Use synthetic division to find the quotient if polynomial P(x) = x³ - 7 x + 6 is divided by x - 2
A) x²+2 x+3
B) x²-2 x-3
C) x²-2 x+3
D) x²+2 x-3

Answer:

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

Given is the quadratic equation.

A quadratic equation has two real solutions if the discriminant is positive.

Hello..!

¿What is consumidores terciarios?

They are the ones that feed on carnivores and their parasites.

An example:

When we see a dead bird, a week goes by and then there are only the bones, since as it says they feed on dead birds, that is, they eat everything without leaving anything, whether they are birds, cows or people.

Organisms that eat secondary consumers are called tertiary consumers and are carnivores that eat carnivores, such as eagles or large fish.

Producers, or autotrophs, make their own organic molecules. Consumers, or heterotrophs, obtain organic molecules by eating other organisms.

A food chain is a linear sequence of organisms through which nutrients and energy pass from one organism to another through consumption.

An equation to represent this situation x is 37/12. The components of a whole or group of items are represented by fractions.

Here 7 is lessoned by 2 of a number.

Consider x be the number.

we get 2x - 7

the result is same as 3 subtracting of the number from 10.

therefore, we get 10 ( 3 - x )

from this two equations we get,

⇒ 2x - 7 = 10 ( 3 - x )

⇒ 2x - 7 = 30 - 10x

Simplifying we get,

⇒ -37 = - 12x

⇒ x = 37/12

Therefore, An equation to represent this situation x is 37/12.

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The smallest total number of pets each could be walking is 2.

Given:

Juan and Malia make money by walking neighborhood pets. During a conversation about their work, they realize that they are both walking the same total number of pets, even though Juan walks pets in groups of 9 and Malia walks pets in groups of 3.

from the given statements:

Juan pets groups = 9

Malia pets groups = 3

so they both can same total number of pets is maximum 3.

so minimum number for each is 1.

Total = 1+1

= 2

Therefore The smallest total number of pets each could be walking is 2.

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Answer:

Step-by-step explanation;

The rate of change of the parabola on the interval [0, 4] is 0.

For any function f(x), we define the rate of change on an interval [a, b] as:

R = (f(b) - f(a))/(b - a)

Here we want to get the rate of change on the interval [0, 4], and we know that the graph has the points:

(0, 4), (2, -4), (4, 4)

Then:

f(0) = 4

f(4) = 4

Replacing that in the rate of change formula we get:

R = ( f(4) - f(0))/(4 - 0)

R = (4 - 4)/4 = 0

The rate of change on that interval is 0.

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The plant's height after x months is 11.25 + 15x.

From the information illustrated, the plant is already 11.25 meters tall, and it will grow 15 centimeters every month.

In this case, let the plant's height be H (in meters)

Let the number of months be x.

The plant height will be:

= 11.25 + (15 × x)

= 11.25 + 15x

This is the height.

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Complete question

A plant is already 11.25 meters tall, and it will grow 15 centimeters every month. When is the plant's height, H (in meters), after x months?

Answer: 30kg

Step-by-step explanation:

100% = 60kg

50% = 100% /2

60kg(100%)/2 = 30kg(50%)

Answer:

Step-by-step explanation:

Proportion:

60 kg  -   100%

X kg - 50%

X = 60·50% / 100% = 30 kg

Answer:

y = - [tex]\frac{10}{3}[/tex] x + 1

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = [tex]\frac{3}{10}[/tex] x - 8 ← is in slope- intercept form

with slope m = [tex]\frac{3}{10}[/tex]

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{3}{10} }[/tex] = - [tex]\frac{10}{3}[/tex] , then

y = - [tex]\frac{10}{3}[/tex] x + c ← is the partial equation of line h

to find c substitute (3, - 9 ) into the partial equation

- 9 = - 10 + c ⇒ c = - 9 + 10 = 1

y = - [tex]\frac{10}{3}[/tex] x + 1 ← equation of line h

The trigonometric ratio tan(2 sin⁻¹(x)) is expressed as 2sec(x)

The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec). In geometry, trigonometry is a branch of mathematics that deals with the sides and angles of a right-angled triangle. Therefore, trig ratios are evaluated with respect to sides and angles.

