A polynomial function has a root of –7 with multiplicity 2, a root of –1 with multiplicity 1, a root of 2 with multiplicity 4, and a root of 4 with multiplicity 1. If the function has a positive leading coefficient and is of even degree, which statement about the graph is true?
The graph of the function is positive on (2, 4).
The graph of the function is negative on (4, infinite).
The graph of the function is positive on (-infinite, –7).
The graph of the function is negative on (–7, –1).

The binomial factors of x³- 4x²+x+6​ are (x+2), (x+3), and (x-1).

Using the splitting and grouping the terms:

x³ + 4x² + x - 6

= x³ + 2x² + 2x² + x - 6  [Splitting 4x² = 2x² + 2x²]

= (x³ + 2x²) + (2x² + x - 6)

= x² (x + 2) + (2x² + 4x - 3x - 6)

= x² (x + 2) + [ 2x (x + 2) - 3 (x + 2)]

= x² (x + 2) + (x + 2) (2x - 3)

= (x + 2) ( x² + 2x - 3)

= (x + 2) ( x² + 3x - x - 3)

= (x + 2) [x (x + 3) - 1 (x + 3)]

= (x + 2) (x + 3) (x - 1)

Hence, the binomial factors are (x + 2), (x + 3) and (x - 1)

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The type of scale commonly used on maps is a graphic scale, which uses a line or bar to represent distances accurately.

The type of scale used on a map is known as a map scale. It is a graphical representation that shows the relationship between distances on the map and their corresponding measurements in the real world. A map scale allows us to understand the size and proportion of features depicted on the map.

There are three main types of map scales: verbal scales, graphic scales, and representative fraction scales.

Verbal Scale: A verbal scale uses words to describe the relationship between distances on the map and real-world measurements. For example, a verbal scale might state "1 inch represents 1 mile" or "1 centimeter represents 10 kilometers." Verbal scales are commonly used on small-scale maps, where the level of detail is not as important.

Graphic Scale: A graphic scale, also known as a bar scale or linear scale, uses a line or a bar marked with specific distances. This line is divided into equal segments that represent units of measurement. By comparing the length of the line on the map to the corresponding distance in the real world, you can determine distances accurately. Graphic scales are often found on the margin or the legend of a map and are commonly used on medium- to large-scale maps.

Representative Fraction (RF) Scale: A representative fraction scale expresses the relationship between map distances and real-world distances using a ratio. For example, a representative fraction of 1:100,000 means that one unit of measurement on the map represents 100,000 of the same units in the real world. This type of scale is useful because it allows for precise calculations and conversions between map distances and real-world distances. Representative fraction scales are commonly used on topographic maps and engineering plans.

It's important to note that a map may include multiple scales to accommodate different levels of detail. For instance, a large-scale map of a city may have a more detailed scale than a small-scale map of an entire country.

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The percentage increase in snakes from last year to this year at the Cincinnati Zoo is 20%.

The percentage increase refers to the ratio of the increase in the number of snakes in the zoo.

The percentage increase can be computed as the quotient of the amount of increase divided by the previous number of snakes, multiplied by 100.

The number of snakes in the zoo last year = 25

The number of snakes in the zoo currently = 30

The increase in the number of snakes = 5 (30 - 25)

The percentage increase = 20% (5/25 x 100)

Thus, we can conclude that the number of snakes in the Cincinnati Zoo has increased by 20 percent since last year.

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The amount Luca needs to charge per client to reach his profit goal is $670.76.

The correct answer is Option D.

Given data:

Let x be the amount Luca needs to charge per client.

Total monthly revenue = Number of clients * Amount charged per client

Total monthly revenue = 37 * x

Total monthly expenses = Fixed monthly expenses + (Variable expenses per client * Number of clients)

Total monthly expenses = $3,345 + ($267 * 37)

Monthly profit = Total monthly revenue - Total monthly expenses

$11,594 = (37 * x) - ($3,345 + ($267 * 37))

On solving for x:

$11,594 = 37x - $13,224

37x = $11,594 + $13,224

37x = $24,818

On simplifying the equation:

x = $24,818 / 37

x ≈ $670.756

Hence, Luca needs to charge $670.76 per client to reach his profit goal.

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Answer:

Step-by-step explanation:

2x - 2 = -18

To cancel the -2, add 2 to both sides.

2x = -16

Divide both sides by two to isolate the x.

X = -8

Answer:

-8

Step-by-step explanation:

\(2x - 2 = -18\)

Add 2 to both sides

\(2x = -16\)

Divide!

\(x=-8\)

Answer:

1.358899 or 3-\sqrt{19}

Step-by-step explanation:

either or

Answer:

77 m^2

Step-by-step explanation:

area of parallelogram = base*height

A = 11*7

A = 77

Answer

2304 feet per day

Step-by-step explanation:

The object will move 2304 feet per day.

Speed is the distance an object moves in per unit of time.Speed is a scaler quantity because in speed the direction is not specified.

According to he given question an object is moving at a speed of 32 yards per hour.

We know 1 yard is = 3 feet.

