A tree casts a shadow 21 m long. The angle of elevation of the sun is 51. What is the height of the tree?
13.2m
25.9 m
17m
16.3m

Answer:

Price of a notepad in terms of k ⇒ (k - 8)/4

Step-by-step explanation:

Let the price of a notepad be n.

8 + 4n = k

In order to get the answer, we've to make n as the subject of the above equation.

8 + 4n = k

4n = k - 8

n = (k - 8) / 4

Answer:

Brand A is the better buy.

Step-by-step explanation:

A:

$4.59/40 = $0.11475

B:

$3.99/30 = $0.133

Brand A:

$0.11 per bag

Brand B:

$0.13 per bag

Brand A is the better buy.

Answer:

\(71.43\)

Step-by-step explanation:

\(5 b+ 2 b\geqslant 500 \\ 7b \geqslant 500 \\ \frac{7b}{7} \geqslant \frac{500}{7} \\ b \geqslant 71.43 \\ \)

\( b= 71.43 < \infty \)

answer:

Step-by-step explanation:

1250 plus 0.25 equals 1250.25 plus 1250.25 plus 3200 equals 4450.25 plus 0.10 equals 4450.35

Answer:

y = 200

Step-by-step explanation:

Use the equation y = kx, where k is a constant.

Plug in the given x and y values, then solve for k:

y = kx

20 = k(8)

2.5 = k

Then, plug in k and the given x value, and find y:

y = 2.5x

y = 2.5(80)

y = 200

So, y = 200 when x = 80

Answer:

30mph

Step-by-step explanation:

The magnitude of the car's acceleration is 2.45 m/\(\rm sec^2\) and this can be determined by using the equation of kinematics.

Given :

According to the kinematics:

\(\rm v = u + at\)     --- (1)

where v is the final speed, u is the initial speed, a is the acceleration and t is time.

Now, put the known terms in equation (1).

0 = 7 + at

at = -7  

\(\rm t = -\dfrac{7}{a}\)      --- (2)

From the kinematics the displacement is given by the equation:

\(\rm S =ut+\dfrac{1}{2}at^2\)

Now, put the values of u, S, and t in the above equation.

\(10=7\times \dfrac{-7}{a}+\dfrac{1}{2}\times a \times \dfrac{49}{a^2}\)

Now, simplify the above equation.

\(10=-\dfrac{49}{a}+\dfrac{49}{2a}\)

20a = -49

a = -2.45

So, the magnitude of the car's acceleration is 2.45 m/\(\rm sec^2\).

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Answer:

Yes, there are exactly 2 ways to solve this triangle.

Step-by-step explanation:

Well we know that to find out a trigonometric ratio we are given an angle and a side, and we have to solve for the other side. In this case only 2 of the legs are given, hypotenuse is neither given nor asked. So we have to use the ratio that doesn't have hypotenuse included. Tangent is the only such ration. Now we can use either Tan(51) or Tan(39) to solve for the "x".

These would be the functions to solve for x:

1.)     Tan(51) = \(\frac{x}{10}\)

2.)    Tan (39) = \(\frac{10}{x}\)

Hope this helps!

Answer:

y = 1.5x(or d) + 8

Step-by-step explanation:

1.5 is the slope and 8 is the y intercept(the constant term)

Answer:

-60

It is -60 because if it takes away 6 points for each cone you hit and you hit 10, then it would be -60 times 10, which equals -60.

Answer:

2) Acute triangle, isosceles

3) Both are 65 degrees

4) (diagram)

5) a) both 25 degrees

b) midpoint

Step-by-step explanation:

2) If you're struggling search up "draw a triangle" and you'll find a website that will draw it for you. It will help you get an idea of it looks like and its nature.

3) We know that sides AB and AC are 5cm. So this triangle is an isosceles which makes the 2 remaining angles equal (if you draw a diagram it will be clear)

So:

180-50/2 = 65

ABC and ACB = 65 degrees each

4) Construct the line AH down the middle like in the diagram I drew.

