If a polygon has an area of 25cm and is dilated by a factor of 3, what will be the area of the dilated polygon?

Answer:

  a) positive real zeros: 2 or 0; negative real zeros: 2 or 0; complex zeros: 0, 2, or 4. (rule of signs)

  b) ∪-shaped, as for an even-degree polynomial with positive leading coefficient. See attached.

  c, d) See attached

Step-by-step explanation:

Descarte's rule of signs gives bounds on the number of positive and negative real roots. The numbers it gives may be reduced by multiples of 2, as complex roots will come in conjugate pairs. The total number of roots of all kinds will match the degree of the polynomial.

Synthetic division is essentially polynomial long division with some modifications:

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The signs of the terms of the given polynomial are + - - - +. There are two sign changes, so 2 possible positive real roots.

When the signs of the odd-degree terms are changed, the signs become + + - + +. There are still two sign changes, so 2 possible negative real roots.

Either or both of these numbers can be reduced by 2 if the roots include a conjugate pair. That is, there may also be 0 possible positive real roots, and 0 possible negative real roots.

The number of non-real (complex) zeros may be any multiple of 2 up to the degree of the polynomial. The may be 0, 2, or 4 possible non-real zeros.

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The graph is the first attachment. It shows 4 real zeros: x = -4, -2, 1, 6.

Since the polynomial is of even degree (4) and has a positive leading coefficient (+1), we expect the general shape to be ∪-shaped. It is.

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The second attachment shows synthetic division using x = -4. (The binomial divisor is (x+4).) The remainder (lower right value in the tableau) is the value of y when x=-4. The third attachment shows synthetic division using the value x=3. (y is -210 when x=3.)

Maybe this is the table you want:

  [tex]\begin{array}{|c|c|c|}\cline{1-3}x&-4&3\\\cline{1-3}y&0&-210\\\cline{1-3}\end{array}[/tex]

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The second attachment shows synthetic division by the factor (x+4).

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Additional comment

The synthetic division attachments show instructions for carrying out the synthetic division and interpreting the results. As we said above, "the entry on the left" is the opposite of the constant in the binomial divisor. It is the actual value of x you want to use to evaluate the function.

The equations shown are merely for the purpose of indicating the operations that are used. An actual synthetic division tableau is simply a 3-row table of numbers, with the bottom row being the quotient coefficients and remainder.

Answer:

131.13

To find the area do w (width) times l (length/breadth) so the equation to find the area would be L*W=A

I have linked a picture with the intervel.

Amy is correct, -7.1 is between -7 and -8.  

A number pattern is a pattern in a series of numbers that represents the common relationship between the numbers.

Two students were asked to graph a rational number -7.1.

Amy states that The number is between -8 and -7, but Laura states that the point is between -7 and -6.

In order to be in between -6 and -7, the number would have to be a decimal with a whole number of 6.

But -7.1 has a whole number of 7 then it is in between -7 and -8.

Thus, Amy is correct, -7.1 is between -7 and -8.  

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Answer:

[tex]y = - 2x + 4[/tex]

Step-by-step explanation:

Thank you

Answer:

60 ft

Step-by-step explanation:

using the sine ratio in the right triangle and the exact value

sin30° = [tex]\frac{1}{2}[/tex] , then

sin30° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{CD}{AD}[/tex] = [tex]\frac{30}{AD}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )

AD = 60 ft

Answer:

D, C

Step-by-step explanation:

for part a, there is a negative slope with the graph shifted two units upwards

for part b, if you plug in C, you get an answer that works

Answer:

A.) 588329.896

B.) 274300

C.) 1657.18474

D.) 1.002

(All answers unrounded.)

Explanation:

I converted each unit to the unit used in the other number (E.g., for question A I converted tons to kilograms, and then finished solving.)

Answer:

9800 cm^2

Step-by-step explanation:

The area of a square is just the length of one of the sides squared. In the first image it's given that one of the sides is 70 cm and the shape is also a square pyramid so the base is going to be a square. So the area the base is (70 cm) ^ 2 = 4,900 cm^2. The area of a triangle is 1/2 bh. The base is given in the first image which is 70 cm and the height is also given which is 140 cm. This gives you the equation 0.5 * 140 cm * 70 cm = 4900 cm^2. Adding these two values gives you 9800 cm^2

Based on the given probability events, we can calculate that Events A and B are independent, because P(B) = P(B|A) = 1/2.

Events are independent if P(B) = P(B|A)

The probability of event B is:

= 3 odd numbers / 6 numbers

= 1 / 2

The probability of A is:

= 3 prime numers / 6

= 1/2

P(B|A) = ((1 / 2) x (1 / 2)) / (1 / 2)

= 1/2

So P(B) = P(B|A) = 1/2.

The events are independent.

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Answer: C

Step-by-step explanation:

[tex]\sqrt{48x^{5}}=\sqrt{16x^{4}} \sqrt{3x}=\boxed{4x^{2}\sqrt{3x}}[/tex]

Answer:

C

Step-by-step explanation:

The y intercept is 3, so eliminate B and D.

Also, the slope is less than 1, so this eliminates A.

This leaves us with C.

The area of the shaded sector must be 144π units².

The area of the circle is defined as the product of the pie and the square of the radius.

