helpppppppp? please thank you

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Complex conjugate example:

2 - 16i >> 2 + 16i

Are you sure this is the entire question?

For this case we have a complex number of the form:

[tex]a + (b) (i)\\[/tex]

Where:

Thus, given 1-8i, its complex conjugate is given by:

[tex]1 + 8i\\[/tex]

On the other hand, the product of both is given by:

[tex](1 + 8i) (1-8i) =\\\\(1 ^ 2-8i + 8i-64 (i ^ 2)) =\\\\1-64 (-1) =\\\\1 + 64 = 65\\[/tex]

Answer:

Conjugate complex: [tex]1 + 8i\\[/tex]

Product: 65

Answer:

The graph in option (c) is the correct answer.

Step-by-step explanation:

The line corresponding to the inequality [tex]x+y<1[/tex] represents the dashed line and the line corresponding to the inequality [tex]2y\geq x-4[/tex] represents the solid line.

In order to figure out the correct shaded region, we test one point from each of the four possible regions and figure out the point at which both the inequalities bold true. The region containing that point would be the correct shaded region.

Let us test the point (0,0).

First inequality [tex]0+0<1[/tex], that is, [tex]0<1[/tex] holds true.

The second inequality [tex]2(0)\geq 0-4[/tex] that is, [tex]0\geq -4[/tex] as well holds true.

Since both the inequalities hold true at point (0,0), therefore, region  containing origin is the correct answer. Thus, the correct answer is forth option. Since the options are not labeled, I have attached the correct graph with my solution in order to make sure you get the correct answer.

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ANSWER

The possible rational roots are [tex]\pm3[/tex]  and [tex]\pm\frac{1}{3}[/tex]

EXPLANATION

According to  the rational roots theorem, the possible rational roots of

[tex]9x^3+14x^2-x+18=0[/tex]

is given by all the possible factors of [tex]18[/tex] which are

[tex]\pm1,\pm2,\pm3,\pm6,\pm9,\pm18[/tex]

expressed over all the possible factors of the coefficient of the highest degree of the polynomial which is  [tex]9[/tex] which are

[tex]\pm1,\pm3,\pm9[/tex]

in their simplest form.

One of this possible ratios are [tex]\pm9[/tex] from the factors of 18, over [tex]\pm3[/tex] from the factors of 9.

This will give us

[tex]\frac{\pm9}{\pm3} =\pm3[/tex].

Another possible rational root is

[tex]\pm \frac{1}{3}[/tex].

Hence the correct options are

A and C.

Secrete: Check if the denominator is a factor of 9 and the numerator is also a factor of 18, then these are the correct answers.

The possible rational roots of the polynomial 9x^3+14x^2-x+18=0, according to the Rational Root Theorem, are ±3 and ±1/3. The other given options, ±1/18 and ±1/2, do not meet the criteria set by the theorem.

The question asks for the possible rational roots of the polynomial 9x^3+14x^2-x+18=0 according to the Rational Root Theorem. The Rational Root Theorem states that if a polynomial has a rational root p/q, where p and q are integers and q is not zero, then p is a factor of the constant term and q is a factor of the leading coefficient.

The constant term here is 18 and its factors are ±1, ±2, ±3, ±6, ±9, and ±18. The leading coefficient is 9 and its factors are ±1, ±3, and ±9. According to the theorem, we divide each factor of the constant term by each factor of the leading coefficient to determine the potential rational roots:

±1/1, ±1/3, ±1/9

±2/1, ±2/3, ±2/9

±3/1, ±3/3, ±3/9

±6/1, ±6/3, ±6/9

±9/1, ±9/3, ±9/9

±18/1, ±18/3, ±18/9

Out of the list, the values that match the options given in the question are ±3 and ±1/3. The other options, ±1/18 and ±1/2, are not rational roots because 1/18 is not a factor of 9 (leading coefficient), and 2 is not a factor of 18 (constant term) when considering the reduced form.

The slope-point form of a line:

[tex]y-y_0=m(x-x_0)[/tex]

We have

[tex]m=\dfrac{3}{4}\\\\(4,\ 1)\to x_0=4,\ y_0=1[/tex]

Substitute:

[tex]y-1=\dfrac{3}{4}(x-4)[/tex]

The slope-intercept form:

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

Solve for y:

[tex]y-1=\dfrac{3}{4}(x-4)\qquad|\text{use distributive property}\\\\y-1=\dfrac{3}{4}x-3\qquad|\text{add 1 to both sides}\\\\y=\dfrac{3}{4}x-2[/tex]

Answer: D.

