The game is played on a square court divided into four smaller squares that meet at the center. If a line is drawn diagonally from one corner to another corner, then a right triangle QTS is formed, where _QTS is 45°. Using a trigonometric function, find the length of the
diagonal for a 15-foot square court.The length of the diagonal is about how many feet. (round to nearest tenth)

1) The legs of △ABC are AB and BC.

2) The name of hypotenuse is AC.

3) The legs of △PQR are PR and RQ.

4) The name of hypotenuse is PQ.

5) The legs of △HLM are LH and ML.

6) The name of hypotenuse is MH.

What is a triangle?

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.

The right angle of △ABC is ∠ABC. Thus AB and BC meet at right angle. Therefore AB and BC are legs of △ABC.

The opposite side of ∠ABC is AC. Therefore the hypotenuse is AC.

The right angle of △PQR is ∠PRQ. Thus PR and RQ meet at right angle. Therefore PR and RQ are legs of △PQR.

The opposite side of ∠PRQ is PQ. Therefore the hypotenuse is PQ.

The right angle of △HLM is ∠HLM. Thus HL and LM meet at right angle. Therefore HL and LM are legs of △HLM.

The opposite side of ∠HLM is MH. Therefore the hypotenuse is MH.

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(a) 2.79 seconds after its release the bag will strike the ground.

(b) At a velocity of 73.28 ft/second it will hit the ground.

What is velocity?

We are given that a balloon, rising vertically with a velocity of 16 feet per second, releases a sandbag at the instant when the balloon is 80 feet above the ground.

Assume the acceleration of the object is a(t) = −32 feet per second.

(a) For finding the time it will take the bag to strike the ground after its release, we will use the following formula;

[tex]s=u t+\frac{1}{2} a t^2[/tex]

Here, s= distance of the balloon above the ground =-80 feet

[tex]$\mathrm{u}=$[/tex] intital velocity =16 feet per second

[tex]$\mathrm{a}=$[/tex]acceleration of the object =-32 feet per second

[tex]$\mathrm{t}=$[/tex] required time

So, [tex]$s=u t+\frac{1}{2} a t^2$[/tex]

[tex]$$\begin{aligned}& -80=(16 \times t)+\left(\frac{1}{2} \times-32 \times t^2\right) \\& -80=16 t-16 t^2 \\& 16 t^2-16 t-80=0 \\& t^2-t-5=0\end{aligned}$$[/tex]

Now, we will use the quadratic D formula for finding the value of t, i.e;

[tex]t=\frac{-b \pm \sqrt{D}}{2 a}[/tex]

Here, a=1, b=-1, and c=-5

Also, [tex]$\mathrm{D}=b^2-4 a c=(-1)^2-(4 \times 1 \times-5)=21$[/tex]

So, [tex]$t=\frac{-(-1) \pm \sqrt{21}}{2(1)}$[/tex]

[tex]t=\frac{1 \pm \sqrt{21}}{2}[/tex]

We will neglect the negative value of t as time can't be negative, so;

[tex]t=\frac{1+\sqrt{21}}{2}=2.79 \approx 3 \text { seconds. }[/tex]

Hence, after 3 seconds of its release, the bag will strike the ground.

(b) For finding the velocity at which it hit the ground, we will use the formula;

v=u+a t

Here, v= final velocity

So,[tex]$v=16+(-32 \times 2.79)$[/tex]

v=16-89.28=-73.28 feet per second.

Hence, the bag will hit the ground at a velocity of [tex]$-73.28 \mathrm{ft} / \mathrm{second}$[/tex].

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The answer is true, if radius OP intersects chord AC in point B and AB=8 units, BC=8 units.

The length of the line segments from a circle's center to its perimeter is referred to as the radius of a circle or sphere in more contemporary use. Radius has two possible plurals: the traditional English plural radiuses or radii. R or r is the most common radius abbreviation and mathematical variable name. Consequently, the diameter D is equal to double the radius.

Given,

In circle radius OP intersects chord AC in point B.

And AB=8 units, BC=8 units

So, OP is perpendicular to AC.

