In this case, we have the fraction 23, which can be written as the improper fraction 23/1. To find an equivalent fraction with a denominator of 12, we need to simplify 23/1 by dividing both the numerator and denominator by a common factor until the denominator becomes 12.

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Step-by-step explanation:

Write each question in order from least to greatest 4/5,3/10,1/2:

4/5 = 8/10

3/10 = 3/10

1/2 = 5/10

least to greatest:

3/10 < 1/2 < 4/5

Answer:

$175.35

Step-by-step explanation:

Answer:

60 toys

Step-by-step explanation:

Answer:

You will get 20 toys in 12 minutes.

Step-by-step explanation:

it's a ratio basically...

3 : 5

12 : 20

From 3 to 12 multiply by 4, so do that on both sides, so then 5 times 4 is 20.

Hope this helped!

Plot it halfway between -2 and -3

Answer:

81

Step-by-step explanation:

The recursive function is given as:

f(n+1)=1/3f(n)

So then we multiply both sides by 3:

3f(n+1)=f(n)

Then we set n=2:

3f(2+1)=f(2)

Which comes to be:

f(2)=3f(3)

Next we set n=1:

f(1)=3f(1+1)

Which is:

f(1)=3f(2)

Then we substitute:

f(1)=3*3f(3)

=9f(3)

=9*9

=81

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Answer:

Step-by-step explanation:

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The value of f(1) for the recursive function is (d) 81

The recursive function is given as:

Multiply both sides of the equation by 3

Rewrite as:

Set n = 2;

Set n = 1 in

Substitute

Substitute 9 for f(3)

Hence, the value of f(1) for the recursive function is (d) 81

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(5 votes)

Adv

Answer:

He can cut 20 1/2m peice of rope from the 10m rope

Step-by-step explanation:

divide

10 / .5 = 20

Answer:

The original price drops by 15%.

Step-by-step explanation:

What was the drop in price?  To answer that, subtract $21.25 from $25, which results in $3.75.

Now compare $3.75 to the original price, $25, through division, as follows:

   $3.75

-------------- * 100% = 15%

     $25

The original price drops by 15%.

Answer:

G < 23/3

Step-by-step explanation:

10g - 8g - 9 < -g + 14

2g - 9 < -g + 14

3g - 9 < 14

3g < 23

g < 23/3

So the system of equations for Table 1 is  y = 2x + 12 and y = 2x - 12 for table 2    y = (13/5)x - 6.4 and y = (3/2)x - 5

what is system of equations?

A system of equations is a set of one or more equations involving the same variables. The solution for system of equations is  set of values for variables that make all   equations in the system true simultaneously.

what is variables ?

In mathematics, a variable is a quantity or value that can change or take on different values in a given problem or equation. Variables are often represented by letters or symbols, and they can be used to represent unknowns, parameters,

In the given question,

To write the system of equations that represents the given tables, we need to find the equations of the two lines that pass through the given points.

Table 1:

X -3 -5 6 -2

Y -6 -10 12 -4

Let's find the equation of the line passing through the first two points (-3, -6) and (-5, -10). The slope of this line can be found using the slope formula:

slope = (y2 - y1) / (x2 - x1)

slope = (-10 - (-6)) / (-5 - (-3)) = -4/-2 = 2

The y-intercept of this line can be found using the point-slope form of the equation:

y - y1 = m(x - x1)

Using the point (-3, -6):

y - (-6) = 2(x - (-3))

y + 6 = 2(x + 3)

y = 2x + 12

Similarly, let's find the equation of the line passing through the last two points (6, 12) and (-2, -4):

slope = (-4 - 12) / (-2 - 6) = -16/-8 = 2

Using the point (6, 12):

y - 12 = 2(x - 6)

y = 2x - 12

So the system of equations for Table 1 is:

y = 2x + 12

y = 2x - 12

Table 2:

X 6 -4 0 2

Y 12 -14 -5 -2

Let's find the equation of the line passing through the first two points (6, 12) and (-4, -14):

slope = (-14 - 12) / (-4 - 6) = -26/-10 = 13/5

Using the point (6, 12):

y - 12 = (13/5)(x - 6)

y = (13/5)x - 6.4

Similarly, let's find the equation of the line passing through the last two points (0, -5) and (2, -2):

slope = (-2 - (-5)) / (2 - 0) = 3/2

Using the point (0, -5):

y - (-5) = (3/2)(x - 0)

y = (3/2)x - 5

So the system of equations for Table 2 is:

y = (13/5)x - 6.4

y = (3/2)x - 5

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Sharon's desired percentile rank of 0.78.

