After it is planted, a tree grows at a rate of 0.4 meters per year. After 3 years the tree is 1.7
meters tall. Write the equation in point-slope form that models the situation. Then, predict
the height of the tree after 8 years.

Multiple Choice Answers:

Oy- 3-0.4(x - 1.7); 5.52 meters
Oy- 1.7= 3(x-0.4); 24.5 meters
Oy- 0.4 1.7(x - 3); 8.9 meters
Oy- 1.7 = 0.4(x - 3); 3.7 meters

Answer: 15cm and 5cm

Step-by-step explanation:

A rectangle's area is the product of the length and width

Given length x and width y, 2x+2y = 40 and x*y = 75.

Verifying my answer:

2(15)+2(5) = 40

30+10 = 40

40 = 40

15*5 = 75

75= 75

This is a week late so I hope this helped.

The length and the width of the rectangle​ are 15cm and 5cm respectively

The given parameters are:

Area (A) = 75

Perimeter (P) = 40

The area of a rectangle is LW, while the perimeter is 2(L + W)

So, we have:

LW = 75

2(L + W) = 40

Divide by 2

L + W = 20

Make L the subject

L = 20 - W

Substitute L = 20 - W in LW = 75

(20 - W)W = 75

Expand

20W - W^2 = 75

Rewrite as:

W^2 - 20W + 75 = 0

Expand

W^2 - 15W - 5W + 75 = 0

Factorize

(W - 15)(W -5) = 0

Split

W - 15 = 0 or W - 5 = 0

Solve for W

W = 15 or W = 5

Recall that:

L= 20 - W

So, we have

L = 20 - 15 or L = 20 - 5

This gives

L = 5 or L = 15

Hence, the length and the width of the rectangle​ are 15cm and 5cm respectively

Read more about areas at:

https://brainly.com/question/11957651

#SPJ1

Let a (n) denote the n-th term in the progression. Consecutive terms in the sequence differ by a fixed constant - call it c - such that

a (n) = a (n - 1) + c

Let a = a (1) be the first term in the sequence. We can solve for a (n) in terms of a alone:

a (n) = a (n - 1) + c

a (n) = (a (n - 2) + c) + c = a (n - 2) + 2c

a (n) = (a (n - 3) + c) + c = a (n - 3) + 3c

and so on, down to

a (n) = a + (n - 1) c

The sum of the first n terms is then

\(\displaystyle\sum_{k=1}^n a(k)=\sum_{k=1}^n(a+(k-1)c)=a\sum_{k=1}^n1+c\sum_{k=1}^n(k-1)=an+\frac{cn(n-1)}2=\frac c2n^2+\left(a-\frac c2\right)n\)

Since this is equal to 3n ^2 + 5n, it follows that

c/2 = 3   =>   c = 6

a - c/2 = 5   =>   a = 8

So the sequence is

a (n) = 8 + (n - 1) 6 = 6n + 2

Answer:

a) 5355

b) 6372.45

Step-by-step explanation:

4500 * 1.19 = 5355

5355 * 1.19 = 6372.45

Answer:

5/11, 2/3, 7/8

Step-by-step explanation:

The missing number in Sequence 2 is 780.

To find the missing number in Sequence 2, let's analyze the pattern:

In Sequence 1, the numbers increase by 1 each time: 126, 127, 128, 129, ...

In Sequence 2, the numbers seem to follow a pattern where each number is obtained by multiplying the corresponding number in Sequence 1 by a certain factor:

2 x 126 = 252

3 x 127 = 381

4 x 128 = 512

5 x 129 = 645

...

Looking at this pattern, we can see that the missing number in Sequence 2 should be:

6 x 130 = 780

For similar question on Sequence.

https://brainly.com/question/7882626  

#SPJ8

Answer:

60 songs.

Step-by-step explanation:

The percentages there are an equal sign so

0.45x=27

x=60

So Brianna listened to 60 songs!

Answer:

1 5 10 10 5 1

Step-by-step explanation:

The complete question has been attached as an image.