[tex]\frac{(new) - (original)}{original} = \frac{\frac{3}{8}- \frac{5}{4} }{\frac{5}{4} }[/tex]

[tex]\frac{3}{8} - \frac{5}{4} (\frac{2}{2}) = \frac{3}{8} - \frac{10}{8} = \frac{-7}{8}[/tex]

 [tex]\frac{-7}{8}[/tex] ÷ [tex]\frac{5}{4}[/tex]

=  [tex]\frac{-7}{8}[/tex] * [tex]\frac{4}{5}[/tex]

= [tex]\frac{-7(4)}{8(5)}[/tex]

= [tex]\frac{-7}{2(5)}[/tex]

=  [tex]\frac{-7}{10}[/tex]

= -0.70

multiply by 100 to get the percent: - 70% (the negative represents decrease)

Answer: 70% decrease

When dividing a positive number by a negative number, the result is negative.

A better estimation would be -3.

Solution:

As the two numbers [tex]15 \frac{1}{3} {\text{and} -4\frac{2}{3}[/tex] are mixed fractions.

[tex]15 \frac{1}{3}= \frac{46}{3} \\\\ -4\frac{2}{3}= \frac{-14}{3}[/tex]

Now,  [tex]\frac{ \frac{46}{3}}{\frac{-14}{3}}[/tex] = - 3

Ankur's answer= 3

The mistake he has committed , while dividing two fractions , he must have forgot that one of the fraction which is in the denominator bears negative sign  before it.

So, [tex]\frac {+}{-}= -[/tex].

Ankur forgot to put negative sign before 3.

So, The correct option which describes ankur's error is : Ankur found that the quotient of a positive number and a negative number is positive.

Option 3 is right choice.

Construction of an angle congruent to a given angle.

Congruent angles are two or more angles that are identical to each other. Thus, the measure of these angles is equal to each other.

For two angles to be congruent their measurements must be equal.

Therefore, we can conclude that the construction above is angle congruent to a given angle.

Learn more about congruent angles here

https://brainly.com/question/28262429

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An angle congruent to a given angle construction is illustrated in the figure. Option B is the right choice.

Congruent angles share an identical measure, establishing equality between their angular dimensions.

In the realm of geometry, the fundamental criterion for angles to be considered congruent is that their measurements are precisely equal. This equality in angular magnitude implies that the angles exhibit indistinguishable orientations and positions.

Consequently, when engaging in geometric constructions, if a constructed angle aligns in measurement with a given angle, it is deemed congruent to the specified angle.

This fundamental concept is pivotal in geometric reasoning and problem-solving, providing a basis for establishing equivalences between angles and facilitating precise angular constructions. In summary, congruent angles signify an equality in measurement, forming a cornerstone in geometric analyses and constructions.

Option B is the right choice.

For similar question on congruent

https://brainly.com/question/29789999

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The slope:

[tex]m=\dfrac{\Delta y}{\Delta x}[/tex]

Look at the picture.

6 units down → -6

2 units right → 2

[tex]m=\dfrac{-6}{2}=-3[/tex]

answer:  [tex] \frac{3}{-1} x[/tex]

explanation:

slope-intercept formula ==> [tex]y = mx + b[/tex]

[tex]m[/tex] is slope , and [tex]b[/tex] is y-intercept

to find the slope you need to start at the y intercept and go 3 units up and 1 unit left. and if you repeat it again, until you reach the top of the graph and that would make partial of the line.

so, the slope is [tex]\frac{rise}{run}[/tex], so if you plug it in it would look like this

[tex]y = \frac{3}{-1} x + b[/tex]

A D D I T I O N A L  I N F O

then you find the y-intercept which would be where the line intersects at the y axis, which is -10. plug the number into the equation

[tex]y = \frac{3}{-1} x - 10[/tex]

and that would make our final answer.

hope this helps! correct me if there is anything wrong ❤ from peachimin

The formula of a slope:

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

We have

[tex](r,\ 6),\ (5,\ -4)\\\\m=\dfrac{5}{7}[/tex]

Substitute

[tex]\dfrac{-4-6}{5-r}=\dfrac{5}{7}\\\\\dfrac{-10}{5-r}=\dfrac{5}{7}\qquad|\text{cross multiply}\\\\5(5-r)=(-10)(7)\qquad|\text{use distributive property}\\\\25-5r=-70\qquad|-25\\\\-5r=-95\qquad|:(-5)\\\\\boxed{r=19}[/tex]

Answer:

Stacy made a blanket using some fabric, she had 3 yards left over and decided to use the leftover pieces to make pot holders. She cut each piece into 8 inches long. Stacy had enough fabric to create 4.5 pieces.

Step-by-step explanation:

we find that 13 full pieces of fabric, each 8 inches long, can be cut from three yards of fabric.

The question asks how many pieces of fabric, each measuring 8 inches in length, can be cut from a total length of three yards of fabric. To begin with, we need to convert yards to inches, because the unit of measurement for the fabric pieces is in inches, not yards. We know that 1 yard is equal to 36 inches (since 1 yard = 3 feet and 1 foot = 12 inches, hence 3 feet x 12 inches/foot = 36 inches). Therefore, three yards of fabric is 3 x 36 inches, which equals 108 inches.

