Divide using synthetic division. (4x² + 3x³ + 9x− -20) + (x + 2)​

Answer: x - 6 = -12

Step-by-step explanation: first, we'll solve for x in 6 - x = 12. We'll isolate the variable by subtracting 6 from both sides, which gives us -x = 6. Now we'll divide both sides by -1 to get x and we will get -6 = x. So for the expression, we'll sub in the value we got for x from the equation, -6. -6 - 6 = -12.

Answer:

-12

Step-by-step explanation:

Number name = 22 million

Expanded form = 20,000,000 + 2,000,000

To write the number name and expanded form for the number of driver ants that could be in two colonies.

Given that Up to 22,000,000 driver of ants can live in a single colony

Now, from number expressions, we know that;

1, 000, 000 = 1 million

Thus number name is;

22,000,000= 22 million

Expanded form of 22,000,000 = 20,000,000 + 2,000,000

Thus, we conclude that;

Number name = 22 million

Expanded form = 20,000,000 + 2,000,000

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Answer:

Step-by-step explanation:

Answer:

$13

Step-by-step explanation:

For 50 people it will cost you 150 + 50(10) or 500

150 +500 = 650  Divide that among 50 people and you get a cost of $13 a person.

At the end of 3 years second account will earn the most interest, that is $148.38

Given,

The amount Cole has with him = $1750

Two types of account bank offered:

First account has simple interest rate = 2.75% annually

Second account has compound interest rate = 2.75% compounded annually.

Number of years = 3

We have to find the account which earn the most interest at the end of 3 years.

Simple interest = PRT/100

Compound interest = A - P

A is the amount

A [tex]=P(1+\frac{R}{N} )^{NT}[/tex]

Where,

P is the principal amount

R is the rate of interest

T is the time period

N is the number of times interest compounded yearly.

Here,

P = 1750

R = 2.75%

T = 3 years

N = 1

Now,

First account:

Simple interest = PRT/100

SI = (1750 × 2.75 × 3) / 100

SI = 14437.5/100

SI = 144.375

First account offers $144.375 as interest for 3 years.

Second account:

Compound interest = A - P

A  [tex]=P(1+\frac{R}{N} )^{NT}[/tex]

A = 1750 [tex](1+\frac{0.0275}{1} )^{1(3)}[/tex]

A = 1750 (1 + 0.0275)³

A = 1750 × 1.0275³

A = 1750 × 1.084789547

A = 1898.381707

A ≈ 1898.38

Compound interest = A - P

CI = 1898.38 - 1750

CI = 148.38

Second account offers $148.38 as interest for 3 years.

So, we can conclude that second account will earn the most interest at the end of 3 years.

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The wages earned depends on the time worked is the correct relationship between the quantities on the given graph that means option C is correct

The graph given in the question shows the time worked on x axis and wages earned on y axis and a ray staring from the origin and moving upward

from the graph we can say that when time worked is zero then wages earned is zero. As the time worked is increasing the wages earned is also increasing .

Hence, it can be said that The wages earned depends on the time worked is the correct relationship between the quantities on the given graph that means option C is correct

The correct question is -Determine the relationship between the quantities on the given graph.

Total Wages

Wages Earned ($)

Time Worked (hours)

OA. The hourly rate depends on the wages earned.

OB. The time worked depends on the wages earned.

OC. The wages earned depends on the time worked.

OD. The time worked depends on the hourly rate.

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The linear equation that represents the point (-2,3) and 3 more points with a slope of -1/2 is y = -1/2x + 2

The given parameters are

Slope, m = -1/2

Point, (x1, y1) = (-2, 3)

The linear equation is calculated as:

y = m(x - x1) + y1

Substitute the known values in the above equation

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

Expand

y = -1/2x - 1 + 3

Evaluate the sum

y = -1/2x + 2

This means that the linear equation that represents the point (-2,3) and 3 more points with a slope of -1/2 is y = -1/2x + 2

See attachment for the graph of the point and the three other points

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Luciana claims that if you add numbers with the same sign, the sum is always greater than each of the addends. He is incorrect

From the information, Luciana claims that if you add numbers with the same sign, the sum is always greater than each of the addends.

Let's add (-3) + (-4)

It should be noted that the addition is equal to -7.

It should be noted that this doesn't corelate with what Luciana said.

Therefore, she is incorrect. It's only correct for positive numbers.

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The solution of the given expression  [tex]5.5 - 8.1[/tex] in decimal form is [tex]-2.6[/tex] which is a negative integer in decimal form.

The numbers of the number line are called integers. They include positive numbers, zero, and negative numbers.

Zero is neither considered a negative nor a positive number.

[tex]5.5\\[/tex] is a positive number and a smaller number when compared from [tex]8.1[/tex].

When a smaller number is subtracted from a larger number it results in subtraction with a negative sign.

[tex]5.5 - 8.1 \\= -2.6[/tex]

The subtraction of the given expression [tex]5.5 - 8.1[/tex] in decimal form is [tex]-2.6[/tex].

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Answer:

0.008 3repeating

Step-by-step explanation:

A square field has an area of 22,500 square feet, then the diagonal distance across the field in nearest foot is equal to 212 foot (approximately).

As given in the question,

Area of the square field = 22,500square feet

Let 'a' be the side and 'd' be the diagonal length of the square

a² =22,500

⇒a =150 foot

Using Pythagoras theorem

d² =a² +a²

⇒d² = 2(150)²

⇒d² =45000

⇒d =212.13

    ≈ 212 nearest foot (approximately)

Therefore, the diagonal distance across the field in nearest foot is 212 foot (approximately) with  area of 22,500 square feet as given.

