6. The graph of an exponential function is
shown. Write an equation for the function.
manu (3,13.5)
(2,4.5)
(1, 1.5)
olismolensando

A graph of the line that passes through the two points (-3/2, -3/2) and (3/2, 3/2) is shown in the image attached below.

In Mathematics and Geometry, the slope of any straight line can be calculated by using this mathematical equation (expression);

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

From the information provided above, we have the following data points located on the line:

Points on the x-coordinate = (-3/2, 3/2).

Points on the y-coordinate = (-3/2, 3/2).

Substituting the given data points into the slope formula, we have the following;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (3/2 + 3/2)/(3/2 + 3/2)

Slope (m) = 3/3 = 1

At point (-3/2, -3/2), an equation of this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

Where:

y - (-3/2) = 1(x - (-3/2))

y + 1.5 = x + 1.5

y = x

Next, we would use an online graphing calculator to plot the linear equation as shown in the graph attached below.

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Please find attached the image of the enlargement of the shape X by a scale factor of -1 created using MS Word, which is a drawing equivalent to option B. The correct option is therefore;

B.

An enlargement transformation is one in which the pri-image object size is scaled about a center of enlargement, using a scale factor, with the sign of the scale factor indicating the direction of the enlargement, which for a +ve sign is on the same side, and for a -ve sign is on the other side of the center of enlargement.

An enlargement by a scale factor of -1, can be obtained by producing the image on the alternate side of the center of enlargement, which with a scale factor of -1, is the same size as the size of the image.

Therefore, the dilation by a scale factor of -1, with the center at the origin, produces an image which is equivalent to a reflection of the original object (pre-image), across the y-axis followed by a reflection across the y-axis.

The image of the object following the dilation will therefore be the mirror image of the mirror image of the object reflected across the y-axis, which takes the shape of a vertically flipped, left flipped F, which is option B

Please find attached a drawing of the shape of the image of the enlargement of shape X by a scale factor of -1, created with MS Word

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a. The length of the arc is 6.28cm

b. The area of the sector is 25.12cm²

The arc of a circle is defined as the part or segment of the circumference of a circle. A sector is the space bounded by the arc and the radii of the circle. The smaller area is known as the minor sector and the bigger area is known as the major sector.

The length of an arc = tetha /360 ×2πr

= 45/360 × 2×3.14× 8

= 2×3.142 = 6.28cm

The area of a sector = tetha / 360 × πr²

= 45/360 × 3.14 × 8× 8

= 3.14× 8

= 25.12 cm²

Therefore, the length of the arc is 6.28cm and the area of the sector is 25.12cm²

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7.21

The Pythagoras theorem allows us to solve for unknown sides of right triangles.

Right Triangles

Right triangles are triangles that have one 90-degree angle (aka a right angle). The side directly across from the right angle is called the hypotenuse. The hypotenuse is always the longest side of a triangle. The other 2 sides of a right triangle are called the legs of the triangle.

Pythagorean Theorem

The Pythagorean theorem states that a² + b² = c², where a and b are the legs of the triangle and c is the hypotenuse. To find the missing side we can plug in the values we know and solve for b.

Then, subtract 12² from both sides.

Finally, take the square root of both sides. When you square root a number, the resulting value is plus or minus, but since we are finding a distance, we will only take the positive answer.

The function is  y = 1500[tex](0.985)^t[/tex].

What is function?

A mathematical function , rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

Here initial population is 1500 .

Rate of decrease = 1.5%

Number of years = 10

After 10 years , the end population = 1290.

Now using formula,

=> P = [tex]P_0[/tex][tex](1-\frac{r}{100})^n[/tex]

Here number of deer, y, in this population at the end of t years then

=> y = 1500[tex](1-\frac{1.5}{100})^t[/tex]

=> y = 1500[tex](1-0.015)^t[/tex]

=> y = 1500[tex](0.985)^t[/tex]

Hence the function is y = 1500[tex](0.985)^t[/tex].

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Answer:

Hi, I'm Za'Riah! I will gladly assist you with your problem. (see explanation)

Step-by-step explanation:

The answer is C

Hope this helped!

