Draw a polygon with the given conditions in the coordinate plane. One side of the polygon is drawn for you. Do not retrace the given side.

a triangle with an area of 15 units2

Answer:

pues quien sabe

Step-by-step explanation:

Answer: 10

Step-by-step explanation:

ex: reciprocal of 2 would be 1/2 because 2 can be written as 2/1; you just switch the demoninator and numerator

Answer:

Check below

Step-by-step explanation:

Laws of indices applied in this worksheet:

[tex]a^{n} . a^{m} = a^{n + m[/tex]

[tex]a^{n} .b^{n} = (ab)^{n}[/tex]

Example 1:  

 a)  [tex]x^{2} . x^{3} . x[/tex]    

                    = [tex]x^{2 + 3 + 1}[/tex]

                    = [tex]x^{6}[/tex]

b) [tex](-3.1)^{3}[/tex]×[tex](-3.1)^{4}[/tex]

                           = [tex](-3.1)^{3 + 4}[/tex]

                           = [tex](-3.1)^{7}[/tex]

You Try:

a) [tex]a^{5} . a^{2} . a^{2}[/tex]

                  = [tex]a^{5 + 2 + 2}[/tex]

                  = [tex]a^{9}[/tex]

b) [tex](-1)^{100} . (-1)^{37}[/tex]

                  = [tex](-1)^{100 + 37}[/tex]

                  = [tex](-1)^{137}[/tex]

y= (1/9)x + b,  plug in the point to solve for b

5= (1/9)(-4) + b

b = 5 + 4/9 = 49/9

y= (1/9)x + 49/9

9y = x + 49

Answer:

circumference: 141.4

Step-by-step explanation:

formula for circumference: 2πr

2 x π x 22.5

= 141.37

The area and circumference of the pool is 1590.43 square units and 141.37 units.

The circumference of the circle that has a radius of r is defined as the product of diameter to the pie value.

The circumference of the circle = 2πr

We are given that;

Radius= 22.5

Now,

we can plug it into the formulas and get:

A=π(22.5)2

≈1590.43

C=2π(22.5)

≈141.37

Therefore, by circumference the answer will be 1590.43 square units and 141.37 units.

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The trigonometric ratios for each triangles are:

Please note that all angles B are the right angle, then:

cos B = 1; sin B = 0; tan B = -

The trigonometric ratio of sin, cos, tan, can be formulated as:

(please refer to the attached triangle below for reference)

cos A = side adjacent to A / Hypotenuse

Cos A = b/c

Sin A = side opposite to A / Hypotenuse

Sin A = a/b

Tan A = Side opposite to A / Side adjacent to A

Tan A = a/b

From these formulas, we can find that:

Triangle 1

Cos A = 40/50 = 4/5

Sin A = 30/50 = 3/5

Tan A = 30/40 = 3/4

Cos C = 30/50 = 3/5

Sin C = 40/50 = 4/5

Tan C = 40/30 = 4/3

Triangle 2

Cos A = 27/45 = 3/5

Sin A = 36/45 = 4/5

Tan A = 36/27 = 4/3

Cos C = 36/45 = 4/5

Sin C = 27/45 = 3/5

Tan C= 27/36 = 3/4

Triangle 3

Cos A = 15/17

Sin A = 8/15

Tan A = 8/15

Cos C = 8/17

Sin C = 15/17

Tan C = 15/8

Please note that all angle B on the three triangles are all a right angle, then:

Cos B = 1

Sin B = 0

Tan B = -

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Answer:

  x ≈ 4.19 meters

Step-by-step explanation:

You want the value of x given a (4x +2) by (2x +3) rectangle with a cutout corner that is (x+2) by (x-1) has an area of 194 square meters.

The difference in area between the enclosing rectangle and the missing corner is ...

  (4x +2)(2x +3) -(x +2)(x -1) = 194

  8x² +16x +6 -(x² +x -2) = 194

  7x² +15x +8 = 194

  7x² +15x -186 = 0 . . . . . . put in standard form

This is best solved using the quadratic formula:

  [tex]x=\dfrac{-b+\sqrt{b^2-4ac}}{2a}=\dfrac{-15+\sqrt{15^2-4(7)(-186)}}{2\cdot7}\\\\=\dfrac{-15+\sqrt{5433}}{14}\approx\boxed{4.193492}[/tex]

The value of x is about 4.19 meters.

