Given:
f(x)=x²- 5x+7 and g(x)=3x² + 4x - 2
Find:
(f- g)(x)
(g-f)(x)
(f + g)(x)
Polynomials

The equation of the plane passing through (0, -3,1) that is orthogonal to the planes 3x + 2y - 4z = 0 and - X+ 2y + 4z = 7 is 16x - 8y + 8z = 32

We know that the equation of plane passing through point (x₁, y₁, z₁) is given by,

A(x - x₁) + B(y - y₁) + C(z - z₁) = 0

where, A, B, and C are direction ratios

In the question,  the plane passes through point (0, -3,1)

Let (x₁, y₁, z₁)  = (0, -3,1)

Using above formula the equation of the plane will be in the form,

A(x -0) + B(y - (-3))+C(z - 1) = 0            

Ax + B(y + 3)+C(z - 1) = 0                   ..........(1)

The required plane is orthogonal to the planes 3x + 2y - 4z = 0 and - X+ 2y + 4z = 7.

So, their normal to the required plane would be perpendicular to the normal of both the planes.

The normal to the required plane is a cross-product of the normals of planes.

A cross-product of the normals of planes 3x + 2y - 4z = 0 and - X+ 2y + 4z = 7 is 16i - 8j + 8k

So, the direction ratios,

A = 16, B = -8, C = 8

So equation (1) becomes,

16x - 8(y + 3) + 8(z - 1) = 0  

16x - 8y - 24 + 8z - 8 = 0

16x - 8y + 8z - 32 = 0 is the required equation of the plane

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The person will have to place the compasses 6 feet away from the point they want the arch to start, and draw the arch with a radius of 9 feet.

The radius of the arch is 9 feet.

The formula for calculating the radius of an arch is [tex]R = (width / 2) / sin(90°)[/tex].

Therefore, the radius of the arch is:

R = (18 ft / 2) / sin(90°) = 9 ft

To calculate the radius of the arch he needs to draw, the person can use the formula R = (width / 2) / sin(90°). In this case, the width of the arch is 18 feet, so the radius of the arch is 9 feet, calculated as R = (18 ft / 2) / sin(90°). The person will have to place the compasses 6 feet away from the point they want the arch to start, and draw the arch with a radius of 9 feet.

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The  value for n that would make the inequality true is 4.5

You should understand that a statement of an order relationship with greater than, greater than or equal to, less than, or less than or equal to between two numbers or algebraic expressions is inequality.

The given inequality is ⁿ⁄₉ > ½

This implies that 2(n) > 1(9)

Opening the brackets to have

2n > 9

Making n the subject of the relation by dividing both sides by 2

2n/2 > 9/2

Therefore n = 4.5

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All of the angles in an acute triangle are less than 90 degrees. Triangles are referred to as right triangles when one of their angles is 90 degrees.

The three vertices of a triangle make it a three-sided polygon. The angles of the triangle are formed by the three sides' end-to-end connections at a point. 180 degrees is the sum of the triangle's three angles. With three sides and three vertices, triangles are a particular kind of polygon in geometry.

It has three straight sides and is a two-dimensional figure. As a 3-sided polygon, a triangle is included. Three triangle angles added together equal 180 degrees. In one plane, the triangle is contained. When three straight lines cross, a triangle is the result. There are always three sides and three corners to a triangle (angles). A triangle's vertex is the location at which two of its sides meet.

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Answer:

Step-by-step explanation:

Pentagon, irregular polygon and convex polygon are the names that apply to the given form.

A polygon is a two-dimensional flat form with straight, completely closed sides. Straight, not curved, sides are required. Polygons, on the other hand, can have any number of sides.

A pentagon is a polygon with five sides, and if these sides are uneven, it is an irregular pentagon, also known as an irregular polygon.

A convex polygon is one with all of its internal angles smaller than 180°.

As a result, the terms for the given form are pentagon, irregular polygon, and convex polygon.

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The question seems incomplete, the missing figure has been attached below

a)

g = m / 40

g = 140 /40

g = 3.5

b)

m = 40g

m / 40 = g

The expression for the cost of gasoline and oil will be C. 3.35c + 2.65g

An expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator.

In this case, it should be noted that Joe bought g gallons of gasoline and c cans ofg oil. The prices were givn as well.

The expression for the cost of gasoline and oil will be:

= 3.35 × c + (2.65 × g)

= 3.35c + 2.65g

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Answer: 5R

Step-by-step explanation:

Half a dozen =6 pieces

R30/6=5R

How much is one dozen?

One dozen is equal to 12, so one half of a dozen is 6.

