(1, 3) and (-3,-5)
Write a linear equation that passes through the given two points

Answer:

x= -10

y= 4

Step-by-step explanation:

it will be easiest to isolate x in the first equation

x+7y=18

 -7y. -7y

x=18-7y

now that we know x we will it into second equation

2(18-7y)+9y=16

36-14y+9y=16

36-5y=16

-36.    -36

-5y=-20

/-5   /-5

y=4

now fill in y to find x

x+7(4)=18

x+28=18

-28   -28

x= -10

hopes this helps please mark brainliest

The slope of the line is 2/3. It represents: b. When y increases by 2, x increases by 3.

The slope of a line can be described as the change in y over the change in x of the line, or the rise over its run.

The slope of a line is given as the value of "m", in the equation expressed in slope-intercept form as y = mx + b.

Given that a line has the equation, y = 2/3x + 5, in slope-intercept form, we can determine its slope (m), which is given as 2/3.

The value of m, which is 2/3, is the rise over the run of the line, which means that when the y value increases by 2, the x value increases by 3.

Therefore, the slope, m = 2/3 represents: b. When y increases by 2, x increases by 3.

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- 6x + 15 < 10 - 5x , are correct representations of the inequality .

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. [1] The majority of the time, size comparisons between two numbers on the number line are made. Different types of inequalities are represented by a variety of notations, including:

The symbol a b indicates that an is smaller than b.

When a > b is used, it indicates that an is bigger than b.

A is not equivalent to b in any scenario. Since an is strictly less than or strictly greater than b, these relationships are known as stringent inequalities[1]. Equivalence is not considered.

There are two forms of inequality relations that are not strict, in contrast to strict inequalities:

The indication of an or b denotes that.

According to our question-

The difference is 5 (-3(2x - 5)). (2 - x)

First, make each side simpler.

∵ -3(2x - 5) = -3(2x) + -3(-5) (-5)

Recall that (+)=(-)

∴ -3(2x - 5) = - 6x + 15

∵ 5(2 - x) = 5(2) + 5(-x) (-x)

Recall that (+)(-) = (-)

∴ 5(2 - x) = 10 - 5x

∴ - 6x + 15 < 10 - 5x

Take 15 away from both sides.

∴ - 6x < -5 - 5x

5 times on both sides

∴ - x < - 5

Because the coefficient of x is negative, you must change the inequality's sign when you divide both sides by it.

The x coefficient is -1.

∴ Add -1 to both sides.

∴ x > 5

The appropriate answers are:

- 6x + 15 < 10 - 5x

Hence, - 6x + 15 < 10 - 5x , are correct representations of the inequality .

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The value of angle x in the right triangle is 35 degrees.

A right triangle is a triangle that has one of it's angles as 90 degrees. A right triangle sides are named according to the position of the angles.

The sides name are as follows:

Therefore, let's find the angle x using trigonometric ratios.

hence,

sin x = opposite / hypotenuse

opposite side  = 4

hypotenuse side = 7

sin x = 4 / 7

x = sin⁻¹ 0.57142857142

x = 34.8499044793

x = 35 degrees

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Answer:

C) 300

Step-by-step explanation:

Butter cookies :-

2 x 50 = 100 cookies

Choco chip cookies

4x 100 = 200 cookies

Total cookies :-

100 + 200 = 300

I hope my answer helps you.

Using trigonometric ratio, the length of BE is 10 units, the value of sin B is 0.64 and cos B is 0.64 respectively

This is the ratio between the angles and sides of a right-angle triangle. The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).

In this problem, we have that

1)

Using tangent of B

tan B = opposite / adjacent

tan B = NE / BE

3/4 = 7.5 / BE

BE = 7.5 / 0.75

BE = 10

2)

To find sin B, we need to calculate the hypothenuse of the triangle which we will use Pythagoras's theorem

NB² = BE² + NE²

NB² = 10² + 7.5²

NB = 12.5

sin B = NE / NB

sin B = 7.5 / 12.5

B = sin⁻¹ (7.5 / 12.5)

B = 0.64

3)

cos B = BE / NB

cos B = 10 / 12.5

B = cos⁻¹ (10/12.5)

B = 0.64

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The rate of change of Area of the circle of ripples when radius is 24 inches is  602.88  in²/sec  .

In the question ,

it is given that ,

a rock dropped in pond causes a circular waves of ripples ,

the rate at which the radius is increasing (dr/dt) = 4 in/sec .

let the radius of the circular ripples is = r ,

the area of the circular ripples is ; A = πr² ,

differentiating Area with respect to time(t) is ,

dA/dt = π×2r×(dr/dt)

to find the rate of change of area when the radius of circle is 24 inches ;

substituting dr/dt = 4 and r = 24 ,

we get ,

dA/dt = π×2×24×4

= 192×3.14    .

