two years ago, a baby elephant was 11 feet shorter than its mother. However it grew 3 feet and bow its mother is only twice its size. How big was the baby elephant two years ago?​

Answer:

a) \(a_n=3n-1\)

b) \(a_n=2n+7\)

Step-by-step explanation:

a)  From inspection, we can see that this is an arithmetic sequence as the difference between each term is the same:

14 - 11 = 3

11 - 8 = 3

8 - 5 = 3

5 - 2 = 3

(so the common difference = 3)

General equation of arithmetic sequence:  \(a_n=a+(n-1)d\)

(where \(a\) is the first term and \(d\) is the common difference between terms)

Given:

\(\implies a_n=2+(n-1)3\)

\(\implies a_n=2+3n-3\)

\(\implies a_n=3n-1\)

b)  From inspection, we can see that this is an arithmetic sequence as the difference between each term is the same:

17 - 15 = 2

15 - 13 = 2

13 - 11 = 2

11 - 9 = 2

(so the common difference = 2)

General equation of arithmetic sequence:  \(a_n=a+(n-1)d\)

(where \(a\) is the first term and \(d\) is the common difference between terms)

Given:

\(\implies a_n=9+(n-1)2\)

\(\implies a_n=9+2n-2\)

\(\implies a_n=2n+7\)

the firm has a total asset turnover of 0.6, which means that for every $1 of total assets, the firm generates $0.6 in sales. This ratio indicates the firm's efficiency in utilizing its assets to generate revenue

Total asset turnover is a financial ratio that measures a company's efficiency in generating sales from its total assets. It is calculated by dividing the total sales by the average total assets. In this case, the firm has $600,000 in sales and total assets of $1 million.

Total Asset Turnover = Total Sales / Average Total Assets

To calculate the average total assets, we sum the beginning and ending total assets and divide by 2:

Average Total Assets = (Beginning Total Assets + Ending Total Assets) / 2

Given that the firm's total assets are $1 million, the average total assets would also be $1 million.

Plugging in the values into the total asset turnover formula:

Total Asset Turnover = $600,000 / $1,000,000 = 0.6

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Answer:

27/4 or negative 3/4

Step-by-step explanation:

Answer:

2(24(15) + 24(3) + 15(3)) = 2(360 + 72 + 45)

= 2(477) = 954

The surface area of this box is 954 square inches.

Answer:

B

Step-by-step explanation:

Answer:

corresponding angles

Alternate angle

cointerior angle

Answer:

289m = 2,890dm

Step-by-step explanation:

you multiply the meters by 10

By solving a system of equations, we conclude that the measure of the third angle is 90°.

First, let's define the variables:

Remember that the sum of the internal angles of a triangle always give 180°, then:

A + B + C  =180°.

We also know that:

B = A + 24°

C = B + 33°

Then we have a system of equations:

A + B + C  =180°

B = A + 24°

C = B + 33°

To solve this, we can first replace the third equation into the first one:

A + B + (B + 33°) =180°

A + 2B + 33° = 180°

Now let's replace the second equation there:

A + 2*(A + 24°) + 33° = 180°

3*A + 48° + 33° = 180°

3*A = 180° - 48° - 33° = 99°

A = 99°/3 = 33°

Then:

C = B + 33° = (A + 24°) + 33° = (33° + 24°) + 33° = 90°

We conclude that the measure of the third angle is 90°.

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Answer:

From the calculation,

KL = 13

NM = √65

Hence KL ≠ NM

Therefore, the quadrilateral KLMN is not a Parallelogram.

Step-by-step explanation:

K(–5, –4), L(0, 8), M(7, 4), and N(8, –4)

Where we have vertices, (x1, y1) , (x2, y2)

We use the formula

√(x2 - x1)² + (y2 - y1)²

Side KL = K(–5, –4), L(0, 8)

√(x2 - x1)² + (y2 - y1)²

√(0 - (-5))² + (8 - (-4))²

√ 5² + 12²

√25 + 144

= √169

= 13

Side KN = K(–5, –4), N(8, –4)

√(x2 - x1)² + (y2 - y1)²

√(8 -(-5))² + (-4 - (-4))²

√13² + 0²

√169

=13

Side MN = M(7, 4), N(8, –4)

√(x2 - x1)² + (y2 - y1)²

√(8 -7)² + (-4 - 4)²

√1² + (-8)²

√1 + 64

√65

Side LM = L(0, 8), M(7, 4),

√(x2 - x1)² + (y2 - y1)²

√(7-0)² + (4 - 8)²

√(49)² +(-4)²

√ 49 + 16

√65

We were asked in the above question to prove that the quadrilateral with the given vertices is not a Parallelogram.

One of the characteristics of a Parallelogram is that the opposite sides are parallel and congruent to one another. This means that, the opposite sides are similar .