If 6 candles are priced at R30, we can divide R30 by 6 to get the cost of 1 candle.

30 ÷ 6 = 5.

Therefore, each candle costs R5.

Answer:

0.07

Step-by-step explanation:

[tex]0.0007*100=0.07[/tex]

Basically, you move the 7 two places to the left since 100 has 2 zeroes.

Answer:82 cm squared

Step-by-step explanation:

Just draw imaginary lines on the shape to turn it into a bunch of squares and rectangles, then find the area of those and add them together.

Kinda hard to explain since there are multiple ways to do it, but I hope that this still helps!

Answer:

8 cups of flour

Step-by-step explanation:

If you want an equation it will be:

[tex]\frac{2}{8} * \frac{32}{1} = \frac{64}{8} = 8[/tex]

So Francessa used 8 cups of flour

The total cost of 6 apples and 3 oranges is $6 + $6 = $12.

The total cost of 4 apples and 4 oranges is $4 + $8 = $12.

The total cost of 5 apples and 4 oranges is $5 + $8 = $13.

The total cost of 8 apples and 2 oranges is $8 + $4 = $12.

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The frequency table is given below.

The probability that a person chosen is a left-handed female is 31/140.

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,

Total number of employees = 140

Male:

Number of male = 65

Right-handed.

= Total number of right-handed - Female right handed

90 - 44 = 46

Left-handed.

= 65 - 46

= 19

Female:

Number of females.

= Total employees - Number of males

= 140 - 65

= 75

Right-handed.

= 75 - 31

= 44

Left-handed.

= 31

Now,

The frequency table.

                                            RH = 46

                                            LH = 19

           Male = 65    

140

          Female = 75  

                                             RH = 44

                                              LH = 31

Now,

The probability that a person is a left-handed female.

= Number of left-handed females / Total number of employees

31/140

Thus,

The frequency table is given above.

The probability that a person is a left-handed female is 31/140.

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The best statistical test to be used is multiple linear regression analysis.

Multiple linear regression is a statistical method that allows you to examine the relationship between two or more independent variables (in this case, level of education, gender, and annual income of the student's parents) and one dependent variable (annual income and student loan debt).

It will help you determine how much of the variation in the dependent variable is explained by the independent variables, and the strength and direction of the relationships between the variables.

In this case, this test will allow us to determine the impact of a student's level of education, gender, and the annual income of their parents on their annual income and student loan debt while accounting for the possible confounding effect of the annual income of their parents on these variables.

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Answer: To find the average of daily income of the week, we need to find the total income of the week and divide it by the number of days in the week.

We know that the average daily income of the week is Rs 1,300 and we know that he earned Rs 2,000 on Saturday. To find the total income for the week, we can add the Saturday income to the average daily income for the 6 days.

Therefore, the total income for the week = Rs 1,300 (average daily income) x 6 (days) + Rs 2,000 (Saturday income) = Rs 7,800 + Rs 2,000 = Rs 9,800

To find the average daily income for the week, we divide the total income by the number of days in the week (7)

Average daily income = Rs 9,800 / 7 = Rs 1,400

Therefore, the average daily income of the plumber for the week is Rs 1,400.

Step-by-step explanation:

As per the given parentage, the highest percentage saying the greens are too fast is females.

In math the term percentage is defined as the number or ratio that can be expressed as a fraction of 100.

Here we have know that the number male players are

Male Golfers                                    Greens Condition              

Handicap                               Too fast                        Fine

Under 15                                       10                             40

15 or more                                     25                           25

And the female players are,

Male Golfers                                     Greens Condition            

Handicap                               Too fast                         Fine

Under 15                                       1                                9

15 or more                                   39                              51

Then the total value of them is calculated as,

                      Too fast                   Fine             Total

Male                   35                          65               100

Female              40                           60               100

So, the group with the highest percentage of too fast is the females.

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Answer:

Step-by-step explanation:

Step 1:

Make a proportion:

10/5 = 22/x

Step 2:

Cross multiply:

10x=22*5

10x=110

Step 3:

Divide by 10 to isolate x:

x=11

The values of x from the given figures are 3 √29 and 24 respectively.

What is triangle ?

Triangle can be defined in which it has three sides , three angles and sum of three angles is always 180 degrees.

Given

In the figure,

The two given triangles are similar ,

So, in the first figure it is given that they are similar ,

√29 / 5  = x / 15

x  = √29 * 15  / 5

x =√29 * 3

x = 3 √29

And in the second figure , here also they gave they are similar

so we get,

12 / 13  =  x /  26

x = 12 * 26 / 13

x = 12 * 2

x = 24

Hence, The values of x from the given similar triangles are 3 √29 and 24 respectively.

