A football team gains 4 yards on their first play. They lose 15 yards on the next play.
Enter two integers that represent the two plays.

The unknown values in the triangle is calculated to be

PL = 14.3 cm

CY = 7.74

NY = 9.9 mm

LJ = 8.3

The unknown values in the triangle is worked using SOH CAH TOA

Sin = opposite / hypotenuse - SOH

Cos = adjacent / hypotenuse - CAH

Tan = opposite / adjacent - TOA

1. using Sin = opposite / hypotenuse - SOH

sin x = PL / PX

sin 54.25 = PL / 17.62

PL = sin 54.25 * 17.62

PL = 14.3 cm

2. using Tan = opposite / adjacent - TOA

tan 52.67 = CY / 5.9

tan 52.67 * 5.9 = CY

CY = 7.74

3. using Sin = opposite / hypotenuse - SOH

sin 33.06 = YC / NY

NY = 5.4 /  sin 33.06

NY = 9.9 mm

4. using Tan = opposite / adjacent - TOA

tan 55.05 = LJ / VJ

tan 55.05 * 5.8 = LJ

LJ = 8.3

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Answer:

4+7-2

=11-2

=9

Step-by-step explanation:

Using it's concept, the percentage of employees with 8 or more years at the company reported that email is their preferred method of communication is:

D. 44.79%.

The percentage of an amount a over a total amount b is given by a multiplied by 100% and divided by b, that is:

P = a/b x 100%

In this problem, there are 96 employees with 8 or more years of experience, of which 43 prefer email, hence the percentage is:

P = 43/96 x 100% = 44.79%.

Hence option D is correct.

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9514 1404 393

Answer:

  LA = 20π square units

  SA = 36π square units

  V = 16π cubic units

Step-by-step explanation:

The value of the radius is needed before any area calculations can be done. It can be found from the Pythagorean theorem:

  r² + 3² = 5²

  r = √(25 -9) = 4

__

The lateral area is given by the formula ...

  LA = πrs . . . . . where r is the radius and s is the slant height

  LA = π(4)(5)

  LA = 20π square units

__

The surface area is the sum of the lateral area and the base area. The latter is the area of a circle of radius 4.

  SA = πr² + LA

  SA = π(4²) +20π = 16π +20π

  SA = 36π square units

__

The volume is given by the formula ...

  V = 1/3πr²h

  V = 1/3π(4²)(3) = 16π

The volume is 16π cubic units.

Answer:

A 1,296

B 1,369

36 answer

Answer:

Area = 324ft²

Perimeter = 72ft

Step-by-step explanation:

Area of a square = length²

Area of a square = (18ft)² = 324ft²

Perimeter of a square = 4*length

Perimeter of a square = 4ft*18 = 72ft

It will take approximately 28.67 years for Talwar's investment of R5,800 to grow to R26,100 at a simple interest rate of 12.2% per annum.

To calculate the number of years it will take for Talwar's investment to grow to R26,100 at a simple interest rate of 12.2% per annum, we can use the formula for simple interest:

Simple Interest = Principal × Rate × Time

Given that the principal (P) is R5,800, the rate (R) is 12.2% (or 0.122 as a decimal), and the desired amount (A) is R26,100, we need to find the time (T) it will take. Rearranging the formula, we get:

Time = (Amount - Principal) / (Principal × Rate)

Plugging in the values, we have:

Time = (R26,100 - R5,800) / (R5,800 × 0.122)

= R20,300 / R708.6

≈ 28.67 years

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Using Side Splitter Theorem, The value of x is 27.

Side Splitter Theorem is a theorem that states that if a triangle has one angle larger than the other two, then the longest side of the triangle is also the longest side of the two other angles. This theorem is helpful in solving a variety of geometry problems.

The Side Splitter Theorem states that if a triangle is split by a line parallel to one side, then the line must divide the other two sides in the same ratio. This means that if a triangle has sides of lengths 8, 12, and 30, and the line is parallel to the side of length 8, then the other two sides must be divided so that the ratio of the two parts is the same as the ratio of the two sides. In this case, the ratio of the two sides is 12:30, or 4:10. Therefore, the line must divide the other two sides so that the ratio of the two parts is 4:10.

Using side - splitter theorem,

x+6 / 12 = 22/8

= (x + 6) × 8 = 22 × 12

= 8x + 48 = 264

= x = 27

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Answer:

9a-65

Step-by-step explanation:

simply write 9a+(add the remaining numbers all together)

Answer:

52%

Step-by-step explanation:

13/25

Answer:

52%

Step-by-step explanation:

If that equals one whole, then it should be 52%

This is correct!

