Solve 5(2x-3a)+2b=3ax-4, for x

The result of the synthetic division is the final row. In this case, the result is -3, 5, -15, 18.

A polynomial is an expression consisting of variable and coefficient and are used to model real world situation it is an equation of degree greater than one where the exponents of the variables can be any non-negative integer for example the polynomial equation x 2 + 3x + 2 represent a parable of windcraft polynomial are used in name variety of field such as mathematics and physics.

The process of synthetic division is used to divide polynomials of the form ax^n + bx^n-1 + ... + c, where a is the coefficient of the highest power of the variable x.

To divide -3 into the polynomial 1 8 9 -18 0, the following steps should be taken:

Step 1: Line up the divisor, -3, to the left of the polynomial, as shown below:

-3 | 1 8 9 -18 0

Step 2: Bring down the first coefficient in the polynomial, which is 1, and place it directly below the -3.

-3 | 1 8 9 -18 0
  -3

Step 3: Multiply the -3 by the first coefficient and place the result in the next row, directly below the 8.

-3 | 1 8 9 -18 0
  -3
 -3

Step 4: Add the result to the 8, and place the new result in the next row.

-3 | 1 8 9 -18 0
  -3
 -3
  5

Step 5: Repeat steps 3 and 4 for each coefficient in the polynomial.

-3 | 1 8 9 -18 0
  -3
 -3
  5
 -15
-15
 18

Step 6: The result of the synthetic division is the final row. In this case, the result is -3, 5, -15, 18.
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Complete questions as follows-
Divide Using Synthetic Division
-3|1 8 9 -18 0

✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅

Option C is correct, the set of vectors is linearly dependent because one of the vectors is the zero vector.

A matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns.

To determine if the set of vectors is linearly independent, we need to check if any of the vectors can be expressed as a linear combination of the others.

Let's consider the first vector [8 -6 4].

If we try to express this vector as a linear combination of the other vectors, we get:

[8 -6 4] = a[12 -9 6] + b[0 0 0]

where a and b are constants.

We can immediately see that this equation has infinite solutions, because the third component of the second vector is zero, which means we can choose any value for b and still satisfy the equation.

Therefore, the set of vectors is linearly dependent.

Hence, Option C is correct, the set of vectors is linearly dependent because one of the vectors is the zero vector.

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Determine by inspection whether the vectors are linearly independent. Justify your answer.

[8  -6  4][12  -9  6]

A. The set of vectors is linearly independent because nothing times the first vector is equal to the second vector. ​(Type an integer or a simplified​ fraction.)

B. The set of vectors is linearly dependent because nothing times the first vector is equal to the third vector. ​(Type an integer or a simplified​ fraction.)

C. The set of vectors is linearly dependent because one of the vectors is the zero vector.

D. The set of vectors is linearly independent because none of the vectors are multiples of the other vectors.

Answer:

An acute angle

Step-by-step explanation:

An acute angle is smaller than an obtuse ad right angle.

hope this helps and hope it was right 'cause I really don't know what you meant. :)

Answer: 377.2 miles

Step-by-step explanation:

m x g. / 18.4 x 20.5

The estimate of 179% of 41 by rounding is about 73.19.

To find this estimate, first convert the percentage to a decimal by dividing it by 100: 179/100 = 1.79. Then, multiply this decimal by 41: 1.79 * 41 = 73.39.

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Answer:

No

Step-by-step explanation:

they are not equivalent

Answer:

169

Step-by-step explanation:

Answer:

18cm

Step-by-step explanation:

If B is the midpoint of CA, it is exactly halfway. Therefore the distance from C to B (9cm) is half the length of CA. 9x2=18

Answer: THE ANSWER IS 2,800

Step-by-step explanation: 7 TIMES 4 = 28 AND THE ZERO FROM 70 AND 40 TAKE THE ZEROS AND PUT TO 28 AND YOU GET 2,800 AND THE PRODUCT IS TWO ZEROS

a) She can make 400 milliliters of the fizzy drink.

b) The change does not affect the greatest amount of drink.

We know that the fizzy drink is 7 parts apple juice and 3 parts lemonade. And Kerry thinks that she has 280ml of apple juice and 180 ml lemonade.

If we divide the total amount of apple juice in 7 parts, then each part has:

280ml/7 = 40ml

Then we need 3 parts of 40ml of the lemonade, this is:

3*40ml = 120ml

Then the total amounf of drink fizz that she can make is:

280ml + 120ml = 400ml.

b) Now she has  160 ml of lemonade, but she needs 120 ml of it, so this change does not affect the greatest amount of fizzy drink she can make.

