What’s the algebraic representation

∠1 and ∠3 are a pair of corresponding angles.

So, in the given image ∠1 and ∠3 are the pair of corresponding angles.

Therefore, ∠1 and ∠3 are a pair of corresponding angles.

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Given:

Given the equation y = x - 2

Required: Classify it as direct variation, inverse variation or neither.

Explanation:

Two variables x and y show direct variation when they satisfies y = ax or y/x = a, where a is non-zero.

Similarly, two variables x and y show inverse variation when they satisfies y = a/x or xy = a, where a is non-zero.

Here, the equation y = x - 2 is in neither of the form y = ax or y = a/x.

So, y = x - 2 show neither direct nor inverse variation.

Final Answer: y = x - 2 show neither direct nor inverse variation.

Answer:

its A

Step-by-step explanation

i took this test

Answer:

tldr: we can set up constant proportions: [tex]\frac{a \text{ units}_1}{b \text{ units}_2} = \frac{c\text{ units}_1}{d\text{ units}_2}[/tex] to solve for values.

Step-by-step explanation:

Proportional Relationships can help in certain situations where values scale proportionally.

For example let's say I take 10 minutes to do 3 pages of work.

I can solve for how long it takes me to do each page: [tex]\frac{3\text{ pages}}{10 \text{ minutes}}[/tex]

Now in real life this isn't going to be constant, because after a certain amount of time humans get tired, and to be this consistent across many minutes is very unrealistic.

But assuming humans don't get tired and it's completely consistent, we can assume this proportion of: [tex]\frac{\text{pages}}{\text{minutes}}[/tex] should be constant, which it represents the amount of pages we do per minute.

This is useful because know this value is equal to [tex]\frac{3\text{ pages}}{10 \text{ minutes}}[/tex] in one scenario, I know this is equal in all scenarios.

So I can set up a proportion as such: [tex]\frac{3\text{ pages}}{10 \text{ minutes}} = \frac{x \text{ pages}}{y \text{ minutes}}[/tex]

to solve for how many pages I can do in "y" minutes, or how many minutes it takes to do "x" pages.

Answer:

Step-by-step explanation:

Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the 10. If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive. So 3.5 times 10 to the power of -11

The mean is halfway between these two integers are = 357 and 789, then the 99.7% of data will lie between  that is it will lie in the range.

We are given that the scores are normally distributed.

The mean of the data is 573.

The standard deviation of this data is 72.

A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.

So,

We can write,

μ = 573

σ = 72

Then, the given expression is,

( μ - 3σ < x < μ +3σ ) = 99.7%

So,

μ - 3σ = 573 - 3*72

μ - 3σ = 573-216

μ - 3σ = 357

μ +3σ = 573 + 3*72

μ + 3σ = 573+216

μ + 3σ = 789

Hence, the mean is halfway between these two integers are = 357 and 789

Empirical rule states that for a normally distributed data that

about 68% data lies between μ + 1σ that is one standard deviation from mean.

about 95% data lies between μ + 2σ that is one standard deviation from mean.

about 99.7% data lies between μ + 3σ that is one standard deviation from mean.

Therefore,

The mean is halfway between these two integers are = 357 and 789, then the 99.7% of data will lie between  that is it will lie in the range.

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The error calculated is 2/5×3/8 = 3/20

An estimate or approximation of a true value and an error are two different things.

An error is defined as a mistake or a state of being incorrect. If you add 2+2 and get 5, that is an error. When a mistake causes you to believe the wrong conclusion about a collusion and you stick with it, that is an example of error.

Given

2/5×3/8 = 3/10

which is not possible, because 2×4 = 8 and the numerator and denominator is divided by 2 at the same time.

1/5×3/4 = 3/20

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The solution to the quadratic equation -3 = 4x² + 9x using quadratic formula is; x = (-9 + √33)/8 or (-9 - √33)/8

The general form of any quadratic equation is written as;

ax² + bx + c = 0

The quadratic formula that is used to solve this is given by;

x = [-b ± √(b² - 4ac)]/(2a)

Now, we are given the quadratic equation as;

-3 = 4x² + 9x

It can be written as;

4x² + 9x + 3 = 0

Thus, using quadratic formula we have;

x = [-9 ± √(9² - (4 * 4 * 3))]/(2 * 4)

x =  [-9 ± √(81 - 48)]/8

x = (-9 ± √33)/8

x = (-9 + √33)/8 or (-9 - √33)/8

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The circle that has the larger circumference is circle B. The difference in the circumference is  9.42 cm.

