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Question 14
Martha is standing 90 feet away from a tree and is flying a kite, which gets caught in the top of a tree. She is holding the string so that it makes a 44º angle of elevation with the ground. Estimate the length of
the string to the nearest whole foot

The sample is baised.

Since all the students who attended the football game will most likely want a football stadium to be built and those that do no want a stadium to be built are not proportionately represented in this sample

Answer:

3a is y=-3x-5 and 3b is y=-2x+13

Step-by-step explanation:

I also poster picture on how I found this out

Hope this helped

Answer:

bonds=22000

stock=4000

Step-by-step explanation:

let b  for bonds , and s for stock

b+s=26000

0.05 b +0.08 s=1420

to solve (by elimination)

1- multiply first equation with 0.05 to eliminate b

0.05 b+0.05 s=1300

0.05b+0.08s=1420

subtract two equations:

0.05b+0.05s-0.05b-0.08s=1300-1420

-0.03s=-120

s=120/0.03=4000

b+s=26000

b=26000-4000=22000

check:0.05(22000)+0.08(4000)=1420

Answer:

$22000

Step-by-step explanation:

x*0.05+(26000-x)*0.08= 1420

0.05x - 0.08x + 2080= 1420

0.03x=2080 -1420

0.03x= 660

x= 660/0.03

x= 22000

$22000 = 5% bonds

$4000 = 8% stocks

Given data:

The diameter of the cut sphere, D=14 in.

The radius of the cut sphere is,

The cut sphere is called a hemisphere.

The surface area of a sphere is

So, the lateral surface area of a hemisphere is half the surface area of sphere. Therefore, the lateral surface area of a hemisphere is,

The hemisphere has a lateral surface and a circular surface. The area of the circular surface is,

Therefore, the total area of the hemisphere is,

The total surface area of a hemisphere is,

Therefore, the total surface area of the cut sphere is 461.8 square inches.

Answer:

4n

Step-by-step explanation:

4mn + 3m + 8n + 6

=4n(m+2)+3(m+2)

=(m+2)(4n+3)

Answer:

-7/4

Step-by-step explanation:

(-1,2) (3,-5)

x1 y1 x2 y2

-5-2=-7

3-(-1)=4

-7/4

The student's final moment of inertia is 18.18 kgm².

The moment of inertia of an objecr is the property of an object which shows its ability to rotate.

Since a student is standing with her arms outstretched, on a platform that is rotating at 1.6 rev/s. She pulls her arms in and the platform now rotates at 2.2 rev/s. Her original moment of inertia (I0) is 25 kgm². To find the r final moment of inertia, we use the law of conservation of angular momentum.

The law of conservation of angular momentum states that for any rotation, angular momnetum is constant.

So, Iω = constant where

So, Iω = I'ω' where

Making I' subject of the formula, we have that

I' = Iω/ω'

So, substituting the values of the variables into the equation, we have that

I' = Iω/ω'

I' = 25 kgm² × 1.6 rev/s ÷ 2.2 rev/s

= 40 kgm²rev/s ÷ 2.2 rev/s

= 18.18 kgm²

So, the final moment of inertia is 18.18 kgm².

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Answer:

52

Step-by-step explanation:

If ABCD ~ EFGH

AND AB = 15 and EF = 18 and ABCD = 40

then

each side of ABCD should be 3cm less then side of EFGH

AB + BC + CD + DA = 40

AB + 3 + BC + 3 + CD +3 + DA + 3= P(EFGH)

40+12 = 52 = P(EFGH)

The ball will fall 35d after 5t seconds.

Equation Of Motion is used to define the basic concept of motion of object at various interval of times.

There are three equation of motion

\((i) v=u+at\\ \\ (ii) s=ut+\frac{1}{2} at^{2} \\ \\ (iii)v^{2}=u^{2} +2as\)  (where s=distance, v=final velocity, u=initial velocity ,t=time,          a=acceleration)

According to the given question

Given distance = d

time=t

Acceleration a=g( gravity)

Using second equation of motion

\(d=ut+\frac{1}{2} at^{2}\)     ( given u=0 as the ball was at rest, a=g , s=d)

\(d=\frac{1}{2} gt^{2}\)........(1)

Using first equation of motion

Speed after t sec

\(v=u+at\\ \\ v=0+gt\\ \\ v=gt\)    ....... (2)

Using second equation of motion distance after 5t seconds

since ball is moving with velocity "v", t=5t.

\(s=ut+\frac{1}{2} at^{2}\\ \\ d=v(5t)+\frac{1}{2} g(5t)^{2}\)

Substituting the value v=gt from equation (2)

\(d=(gt)(5t)+\frac{1}{2} g(5t)^{2}\\ \\ =5gt^{2} +\frac{1}{2} g(5t)^{2}\)taking LCM as 2 and solving further we get

\(=35(\frac{1}{2}gt^{2} )\)    

using equation (1) we get

=35d

Therefore , The ball will fall 35d after 5t seconds.

