4.4.45
For the following polynomial, one zero
is given. Find the remaining zeros.
The
(Sim
to se!
P(x) = x4 + 27x^2 - 324, 6i is a zero.

Answer: No Solutions exist

Step-by-step explanation:

We have the following system of equations

[tex]-10=-2y+x[/tex]

[tex]6y=3x+11[/tex]

Rewriting the second equation we have:

[tex]-11=-6y+3x[/tex]

Now we multiply the first equation by -3 and add it to the second equation

[tex]30=6y-3x[/tex]

[tex]-11=-6y+3x[/tex]

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

[tex]19=0[/tex]

Equality is not satisfied. Then the system has no solution

Answer:

d = 5 and a₁ = - 4

Step-by-step explanation:

The n th term of an arithmetic sequence is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

Given a₃ = 6, then

a₁ + 2d = 6 → (1)

The sum to n terms of an arithmetic sequence is

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]

Given [tex]S_{12}[/tex] = 282, then

6 [ 2a₁ + 11d ] = 282 ( divide both sides by 6 )

2a₁ + 11d = 47 → (2)

We can now solve (1) and (2) for d and a₁

Multiply (1) by - 2

- 2a₁ - 4d = - 12 → (3)

Add (2) and (3) term by term

7d = 35 ( divide both sides by 7 )

d = 5

Substitute d = 5 in (1) and solve for a₁

a₁ + 10 = 6 ( subtract 10 from both sides )

a₁ = - 4

Answer:

400cm^3

Step-by-step explanation:

Volume = length * height * width

Volume = 5 * 8 * 10 = 400 cm^3

Answer:

C

Step-by-step explanation:

The actual answer is 1.60943

When you round it to the hundredths place, the answer becomes 1.61

C

Answer:

The correct answer is C.  1.61.

Step-by-step explanation:

Answer: 359 ft

Step-by-step explanation:

Whenever you have a problem like this, you must first make an assumption that the building (in this case the lighthouse) is perpendicular to the ground (or sea).  This allows you to create a right triangle (see attached image).

The angle of depression is the angle from an imaginary perpendicular line passing through the top of the building.  Since that imaginary line is parallel to the ground (or sea), you can use alternate interior angles to place that angle in the triangle.

NOTE: BOTH angle of elevation and angle of depression are placed in the lower corner of the triangle. Don't let the names confuse you!

Now you can use trigonometry to solve ....

In the given problem, we have the side OPPOSITE of the given angle (24°) and need the side ADJACENT to the angle, so we will use tan to solve for x.

[tex]tan\ \theta=\dfrac{opposite}{adjacent}\\\\\\tan\ 24^o=\dfrac{160}{x}\\\\\\\rightarrow x=\dfrac{160}{tan\ 24^o}\\\\\\\rightarrow x=359.4\\\\\\\rightarrow x\approx 359[/tex]

Answer:

x - 1\x + 3

Step-by-step explanation:

Factoring quadratic expressions with a Leading Coefficient of 1 → In the first equation, you have to find two numbers that when differed to 5, they also multiply to 6, and those numbers are 1 and 6. Now, the tough part for you might be figuring out which term gets which sign. Well, if you look at your MIDST term [5], you would know that the negative symbol goes to 1 [-1] and the positive symbol goes to 6, so your numerator is [x - 1][x + 6]. Now, for the second equation, it is applied the same way, but in this case, we need two numbers that when added to 9, they also multiply to 18, and those numbers are 3 and 6, and automatically receive positive symbols, so your denominator is [x + 3][x + 6]. Now that we have our denominator and numerator, we now set it up: [x - 1][x + 6]\[x + 6][x + 3]. What do you see that is... MAGIC--AL? That is correct! The factors x - 6 neutralize each other and are left with x - 1\x + 3.

To be honest, if you had posted quadratic expressions with Leading Coefficients greater than 1, that would be a little bit more tough for you, meaning taking extra steps further, but if you post one in the future, it will be there to assist you because as always...,

I am joyous to assist anyone at any time.

Answer:

The 1st, 3rd, and 5th statements are correct.

Step-by-step explanation:

YZ has the same angle as XY, so the length is the same.

A^2+B^2=C^2 shows that XZ equals 9 sqrt 2 cm.

The hypotenuse is always the longest segment in the triangle.

Answer: D. $4.50.

Step-by-step explanation: You need to find the individual cost of 1 muffin. To do this, divide 1.35 by 3. 1.35/3=0.45. Each muffin costs $0.45. Multiply this by 10 to get $4.50 for 10 muffins.