∴ 32 yards is = 3×32 = 96 feet.

So, the object is moving at a speed of 96 feet per hour.

We also know that 24 hours is = 1 day.

The object moves 96 feet hour.

∴ The will move (96×24) feet per day.

= 2304 feet per day.

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Answer:

The cost per gram for each bag is:

Small bag: 0.00314 £

Medium bag: 0.00335 £    

Large bag: 0.00305 £  

Step-by-step explanation:

Small bag:

If 175 g cost 0.55 £, 1 g will be:

\( \frac{1g*0.55 \£}{175\: g} = 0.00314 \£\)

Medium bag:

If 525 g cost  £ 1.76, 1g will be:

\( \frac{1g*1.76 \£}{525\: g} = 0.00335 \£\)    

Large bag:  

If 1150 g cost  £ 3.51, 1g will be:

\( \frac{1g*3.51 \£}{1150\: g} = 0.00305 \£\)        

I hope it helps you!

Answer:

apple's iPhone iPad Android blackberry windows etc

Answer : 66.67

Step-by-step explanation : Convert 16/24 to Percentage by Changing Denominator

Our percent fraction is 66.666666666667/100, which means that 1624 as a percentage is 66.67%.

Answer:

33.33%

Step-by-step explanation:

Total Answers=20

correct answers= 8

Percentage =

\( \frac{8}{24} \times 100\)

= 33.33%

The equations x² + 4x + 3 = 0 and x² -6x + 13 = 0 are equivalent to (x + 2)² = 1 and (x - 3)² = -4

An equation is an expression that shows the relationship between two or more numbers and variables. An equation can either be linear, quadratic, cubic and so on

The standard equation of a quadratic function is:

y = ax² + bx + c

1) Given that:

x² + 4x + 3 = 0

subtract 3 from both sides:

x² + 4x = -3

add to both sides the square of half the coefficient of x:

x² + 4x + 4 = -3 + 4

(x + 2)² = 1

2) Given that:

x² - 6x + 13 = 0

subtract 13 from both sides:

x² - 6x = -13

add to both sides the square of half the coefficient of x:

x² - 6x + 9 = -13 + 9

(x - 3)² = -4

The equations are (x + 2)² = 1 and (x - 3)² = -4

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Answer:

x = 15 , y = 21

Step-by-step explanation:

using Pythagoras' identity

in Δ ABD

x² + 8² = 17²

x² + 64 = 289 ( subtract 64 from both sides )

x² = 225 ( take square root of both sides )

x = \(\sqrt{226}\) = 15

in Δ ADC

8² + DC² = 10²

64 + DC² = 100 ( subtract 64 from both sides )

DC² = 36 ( take square root of both sides )

DC = \(\sqrt{36}\) = 6

then

y = x + DC = 15 + 6 = 21

Ali's strategy is essentially the same as Mary's strategy. Both strategies estimate the HST as 15% of the price. However, Mary's strategy involves taking half of 10% of the price.

Mary suggests estimating the HST in Ontario as finding 10% of the price, taking half of this answer and adding the two. Ali proposes finding 10% of the price, then 5% of the price and adding the two answers.

Their strategies differ in the way they approach finding the estimate, but both methods can be used to arrive at the same result.

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The HST in Ontario is 13%, which can be estimated using 15%. Mary tells Ali that it can be estimated as: find 10% of the price, take a half of this answer and add the two. Ali tells Mary that he thinks they should find 10% of the price, then 5% of the price and add the two answers. Compare their strategies.

Answer:

growth factor for what?

Answer:

C. 216

Step-by-step explanation:

6³ = 6 x 6 x 6

6 x 6 = 36

36 x 6 = 180 + 36

180 + 36 = 216

hope this helps

The weight on the inflation gap has increased from 0.5 to 0.75. The real interest rate is 16.86% and Nominal interest rate is 20%

a. In the base scenario, the real interest rate will be 20%, and the nominal interest rate will be 20%.

b. In scenario B, inflation rate will be higher (4%) compared to the base scenario (3.14%).

Output gap is 0% in both the scenarios, however, in the base scenario inflation gap is 0% (3.14 - 3.14) and in scenario B, inflation gap is 0.86% (4 - 3.14).

Now, let's calculate the real interest rate.

Real interest rate in base scenario = 20% - 3.14%

= 16.86%.

Real interest rate in scenario B = 20% - 3.14% + 1.5 + 0.5 (4-3.14) + 0.5 (0-0/0)

= 19.22%.

The real interest rate has moved in the direction to move inflation rate towards its target.

c. In scenario C, the output gap will be 20% compared to 0% in the base scenario.

Inflation gap is 0% in both the scenarios

Inflation rate is 3.14% and in scenario C, inflation rate is 2%.

Let's calculate the real interest rate. Real interest rate in the base scenario = 20% - 3.14%

= 16.86%.

Real interest rate in scenario C = 20% - 2% + 1.5 + 0.5 (3.14 - 3.14) + 0.5 (20-0/20)

= 20.15%.