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If two lines intersect, then the vertical angles formed must be both equal in measure.

The  intersection of a line can be described as when two or more lines cross each other in a plane as a result of this they are been referred to as   intersecting lines.

Therefore, intersecting lines share a common point, hence , If two lines intersect, then the vertical angles formed must be both equal in measure.

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Answer:

x = 80

Step-by-step explanation:

This shape is a pentagon, and all of the angles in a pentagon always add up to 540. So, using this, we can create an equation, 3x + 300 = 540. we can then use the reverse order of operations to solve this, first subtracting 300 from both sides. this gets us the equation 3x = 240. We then divide 3 from both sides to get x alone and get x = 80.

Answer:

  x = 80°

Step-by-step explanation:

You want the value of x given a pentagon with two angles marked with expressions in x.

The sum of interior angles in an n-gon is 180° × (n -2). For the 5-sided figure shown, the sum of angles is 180° × 3 = 540°.

Using this value, we have ...

  (x +40°) +125° +(x +5°) +(x +50°) +80° = 540°

  3x +300° = 540° . . . . . . simplify

  x +100° = 180° . . . . . . . divide by 3

  x = 80° . . . . . . . . . . . . subtract 100°

The value of x is 80°.

Answer:

This is your answer ☺️

The ratio of the error is; 0.3333

The Percent error of the given problem is;  33.33%

We are given;

Amount spent by John on shopping = $75

Amount expected to spend = $100

Since this is what was given then it means we will have the following;

The approximate value to be spent = 100 dollars

Exact Value  spent = 75 dollars

Therefore, the error made is;

Error = Approximate value - Exact value  

Error = 100 - 75

Error =  25 dollars

Thus, the error when it is absolute is;

Absolute Error = ±25 dollars

Now, the ratio will be;

Ratio(e) = Error/exact value spent

e = 25/75 = 0.3333

Percent Error = error * 100%

Percent error = 0.3333 * 100%

Percent error =  33.33%

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Answer: 363

Step-by-step explanation:

First you’d do 11 X 11=121 divide by 2 and get 60.5 X 4 (Because there are for triangle sides) and get 242 plus the rectangular base 11X11=121+242=363

The T(V) using the follwing properties is:D. x

To find T(v), where T is a linear transformation from P₂ (polynomials of degree 2 or less) to P₃ (polynomials of degree 3 or less), we can use the properties given:

T(x²) = x³

T(x + 1) = 0

T(x - 1) = x

First, we can express the polynomial v = x² + x + 1 in the standard basis for P₂, which is {1, x, x²}. We can write v as a linear combination of the standard basis polynomials:

v = 1 * 1 + 1 * x + 1 * x²

Now, we can apply the linear transformation T to each term separately, using the given properties:

T(1) = 0 (since T(x + 1) = 0)

T(x) = T(x - 1 + 1) = T(x - 1) + T(1) = x + 0 (using T(x - 1) = x and T(1) = 0)

T(x²) = x³ (using T(x²) = x³)

So, we can write T(v) as:

T(v) = 0 + x + x³ = x + x³

Therefore, the correct choice for T(v) is (d) x.

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Answer:

-24x²

Step-by-step explanation:

remove the parentheses, multiply the numbers, apply exponent rule and add the numbers

Answer:

Step-by-step explanation:

do 5 divided by 4/9 to equal 45/4 icing is remaining

the maximum height of a quadratic equation can be find Use the formula: x = -b / (2a) then Substitute the value of x back into the quadratic equation to find the corresponding maximum height.

To find the maximum height of a quadratic equation, you need to determine the vertex of the parabolic curve. The vertex represents the highest or lowest point of the quadratic function, depending on whether it opens upward or downward.

A quadratic equation is generally written in the form of y = ax² + bx + c, where "a," "b," and "c" are coefficients.

The x-coordinate of the vertex can be found using the formula: x = -b / (2a). This formula gives you the line of symmetry of the parabola.

Once you have the x-coordinate of the vertex, substitute it back into the original equation to find the corresponding y-coordinate.

The resulting y-coordinate represents the maximum height (if the parabola opens downward) or the minimum height (if the parabola opens upward) of the quadratic equation.

Here's an example:

Consider the quadratic equation y = 2x² - 4x + 3.

1. Identify the coefficients:

a = 2

b = -4

c = 3

2. Find the x-coordinate of the vertex:

x = -(-4) / (2 * 2) = 4 / 4 = 1

3. Substitute x = 1 back into the equation to find the y-coordinate:

y = 2(1)² - 4(1) + 3 = 2 - 4 + 3 = 1

Therefore, the maximum height of the quadratic equation y = 2x² - 4x + 3 is 1.