Answer:

Step-by-step explanation:

To work out the given expression without a calculator, we need to convert the numbers from their respective bases to decimal form and then perform the arithmetic operations. Let's break it down step by step:

11101010 base 2: To convert a binary number to decimal, we multiply each digit by the corresponding power of 2 and sum the results. So, let's calculate:

1 * 2^7 + 1 * 2^6 + 1 * 2^5 + 0 * 2^4 + 1 * 2^3 + 0 * 2^2 + 1 * 2^1 + 0 * 2^0 = 234.

2122 base 8: To convert an octal number to decimal, we multiply each digit by the corresponding power of 8 and sum the results. Let's calculate:

2 * 8^3 + 1 * 8^2 + 2 * 8^1 + 2 * 8^0 = 1090.

ABC base 16: To convert a hexadecimal number to decimal, we multiply each digit by the corresponding power of 16 and sum the results. Let's calculate:

10 * 16^2 + 11 * 16^1 + 12 * 16^0 = 2748.

123 base 8: We already know that 123 is in base 8 (octal), so we can directly convert it to decimal:

1 * 8^2 + 2 * 8^1 + 3 * 8^0 = 83.

Now, let's perform the arithmetic operations:

234 + 1090 + 2748 - 83 = 3989.

Therefore, the result of the given expression in decimal form is 3989.

Answer:

1/4, 1/4, 6/10, 7/10

Step-by-step explanation:

1/4 = 0.25

7/10 = 0.7

6/10 = 0.6

Answer:

SA = 292 m²

Step-by-step explanation:

SA = (2x6x8)+(2x7x6) + (2x7x8) = 292 m²

Answer:

Formula for area of rectangle;

A = L x W

Where L represents the length, and W represents the width.

Plug in the actual values:-

A = 2 1/3 x 3 1/2

A = 8 1/6

Step-by-step explanation:

If we have f(x) and it's inverse, and we compose them

we will get

\(f {}^{ - 1} (f(x) = x\)

So here we compose

\(( \frac{1}{ \frac{1 + x}{x} - 1} )\)

\(( \frac{1}{ \frac{1}{x} + 1 - 1} \)

\( \frac{1}{ \frac{1}{x} } \)

\(x \)

So the composition is x, so they are inverses.

Expression for given numerical is: 9+ (2/x)

Given that we have an word equation that is 9 more than the quotient of 2 and  x

A quotient is a quantity produced by the division of two numbers.

Quotient of 2 and x is \(\frac{2}{x}\).

Nine(9) more  than 2/x is = 9+ (2/x)

So we have an expression that is:

              9+ (2/x)                          

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Answer:

12, 35, 37 , I think..

Step-by-step explanation:

Answer:

{29, 45, 53}

Step-by-step explanation:

12^2+35^2=37^2

144+1225=1369

√1369=37

9^2+40^2=41^2

81+1600=1681

√1681=41

32^2+60^2=68^2

1024+3600=4624

√4624=68

29^2+45^2≠53^2

841+2025=2866

√2866=53.54

√2866≠53

Answer:

16c

Step-by-step explanation:

The range of a function y = x² + 9 is y ≥ 9

A function is a mathematical expression rule or law that defines the relationship between one variable (dependent variable) and another (independent variable)

The range of a function is the set of output values of that function.

Given the function y = x² + 9, to find the range of the function, we need to find the values of y for which the function is valid.

Making y subject of the formula, we have

x = √(y - 9)

So, the function is valid for √(y - 9) ≥ 0

⇒ y - 9 ≥ 0

⇒ y ≥ 9

So, the range of a function is y ≥ 9

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Answer:

Sine 3 books are for 60-

60/3

Rs20 (per book)

and 5 books for Rs 90-

90/5

Rs18 (per book)

Thus we can save 2Rs and 5 books for Rs 90 iscthe best buy

Answer:

0 -2, -1,0,1,2

Step-by-step explanation:

The additional information would allow you to prove the quadrilateral is a parallelogram according to the minimum criteria is

EJ ≅ GJ. Option A

We need to know the properties of a parallelogram, we have;

We know that FJ  ≅ JH, it's given by the marks, now if it were to happen that EJ ≅ GJ, that would mean that the diagonals on that quadrilateral are bisecting each other, and if that's so, then the quadrilateral it's indeed a parallelogram.

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The complete question:

What additional information would allow you to prove the quadrilateral is a parallelogram according to the minimum criteria?