Real interest rate in scenario C = 20% - 2% + 1.5 + 0.75 (3.14-3.14) + 0.25 (20-0/20) = 18.78%.

The new policy rule has changed the weight of the output gap in the Taylor Rule from 0.5 to 0.25.

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Answer:

65 packets and 4 stamps

Step-by-step explanation:

The first thing we see is that the stamps are mixed... which means they must be added.

208 + 186 = 394 stamps total

Now we see that each packet has 6 stamps. So we divide the number of stamps in total by 6.

394/6= 65.66667

Now we see from that number that the stamps can't quite make 66 packets, so there are 65 packets.

Now we find the number of stamps left over by multiplying the number of packets by 6.

65 x 6= 390

Now we take the total number of stamps minus the number of stamps in packets.

394 - 390 = 4

Therefore, there are four stamps left over.

Hope this helps!

Answer:

13.48

Step-by-step explanation:

So I used the Order of Operation and went in order to solve the problem. First is P (Parentheses)

(1.74) = 1.74

Next, Exponents (E).

There are none.

Then, Multiplication and Division (from left to right).

2(1.74) = 3.48 | 15-9+2.65+1.35+3.48.

The fourth is Addition and Subtraction (from left to right).

15-9+2.65+1.35+2= 13.48

The biconditional statement for the given conditional statement would be:

2x = 18 if and only if x = 9.

The given conditional statement "If 2x = 18, then x = 9" can be represented symbolically as p → q, where p represents the statement "2x = 18" and q represents the statement "x = 9".

To form the biconditional statement, we need to determine if the converse of the conditional statement is also true. The converse of the original statement is "If x = 9, then 2x = 18". Let's evaluate the converse statement.

If x = 9, then substituting this value into the equation 2x = 18 gives us 2(9) = 18, which is indeed true. Therefore, the converse of the original statement is true.

Based on this, we can write the biconditional statement:

2x = 18 if and only if x = 9.

The biconditional statement implies that if 2x is equal to 18, then x must be equal to 9, and conversely, if x is equal to 9, then 2x is equal to 18. The biconditional statement asserts the equivalence between the two statements, indicating that they always hold true together.

In summary, the biconditional statement is a concise way of expressing that 2x = 18 if and only if x = 9, capturing the mutual implication between the two statements.

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The Area of the shaded portion is: 72 square inches

The formula for the area of a triangle is given by the formula:

Area = ¹/₂ * base * height

Now, to get the area of the shaded portion, we will get the area of the larger triangle and subtract the area of the smaller one from it.

Thus:

Area of larger triangle = ¹/₂ *  17 * 13 = 110.5 square inches

Area of smaller triangle =  ¹/₂ * 11 * 7 = 38.5 square inches

Thus:

Area of shaded portion = 110.5 square inches - 38.5 square inches

Area of shaded portion = 72 square inches

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Answer:

when x=-9, y=1

Step-by-step explanation:

the graph shows when the x is at -9, the y is at 1

Answer:

Step-by-step explanation:

A new baby grew:

Total inches during two months:

Answer:

C. Both statements are true

In mathematics, an algebraic expression is an expression built up from integer constants, variables, and the algebraic operations (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number). For example, 3x2 − 2xy + c is an algebraic expressio

Answer:

Algebra is a branch of mathematics that substitutes letters for numbers. Algebra is about finding the unknown or putting real-life variables into equations and then solving them. Algebra can include real and complex numbers, matrices, and vectors. An algebraic equation represents a scale where what is done on one side of the scale is also done to the other and numbers act as constants.

Expressions is a Numbers, symbols and operators (such as + and ×) grouped together that show the value of something.  

Examples:

• 2 + 3 is an expression

• 3 − x/2 is also an expression

Step-by-step explanation:

The answer is B

Answers is B

The smaller amount of total calories consumed is 359 calories.

Algebra is a branch of mathematics that deals with mathematical symbols and the rules for manipulating these symbols. It is a broad area of study that includes a wide range of topics, such as equations, inequalities, functions, polynomials, matrices, and more.

Algebraic expressions are composed of variables, constants, and mathematical operations, such as addition, subtraction, multiplication, division, exponentiation, and logarithms. Equations, on the other hand, are mathematical statements that assert the equality of two algebraic expressions. Inequalities are mathematical statements that assert the relationship between two algebraic expressions using the symbols "<", ">", "<=", or ">=".

Functions in algebra are mappings from one set of numbers to another set of numbers that obey certain rules. These rules may involve properties such as continuity, differentiability, and invertibility.

Jane consumes:

Half a blueberry muffin: 0.5 * 270 = 135 calories

Whole fruit platter: 190 calories

A third of a glass of milk: (1/3) * 102 = 34 calories

So her total calorie intake is: 135 + 190 + 34 = 359 calories (rounded to the nearest whole calorie).

Rob consumes:

Hashbrowns and eggs: 2 * 190 = 380 calories

Half a glass of orange juice: 0.5 * 40 = 20 calories

So his total calorie intake is: 380 + 20 = 400 calories.

Therefore, the smaller amount of total calories consumed is 359 calories.

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