Solve for x: 3-(2x-5) is less than -4(x+2)

the solution of the equation x²+27 = 0 is 3√3 i

What are real and imaginary roots ?

A real root to an equation is a real number. A complex root to an equation is an imaginary root represented as complex numbers.

In other words real roots can be represented in a number line where as imaginary roots can not.

In order to determine the simplification, we have to know the rule of the imaginary numbers.

The imaginary numbers are the same than real numbers, but they add just one term more, which is :

√-1 = i

So, to implicate this term, we have to use the rules of the roots:

given equation is :

x²+27 = 0

solving for x by Subtracting 27 from both sides

x²+27 -27 = -27

x² = -27

To remove square root , take square root on both sides

√x² = √-27

x = √-27

The value of √-1 is 'i' therefore,

x = i√27

x =3√3 i

Therefore, The solution of the equation x²+27 = 0 is 3√3 i

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Answer:

C. [tex]2\times 10^7[/tex] is 5 times larger than [tex]4\times 10^6[/tex]

Step-by-step explanation:

We want to compare [tex]4\times 10^6[/tex] and [tex]2\times 10^7[/tex].

In order to determine how many times

[tex]2\times 10^7[/tex]

is larger than

[tex]4\times 10^6[/tex],

we need to divide [tex]2\times 10^7[/tex] by  [tex]4\times 10^6[/tex] to obtain;

[tex]\frac{2\times 10^7}{4\times 10^6} =\frac{10}{2} =5[/tex]

Therefore we can see that;

[tex]2\times 10^7[/tex] is 5 times larger than [tex]4\times 10^6[/tex]

The correct answer is C.

The midpoint of the given line segment with endpoints (-2, 3) and (10, 3) is (4, 3). Thus, the option B is correct.

To determine the midpoint of a line segment, we can use the midpoint formula.

The midpoint formula states that the midpoint coordinates of a line segment with endpoints [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are given by:

[tex]Midpoint = (\dfrac{(x_1 + x_2)} {2}, \dfrac{(y_1 + y_2)} { 2})[/tex]

As per the question, the endpoints of the line segment are (-2, 3) and (10, 3).

Using the given midpoint formula:

Midpoint = ((-2 + 10) / 2, (3 + 3) / 2)

Midpoint = (8 / 2, 6 / 2)

Midpoint = (4, 3)

Therefore, the midpoint of the line segment with endpoints (-2, 3) and (10, 3) is (4, 3).

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Since each shelf holds 9 books and the teacher has 55, you'll need to divide 55 ÷ 9 to find the number of shelves used. After dividing, you'll get 6.11. Round up the 6.11 to 7 since the teacher is using 6 shelves and a part of the seventh one.

The teacher fills 7 shelves with 55 books.

To find out how many shelves can be filled with 55 books where each shelf holds 9 books, simply divide 55 by 9. This gives approximately 6.11, but since you can't have a part of a shelf, we round down to 6.

The subject of this question is Mathematics, specifically division. To determine the number of shelves filled by the teacher, we should divide the total number of books by the number of books every shelf can hold. As given, the teacher has 55 books and each shelf holds 9 books.

So, you carry out the division: 55 ÷ 9. The answer is 6.111... Since we can't have a fraction of a shelf, we round this down to the nearest whole number. So, the teacher fills 6 shelves fully with books. Remember, this means there are some books that don't fill up a seventh shelf completely.

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I think its B. $93!!!!!!!!

b hope this helps!!!!!!!!!!!!!!

definition of parallelogram

∠2

∠3

transitive property of congruence

The answer of this expression is - 4 1/6

Answer:

30 workers are required.

Step-by-step explanation:

If the site measured 30 acres and was completed in 10 days, then it can be said that on average [tex]\frac{30}{10} = 3\frac{acres}{day}[/tex] were made.

Then, 24 workers completed 3 acres / day.

