Marcella is flying a kite in a competition. To win the competition, her kite string must have at least 162 feet released. The kite is 75 feet above her. The angle of the string and her hand is forming a 28 degree angle. Will she be able to win the competition? Show your work.


For question 1, will she win the competition? Type yes or no

Answer:

Statement 1 and 2

Step-by-step explanation:

If you take t^2 - 16t + 55 and find some of its graphical values, you will get:

Turning point: (8,-9)

Roots: (5,0) and (11,0)

When this graph is plotted and you imagine the x axis to be time (as stated in the question), each of the roots (x - intercept) must be when the swimmer goes under and when they come back up.

This means that the swimmer dived under the water at 5 seconds and came back up at 9, making the first 2 statements correct.

Now the fourth statement is ruled out.

The fifth statement is not plausible as the graph would have to have more than 2 roots for the swimmer to enter the water twice.

That leaves the third statement. If you imagine the depth of the swimmer to be the y axis of our imaginary graph, and we know that the y axis of the turning point is -9, that means that the swimmer's deepest dive was 9 feet under the water, ruling out the third statement too.

Hope this helps :D

Answer:

[tex]h(t)= (t-5)(t-11)[/tex]

The swimmer comes back up 11 seconds after the timer is started.

The swimmer dives into the water 5 seconds after the timer is started.

Step-by-step explanation:

Given function:

[tex]h(t)=t^2-16t+55[/tex]

To factor a quadratic in the form [tex]ax^2+bx+c[/tex],

find two numbers that multiply to [tex]ac[/tex] and sum to [tex]b[/tex]:

[tex]\implies ac=55[/tex]

[tex]\implies b=-16[/tex]

Two numbers that multiply to 55 and sum to -16 are: -11 and -5

Rewrite b as the sum of these two numbers:

[tex]\implies t^2-11t-5t+55[/tex]

Factorize the first two terms and the last two terms separately:

[tex]\implies t(t-11)-5(t-11)[/tex]

Factor out the common term (t - 11):

[tex]\implies (t-5)(t-11)[/tex]

Therefore, the given formula in factored form is:

[tex]h(t)= (t-5)(t-11)[/tex]

The swimmer's depth is modeled as h(t).  Therefore, when h(t) = 0 the swimmer will be at the surface of the water.

[tex]\implies h(t)=0[/tex]

[tex]\implies (t-5)(t-11)=0[/tex]

[tex]\implies t-5=0\implies t=5[/tex]

[tex]\implies t-11=0 \implies t=11[/tex]

Therefore, the swimmer will be at the surface of the water at 5 s and 11 s.

The swimmer's maximum depth is the vertex of the function. The x-value of the vertex is the midpoint of the zeros.  Therefore, the x-value of the vertex is t = 8.

Substitute t = 8 into the function to find the maximum depth:

[tex]\implies h(8)=8^2-16(8)+55=-9[/tex]

So the swimmer's maximum depth is 9 ft.

True Statements

The swimmer comes back up 11 seconds after the timer is started.

The swimmer dives into the water 5 seconds after the timer is started.

The length of the chord CE is 24.46 in

To find the length of the chord CE, we solve the question using pythagoras' theorem

A chord is a line segment touching two points in a circle.

Pythagoras' theorem states that in any right angled triangle with sides a, b and c where c is the hypotenuse side, we have that

c² = a² + b²

Now form the diagram the radius of the circle BE forms a right angled triangle with the perpendicular to the chord, BO and the midway between the chord, OE.

BO = BD - OD

= 20 in - 5 in

= 15 in

From pythagoras,

BE² = DE² + BO²

making DE subject of the formula, we have

DE = √(BE² - BO²)

DE = √((20 in)² - (15 in)²)

DE = √(400 in² - 225 in²)

DE = √(175 in²)

DE = 13.23 cm

Since the chord CE = 2DE,

So, CE = 2 × 13.23 in

= 26.46 in

So, the length of the chord CE is 24.46 in

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Answer:

See below

Step-by-step explanation:

Each 32 feet of depth is 1 more atmosphere of pressure on the diver  

A graph is a way to represent a lot of data in a visual format. The graph can be drawn as using the equation y=100x+24.

A graph is a way to represent a lot of data in such a visual format that it is easy for the user to understand the complete information in one go. Usually, the line of the graph is a function that follows the graph.

Given a factory-made 424 items in 4 hours at a constant rate. Also, the table is given, therefore, the slope of the line can be written as,

m = (400-300)/(4-3) = 100

Therefore, the equation can be written as y=100x+C

now, substituting the point we will get,

424 = 100(4) + C

424 - 400 = C

C = 24

Therefore, the graph can be drawn as using the equation y=100x+24.

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Answer:

x ≈ 0.5

Step-by-step explanation:

using the tangent ratio in the right triangle

tan63° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{IJ}{JK}[/tex] = [tex]\frac{1}{x}[/tex] ( multiply both sides by x )

x × tan63° = 1 ( divide both sides by tan63° )

x = [tex]\frac{1}{tan63}[/tex] ≈ 0.5 ( to the nearest tenth )

Answer:

x = 0.5

Step-by-step explanation:

We can use tan Θ to find the value of x.

tan Θ = Opposite ÷ Adjacent

Let us solve it now

tan 63 = 1 ÷ x

1.9626 = 1 ÷ x

x = 1 ÷ 1.9626

x = 0.5095

x ≈ 0.5  ( nearest 10th )

Answer: 60 square units

Step-by-step explanation: i hope that helps buddy :)

Answer:

Step-by-step explanation:

jenny spin a fair-4 spinner

The probability that the spinner will land on a or b will be 0.50.

Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.

Then the probability is given as,

P = (Favorable event) / (Total event)

Jenny spins a fair 4-sided spinner.

Let the section be marked as a, b, c, and d.

Then the total number of the event will be given as,

Total events = 4

Then the probability that the spinner will land on a or b will be given as,

P = 1/4 + 1/4

P = (1 + 1)/4

P = 2/4

P = 1/2

P = 0.50

The probability that the spinner will land on a or b will be 0.50.

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Using it's concept, it is found that the correct option regarding whether the relation is a function is given by:

b. Yes, each year is paired with only one value for the birth rate.

It represents a function if each value of the input is mapped to only one value of the output.

In this problem, the inputs are the decades(1950 to 2000), and each has only one rate, hence it is a function and option b is correct.

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Answer:

B and C

Step-by-step explanation:

vertical angles are angles that are opposite of each other when two lines cross. Vertical angles are congruent = they are equally large.

the angles listed in B and C are mirrored across either an imaginary or a directly visible line. and that makes them vertical angles.

Answer:

[tex]x = -2 +2\sqrt 3\\\\x = -2 -2\sqrt 3[/tex]

Step by step explanation:

[tex]~~~~~~x^2 +4x +4 = 12\\\\\implies x^2 +2\cdot 2x + 2^2 = 12\\ \\\implies (x+2)^2 = 12\\\\\implies x +2 = \pm\sqrt{12}\\\\\implies x = -2 \pm\sqrt{12}\\\\\implies x = -2\pm\sqrt{4 \times 3}\\\\\implies x = -2 \pm2\sqrt 3[/tex]

The dimensions of the rectangle will be 4 and 6.

