Solve the inequality.
|5 - 2x|> 14

The equation of the line that passes through the point (3,2) and has a slope of 4 is; y = 4x - 10

The equation of the straight line has its slope and given point.

If we have a non-vertical line that passes through any point(x1, y1) and has a gradient m. then general point (x, y) must satisfy the equation

y-y₁ = m(x-x₁)

Which is the required equation of a line in a point-slope form.

Point (3,2)

Then Slope m = 4

Now Write the equation as;

y - 2 = 4(x - 3)

y = 4x - 10

Hence, The equation of the line is; y = 4x - 10

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The total amount of sugar that was consumed by Kylie in the past nine (9) days is equal to 3 units of sugar.

In Mathematics and Statistics, a line plot refers a type of graph that is used to graphically represent a data set above a number line, while using crosses, dots, or any other mathematical symbol.

Based on the data and information provided in the line plot shown in the image attached above, we can calculate the total amount of sugar that was consumed by Kylie in the past nine (9) days as follows:

Total sugar consumed = (1/8 + 1/8 + 1/8) + 1/4 + (3/8 + 3/8 + 3/8) + (5/8 + 5/8)

Total sugar consumed = 3(1/8) + 1/4 + 3(3/8) + 2(5/8)

Total sugar consumed = 3/8 + 1/4 + 9/8 + 10/8

Total sugar consumed = 22/8 + 1/4

Total sugar consumed = (22 + 2)/8

Total sugar consumed = 24/8

Total sugar consumed = 3 units of sugar.

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Certainly! The problem can be solved using the Pythagorean theorem,

which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

In this case, the ladder acts as the hypotenuse, and we need to find the length of the vertical side (height) it reaches up the wall.

The ladder forms the hypotenuse, and its length is given as 12 meters. The distance from the foot of the ladder to the base of the wall represents one side of the triangle, which is 4.5 meters.

By substituting the given values into the Pythagorean theorem equation: (12m)^2 = h^2 + (4.5m)^2, we can solve for the unknown height 'h'.

Squaring 12m gives us 144m^2, and squaring 4.5m yields 20.25m^2. By subtracting 20.25m^2 from both sides of the equation, we isolate 'h^2'.

We then take the square root of both sides to find 'h'. The square root of 123.75m^2 is approximately 11.12m.

Therefore, the ladder reaches a height of approximately 11.12 meters up the wall.

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Answer:

the third option

Step-by-step explanation:

that is actually the proof for Pythagoras :

both squares have the total area of (a + b)².

each of the triangles (4 in figure 1, 4 in figure 2) has the same area as the others : a×b/2

so, for figure 1

(a + b)² = 4×a×b/2 + c² = 2×a×b + c²

and for figure 2

(a + b)² = 4×a×b/2 + a² + b² = 2×a×b + a² + b²

2×a×b + c² = 2×a×b + a² + b²

c² = a² + b²

math is hard, but sometimes it can be easy

Answer:

a little bit of bth

Step-by-step explanation:

For the function  f(x) = 2x + 3 the third iterate x₃  is 37

To find the third iterate, x3, of the function f(x) = 2x + 3, given an initial value of x₀ = 2,

we can apply the function repeatedly.

Starting with x₀ = 2:

x₁ = f(x₀)

= 2(2) + 3

= 7

x₂ = f(x₁)

= 2(7) + 3 = 17

x₃ = f(x₂)

= 2(17) + 3

= 37

Therefore, the third iterate x₃  is 37.

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$2010.458 is her new balance after she makes one new transaction for $51.

What does a credit balance mean?

The amount that the credit card company owes you is shown as a credit balance on your billing statement. Each payment you make results in credits being added to your account.

                                   When you return something you purchased with your credit card, you can receive an additional credit.

Credit balance  = $1,603

   APR = 28.6%

        = 28.6%  * $1,603

         =   458.458

Credit balance  = $1,603 + 458.458

                        = $2061.458

  net balance =  $2061.458 - 51

                      = $2010.458

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The cost per ounce of the premium walnut is $0. 23

To determine the value of the cost, we need to note that proportion is simply described as the comparison of numbers such  that they are made equal to another.

From the information given, we have that;

54 ounces of premium walnuts costs $12.95

This is represented as;

54 ounces = $12. 95

Then 1 = x

cross multiply the values, we get;

x = $12.95/54

Divide the values, we get;

x = $0. 23

Hence, the value is $0. 23 per premium walnut

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Answer:

 6.47

Since it's just asking for the other side of the diameter, it's equivalent to the radius given already.

Answer:

6.47

Since it's just asking for the other side of the diameter, it's equivalent to the radius given already.

Step-by-step explanation:

The distance will be in the decimal form is :41.34

Consider the triangle :

Where “a” is the perpendicular,

“b” is the base,

“c” is the hypotenuse.

According to the definition, the Pythagoras Theorem formula is given as:

\(Hypotenuse^2 = Perpendicular^2 + Base^2\)

\(c^2 = a^2 + b^2\)

We have the points are:

15,-17 and -20, -5

To find the distance between them.

The distance of x- axis is:

15 - (-20)

= 15 + 20

= 35

The distance of y- axis is:

|17 - 5| = |-22| = 22

We can now use the Pythagorean theorem (a²+b²=c²) with our imaginary triangle:

\(x^2+y^2=(distance)^2\)

\(35^2+22^2=distance^2\)

\(1709= distance^2\\Distance = \sqrt{1709}\)

In decimal form the distance would be around 41.34.

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Answer:

d. 2x^2

Step-by-step explanation

The total interest for the loan is $4,550. This means that over the course of 5 years, you will pay back the original loan amount of $13,000 plus $4,550 in interest for a total of $17,550.

To calculate the total interest for this loan, we need to use the simple interest formula:
Monthly EMI formula :
Interest = Principal x Rate x Time

In this case, the principal (amount borrowed) is $13,000, the rate is 7%, and the time is 5 years.

So,

Interest = $13,000 x 0.07 x 5

Interest = $4,550

It's important to keep in mind that this calculation assumes that the interest rate remains constant over the entire 5-year period.

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If Gopal, Krishna and Govind are partners sharing profits and losses in the ratio of 5 4 3. The gaining ratio will be: (a) 5:3.

Since Krishna is retiring, her share of profit will now be divided between Gopal and Govind in the same ratio as their existing profit-sharing ratio.

The total amount paid to Krishna is 1,20,000. Out of this, Gopal has paid 80,000 and Govind has paid 40,000.

So, the share of profit purchased by Gopal is:

5/12 x 120,000 = 50,000

And the share of profit purchased by Govind is:

3/12 x 120,000 = 30,000

Now, the total profit sharing ratio of the remaining partners (Gopal and Govind) will be:

5:3 + 3:3 = 8:3

Therefore, the gaining ratio will be:

Gopal = 50,000 / (50,000 + 30,000) = 5/8

Govind = 30,000 / (50,000 + 30,000) = 3/8

So, the gaining ratio of Gopal and Govind will be 5:3, which is option (a).

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The statements that are true are:

Clayton could use the relationship (x, y) right-arrow (y, x) to find the points of the image.

Clayton could negate both the x and y values in the points to find the points of the image.

C’ will move because all points move in a reflection.

The image and the pre-image will be congruent triangles.

The image and pre-image will not have the same orientation because reflections flip figures.

Options A, B, D, E, and F.

There are two ways of reflection.

Along x-axis:

(x, y) – (x, -y)

Along y-axis:

(x, y) - (-x, y)

We have,

Clayton could use the relationship (x, y) → (y, x) to find the points of the image.

This is the y = x reflection rule.

This is true.

Clayton could negate both the x and y values in the points to find the points of the image.

Reflection of (x, y) along the x-axis and y-axis consecutively will give us

(-x, -y).

This is true.

C’ will remain in the same location as C because it is on the line of reflection.

This is not true.

C’ will move because all points move in a reflection.

This is true.

The image and the pre-image will be congruent triangles.

This is true.

The image and pre-image will not have the same orientation because reflections flip figures.

This is true.

Thus,

All statements are true except the statement:

C’ will remain in the same location as C because it is on the line of reflection.

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Answer:

25

Step-by-step explanation:

l x w = h

25 x 7.2 = 180

Answer:

11

Step-by-step explanation:

GIVEN

x = 6

y = 2

STEPS

(4x - 12) + (1/3xy - 5 )

(4(6) - 12 ) + ( 1/3(6x2) - 5)

(24 - 12) + ( 1/3(12) - 5)

12 + (4 - 5)

12 + (-1)

(12 - 1)

11

The theoretical yield, for this reaction, is 415 mg.

Percent yield is defined as the percent ratio of actual yield to the theoretical yield, and it is calculated as the experimental yield divided by the theoretical yield and multiplied by 100%.

The formula for Percent yield is given as:

Percent yield =Actual yield/theoretical yield*100

The given information is

Percent yield = 44.0%

Actual yield = 183 mg

Now plug the values in the above equation:

44=183/theoretical yield*100

theoretical yield=183/44*100

theoretical yield=415.900mg

Therefore, the theoretical yield, for this reaction, is 415 mg.

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Answer:

24 yards

Step-by-step explanation:

If the ratio is 25:20:15, we can assume that the pieces added together would equal 60. Not 60 yards, just 60 for now. 6 yards represents 15 in 25:20:15, and 15/60 = 1/4. So the piece that is 6 yards is 1/4 the length of the whole cloth. So in order to get the whole length, we multiply 6 by 4, which is equal to 24.

Answer:

51 miles

Step-by-step explanation:

hope it's clear and understandable

:)

Answer:

3 gallons

Step-by-step explanation:

For every value of green ( 'x') ....white is 3 times as much

  for 1 gallon green     ====> 3 gallons white

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:252 committees

Step-by-step explanation: This is a question of permutation and combinations.

Let us first know what permutations and combinations.

A number of permutations (order matters) of n things taken r at a time:

nPr=n!(n−r)!

A number of combinations (order does not matter) of n things taken r at a time:

nCr=n!(n−r)!r!

So, in this question, we have to find that in how many ways, we can select a committee of five members from a group of 10 people.

So, in this question, the process of choosing the persons does not matter which means the order of choice does not matter.

So, we are going to use the formula for this question is nCr=n!(n−r)!r!

We are choosing 5 persons from 10 persons where order does not matter.

Then, the numbers of ways are 10!(10−5)!5!

As we know that n!=n×(n−1)×(n−2)×(n−3)×........×2×1

Then, 10!(10−5)!5!

can be written as

10!(10−5)!5!=10!5!×5!=10×9×8×7×6×5×4×3×2×1(5×4×3×2×1)×(5×4×3×2×1)

Which is also can be written as

10!(10−5)!5!=10×9×8×7×65×4×3×2×1=105×9×84×7×63×2=2×9×2×7×1=252

Hence, 10!(10−5)!5!=252

Therefore, the number of ways of selecting a committee of 5 members from a group of 10 persons is 252.

Answer:

B. \( \sqrt{106} \)

Step-by-step explanation:

Distance between A(-4, 3) and B(5, -2) using distance formula, \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \)

Let,

\( (-4, 3) = (x_1, y_1) \)

\( (5, -2) = (x_2, y_2) \)

Plug in the values into the formula

\( d = \sqrt{(5 -(-4))^2 + (-2 - 3)^2} \)

\( d = \sqrt{(9)^2 + (-5)^2} \)

\( d = \sqrt{81 + 25} \)

\( d = \sqrt{106} \)

Answer:

Discrete random variable.

Step-by-step explanation:

Discrete variable:

Countable numbers(0,1,2,3,...)

Continuous variable:

Can assume decimal values, such as 0.5, 2.5,...

Number of bald eagles:

Number of bald eagles is a countable value, either there a 0, 100, 1000,... so it is a discrete random variable.

Answer:

Discrete random variable.

Step-by-step explanation:

A) The distance that a force of 3 newtons would stretch the rubber band is; 0.015 m

B) The amount of work it takes to stretch the rubber band this far is; 0.0225 J

From Hookes's law, as long as the elastic limit is not exceeded the extension is directly proportional to the force applied.

F = Ke

Where;

F = force

K = force constant

e = extension

Thus,  for a restoring force of magnitude 2 newtons ;

2 N = K(1 × 10⁻²) m

K = 2 N /(1 × 10⁻²) m

K = 200 N/m

a) For a force of 3 newtons, we have;

3N = 200 N/m × a

Where a is the extension in meters

a = 3N/200 N/m

a = 0.015 m

b) The formula to find the work done is;

P.E = ¹/₂Ke²

P.E = ¹/₂ * 200 * 0.015²

P.E = 0.0225 J

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You should buy approximately 1.067 kilograms of apples at $10.20 per kilogram in order to have the kilogram of fruit cost $8.15.

Let's assume that Sally bought x kilograms of apples at $10.20 per kilogram.

The total cost of bananas is given as AED 7.35 per kilogram, and Sally bought 1.4 kilograms of bananas. So, the cost of the bananas is:

Cost of bananas = AED 7.35 * 1.4 = AED 10.29

The total cost of apples is given by the equation:

Cost of apples = $10.20 * x

The total cost of the fruits combined should be AED 8.15 per kilogram. So, the equation becomes:

Total cost of fruits = (Cost of bananas + Cost of apples) / (1.4 + x) = AED 8.15

Substituting the known values, we have:

(10.29 + 10.20 * x) / (1.4 + x) = 8.15

Cross-multiplying and simplifying, we get:

10.29 + 10.20 * x = 8.15 * (1.4 + x)

Expanding the equation, we have:

10.29 + 10.20 * x = 11.41 + 8.15 * x

Rearranging the equation, we get:

10.20 * x - 8.15 * x = 11.41 - 10.29

1.05 * x = 1.12

Dividing both sides by 1.05, we find:

x = 1.12 / 1.05

x ≈ 1.067

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The number of short sleeves that Maria sold is 819.

Ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them.

In this case, Maria’s clothing store sold 1547 shirts with the ratio of short sleeve to long sleeve shirt being 9:8.

The number of short sleeves will be:

= Ratio for short sleeve / Total ratio × Total number of clothes

= 9 / (8 + 9) × 1547

= 9/17 × 1547

= 819

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