On solving the expression, the standard form is obtained as 8x³ + 26x² - 32x + 6.

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

The given expression is - (−4x + 3)(−2x² − 8x + 2)

To solve this expression first expand the equation using arithmetic operation of multiplication.

(−4x + 3)(−2x² − 8x + 2)

-4x(−2x² − 8x + 2) + 3(−2x² − 8x + 2)

8x³ + 32x² - 8x - 6x² - 24x + 6

Collect the like terms together -

8x³ + 32x² - 6x² - 8x - 24x + 6

Perform the arithmetic operation of addition and subtraction -

8x³ + 26x² - 32x + 6

Therefore, the standard form is 8x³ + 26x² - 32x + 6.

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The correct option regarding which cap Louay can buy is given as follows:

D. Cap 1 or 3.

The fraction of white stars is obtained using a proportion, dividing the number of white stars by the total number of stars.

Hence the fractions for each cap are given as follows:

Meaning that Cap 1 and Cap 3 have the desired ratio of white stars relative to total stars, and thus the correct option is given by option D.

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The number of hours that Jenny drove in her new car is 3.2 hours

The speed is 62 miles

The distance is 198.4 miles

The number of hours can be calculated as follows

speed= distance/time

62= 198.4/x

cross multiply both sides

62x= 198.4

x= 198.4/62

x= 3.2

Hence the number of hours that Jenny drove is 3.2 hours

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The breaking of number using addition is discussed above.

Given is the breaking apart of numbers with addition.

We can breaking apart the numbers with addition as follows. Assume the number to be 50. We can break the number 50 as follows -

50 = 25 + 25

50 = 15 + 10 + 15 + 10

50 = 10 + 10 + 10 + 10 + 10

50 = 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5

Therefore, the breaking of number using addition is discussed above.

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The selling price for the article if it is equal to marked price will be $117

using profit and loss formulas.

What is profit and loss formula?

Profit and Loss formula is used in mathematics to determine the price of a commodity in the market and understand how profitable a business is. Every product has a cost price and a selling price. Based on the values of these prices, we can calculate the profit gained or the loss incurred for a particular product. The important terms covered under this are cost price, fixed, variable and semi-variable cost, selling price, marked price, list price, margin, etc.

For example, for a shopkeeper, if the value of the selling price is more than the cost price of a commodity, then it is a profit and if the cost price is more than the selling price, it becomes a loss.

Now,

Given Cost price=$65

Marked up price = 180%*$65

As

Marked up price = selling price

Therefore

     selling price= 180%*$65

                 selling price =$117

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The tenth term of the given arithmetic sequence is; -49

The formula for the nth term of an arithmetic sequence is;

aₙ = a + (n - 1)d

where;

a is first term

d is common difference

From the given sequence, we see that;

a = -13

d = -17 - (-13)

d = -17 + 13

d = -4

Thus, the tenth term of the arithmetic sequence is;

a₁₀ = -13 + (10 - 1)-4

a₁₀ = -13 -36

a₁₀ = -49

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The possible equation of the sequence is f(x) = -2x + 5

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

Sequence type = arithmetic

Also, we have the following features

slope = negative

y-intercept = positive

A linear equation (or an arithmetic sequence) can be represented as

y = mx + c

Where

slope = m

y-intercept = c

Using the given features, we can use the following assumed values

m = -2

c = 5

So, the sequence is

f(x) = -2x + 5

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Answer:

x = 60.4

Step-by-step explanation:

First, let's remember the three different trigonometric functions: sine, cosine, and tangent. In this case, we would use cosine because the adjacent side to the angle and hypothenuse are used/given.

[tex]cos(22) = \frac{56}{x}[/tex]

We need to set up a proportion because there is not much else you could do here.

[tex]\frac{cos(22)}{1} =\frac{56}{x}[/tex]

Then, cross-multiply.

[tex]cos(22) * x = 56[/tex]

Finally, divide both sides by cos(22). You'll probably need your calculator and make sure it's in degrees mode and not radians!