Looking at the triangle, we see a pattern. The first level we have 1, in the next level we have 1 1, the next evel we have 1 2 1, the next level we have 1 3 3 1 and so on. From here, we see that to get the numbers of the next level, we have to write 1 as the first number, then add 1 to the next number after it in the previous level to get the second number in the next level then add the second number of the previous level to the next number beside it to get the third number in the next level and so on until you get to the last number before 1 in the previous level, add that number to 1 to get the second to the last number in the next level and finally put 1 as the last number in the next level. Now, we have

1 4 6 4 1

1 5 10 10 5 1

And that is the required set of numbers.

1. Andy's oldest daughter ate the most pizza. She ate the entire personal pizza, which is 10 inches in diameter

2. If the company offered an extra large pizza, you could find out how much of it a person ate if they cut their own piece with a central angle of M°

Andy's oldest daughter ate the most pizza. She ate the entire personal pizza, which is 10 inches in diameter. This means that she ate 100% of the pizza. Andy's wife ate 2/6 of the small pizza, which is 12 inches in diameter. This means that she ate 1/3 of the pizza. Andy's younger daughter ate 1/8 of the medium pizza, which is 14 inches in diameter.

This means that she ate 12.5% of the pizza. Andy cut himself a piece that had a central angle of 180° from the large pizza, which is 16 inches in diameter. This means that he ate 50% of the pizza.

The least amount of pizza was eaten by Andy's younger daughter. She only ate 1/8 of the medium pizza.

2. If the company offered an extra large pizza, you could find out how much of it a person ate if they cut their own piece with a central angle of M° by using the following formula:

Percentage of pizza eaten = (M° / 360°) * 100%

For example, if a person cut themselves a piece of an extra large pizza with a central angle of 180°, they would have eaten 50% of the pizza.

Percentage of pizza eaten = (180° / 360°) * 100% = 50%

Learn more about diameter on

https://brainly.com/question/23220731

#SPJ1

Sue's total pay for the year given the salary, bonus and share of profit is  £38,110.

Sue's total pay for the year is a function of the salary, the share of the profit that she earns and the bonus.

Salary for the year = monthly salary x number of months in a year

£1410 x 12 = £16,920

The next step is to determine the profit last year

Profit = total revenue - total cost

£549,000 - £473,500 = £75,500

Now determine the share of profit that Sue would earn.

Share of profit = 26% x  £75,500

0.26 x  £75,500 = £19,630

Now determine the total bonus she would earn : 4 x £390 = £1560

Total salary = £1560 +  £19,630 +  £16,920 = £38,110

To learn more about profit, please check: https://brainly.com/question/26181966

#SPJ1

The area of a trapezoid and the given measurements, we found that the area of the trapezoid is 15.64 square centimeters.

To find the area of the trapezoid, we can use the formula:

Area = (b1 + b2)h / 2

where b1 and b2 are the lengths of the parallel sides, and h is the height (or distance between the parallel sides).

In this case, the left side (b1) is 5cm, the right side (b2) is 2cm, the top is 6cm, and the height is the distance between the top and bottom sides, which can be calculated using the Pythagorean theorem as:

h =\(sqrt(5.4^2 - (6-2)^2) = sqrt(20.16)\) = 4.49cm (rounded to two decimal places)

Substituting these values into the formula, we get:

Area = (5 + 2) * 4.49 / 2 = 15.64 square centimeters (rounded to two decimal places)

Therefore, the area of the trapezoid is 15.64 square centimeters.

To learn more about trapezoid please click on below link        

https://brainly.com/question/21025771

#SPJ1

Answer:

\( - \frac{1}{10} \times (25z + 52)\)

Step-by-step explanation:

-1/2 (7z + 4) + 1/5 (5z - 16)

-1/10 × (5(7z + 4) - 2 (5z - 16))

-1/10 × (35z + 20 - 10z + 32)

= -1/10 × (25z + 52)

Since an even number can be represented as:

With n a natural number, and the next even number is:

Set the sum of both even numbers equal to 126:

Solve for n:

Substitute back n=31 into the expressions for the even numbers to find them:

Therefore, the two consecutive even numbers whose sum is 126, are 62 and 64.

Answer:

a

Step-by-step explanation:

Answer:

  288 square inches

Step-by-step explanation:

Assuming your "altitude" is the height of the prism--the distance between bases, the lateral area is the sum of the areas of the six rectangular faces. Each of those has an area of ...

  (8 in)(6 in) = 48 in^2

so the 6 of them will have an area of ...

  lateral area = 6×48 in^2 = 288 in^2

_____

Comment on nomenclature

'Altitude' is usually associated with the height of a triangle. In the case of a regular polygon, the 'altitude' of a triangular section of the polygon is called the 'apothem', and is often designated using the letter 'a'. If the polygon is regular, the apothem can be calculated from the side length and the number of sides, but it is often given in problems involving area, perimeter, and/or volume.

The distance between the parallel bases of a prism is often referred to as the prism height or length. The use of the word 'altitude' is confusing in this case.

Since the lateral area is the product of the perimeter of the base and the distance between bases, we have to assume that your 'altitude' refers to the distance between bases. Otherwise, there is not sufficient information to work the problem.

Answer:

I think +5 or 5

Answer:

there both 5

Step-by-step explanation: did the question on edg

The values of functions are

(a) f(0) = -3.                           (b) f(4) = 77.

(c) f(-4) = 45.                         (d) -f(x) = -4x² - 4x + 3.

(e) f(x+1) =  4x² + 12x + 1.       (f) f(-x) =  4x² - 4x - 3.

(g) f(3x) =  36x² + 12x - 3.

(h) f(x+h) =  4x² + 8xh + 4h² + 4x + 4h - 3.

The concept used in this question is evaluating a polynomial function for different values of the input variable. To do this, we substitute the given value into the function in place of the input variable and simplify the resulting expression.

Here we have

The function f(x) = 4x² + 4x-3.

To find the values of functions can be done by replacing x

(a) f(0) = 4(0)² + 4(0) - 3 = 0 + 0 - 3 = -3

(b) f(4) = 4(4)² + 4(4) - 3 = 64 + 16 - 3 = 77

(c) f(-4) = 4(-4)² + 4(-4) - 3 = 64 - 16 - 3 = 45

(d) -f(x) = -[4x² + 4x - 3] = -4x² - 4x + 3.

(e) f(x+1) = 4(x+1)² + 4(x+1) - 3 = 4(x² + 2x + 1) + 4x + 4 - 3 = 4x² + 12x + 1.

(f) f(-x) = 4(-x)² + 4(-x) - 3 = 4x² - 4x - 3.

(g) f(3x) = 4(3x)² + 4(3x) - 3 = 36x² + 12x - 3.

(h) f(x+h) = 4(x+h)² + 4(x+h) - 3 = 4(x² + 2xh + h²) + 4x + 4h - 3

= 4x² + 8xh + 4h² + 4x + 4h - 3.

Hence,

The values of functions are

(a) f(0) = -3.                           (b) f(4) = 77.

(c) f(-4) = 45.                         (d) -f(x) = -4x² - 4x + 3.

(e) f(x+1) =  4x² + 12x + 1.       (f) f(-x) =  4x² - 4x - 3.

(g) f(3x) =  36x² + 12x - 3.

(h) f(x+h) =  4x² + 8xh + 4h² + 4x + 4h - 3.

Learn more about Functions at

https://brainly.com/question/16935080

#SPJ9

The numeric value of the expression -b + 8x when b = 5 and x = -6 is given as follows:

-53.

To find the numeric value of a function or of an expression, we replace each instance of the variable/variables in the function or in the expression by the value/values at which we want to find the numeric value.

In this problem, the expression is given as follows:

-b + 8x.

The values at which the numeric value is to be found are:

b = 5, x = -6.

Hence:

Thus the numeric value of the expression is obtained as follows:

-5 + 8(-6) = -5 - 48 = -53.

The problem is given by the image at the end of the answer.