Answer:

Step-by-step explanation:

x=1, y=-1

Answer:

see explanation

Step-by-step explanation:

Given the 2 equations

y = 2x² - 6x + 3 → (1)

y = x - 2 → (2)

Since both equations express y in terms of x we can equate the right sides, that is

2x² - 6x + 3 = x - 2 ( subtract x - 2 from both sides )

2x² - 7x + 5 = 0 ← in standard form

Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term

product = 2 × 5 = 10 and sum = - 7

The factors are - 2 and - 5

Use these factors to split the x- term

2x² - 2x - 5x + 5 = 0 ( factor the first/second and third/fourth terms )

2x(x - 1) - 5(x - 1) = 0 ← factor out (x - 1) from each term

(x - 1)(2x - 5) = 0

Equate each factor to zero and solve for x

x - 1 = 0 ⇒ x = 1

2x - 5 = 0 ⇒ 2x = 5 ⇒ x = [tex]\frac{5}{2}[/tex]

Substitute these values into (2) for corresponding values of y

x = 1 : y = 1 - 2 = - 1 ⇒ (1, - 1)

x = [tex]\frac{5}{2}[/tex] : y = [tex]\frac{5}{2}[/tex] - 2 = [tex]\frac{1}{2}[/tex]

Solutions are (1, - 1) and ( [tex]\frac{5}{2}[/tex], [tex]\frac{1}{2}[/tex] )

Answer:

The correct option is A. The given statement is true.

Step-by-step explanation:

Given statement: If A and B are two points in the plane , the perpendicular bisector of AB is the set of all points equidistant from A and B.

Let a line is perpendicular bisector of AB at point D and C be a random point of perpendicular bisector.

In triangle ACD and BCD,

[tex]AD=BD[/tex]                          (Definition of perpendicular bisector)

[tex]\angle ADC=\angle BDC[/tex]                          (Definition of perpendicular bisector)

[tex]DC=DC[/tex]                       (Reflexive property)

By SAS postulate of congruence,

[tex]\triangle ACD\cong \triangle BCD[/tex]

The corresponding parts of congruent triangles are congruent.

[tex]AC\cong BC[/tex]               (CPCTC)

[tex]AC=BC[/tex]

The distance between A to C and B to C are same. So, the set of all points on perpendicular bisector are equidistant from A and B.

The given statement is true. Therefore the correct option is A.

Final answer:

The statement is True because the perpendicular bisector is defined as the line that divides a line segment into two equal parts at its midpoint and is perpendicular to the segment, making all points on it equidistant from both endpoints of the segment.

Explanation:

The statement 'If A and B are two points in the plane, the perpendicular bisector of AB is the set of all points equidistant from A and B' is True. The definition of a perpendicular bisector is that it is a line which is perpendicular to another line segment (AB in this case) and divides it into two equal parts at its midpoint. Therefore, any point on the perpendicular bisector is equidistant from points A and B, which is a direct consequence of the definition.

This is further supported by Theorem 11, which states that if two equal lines in a plane are erected perpendicular to a given line, the line joining their extremities makes equal angles with them and is bisected at right angles by a third perpendicular erected midway between them, ensuring that any point on this third perpendicular (the perpendicular bisector) is equidistant from A and B.

Answer:

Starting at the origin, go 2.5 spaces to the right and then 5 spaces up.

Step-by-step explanation:

This is the RIGHT answer. It only goes 2.5 spaces on the X axis and the X axis is at 5

Answer:

Startingat the origin, go 2.5 spaces to the right and then go 5 spaces up.

Step-by-step explanation:

I got it right on IM

Remember it was asking for the wrong answer in the problem! This is the way that you SHOULDN'T answer the problem!

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}4x+y=4\\2x+6y=24&\text{multiply both sides by (-2)}\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}4x+y=4\\-4x-12y=-48\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad11y=-44\qquad\text{divide both sides by 11}\\.\qquad\qquad y=-4\\\\\text{put the value of y to the first equation:}\\\\4x+(-4)=4\\4x-4=4\qquad\text{add 4 to both sides}\\4x=8\qquad\text{divide both sides by 4}\\x=2[/tex]

Answer:

Multiply the second equation by -2 to get [tex]- 4x - 12y = -48[/tex]

Step-by-step explanation:

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

[tex]2x + 6y = 24[/tex]

To eliminate one variable the coefficient of a variable should be same with opposite sign.

LEts check with each option

Multiply the first equation by -4 to get  [tex]-16x - 4y = -16[/tex]

the coefficient of x or y are not same when we compare with second equation

Multiply the second equation by -4 to get [tex]- 8x - 24y = -96[/tex]

the coefficient of x or y are not same when we compare with first equation

Multiply the first equation by -2 to get [tex]-8x - 2y = -8[/tex]

the coefficient of x or y are not same when we compare with second equation

Multiply the second equation by -2 to get [tex]- 4x - 12y = -48[/tex]

The coefficient of x terms are same with different sign when compare with first equation

So when we add first and second equation , the x will get eliminated.

Answer:  29/28

Step-by-step explanation:

To add fractions we have to calculate the Least Common Denominator of the denominators. Then we have to change each fraction (using equivalent fractions) to make their denominators the same as the Least Common Denominator. Then we can add (or subtract) the fractions.

LCD (4,7,2)= 4·7 = 28

1/4 = 7/28

2/7 = 4·2/28 = 8/28

1/2 = 14/28

Since the fractions have the same denominator we can add them

7/28 + 8/28 + 14/28 = (7+8+14)/28 = 29/28

[tex]\textit{\textbf{Spymore}}[/tex]

Answer:

102

Step-by-step explanation:

89 + a

Let a=13

89+13

102

Answer:

I'm not quite sure because its not clear enough, but, it might be on the left side on the green pillow.... What game is this though?

Answer:

All of them are polynomials except c.

Step-by-step explanation:

Polynomials are in the form:

[tex]a_0+a_1x+a_2x^2+a_3x^3+a_4x^4+a_5x^5+a_6x^6+\cdots +a_nx^n[/tex]

You can see here there are no extra symbols like square root, cube root, absolute value, and so on on the variable x...

We also don't have division by a variable.  All the exponents are whole numbers.

a) While it has a square root, it is not on a variable so a is a polynomial.  The exponents on the variables are whole numbers.

b) b is a polynomial also because all the exponents are whole numbers.

c) This is not a polynomial because there is a square root on a variable.

d) This is a polynomial.  All the exponents are whole numbers.

Answer:

He needs to sell the rest of the oranges at 75 paisa each.

Step-by-step explanation:

Consider the given information that, Shishir bought 4000 orange at 70 paisa each.

Note: 1 rupees = 100 paisa

Thus, 70 paisa = 70/100 rupees = 0.70 rupees

Therefore, the cost price of 4000 oranges is:

4000×0.70 rupees = 2800 rupees

The selling price of 2000 oranges is:

2000×0.90 rupees = 1800 rupees

The number of oranges now Shishir have:

4000 - 2000 - 400 = 1600

He wants to make a profit of RS 200. Thus the selling price of 4000 oranges should be:

2800 rupees + 200 rupees = 3000 rupees

He earned 1800 rupees by selling 2000 oranges at 90 paisa. So, the remaining amount that he needs to make with 1600 oranges is:

3000 rupees - 1800 rupees = 1200 rupees

Therefore, the cost of one orange is:

1600 oranges = 1200 rupees

1 orange = 1200/1600 rupees

1 orange = 0.75 rupees

Hence, he needs to sell the rest of the oranges at 75 paisa each.

Answer:

look at the attached photo

Step-by-step explanation:

- figure out slope intercept form and write an equation

- draw a graph

- go up positive two on the y axis and to the right one and mark the spot

- mark -3 on the y axis

- use a ruler t connect the two points

Answer:

B. Graph B

Step-by-step explanation:

A graph with no solutions is one where the lines never intersect.

In Graph A, you have a solution at about (-2, 2).

In Graph C, all real numbers are solutions.

[tex]\large\boxed{59\,\text{years old}}[/tex]

In this question, it's asking you to figure how old the oldest person in the company is.

To solve this, we would need to gather some important information from the question.

Important information:

With the information above, we can get closer to our answer.

We need some prior knowledge to solve this. The "range" is the highest number subtracted by the lowest number.

This means that the the 22 was already subtracted to get 37.

What we would do is reverse to solution and add 22 to 37 to get our highest number (oldest person).

[tex]37+22=59[/tex]

When you add them together, you should get 59.

This means that the oldest person in the company is 59 years old.

Answer:

Age of oldest person = 59 years

Step-by-step explanation:

Points to remember

Range of a data set is the difference between smaller value and larger value value in the set.

It is given that, the youngest person in the company is 22 years old. The range of ages is 37 years.

To find the age of oldest person

Range = 37 years

Youngest age =  22 years

Range = oldest age  - youngest age

oldest age = range + youngest age

 = 37 + 22

 = 59

Age of oldest person = 59 years

Answer:

A.16b^4/81

step-by-step explanation:

(2b/3)^4

= (2b)^4/3^4

= (2^4×b^4)/3^4

=16b^4/81

(as 16 and 81 cant simplify each other)

Answer:

A. 16b^4/81

Step-by-step explanation:

(2b/3)^4

We know (a/b)^c = a^c / b^c

(2b)^4  / 3^4

We also know (ab)^c = a^c * b^c

2^4 * b^4   / 3^4

16 b^4/ 81

Answer:

1.3 repeating or 4/3

Step-by-step explanation:

if you take 24 and divide it by 18 this is the answer you receive

A box plot displays the distribution of a set of data values. To determine the correct statement, analyze its components: minimum, first quartile, median, third quartile, and maximum.

A box plot, also known as a box-and-whisker plot, is a type of graph that displays the distribution of a set of data values. It shows the minimum, first quartile, median, third quartile, and maximum values of the data set.

To interpret the box plot and determine which statement is correct, you need to analyze its components:

By analyzing the position and spread of these values in the box plot, you can determine which statement is correct.

https://brainly.com/question/31856042

#SPJ1

Answer:

-7.64%

Step-by-step explanation:

1. Find out how much the car went down in value.

    21,330 - 19,700 = 1,630

2.  Calculate how much 1% of the original value ($21,330) was. One percent is 1/100, which is .01 when divided.

    21,330 × .01 = 213.3

3. Since we now know 1% is equal to $213.30 we can divide $1,630 by $213.30. Doing this will show us how many 1%s are in 1,630.

    1,630/213.30 = 7.64181903

4. There are 7.64181903 1%s in 1,630. Because the car's value went down by 1,630, this also means it went down by 7.64181903% We will round this to the nearest hundredth for simplicity's sake.

    7.64181903 → 7.641 one is less than 6 so we will round down → 7.64

5. The car decreased by 7.64% in value. This will be written as -7.64% because a decrease is negative.

Answer:

-7.64%

Step-by-step explanation:

Answer:

y = -7x+34

Step-by-step explanation:

We have 2 points, so we can find the slope

m = (y2-y1)/(x2-x1)

    = (6--1)/(4-5)

    = (6+1)/(4-5)

     = 7/-1

    = -7

We can use point slope form to make an equation

y-y1 = m(x-x1)

y--1 = -7(x-5)

y+1 = -7(x-5)

Distribute

y+1 = -7x+35

Subtract 1 from each side

y+1-1 = -7x+35-1

y = -7x+34

Answer:

C​The volume of the prism depends on the product of the length, the width, and the height.

Step-by-step explanation:

V = lwh

Volume is the product of l, which is length, w which is width and h which is height

Answer:

C​.The volume of the prism depends on the product of the length, the width, and the height.

Step-by-step explanation:

If the volume of a rectangular prism is given by the function V = lwh, the volume of the prism depends on the product of the length, the width, and the height.

Answer:

Explanation:

That the discrepancy in diameter is more than 0.002 mm means that the difference between the measured diameter of a ball and the standard diameter is greater than 0.002.

That is:

So, the function is f(x) = |x - 42.67| > 0.002, where x and f(x) are in mm.

Answer:

First one is B f(x) = (42.67-x)

Second is 42.6668 mm, 42.673 (options b and d)

Hope this helps

Checked on edge

Only statement B is true, so you would select that as the answer.

We can check if statement A is true by finding the ratio of cows to all animals, which we do by finding the total number of animals, 5 + 3 + 2 + 6 = 16.

Then we can say that the ratio of cows to all animals is 2:16, which simplifies to 1:8, so statement A is false.

Statement B is just another way of saying that the ratio of rabbits to all animals is 3:8, so we can see if this is true by finding the ratio of rabbits to all animals. There are 6 rabbits, so it would be 6:16, which simplifies to 3:8. This means that statement B is true.

I hope this helps! Let me know if you have any questions :)

Answer:

2n-7

Step-by-step explanation:

"7 less than twice a number n"

is the same as

"7 less than (twice a number n)".

I put ( ) around that one part because I want you to focus on that part first.

Twice a number n means 2 times that number n or 2n.

So now we have

"7 less than 2n".

This means 2n-7.

Answer:

Step-by-step explanation:

Put the values of x = 1 and y = -3 to the equations of a line and check the equality:

1. 4x - y = 7

4(1) - (-3) = 4 + 3 = 7   CORRECT

2. 2x + 5y = 4

2(1) + 5(-3) = 2 - 15 = -13 ≠ 7

3. 7x - y = 15

7(1) - (-3) = 7 + 3 = 10 ≠ 15

4. x + 5y = 21

1 + 5(-3) = 1 - 15 = -14 ≠ 21