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Answer:

(a) The average rate of change from 0 to 2 is 6

(b) The average rate of change from 3 to 5 is 24

(c) The average rate of change from -3 to 0 is -9

Step-by-step explanation:

The formula for the average rate of change (AROC) is given by:

\(AROC=\frac{f(b)-f(a)}{b-a}\)

(a):

Finding the AROC from 0 to 2

To find the average rate of change from 0 to 2, we use f(2) and f(0), while we plug in 2 for b and 0 for a:

\(\frac{f(2)-f(0)}{(2-0)}\\ \\\frac{((3(2)^2+4)-(3(0)^2+4))}{(2-0)} \\\\\frac{(16-4)}{(2)}\\ \\\frac{12}{2}\\ \\6\)

Thus, the average rate of change from 0 to 2 is 6.

(b):

Finding the AROC from 3 to 5:

To find the average rate of change from 3 to 5, we use f(5) and f(3), while we plug in 5 for b and 3 for a:

\(\frac{f(5)-f(3)}{(5-3)}\\ \\\frac{((3(5)^2+4)-(3(3)^2+4))}{(2-0)} \\\\\frac{(79-31)}{(2)}\\ \\\frac{48}{2}\\ \\24\)

Thus, the average rate of change from 5 to 3 is 24.

(c):

To find the average rate of change from -3 to 0, we use f(0) and f(-3), while we plug in 0 for b and -3 for a:

\(\frac{f(0)-f(-3)}{(0-(-3))}\\ \\\frac{((3(0)^2+4)-(3(-3)^2+4))}{(0+3)} \\\\\frac{(4-31)}{(3)}\\ \\\frac{-27}{3}\\ \\-9\)

Thus, the average rate of change from -3 to 0 is -9.

Answer:

x=58

Step-by-step explanation:

ok this is a 5 sided polygon

5 sided polygon has 540 degrees

540-90-120-108-100= the unkown angle

122

but look at the line exterior plus interior = 180 degrees

180=122+x

subtract 122 from both sides

x=58

Answer:

20 words

Step-by-step explanation:

Answer:

-439

Step-by-step explanation:

Think of the question as s(f(-7))

First replace x with -7 in the equation f(x)= 3x

s(-7) = 3*(-7)

s(-7) = -21

now it is s(-21)

we substitute -21 into the s(x) equation to get \(2-(-21)^2\)

That gives you 2-441 = -439

There are X automobiles, with a mean of 12.5 cars. The standard deviation for X is also SD = 12.0.

First, a data set's mean and standard deviation convey distinct information. The average (center) of a data collection is provided by mean (it is a measure of central tendency). You may learn about the range (dispersion) of data around the mean by looking at the standard deviation. We may investigate a data set's characteristics and characterize it using both the mean and standard deviation. To provide confidence intervals for data that has a normal distribution, they are frequently combined. If two or more data sets need to be compared:

The mean reveals whether data set is, on average, greater or lower (or better or worse). We can determine whether data set has a wider dispersion using the standard deviation (higher standard deviation means data is more spread out from the mean). Second, there are variations in how each metric is calculated. In particular, we utilize squaring to get the standard deviation but not the mean. We completely avoid using squaring when determining the mean of a data collection. Simply multiplying the total number of data points in the set by the sum of all the values in the data set yields the answer.

The mean is calculated as follows:

Mean = (all data values added together) / (number of data values)

However, when calculating standard deviation, we do employ squaring. We take the square of the deviation between each data point and the mean in particular.

The standard deviation equation is as follows:

Finally, when we add the identical value to each data point in the data set, the mean and standard deviation "respond" differently. If we multiply every value in a data collection by the constant "K":

No of the size of the data collection, the mean rises by precisely K.

No matter how many observations are in the data collection, the standard deviation does not vary. The identical value is then added.

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Three reasons why the other method is not better is because to use drawing program would mean you would need some sort of technology and electricity to use it and some places, like third world countries, do not have access to that, so most probably you would have to resort to paper. Also, drawing programs are based off the skills needed to create geometric figures with a straightedge and compass. And lastly, what if we had no more technology anymore? Then how would we use a drawing program? Drawing programs are only reliable when electricity is located.

SO THE ANSWER IS A hope it help :)

I believe that there is a need for students to understand and be able to construct geometric figures using a compass and straightedge.

The compass and straightedge can be used anywhere. The compass and straight edge have been around for lots of years. They are a valuable tool for students in math and in real world applications. The compass and straightedge are portable and handy to use any given time. That is why there is a need for students to understand and be able to construct geometric figures using a compass and straight edge.