Learn more about the numeric values of a function at brainly.com/question/28367050

#SPJ1

Answer:

a = \(\frac{d}{b+c}\)

Step-by-step explanation:

a(b + c) = d

isolate a by dividing both sides by b + c

a = \(\frac{d}{b+c}\)

Answer:  dont know

Step-by-step explanation:

1. The x - intercepts of the parabola are

2. The meaning of the x-intercepts are the plane takes of at x = 2.5 s and lands at x = 7.5 s

3. The vertex of the parabola is at (5, 80).

A parabola is a curved shape

1. Given the parabola above, to find the x - intercepts, we proceed as follows.

The x-intercepts are the points at which the graph cuts the x-axis.

They are

2. The meaning of the x-intercepts in this problem are the points where the plane takes off and lands on the ground.

The plane takes of at x = 2.5 s and lands at x = 7.5 s

3. The vertex is the maximum point on the graph.

So, we see that the vertex is at x = 5 s and y = 80 ft

So, the vertex is at (5, 80).

Learn more about parabola here:

https://brainly.com/question/28094027

#SPJ1

The value of x that makes the line containing (1,2) and (5,3) perpendicular to the line containing (x,4) and (3,0) is x = 2.

To determine the value of x such that the line containing (1,2) and (5,3) is perpendicular to the line containing (x,4) and (3,0), we need to find the slope of both lines and apply the concept of perpendicular lines.

The slope of a line can be found using the formula:

slope = (change in y) / (change in x)

For the line containing (1,2) and (5,3), the slope is:

slope1 = (3 - 2) / (5 - 1) = 1 / 4

To find the slope of the line containing (x,4) and (3,0), we use the same formula:

slope2 = (0 - 4) / (3 - x) = -4 / (3 - x)

Perpendicular lines have slopes that are negative reciprocals of each other. In other words, if the slope of one line is m, then the slope of a line perpendicular to it is -1/m.

So, we can set up the equation:

-1 / (1/4) = -4 / (3 - x)

Simplifying this equation:

-4 = -4 / (3 - x)

To remove the fraction, we can multiply both sides by (3 - x):

-4(3 - x) = -4

Expanding and simplifying:

-12 + 4x = -4

Adding 12 to both sides:

4x = 8

Dividing both sides by 4:

x = 2

For more such questions on line.

https://brainly.com/question/280216

#SPJ8

Answer:

the correct answer is B and E

Step-by-step explanation:

Answer:

57% incorrect

Step-by-step explanation:

100- 43= 57. Assuming that the test is out of 100%, he got 57% of the test incorrect

Answer:

1. 66.22

2. 4.03  

3. 0.108

Step-by-step explanation:

divide the answers by the other numbers (10,100,1000)  

662.2 ÷ 10 = 66.22

403 ÷ 100 = 4.03

108 ÷ 1000 =0.108

~R3V0

Answer:

\(P=\$276646.153\)

Step-by-step explanation:

Time \(T=30years\)

Rate \(r=0.325\%\)

Payment per month \(P=\$ 900\)

Generally the equation for Principle  is mathematically given by

\(M=\frac{P r}{1-(1+r)^{-n}}\)

\(900=\frac{P \frac{0.325}{100}}{1-(1+( \frac{0.325}{100}))^{- 30*12}}\)

\(P=\frac{900*100*0.99}{0.325}\)

\(P=\$276646.153\)

Answer:

Step-by-step explanation:

49255-1674.67=47580.33

Answer:

Hi

Please mark brainliest ❣️

Thanks

Step-by-step explanation:

The answer is NO

Reason

x= 2 y= 1

Now input in the first inequality

y≤ -x + 4

1 ≤ -2 +4

1≤ 2 i.e 1 is less than two

Next inequality

y≤ x +1

1 ≤ 2 + 1

1≤ 3 i.e 1 is less than 3

But 1 is not equal to 3 and also not equal to 2

Hence our answer is NO

Answer:

3/17×100= approximately 17.6

Step-by-step explanation:

if you have 1,2,4,5,10.20,25,50, you'll multiply both sides by a number that this number when you multiply it by the denominator it will be 100

if any other numbers you can multiply immediately by 100