5) a) Since AH is a straight line, we know that the angle AHB will be 90 degrees. After question 3 we also know that angle ABH is 65 degrees.

BAH = 180-90-65

BAH = 25 degrees

CAH = 50 - 25

CAH = 25 degrees

b) AH is the midpoint for BAC because the 2 segments formed are both 25 degrees.

Answer:The inverse is 3.3x

Step-by-step explanation:

Answer:

x times 10

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3

Step-by-step explanation:

A function g is the incerse of function f if y=f(x), x=g(y)

Answer:

1. 6 + 45 -10 = 41 2. -20 - 20 - 10 = -50 3. 40 4. -18 - 15 + 10 = -23

Step-by-step explanation:

adding/multiplying a negative and a negative = a positive

The sum of the sequence based on the function Sn = ( -1 )n + 1 will be -6.

The formula for finding the nth term in an arithmetic sequence given as:

= a + (n - 1)d

Here, Sn is given as ( -1 )n + 1. This is used to illustrate the sum in the sequence. Based on the function given, let's assume that n = 5. Therefore, the 5th term will be:

= (-1)n + 1

= (-1)5 + 1

= (-1)6

= -6

Here is the complete question:

Find the 5th term of a sequence given the function Sn = ( -1 )n + 1.

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Answer:

y = 5/4x - 8

Step-by-step explanation:

first you convert the equation to y = mx + b

then you add the the -8 into the x and the 2 into the y and solve for b

b = -8 and since it is parallel same slope.

hope this helps :)

2 cups you need to fill the jug to 4.

The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.

It depends on the size and markings of the jug.

If we assume that the jug is divided into equal intervals and each interval represents an equal volume,

then we can say that filling the jug to the second interval means that the jug is 1/2 full.

To fill the jug to the fourth interval, we need to fill the remaining 2 intervals, which means we need to add another 2 cups of liquid.

So, the answer is 2 cups.

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The angles in the parallel lines are as follows;

When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate interior angles, alternate exterior angles, linear angles, vertically opposite angles etc.

Therefore, let's find the angles m∠1 and m∠2.

Hence,

138 + m∠1 = 180(angles on a straight line)

The sum of angles on a straight line is 180 degrees.

m∠1 = 180 - 138

m∠1 = 42 degrees

Therefore,

m∠1 =  m∠2 (alternate exterior angles)

Alternate exterior angles are the pair of angles that are formed on th outer side of the parallel lines but on the opposite side of the transversal.

Alternate exterior angles are congruent.

Therefore,

m∠1 =  m∠2 = 42 degrees.

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Using compound interest formula, her balance after retirement is $430797.77

To calculate the balance of Marissa's retirement account after 30 years, we need to determine how much her savings account and index fund will be worth after 30 years, taking into account the interest earned and her monthly contributions.

First, we'll calculate the balance of her savings account:

Initial deposit: $2000

Interest rate: 1.5%

Monthly contribution: $150

Number of months: 30 years * 12 months/year = 360 months

Using the compound interest formula, the balance of her savings account after 30 years will be:

2000*(1+0.015/12)^360 + 150*(((1+0.015/12)^360-1)/(0.015/12))

A = $71280.33

Next, we'll calculate the balance of her index fund:

Initial deposit: $1000

Interest rate: 6.8%

Monthly contribution: $300

Number of months: 30 years * 12 months/year = 360 months

Using the compound interest formula, the balance of her index fund after 30 years will be:

A = 1000*(1+0.068/12)^360 + 300*(((1+0.068/12)^360-1)/(0.068/12))

A = $359517.44

Then we can add the balance of both the savings account and the stock market to get the total balance of Marissa's retirement account.

Her balance = $71280.33 + $359517.44 = $430797.77

Please note that the above answer is an estimation, in reality there are other factors such as taxes, inflation, fees, and market conditions that should be considered in a real-world scenario.