The compass and straight edge have been used to accurately create geometric figures for thousands of years. This shows that they are accurate and useful to us. Using technology is less reliable for many reasons. Technology can break, or glitch and shut down, making you lose all your work. You cannot draw on physical objects with an iPad like you could with a pencil or pen. Having a physical copy of things makes things easier to keep track of. Having a blueprint would be better than having a drawing on your phone. You can get another blueprint, but if your phone breaks and that drawing isn't saved, it's gone.

These are only a few reasons why I believe that there is a need for students to understand and be able to construct geometric figures using a compass and straightedge.

Answer:

LxWxH

Step-by-step explanation:

The expression simplified can be written as:

16m +  8

Here we want to simplify the following expression:

(8m + 4) + (8m + 4)

To simplify, we start by removing the parenthesis:

8m + 4 + 8m + 4

Now we can change the order of the terms so we get:

8m + 8m + 4 + 4

Now we can group the like terms to get:

(8m + 8m) + (4 + 4)

And simplify this to get:

16m +  8

That is the simplified expression.

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Answer:

y=2x-6

Step-by-step explanation:

y+4=-2(x-1)

Since the slope intercept form is in the form of:

y=mx+c

Making above equation in this form.

y+4=-2(x-1)

opening bracket

y+4=2x-2

subtracting both side by 4.

y+4-4=2x-2-4

y=2x-6

This equation is the slope intercept form.

Answer:

2 1/5 acres

Step-by-step explanation:

I'm guessing you want to find the area of an equally sized section. If so, you can divide the total of 8 4/5 by 4.

Convert to an improper fraction. 8*5 = 40+4= 44/5

Dividing is the same as multiplying by the reciprocal.

44/5 * 1/4 = 44/20

or 2 4/20 -> 2 1/5 acres

Answer:

(a) 0.14%

(b) 2.28%

(c) 48%

(d) 68%

(e) 34%

(f) 50%

Step-by-step explanation:

Let X be a random variable representing the prices paid for a particular model of HD television.

It is provided that X follows a normal distribution with mean, μ = $1600 and standard deviation, σ = $100.

(a)

Compute the probability of buyers who paid more than $1900 as follows:

\(P(X>1900)=P(\frac{X-\mu}{\sigma}>\frac{1900-1600}{100})\)

                   \(=P(Z>3)\\=1-P(Z<3)\\=1-0.99865\\=0.00135\\\approx 0.0014\)

*Use a z-table.

Thus, the approximate percentage of buyers who paid more than $1900 is 0.14%.

(b)

Compute the probability of buyers who paid less than $1400 as follows:

\(P(X<1400)=P(\frac{X-\mu}{\sigma}<\frac{1400-1600}{100})\)

                   \(=P(Z<-2)\\=1-P(Z<2)\\=1-0.97725\\=0.02275\\\approx 0.0228\)

*Use a z-table.

Thus, the approximate percentage of buyers who paid less than $1400 is 2.28%.

(c)

Compute the probability of buyers who paid between $1400 and $1600 as follows:

\(P(1400<X<1600)=P(\frac{1400-1600}{100}<\frac{X-\mu}{\sigma}<\frac{1600-1600}{100})\)

                              \(=P(-2<Z<0)\\=P(Z<0)-P(Z<-2)\\=0.50-0.0228\\=0.4772\\\approx 0.48\)

*Use a z-table.

Thus, the approximate percentage of buyers who paid between $1400 and $1600 is 48%.

(d)

Compute the probability of buyers who paid between $1500 and $1700 as follows:

\(P(1500<X<1700)=P(\frac{1500-1600}{100}<\frac{X-\mu}{\sigma}<\frac{1700-1600}{100})\)

                              \(=P(-1<Z<1)\\=P(Z<1)-P(Z<-1)\\=0.84134-0.15866\\=0.68268\\\approx 0.68\)

*Use a z-table.

Thus, the approximate percentage of buyers who paid between $1500 and $1700 is 68%.

(e)

Compute the probability of buyers who paid between $1600 and $1700 as follows:

\(P(1600<X<1700)=P(\frac{1600-1600}{100}<\frac{X-\mu}{\sigma}<\frac{1700-1600}{100})\)

                              \(=P(0<Z<1)\\=P(Z<1)-P(Z<0)\\=0.84134-0.50\\=0.34134\\\approx 0.34\)

*Use a z-table.

Thus, the approximate percentage of buyers who paid between $1600 and $1700 is 34%.