From the information given, we are told that the area is given by x² + 2x - 24. We will expand this as follows:

x² + 2x - 24

x² + 6x - 4x - 24

x(x + 6) + 6(x - 4)

x - 4 = 0

x = 0 + 4

Therefore, the other dimension will be:

= 24/4

= 6

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Reason:

Rewrite the given equation into [tex](x-6)^2 + (y-(-5))^2 = 5^2[/tex]

I changed the y+5 into y-(-5), and also replaced 25 with [tex]5^2[/tex]

Then compare that to the circle template of [tex](x-h)^2 + (y-k)^2 = r^2[/tex]

We see that h = 6 and k = -5 to give a center of (h,k) = (6, -5)

Side note: the radius is r = 5 units

Step-by-step explanation:

please mark me as brainlest

Answer:

-[tex]\frac{17}{3}[/tex]

Step-by-step explanation:

The statement that best describes the end behavior of the graph is given as follows:

As [tex]x \rightarrow -\infty, f(x) \rightarrow -\infty[/tex], and as [tex]x \rightarrow -\infty, f(x) \rightarrow \infty[/tex].

It is given by it's limits as x goes to negative and positive infinity.

From the given table, it is found that f(x) starts with negative values, increases until it's maximum value then decays again, hence the correct statement is:

As [tex]x \rightarrow -\infty, f(x) \rightarrow -\infty[/tex], and as [tex]x \rightarrow -\infty, f(x) \rightarrow \infty[/tex].

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After 10 years, there will be 108 rabbits left in the park.

An exponential function is a function of form f (x) = aˣ, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.

Here, the given equation;

       R = 120 (0.99)ⁿ

where, n is the number of years

n = 10 years (given)

R = 120 (0.99)¹⁰

R = 120 X 0.904

R = 108.52

Thus, After 10 years, there will be 108 rabbits left in the park.

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Answer:

the green box is 0

Step-by-step explanation:

we are asked to find the x-intercept, which means y = 0

(x, y)

Another way to test this is plug it in 1 for x!  (1, y) where x = 1

[tex]y = \frac{2x^{2} -3x+1}{2x^{2} +8x+6} \\\\[/tex]

[tex]y = \frac{2(1)^{2} -3(1)+1}{2(1)^{2} +8(1)+6}[/tex]

[tex]y = \frac{2(1) -3(1)+1}{2(1) +8+6}[/tex]

[tex]y = \frac{2 - 3 + 1}{2 + 8 + 6}[/tex]

[tex]y = \frac{-1+1}{10 + 6}[/tex]

[tex]y = \frac{0}{16}[/tex]

y = 0

So we all know the FORMULA for a sphere is v=4/3 x π x r^3

So, now we SUBSTITUTE ,V=4/3 x π x 7^

This leaves us with the answer of 1436.76 ft ^2 maybe?

(hope this is correct!)

Answer:

Scientific notation: 4 ⋅ 10 -4

expanded form: 0.0004

Answer: is C

Step-by-step explanation: like i said making it easier .

Answer:

Yes, she should have only added the area of five of the six faces.

Step-by-step explanation:

The formula for determining the surface area of a cuboid or box is expressed as

Surface area = 2lw + 2lh + 2wh

Where l, w and h represents length, width and height of the box respectively.

2lw represents the area of the top and the bottom of the box. Since she doesn't want to cover the bottom, it becomes lw. Therefore,

Surface area = 15 + 6 + 6 + 10 + 10 = 47 in².

The cost would be

0.25 × 47 = $11.75

Therefore,

Yes, she should have only added the area of five of the six faces.

Answer: 210

Step-by-step explanation:

      ! means, for example, 6! = 6 * 5* 4 * 3 * 2 * 1

Given:

[tex]\displaystyle \frac{10!}{6!(12-8)!}[/tex]

Subtract:

[tex]\displaystyle \frac{10!}{6!(4)!}[/tex]

Distribute:

[tex]\displaystyle \frac{10!}{6!*4!}[/tex]

Expand:

[tex]\displaystyle \frac{10 * 9 * 8 * 7 * 6 * 5* 4 * 3 * 2 * 1}{(6 * 5* 4 * 3 * 2 * 1)*(4 * 3 * 2 * 1)}[/tex]

Cancel out (6*5*4*3*2*1) in both the top and bottom as they equal 1:

[tex]\displaystyle \frac{10 * 9 * 8 * 7 }{4 * 3 * 2 * 1}[/tex]

Multiply:

[tex]\displaystyle \frac{5,040 }{24}[/tex]

Divide:

210

Answer:

AB and DE are parallel because they have the same slope.