In the question given, we have;

tan(2 sin⁻¹(x))

tan = sin / cos

sin/cos(2 * 1/sin x)

The expression becomes 2/cosx or 2cos⁻¹(x)

But cos⁻¹ = sec

tan(2 sin⁻¹(x)) = 2sec(x)

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The x-intercept of the equation, 1.50 x + 2.50y = 60, is x = 40

The y-intercept of the equation, 1.50 x + 2.50y = 60, is y = 24

From the question, we are to determine the x-intercept and y-intercept of the given equation.

The given equation is

1.50 x + 2.50y = 60

The x-intercept is the point where y = 0

and

The y-intercept is the point where x = 0

Determining the x-intercept

1.50x + 2.50y = 60

Put y = 0

1.50x + 2.50(0) = 60

1.50x + 0 = 60

1.50x = 60

x = 60/1.50

x = 40

The x-intercept is x = 40

Determining the y-intercept

1.50x + 2.50y = 60

Put x = 0

1.50(0) + 2.50y = 60

0 + 2.50y = 60

2.50y = 60

y = 60/2.50

y = 24

Hence, the y-intercept is y = 24

The x-intercept represent the number of pens that could be bought for $60 when one is not buying any notebooks.

The y-intercept represent the number of notebooks that could be bought for $60 when one is not buying any pens

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Answer:B

Step-by-step explanation:

A is equal to 6.3'.

none of the others are equal to 3.3 exactly.

Answer: -2.4x-3

Step-by-step explanation:

Answer:

ABC

Step-by-step explanation:

Think of a plane as a piece of paper that went on forever in all directions.  Which points would be on the paper?  Three examples would be points A, B and C.

The distance between points (2,3) and (5, -2) is [tex]\sqrt{34}[/tex] units.

The given points are (2,3) and (5, -2)

The distance (D) between two points [tex](x_{1} ,y_{1} )[/tex]  [tex](x_{2} ,y_{2} )[/tex] is

D = [tex]\sqrt{(x_{1} -x_{2} )^{2} +(y_{1} -y_{2} )^{2} }[/tex]

For evaluating the distance between the points (2,3) and (5, -2)

The distance (D) = [tex]\sqrt{(2 - 5)^{2} +(3 -(-2) )^{2} } = \sqrt{(-3)^{2} +5^{2} } = \sqrt{9+25} = \sqrt{34}[/tex]

Hence, the distance between points (2,3) and (5, -2) is [tex]\sqrt{34}[/tex] units.

Distance is a numerical or occasionally qualitative dimension of how a ways apart objects or points are.

In normal utilization, distance may additionally discuss with a bodily duration or an estimation primarily based on different standards.

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The length of the base is 22.1

An isosceles triangle with congruent sides of length 49.3 inches has a perimeter of 121.7 inches

An triangle is said to be isosceles if two sides of the trainagle have same length.

The two sides of this triangle is congurent that is they have same length = 49.3

perimeter of a triangle is the summation of all three sides.

Perimeter = length + base + length

121.7 = 49.3 + base + 49.3

base = 121.7 - 99.6

base = 22.1

Therefore, the length of the base is 22.1

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Answer: 2 gallons

Step-by-step explanation:

If they drink 12 gallons of milk every 6 weeks, to find how many gallons they drink per week, you need to divide the number of gallons by the time.

So,

12/6 = 2 gallons

Thus, they drink 2 gallons per week.

Answer:

The zeros are (158.017, 0) and (1489.042, 0)

The profit earned in 158.017 days and 1489.042 days is equal to 0. This means that Sean only earns money (makes a profit) when the amount of days he promotes a brand is greater than 158.017 but less than 1489.042 days.