Now, if each piece is to be 8 inches long, we divide the total number of inches by the length of one piece to find out how many pieces can be made:
108 inches / 8 inches/piece = 13.5 pieces.

However, since we cannot have half a piece of fabric, we can only make 13 full pieces, with a small remaining piece that would be less than 8 inches long.

It is 165 degrees celcius

Answer: 10 & 16

Step-by-step explanation:

Answer:

24 dozen chocolate chip

14 dozen peanut butter

Step-by-step explanation:

x = number of dozen chocolate chip cookies

y = number of dozen peanut butter cookies

Total number of cups of flour is:

2x + 3y ≤ 90

Total number of eggs is:

x + 4y ≤ 80

Total profit is:

P = x + 1.5y

Since this is multiple choice, one method would be to calculate the profit for each option, then choose the one that's largest.

But let's try solving this algebraically.  x and y are positive integers, and we want them to be as large as possible.

Let's start by assuming the solution is on the line 2x + 3y = 90.

x + 4y ≤ 80

2x + 8y ≤ 160

90 − 3y + 8y ≤ 160

5y ≤ 70

y ≤ 14

If y = 14, x = 24, and P = 45.

Now let's assume the solution is on the line x + 4y = 80.

2x + 3y ≤ 90

2 (80 − 4y) + 3y ≤ 90

160 − 8y + 3y ≤ 90

70 ≤ 5y

14 ≤ y

Therefore, to maximize the profit, they should bake 24 dozen chocolate chip cookies and 14 dozen peanut butter cookies.

Rays are always named with two points rays

Answer: [tex]\frac{4}{15}[/tex]

Step-by-step explanation:

First pick (blue)     and        Second pick (red)

             [tex]\frac{6}{10}[/tex]                  x                    [tex]\frac{4}{9}[/tex]

= [tex]\frac{6(4)}{10(9)}[/tex]

= [tex]\frac{2(2)}{5(3)}[/tex]

= [tex]\frac{4}{15}[/tex]

Answer:

The answer is 4/15 hopefully this helps!

37 and 38

consecutive integers have a difference of 1 between them

let n and n + 1 be the consecutive integers, then

n + n + 1 = 75 ( subtract 1 from both sides )

2n = 74 ( divide both sides by 2 )

n = [tex]\frac{74}{2}[/tex] = 37

the integers are 37 and 37 + 1 = 38

Answer: C

Step-by-step explanation:

(x - y)²

we want (8)², so need: x - y = 8

There are many options that satisfy x - y = 8  but of the options provided to you, 10 - 2 is the only one that works.

A) 2 - 6 = -4

B) 64 - 0 = 64

C) 10 - 2 = 8

D) 8 - 64 = -56

Answer:

Step-by-step explanation:

(2005, 12,000)        (2005, 12,000)

   x1          y1                x2           y2

m= (12,250-1200) /  (2010-2005) = 250/5 = 50/1 = or 50

For this one, I would go with D.

D makes the most sense, giving that there is two sets of each and, that it is just a shorter way to say "add all the sides."  

B and C would only give us half or part of the perimeter and then A does not make much sense.

D would be the answer through process of elimination.

Always remember (y2-y1)/(x2-x1) for finding slope

So (-3)-4 / 1-1=

-7 / 0

So undefined

The solution to the equation x² + 24 = 0 over the complex numbers is x = ±2√(6)i. After isolating x² on one side, we take the square root of both sides and introduce the imaginary unit i because the number under the square root is negative.

To solve the equation x² + 24 = 0 over the complex numbers, we need to find values of x that satisfy the equation. This is a quadratic equation with 'a' as 1 (the coefficient of x²), 'b' as 0 (since there is no x term), and 'c' as 24.

We will first isolate x² by subtracting 24 from both sides of the equation:

x² = -24

Next, to find x, we take the square root of both sides. Remember that when we take the square root of a negative number, we get an imaginary number. The square root of -24 can be expressed as:

x = ±√(-24)

This simplifies to:

x = ±√(24) × ±i

Since √(24) is √(4 × 6), which simplifies to 2√(6), the final solution in terms of complex numbers is:

x = ±2√(6)i

Answer:

Step-by-step explanation:

(g/h)(t) = g(t) / h(t)

              =( t³-5t² ) /(t+5) we cannot simplify this further so

(g/h)(t) = ( t³-5t² ) /(t+5)

               =

Answer:

The awnser is C and trust me

Step-by-step explanation:

Answer:

No

Step-by-step explanation:

11-10 = 1

He spent 1 hour more this week

Which is:

1/10 × 100 = 10% more

Marcus spent 10% more time doing homework this week. His calculation is wrong.

Time used last week by marcus = 10 hours

Time used this week by marcus = 11 hours

Difference in hours  = 11  - 10  = 1 hour

This means that Marcus used 1 more hour this week than last week

% increase = 1/10 * 100

% increase  = 10%

This shows that he spent 10% more time doing homework this week.

Learn more here: https://brainly.com/question/20710281

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