Then, [tex]\frac{24.workers}{\frac{3acres}{day}} = \frac{8..Workers * days}{acre}[/tex]

8 workers can complete 1 acre per day

Now to know how many workers are needed to complete 45 acres in 12 days, we multiply:

[tex]8\frac{Workers * days}{acre}*\frac{45}{12} \frac{acres}{days} = 30.workers[/tex].

Finally, 30 workers are required.

To solve this problem it was assumed that everyone worked at the same pace, which may not be true, the fact that some work at a slower or faster pace than another could alter the result, causing them to finish less or more acres by day.

This is actually quite easy.  

Britt=4c+12 because 4 boxes and 12 extra

Jim=3c+5 because 3 boxes and 5 extra

Final answer:

The total number of CDs that Britt and Jim have is represented by the expression 7c + 17, where c is the number of CDs in each full box.

Explanation:

The total number of CDs that Britt and Jim have can be expressed using the variable c, which represents the number of CDs in each full box. Britt has 4 full boxes and 12 extra CDs, so her total is given by the expression 4c + 12. Jim has 3 full boxes plus 5 extra CDs, so his total is 3c + 5. To find the combined total number of CDs for both Britt and Jim, we add their individual totals:

Total CDs = Britt's CDs + Jim's CDs

Total CDs = (4c + 12) + (3c + 5)

By combining like terms, we get:

Total CDs = 7c + 17

This expression represents the total number of CDs that Britt and Jim have together in terms of c, the number of CDs per box.

Hi,

Solution:

Find Common Denominators,

2/5 = 8/20

2 7/20

Turn into improper fractions,

2 7/10 = 47/20

Divide,

47/20 ÷ 8/20 = 5.875/1 = 5 7/8

Answer,

5 7/8

Answer: 40 cups

If you have 2.5 gallons and need to convert it to cups, you first need to know how these two units of liquid volume compare to each other in size.

There are 16 customary cups in one gallon. To find how many cups are in 2.5 gallons, you'd multiply 2.5 (the number of gallons you have) by 16 (the number of cups in one gallon).

2.5 x 16 equals 40. This tells you that 2.5 gallons is equivalent to 40 cups

Question: If one gallon is the same amount as 16 cups, how many cups equal 2.5 gallons? (Only input whole numbers.)

Explantion: 16(number of cups per gallon)×2.5(amount of gallons)

The equation would be [tex]16*2.5[/tex] and that equals 40.

Answer: 40 cups

Answer: Independent variable

Step-by-step explanation:

The variable usually on the x-axis, which is used to predict y-values, is called the Independent variable.

Discussion:

In most mathematical relations including linear programming problems; we usually have a combination of two variables namely;

The variable whose value determines the value of other variables is termed the independent variable and is usually plotted on the x-axis.

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The slope-intercept form:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have the points (-1, 1) and (2, 13). Substitute:

[tex]m=\dfrac{13-1}{2-(-1)}=\dfrac{12}{3}=4[/tex]

Therefore the equation of a line is

[tex]y=4x+b[/tex]

Put the coordinates of the point (2, 13) to the equation of a line:

[tex]13=4(2)+b[/tex]

[tex]13=8+b[/tex]     subtract 8 from both sides

[tex]5=b\to b=5[/tex]

12*7 = 84

84 Pumpkin Plants

12 links long because 5 + 7 = 12

Answer:

291 - 5y

Step-by-step explanation:

x- a measure of the fourth angle

The equation

[tex]x+60+(2y+8)+(3y+1)=360\qquad|\text{combine like terms}\\\\x+(2y+3y)+(60+8+1)=360\\\\x+5y+69=360\qquad|\text{subtract 5y and 69 from both sides}\\\\x=291-5y[/tex]

The answer would be -5 because:

-6-(-1)

Keep Change Flip

-6 + 1

Different signs Subtract..so the answer would be 5 but then you add the negative to it because -6 is greater than the positive 1

Solution

Here the first term = -2

5th term = -1/8

Now we have to find the common ratio (r)

Fifth term A5 = -1/8

-1/8 =[tex]a_{1} r^{4}[/tex]

Here [tex]a_{1} = -2[/tex]

Plug in [tex]a_{1}  = -2[/tex] in the fifth term and find the value of r.