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The maximum height of a quadratic equation can be found by determining the vertex of the parabolic shape represented by the equation. The x-coordinate of the vertex can be found using the formula x = -b / (2a), and the corresponding y-coordinate represents the maximum height.

To find the maximum height of a quadratic equation, we need to determine the vertex of the parabolic shape represented by the equation. The vertex is the point where the parabola reaches its highest or lowest point.

The general form of a quadratic equation is ax^2 + bx + c, where a, b, and c are constants. To find the x-coordinate of the vertex, we can use the formula x = -b / (2a).

Once we have the x-coordinate, we can substitute it back into the equation to find the corresponding y-coordinate, which represents the maximum or minimum height of the quadratic equation.

Let's take an example to illustrate this process:

Suppose we have the quadratic equation y = 2x^2 + 3x + 1. To find the maximum height, we first need to find the x-coordinate of the vertex.

Using the formula x = -b / (2a), we can substitute the values from our equation: x = -(3) / (2 * 2) = -3/4.

Now, we substitute this x-coordinate back into the equation to find the y-coordinate: y = 2(-3/4)^2 + 3(-3/4) + 1 = 2(9/16) - 9/4 + 1 = 9/8 - 9/4 + 1 = 9/8 - 18/8 + 8/8 = -1/8.

Therefore, the maximum height of the quadratic equation y = 2x^2 + 3x + 1 is -1/8.

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On 21st day of the month will she have 40 sweets left given that on 1st November Joan had 200 sweets in a box, she eats no sweets the first day and she eats 8 sweets per day from the box thereafter. This can be obtained by the formula of arithmetic sequence formula.

The arithmetic sequence formula of nth term of the sequence a, a+d, a+2d... is,

⇒ aₙ = a + (n - 1)d,

where a is the first term, d is the common difference and d = aₙ - aₙ₋₁

Here in the question it is given that,

We have to find that on what day of the month will she have 40 sweets left.

From the given data we can write that,

⇒ Day 1 = 200 sweets

⇒ Day 2 = 192 sweets (8 sweets are eaten)

⇒ Day 3 = 184 sweets (8 sweets are eaten)

...

⇒ Day n = 40 sweets

Thus we can form an arithmetic sequence

⇒ 200, 192, 184,...,40 is an arithmetic sequence.

Here, first term = a = 200

Common difference = d = 192 - 200 ⇒ d = -8

By using the formula, nth term will be,

⇒ a + (n - 1)d = 40

⇒ 200 + (n -1)(-8) = 40

⇒ 200 - 8n + 8 = 40

⇒ 208 - 8n = 40

⇒ 8n = 208 - 40

⇒ 8n = 168

⇒ n = 168/8

⇒ n = 21

Hence on 21st day of the month will she have 40 sweets left given that on 1st November Joan had 200 sweets in a box, she eats no sweets the first day and she eats 8 sweets per day from the box thereafter.

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∠ 1 and ∠ 2 are consecutive angles, the measures are 78° and 102° respectively and converse of consecutive angles theorem will prove the oars parallel.

A pair of angles formed on each side of the transversal when it interacts with two parallel lines are known as consecutive angles. The angles in the same region (either interior or exterior) on each of the parallel lines form consecutive angles pairs and are supplementary.

Given that, in a race, all members of a rowing team should keep the oars parallel to produce maximum speed, and m∠1 = 6x + 18 and

m∠2 = 9x+12, and x = 10.

Putting the value of x, we get,

m∠1 = 6x + 18 = 6*10 + 18 = 78°

m∠2 = 9x+12 = 9*10 + 12 = 102°

m∠1 + m∠2 = 180°

Therefore, ∠1 and ∠2 are consecutive angles pairs.

We can prove that oars are parallel by converse of consecutive angles theorem.

Hence, ∠ 1 and ∠ 2 are consecutive angles, the measures are 78° and 102° respectively and converse of consecutive angles theorem will prove the oars parallel

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The graph on the right depicts the linear function y=2x.

Linear function graph is a straight line that depicts linear function y = f(x) = mx + k. It tells the dependent variable y changes by a constant amount as the independent variable x also changes by a constant amount. Whilst variable k is the y-intercept.

The slope of the graph, m, is determined by:

m = (y₂-y₁) / (x₂-x₁)

We are given two graphs. The left graph depicts the line y=x. We want to know what the right graph depicts.

Firstly, we pick two random points on the left graph to find the slope of the graph. Let's say we pick (1,2) and (5,10).

m = (y₂-y₁) / (x₂-x₁)

   = (10-2) / (5-1)

   = 8 / 4

   = 2

Then we find the y-intercept (k), the point where the graph intersects the y-axis. Its value is 0.