= 602.88 in²/sec

Therefore , the rate of change of Area is = 602.88  in²/sec   .

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Answer:4x+4

Step-by-step explanation:

6-3= 3+1= 4 =4x+4

Answer: -3x³ - 6x²  + 8x

Step-by-step explanation:

      In standard form, we order the terms in a polynomial with the highest degree on the left down to the lowest degree on the right. Make sure to keep the positive or negative "attached" to the mathematical term you are moving.

    Given;

8x - 6x² - 3x³

    3 > 2 > 1, so we will reorder:

-3x³ - 6x²  + 8x

-3x^3-6x^2+8x is the standard form of polynomial 8x-6x^2-3x^3.

Often, we arrange the terms in a polynomial in standard form in which the term with the highest degree is first and is followed by the other terms in order of decreasing powers.

The first term of a polynomial in this form is called the leading term, and the coefficient in this term is called the leading coefficient.

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214.12  in standard form .

What does a math standard form mean?

It is possible to express a number in a way that adheres to certain standards by writing it in its standard form.

                     Any value between 1.0 and 10.0 that can be expressed as a decimal number and multiplied by a power of 10 is referred to as being in standard form.

What does standard form look like?

Ax+By=C is the typical form for linear equations involving two variables. A linear equation in standard form is, for instance, 2x+3y=5. In order to better understand phenomena and make useful predictions, scientists can compare

                          the orders of magnitude of various quantities using standard form.

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Answer:

81

Step-by-step explanation:

Area is multiplying all side

9 x 9 = 81

Therefore , the we need to pick n + 2 numbers  to be sure of random selection is an odd number.

In statistic, a simple random sample is a subset of people chosen at random from a larger group, all of whom were chosen with the same probability. This procedure involves choosing a sample at random.

Here,

You must choose n + 2 numbers at random in order to guarantee that you will get at least one odd number.

Since n is a positive integer, the following values of n are possible:

{1, 2, 3, 4, ...}

Let's assume n = 1.

Now, in order to guarantee that you choose at least one odd integer from 0 to 2n = 2*1 = 2, how many must you choose (at random)?

There are three numbers from 0 to 2:

0, 1, 2

If you choose these at random, selecting all three digits will guarantee that you receive an odd number.

From 0 to 2*n, there are the following options if n = 2.

0, 1, 2, 3, 4

Five choices.

If you wish to choose at least one odd number for certainty after picking 3 even numbers, you must choose 4 numbers.

From 0 through 2*n, if n = 3, we get:

0, 1, 2, 3, 4, 5, 6

Since 4 of these are even, you must choose 5 of them to guarantee an odd number.

The amount of even numbers is always n + 1, therefore given a random integer n, we will have n + 1 even numbers from 0 to 2n. Therefore, if we want to be certain that we are selecting an odd number at random, we must choose n + 2 numbers.

Therefore , the we need to pick n + 2 numbers  to be sure of randomly selecting an odd number.

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Answer: Elise's number is 37

Step-by-step explanation:

-5(x-19)=-90

-5x+95=-90

-5x=-185

x=37

The table represents the description of the proportional relationship is Swiss Cheese (oz) 3 6 9 Cheddar Cheese (oz) 5 10 15

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Since the restaurant makes cheese sandwich with  3 oz of Swiss cheese and 5 oz of cheddar cheese.

Thus, the table that represents the proportional relationships will be the one that contains  3 oz of Swiss cheese with a corresponding value of 5 oz of cheddar cheese.

the constant of proportionality (k) must be the same (i.e. k = 5/3) for all the values.

Swiss Cheese (oz)     3  6   9

Cheddar Cheese (oz) 5  10 15

k = 5/3 = 10/6= 15/9 =5/3

Hence,  the table represents the description of the proportional relationship is Swiss Cheese (oz) 3 6 9 Cheddar Cheese (oz) 5 10 15

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The required equation of a line is y = 9/5 (4x - 12)

Given-

The point from which the line passes through is (3,2)

The slope of the given line m is -4/5.

Equation of the line

The linear equation of a line can be represented by a set of points on a graph using the equation of the line.

The standard form of the line passing through the point x₁, y₁

The slope m is given by,

m = (y - y₁) / (x - x₁)

Put the values of points and slope in the above equation, we get,

-4/5 = (y - 2) / (x - 3)

-4/5(x - 3) = y -2

-4x/5 + 12/5 = y - 2

-1/5 (4x - 12) + 2 = y

y = 9/5 (4x - 12)

The linear equation of a line can be represented by a set of points on a graph using the equation of the line. The following equation depicts a line that crosses (3, 2) and has a slope of -4/5: y = 9/5 (4x - 12)

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Answer:f - 1 ( x ) to show the final answer. Verify if f−1(x)=x2+1 f - 1 ( x ) = x 2 + 1 is the inverse of f(x)=2x−2 f ( x ) = 2 x - 2 .