-1/8 = -2[tex]r^{4}[/tex]

[tex]r^{4} = \frac{-1/8}{-2}[/tex]

[tex]r^{4} = \frac{1}{16}[/tex]

Taking 4th root, we get

r = [tex]\frac{1}{2}[/tex]

Now let's find the second term.

[tex]a_{2} =[/tex] first term *r = -2 *1/2 = -1

2nd term = -1

3rd term = second term * 1/2 = -1 * 1/2 = -1/2

4th term = 3rd term *r = -1/2 *1/2 = -1/4

Thank you :)

The 2nd term is  -1 , the 3rd term is [tex]\( -\frac{1}{2} \)[/tex], and the 4th term is [tex]\( -\frac{1}{4} \)[/tex].

To find the 2nd, 3rd, and 4th terms of the sequence, we need to determine the common ratio of the sequence since the given terms suggest it is a geometric sequence. A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.

Let's denote the first term of the sequence as [tex]\( a_1 \)[/tex] and the common ratio as r. The n-th term of a geometric sequence can be found using the formula:

[tex]\[ a_n = a_1 \cdot r^{(n-1)} \][/tex]

Given:

[tex]\[ a_1 = -2 \] \[ a_5 = -\frac{1}{8} \][/tex]

We can use the fifth term to find the common ratio r by plugging in the values into the formula for the n-th term:

[tex]\[ a_5 = a_1 \cdot r^{(5-1)} \] \[ -\frac{1}{8} = -2 \cdot r^4 \] \[ r^4 = \frac{-2}{-8} \] \[ r^4 = \frac{1}{4} \] \[ r = \pm\sqrt[4]{\frac{1}{4}} \] \[ r = \pm\frac{1}{2} \][/tex]

Since we are dealing with a sequence where the terms are decreasing in absolute value and changing sign (from negative to positive), we choose the positive value for r:

[tex]\[ r = \frac{1}{2} \][/tex]

Now we can find the 2nd, 3rd, and 4th terms:

[tex]\[ a_2 = a_1 \cdot r^{(2-1)} = -2 \cdot \left(\frac{1}{2}\right)^1 = -1 \] \[ a_3 = a_1 \cdot r^{(3-1)} = -2 \cdot \left(\frac{1}{2}\right)^2 = -\frac{1}{2} \] \[ a_4 = a_1 \cdot r^{(4-1)} = -2 \cdot \left(\frac{1}{2}\right)^3 = -\frac{1}{4} \][/tex]

The final answer is:

[tex]\[ a_2 = -1, \quad a_3 = -\frac{1}{2}, \quad a_4 = -\frac{1}{4} \][/tex]

Assuming that the inequality you were going for was a ≤, set both polynomials less than or equal to 0.

x - 3 ≤ 0

x + 5 ≤ 0

For the first equation add 3 to both sides of the inequality. For the second, subtract 5 from both sides.

x ≤ 3

x ≤ - 5

These would be your solutions I guess, however, if you want to expand upon that, your actual answer is (- ∞, - 5] because if you were to plot these two inequalities on a number line, that is where the overlap would occur.

ANSWER TO QUESTION 1

Check attachment for long division.