For the Quadrilateral KLMN above to be a Parallelogram, this means

KL = NM

From the above calculation,

KL = 13

NM = √65

Hence KL ≠ NM

Therefore, the quadrilateral KLMN is not a Parallelogram.

Input quantity: Time t in years since it was planted

Output quantity: Height h in feet of the tree.

Input variable: time t

Output variable: height h.

Ordered pairs are represented as (t, h).

Use function notation to illustrate the relationship between h and t.

h = f(t) where f is a function of time t.

The notation h(20) = 60 means that when the tree is 20 years old, its height is 60 feet. It means that after 20 years of planting the tree, its height is 60 feet.

The input quantity is time, the output quantity is height, the input variable is t, and the output variable is h. The relationship between height and time can be expressed as a function h = f(t).

Finally, the function notation h(20) = 60 means that the tree's height is 60 feet after 20 years.

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Answer:

its called a calculator division and multiplication

Step-by-step explanation:

Answer:

Therefore, x > -4 .

Step-by-step explanation:

First, you have to collect like terms :

5x + x - 3x > -12

3x > -12

Next, you have to divide both sides by 3 in order to eliminate 3 on the left side :

3x > -12

3x ÷ 3 > - 12 ÷ 3

x > -4

By using trigonometric relations, we will see that:

x = √3

In the image, we can see a right triangle, where the hypotenuse measures √6, and the two legs have the same measure.

Then this is a 45°, 45°, 90° right triangle.

Then we can use the relation:

cos(a) = (adjacent cathetus)/(hypotenuse).

Where a = 45°, adjacent cathetus = x, hypotenuse = √6

Replacing that, we get:

cos(45°) = x/√6

Remember that cos(45°) = 1/√2

Replacing that we get:

1/√2= x/√6

√6/√2 = x

√(6/2) = x

√3 = x

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Answer:

A

Step-by-step explanation:

Because if you look up y=2x+2 that graph rises and if you look up y=-2x+2 it decreases

Answer:

5. ABC and XYZ

Step-by-step explanation:

matching angle values

Answer:

it would be 748 feet, sorry if im worng!

The line x - y = 0 bisects the line segment. To prove that the line x - y = 0 bisects the line segment joining the points (1, 6) and (4, -1), we need to show that the line x - y = 0 passes through the midpoint of the line segment.

To prove that the line x - y = 0 bisects the line segment joining the points (1, 6) and (4, -1), we need to show that the line x - y = 0 passes through the midpoint of the line segment.
The midpoint of the line segment joining the points (1, 6) and (4, -1) can be found using the midpoint formula. This formula states that the coordinates of the midpoint of a line segment with endpoints (x1, y1) and (x2, y2) are:
Midpoint = ((x1 + x2)/2, (y1 + y2)/2)
Using this formula, we find that the midpoint of the line segment joining (1, 6) and (4, -1) is:
Midpoint = ((1 + 4)/2, (6 + (-1))/2) = (2.5, 2.5)
Therefore, the midpoint of the line segment is (2.5, 2.5).
Now we need to show that the line x - y = 0 passes through this midpoint. To do this, we substitute x = 2.5 and y = 2.5 into the equation x - y = 0 and see if it is true:
2.5 - 2.5 = 0
Since this is true, we can conclude that the line x - y = 0 passes through the midpoint of the line segment joining (1, 6) and (4, -1). Therefore, the line x - y = 0 bisects the line segment.

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Answer: The youngest age yolanda's daughter can be is 24 years old.

The youngest age of Yolanda's daughter is 23 years if Yolanda is 4 years younger than 3 times her daughter's age. The sum of their ages is greater than 88.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

Yolanda is 4 years younger than 3 times her daughter's age. The sum of their ages is greater than 88.

Let the age of Yolanda's is y and

The age of the Daughters is x

From the data given we can frame two linear equations in two variables as follows:

y = 3x - 4

x + y = 88

After solving the above two equations using the substitution method:

x + (3x-4) = 88

x + 3x - 4 = 88

4x = 92

x = 92/4

x = 23

y = 88 - 23 = 65

Thus, the youngest age of Yolanda's daughter is 23 years if Yolanda is 4 years younger than 3 times her daughter's age. The sum of their ages is greater than 88.

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The solution and the answer are in the photograph.

Answer:

VW = 44

Step-by-step explanation:

the line VX is parallel to ZY and intersects the other 2 sides of the triangle then it divides those sides proportionally , that is

\(\frac{ZV}{VW}\) = \(\frac{YX}{XW}\) ( substitute values )

\(\frac{22}{VW}\) = \(\frac{18}{36}\) = \(\frac{1}{2}\) ( cross- multiply )

VW = 2 × 22 = 44

Answer:

B. 1.32 h : 1 point 3 2 h

Step-by-step explanation:

Year 1 = h hits

Year 2 = 132 % of the hits it received the first year

Number of hits the company's website received the 2nd year = 132% of h

= 132/100 × h

= 1.32 × h

= 1.32h

A. 1 + 0.32h : 1 plus 0 point 3 2 h,

B. 1.32 h : 1 point 3 2 h,

C. ( 1 + 1.32 ) h : open paren 1 plus 1 point 3 2 close paren times h,

D. h + 1.32 h : h plus 1 point 3 2 h,

Answer:

There are 3 Types of triangle . Equilateral , Scalence Isosceles triangle.