A circle is a bounded object in which points from the center is equidistant to the circumference. The circumference of a circle is the perimeter of the circle. The diameter of a circle is a straight line that touches two opposite points on the circumference of a circle and also passes through the center. Radius is half the diameter of a circle.

The circumference of a circle = 2πr

Where:

Circumference of Circle A = 22/7 x 2 x (9/2) = 28.29 cm

Circumference of Circle B = 22/7 x 2 x 6 = 37.71 cm

Difference in circumference = 37.71 - 28.29 = 9.42 cm

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Answer:

Step-by-step explanation:

A!

Answer: Function A is faster by 1 meter per second.

Step-by-step explanation:

The first function has a greater speed because by taking the meters per second, you get 14 meters per second. Meanwhile, function B has only 13 meters per second, therefore function A is faster by 1 meter per second.

ANSWER :

He should use 110 cc of 10% solution

EXPLANATION :

Note that the percent solution is the amount of salt divided by the total volume or quantity.

From the problem, 40 cc of a 70% saline solution.

The amount of salt is 0.70(40) = 28 cc

Another solution is "x" cc of 10% saline solution.

The amount of salt is 0.10x cc

When added together, the total volume is 40 + x

and the amount of salt is 28 + 0.10x

The resulting solution is 26% saline solution.

So we can have :

Substitute the results :

The variables all have the same identity for all conceivable values. A conditional equation can only be true in particular situations where the values of the variables match.  A linear equation is an identity if solving it results in a true assertion, such as 0 = 0. The answer is 16 cookies

The classification of various types of functions can be done using four primary categories. depending on a factor Onto function, one-to-one relationship, many-to-one relationship, and into function are all examples of relationships between function.

A number, a variable, or a mix of numbers, variables, and operation symbols make up an expression.

Equations' true strength is in their ability to explain numerous aspects of the world in a highly accurate manner. (This is why, if one can be found, an equation's solution can be helpful.)

Hence, A linear equation is an identity if solving it results in a true assertion, such as 0 = 0. The answer is 16 cookies

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The formula for calculating the volume of a sphere is expressed as

Volume = 4/3 x pi x radius^3

From the information given,

pi = 3.14

radius = 6.2

By substituting these values into the formula, we have

Volume = 4/3 x 3.14 x 6.2^3

Volume = 997.7999

Rounding to the nearest tenth,

Volume = 997.8 m^3

The equation is:

If x grows then y is going to reduce, and if y gets smaller, then t grows. this means that is an inverse variation

1 ) Let's solve this Linear System with the elimination method

Choose the x, as the first variable to be eliminated

2x + 5y = 8 Multiply by 5 the whole equation

-10x – 9y = -72

Adding both equations:

10x +25y=40

-10x -9y=-72

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

0 16y=-32 Dividing both equations by 16

y=-2

2) Plugging into the simplest equation within that Linear System:

2x +5(-2) = 8

2x -10 = 8 Adding 10 to both sides

2x = 18 Dividing both sides by 2

x=9

3) So the answer is the pair (9,-2)

Answer:

r ≤ -24.32

Step-by-step explanation:

r/-3.2 > 7.6

r /-3.2 × 3.2 > 7.6 × -3.2

r ≤ -24.32

Answer: r ≤ −24.32

Step-by-step explanation:

The inequality you provided is:

r/-3.2 >= 7.6

To solve for r, we can multiply both sides of the inequality by -3.2 to get:

r <= -24.32

Therefore, r is less than or equal to -24.32.

I hope this helps! Let me know if you have any other questions.

Answer:2000 will be the nearest thousand.

Step-by-step explanation:

By definition, Scientific notation has the following form:

Where the coefficient "a" is a number from 1 to 10, but not including 10 and the exponent "n" is an Integer. The base will be always 10.

When you write a number in Scientific notation, the decimal point must be after the first digit of the coefficient.

In this case, you have:

So, in order to write that product in Scientific notation, you must move the decimal point one space to the left. This must be represented in the exponent. If you move it just one space, to the left, then the exponent will be 1 and will be positive.

Therefore, you get that this is:

Therefore, you can determine that the answer is:

The ordered pair is [4k , 3k]

In first equation, 3x - 4y = 0

∴ 3x = 4y

  x = 4y/3.   ----1

Placing the value of x in second equation:

 4x - 5y = k

 4[4y/3] - 5y = k

16y/3 - 5y = k

[tex]\frac{16y - 15y}{3}[/tex] = k

16y - 15y = 3k

y = 3k

Replacing the value of y in eq. 1, we get

x = 4k

∴ The ordered pair is [4k , 3k]

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The most appropriate choice for trigonometry will be given by -

AB = 32

AC = [tex]16\sqrt{3}[/tex]

What is Trigonometry?