Due to the fact that OA and OC have equal sides and a base length of AC, OAC forms a triangle (the radius of the circle)

When you trace AC, you discover that O, a line perpendicular to AC, intersects the circle's center.

So, the answer is true.

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Answer:

x = -2

Step-by-step explanation:

hope this will help you

Nancy can buy maximum 8 video games.

Steps to solve inequality:

The inequality will not change if the coefficient is positive.

The inequality will be the other way around if the coefficient is negative.

If Nancy wants to keep at least $120 in her account and at present, she is having $240

So, she can spend = 240-120= $120

And, one video game price= $15

Let us consider she can buy maximum 'X' games

15×X=$120

X = 8 units

Hence, she can buy a maximum of 8 video games.

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Using the interest rates formula, we know that an automobile that costs $24588.44 is within our means.

The amount of interest due each period expressed as a percentage of the amount lent, deposited, or borrowed is known as an interest rate.

The total interest on a loaned or borrowed sum is determined by the principal amount, the interest rate, the frequency of compounding, and the period of time the loan, deposit, or borrowing took place.

So, let's say the car's affordable price is P:

The entire payback is equal to P r/100 T + P.

In this case, P, r = 4.75, and T = 9 years.

$351,00 = P × (4.75/100 × 9 + 1)

$351,00 = P × ( 0.4275 + 1)

$351,00 = P × 1.4275

P = 351,00 / 1.4275

When you use the division operation, we receive:

P = $24588.44

Therefore, using the interest rates formula, we know that an automobile that costs $24588.44 is within our means.

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Lines with a slope of zero can be thought of as y = 0x + b, which simplifies to just "y = b".

In this case, your equation is y = 16.

If you want to force it explicitly into standard form, you could write it at
   0x + 1y = 16

Answer:

Here,

the length=8x

the width =3y-2

We know that,

Area of rectangle=l×b

or, 8x × 3y-2

8x(3y-2)

24xy-16x

Hence, the correct answer is 24xy-16x

Answer: The correct answer is D, Lines are skew if and only if they are non-coplanar.

In geometry, lines are said to be skew if they are non-coplanar, meaning they do not lie in the same plane. They also do not intersect.

Option A is incorrect because angles can be supplementary (add up to 180 degrees) even if they do not form a linear pair (meaning they do not share a common vertex and a common side).

Option B is incorrect because Valentine's Day does not always fall in February. It is February 14th, but it could fall on a different month in a different year.

Option C is correct because a number is even if and only if it is divisible by 2. An even number can be divided evenly by 2, while an odd number cannot.

Answer:

x = 79

Step-by-step explanation:

To find the value of x we first need to find the missing angle of the triangle in the image.

101 + 29 + missing angle = 180

130 + missing side = 180

missing side = 50

Now, the sum of two interior angles in a triangle is equal to an exterior angle that is supplementary to the third interior angle.

So the value of x:

29 + 50 = 79

Answer:

0.60

Hope this helps, I believe in you!

Answer: The answer is C 0.60

Step-by-step explanation:

We want to study the population formula of a given US state according to exponential equation.

a) 23.1 millions.

b) in 2013 - 2014

What is exponential equation?

The exponential function may be a function denoted by f(x)=\exp or e^. Unless otherwise fixed, the term usually refers to the positive-valued operate of a true variable

Main body:

The population state is:

A = 23.1*e^(0.0153*t)

In millions.

Where t represents the number of years after 2000.

a) For the population at the year 2000, we need to evaluate the function at t = 0 (2000 is 0 years after 2000).

A(0) = 23.1*e^(0.0153*0) = 23.1

The population at year 2000 was 23.1 millions.

b) Now we want to solve:

A(t) = 28.3 = 23.1*e^(0.0153*t)

       28.3/23.1 = e^(0.0153*t)

      1.23 = e^(0.0153*t)

Now we can apply the natural logarithm to both sides:

ln(1.23) = ln( e^(0.0153*t) )

ln(1.23) = 0.0153*t

ln(1.23)/0.0153 = t = 13.5

Hence, 13.5 years after 2000 the population will be 28.3 million.

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The system of equations has infinite solutions, actually, any pair (x, y) is a solution.

To solve a system by elimination, we just need to add/subtract the equations in such a way that we can remove one of the variables.

Here the system of equations is:

-2x-3y = -9

-2x-3y = -9

If we subtract the two equations we will get:

(-2x-3y) - (-2x-3y) = -9 - (-9)

0 = 0

This is a trivial equation, that happens because both equations of the system are the same one.

So the system is true for all real values of x and y.

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Answer:

the digit 1 is less than 5, so we round 54.71 down to 54.7.

Step-by-step explanation:

Answer:

C. DIvide both sides by -6 to get 1/9.

Step-by-step explanation:

Answer:

x=9.8

Step-by-step explanation:

ax + by = 6000 and a + 5 = b are two equations that might be used to calculate how many soup cans and frozen dinners were purchased.

There are several methods to define a formula. A mathematical statement that establishes the equivalence of two mathematical expressions is the definition of an equation in algebra.

This is best shown by the formula 3x + 5 = 14. In this instance, the word equal comes between the phrases 3x + 5 and 14. Even the most basic algebraic equations include the usage of mathematical variables.

Let frozen supper be y and soup cans be x.

X now has 300 mg of sodium in it.

x = 300

Y also has 450 mg of sodium in it.

y = 450

Samuel reportedly buys five more frozen dinners than soup cans, and they all have a combined salt content of 6000 mg.

Let the number of frozen dinners be "b," and the number of soup cans be "a."

ax + by = 6000

⇒ a(300) + b(450) = 6000 ...1

Samuel bought 5 more frozen dinners than soup cans, according to the inquiry, which results in equation

a + 5 = b ...2

Now, by changing the value of b in equation 1 we obtain,

⇒ a(300) + (a + 5)(450) = 6000

⇒ 300a + 450a = 6000 - 2250

⇒ 750a = 3750

⇒ a = 3750/750

⇒ a = 5

By changing the value of an in equation 2, we obtain

⇒ 5 + 5 = b

⇒ b = 10

So, ax + by = 6000 and a + 5 = b are two equations that might be used to calculate how many soup cans and frozen dinners were purchased, respectively, where x and y stand for soup cans and frozen dinners, respectively, and a and b stand for the quantity of soup cans and frozen dinners.

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The surface area of the frustum is 1744 square units

The volume of the pyramid is 2031.33 cube units.

What is a frustum of a pyramid?

By cutting the top of a typical pyramid, the frustum is created, which is a pyramid. Because of this, it is known as a truncated pyramid. The frustum of the pyramid is that portion of a pyramid that is cut through by a plane parallel to its base and lies between the vertex and the base.

a) First, we calculate the height of the frustum.

Let height be H

The base length be L1=24

Base width be W1=12

Top length is L2=14

To width be W2=13

Side height be C=13

Using the formula, H

[tex]H=\sqrt{ C^{2} - \frac{(L1-L2)^{2}}{2}}\\H=\sqrt{ 13^{2} - \frac{(24-14)^{2}}{2}}\\H=\sqrt{ 169 -50}\\H=\sqrt{119} \\H=11[/tex]

Now, the surface area of the frustum is LSA+area of bases of a frustum

Here, P1= perimeter of the base1 of the frustum

P2 is the perimeter of the base 2 of the frustum

[tex]L.S.A=\frac{1}{2} .(P1+P2).L \\=\frac{1}{2} .(72+42).24 \\=\frac{1}{2} .(114).24 \\=1368[/tex]

Now, S1 =area of base1 of frustum =288

S2= area of base 2 of frustum=98

TSA is given by LSA+area of bases of a frustum

=1368+288+98

=1724.

Therefore the surface area is 1724 square units.

b) Volume is given by

[tex]V=\frac{1}{3}.H.(S1+S2+\sqrt{S1S2} )\\ V=\frac{1}{3} . 11.(386+168)\\V=2031.33[/tex]

Therefore the volume is 2031.33 cube units.

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Answer:

The slope is -1

Step-by-step explanation:

To find the slope using two points, you must do this:

(y2-y1) divided by (x2-x1) which is -1-4 divided by 2+3 and the answer will be -5/5 or just simply -1

The required radius of the circle is given as  3.18 m.

Given that,
A circle has a circumference of 20 m. the radius of the circle is to be determined.

Perimeter is the measure of the figure on its circumference.

Here,
The perimeter of the circle = 20m
2πr = 20
r = 20/2π
r = 3.18 m

Thus, the required radius of the circle is given as  3.18 m.

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Answer:

thanks.

0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

Answer:

y=3x-4

Step-by-step explanation:

-9x+3y=-12

3y=12-9x

y=3x-4

The recursive formula for the arithmetic succession will be written as aₙ = 25 - 5n.

A series of integers called an arithmetic succession or arithmetic chain of events has a fixed difference between the terms.

Let a₁ be the first term and d be a common difference.

Then the nth term of the arithmetic sequence is given as,

aₙ = a₁ + (n - 1)d

The sequence is given below.

20, 15, 10, 5, .....

The first term is 20 and the common difference is given as,

d = 15 - 20

d = - 5

Then the recursive formula given the following sequence is given as,

aₙ = a₁ + (n - 1)d

aₙ = 20 + (n - 1) × (-5)

aₙ = 20 - 5n + 5

aₙ = 25 - 5n

The formula for the arithmetic sequence will be written as aₙ = 25 - 5n.

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In the given congruent triangle  ΔPHS ≅ ΔCNF,  the values of x, y, and z are 24° , 37/3° , 61/4° respectively

What is a congruent triangle ?

The meaning of congruent in Maths is addressed to those figures and shapes that can be repositioned or flipped to coincide with the other shapes. These shapes can be reflected to coincide with similar shapes.

Two shapes are congruent if they have the same shape and size. We can also say if two shapes are congruent, then the mirror image of one shape is the same as the other.

Two triangles are said to be congruent if their sides have the same length and angles have same measure. Thus, two triangles can be superimposed side to side and angle to angle.

In mathematics, the term "congruent" refers to figures and forms that may be flipped or rearranged to match up with other ones. These forms can be mirrored to produce related shapes. If two forms are similar in size and shape, they are congruent. We may also state that if two forms are congruent, then their mirror images are identical .Triangles that line up. A triangle is a closed polygon with three line segments that intersect at each of its three angles.

When the sides and angles of two triangles match, the triangles are said to be congruent. Thus, two triangles may be placed side by side and angle by angle on top of one another.

Since both the triangles are congruent this means the side , angles of both the triangles are equal

therefore,

∠ H = ∠ N

∠ S = ∠ C

∠ P = ∠ F

which means,

6x-29° = 115°

6x=144°

x=24°

∠ S  = 180° - ∠ H - 36°

∠ S = 180°-6x+29°-36°

∠ S = 173°-6x

173°-6x=4z-32°

173°-144°+32° = 4z

61/4° = z

3y-1° = 36°

y= 37/3°

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Answer: Cory can have 6 different schedules

Step-by-step explanation:

Add them all together and divide by fifteen

to get the slope of any straight line, we simply need two points off of it, let's use those in the picture below.

[tex]\stackrel{\textit{\LARGE line of reflection}}{(\stackrel{x_1}{-1}~,~\stackrel{y_1}{-4})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{-2})} \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-2}-\stackrel{y1}{(-4)}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{(-1)}}} \implies \cfrac{-2 +4}{1 +1} \implies \cfrac{ 2 }{ 2 } \implies \text{\LARGE 1}[/tex]

now, keeping in mind that perpendicular lines have negative reciprocal slopes, there are three dotted lines, each one of them, hits the line of reflection perpendicularly, so their slope must be

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{1\implies \cfrac{\boxed{1}}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{\boxed{1}}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{\boxed{1}}\implies \text{\LARGE -1}}}[/tex]