From our long division we can write the following;

[tex]\frac{8x^4-6x^3+7x^2-11x+10}{2x-1} =4x^3-x^2+3x-4+\frac{6}{2x-1}[/tex]

Since the polynomial

[tex]8x^4-6x^3+7x^2-11x+10[/tex] leaves a non zero  remainder of [tex]6[/tex] when divided by [tex]2x-1[/tex], we conclude that [tex]2x-1[/tex] not a factor of the dividend,

ANSWER TO QUESTION 2

We want to factor

[tex]f(x)=x^4+x^3-8x^2+6x+36[/tex]

The possible rational roots are;

[tex]\pm1, \pm 2,\pm 3, \pm 4,\pm 6,\pm 9, \pm18, \pm 36[/tex]

We found

[tex]f(-2)=(-2)^4+(-2)^3-8(-2)^2+6(-2)+36[/tex]

[tex]f(-2)=16+-8-32+-12+36[/tex]

[tex]f(-2)=-36+36[/tex]

[tex]f(-2)=0[/tex]

and

[tex]f(-3)=(-3)^4+(-3)^3-8(-3)^2+6(-3)+36[/tex]

[tex]f(-3)=81-27-72-18+36[/tex]

[tex]f(-3)=-36+36[/tex]

[tex]f(-3)=0[/tex].

This means that [tex](x+2)[/tex] and [tex](x+3)[/tex] are factors of the polynomial.

This also means that

[tex](x+2)(x+3)=x^2+5x+6[/tex] is also a factor of the polynomial

So we apply long division to obtain the remaining factors as shown in the attachment.

[tex]\Rightarrow f(x)=x^4+x^3-8x^2+6x+36=(x+2)(x+3)(x^2-4x+6)[/tex]

We factor further to obtain;

[tex]\Rightarrow f(x)=x^4+x^3-8x^2+6x+36=(x+2)(x+3)(x-(2-\sqrt{2}i))(x-(2+\sqrt{2}i))[/tex]

Let f = first lucky number, and let s = second lucky number.

Translate the sentences into two equations in two unknowns, and solve the system of equations to find the two unknowns.

"when I multiply my first number by 3 and my second lucky number by 2, the addition of the resulting produces a sum of 93."

3f + 2s = 93

"when I add twice my first lucky number to my second lucky number the sum is 53."

2f + s = 53

Now you have a system of equations.

3f + 2s = 93

2f + s = 53

Let's use the substitution method. Solve the second equation  for s.

s = 53 - 2f

Now we substitute 53 - 2f for s in the first equation.

3f + 2s = 93

3f + 2(53 - 2f) = 93

Distribute the 2.

3f + 106 - 4f = 93

Combine like terms on the left side.

-f + 106 = 93

Subtract 106 from both sides.

-f = -13

Divide both sides by -1.

f = 13

Now substitute f = 13 in the second original equation.

2f + s = 53

2(13) + s = 53

26 + s = 53

Subtract 26 from both sides.

f = 27

Answer: The first lucky number is 13, and the second lucky number is 27.

the answer is -4

hope it helpsss

5^-4 is 5 to power of negative 4

Answer:

[tex]\frac{M}{1-0.8}[/tex] and [tex]5M[/tex]

Step-by-step explanation:

1. Let's imagine that you have 100 e-mails unread. When you read 80% of these e-mails you have the following amount [tex]M[/tex] unread:

[tex]100-(0.8)(100)=20[/tex] e-mails

2. If you substitute 20 e-mails into the equations shown above, you will obtain the original amount:

[tex]\frac{20}{1-0.8}=100\\5(20)=100[/tex]

answer :  option A  and B

After reading 80% of her emails in her inbox, Danette still has M unread emails

M unread emails

Let x be the number of emails before reading

80% of emails are left in the box. So, 0.08x  emails are left in the box

Now we make an equation

number of emails - 80% of unread emails= number of unread mails

x  - 0.08x = M

Now we factor out x

x ( 1- 0.08) = M

So [tex]x = \frac{M}{1-0.8}[/tex]

or [tex]x = \frac{M}{0.2}= 5M[/tex]

(1,1)

(5, 3)

(6, 4)

(1, 2)

1

For this, all you need to do is plug in the x and y values.