(f)

Compute the probability of buyers who paid between $1600 and $1900 as follows:

\(P(1600<X<1900)=P(\frac{1600-1600}{100}<\frac{X-\mu}{\sigma}<\frac{1900-1600}{100})\)

                              \(=P(0<Z<3)\\=P(Z<3)-P(Z<0)\\=0.99865-0.50\\=0.49865\\\approx 0.50\)

*Use a z-table.

Thus, the approximate percentage of buyers who paid between $1600 and $1900 is 50%.

Answer:

Step-by-step explanation:

Answer:

836.2

Step-by-step explanation:

Answer:

836.2

Step-by-step explanation:

order of operations

(1.2x456)-10+251+98-50

(547.2-10)+251+98-50

(537.2+251)+98-50

(788.2+98)-50

(886.2-50)

836.2

The ratio of girls to boys in the class is 3:7.

To calculate the ratio of girls to boys in the class, we need to determine the number of girls in the class.

Given that there are 50 students in total and 35 of them are boys, we can find the number of girls by subtracting the number of boys from the total number of students:

Number of girls = Total number of students - Number of boys

Number of girls = 50 - 35

Number of girls = 15

Now that we know there are 15 girls in the class and 35 boys, we can calculate the ratio of girls to boys.

Ratio of girls to boys = Number of girls / Number of boys

Ratio of girls to boys = 15 / 35

To simplify the ratio, we can divide both the numerator and denominator by their greatest common divisor, which in this case is 5:

Ratio of girls to boys = (15 ÷ 5) / (35 ÷ 5)

Ratio of girls to boys = 3 / 7

This means that for every 3 girls, there are 7 boys in the class. The ratio provides a relative comparison of the number of girls to the number of boys, helping to understand the gender distribution within the class.

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Answer:

he should have subtracted 17 from both sides of the equation

Step-by-step explanation:

x+ 17 = 22

subtract 17 from both sides

X + 17 = 22

-17 -17

x = 5

Answer:

the probability that they are assigned adjacent cubicles is  1 ÷ 4

Step-by-step explanation:

Given that

There is 8 new graduates are hired

2 of the graduates are bill and cathy

And, each one is assigned on random basis

We need to find out the probability

So,

= (2) (7!) ÷ (8!)

= (2) ÷ (8)

= 1 ÷ 4

Hence, the probability that they are assigned adjacent cubicles is  1 ÷ 4

The same would be relevant

Answer:

just a

Step-by-step explanation:

because if you do anything times by zero, it is zero.

Answer:

A^6

Step-by-step explanation:

This is the answer bc A^0 would stay the same so you would adding the exponents when you multiply therefore it's A^6

It would take approximately 17.12 years for the amount to reach Birr 56,398.43 with a deposit of Birr 500 at the end of each six-month period, compounded semi-annually at an interest rate of 6%.

To solve this problem, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = Final amount

P = Principal amount (initial deposit)

r = Annual interest rate (in decimal form)

n = Number of compounding periods per year

t = Number of years

In this case, the principal amount is Birr 500, the annual interest rate is 6% (or 0.06), and the interest is compounded semi-annually, so there are 2 compounding periods per year.

We need to find the number of years (t) it takes for the amount to reach Birr 56,398.43.

Let's substitute the given values into the formula and solve for t:

56,398.43 = 500(1 + 0.06/2)^(2t)

Divide both sides by 500:

112.79686 = (1 + 0.03)^(2t)

Take the natural logarithm of both sides to eliminate the exponent:

ln(112.79686) = ln(1.03)^(2t)

Using the property of logarithms, we can bring down the exponent:

ln(112.79686) = 2t * ln(1.03)

Now, divide both sides by 2 * ln(1.03):

t = ln(112.79686) / (2 * ln(1.03))

Using a calculator, we find t ≈ 17.12.

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Answer:6 hours have passed by.

Step-by-step explanation:

0.8x= 84-79.2 where x is the number of hours.

O.8x = 4.8

Divide both sides by 0.8

X= 6

The value of n, considering the intersecting chords in the circle, is given as follows:

n = 6m.

A chord of a circle is a straight line segment that connects two points on the circle. Specifically, it is a line segment whose endpoints are on the circle. A chord is often denoted by drawing a line segment between the two endpoints, with the segment passing through the interior of the circle.

When two chords intersect each other, then the products of the measures of the segments of the chords are equal.

Considering the two intersecting chords for the circle in this problem, the value of n is obtained as follows:

5n = 15 x 2

5n = 30

n = 30/6

n = 6m.

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