To determine the goal Sharon set for herself, we need to understand the relationship between standardized scores and percentile ranks.

In a standardized test, such as Sharon's Statistics final, the standardized score represents how well a student performed relative to the average score of the test-takers.

The percentile rank, on the other hand, indicates the percentage of test-takers that scored below a particular student.

In Sharon's case, she wants her standardized score to be equal to her percentile rank.

Therefore, her goal is to achieve a standardized score of 0.78 (written as a decimal) on her Statistics final.

This means she aims to score better than approximately 78% of her classmates, as indicated by her desired percentile rank of 0.78.

Hence her desired percentile rank of 0.78.

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The limit definition of a derivative is a mathematical method used to calculate the instant rate of change of a characteristic at a particular point. it is based at the idea of the limit of a function because the input techniques a certain cost.

The limit definition of a derivative is expressed as follows:

\(f'(x) = lim (h → 0) [f(x + h) - f(x)] /h\)

Wherein f'(x) represents the derivative of the function f(x) at a particular factor x. The expression \(( f(x + h) - f(x)) / h\) represents the common price of alternate of the characteristic over a small interval of size h, focused at x. The limit of this expression as h approaches 0 represents the instant fee of change of the characteristic at x, or the slope of the tangent line to the function at that factor.

The limit definition of a derivative is a fundamental concept in calculus and is used to calculate the slopes of tangent lines, to find maximum and minimum factors, and to clear up optimization issues in a huge variety of packages.

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Answer:

3 inch    6 inch  16 inch             3+6+16 = 25

Step-by-step explanation:

First piesce = F

Second piece = 2F

third piece = 5F+1

F + (2F) + (5F+1) = 25

8F +1 = 25

subtract 1 om both sides

8F = 24

divide both sides by 8

F= 3

3X2= 6

3X5 +1 = 16

After the conversion of $500 in japanese yen Ben will have 61,650 yen.

According to the question.

The amount of money in US dollars Ben wishes to convert in Japanese yen is $500.

Also, it is given that

$1 = 123.3yen

Therefore,

The number of yen Ben have after the conversion of dollars in yen

= 500 × 123.3

= 61,650

Hence, after the conversion of $500 in japanese yen Ben will have 61,650 yen.

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Answer: equal to

Step-by-step explanation:

If c is zero and b+c=a then b would equal a

Answer:

14

Step-by-step explanation:

(2 x 6) + ( \(\sqrt{16\\}\) - 8 ÷ 2^2) =

12 + (4 - 8 ÷ 4)

12 + (4 - 2)

12 + 2

14

The proof of expression include:

The cosine law, also known as the law of cosines, is a trigonometric formula that relates the sides and angles of a triangle. It states that for any triangle with sides a, b, and c, and angles opposite those sides A, B, and C, the following equation holds true:

c² = a² + b² - 2ab cos(C) or a² = b² + c² - 2bc cos(A) or b² = a² + c² - 2ac cos(B)

These equations can be used to find the length of a side or the measure of an angle in a triangle if the lengths of the other sides and angles are known.

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Image transcribed:

Note: Type x in place of theta for any answers where you need the angle/variable, and type pi instead of using the symbol

cos (Θ-(3π)/2)=-sin Θ

Proof:

1. cos (Θ-(3π)/2)

2. Use the sum to product identity: cos Θ ________ + sin Θ ___________

3. Replace the values that you know in the function. (i.e. replace any specific angle values)

cos Θ ________ + sin Θ ___________

4. Simplify: __________

We have that the amount he will get back at the end of this period is

x=1080

From the question we are told that

Rs 6000

r=6\%

time t=3yrs

Generally

A=P(1+rt)

A=P(1+rt)A=7080

Therefore

The amount he will get back at the end of this period is

7080-6000

7080-6000x=1080

In conclusion

The amount he will get back at the end of this period is

x=1080

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Answer:

i d k so ima just say no

Step-by-step explanation:

Answer:

ok I will try that thx for telling

Answer:

In the given triangle △ABC, AB is equal to 4 and m∠F is equal to 30°. In the triangle △DEF, AB is equal to 6 and m∠F is equal to 50°.