When adding, add the two x values together to get your final x value, and add your y values to get your final y value.

a + b = (3 + (-2), 2 + (-1))

a + b = (1, 1)

When subtracting, subtract the two x values from each other to get your final x value, and subtract your y values to get your final y value.

a - b = (3 - (-2), 2 - (-1))

a - b = (5, 3)

When multiplying set a by 2, all you need to do is distribute.

2a = (3x2, 2x2)

2a = (6, 4)

For this, all you need to do is multiply the x and y values in set a by 2, and multiply the x and y values in set b by 4. Then add the product of the x value in set a to the product of the x value in set b.

2a + 4b = (2(3) + 4(-2), 2(2)+ 4(-1))

2a + 4b = (6 + (-8), 4 + (-4))

2a + 4b = (-2, 0)

For the last one you just need to find the absolute value.

|a| = (3, 2)

If you have any further questions feel free to ask. Hope this helps.

x = 25

The 3 angles are marked as equal , indicated by the arc at each angle.

Thus Δ ABC is equilateral with all 3 sides equal

Equate any 2 sides to solve for x

4x - 30 = 3x - 5 ( subtract 3x from both sides )

x - 30 = - 5 ( add 30 to both sides )

x = 25

As a check :

4x - 30 = ( 4 × 25 ) - 30 = 100 - 30 = 70

3x - 5 = ( 3 × 25 ) - 5 = 75 - 5 = 70

2x + 20 = ( 2 × 25 ) + 20 = 50 + 20 = 70

All 3 sides are equal for x = 25

Answer: x=25

Step-by-step explanation:

I took the k12 test.

4 yards, 2 feet, and 1 inch

Answer: The perimeter is 17.52

Step-by-step explanation:

1. You can plot the points, as you can see in the graph attached.

2. As you can see in the graph, the points are:

[tex]A(-2,-2)\\B(-2,3)\\C(2,4)\\D(3,1)\\E(0,-2)[/tex]

And the lenghts AB and EA are:

[tex]AB=5[/tex]

[tex]EA=2[/tex]

3. To find the other lenghts, you can apply the formula for calculate the distance between two points:

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

4. Thefore, you have:

[tex]BC=\sqrt{(2-(-2))^{2}+(4-3)^{2}}=4.12\\CD=\sqrt{(2-3)^{2}+(4-1)^{2}}=3.16\\DE=\sqrt{(3-0)^{2}+(1-(-2))^{2}}=4.24[/tex]

5. The perimeter is:

[tex]P=AB+CD+DE+EA\\P=5+4.12+3.16+4.24+2\\P=17.52[/tex]

The perimeter of the polygon is 18.64 units.

To find the perimeter of a polygon, we need to sum the lengths of all its sides. Let's calculate the distance between each consecutive pair of vertices and add them up.

The distance between (-2, -2) and (-2, 3) is 5 units.

The distance between (-2, 3) and (2, 4) is 4.24 units (rounded to the nearest tenth).

The distance between (2, 4) and (3, 1) is 3.16 units (rounded to the nearest tenth).

The distance between (3, 1) and (0, -2) is 4.24 units (rounded to the nearest tenth).

The distance between (0, -2) and (-2, -2) is 2 units.

Adding up these distances, the perimeter of the polygon is 5 + 4.24 + 3.16 + 4.24 + 2 = 18.64 units (rounded to the nearest tenth).

On the 40th and the 80th you will receive both a free beverage and a free appetizer. You can find this by simply finding the multiples of both number up to 100 (or a little more than 100) to find out on which dates you'd get bothe an appetizer and beverage for free. Here are the multiples of both, to prove this answer.

Thus making 40 and 80 the answers. I hope this helps!

Answer:

NNN

Step-by-step explanation:

Fifteen of thirty-five is 5.25

it would be 5.25 because how to do a percent of something is to change it to a decimal. 15% = .15 so .15 x 35 = 5.25 :) hope this helps