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mous this mobail phonffyuuyy

Answer: m<ABC = 45 degrees, m<DBC = 36 degrees

Step-by-step explanation:

set both equations equal to 81 because they add up to form one angle:

5x + 6 + 9x - 9 = 81

Combine like terms

14x - 3 = 81

Add three to both sides

14x = 84

Divide by 14 to find x

x = 6

To find the angles:

Measurement of angle ABC:

9(6) - 9 = 45 degrees

Take the original angle of 81 and subtract the angle you just found to find the remaining angle:

81 - 45 = 36

Therefore, the angle of DBC is 36 degrees

The value of the given expression when simplified is equal to 318.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The given expression can be simplified using the PEMDAS as shown below.

-7 + 5 - 40 × -8

As per the PEMDAS multiplication should be solved first,

= -7 + 5 + 320

Further, solve addition,

= -7 + 5 + 320

= -7 +325

= 318

Hence, the value of the given expression when simplified is equal to 318.

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The two lines have only one intersection

[tex]\therefore[/tex] There are only one solution to the system of equation.

Answer:

900,000 mph

Step-by-step explanation:

I am assuming the m in he problems is standing for miles.

250m/sec x 60 sec/min x 60min/hour  The sec cross out and the minutes cross out and you are left with miles be hour.

The value of x will be 2. So, Option B is correct for the equation [tex]3^{2x} = 9^{3x - 4}[/tex]

In the given question, the equation is [tex]3^{2x} = 9^{3x + 4}[/tex], we have to find out the value of x. First, we need to re-arrange the equation in order to apply the property of exponents. So,

           => [tex]3^{2x} = 9^{3x -4}[/tex]  => [tex]3^{2x} = 3^{2(3x - 4)}[/tex]

We know according to the property of exponents if [tex]x^{m} = x^{n}[/tex], then m = n.

Similarly, in this equation the base of both RHS and LHS are the same, We get

           => 2x = 2(3x - 4)

           => 2x = 6x - 8   =>  4x = 8

           =>  x = 2

We get value of x = 2.

Hence the value of x for this equation will be 2 and option B is correct.

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Answer:

514 grams is equal to 0.514 kilograms

For x = -2,-6, and -10 the value of the polynomial will be satisfied.

Roots of an equation are the solution of that equation since an equation consists of hidden values of the variable to determine them by different processes and then the resultant is called roots.

Given the polynomial,

x³ + 18x² + 92x + 120 = 0

By hit trial method let's put x = -2

-8 + 72 - 184 + 120 = 0

-192 + 192 = 0

0 = 0

Now,divide x³ + 18x² + 92x + 120 = 0 by x + 2

(x + 2)(x²+ 16x + 60) = 0

(x + 2)(x + 6)(x + 10) = 0

x = -2,-6 and -10.

Hence "For x = -2,-6, and -10 the value of the polynomial will be satisfied".

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The number of minutes per day that Dominie practise the piano is 51 minutes per day.

The first step is to convert two weeks to days.

1 week = 7 days

2 weeks : 7 x 2 = 14 days

The second step is to divide the total minutes Dominie practices by the total number of days. Division is the mathematical operation that is used in grouping a number into equal parts using another number. The result of a division is known as the quotient. The sign used to represent division is ÷.

Number of minutes they practice per day : total practice / number of days in two weeks

714 / 14 = 51 minutes per day

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Answer:

.033

Step-by-step explanation:

When there is a proportional relationship the constant of proportionality is y/x and in this case that would be  10/300 and that would be .033 rounded to three decimal places.

Answer:

[tex]m = - \frac{1}{5} n + 2[/tex]

Answer:

x = 5j-k

Step-by-step explanation:

(x-j) (5x+k) = 0

(x-j) * (5x+k) = 0

x - 5j + k = 0

x + k = 5j

x = 5j - k

Answer:

its 1

Step-by-step explanation:

i just know

Answer:

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

Prime factors of 168 are:

In order to make 168n a square number we need to use each prime factor even number of times.

Add 2, 3 and 7 to the prime factors (as a minimum) to get:

Triangle ABC is an isosceles right triangle.

Because of A(-8,7) B(-4,2) C(1,6)

So AB=√[-8-(-4)]²+(7-2)²

=√41

BC=√(-4-1)²+(2-6)²

=√42

AC=√(-8-1)²+(7-6)²

=√82

AB=BC

AB²+BC²=AC²

So triangle ABC is an isosceles right triangle.

What is isosceles right triangle?

An Isosceles Right Triangle is a right triangle that consists of two equal length legs. Since the two legs of the right triangle are equal in length, the corresponding angles would also be congruent. Thus, in an isosceles right triangle, two legs and the two acute angles are congruent.

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The true statement is that (a) in approximately 50% of the months he sold less than 9 cars.

The given parameter is the box and whisker plot

As mentioned above, the box and whisker plot is a great tool to show the five-number summary.

The five-number summaries are:

On the box and whisker plot, we have the following five-number summaries:

The difference between the quartlles is

Difference = Upper quartile - Lower quartile

So, we have

Difference = 12 - 4

Evaluate

Difference = 8

This means that in approximately 50% of the months he sold 8 cars

8 is less than 9

This means that in approximately 50% of the months he sold less than 9 cars.

Hence, the true statement is that (a) in approximately 50% of the months he sold less than 9 cars.

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