Trigonometry shows the relationship between sides and angles of a right angled triangle.

There are six trigonometrical functions. They are

[tex]sin\theta,[/tex] [tex]cos\theta[/tex], [tex]tan\theta[/tex], [tex]cot\theta[/tex], [tex]sec\theta[/tex], [tex]cosec\theta[/tex]

[tex]sin\theta=\frac{perpendicular}{hypotenuse}\\\\cos\theta=\frac{base}{hypotenuse}\\\\tan\theta=\frac{perpendicular}{base}\\\\cot\theta=\frac{base}{perpendicular}\\\\sec\theta=\frac{hypotenuse}{base}\\\\cosec\theta=\frac{hypotenuse}{perpendicular}[/tex]

Trigonometry is a very important tool in mathematics.

Here,

The figure has been attached here.

Since this is a right angled triangle, trigonometry can be applied here,

Since ∠C = 90°, AB is the hypotenuse of [tex]\DeltaABC[/tex][tex]\Delta ABC[/tex] as the side opposite to 90° angle is the hypotenuse.

Let BC be the base of  [tex]\DeltaABC[/tex][tex]\Delta ABC[/tex]

BC = 16

m∠B = 180 - (90 + 30)

        = 180 - 120

        = 60°

cos 60 = [tex]\frac{BC}{AB}[/tex]

[tex]\frac{1}{2} = \frac{16}{AB}\\AB = 16\times 2\\AB = 32[/tex]

sin 60 = [tex]\frac{AC}{AB}[/tex]

[tex]\frac{\sqrt{3}}{2} = \frac{AC}{32}\\\\AC = 32 \times \frac{\sqrt{3}}{2}\\\\AC = 16\sqrt{3}[/tex]

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Answer: 16 inches

Step-by-step explanation: well, if you do 76/19, it gives you four, so the ratio is 1-inch costs 4 cents.

Then you just have to do 64/4, which gives you 16. You can buy 16 inches of wire with 64 cents

The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equivalent.

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The  five solution of the linear equation x+y=3 is = (0,3), (1,2), (2,1), (3,0) and (4, -1).

Equations are logical formulations of the connection between two values. A mathematical equation can be defined in a variety of ways. Mathematical variables are used in even the most fundamental and straightforward algebraic equations.

There could be multiple variables in a linear equation. A linear equation is one in which the variable's maximum power is consistently 1.

A one-degree equation is another name for it. At least one variable should be raised to exponent 2 in quadratic equations.

Ax+By=C is the usual form for two-variable linear equations. For example, 2x+3y=5 is a linear equation in standard form.

Let the value of

x = 0,

then,

0 + y = 3

⇒

y = 3

One of the solutions

for x + y =3, is =(0,3)

Similarly, If x = 1,

then,

1 + y =3 ⇒ y = 3 - 1 = 2

One of the solutions for x + y =3, is

(1,2)

If x = 2,

then,

2 + y = 3

⇒ y = 3 - 2 = 1

One of the solutions for x + y =3, is

(2,1)

If x = 3, then,

3 + y = 3

⇒ y = 3 - 3 = 0

One of the solutions for x + y =3, is

(3,0)

If x = 4,

then,

4 + y = 3

⇒ y = 3 - 4 = -1

One of the solutions for x + y =3, is

(4, -1)

Hence,

five

solutions of the equation x + y = 3, are:

(0,3), (1,2), (2,1), (3,0) and (4, -1).

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Answer:

x = 25°

Step-by-step explanation:

Hello!

If the angles are vertical, the measures of the angles are equal.

Vertical angles are formed by the intersection of two lines, and are non-adjacent angles. The measures of the two angles are equal to each other.

We can set up an equation for x, and solve for it.

The value of x is 25°.

Answer:

x= -2, y= 3

Step-by-step explanation:

5. Solve the system using substitution.

4x + 5y = 7

y= 3x + 9

What variable in the top equation will you substitute the bottom equation into? y

6. Using the information from question 5, what does the top equation look like after you substitute from the bottom equation into the top equation?

4x + 5(3x+9) = 7

7. Using the equation you came up with for question 6, what does it look like simplified?

4x+5(3x+9) = 7, distribute 5 over the sum in parenthesis

4x+15x+45 = 7, subtract 45 from both sides of the equation

4x+15x+45-45 = 7-45, combine like terms

19x = -38, divide both sides by 19

x = -2

8. What is the solution to the equations from question 5?

y= 3x+9, substitute x for -2

y = 3(-2) +9

y = -6+9

y = 3

The solution for the system of equations

4x + 5y = 7

y= 3x + 9

is x= -2, y= 3

This means that the point (-2, 3) is the intersection of line 4x+5y=7 and line y=3x+9 and that point belongs to both lines.

Answer:

Below in bold.

Step-by-step explanation:

5. 4x + 5y = 7

y= 3x + 9

Substitute for y from the top equation.

5y = -4x + 7

y = (-4x + 7)/5

Substituting:

(-4x + 7)/5 = 3x + 9

6. Substituting from bottom equation, we get:

4x + 5(3x + 9) = 7

7. Simplifying the above:

4x + 15x + 45= 7

19x = -38

8. Solving equations from part 5:

(-4x + 7)/5 = 3x + 9

-4x + 7 = 15x + 45

-38 = 19x

x = -2.

Now substitute x = -2 into y = 3x + 9

y = 3(-2) + 9

= 3.

Solution is x = -2, y = 33

Answer:

24

Step-by-step explanation:

mutiples of fours under 30 leave 7 possible numbers

but the only number w 8 factors under 30 is 24

(if you're too lazy to read all of the below im about to say then because it is divisible by 2,3,4 and less than 30 the number is 2 x 3 x 4 = 24)

First, we exclude 0 cause it has more than 8 factors (literally)

Since 2 and 3 are 2 of the number's factors, it must be divisible by 6.

Therefore, we have 4 options : 6,12,18,24 (30 does not count)

Since it is divisible by 4, we are left with 2 : 12 and 24.

(here's something extra which is how to identify the number of factors a number has, not necessary in this case cause we can just count, but it's useful anyways)

We do the prime factorization of that number :
For example : 120
The prime factorization of 120 is 2^3 x 3 x 5.
Now, we take the index number of every single one of the prime numbers in the factorization, add each of them by 1 and multiply them

So, the index number of 2 is 3, 3 is 1 and 5 is 1 (2^3 x 3^1 x 5^1)
-> 120 has (3+1)(1+1)(1+1) = 16 (factors).

Applying it to this case, only 24 would work, as :
24 = 3 x 2^3
So, it has (3+1)(1+1) = 8 (factors), just as it says.

Answer:

3 spacesto the right and 4 spaces up

Answer:

-49.

Step-by-step explanation:

Convert to vertex form:

f(x) = -7x^2 - 14x - 56

     = -7(x^2 + 2x + 8)

     = -7 [(x + 1)^2 - 1 + 8)

      = 7(x + 1)^2  - 49

- so the maximum value is -49.

A function that "undoes" another function is referred to as an inverse in mathematics. To put it another way, if f(x) yields y, then y introduced into the inverse of f yields x. A function that can be inverted has an inverse, which is denoted by the symbol f1. The solution is: x>4;r-1(x)=4-(root of (11/x)

Something that is opposite or reversal in nature or quality. The inverse of "if A then B" is "if not-A then not-B" — compare contrapositive. 2: a proposition or theorem constructed by opposing both the subject and predicate or both the hypothesis and conclusion of a given proposition or theorem.

reciprocal, inverse multiplicative. (Mathematics) One of two numbers whose product is 1: the multiplicative inverse of 7 is 1/7, while the reciprocal of 2/3 is 3/2. type: antagonism, oppositeness. the connection between seemingly opposing parties.

If there is just one value of x in the domain where f(x)=y, then a function f does not have an inverse function. The term "f inverse" is widely used to refer to this particular inverse function, which is singular.

The solution is: x>4;r-1(x)=4-(root of (11/x)

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There are 14 pizza rolls in the combination meal and 2 mini hotdogs in the combination meal.

In the above question, it is given that

At a particular restaurant,

Number of calories in Pizza roll = 55 calories

Number of calories in mini hotdogs = 70 calories

A combination meal with pizza rolls and mini hotdogs is shown to have total = 910 calories

We need to find , the number of pizza rolls and number of mini hotdogs in the combination meal

Let the number of mini hot dogs be x

Then number of pizza roll be x+12 ( given )

The following equation is generated from the given information as

55( x + 12) + 70x = 910

55x + 70x + 660 = 910

125x = 910 - 660

Then, number of hotdogs are x = 2

and, number of pizza rolls = x + 12 = 2+12 = 14

Hence, there are 14 pizza rolls in the combination meal and 2 mini hotdogs in the combination meal

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