Answer:

95

Step-by-step explanation:

Answer:

x = you sold

y = friend sold

---

x + y = 58

x = y + 14

---

put the system of linear equations into the standard form:

---

x + y = 58

x - y = 14

x= you sold 36

y= friend sold 22

Step-by-step explanation:

Answer:

The Answer is 6.

Step-by-step explanation:

12x = 72

12 x 6 = 72

X = 6 because 6 can go into 72 12 times

Answer:

x = 6

Step-by-step explanation:

following the working through

substitute y = - x + 2 into the other equation

5x - 7y = 58

5x - 7(- x + 2) = 58 ← distribute parenthesis by - 7

5x + 7x - 14 = 58

12x - 14 = 58 ( add 14 to both sides )

12x = 72 ( divide both sides by 12 )

x = [tex]\frac{72}{12}[/tex] = 6

substitute x = 6 into y = - x + 2

y = - 6 + 2 = - 4

The polygons from the figure given below that are similar are Polygon B and Polygon C .

In the question ,

it is given that there are three polygons ,

we have to check which polygons are similar ,

to find the similarity we compare the length of all the polygons .

Let us first check for  Polygon A and Polygon B ,

105/120 = 7/8

80/90 = 8/9.

and  105/120 ≠ 80/90 ,

So , Sides are not in proportion for Polygons A and B.

Hence , the Polygons A and B are not Similar.

Let us check for Polygon A and C .

105/100 = 21/20

80/75 = 16/15.

and 105/100 ≠ 80/75

So , sides are not in proportion for Polygons A and C.

Hence , the Polygons A and C are Non Similar.

Now  for Polygon B and C .

120/100 = 6/5.

90/75 = 6/5.

and  120/100 = 90/75 = 6/5

So , Sides are in proportion for Polygons B and C .

Hence , the Polygons B and Polygon C are Similar.

Therefore , the Polygon B and Polygon C are similar .

The given question is incomplete , the complete question is

Which pairs of rectangles are similar polygons ? select similar or not similar for each pair of rectangles from the figure given below .

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The function h(x) is the result of two rigid transformations, reflecting the function f(x) about the x-axis and translating it vertically 7 units down.

In this problem we must determine the difference between the quadratic functions f(x) = x² and h(x) = - x² - 7, we can infer the change necessary to derive h(x) by means of rigid transformations, that is, transformations applied on a function such that the features of the functions are conserved.

All the rigid transformations required to transform f(x) into h(x) are listed below:

Now we proceed to plot the two functions. From the graph we noticed that h(x) is the result of reflecting f(x) about the x-axis and translating 7 units in the -y direction.

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As per the given options, one which does not have a unit price of $24 for one sweater is $38 for 2 sweaters. Hence, option A is correct.

The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or even more items.

Included in them is the study of integers, especially the order of operations, which is important for all other areas of mathematics, notably algebra, data management, and geometry.

As per the information in the question,

The unit price of the sweater is $24.

Now, let's check the options for a unit price of the sweater.

1.

$38 for 2 sweaters

So, the unit price = 38/2 = $19, it does not have the unit price of $24 for one sweater.

2.

$72 for 3 sweaters

So, the unit price = 72/3 = $24, so this is correct.

3.

$96 for 4 sweaters

So, the unit price = 96/4 = $24, this one is correct.

4.

$120 for 5 sweaters

So, the unit price = 120/5 = $24, this one is also correct.

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Your question seems incomplete, the complete question may be:

Which of the following does NOT have a unit price of $24 for one sweater?

$38 for 2 sweaters

$72 for 3 sweaters

$96 for 4 sweaters

$120 for 5 sweaters

Answer:

x = 17

Step-by-step explanation:

x + 6 + 7x + 4 + 2x = 180  Combine like terms

10x + 10 = 180  Subtract 10 from both sides

10x = 170  Divide both sides by 10

x = 17

x = 17

1. Add the numbers

x + 6 + 7x + 4 + 2x = 180

x + 10 + 7x + 2x = 180

2. Combine like terms

x + 10 + 7x + 2x = 180

10x + 10 = 180

3. Subtract 10 from both sides

10x + 10 = 180

10x + 10 - 10 = 180 - 10

4. Simplify

Subtract the numbers:

10x + 10 - 10 = 180 - 10

10x = 180 - 10

Subtract the numbers:

10x = 180 - 10

10x = 170

5. Divide both sides by the same factor

10x = 170

[tex]\frac{10x}{10}[/tex] = [tex]\frac{170}{10}[/tex]

6. Simplify

Cancel terms that are in both the numerator and denominator:

[tex]\frac{10x}{10}[/tex] = [tex]\frac{170}{10}[/tex]

x = [tex]\frac{170}{10}[/tex]

Divide the numbers:

x = [tex]\frac{170}{10}[/tex]

x = 17

x = 17

I hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!