[tex]\frac{cos(22) * x}{cos(22)} = \frac{56}{cos(22)}[/tex]

[tex]x = 60.4[/tex]

Rounded to the nearest tenth, x = 60.4.

The range of values of x which satisifies both of the inequalities is:

(-3, 2)

Here we have two inequalities:

3 + x < 5

8 + x > 5

And we want to see which range of values of x satisfie both of these inequalities.

If we isolate x on both inequalities, we will get:

3 + x < 5

x < 5 - 3

x < 2

And the other one is:

8 + x > 5

x > 5 - 8

x > -3

Then we havethe compound inequality:

x < 2

x > -3

Then the range of values that satisfies both inequalities is (-3, 2)

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From the inequalities 30x + 20y ≤ 200 and x + y ≥ 6, Roger can buy 3 pants and 3 shirts.

An equation is an expression that shows the relationship between numbers and variables.

Inequalities is used for the non equal comparison of these numbers and variables.

Let x represent the number of pants that Roger buys and y represent the number of shirts he buys.

He can buy pants for $30 and shirts for $20. Roger received $200 for his birthday, therefore:

30x + 20y ≤ 200    (1)

Also:

He wants at least 6 new items. hence:

x + y ≥ 6    (2)

From both equations, the solution to these equalities is (3, 3)

Roger can buy 3 pants and 3 shirts.

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Answer:

The machine makes 45 bottles per minute.

Step-by-step explanation:

We can first find the slope through this equation: [tex]\frac{y2-y1}{x2-x1}[/tex]

Since we are given two points, (2,90) and (7,315), we can plug those two points into the formula given above:

[tex]\frac{315-90}{7-2}[/tex]

= 45

Therefore, m = 45.

Now, we can pick one of the two points given--in this case, I'll use (2,90)--to find the equation of the line: [tex]y-y1 = m(x-x1)[/tex]

For (2,90), y1 will be 90, and x1 will be 2. Let's also plug in m:

y - (90) = 45(x - 2)

We can solve for y now to find what y=mx+b is:

y = 45(x-2) + 90

y = 45x

Since the problem asks how many bottles the machine can make per minute, we can plug x = 1: 45(1) = 45

The machine makes 45 bottles per minute.

Answer:

y= -2x + 0

Step-by-step explanation:

to get to y you need to multiply by -2 and add 0 to that to get the final y answer

Answer:

y=f(x)-6 is a vertical translation down by 6 units so draw the same graph but 6 units down with the point at which it crosses the y-axis as (0,-4)

If Line segment SU is dilated to create S'U' using the dilation rule DQ₂.₅ , then the distance "x" between points U' and U is (c) 6 units .

The Scale Factor is written as ratio of the distance from center to  image of a point and distance from center to corresponding point.

the scale factor from the figure can be written as : QU'/QU  ;

From the figure , we can see that QU = 4 units and scale factor is = 2.5 ;

⇒ 2.5 = QU'/4 ;

On simplifying ,

we get ;

⇒ QU' = 2.5 × 4 = 10 ;

From the figure : UU' = QU' - QU  ;

⇒ UU' = 10 - 4 = 6 .

Therefore , the distance between points U and U' denoted by "x" is 6 units .

The given question is incomplete , the complete question is

Line segment SU is dilated to create S'U' using the dilation rule DQ₂.₅ , What is the distance, x, between points U' and U?

(a) 4 units

(b) 4.8 units

(c) 6 units

(d) 10 units

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Answer:

The equation of a line in the form of y = mx + b, where m is the slope, x is the variable and b is the y-intercept.

Given a point and the slope, we can find the equation of the line that passes through that point. We know that the slope of the line is 0, so we can write the equation of the line as:

y = 0x + b

We also know that the line passes through the point (-3,-8), so we can substitute these values into the equation and solve for b, the y-intercept:

-8 = 0(-3) + b

-8 = 0 + b

b = -8

So the equation of the line that passes through the point (-3,-8) and has a slope of 0 is:

y = 0x - 8

This line is a horizontal line with y-intercept -8, which means that the line passes through the point (0,-8)

You can substitute a homework grade of 37 into the equation in place of x, to find the projected test grade.