Her painting rate in window frames per hour will be;

⇒ 1.6 frames per hour

Her painting rate in hours per window frame will be;

⇒ 0.25 hours per window frame

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

Joyce painted 8 window frames in 5 hours while earning money for college.

Here, Joyce painted 8 window frames in 5 hours while earning money for college.

Hence, Her painting rate in window frames per hour is,

⇒ 8/5

⇒ 1.6 frames per hour

And, Her painting rate in hours per window frame is,

⇒ 5/8

⇒ 0.25 hours per window frame

Thus, Her painting rate in window frames per hour = 1.6 frames per hour

Her painting rate in hours per window frame = 0.25 hours per window frame

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Answer:

y = 4x + 14

Step-by-step explanation:

slope-intercept form: y = mx + b

Slope formula: \(\frac{y2-y1}{x2-x1}\)

To write the equation in y = mx + b form, we need to find the slope(m) and the y-intercept(b) of the equation.

To find the slope, take two points from the table(in this example I'll use points (0, 14) and (1, 18)) and input them into the slope formula:

\(\frac{18-14}{1-0}\)

Simplify:

18 - 14 = 4

1 - 0 = 1

\(\frac{4}{1}=4\)

The slope is 4.

To find the y-intercept, input the values of the slope and one point(in this example I'll use point (1, 18)) into the equation format and solve for b:

y = mx + b

18 = 4(1) + b

18 = 4 + b

14 = b

The y-intercept is 14.

Now that we know the slope and the y-intercept, we can write the equation:

y = 4x + 14

Based on the triangle midpoint theorem, the statement which must be shown is that: B. the length of GH is half the length of KL.

Triangle midpoint theorem states that the line segment which joins the midpoints of two (2) sides of a triangle is parallel to the third side, and it's congruent to one-half of the third side.

Based on the triangle midpoint theorem, we can infer and logically deduce that the statement which must be shown is that the length of GH is half the length of KL.

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Answer:  B. The length of GH is half the length of KL.

Step-by-step explanation:   TRUST ME!  The answer is correct on Edge.  :)

We have that the formula for the surface area of a cylinder is the following:

in this case, we have the following:

therefore, the length of the height is 17 inches

Answer:

k=24

Step-by-step explanation:

The tangent of the function f at x=a, can be found by differentiating f w.r.t. x and then replacing x with a.

f=-x^2+8x+20

Differentiating both sides:

f'=(-x^2+8x+20)'

By sum rule:

f'=(-x^2)'+(8x)'+(20)'

By constant multiple rule:

f'=-(x^2)'+8(x)'+(20)'

By constant rule:

f'=-(x^2)+8(x)'+0

By power rule:

f'=-2x+8

f' at x=a is -2a+8

This is the slope of any tangent line to the curve f.

The slope of g is 4 if you compare it to slope intercept form y=mx+b.

So we gave -2a+8=4.

Subtracr 8 on both sides: -2a=-4

Divide both sides by -2: a=2

The tangent line to the curve at x=2 is y=4x+k.

To tind y we must first know the y-coordinate of the point of tangency.

If x=2, then

f(2)=-(2)^2+8(2)+20=-4+16+20=12+20=32

So the point is (2,32).

g(x)=4x+k and we know g(2)=32.

This gives us:

32=4(2)+k

32=8+k

k=32-8

k=24

From the tangent given, the value of k will be 24.

From the information given, g(x) = 4x + k and this is a tangent to f(x)= -x² +8x + 20.

f(x)= -x² +8x + 20

= f'(x)  = -2x  + 8

The slope of tangent = -2x + 8  at (x , y)

g(x) = 4x  + k  

Hence, slope = 4

-2x + 8 = 4

Collect like terms

-2x = 4 - 8

-2x = - 4

Divide both side by -2

-2x/-2 = -4/-2

x = 2

f(x)= -x² +8x +20

where, x = 2

y = -2² + 8(2) + 20  

y =  32

Hence (2 , 32) lies on g(x)= 4x+k

32 = 4(2) + k

32 = 8 + k

k = 32 - 8

k = 24

In conclusion, the value of k is 24.

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