Enter your answer and show all the steps that you use to solve this problem in the space provided. Simplify ( 6 x − 2 ) 2 ( 0 . 5 x ) 4 . Show your work.

Answer:

Step-by-step explanation:

The the 3 consecutive numbers be

X, X + 1, X + 2

: X + X + 2 = 60

2X = 60 - 2

2X = 58

X = 58/2

X = 29

THE NUMBERS ARE 29, 30 AND 31

{y|y is a real number}

The range of the translated function is {[tex]y|y[/tex] is a natural number}.

Real numbers are numbers that include both rational and irrational numbers. Rational numbers such as integers (-2, 0, 1), fractions(1/2, 2.5), and irrational numbers such as √3, π(22/7), etc., are all real numbers.

The numbers which are not real and are Imaginary are known as not real or non-real numbers. Non-real numbers cannot be represented on the number line. Some of the types or examples of the non-real numbers are √−2,6√−54.

The real number, in mathematics, is a quantity that can be expressed as an infinite decimal expansion. Real numbers are used in measurements of continuously varying quantities such as size and time, in contrast to the natural numbers 1, 2, 3, …, arising from counting.

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Answer:

22.5

Step-by-step explanation:

1) Arrange the numbers in order by size.

(5,5,5,10,10,15,15,20,25,30,35,40,40,45,50,50)

2) If there is an odd number of terms, the median is the center term.

3) If there is an even number of terms, add the two middle terms and divide by 2.

(25+20=45)

45 divided by 2 is 22.5

22.5 is your median

Answer: 1/3

Step-by-step explanation:

Answer:54

Step-by-step explanation:

(12 x 4) = 48

(12 x .5) = 6

48 + 6 = 54

Answer:

Length = 39 inches , breadth = 13 inches

Step-by-step explanation:

Given:

The perimeter of a rectangular atrium is 104 inches.

The length of the atrium is three times the width.

Question asked:

The length and the breadth of rectangular atrium = ?

Solution:

Let breadth of rectangular atrium = [tex]x[/tex]

Then, the length of rectangular atrium = [tex]3x[/tex]    (given)

Perimeter of rectangle = [tex]2\times(length + breadth)[/tex]

                               [tex]104 = 2\times( 3x + x )[/tex]

                               [tex]104 = 2\times 4x[/tex]

                               [tex]104 = 8x[/tex]

Dividing both side by 8

                               [tex]13 = x[/tex]

breadth of rectangular atrium = [tex]x[/tex] = 13 inches

length of rectangular atrium = [tex]3x[/tex] = [tex]3 \times13 = 39[/tex] inches

Thus, length and the breadth of rectangular atrium are 39 and 13 inches.

Answer:

Step-by-step explanation:

so he bought a wallet for 19.95 and y hats for 5.99

y = number of hats

19.95 + 5.99y....because each hat is 5.99

Answer:

[tex]R=5N +7[/tex]

Step-by-step explanation:

We want to write a formula for the statement:

Ann thought of a number N, multiplied it by 5 and added 7.

When we multiply N by 5, we get 5N

When we add 7 to 5N we get 5N+7

Our formula now becomes:

R=5N +7

Answer:

20 degrees.

Step-by-step explanation:

The 3 angles of a triangle add up to 180 degrees.

Therefore the third angle in this triangle

= 180 - (120 + 40)

= 180 - 160

= 20 degrees.

Answer:

Therefore other two sides of the triangle are 4 and 5.

Step-by-step explanation:

Given one leg of a right triangle has a length of 3

Let other sides of the triangle be x and x+1 [ since they are consecutive]

According to the problem,

3²+x²=(x+1)²

⇔9 + x²=x²+2x+1

⇔2x+1=9

⇔2x=9-1

⇔2x=8

⇔x=4

Therefore other two sides of the triangle are 4 and 5.

To find the lengths of the other two sides of the right triangle with one leg of length 3, we can use the Pythagorean theorem. The lengths of the other two sides are 4 and 5.

To find the lengths of the other two sides of the right triangle, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Since one leg has a length of 3, let's call the lengths of the other two sides x and x+1. We can set up the equation:

3^2 + x^2 = (x+1)^2

Simplifying the equation:

9 + x^2 = x^2 + 2x + 1

Subtracting x^2 from both sides:

9 = 2x + 1

Subtracting 1 from both sides:

8 = 2x

Dividing both sides by 2:

4 = x

So, the lengths of the other two sides are 4 and 5.

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Answer: 20 tests

Step-by-step explanation: She does every test in 2 1/2 mins. So she can do 20 in 50 mins.

21+1.7+0.25=22.95

You add 21+1.7, which equals 22.7, then add 0.25 to get 22.95.

Answer:

x = 1

Step-by-step explanation:

Step 1:  Choose one of the equations to solve for y:

x - y + 1 = 0

(-y) / -1 = (-1 - x) / -1

y = 1 + x

Step 2:  Plug in y into either equation

3x + 2(1 + x) = 7

3x + 2 + 2x - 2= 7 - 2

5x / 5 = 5 / 5

x = 1

Answer:  x = 1

Answer:

3468

Step-by-step explanation:

We can make four digit number from the digits 6,4,3,8

Smallest digit for thousands is 3=3000

Smallest digit for hundreds (out of remaining 6,4,8) is 4 = 400

Smallest digit for tenths (out of remaining 6,8) is 6= 60

And unit digit is 8

So the smallest number is 3000+400+60+8=3468 answer

Answer:

See the attached image for the answers and the working out.

Step-by-step explanation:

The nth term of the sequences 2, 5, 10, 17... and 2, 8, 18, 32... are n² + 1 and 2n² respectively.

Sequences are a group of numbers written in a specific order such that the nth term of the sequence can be determined using some logic or formula.

It is given that the nth term of the sequence 1, 4, 9, 16... is n squared.

2, 5, 10, 17...

1² + 1, 2² + 1, 3² + 1, 4² + 1...

This is of the form n² + 1. The nth term can be found using the formula n² + 1.

2, 8, 18, 32...

2×1², 2×2², 2×3², 2×4²...

This is of the form 2n². The nth term can be found using the formula 2n².

Therefore, we have found that the nth term of the sequences 2, 5, 10, 17... and 2, 8, 18, 32... are n² + 1 and 2n² respectively.

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Answer:

Given:

Area of the rectangle  = 30 square inches.

length of the sides are whole numbers.

Solution:

The base of the rectangle  is  x and the height is y

We know that Area of the rectangle  = [tex]length \times breadth[/tex]

That is

30 = [tex]x \times y[/tex]

The possible values of length and breadth

length x : 1    2      3      5    6    10   15    30

breath  y: 30   15    10   6     5    3      2      1

Now

30 =  xy

[tex]y = \frac{30}{x}[/tex]

when y increases x decreases and vice versa

[tex]\bf \pm\sqrt{-14}\implies \pm\sqrt{(-1)(14)}\implies \pm\sqrt{-1}\cdot \sqrt{14}\implies \stackrel{\sqrt{-1}}{\pm\stackrel{\downarrow }{i}\sqrt{14}}[/tex]

==============================

Work Shown:

d = number of dimes

n = number of nickels

10d = value of all the dimes in cents

5n = value of all the nickels in cents

10d+5n = total value of all the coins in cents

$3.30 = 3.30*100 = 330 cents

so one equation is 10d+5n = 330

-------

Let's set up the second equation

we have 42 coins, so n+d = 42

subtract d from both sides to get n = 42-d

-------

Go back to the first equation and apply substitution to solve for d.

10d+5n = 330

10d+5(42-d) = 330 ... plug in n = 42-d

10d+5(42)+5(-d) = 330 ... distribute

10d+210-5d = 330

5d+210 = 330

5d = 330-210 ... subtract 210 from both sides

5d = 120

d = 120/5 ... divide both sides by 5

d = 24

-------

Now we can use that to find n.

n = 42-d

n = 42-24 ... plug in d = 24

n = 18

------

Check:

n = 18 nickels

5*n = 5*18 = 90 cents from just the nickels

d = 24 dimes

10*d = 10*24 = 240 cents from just the dimes

5n+10d = 90+240 = 330 cents = $3.30 total from all the coins

n+d = 18+24 = 42 coins total

Answers are confirmed

Final answer:

To solve the question, set up a system of linear equations based on 0.10d + 0.05n = 3.30 and d + n = 42. Solve the system to find there are 33 dimes and 9 nickels in the collection.

Explanation:

The question involves solving a system of linear equations based on the given conditions involving dimes and nickels. To find out how many of each kind of coin there are, we can set up the following equations using the facts provided:

Let d be the number of dimes.

Let n be the number of nickels.

Since the total value is $3.30, we can write the equation: 0.10d + 0.05n = 3.30 (since a dime is worth 10 cents and a nickel is worth 5 cents).

We are also told that there are 42 coins in total, which gives us the equation: d + n = 42.

Now we have a system of equations:

0.10d + 0.05n = 3.30

d + n = 42

To solve this system, we can multiply the second equation by 0.10 to make the coefficient of d the same in both equations:

0.10d + 0.05n = 3.30

0.10d + 0.10n = 4.20

We then subtract the first equation from the second to eliminate d:

0.10n = 0.90

n = 9 nickels

Plugging n = 9 into the second original equation d + 9 = 42, we get:

d = 42 - 9

d = 33 dimes

Therefore, there are 33 dimes and 9 nickels in the collection.

Answer:

The question is not complete, nut here is the complete question ; A company produces alarm clocks. During the regular​ workweek, the labor cost for producing one clock is ​$4.00. ​However, if a clock is produced on​ overtime, the labor cost is ​$5.00. Management has decided to spend no more than a total of ​$51,000 per week for labor. The company must produce 12,000 clocks this week. What is the minimum number of clocks that must be produced during the regular​ workweek?

Step-by-step explanation:

Tthe detailed analysis and step by step calculation is as shown in the attached file.

Answer:

  x = 17

Step-by-step explanation:

Vertical angles are congruent, so ...

  5x° = 85°

  x = 85°/5° . . . . . . divide by the coefficient of x

  x = 17

Answer:

c

Step-by-step explanation:

Answer:

[tex]x=14[/tex]

Step-by-step explanation:

Considering the small triangle in which the one side and two angles are given:

Finding the third angle of the small triangle

Sum of angles of the triangle is [tex]180[/tex]°

as two angles are given i.e 90° and 45°, so third angle is 180°-(90°+45°)

Third angle in the small triangle is 45°.

As the opposite angles are 45° joining together to form 90° angle, therefore the small triangle is an isosceles triangle in which the opposite sides are equal.

Therefore the two sides are 7 and 7 of small triangle, so By Pythagoras theorem the third side is

[tex]H=\sqrt{P^2+B^2}\\ \\=\sqrt{7^2+7^2}\\\\=\sqrt{98} \\H=7\sqrt{2}[/tex]

Similarly the bigger triangle is also an isosceles triangle whose base is determined i.e  [tex]7\sqrt{2}[/tex] = perpendicular length of bigger triangle.

Applying the Pythagoras theorem in bigger triangle:

           [tex]x=\sqrt{(7\sqrt{2})^2+(7\sqrt{2})^2 }\\x=\sqrt{98+98}\\\\ x=\sqrt{196} \\\\x=14[/tex]

Answer:

A=B-5

Step-by-step explanation:

Albert is known as the variable A.

Bill is known as the variable B.

If Albert is 5 years younger than Bill. Then the equation will be

a=b-5

Answer:

16mm and 12mm

Step-by-step explanation:

Final answer:

The median rainfall for the highland storms is 19 mm and for the lowland storms is 13 mm.

Explanation:

To find the median rainfall for the highland storms, we need to locate the middle value in the dot plot. Since there are 14 observations, the median is between the seventh value, 18, and the eighth value, 20. To find the median, add the two values together and divide by two: (18 + 20) / 2 = 19.

To find the median rainfall for the lowland storms, we also need to locate the middle value in the dot plot. Since there are 14 observations, the median is between the seventh value, 12, and the eighth value, 14. To find the median, add the two values together and divide by two: (12 + 14) / 2 = 13.

Step-by-step explanation:

-5 5/6 ÷(-2 1/6)

Turn them into improper fractions

-35/6 and -13/6

Change the division sign to multiply

-35/6 × -13/6

Making -13/6 into -6/13

Solve

-35/6 × -6/13 = 210/78

Simplify

Answer:

35/13

Edit: if you want it to be a mixed number, it will be 2 9/13

Answer:

-5 5/6 ÷(-2 1/6)

Turn them into improper fractions

-35/6 and -13/6

Change the division sign to multiply

-35/6 × -13/6

Making -13/6 into -6/13

Solve

-35/6 × -6/13 = 210/78

Simplify explanation:

Answer:

u = 5

Step-by-step explanation:

Answer:460

Step-by-step explanation:

To sum the numbers in scientific notation, you add the coefficients and keep the exponent. The correct sum of 2.5 \(\times\) 10^10 and 7.8 \(\times\) 10^10, expressed in proper scientific notation, is 1.03 \(\times\) 10^11.

To find the sum of 2.5 \(\times\) 10^10 and 7.8 \(\times\) 10^10, you add the two numbers while keeping the same exponent since they are like terms in scientific notation. You calculate 2.5 + 7.8 which equals 10.3. Therefore, the sum in scientific notation is 10.3 \(\times\) 10^10.

However, in proper scientific notation, this number should have only one non-zero digit to the left of the decimal point. So, we adjust this sum by writing it as 1.03 \(\times\) 10^11 by moving the decimal one place to the left and increasing the exponent by 1. Thus, the correct answer is 1.03 \(\times\) 10^11, which correlates with option C.

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Answer:

Part 1) [tex]f(x)=(x-2)^{2}-16[/tex]

Part 2) The function's correct axis of symmetry is x=2

Option f(x) = (x - 2)² - 16, x = 2

Step-by-step explanation:

we have

[tex]f(x)=x^{2} -4x-12[/tex]

This is a vertical parabola open upward

The vertex is the minimum

Part 1) Convert to vertex form

Complete the square. Remember to balance the equation by adding the same constants to each side.

[tex]f(x)=(x^{2} -4x+2^2)-12-2^2[/tex]

[tex]f(x)=(x^{2} -4x+4)-16[/tex]

Rewrite as perfect squares

[tex]f(x)=(x-2)^{2}-16[/tex] ----> function in vertex form

Te vertex is the point (2,-16)

Part 2) Find the axis of symmetry

we know that

The equation of the axis of symmetry of a vertical parabola  is equal to the x-coordinate of the vertex

The vertex is the point (2,-16)

therefore

The function's correct axis of symmetry is x=2

Final answer:

The function f(x) = x² - 4x - 12 rewritten in vertex form is f(x) = (x - 2)² - 16, and the axis of symmetry for this function is x = 2.

Explanation:

To rewrite the function f(x) = x² - 4x - 12 in vertex form, we need to complete the square. This involves the following steps:

The axis of symmetry for a parabola in the form (x - h)² is always x = h, which in this case is x = 2.

Therefore, the correct answer is f(x) = (x - 2)² - 16, x = 2.

Answer:

(-9,-9)

I Agree

Step-by-step explanation: