What is the "mathematical term" used to describe fractions that name the same amount?

The smallest whole numbers that makes the statement true are:

(a) 41 - 9 ≡ 2 (mod 5)

(b) 17 + 8 ≡ 4 (mod 7)

Let a, b and m be integers. Then a is said to be congruent to b modulo m if m divided a-b. That is,

a ≡ b(mod m) if and only if m divided a-b.

Also here, if b is the smallest integer satisfying this relation, then b is the remainder when a is divided by m.

(a) So for  41 - 9 ≡   (mod 5)

⇒ 32 ≡    (mod 5)

The smallest whole number satisfying this congruence is the remainder when 32 is divided by 5 which is 2.

That is,  41 - 9 ≡ 2 (mod 5)

(b) Similarly for 17 + 8 ≡   (mod 7)

⇒ 25 ≡   (mod 7)

The smallest whole number which makes this statement true is the remainder when 25 is divided by 7, which is 4.

Hence, 17 + 8 ≡ 4 (mod 7)

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Answer:

E empty set

Step-by-step explanation:

The answer is empty at

Answer:

The equation would be y = -3/2x - 1

Step-by-step explanation:

The slope is -3/2 and the y-intercept is -1.

Answer:

x=2 (option B)

Explanation

x²-4=0

x²=4

x=2

Using a graphing calculator :

The scatter plot will look thus:

Answer:

The answer is below

Step-by-step explanation:

Acceleration is the time rate of change in velocity. Acceleration is given by:

Acceleration = change in velocity / time taken

Acceleration = (final velocity - initial velocity) / time

1) The Ferrari is from rest, hence initial velocity = 0. The final velocity = 100 km/h = \(\frac{100\ km*1000\ \frac{m}{km} }{1\ hr*\frac{3600\ s}{1\ hr} } =27.78\ m/s\), time = 5 s

Acceleration = (0 - 27.78) / 5 = 5.56 m/s²

2) The car has initial velocity = 10 m/s. The final velocity = 10 m/s since velocity is constant. time = 20 s

Acceleration = (10 - 10) / 20 = 0 m/s²

3) The ball has initial velocity = 12 m/s. The final velocity = 0 m/s since it stops. time = 36 s

Acceleration = (0 - 12) / 36 = -0.33 m/s²

The value of the expression 18 + 4(28) will be 130.

When the relevant factors and natural laws of a mathematical model are given values, the outcome of the calculation it describes is the expression's outcome.

PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.

The expression is given below.

⇒ 18 + 4(28)

Simplify the expression, then the value of the expression will be

⇒ 18 + 4 x (28)

⇒ 18 + 4 x 28

⇒ 18 + 112

⇒ 130

Thus, the value of the expression 18 + 4(28) will be 130.

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Answer:

  B.  129.7°

Step-by-step explanation:

The law of sines tells you ...

  sin(C)/c = sin(A)/a

  sin(C) = (c/a)sin(A)

  C = arcsin((c/a)sin(A)) = arcsin(117/57·sin(22°)) = 50.3°

The value shown is the result of using the arcsin function, but we know that the supplement of this angle has the same sine value. Then, we could have ...

  C = 180° -50.3° = 129.7°

The figure shows C as an obtuse angle, so we choose this latter value as the appropriate answer to this question.

  C = 129.7° . . . . . matches choice B

_____

Comment on the answer

We note that choice C (50.3°) matches the result of straightforward use of the law of sines. This triangle actually has two solutions for angle C, as we have noted above. Often, figures are "not to scale," so the appearance of angle C as an obtuse angle cannot always be taken at face value. Here, because both choices for angle C are offered, we use the appearance of the figure to help decide the right one.

Answer:

50°

Step-by-step explanation:

The missing angle is an exterior angle

The formula says, that the sum of the two apposite adjacent angles inside the triangle equals two the exterior angle.

So 30° + 20° = 50°

The missing angle is 50°

If my answer is incorrect, pls correct me!

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-Chetan K

The value of a and b in the given complex expression is  1/10 and -1/10 respectively.

