Find the median, mean, mode, and range of the data.

Answer:

the answer is the 3rd to the 4th power and

The end behavior of the polynomial y=-4x+8x-21'+3 is y = -4x^3.

Degree of a polynomial is the highest power that its terms pertain (for multi-variables, the power of term is addition of power of variables in that term).

Thus, in the degree of the polynomial is 3 as the highest power in its terms is 3.

(power and exponent are same thing)

We are given that;

The functions (a) 1=3x-2x+12

(b) 1-10-8.x2

(c) y=6r-4r+x-120

(d) y=-3x+2x-4x+7

(e) y=5x+2x2

(f) y=-4x+8x-21'+3

Now,

To find the power function that best represents the end behavior of a polynomial, we need to look at the leading term (the term with the highest degree) of the polynomial.

(a) The leading term of this polynomial is 3x. So the power function that best represents its end behavior is y = 3x.

(b) The leading term of this polynomial is -8x^2. So the power function that best represents its end behavior is y = -8x^2.

(c) The leading term of this polynomial is 6r. So the power function that best represents its end behavior is y = 6r.

(d) The leading term of this polynomial is -3x^3. So the power function that best represents its end behavior is y = -3x^3.

(e) The leading term of this polynomial is 2x^2. So the power function that best represents its end behavior is y = 2x^2.

(f) The leading term of this polynomial is -4x^3. So the power function that best represents its end behavior is y = -4x^3.

Therefore, by polynomials the answer will be y = -4x^3.

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Answer:

2.89

Step-by-step explanation:

GPE = U * 1/2

GPE = 5.78 * 1/2

GPE = 2.89

Answer:

19 in and 35 in

Step-by-step explanation:

Let the width be w and the length be 2w-3. Then,

[tex]2(w+2w-3)=108 \\ \\ 3w-3=54 \\ \\ 3w=57 \\ \\ w=19 \\ \\ \implies 2w-3=35[/tex]

Answer:

The slope should be -1.

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Hope this helps!

Have a great day and God bless! :)

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Work Shown:

[tex](x_1,y_1) = (1,-1) \text{ and } (x_2,y_2) = (2,-2)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{-2 - (-1)}{2 - 1}\\\\m = \frac{-2 + 1}{2 - 1}\\\\m = \frac{-1}{1}\\\\\boldsymbol{m = -1}\\\\[/tex]

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

Side notes:

Slope = rise/run

rise = change in y value = [tex]y_{2} - y_{1}[/tex]

run = change in x value = [tex]x_{2} - x_{1}[/tex]

Make sure you subtract in the same order each time.

The two expressions to represent the perimeter of this rectangle include the following:

An expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.

Mathematically, the perimeter of a rectangle can be calculated by using this formula;

P = 2(L + W)

Where:

Substituting the given variables into the given expression, we have;

P = 2(2x + 6 + x)    ......expression 1.

For the second expression, we have:

P = 2(2x + 6 + x)

P = 2(3x + 6)        ......expression 2.

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Complete Question:

The length of a rectangle is 2x+6 and the width is x. Write two expressions to represent the perimeter.

The actual width of Tyrone's patio using the scale drawing is 16 feet's

The scale from the backyard to the drawing is 2 ft to 1 inches.

The width of the patio on the drawing is 8 inches.

Therefore, the width of the Tyrone's actual patio is as follows;

Hence,

1 inches = 2 feet's

8 inches = ?

cross multiply

actual length of Tyrone's patio = 8 × 2

actual length of Tyrone's patio = 16 feet's

Therefore, using the scale drawing, the actual length of Tyrone's patio is 16 feet's.

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Answer:

no

Step-by-step explanation:

it is divisble by 1, 2, 4, 8, 89, 178, 356, 712

Answer: ABD=67 degrees

CBD=67 degrees

ABC=134 degrees

Step-by-step explanation:

ABC=ABD+CBD

25x+34=ABD+11x+23

14x+34=ABD+23

ABD=14x+11

ABD=CBD ==> Bisected angles are equal to each other since angle ABC is divided into two equal angles when bisected.

14x+11=11x+23

3x+11=23

3x=12

x=4

ABD=14x+11

ABD=14(4)+11

ABD=56+11

ABD=67 degrees

CBD=11x+23

CBD=11(4)+23

CBD=44+23

CBD=67 degrees

ABC=25x+34

ABC=25(4)+34

ABC=100+34

ABC=134 degrees

Answer:

∠ ABD = 67° , ∠ CBD = 67° , ∠ ABC = 134°

Step-by-step explanation:

since BD bisects ∠ ABC , then

∠ ABD = ∠ CBD = 11x + 23

∠ ABC = ∠ ABD + ∠ CBD ( substitute values )

25x + 34 = 11x + 23 + 11x + 23

25x + 34 = 22x + 46 ( subtract 22x from both sides )

3x + 34 = 46 ( subtract 34 from both sides )