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The image of the point (-1, 3) is (1, 1).

A translation is a transformation that moves every point in a figure the same distance in the same direction.

For example, this transformation moves the parallelogram to the right 5 units and up 3 units. It is written ( x , y ) → ( x + 5 , y + 3 ) .

Given:

Pint( -1, 3).

Translating unit = 2 units down

According to the 270°-counterclockwise rotation [90°-clockwise rotation] rule, you take the y-coordinate, move it to your new x-coordinate, and then take the opposite of the x-coordinate and set it as your new y-coordinate:

Extended Rotation Rules

270°-clockwise rotation [90°-counterclockwise rotation] = (x, y) → (-y, x)

270°-counterclockwise rotation [90°-clockwise rotation] =(x, y) → (y, -x)

and, 180°-rotation = (x, y) → (-x, -y)

Thus, the 270°-counterclockwise rotation [90°-clockwise rotation] will be

[-1, 1] moves to [1, 1].

Hence, the translation is (1, 1).

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Answer:

The unit price for a coffee mug is $0.55.

Step-by-step explanation:

The unit price is simply just the price per unit.

We have a 4-pack of coffee mugs that costs $2.20.

He have 4 units and the price per 4 units.

Lets evaluate the price per 1 unit.

[tex]\frac{2.20}{4} =\frac{x}{1}[/tex]

Lets solve for [tex]x[/tex].

Divide [tex]x[/tex] by 1.

[tex]x=\frac{2.20}{4}[/tex]

Divide 2.20 by 4.

[tex]x=0.55[/tex]

Assuming all the workers employed at the beanbag factory are of equal ability, the beanbag factory invest in more equipment to address the diminishing marginal returns it experiences after the hire of its third worker. So the option B is correct.

It is assumed that all of the factory's employed employees have the same level of skill. Additionally, it must follow that if they are working to their maximum ability, they will be able to accomplish the same amount of work as before.

Since the third man was hired, the quantity of work the three of them have completed has decreased, making it clear that he is to blame for the diminishing returns.

Therefore, it seems sense to fire the individual since he is either not performing to his full capacity or encouraging other employees to do the same.

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Answer: The answer is $13.19.

Step-by-step explanation:

1- Turn the percentage into a decimal by moving the percent sign twice to the left.

2- Multiply the bill by the decimal.

3-youll get 13.185 so you'll round up to 13.19.

hope this helps!!

If the 3 times of total number of adults was 17 less than number of children who visited the petting zoo , then the equation to model this relationship is written as c = 3a + 17   ;

let the number of children in the petting zoo be = c ;

and the number of adults in the petting zoo is = a ;

given that the the number of children are 3 times the number of adults ;

that means ⇒ c = 3a ;

and also given that the difference between the number of children and number of adults is 17 .

This situation can be represented as :

⇒ c - 3a = 17 ;

⇒ c = 3a + 17 .

Therefore , the equation to model this relationship is "c = 3a + 17" .

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The expression for the amount earned in one week per hour is 18 x $10

The expression for the amount earned in four weeks is 18 x $10 x 4

An expression is when numbers or letters are connected together by a mathematical operation without an equal to sign. An example of an expression is a + 3b.

The amount earned in one week = total number of hours worked in a week x amount earned per hour

18 x $10

The amount earned in four weeks = total number of hours worked in a week x amount earned per hour x 4

18 x $10 x 4

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Answer:

To find the coordinates of Q, we can use the concept of proportional division of line segments.

Given that MQ:ON = 2:3, it means that the ratio of the length of MQ to ON is 2:3.

Let's first find the vector that represents the direction of MN, which is the vector pointing from M to N. We can find this by subtracting the coordinates of M from the coordinates of N:

(8,10) - (-12,-5) = (20, 15)

This is the vector <20,15>

Now, we can find the point Q, which is located two thirds of the way from M to N, by multiplying the vector <20,15> by 2/5 and adding the result to the coordinates of M:

Q = M + (2/5) * <20,15>

= (-12,-5) + (2/5) * <20,15>

= (-12,-5) + <8,6>

= (8,1)

So, the coordinates of Q are (8,1)

The simplified algebraic expression for this problem is given as follows:

5x + 2y + 11.

The algebraic expression for this problem is defined as follows:

9x + 2y + 3 - 4x + 8.

To simplify the expression, we combine the like terms, which are the terms that have the same unknown variable, hence:

Hence the simplified algebraic expression for this problem is given as follows:

5x + 2y + 11.

Meaning that the third option is the correct option.

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