Step-by-step explanation:

There are 3 Types of triangle .It is given above.

Answer:

scalene triangle, Isosceles Triangle, Equilateral Triangle

The ∛-(8/4913) = -2/17 because -2/17 × -2/17 × -2/17 = -8/4913

From the question, we are to explain why the cube root of -8/4913 is equal to -2/17

Cube root of a number is a value which when multiplied by itself thrice or three times produces the original value.

Thus,

We will determine the number which when multiplied by itself three times gives -8/4913

First, we will determine the cube root of -8.

The cube root of -8 is -2.

This is because -2 × -2 × -2 = -8

Now, we will determine the cube root of 4913.

The cube root of 4913 is 17.

This is because 17 × 17 × 17 = 4913

∴  -2/17 × -2/17 × -2/17 = -8/4913

Hence,

The reason ∛-(8/4913) = -2/17 is explained above

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Answer:

Surface area = 972 mm^2

Step-by-step explanation:

One of the formula we can use for surface area of a triangular prism is

SA = bh + L(s1 + s2 + s3), where

In the figure, the base (b) is 27 mm, the height (h) is 14 mm, the length (L) is 9 mm, and we can use 18, 27, and 21 for s1, s2, and 23:

SA = 27 * 14 + 9(18 + 27 + 21)

SA = 378 + 9(66)

SA = 378 + 594

SA = 972 mm^2

Thus, the surface area of the figure is 972 mm^2

Answer:

3 + 2k

Step-by-step explanation:

1/5(15+10k)

distribute

1/5 * 15 + 1/5 * 10k

3 + 2k

Answer:

3 + 2k

Step-by-step explanation:

First, I am going to explain what the distributive property is. Lets say he had the expression a(b + c). We can "distribute" the a to the b and c:

a(b + c) = ab + ac

We can apply the distributive property to the expression 1/5(15 + 10k):

1/5(15 + 10k)

= (1/5)(15) + (1/5)(10k)

= 3 + 2k

By using the distributive property, we found the expression 3 + 2k.

I hope you find my answer helpful.

AO in terms of P and/or Q is OA = Q = Q

OB in terms of P and/or Q is OB = P =Q

EB in terms of P and/or Q is EB = 2P =2Q

A hexagon, also known as a sexagon, is a six-sided polygon that forms the shape of a cube in geometry. Any basic hexagon has a total internal angle of 720°.

In a regular hexagon, all sides are equal

Which means:

AB= BC

5p + q -5p = 6p-5p

q = p

So, every side of the hexagon is p = q

Which means that AB = BC = CD = DE = EF = FA = p =q

Recall that at the center, each side forms an angle

There are six sides in a hexagon.

Total angle = 360°

6x= 360°

x= 60°.

By the symmetry of regular hexagon, OA = OB

<OAB = <OBA

<AOB = x = 60°

Sum of all angles in a triangle is 180°

We add the values

<OAB = 60°.

<OAB is an equilateral triangle, thus every side is equal

Hence,

a. OA = Q = Q

b. OB = P =Q

c. EB = 2P =2Q.

From the figure, <BOE= 180° which makes it a straight line.

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To maintain the current capital structure, $6.67 million of the new investment must be financed by common equity.The total market value of Tysseland Company is $80 million, and the new investment is $10 million.

To maintain the capital structure, we need to find the portion financed by common equity. First, calculate the portion financed by debt:

Debt portion = Total market value - Common equity portion

Debt portion = $80 million - Common equity portion

Next, calculate the coupon payment on new bonds:

Coupon payment = New investment * Coupon rate

Coupon payment = $10 million * 7%

= $0.7 million

Since the new bonds are sold at par, the debt portion financed by new bonds is equal to the coupon payment:

Debt portion financed by new bonds = $0.7 million

Now, we can set up an equation to find the common equity portion:

$80 million - Common equity portion = $0.7 million

Common equity portion = $80 million - $0.7 million

= $79.3 million

Finally, subtract the existing common equity from the common equity portion to find the portion financed by common equity:

Portion financed by common equity = Common equity portion - Existing common equity

Portion financed by common equity = $79.3 million - $80 million = -$0.7 million .To maintain the current capital structure, $6.67 million of the new investment must be financed by common equity. The WACC cannot be determined without information on the cost of equity and the cost of debt.

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Answer:

20 feet

Step-by-step explanation:

Using Pythagoras rule:

25^2 - 15^2

625 - 225

400

√400 = 20 feet