3x = 12 ( divide both sides by 3 )

x = 4

Then

∠ ABD = 11x + 23 = 11(4) + 23 = 44 + 23 = 67°

∠ CBD = ∠ ABD = 67°

∠ ABC = 25x + 34 = 25(4) + 34 = 100 + 34 = 134°

Answer:

[tex]13\frac{1}{8}[/tex]

Step-by-step explanation:

Given expression:

[tex]\left(-5 \frac{5}{8}\right) \cdot \left(-2 \frac{1}{3} \right)[/tex]

Convert the mixed numbers into improper fractions by multiplying the whole number by the denominator, adding it to the numerator of the fraction, and placing this as the numerator:

[tex]\implies -\dfrac{5 \cdot 8+5}{8} \cdot -\dfrac{2 \cdot 3+1}{3}[/tex]

[tex]\implies -\dfrac{40+5}{8} \cdot -\dfrac{6+1}{3}[/tex]

[tex]\implies -\dfrac{45}{8} \cdot -\dfrac{7}{3}[/tex]

[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{b} \cdot \dfrac{c}{d}=\dfrac{a \cdot c}{b \cdot d}:[/tex]

[tex]\implies \dfrac{-45 \cdot -7}{8 \cdot 3}[/tex]

[tex]\implies \dfrac{315}{24}[/tex]

Convert the improper fraction into a mixed number:

[tex]\implies 315 \div 24 = 13\: \text{r}\:3[/tex]

[tex]\implies 13\frac{3}{24}[/tex]

[tex]\implies 13\frac{1}{8}[/tex]

Answer:

Product = 13 1/8

Step-by-step explanation:

The equation is,

→ (-5 5/8) × (-2 1/3)

Now the product of equation will be,

→ (-5 5/8) × (-2 1/3)

→ (-45/8) × (-7/3)

→ (-15 × -7)/8

→ 105/8

→ 13 1/8 {mixed fraction}

Therefore, the product is 13 1/8.

a The absolute value of ax will be considered while for the second the absolute value of ax + b will be considered.

b The absolute value of ax will be considered while for the second the absolute value of ax + b will be considered.

Given data

a, b, c, and x be real numbers.

|ax| + b = c

The equation here contains the modulus sign only for ax hence only the absolute value of ax is considered.

|ax + b| = c

Here the modulus sign covers both ax and b hence the absolute values  of ax + b is considered.

|ax| + b ≤ c

The equation here contains the modulus sign only for ax hence only the absolute value of ax is considered.

|ax + b| ≥  c

Here the modulus sign covers both ax and b hence the absolute values  of ax + b is considered.

Note that absolute values do not consider the signs

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Answer: 20

Step-by-step explanation:

The expressions can be simplified as follows-

1. (9 − 3) 2− (5 • 4)0 = 12

2. (2 + 3)5 ÷ (5 × 2)2 = 5/4

3. 4 × 2 ÷ (6 − 2)4 = 1/2

4. [(1 + 7) 2] 2• (12 2 )0 = 0

Let us look at each expression one by one-

1. (9 − 3) 2− (5 • 4)0

Zero multiplied by any number is 0 itself. Thus, the expression becomes-

= (9 - 3) 2

= 6 × 2

= 12

2. (2 + 3)5 ÷ (5 × 2)2

According to the rules of BODMAS, we first solve the brackets-

(5)5 ÷ (10)2

= 25 ÷ 20

= 25/20

= 5/4

3. 4 × 2 ÷ (6 − 2)4

= 4 × 2 ÷ (4)4

= 8 ÷ (4)4

= 8/16

= 1/2

4. [(1 + 7) 2] 2• (12 2 )0

= [(8)2]2• 0

= 0

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By solving a system of equations, we can see that each geranium costs 3 dollars.

First, let's define the two variables:

x = price of one rose bush.

y = price of one geranium

Now, with the information on the problem we can write two equations, thus, we will have a system of equations:

$122 = 14*x + 8*y

$120 = 12*x + 12*y

We want to solve that system, if we isolate x on the first equation we will get:

x = ($122 - 8y)/14

Now we can replace this on the other equation:

$120 = 12*($122 - 8y)/14 + 12*y

Now we can solve this for y.

14*$120 = 12*($122 - 8y) + 12*14*y

$1,680 = $1,464 + 72y

($1,680 - $1,464 )/72 = y = $3

Each geranium costs 3 dollars.

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The set of points on this graph is a relation but not a function

We know that every function can be a relation but every relation cannot be a function.

A relation means the connection between the input and the output.

A function means that for every input there should only be one output.

Here, we have the data as:

(2,5), (1,2), (3,4), (3, 1), (6,5) and  (5,3)

We can say that it is a relation as for every input, there is an output.

But, it is not a function.

This is because the input 3 has 2 outputs as 1 and 4 which is not possible in a function.

Therefore, the set of points on this graph is a relation but not a function.