Answer: -2.19 or 1.69

x = −2.18723​509003  

or

x = 1.687​23509003

Step-by-step explanation:

Answer:

Step-by-step explanation:

The equation 12sec²x - 16 = 0 is not a polynomial equation and cannot be factored into the product of two or more polynomials.

To solve for x, we need to isolate sec²x by adding 16 to both sides and then dividing by 12:

12sec²x - 16 + 16 = 0 + 16

12sec²x = 16

sec²x = 16 / 12

sec²x = 4/3

Now that we have isolated sec²x, we can find x by finding the inverse secant of 4/3.

Note that the inverse secant is a multi-valued function, so there may be multiple solutions for x, which can be obtained using a calculator or tables of trigonometric functions.

If jack has three packs of gum and sam has 4 packs of gum, then the total amount of gum they have together is 7 packs.

What is the addition?

The addition is putting numbers together to make a sum or total. The plus sign + tells you to add two numbers. = is an equals sign. It shows that things on either side of it are equal.

We have given,

Jack has 3 packs of gum and Sam has 4 packs of gum.

To find the total number of packs of gum they have together, we simply add their individual amounts:

3 packs (Jack) + 4 packs (Sam) = 7 packs

Therefore, the total amount of gum they have together is 7 packs.

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If Arnav applies the Distributive Property to the expression 4 + 8(y + 3) + x, the expression that he will get is 4 + 8y + 24 + x or 8y + x + 28

As per the data given:

Arnav applies the Distributive Property to the expression 4 + 8(y + 3) + x.

Here we have to determine the equivalent expression after applying the Distributive Property to the expression 4 + 8(y + 3) + x.

Distributive property states that, for real numbers a, b, and c:

a (b + c) = ab + ac

An expression of the form A(B + C) can be solved as A × (B + C) = AB + AC.

From the given expression the part which we have to apply distributive property is 8(y + 3)

Here a = 8

b = y

c = 3

So, applying property in the expression

= 4 + 8(y + 3) + x

= 4 + 8y + 24 + x

= 8y + x + 28

Therefore, the equivalent expression is 4 + 8y + 24 + x or 8y + x + 28

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Answer:

A) 11.26

Step-by-step explanation:

To find the state disability insurance (SDI) amount deducted from Caroline's paycheck, we need to calculate 1% of her gross earnings.

1% of $1,126 is (1/100) x $1,126 = $11.26

So, the SDI amount deducted from Caroline's paycheck would be $11.26.

The dimensions are Width = 10 inches and Length = 13 inches

Draw a rectangle.  If the length is 4 inches longer than three times its width, we can write the width as "w" and the length as the 3*width + 4

Area is (width)(Length) = (width)(3*width+4)

    W

 ----------

 |         |

 |         |

 |          |  L = 3w+4

 |         |

 |          |

 -----------

A = (3w+4)(w)

A = 3w² + 4w = 340.

(Problem states that area is 340 sq in)

Need to solve this quadratic equation

3y² + 4y - 340 = 0

Factor:

(w - 10) (w + 13) = 0

So

w - 10 = 0.    or.    w + 13 = 0

Solve these and get

w = 10. or. w = -13

Only one that makes sense in real life is the positive one.

So the dimensions are

Width = 10 inches

Length = 13 inches

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Answer: $34

Step-by-step explanation:

204 divided by 6 = 34

Answer:

6(2x + 3y)

Step-by-step explanation:

             Two x plus three = 2x + 3y

      Six times of (2x + 3y) = 6 *(2x + 3y)

The geometric mean of x and y is [tex]\sqrt{xy}[/tex]

So the geometric mean of 4 and 5 is [tex]\sqrt{4*5} = \sqrt{20} \approx 4.472[/tex]

Answer:

[tex]2\sqrt{5}[/tex]

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

Geometric mean of two numbers is the square root of their product.