Step-by-step explanation:

Slope of the line AB :

[tex]=\frac{\text{rise} }{\text{run} } =\frac{CA}{-BC} =\frac{12}{-8} =-\frac{3}{2}[/tex]

Slope of the line DE :

[tex]=\frac{\text{rise} }{\text{run} } =\frac{CE}{-DC} =\frac{9}{-6} =-\frac{3}{2}[/tex]

The factor if the root is 2 is x - 2 and the factor if the root is -3 is c + 3

According to the question, we are to find the factors of the polynomial expression

Given the polynomial expression

y = x² + x - 6

Factorize

y = x² + 3x - 2x - 6

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

Hence the factor if the root is 2 is x - 2 and the factor if the root is -3 is c + 3

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Answer:

6.4

Step-by-step explanation:

E bisects side MO, plot it in the center of M and O

MO is 8, split into two even parts, 4 and 4

TE is 5

set up Pythagorean theorem, 5^2 + 4^2 = x^2 to find MT

25+16=x^2

41=x^2

x=6.403

The position of the angles are corresponding angles.

The value of x should be 6 for the slats to be parallel.

The theorem use to prove the parallel slat is the corresponding angle theorem.

The measure of the indicated angles are 42 degrees.

Corresponding angles are the angles that are formed when two parallel lines are intersected by the transversal.

Therefore, the position  of the angles are corresponding angles

Since the angles are corresponding angles, they are congruent.

Therefore,

3x + 24 = 7x

24 = 7x - 3x

24 = 4x

x = 6

The theorem use to prove the postulate is the corresponding  angle theorem.

The measure of the indicated angle can be calculated as follows:

7(6) = 42 degrees.

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Answer:

34/48

Step-by-step explanation:

So to answer this problem, we need to know two things:
1) The number of people who made a purchase
2) The number of people who came into the store

The problem gives us 1), which is 34.
The answer for 2) is 34+14, since that's the total number of people who came into the store. This means that the ratio is 34/48.

The correct value of this equation is m = 24

This equation contains a fractional term. We note that the denominator of this equation is the term 4. Therefore, we will multiply the sides by 4:

13 = m/4 + 7

13 . 4 = 4(m/4) + 7 . 4

52 = m + 28

Now, let's isolate the variable "as negative" and after the equality - we'll be subtracting the terms:

52 = m + 28

-m = 28 - 58

-m = -24

m = 24

Therefore, the correct value of this equation will be m = 24

Answer:

8x+19=9x+9

Step-by-step explanation:

Simplifying

(8x + 19) = (9x + 9)

Reorder the terms:

(19 + 8x) = (9x + 9)

Remove parenthesis around (19 + 8x)

19 + 8x = (9x + 9)

Reorder the terms:

19 + 8x = (9 + 9x)

Remove parenthesis around (9 + 9x)

19 + 8x = 9 + 9x

Solving

19 + 8x = 9 + 9x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-9x' to each side of the equation.

19 + 8x + -9x = 9 + 9x + -9x

Combine like terms: 8x + -9x = -1x

19 + -1x = 9 + 9x + -9x

Combine like terms: 9x + -9x = 0

19 + -1x = 9 + 0

19 + -1x = 9

Add '-19' to each side of the equation.

19 + -19 + -1x = 9 + -19

Combine like terms: 19 + -19 = 0

0 + -1x = 9 + -19

-1x = 9 + -19

Combine like terms: 9 + -19 = -10

-1x = -10

Divide each side by '-1'.

x = 10

Simplifying

x = 10

Answer:

Step-by-step explanation:

8x + 19 = 9x +9

19 - 9 = 9x - 8x

10 = 1x

x = 10

check

-------------------

8 * 10 + 19 = 9 * 10 + 9

80 + 19 = 90 + 9

99 = 99

the answer is good