The area of the circle = [tex]\pi r^{2}[/tex]

We know that the angle measurement of central angle QRS is less than π radians.

for r = 18 units

The area of the circle = π18² = 324π  units²

The area of ​​the half of a circle = 324π /2 = 162π units²

The area of ​​a quarter of a circle = 324π /4 = 81π  units²

so

The area of the shaded sector < 162π  units²

and

The area of the shaded sector > 81π  units²

Hence the answer must be 144π units²

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Answer:

[tex]\fbox {Work is attached below.} \downarrow[/tex]

Step-by-step explanation:

Answer:

Step-by-step explanation:

Ratio and proportion:

   [tex]\sf \dfrac{x}{3}=\dfrac{6}{9}\\\\ x = \dfrac{6*3}{9}\\\\x = 2[/tex]

[tex]\sf \dfrac{8}{y}=\dfrac{6}{9}\\\\Cross \ multiply,\\\\y*6=9*8\\\\y=\dfrac{9*8}{6}\\\\y=3*4\\\\\bf y = 12[/tex]

[tex]\sf \dfrac{a}{15}=\dfrac{6}{9}\\\\a =\dfrac{6}{9}*15\\\\a=2*5\\\\\bf a = 10[/tex]

The correct answer is option B which is {x | x ≤ 4.5}

A number line is a representation of a graduated straight line used to represent real numbers in introductory mathematics.

Because the arrow is pointing to the left, the answer to the solution set needs to be less than the number the dot is on.

A solid dot on a number means that that number is included in the solution set.

In the picture the solid dot is on 4.5, so the solution set needs to be equal to or less than 4.5.

Therefore the correct answer is option B which is {x | x ≤ 4.5}

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Answer:

I'm not sure how to interpret "y = 3√x+1-2."

I'll assume y = 3[tex]\sqrt{x+1}[/tex] - 2

Step-by-step explanation:

Use the free online app DESMOS.  Either enter the equation, or make a table of individual points and plot them as ordered pairs.

GRAPH:   See attached image

PLOT:  Calculate a few points, mark them on the graph and then connect the dots.  I selected a few values of x and calculated y from the equation.  Each calculation provides a (x,y) ordered pair which can be marked on the graph and the dots are then connected.  Note that x values less than -1 result in a value of y that includes i, an imaginary number.  So the graph ends abruptly at that point.

Inequalities help us to compare two unequal expressions. The correct option is A.

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.

The complete question is:

The sum of 16 and a number is less than 24. Which of the following inequalities expresses the solution?

x<8

x>8

x=8

x<-8

Given the sum of 16 and a number is less than 24. Let the number be represented by x, therefore,

16 + x < 24

x < 24 - 16

x < 8

Hence, the correct option is A.

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Answer:

- 24

Step-by-step explanation:

4(m + 2p) ← substitute m = 2 and p = - 4 into the expression

= 4(2 + 2(- 4) )

= 4(2 - 8)

= 4(- 6)

= - 24

Answer:

×=-3

y=-4

Step-by-step explanation:

13×-3y=51

(-) 5×-y=19

-5×+y=-19

13×-3y=51

8×-2y=32

2/8x-2y=32

4x-y=16

4×-y=16

-5×+y=-19

-×=-3

×=3

Answer:

x = 3
y = -4
(3,-4)

Step-by-step explanation:

Hello!

We can use the Elimination Method to solve the system.

To eliminate, we want atleast one variable to have the same coefficients on both equations. To do that, we can multiply the first equation by 3 to get -3y.

Now, we can vertically subtract them to eliminate -3y.

Solve for x

The value of x is 3.

To solve for y, we can plug in 3 into the original first equation and solve for y.

Solve for y

The value of y is -4.

The solution to the system is (3,-4).

Answer:

12 is the correct answer

Answer:

Step-by-step explanation:

THIS WILL BE A STRAIGHT LINE rising to the left as the coefficient of x is negative ( -3/2),

When x = 0  y = -3 so mark the point (0, -3) on your graph paper.

When x = 6, y = -3/2 * 6 - 3 =  -9 - 3 = -12

So mark  the point (6, -12)

The graph will be the straight  line passing through the above 2 points.

Step-by-step explanation:

Answer:

slope is 7 and point on line is (1, 4 )

Step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

given line A has equation in point- slope form of

y - 4 = 7(x - 1) , then

slope of line is 7 and a point on the line is (1, 4 )

The highest common factor of [tex]x^2 y[/tex] and [tex]x[/tex] is [tex]\boxed{x}[/tex]

Answer:

-1

Step-by-step explanation:

The y-intercept is where the line crosses the y-axis.

Answer:

[tex]\huge\boxed{\sf y-intercept = -1}[/tex]

Step-by-step explanation:

Here,

Since, this is the point where x = 0 and where the line passes through the y-axis.

[tex]\rule[225]{225}{2}[/tex]

Answer:

Step-by-step explanation:

12 becuase you have to read the equasion and do the problem

The difference of the fractions as given in the task content is; (4-2x) / (x²-16).

According to the task content, the fractions whose difference is to be evaluated are as indicated below;

[tex] \frac{x}{( {x}^{2 } - 16)} - \frac{3}{x - 4} [/tex]

Hence, the LCM of the denominators of both fractions can be evaluated as;

x -3(x+4)/(x²-16).

(4-2x) / (x²-16)

Hence, the difference of the two fractions is; (4-2x) / (x²-16).

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average speed equals distance over time 100/80 will give you 5/4