The number we are looking for is:

False. The minimum of two independent exponential random variables is not necessarily exponential.

For two independent exponential random variables X and Y, with rate parameters λ1 and λ2 respectively, the minimum of X and Y is a random variable Z with the cumulative distribution function (CDF) given by

[tex]F_Z(z) = 1 - e^(-(λ1+λ2)z)[/tex].

The survival function of Z is given by

[tex]S_Z(z) = e^(-(λ1+λ2)z)[/tex].

Therefore, the probability density function of Z is

[tex]f_Z(z) = (λ1 + λ2)e^(-(λ1+λ2)z)[/tex].

This is not an exponential distribution because the form of the probability density function is not of the form [tex]f(z) = λe^(-λz)[/tex].

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Answer:

To find f(2), we simply substitute 2 for x in the function f(x)=5x+12 and simplify:

f(2) = 5(2) + 12

= 10 + 12

= 22

Therefore, f(2) = 22.

Step-by-step explanation:

El precio de cada refresco es de 4.35$  

⭐Explicación paso a paso:

En este caso lo que hay que hacer es el precio unitario de cada refresco.  

El precio unitario se obtiene al dividir el total de dinero entre la cantidad de refrescos que trae cada caja:  

Precio de cada refresco = Precio total/Cantidad de refrescos 

 Precio de cada refresco = 104.40$/24 

Precio de cada refresco = 4.35$  Por lo tanto, el precio de cada refresco es de 4.35$

Answer:

#7:  x = 7

#8:  AC = 52

Step-by-step explanation:

We know that part + part = whole.

Thus, AB + BC = AC

Using this fact, we can solve for x:

[tex]6x-3+2x-1=10x-18\\8x-4=10x-18\\8x=10x-14\\-2x=-14\\x=7[/tex]

We can simply plug in x in 10x-18 to find the length of AC:

[tex]10(7)-18=AC\\70-18=AC\\52=AC[/tex]

You can also check that AB + BC = AC by plugging in x for 6x -3 and 2x -1 and finding the sum of the two parts of the line:

[tex]6(7)-3+2(7)-1=52\\42-3+14-1=52\\39+13=52\\52=52[/tex]

The graph of the first function is y = √(x - 5).

The graph of the second function is y =  |x - 1| + 4.

Suppose we have a function f(x).

f(x) ± d = Vertical upshift/downshift by d units (x, y ±d).

f(x ± c) = Horizontal left/right shift by c units (x - + c, y).

(a)f(x) = Vertical stretch for a > 0, vertical shrink a < 0. (x, ay).

f(bx) = Horizonatal compression b > 0, horizontal stretch for b < 0. (bx , y).

f(-x) = Reflection over y-axis, (-x, y).

-f(x) = Reflection over x-axis, (x, -y).

The graph of the first function is f(x) = y = √x.

Now, f(x - 5) would be the same function shifter 5 units to the right,

f(x) = √(x - 5).

The graph of the second function is  a modulus function shifted up 2 units and to right by 1 unit g(x) = |x - 1| + 2 and again g(x) + 2 =  |x - 1| + 4.

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Answer:

20

Step-by-step explanation:

1 hour is 60 minutes 1/3x60=20

Answer:

1200 seconds

Step-by-step explanation:

1/3 of an hour is 20 minutes. There are 60 seconds in a minute. 60 times 20 = 1200.

The graph of G(x) is the graph of F(x) compressed vertically.

The equation of the graph of F(x) is given by x^2 and that of G(x) is given by 4/5 x^2.

The coefficient of x^2 in the equation of G(x) is 4/5, which is smaller than the coefficient of x^2 in the equation of F(x), which is 1.

This means that for a given value of x, the value of G(x) will always be less than the value of F(x). In other words, the graph of G(x) will be closer to the x-axis compared to the graph of F(x), which is equivalent to compressing the graph of F(x) vertically.

Therefore, the statement that best compares the graph of G(x) with the graph of F(x) is "The graph of G(x) is the graph of F(x) compressed vertically".