This is a problem related to the complex numbers. The complex numbers has a general form of (a+bi) where 'i' is the imaginary number or √-1. The part without an 'i' is called Real Part and the part with an 'i' is called Imaginary Part.

(2i/2+i) - 3i/(3+i) = a + bi

{ 2i(3+i) - 3i(2+i) }/ (2 + i)(3 + i) = a+bi

6i + 2i² - 6i - 3i² / (2 + i)(3 + i) = a+bi

(-2 + 3) / (6 + 5i - 1) = s+bi

1 / (5 + 5i) = a+bi

Now we multiply top and bottom by 5 - 5i :

5 - 5i / (5 + 5i)(5 - 5i) = a+bi

5 - 5i / 25 -25i² = a+bi

5 - 5i / 50 = a+bi

1/10 - 1/10i = a+bi

On comparing the real and imaginary part on the both sides:

a= 1/10 , b= -1/10.

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Answer:

the answer is A........

The 8 will end up in the "ones place".

When 'a' is divided by 'b', then the result we get from the division is the part of 'a' that each one of 'b' items will get. Division can be interpreted as equally dividing the number that is being divided into total x parts, where x is the number of parts the given number is divided.

We need to find the 8 will end up in which place

A negative divided by a negative is positive, then;

2380/ 10 = 238

Therefore, The 8 will end up in the _ ones_ place.

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Producing 73.8 units gives the lowest possible average cost.

The average cost (AC) is the ratio of the total cost to the number of units produced. It is given by:

AC = C(x) / x

AC = (0.2x³ – 24x² + 1514x +30064) / x

AC = 0.2x² - 24x + 1514 + 30064/x

The lowest possible average cost is at AC' = 0. Hence differentiating the average cost, gives:

AC' = 0.4x - 24 - 30064/x²

0.4x - 24 - 30064/x² = 0

0.4x³ - 24x² - 30064 = 0

Solving the cubic polynomial gives:

x = 73.8 units

Therefore the lowest possible average cost is when 73.8 units are produced.

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1. The slope of the curve y⁴ = y² - x² at (-√3/4, - 1/2) is √3/2

2. The slope of the curve y⁴ = y² - x² at (√3/4, - √3/2) is -1/2

The slope of a curve is the tangent to the curve at that point.

Given the curve y⁴ = y² - x², to find the slope of the curve ata the points (-√3/4, - 1/2) and (√3/4, - √3/2), we proceed as follows.

To find the slope of the curve, we find the derivative of the curve. So,

y⁴ = y² - x²

dy⁴/dx = d(y² - x²)/dx

dy⁴/dy × dy/dx = dy²/dy × dy/dx - dx²/dx

4y × dy/dx = 2y × dy/dx - 2x

4y × dy/dx - 2y × dy/dx = - 2x

2ydy/dx = -2x

dy/dx = -2x/2y

dy/dx =-x/y

1. The slope at (-√3/4, - 1/2) is

dy/dx = -x/y

= -√3/4 ÷ - 1/2

=  -√3/4 × 2

= √3/2

2. The slope at (√3/4, - √3/2) is

dy/dx = -x/y

= √3/4 ÷ - √3/2

=  √3/4 × -2/√3

= -2/4

= -1/2

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The outcomes that are contained in the events are

1 - P(X) = 4/5 and 1 - P(X) is the same as P(Not X)

From the question, we have the following parameters that can be used in our computation:

X = gray colours

Given that

gray colours = 3 and 10

We have

X = 3 and 10

Not X =1, 2, 4, 5, 6, 7, 8

The probability is then calculated as

P(X) = 2/10 = 1/5

For P(Not X), we have

P(Not X) = 1 - 1/5 = 4/5

In (a), we have

P(Not X) = 1 - 1/5 = 4/5

This means that

P(Not X) = 1 - P(X)

So, the solution is

1 - P(X) = 4/5

Using the above (a) and (b) as a guide, we have the following:

1 - P(X) is the same as P(Not X)

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The factory must produce 6,400 parts  so that there is 1 ton of scrap aluminum for recycling.

It is given that For every part produced by a factory there are 5 ounces of scrap aluminum that can be recycled there are 16 ounces in 1 pound and 2,000 in 1 ton we need to find how many parts must the factory produce so that there is 1 ton of scrap aluminum for recycling

What is a Ratio?

A quantitative relation between two amounts showing the number of times one value contains in another

1 part produced  ⇒ 5 ounces scrap aluminium recycled.

So, the ratio of parts produced : Scrap of aluminium = 1   : 5  .... (a)

Let us assume for m parts produced ,  1 ton of scrap is recycled.

Also, 1 ton = 2, 000 pounds

and 1 pound = 16 ounces

⇒ 1 ton = 2000 x (16 ounces)  = 32,000 ounces

So, for m parts made in the  factory, 32,000 ounces scrap is recycled.

So, the ratio of parts produced : Scrap of aluminium =  m   : 32,000  .... (b)

From both the given ratio, we get

1   : 5  = m   : 32,000

m=32000/5

m=6400

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Answer:

Yes, in solving she used Cross multiplication, multiplying 3 to 10 and 5 to 2 and arriving at the answer of 30/10, she then divided 30 by 10, getting the final answer which is 3.

\( \frac{3}{5} \ \times \frac{2}{10} = \frac{30}{10} = 3\)

Answer:

3+k+j

Explanation:

Given the statement: add k to 3 then add j to the result​

We are required to write an expression for the sequence.

The first part add k to 3 can be written mathematically below:

Next, it is required that j is added to the result.

Thus, an expression for the sequence is 3+k+j.

It would take 370 days to build the wall with the given conditions.

If 60 men can build a wall in 40 days, then the total man-days required to build the wall is:

60 men x 40 days = 2400 man-days

However, 55 men quit every ten days, which means that after 10 days, there are only 60 - 55 = 5 men left to work on the wall. After 20 days, there are only 5 - 55 = -50 men left, which means that the remaining 5 men cannot work any faster than they were already working. Therefore, we can assume that the remaining 5 men complete the wall on their own.

The number of man-days required for the first 10 days is:

60 men x 10 days = 600 man-days

The number of man-days required for the second 10 days is:

5 men x 10 days = 50 man-days

The total number of man-days required for the first 20 days is:

600 man-days + 50 man-days = 650 man-days

The remaining work can be completed by the 5 men in:

2400 man-days - 650 man-days = 1750 man-days

Therefore, the total time needed to build the wall is:

20 days + 1750 man-days / 5 men = 20 + 350 days = 370 days

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Answer:Write x² + 10x + 29 in the form (x + c)² + d, where c

Step-by-step explanation:

Answer:

(x+5)² + 4, so c is 5 and d is 4

Step-by-step explanation:

x² + 10x + 29 is a quadratic equation which can be witten as x² + bx + c, where b is 10 and c is 29.

We need to complete the square to get it in the form

(x + c)² + d

Completing the square uses the form:

\((x + \frac{b}{2} ) {}^{2} - ( \frac{b}{2} ) {}^{2} + c\)

substitute b = 10 and c = 29 in this form:

\((x + \frac{10}{2}) {}^{2} - ( \frac{10}{2} ) {}^{2} + 29\)

Simplify further:

\((x + 5) {}^{2} - 25 + 29\)

\((x + 5) {}^{2} + 4\)

c = 5, d = 4

The exact values of the given trigonometric functions are:

cos(330) = \(\sqrt{3}/2\) or 0.866

sin(330) = 1/2 or 0.5

To find the trigonometric values of cos(330) and sin(330) exactly, we can use the unit circle and the properties of the trigonometric functions.

In the unit circle, the angle of  330 degrees is equivalent to -30 degrees or \(-\pi/6\) radians. Since cosine is an even function, we know that \(cos(-\theta) = cos(\theta)\), so we can find cos(-30).

Using the special triangles and the reference angle of 30 degrees, we can determine the exact values:

cos(-30) = cos(30) = \(\sqrt{3}/2\)

Similarly, the sine of -30 degrees is the same as the sine of 30 degrees:

sin(-30) = sin(30) = 1/2

Therefore, the exact values are:

cos(330) = cos(-30)= cos(30) = \(\sqrt{3}/2\) or 0.866

sin(330) = sin(-30)= sin(30)= 1/2 or 0.5

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Answer:

$58.80

Step-by-step explanation:

The subtotal is $56.

56*1.05=$58.80.

Answer:

0.58333333....

can i have brainliest plz

Answer:

0.375 or 3/8

Step-by-step explanation:

calculator :)

Answer:GCF of 45 and 63 is 9.

Step-by-step explanation:

factors of 45 are 1,3,5,9,15,45

factors  of 63 are 1,3,7,9,21,63

so the greatest common factor or GCF of 45 and 63 is 9

The greatest common factor of 45 and 63 is equal to 9.

To find the greatest common factor (GCF) of 45 and 63;

First List the factors of each number.

The factors of 45 are;

1, 3, 5, 9, 15, 45.

The factors of 63 are:

1, 3, 7, 9, 21, 63.

Now, Identify the common factors.

The common factors of 45 and 63 are:

1, 3, 9.

To Determine the greatest common factor.

The greatest common factor of 45 and 63 is 9.

Therefore, the GCF of 45 and 63 is 9.

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There are 2100 workers in​ the company

Word problems are sentences describing a 'real-life' situation where a problem needs to be solved by way of a mathematical calculation.

Since 85​% of the workers are women, we can say:

The percentage of worker that aren't women = 100% - 85​% = 15​%

Let N represent the number of all workers. If 315 people work for the company who​ aren't women. We can say:

15​% of N = 315

15/100 × N = 315

0.15N = 315

N = 315/0.15

N = 2100 workers

Method 2:

We can write:

N - 0.85N = 315

0.15N = 315

N = 315/0.15

N = 2100 workers

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The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

To find the quotient of z₁ by z₂ in trigonometric form, we'll express both complex numbers in trigonometric form and then divide them.

Let's represent z₁ in trigonometric form as z₁ = r₁(cosθ₁ + isinθ₁), where r₁ is the magnitude of z₁ and θ₁ is the argument of z₁.

We have:

z₁ = 7(cos(577°) + i sin(577°))

Now, let's represent z₂ in trigonometric form as z₂ = r₂(cosθ₂ + isinθ₂), where r₂ is the magnitude of z₂ and θ₂ is the argument of z₂.

From the given information, we have:

z₂ = 21(cos(-7°) + i sin(-77°))

To find the quotient, we divide z₁ by z₂:

z₁ / z₂ = (r₁/r₂) * [cos(θ₁ - θ₂) + i sin(θ₁ - θ₂)]

Substituting the given values, we have:

z₁ / z₂ = (7/21) * [cos(577° - (-7°)) + i sin(577° - (-7°))]

= (7/21) * [cos(584°) + i sin(584°)]

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

Option C, 21(cos(-7°) + i sin(-77°)), is not the correct answer as it does not represent the quotient of z₁ by z₂.

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line AB is original figure, line A'B' is transformed figure. the length A'B' is given by √[(2.5x₂-2.5x₁)²+(2.5y₂-2.5y₁)²]

What is dilation?

A process of transformation in which an image or figure changes from the original shape.

What is dilating point?

The point which is acted as the center for all contraction and expansion is termed as dilation point.

let, point A is (x₁,y₂) and point B is (x₂,y₂). By using scale factor 2.5, both A and B transformed to the position A' and B'.

hence, A' = (2.5x₁, 2.5y₁) and B'=(2.5x₂,2.5y₂)

now length of A'B' =√[(2.5x₂-2,5x₁)²+(2.5y₂-2.5y₁)²]

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The compound statement "If there are penguins and the aquarium is full of fish, then this is an octopus" can be written in symbolic form as: r ∧ q → o

Let's assign variables to represent the statements:

q: The aquarium is full of fish.

r: There are penguins.

The compound statement "If there are penguins and the aquarium is full of fish, then this is an octopus" can be written in symbolic form as: r ∧ q → o

∧ represents the logical operator "and" which connects the statements r and q.

→ represents the logical operator "implies" or "if...then".

o represents the statement "this is an octopus".

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