Linear regression is a statistical method that is used to study the relationship between two continuous variables, often referred to as the independent variable (x) and the dependent variable (y). The goal of linear regression is to find the best-fitting line that describes the relationship between these two variables. The best-fitting line is known as the regression line, and it is represented by the equation y = mx + b, where m is the slope of the line, and b is the y-intercept.

To find the linear regression equation, we need to use the least squares method to find the line of best fit that describes the relationship between the homework grade (x) and the test grade (y). The equation of the line is in the form of y = mx + b, where m is the slope and b is the y-intercept.

To find the slope (m) and y-intercept (b) we can use the following formulas:

m = (n(Σxy) - (Σx)(Σy)) / (n(Σx²) - (Σx)²)

b = (Σy - m(Σx)) / n

where n is the number of data points, Σx and Σy are the sum of x and y values, Σxy is the sum of the product of x and y values, and Σx² is the sum of the squares of x values.

Given the data points, we can use this information to calculate the slope and y-intercept, and write the linear regression equation.

Given the linear regression equation of the form y = mx + b

You can substitute a homework grade of 37 into the equation in place of x, to find the projected test grade.

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The factored expression to the expression is (4y + 1)(y + 6)

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

4 y2 + 25 y + 6

Express properly

So, we have the following representation

4y² + 25 y + 6

Expand the expression

This gives

4y² + 24y + y + 6

Next, we factor the expression

4y(y + 6) + 1(y + 6)

Factor out y + 6

(4y + 1)(y + 6)

Hence, the solution is (4y + 1)(y + 6)

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The quotient from the synthetic division (9a^4-31a^3-21a^2+6a-13)/(a-4) is 9a⁴ - 22a³ - a² + 5a - 8/a -4

Synthetic division can be defined as a mathematical method of dividing a polynomial by a  binomial x - c

Such that, c is a constant.

The steps to take in synthetic division;

Given the polynomial;

(9a^4-31a^3-21a^2+6a-13)/(a-4)

[tex]\sqrt[a -4]{9a^4 -31a^3 +6a -13}[/tex]

c of divisor x-c

                4         coefficients of dividend

                           9     -31     -21      6     -13

                          _____9__-22__-1___ 5_______

                          9       -22     -1      5       -8

The quotient is the;

9a⁴ - 22a³ - a² + 5a - 8/a-4

Hence, the expression is  9a⁴ - 22a³ - a² + 5a - 8/a-4

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The correct statement relative to the polynomial function is given as follows:

A. p(1)= 4

B. p(x)= (x^2 + 5x + 2) +4/x-1

The polynomial function for this problem is given as follows:

p(x) = x^3+4x^2-3x+2

Dividing the polynomial function by x - 1, the quotient and the remainder are given as follows:

Meaning that:

Hence the correct options are given by option A and option B.

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Answer:

8

Step-by-step explanation:

42/7 =

6..

Since +6 more to 42 = 48 =

42+6=

48.

Just add 1 more month =

7+1=

8

Need more explanation I am happy to help :)

Terra is correct. In order for a relationship to be a function, each input value must result in only one input.

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a connection between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input. A function is often represented as y = f. (x).

We know that for a function each input value must result in a unique output value. Terra claims this statement, and hence she is correct.

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well, let's first find out how many cups was that in 24 hours anyhow.

so in 1hr the hose leaks 0.25 cups, so in 24 hrs that'd be (24)(0.25) = 6 cups.

Since a gallon has 16 cups, that'd be 6/16 gallons or 3/8 = 0.375 of a gallon.

Answer:

Step-by-step explanation:

If the problem was supposed to be "3.4 + 2.8d + 2.8d -1.3". Then the answer would be 5.6d + 2.1. you can combine the "d" terms because they have the same variable and you can combine the number terms because they are like. This result in 2.8d+2.8d + 3.4 - 1.3. This simplifies to the correct answer given above.