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Answer:

Step-by-step explanation:

Answer: 227=4x+127

x=$25

Step-by-step explanation:

227=4x+127  ==> equation

227-127=4x+127-127

4x=227-127

4x=100

4x/4=100/4

x=100/4

x=$25

This is just a linear equation, then the domain is the set of all real numbers and the range is the set of all real numbers.

Here we have the function:

f(x) = (x^2 + 5x + 4)/(x + 4)

The numerator can be rewritten if we find the zeros:

x = (-5 ± √( 5^2 - 4*1*4))/(2*1)

x = (-5 ± 3)/2

Then the zeros are:

x = (-5 - 3)/2 = - 4

x = (-5 + 3)/2 = -1

So the numerator can be rewritten to (x + 4)*(x + 1)

And the function is rewritten to:

f(x) = (x^2 + 5x + 4)/(x + 4) = (x + 4)*(x + 1)/(x + 4) = (x + 1)

This is just a linear equation, then the domain is the set of all real numbers and the range is the set of all real numbers.

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Answer:

4×9=36

1-3=-2

36÷2=18

Step-by-step explanation:

4×+1,9×-1.

4×9=36

1-3=-2

Answer:

Step-by-step explanation:

From the given numbers :

Integers: -50,000,000

Rational numbers : -1/2 and -1.5

Real numbers : −√5 , -1/2, -50, 000, 000 , -1.5.

As given,

Given numbers:

A. −√5 :It is an irrational number.

Therefore belongs to real numbers.

B. -1/2 :In p/q form .

It is a rational and real number.

C. -50,000,000

It is a negative integer and real number.

D. -1.5 =-15 /10

          =3/2

It is a rational and real number.

Therefore, from the given numbers :

Integers: -50,000,000

Rational numbers : -1/2 and -1.5

Real numbers : −√5 , -1/2, -50, 000, 000 , -1.5.

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The expected foot length of an adult male who is 1.8 m tall is 30.8 cm.

Based on the information given, Jerry surveyed adult males to study the relationship between their high and the length of their footwear both are measured in centimeters and he found the equation y equals 75 + 3.4 x.

This will be illustrated as:

y = 75 + 3.4x..

y = 1.8m = 180

Therefore, y = 75 + 3.4x.

180= 75 + 3.4x

180 = 75 + 3.4x

Collect like terms

3.4x = 180 - 75

3.4x = 105.

Divide

x = 105 / 3.4

x = 30.8 cm

Therefore, the expected foot length of an adult male who is 1.8 m tall is 30.8 cm.

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Answer:

3796 length of the box

Step-by-step explanation:4,238-26×17=3,796

Answer:

  (b)  √(4x+2)√(25x-4)

Step-by-step explanation:

Given two functions f(x) = √(4x+2) and g(x) = √(25x-4), you want the function fg.

The product fg is a bit of shorthand notation:

  [tex]fg = fg(x) = f(x)\cdot g(x)[/tex]

Substituting the given function definitions, we have ...

  [tex]f(x)\cdot g(x) = \sqrt{4x+2}\cdot\sqrt{25x-4}[/tex]

The product of the radicals could be combined into one radical, but that has not been done in your answer choices. This means ...

  [tex]\boxed{fg=(\sqrt{4x+2})(\sqrt{25x-4})}[/tex]

There were 61 youth tickets sold and 34 general admission tickets in linear equation .

What in mathematics is a linear equation?

GA= GENERAL ADMISSION =$10

Y= YOUTH =$8

GA+Y= 95

GA=95-Y

10GA+8Y=828

10(95-Y)+8Y=828

950-10Y+8Y=828

-2Y= 122 MULTIPLY BY (-1)

2Y= 122

Y= 61

GA= 34

There were 61 youth tickets sold and 34 general admission tickets.

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Answer:

Step-by-step explanation:

ln(xy²/z)

Answer:

192 [in²]

Step-by-step explanation:

Area=(4*4)*2+(4*10)*4=192.

Answer:

(0,3)

Step-by-step explanation:

x - y = -3

y = -1/4x + 3

x - (-1/4x + 3) = -3

x = 0

y = -1/4 x 0 + 3

y = 3

(0,3)

Answer: 24

Step-by-step explanation:

−3−6=−

4

1

​

(x+12)

Subtract 6 from −3 to get −9.

−9=−

4

1

​

(x+12)

Use the distributive property to multiply −

4

1

​

 by x+12.

−9=−

4

1

​

x−

4

1

​

×12

Express −

4

1

​

×12 as a single fraction.

−9=−

4

1

​

x+

4

−12

​

Divide −12 by 4 to get −3.

−9=−

4

1

​

x−3

Swap sides so that all variable terms are on the left hand side.

−

4

1

​

x−3=−9

Add 3 to both sides.

−

4

1

​

x=−9+3

Add −9 and 3 to get −6.

−

4

1

​

x=−6

Multiply both sides by −4, the reciprocal of −

4

1

​

.

x=−6(−4)

Multiply −6 and −4 to get 24.

x=24