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Answer:

127 degree

Step-by-step explanation:

because angle 6 is alternate to 127 degree. Alternate makes a=b which is angle 6 is equal to 127 degree

Step-by-step explanation:

the slope if the equation will be -8

Answer:

1-(4×z) is the expression

Answer:

1 - 4z

Feel free to mark this as brainliest :D

The given differential equation is a third-order linear homogeneous equation.

According to the Existence and Uniqueness Theorem, a unique solution exists if the coefficients of the differential equation are continuous on the given interval, which is the case here. Since the initial conditions y″(0) = 2, y'(0) = 1, and y(0) = 0 are also given, the existence and uniqueness of a solution are guaranteed by the theorem. Therefore, the given differential equation is guaranteed to have a unique solution on the specified interval. A differential equation is an equation that relates a function to its derivatives (or differentials) of one or more independent variables. In other words, it expresses a relationship between an unknown function and its rate of change.

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The complete question is :

According to the Existence and Uniqueness Theorem, which of the following differential equations are guaranteed to have a unique solution on the specified interval. Explain your reasoning.

x2d3ydx3-4x-1d2ydx2+3dydx+2y=0,y″(0)=2,y'(0)=1,y(0)=0

Answer:

\(6x^2-1y+5+18x\)

Step-by-step explanation:

\(7x^2+2y-x^2+18x+5-3y\)

\(6x^2-1y+5+18x\)

Answer:

C

Step-by-step explanation:

444.50 * 6.5% = 28.89

444.50 + 28.89 = 473.39

Answer:

4.7x10 equals 47, the decimal moves to the right one time

The Fallacy mentioned in the arguments is the accident fallacy.

Fallacies are common crimes in logic that will undermine the sense of your argument. Fallacies can be moreover illegitimate arguments or inapplicable points and are frequently linked because they warrant substantiation that supports their claim.

Logical fallacies make an argument weak by using incorrect beliefs ideas, invalid arguments, fallacious arguments, and/or deceptiveness. However, avoid fallacies of study because they produce sins in an argument If you're arguing.

An accident fallacy is a logical fallacy, meaning a logical error that weakens the argument being made, in which a conception is applied to a situation where, in reality, it doesn’t apply. It may be committed due to neglectfulness or because one has the supposition that conceptions will apply to all analogous situations, indeed though there are clear exceptions.

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Work accounts for approximately 60° of the pie chart, or 15.48% of the total 360°.

To calculate a pie chart, first, categorize the data and calculate the total.

Each slice of the pie chart represents a numerical value and has a size proportional to the value.

The sum of all the data is equal to 360°, with the total value always being 100%.

To find the percentage for each slice of the pie chart, divide the categories by the total and convert them into percentages.

Finally, calculate the degrees using the formula (Given Data/Total value of Data) × 360°.

For example, let's say we have data on sleep, work, family care, personal care, and leisure, with a total of 168 hours.

To find the percentage for each category, we can use the following calculations:

Therefore, work accounts for approximately 60° of the pie chart, or 15.48% of the total 360°.

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Explanation:

The room is 14 ft by 16 ft.

The floor area is 14*16 = 224 sq ft.

Since oak costs $5.25 per sq ft, this means the total cost of an oak floor is 5.25*224 = 1176 dollars.

Meanwhile, maple flooring will have a total cost of 7*224 = 1568 dollars

If you go with the cheaper option (oak), then the savings is 1568-1176 = 392

----------

Alternative Route:

The difference in per sq ft costs is 7.00-5.25 = 1.75, meaning you save $1.75 per sq ft if you go with the cheaper option.

Multiply this with the total floor area to get 1.75*224 = 392

it's 3817.04 but you round to the nearest tenth

Answer:

Option 4

Step-by-step explanation:

Both the quadrilaterals are similar,

ABCD ~ WXYZ

Therefore, ratio of the corresponding sides will be constant in other words ratio of the corresponding sides will be common.

Scale factor = \(\frac{AD}{WZ}\)

                    = \(\frac{15}{6}\)

                    = \(\frac{5}{2}\)

Therefore, option (4) will be the correct option.