Answer: 3, -1/3x - 1

Step-by-step explanation:

Answer:

y= -1/3x-1

Step-by-step explanation:

Find the slope of the line by plugging two points into the slope formula

[tex]\frac{y_{2}-y_{1} }{x_2-x_1}[/tex]

[tex]\frac{-1-0}{0-(-3)}[/tex]

m= -1/3

Find the y-intercept by seeing where the graph intersects the y-axis

b = -1

y=mx+b

y= -1/3x-1

The final balance is $895.7.

What is simple interest?

Simple interest is a quick and easy method of calculating the interest charge on a loan. Simple interest is determined by multiplying the daily interest rate by the principal by the number of days that elapse between payments.

Interest = principal ×rate× time

Given, principal = $845

rate = 4%

time = 18 months = 3/2 years.

After substituting the values, we get

Interest = 845(4)(3/2)/100

= 50.7

Final balance = initial balance + interest

Therefore,

Final balance = 845 + 50.7

= $895.7

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Answer:

The answer is 48

Step-by-step explanation:

First you have to get the number or crayons ehich is 12 then you can multiply it by the denominator in 1/4 so 12x4=48

The Prime factorization of 144 is  ([tex]2^4[/tex]) x (3²).´

What is a factor?

A factor is a number/expression that divides another number/expression, leaves zero remainder . In other words, if multiplying two numbers/expressions gives us a product, then the numbers/expressions we are multiplying are factors of the product because they are divisible by the product.

Factors of 144:

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144.

Prime factorization:

144 = 2 x 2 x 2 x 2 x 3 x 3, which can also be written as

144 = ([tex]2^4[/tex]) x (3²).´

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Answer: 7/5

Step-by-step explanation:

[tex]12x-15=6-3x\\\\15x-15=6\\\\15x=21\\\\\boxed{x=21/15 \ or\ 7/5}[/tex]

The a ,h and k values affect the parent absolute function ,by altering  the the size , causing horizontal and vertical movements respectively.

a )a values

b ) h values

c ) k values

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Each element in the domain of a function corresponds to exactly one

element in the range.

What is an element ?

A pure substance made entirely of one species of atoms, or a chemical element, is a species of atoms with a specific number of protons in their nuclei. Chemical elements, in contrast to chemical compounds, cannot be converted through any chemical reaction into simpler substances.

The items in a set are its elements. A property that all the objects share may serve to define a set. Consider the set E, which consists of all positive even integers. E is equivalent to 2, 4, 6, 8, or 10 dots. E={2,4,6,8,10…}.

A function is a relation in which each element of the domain corresponds to exactly one element of the range.

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Because there is a slope of 0, the graph is a horizontal line.

Plug into the slope-intercept form: y=mx+b

Where

m = slope & b = y-intercept

m=0

y=-1

So,

y=(0)x+(-1)

therefore your final answer is:

y=-1

In the decimal for, the value of 13 tenths + 8 tenths + 32 hundredths is 2.42

Decimal

Decimal means a number that has a decimal point followed by digits that show the fractional part.

Given,

Here we have the expression 13 tenths + 8 tenths + 32 hundredths

Now, we need to find the value of this expression.

We know that, Tenths means we have one digit after the decimal point and the hundredths have two digits after the decimal point.

So, in the given expression 13 tenths is written as 1.3

And the  8 tenths is written as 0.8

And finally, the 32 hundredths is written as 0.32

Now, we have to add these numbers, then we get,

=> 1.3 + 0.8 + 0.32

=> 2.42

Therefore, the value of 13 tenths + 8 tenths + 32 hundredths is 2.42

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The additional information is required in order to know that the triangle are congruent is, GW ≅ WX.

What is congruent triangles?

If each of the three corresponding sides and each of the three corresponding angles in two triangles equals one another, then the two triangles are said to be congruent.

We have to show that the the triangles ΔVWX and ΔEWG are congruent by using the AAS (angle, angle, side) criteria.

From the given reasons,

∠V ≅ ∠E

∠VWX ≅ ∠EWG

From this the AA criteria is satisfied.

We want sides of the triangle are congruent.

From the figure, GW ≅ WX

Therefore, by AAS the two triangles ΔVWX and ΔEWG are congruent.

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