Now we put the value of m and k into the linear function:

y = f(x) = mx + k

           = 2x + 0

           = 2x

Thus, the graph on the right shows the line y=2x

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Answer:

3/4

Step-by-step explanation:

you would get 6/8 but need to simplfiy to 3/4 since they both can divide by 2

Answer:

slope = \(\frac{3}{4}\)

Step-by-step explanation:

Calculate the slope m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (- 4, - 2) and (x₂, y₂ ) = (4, 4) ← 2 points on the line

m = \(\frac{4-(-2)}{4-(-4)}\) = \(\frac{4+2}{4+4}\) = \(\frac{6}{8}\) = \(\frac{3}{4}\)

Answer:

The answer would be C

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

\(\sqrt{\dfrac{36}{25}}=\sqrt{\dfrac{6^2}{5^2}}=\dfrac{6}{5}\)

Therefore, the correct answer is choice C. Hope this helps!

Answer:

1. 7.5

2. 0.75

3. 0.075

4. 0.375

Step-by-step explanation:

Yw, and have a good day to everyone who reads this <3 :)

The length of Adrianna's bedroom that has a perimeter of 90 feet and a width of 15 feet is 30 feet.

To find the length of Adrianna's bedroom, we can use the formula for the perimeter of a rectangle:

P = 2l + 2w

where P is the perimeter, l is the length, and w is the width.

We are given that the perimeter is 90 feet and the width is 15 feet, so we can substitute those values into the formula:

90 = 2l + 2(15)

Simplifying:

90 = 2l + 30

Subtracting 30 from both sides:

60 = 2l

Dividing both sides by 2:

30 = l

Therefore, the length of Adrianna's bedroom is 30 feet.

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To prove that the triangles are similar by the SSS (Side-Side-Side) similarity theorem, the corresponding sides of the triangles MN and SR must be proportional to each other.

In the SSS similarity theorem, for two triangles to be similar, all three pairs of corresponding sides must be proportional. In the given scenario, we have triangles MN and SR. To establish similarity using the SSS theorem, we need to compare the lengths of the corresponding sides of these triangles.

We are given that MN is proportional to SR, and based on the information provided, we can conclude that QR is proportional to NO.

However, we don't have information about the third pair of sides, which is MN and QR, to establish similarity using the SSS theorem. Therefore, we cannot prove the similarity of these triangles solely based on the given information.

To prove the similarity of triangles MN and SR using the SSS similarity theorem, we also need to compare the lengths of the remaining pair of corresponding sides, MN and QR. Without that information, we cannot establish similarity solely based on the provided sides and angles.

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There are no perfect cubes between 4^3 = 64 and 5^3 = 125. Therefore, no full m-ary tree with 84 leaves and height 3 exists.

We can show that no full m-ary tree with 84 leaves and height 3 exists as follows:

A full m-ary tree with height 3 has 1 + m + m^2 nodes (including the root). If we let the number of leaves be L, then we have:

L = m^3

Since we want L = 84, we need to find a positive integer m such that m^3 = 84. However, this equation has no integer solutions. To see this, we can note that 84 is not a perfect cube, and we can check that there are no perfect cubes between 4^3 = 64 and 5^3 = 125. Therefore, no full m-ary tree with 84 leaves and height 3 exists.

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Answer: Let's solve this problem step by step.

First, let's assume the salaries of An and B to be 5x and 3x, respectively, where x is a common multiplier.

According to the given information, they save Rs. 2600 and Rs. 1800, respectively. Since savings come from the remaining portion of their incomes after spending, we can calculate their expenditures as follows:

For An:

Income of An = Salary of An + Savings of An

Income of An = 5x + 2600

For B:

Income of B = Salary of B + Savings of B

Income of B = 3x + 1800

Now, let's consider the proportion of their expenditures. It is given that the proportion of their expenditures is 9:5. So, we can write the following equation:

(Expenditure of An)/(Expenditure of B) = 9/5

Since expenditure is the complement of savings, we have:

[(Income of An - Savings of An)] / [(Income of B - Savings of B)] = 9/5

Substituting the previously derived expressions for income, we get:

[(5x + 2600 - 2600)] / [(3x + 1800 - 1800)] = 9/5

Simplifying the equation, we have:

5x / 3x = 9/5

Cross-multiplying, we get:

5 * 3x = 9 * 3x

15x = 27x

Subtracting 27x from both sides, we have:

0 = 12x

This implies that x = 0, which is not a valid solution. Therefore, there seems to be an error or inconsistency in the given information or equations. Please recheck the problem statement or provide additional information to help resolve the issue.

Answer:

24

Step-by-step explanation:

8(5-2)   (insert x=5 , y=2)

8(3)

24