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Suppose that F(x) = x^2 and G(x) =4/5x^2 Which statement best compares the graph of G(x) with the graph of F(x)? The graph of G(x) is the graph of F(x) compressed vertically and flipped over the x-axis. The graph of G(x) is the graph of F(x) stretched vertically. The graph of G(x) is the graph of F(x) stretched vertically and flipped over the x-axis. The graph of G(x) is the graph of F(x) compressed vertically.

If 6 times the 6th term of an A.P is equal to 9 times the 9th term, then 15th term of the A.P. is -2d with d as the common difference.

Let's call the common difference of the arithmetic progression (A.P.) "d". The nth term of an A.P. is given by the formula T = a + (n - 1)d, where a is the first term and n is the term number.

Using this formula, we can write two expressions for the 6th and 9th terms:

T₆ = a + (6 - 1)d = a + 5d

T₉ = a + (9 - 1)d = a + 8d

According to the problem, 6 times the 6th term of the A.P. is equal to 9 times the 9th term, so we can write the following equation:

6T₆ = 9T₉

Substituting the expressions for T₆ and T₉, we get:

6(a + 5d) = 9(a + 8d)

Expanding and solving for a, we get:

6a + 30d = 9a + 72d

Subtracting 6a from both sides:

24d = 3a + 72d

Subtracting 72d from both sides:

-48d = 3a

Dividing both sides by 3:

-16d = a

So, the first term of the A.P. is -16d.

To find the 15th term, we can use the formula for the nth term:

T₁₅ = a + (15 - 1)d = -16d + 14d = -2d

So, the 15th term of the A.P. is -2d.

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The initial amount, a, in the exponential function g(x) = 14 × 2x is 14, and the growth factor, b, is 2.

This can be determined by looking at the equation and noting that the coefficient of x is 2, which indicates that the base of the exponential is 2. We can also calculate the initial amount and growth factor mathematically.

To calculate the initial amount, a, we can take the equation g(x) = 14 × 2x and set x = 0, yielding g(0) = 14 × 20, which simplifies to 14. To calculate the growth factor, b, we can take the natural log of both sides of the equation to yield ln(g(x)) = ln(14 × 2x).

Simplifying this gives

ln(g(x)) = ln(14) + ln(2x).

We can then divide both sides by x to yield

ln(g(x))/x = ln(14) + ln(2)/x.

We can then take the limit as x approaches 0, which yields

ln(g(0))/0 = ln(14) + ln(2)/0.

This simplifies to

ln(g(0)) = ln(14) + ln(2), which can be rearranged to

ln(2) = ln(g(0)) - ln(14).

Taking the exponential of both sides gives us

2 = e^(ln(g(0)) - ln(14)), which simplifies to

2 = g(0)/14, or b = g(0)/14 = 2.

This shows that the initial amount, a, is 14, and the growth factor, b, is 2.

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The parallelogram EFGH has the following coordinates at point H: H(x, y) = (6, 4).

Parallelograms are quadrilaterals with two pairs of parallel sides and any quadrilateral can be generated by the knowledge of four vertices. Based on this fact, the following conditions must be observed:

[tex]\overline {EF} \parallel \overline {GH}[/tex]

The coordinates of the missing vertex can be found by the following vector sum:

F(x, y) - E(x, y) = H(x, y) - G(x, y)

H(x, y) = G(x, y) + F(x, y) - E(x, y)

H(x, y) = (4, 2) + (3, 5) - (1, 3)

H(x, y) = (6, 4)

The coordinates of point H in parallelogram EFGH are H(x, y) = (6, 4).

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The domain of the function is composed by all the integer numbers that are greater than or equal to zero.

The domain of a function is the set containing all the possible input values that the function can accept.

For this problem, the input is the number of tickets purchased, which must be a countable amount (you cannot purchase a negative number of tickets nor a decimal number of tickets), hence the domain of the function is composed by all the integer numbers that are greater than or equal to zero.

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Answer: (1,2.5), (2, 3.5), (3, 4.5)

Step-by-step explanation: The question states that the frame is one and a half inches wider than the picture, so the equation would be f = p+ 1.5. Add 1.5 to each value of p to find the value of f