A)

ej ≅ gj

B)

ej || gj

C)

fg || eh

D)

ef ≅ hg

Answer:

symmetric

Step-by-step explanation:

Answer:

y=x/3+2

Step-by-step explanation:

Slope-intercept form is y=mx+b where m is the slope and b is the y-intercept.

3y=x+6

We need y so we divide both sides by 3 and we get

y=x/3+2

Answer:

y=1/3 + 2

Step-by-step explanation:

-x+3y=6

add x to both sides (if you add the same amount to both sides, the equation is still equal)

3y=-x+6

divide the whole thing by 3

y=1/3 + 2

so basically your slope is 1/3. That means you rise one, over three.

Plot a point at 2 on the y axis, which is the vertical line on the graph.

Go up one box, and then go right 3 and plot another point.

Keep doing the rise 1 over 3 until you have enough points for a line. 2 points should do, but more points on a graph = a better line.

By the way, slope-intercept form is y=mx+b.

m = slope (steepness of line, 1/3)    b = y-axis intercept (the place that the line touches the y axis)

If you're still stuck with linear equations, take your equation and put it into Desmos graphing calculator, which can be found with a simple search.

Thanks, friend,

- throckmorton

The value of x in 1st equation is x ≤ 3 i.e.  x ∈ (-infinity,3] and the value of x in 2nd equation is x > 18 i.e.  x ∈ (18,infinity)

Given two equations  1)6x-10<8 and 2) \(\frac{x}{3}\)+6 > 12

Solving the above equations

1) 6x-10≤8

⇒6x ≤ 18

⇒X≤ 3

⇒x ≤ 3 i.e.  x ∈ (-infinity,3]

2)\(\frac{x}{3}\)+6 > 12

⇒\(\frac{x}{3}\) > 6

⇒x>18

⇒ x > 18 i.e.  x ∈ (18,infinity)

Therefore,The value of x in 1st equation is x ≤ 3 i.e.  x ∈ (-infinity,3] and the value of x in 2nd equation is x > 18 i.e.  x ∈ (18,infinity)

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Answer:

2

Step-by-step explanation:

Given the system of equations:

[Tex]x^2+y^2=9\\9x+2y=16\)

Comparing [Tex]x^2+y^2=9\) with the general standard equation of a circle [Tex](x-h)^2+(y-k)^2=r^2\).

The first equation is an equation of a circle centred at (0,0) with a Radius of 3.

The second equation 9x+2y=16 is a straight line equation.

A straight line can only intersect a circle at a maximum of 2 points.

Therefore the greatest possible number of solutions to the equations in the system is 2.

Answer:

2

Step-by-step explanation:

and jj is gay of outer banks

The only automorphism of a well-ordered set is the identity.

To prove this statement, we need to show that any automorphism of a well-ordered set must be the identity function. An automorphism is a bijective function that preserves the order structure of the set.

Assume we have a well-ordered set (W, ≤), where W is the set and ≤ is the order relation.

Let f: W → W be an automorphism of the set.

We aim to prove that f is the identity function, i.e., f(x) = x for all x ∈ W.

Suppose, for contradiction, that there exists an element a ∈ W such that f(a) ≠ a.

Since f is a bijective function, there must exist some b ∈ W such that f(b) = a.

Since (W, ≤) is well-ordered, there is a least element c in the set {x ∈ W : f(x) ≠ x}.

Let d = f(c). Since f is an automorphism, f(c) ≠ c, and thus d ≠ c.

Since (W, ≤) is well-ordered, there is a least element e in the set {x ∈ W : f(x) = d}.

Consider the element f(e). Since f is a bijective function, there must exist some f^{-1}(f(e)) = e' ∈ W such that f(e') = f(e) = d.

By the definition of automorphism, f(f^{-1}(y)) = y for all y ∈ W. Applying this property to e', we have f(f^{-1}(f(e'))) = f(e') = d.

However, f^{-1}(f(e')) = e' ≠ c, and thus f(e') ≠ d. This contradicts the fact that e is the least element in the set {x ∈ W : f(x) = d}.

Therefore, our assumption that there exists an element a such that f(a) ≠ a is false.

Since we assumed f(a) ≠ a for arbitrary a ∈ W, it follows that f(x) = x for all x ∈ W.

Hence, the only automorphism of a well-ordered set is the identity function.

Therefore, we have proven that the only automorphism of a well-ordered set is the identity function.

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Answer:

Company A is cheaper than Company B when x > 40  miles

Step-by-step explanation: