How do you know if a point is a solution to a linear inequality

Answer:

If you're saying Jan ate 1/4 of what was left. How much of the pie did Jan eat?

then the answer is 5/32

Step-by-step explanation:

The simplified fraction of the given expression would be 19/30.

What is a fraction?

A fraction is a portion of a whole or, more broadly, any number of equal parts. In everyday English, a fraction describes the number of parts of a specific size, such as one-half, eight-fifths, or three-quarters.

The given expression is

                         \(6\frac{5}{6} + (-6\frac{1}{5})\)

Now simplifying the above expression, we get

                                \(=6\frac{5}{6} + (-6\frac{1}{5})\\\\\=\frac{36+5}{6} -(\frac{30+1}{5})\\\\=\frac{41}{6} - \frac{31}{5}\\\\=\frac{41*5-31*6}{6*5}\\\\=\frac{205-186}{30}\\\\=\frac{19}{30}\)

Hence the simplified fraction of the given expression would be 19/30.

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Answer:

25

Step-by-step explanation:

Answer:

$101.64

Step-by-step explanation:

Step one:

Given data

Original price is $77.00

markdown is 32%​

Required

The sale price

Step two:

Percent markdown= sale-original/origal*100

32=sale-77/77*100

32/100=sale-77/77

cross multiply

0.32*77= sale- 77

24.64=sale-77

add 77 to both sides

24.64+77= sale

101.64= sale

sale= $101.64

When Henry ran 1 5/8 miles in the morning and 9/10 miles in the afternoon, In all he a total of 2 21/40 miles

The number of miles Henry ran is calculated by addition operation

The sum of the miles Henry ran in the morning plus the number of miles he ran in the afternoon gives the what Henry ran in all

The procedure involves addition of tractions and done as follows

= 1 5/8 + 9/10

= 13/8 + 9/10

adding both fractions will result to

= 101/40 miles

= 2 21/40 miles (as a mixed number)

Henry ran a sum of 2 21/40 miles

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All the values of x, y and z are,

z = 12.99

y = 7.01

x = 28.3 degree

We have to given that;

In a triangle,

Two angles are, 61.7 degree and 90 degree

And, One side is, 14.76.

Now, We can formulate;

sin 61.7° = Perpendicular / Hypotenuse

sin 61.7° = z / 14.76

0.88 = z / 14.76

z = 0.88 x 14.76

z = 12.99

And, By Pythagoras theorem we get;

14.76² = z² + y²

14.76² = 12.99² + y²

217.85 = 168.74 + y²

y² = 217.85 - 168.74

y² = 49.1

y = 7.01

And, By sum of all the angles in triangle, we get;

x + 61.7 + 90 = 180

x + 151.7 = 180

x = 180 - 151.7

x = 28.3 degree

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Answer:

Um the North China Plain

Step-by-step explanation:

Is dis math...

Answer:

you would need 2 1/2 cups of flour

Answer:

2.5 cups of flour is needed for 5 eggs.

Step-by-step explanation:

The crepe recipe calls for 2 eggs, 1 cup of flour, and 1 cup of milk. This means that the ratio of eggs to cup of flour to cup of milk required is 2:1:1

Therefore, if you use 5 eggs, the proportions would increase by 2.5. Multiplying by 2.5, it becomes

5 : 2.5 : 2.5

Therefore, you would need 2.5 cups of flour for 5 eggs.

\( \bf \underline{Given-} \\ \)

\( \sf{x = \frac{ \sqrt{p + 2q} + \sqrt{p - 2q} }{ \sqrt{p + 2q} - \sqrt{p - 2q} } } \\ \)

\( \bf \underline{To\: show-} \\ \)

\( \sf{prove \: that : \: {qx}^{2} - px + q = 0 } \\ \)

\( \bf \underline{Solution-} \\ \)

\(\textsf{We have,}\\\)

\( \sf{x = \frac{ \sqrt{p + 2q} + \sqrt{p - 2q} }{ \sqrt{p + 2q} - \sqrt{p - 2q} } } \\ \)

\(\textsf{The denominator is : √(p+2q) - √(p-2q)}\\\)

\(\textsf{We know that}\\\)

\(\textsf{The rationalising factor of : √(a + b) - √(a-b) = √(a+b) + √(a-b).}\\\)

\(\textsf{Therefore, the rationalising factor of: √(p+2q) - √(p-2q) = √(p+2q) + √(p-2q).}\\\)

\(\textsf{On, rationalising the denominator,we get}\\\)

\( \sf{x = \frac{ \sqrt{p + 2a} + \sqrt{p - 2q} }{ \sqrt{p + 2q} - \sqrt{p - 2q} } \times\frac{ \sqrt{p + 2q} + \sqrt{p - 2q} }{ \sqrt{p + 2q} + \sqrt{p - 2q} } } \\ \)

\( \sf{x = \frac{ (\sqrt{p + 2q} + \sqrt{p - 2q})( \sqrt{p + 2q} + \sqrt{p - 2q}) }{( \sqrt{p + 2q} - \sqrt{p - 2q})( \sqrt{p + 2q} + \sqrt{p - 2q} )} } \\ \)

\( \sf{x = \frac{ (\sqrt{p + 2q} + \sqrt{p - 2q} {)}^{2} }{( \sqrt{p + 2q} - \sqrt{p - 2q})( \sqrt{p + 2q} + \sqrt{p - 2q} )} } \\ \)

\(\textsf{★ Now, comparing the denominator with (a-b)(a+b), we get}\\\)

\( \sf{ \: \: \: \: \: a = \sqrt{p + 2q} \: and \: b = \sqrt{p - 2q} } \\ \)

\(\textsf{Using identity (a+b)(a-b) = a²-b², we get}\\\)

\( \sf{x = \frac{ (\sqrt{p + 2q} + \sqrt{p - 2q} {)}^{2} }{( \sqrt{p + 2q} {)}^{2} - (\sqrt{p - 2q} {)}^{2} } } \\ \)

\( \sf{x = \frac{ (\sqrt{p + 2q} + \sqrt{p - 2q} {)}^{2} }{p + 2q - (p + 2q) } } \\ \)

\( \sf{x = \frac{ p + 2q + p - 2q + 2 \sqrt{ {p}^{2} - {4q}^{2} } }{p + 2q - (p + 2q) } } \\ \)

\( \Rightarrow\sf{x = \frac{p + \sqrt{ {p}^{2} - {4q}^{2} } }{2q} } \\ \)

\(\Rightarrow\sf{2qx =p + \sqrt{ {p}^{2} - {4q}^{2} } } \\ \)

\(\Rightarrow\sf{2qx - p = \sqrt{ {p}^{2} - {4q}^{2} } } \\ \)

\(\textsf{Squaring on both sides,we get}\\\)

\( \sf{(2qx - p {)}^{2} = {p}^{2} - 4 {q}^{2} } \\ \)

\(\Rightarrow\sf{ {4q}^{2} {x}^{2} + \cancel{{p}^{2}} - 4pqx - \cancel{ {p}^{2}} + {4q}^{2} =0} \\ \)

\(\Rightarrow\sf{ {4q}^{2} {x}^{2} - 4pqx + {4q}^{2} =0 \: \: \Rightarrow\sf{4( {q}^{2} {x}^{2} - pqx + {4q}^{2} ) =0} } \\ \)

\(\Rightarrow\sf{{q}^{2} {x}^{2} - pqx + {4q}^{2} =0 \: \: \: \: \: \Rightarrow\sf{q( {q}{x}^{2} - px + {q} ) =0} } \\ \)

\(\Rightarrow\sf{{q}{x}^{2} - px + {q} =0} \\ \)

\( \bf \underline{Hence, proved.} \\ \)

The size of angle x from the figure is 16 degrees

The sum of the interior angle of a triangle is 180 degrees, hence to get the value of X, we will take the sum of all the given angles and equate them to 180 degrees.

127 + 37 + X = 180

164 + x = 180

Subtract 164 from  both sides

164 + x - 164 = 180 - 164

x =16 degrees

Hence the size of angle x from the figure is 16 degrees

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Answer:

As we know that the sum of interior angles of triangle is 180⁰.

Accounting to the question :

\(\implies\) Sum of angles = 180⁰

\(\implies\) 127⁰ + 37⁰ + X = 180⁰

\(\implies\) 164⁰ + X = 180⁰

\(\implies\) X = 180⁰ - 164⁰

\(\implies\) X = 16⁰

Hence, the size of angle is 16⁰.

\(\rule{300}{1.5}\)

Answer:

£16

Step-by-step explanation:

Let's assume the normal price of the coat is represented by the variable "P."

According to the information given, the normal price of the coat is reduced by £12. This can be expressed as:

P - £12

Additionally, in the sale, normal prices are reduced by 25%. This reduction can be calculated by multiplying the normal price by 25% (or 0.25):

0.25P

To find the sale price after the 25% reduction, we subtract the reduction amount from the normal price:

P - 0.25P = £12

Simplifying the equation:

0.75P = £12

To solve for P, we divide both sides of the equation by 0.75:

P = £12 / 0.75

Performing the calculation:

P = £16

Therefore, the normal price of the coat is £16.

The value of x for the given trigonometric function is (15/18)π.

The fundamental 6 functions of trigonometry have a range of numbers as their result and a domain input value that is the angle of a right triangle.

The trigonometric function is very good and useful in real-life problems related to the right angle.

As per the given,

secx = (-2√3)/3

1/cosx = -2/√3

cosx = -√3/2

x  = 150° = (15/18)π

Thus, x goes into the second quadrant as shown below.

Hence"The value of x for the given trigonometric function is (15/18)π".

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Answer:

20 feet

Step-by-step explanation:

6(3)=18

60/3=20

Answer: The building would be 20 feet tall

Step-by-step explanation: If the 6 foot man was casting a shadow of 18 feet you can figure out that 6 times 3 is 18 and then take 60 divided by three to get an answer of 20 feet.

Answer:

x = 17

Step-by-step explanation:

Line l and m are two parallel lines cut across by the transversal line, therefore, the angle measuring 53° and (8x - 9)° are interior angles on the same side. Interior angles on the same side are supplementary.

Therefore:

53° + (8x - 9)° = 180°

Solve for x

53 + 8x - 9 = 180

Collect like terms

53 - 9 + 8x = 180

44 + 8x = 180

Subtract 44 from both sides

44 + 8x - 44 = 180 - 44

8x = 136

Divide both sides by 8

8x/8 = 136/8

x = 17

Answer: 3 part answer

-2

-10

10

Step-by-step explanation:

If you move twice to the left, end up at -2

2 × -5 = -10

opposite of -10 is 10

The proof demonstrates that given a well-ordered set W, an isomorphic ordinal can be found using the function F. The uniqueness of this ordinal is established using the Replacement Axioms. The set F(W) is shown to exist for each x in W, and if the least F(W) exists, it serves as an isomorphism of VV onto -y.

Lemma 2.7: This is a previously stated lemma that is referenced in the proof. Unfortunately, without the specific details of Lemma 2.7, it's difficult to provide further explanation for its role in the proof.

Well-ordered set W: A well-ordered set is a set where every non-empty subset has a least element. In this proof, W is assumed to be a well-ordered set.

Isomorphic ordinal: An ordinal is a mathematical concept that extends the notion of natural numbers to represent order and magnitude. An isomorphic ordinal refers to an ordinal that has a one-to-one correspondence or mapping with another ordinal, preserving their order and magnitude properties.

Function F: The function F is defined to assign an ordinal o to each element x in W. This means that for every x in W, there is a corresponding ordinal o.

Existence and uniqueness: The proof asserts that if there exists an ordinal o that is isomorphic to a specific initial segment of the ordinal VV (the set of all ordinals), then this ordinal o is unique. In other words, there is only one ordinal that can be mapped to the initial segment of VV given by x.

Replacement Axioms: The Replacement Axioms are principles in set theory that allow the construction of new sets based on existing ones. In this case, the Replacement Axioms are used to assert that the set F(W) exists, which is the collection of all ordinals that can be assigned to elements of W.

For each x in W: The proof states that for every x in W, there exists an ordinal o that can be assigned to it. If there is no such ordinal, the proof suggests considering the least x for which such an ordinal does not exist.

The least F(W): The proof introduces the concept of the least element in the set F(W), denoted as the least F(W). If this least element exists, it serves as an isomorphism (a one-to-one mapping) of the set of all ordinals VV onto the ordinal -y.

Overall, the proof outlines the existence and uniqueness of an isomorphic ordinal that can be obtained from a well-ordered set W using the function F, and it relies on the Replacement Axioms and the concept of least element to establish this result.

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The number of boxes that Amanda can cover with W square inches of wallpaper will be equal to W/2(lw + lh + wh).

Let's assume that Amanda wants to build n wooden storage boxes. All of these boxes are shaped like rectangular prisms, as shown in the image below.

She wants to cover all the sides of each box with special wallpaper. If she has a total of W square inches of wallpaper, we need to find out how many boxes she can cover. Let's solve this problem mathematically.

Mathematical Solution:

Each rectangular prism has six sides (faces). If we want to cover all the six sides of a rectangular prism with special wallpaper, we need to find the total surface area of that rectangular prism. Therefore, the surface area of each rectangular prism can be calculated by the formula:

Surface Area = 2lw + 2lh + 2wh,

where l, w, and h are the length, width, and height of the rectangular prism, respectively.

We know that Amanda has W square inches of wallpaper to cover all the boxes. Therefore, the total surface area of n boxes will be:

n × Surface Area = W.

Substituting the value of the Surface Area, we have:

n × (2lw + 2lh + 2wh) = W

2n(lw + lh + wh) = W

n(lw + lh + wh) = W/2

n = W/2(lw + lh + wh).

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The distance between point T (-5, 1) and point I (-1, 1) is 4 units.

To find the distance between two points, we can use the distance formula, which is derived from the Pythagorean theorem. The formula is:

Distance = √((x2 - x1)² + (y2 - y1)²)

Let's apply this formula to find the distance between point T (-5, 1) and point I (-1, 1):

x1 = -5, y1 = 1 (coordinates of point T)

x2 = -1, y2 = 1 (coordinates of point I)

Plugging these values into the formula, we have:

Distance = √((-1 - (-5))² + (1 - 1)²)

        = √(4² + 0²)

        = √(16 + 0)

        = √16

        = 4

Therefore, the distance between point T (-5, 1) and point I (-1, 1) is 4 units.

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Answer:

b=9

Step-by-step explanation:

since a varies directly as b,

a=kb

k=a/b

k=8/3

but when a=24, b will be given by

b=a÷k

b=24÷8/3, b=24×3/8

b=9

Answer: 50 large box

Step-by-step explanation:

First, "boxes of two sizes" means we can assign variables:

Let x = number of large boxes

y = number of small boxes

"There are 115 boxes in all" means x + y = 115 [eq1]

Now, the pounds for each kind of box is:

(pounds per box)*(number of boxes)

So,

pounds for large boxes + pounds for small boxes = 4125 pounds

"the truck is carrying a total of 4125 pounds in boxes"

(50)*(x) + (25)*(y) = 4125 [eq2]

It is important to find two equations so we can solve for two variables.

Solve for one of the variables in eq1 then replace (substitute) the expression for that variable in eq2. Let's solve for x:

x = 115 - y [from eq1]

50(115-y) + 25y = 4125 [from eq2]

5750 - 50y + 25y = 4125 [distribute]

5750 - 25y = 4125

-25y = -1625

y = 65 [divide both sides by (-25)]

There are 65 small boxes.

Put that value into either equation (now, which is easier?) to solve for x:

x = 115 - y

x = 115 - 65

x = 50

There are 50 large boxes.

Check (very important):

Is 50+65 = 115 ? [eq1]

115 = 115 ?yes

Is 50(50) + 25(65) = 4125 ?

2500 + 1625 = 4125 ?

4125 = 4125 ? yes

Hi

f(x) = -3x +8

to calculate an image, remplace x by your number  

f(5) = -3(5) +8 =   -15 +8 = -7

Answer: The answer to your question is C. Brainliest?

Step-by-step explanation:

For the first square, we can multiply both the numerator and denominator by 5 to get an equivalent fraction with a denominator of 60:

2/12 = (2 x 5) / (12 x 5) = 10/60

For the second square, we can multiply both the numerator and denominator by 4 to get an equivalent fraction with a denominator of 60:

2/15 = (2 x 4) / (15 x 4) = 8/60

Now, we can add the two fractions:

10/60 + 8/60 = 18/60

Simplifying this fraction by dividing both numerator and denominator by 6, we get:

18/60 = 3/10

Therefore, the total shaded area in the diagram is 3/10 or 0.3 in decimal form.

The answer is C. 0.3.

Answer:

8

Step-by-step explanation:

i guessed

children

25.5 %

so 25.5% of 100

495

The sales tax rate is 2%.

Answer:

Step-by-step explanation:

Since we are dealing with binomial probability in this scenario, then the outcome is either a success or a failure. A success in this case means that a chosen adult has a bachelor's degree. The probability of success, p would be 20/100 = 0.2

The number of adults sampled, n is 100

The number of success, x is 60

The probability that more than 60 adults have a bachelor's degree P(x >60) would be represented as

d. P(x<60)=binomcdf (100.0.20.60)

binompdf is used when we want to determine P(x = 60)

Answer:

12 is the answer

Step-by-step explanation:

18- 3×2= 18- 6 = 12