Answer: No, they are not inverses of one another.

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

Explanation:

There are at least 3 methods we can use to prove the functions aren't inverses of each other.

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

Method 1

Let's say we plugged x = 0 into f(x).

[tex]f(\text{x}) = 2\text{x}+1\\\\f(0) = 2*0+1\\\\f(0) = 1\\\\[/tex]

The input x = 0 leads to the output y = 1.

Then let's treat y = 1 as the input of the g(x) function, so we'll plug x = 1 into here.

[tex]g(\text{x}) = -2\text{x}-1\\\\g(1) = -2*1-1\\\\g(1) = -3\\\\[/tex]

If g(x) was the inverse of f(x), then the g(1) output value should be 0 to get us back where we started. However, we get an output of -3 instead.

This is sufficient evidence to conclude that f(x) and g(x) are not inverses of each other. We only need one counter-example to disprove this claim.

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

Method 2

Recall that if f(x) and g(x) are inverses of each other, then we have the following two properties

The left hand side of each equation involves the concept of "function composition".

Let's see what f(g(x)) is equal to in this case.

[tex]f(\text{x}) = 2\text{x}+1\\\\f(g(\text{x})) = 2(g(\text{x}))+1\\\\f(g(\text{x})) = 2(-2\text{x}-1)+1\\\\f(g(\text{x})) = -4\text{x}-2+1\\\\f(g(\text{x})) = -4\text{x}-1\\\\[/tex]

We do not get an output of simply x only, so this is another way to see how we don't have inverses.

Through similar steps, you should find that [tex]g(f(\text{x})) = -4\text{x}-3[/tex] which is further confirmation that f(x) and g(x) are not inverses of each other.

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

Method 3

Let's ignore g(x) for now. We'll start with f(x) and find the inverse of it.

The process involves this basic outline:

So,

[tex]f(\text{x}) = 2\text{x}+1\\\\\text{y} = 2\text{x}+1\\\\\text{x} = 2\text{y}+1\\\\\text{x}-1 = 2\text{y}\\\\\text{y} = \frac{\text{x}-1}{2}\\\\f^{-1}(x) = \frac{\text{x}-1}{2}\\\\[/tex]

Unfortunately we do not end up with -2x-1 as the actual inverse.

So if [tex]g(\text{x}) = \frac{\text{x}-1}{2}[/tex] was the case, then f(x) and g(x) would be inverses of each other.

Through similar steps, the inverse of [tex]g(\text{x}) = -2\text{x}-1\\\\[/tex] is [tex]g^{-1}(\text{x}) = -\frac{\text{x}+1}{2}\\\\[/tex]

Answer: $0.12

Step-by-step explanation:

50x = 6

Use x as your variable

In polynomial, x - 2 is not a factor f(x) [By factor theorem]

What is Polynomials ?

Sums of terms with the pattern kxn—where k is any positive integer and n is an arbitrary number—are known as polynomials.

                    For instance, the polynomial 3x+2x-5. a description of polynomials. In this video, basic terms like terms, degrees, standard form, monomial, binomial, and trinomial are covered.

p(x) = 4x^3 + 10x^2 - 6x - 20  

put x = -2 in equation

p(x) = 4 * (-2)³ + 10 * ( -2)² - 6 * -2 - 20

       = 4 *  -8 + 10 * 4 + 12 - 20

        = -32 + 40 + 12 - 20

        = 52 - 52

        = - 2

p(x) ≠ 0

Which is not equal to zero

x - 2 is not a factor f(x) [By factor theorem]

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1/3x+3/4+2/3x-1/4-2/3x=0.66666...x+0.5

By the Centroid Theorem, we can conclude that the length of a segment of the median from a vertex to a centroid is equal to the two-thirds of the length of the median from that vertex.

What is Centroid Theorem?

The point that may be used to represent the centre of a one- or two-dimensional figure, with all points' distances from this point adding up to zero. centre of mass is comparable. also known as the median point Geometry. the location where a triangle's medians meet.

The common endpoint of two or more rays or line segments Vertex typically means a corner or a point where lines meet.

Here given that,

The length of a segment from a vertex to the centroid is the length of the median from that vertex.

So, the length of a segment from a vertex to the centroid is  which is the median of that vertex.

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An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

The number of points Eric have is 8x - 16.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Joseph points = 2x - 6

Thomas points = 2x - 6 + 4 = 2x - 2

Eric points = 2 ( 2x - 6 + 2x - 2 )

Now,

The points Eric have is.

= 2 (4x - 8)

= 8x - 16

Thus,

The number of points Eric have is 8x - 16.

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