Find ZABD if ZABC = 121° in the given figure.

Answer:

[tex](f/g)(x)=\frac{x^4-x^3-7x^2+9x-2}{x-1} =x^3-7x+2\,\,\,for\,\,x\neq 1[/tex]

[tex](f/g)(2)=-4[/tex]

Step-by-step explanation:

[tex](f/g)(x)=\frac{x^4-x^3-7x^2+9x-2}{x-1} =x^3-7x+2\,\,\,for\,\,x\neq 1[/tex]  and undefined for x = 1.

Notice that (x-1) is in fact a factor of f(x), so the quotient of the two functions introduces a "hole" for the new function at x = 1.

f(2) can be found by simply evaluating the expression for x = 2:

[tex](f/g)(2)=2^3-7(2)+2=-4[/tex]

Answer:

x=4

Step-by-step explanation:

5x - 17 = -x +7

Add x to each side

5x+x - 17 = -x+x +7

6x -17 = 7

Add 17 to each side

6x-17+17 = 7+17

6x =24

Divide each side by 6

6x/6 = 24/6

x = 4

Answer:

4

Step-by-step explanation:

5x - 17 = -x + 7

Add x on both sides.

5x - 17 + x = -x + 7 + x

6x - 17 = 7

Add 17 on both sides.

6x - 17 + 17 = 7 + 17

6x = 24

Divide both sides by 6.

(6x)/6 = 24/6

x = 4

Answer:

1) 18

2) P

Step-by-step explanation:

1) Multiply the top number by itself and then reverse the digits!

9*9 = 81 reversed is 18

2) Seems to be the number of line ends a letter has when you write it down. P only has one end, at the bottom.

Answer:

P

Step-by-step explanation:

2.

The number of strokes of the letter that come to an end.

The bottom of the A has two sticks that come to an end.

A = 2

The B has no sticks coming to an end.

B = 0

The C and an upper and a lower stroke coming to an end.

C = 2

D has none.

D = 0

E has 3 sticks coming to an end.

E = 3

etc.

M has 3.

N has 2.

O has 0.

P has 1 stick coming to an end.

Q has none.

R has 2.

S has 2.

T has 3.

U has 2.

V has 2.

W has 3.

X has 4.

Y has 3

Z has 2.

Of all letters after L, only P has exactly 1 stroke coming to an end.

Answer: P

Answer:

OD is false, because it condradicts OA, and we know that OA is true, I mean, we write 2<3

Answer

The inequality sign always open up to the smaller number

The answer is D

Answer:

Brian is 6 years old, John is 9 years old

Step-by-step explanation:

i.

J = 3 + B

J x B = 54

ii.

(3 + B) x B = 54

B² + 3B = 54

iii.

(B + 9)(B - 6) = 0

B = -9 or 6 -- -9 is irrational as one cannot be negative years old

Brian = 6 years old; therefore, John = 9 years old

Answer:

5 + 12i

Step-by-step explanation:

(3 + 2i)^2 = (3 + 2i)(3 + 2i) = 9 + 6i + 6i + 4i^2 = 9 + 12i - 4 = 5 + 12i

Answer:

5 + 2i

Step-by-step explanation:

since [tex]\sqrt{-1} = i[/tex]

Use the perfect square formula ( a + b )^2

= 3^2 + 2 · 3 · 2i + (2i)^2

= 5 + 2i

or,

[tex]5+2\sqrt{-1}[/tex]

The company must produce and sell 350 dishwashers in order to maximize profit.

To determine the number of dishwashers the company must produce and sell in order to maximize profit, we need to find the value of x that corresponds to the maximum point of the profit function.

The profit (P) is given by the equation:

P(x) = Revenue - Cost

The revenue is calculated by multiplying the price per dishwasher (p) by the number of dishwashers sold (x):

Revenue = p * x

The cost is given by the function C(x):

Cost = C(x)

Therefore, the profit function can be expressed as:

P(x) = p * x - C(x)

Substituting the given expressions for p and C(x):

P(x) = (420 - 0.3x) * x - (5000 + 0.3x²)

Expanding and simplifying the equation:

P(x) = 420x - 0.3x² - 5000 - 0.3x²

Combining like terms:

P(x) = -0.6x² + 420x - 5000

To find the value of x that maximizes profit, we need to find the vertex of the quadratic function. The x-coordinate of the vertex can be determined using the formula:

x = -b / (2a)

In our case, a = -0.6 and b = 420:

x = -420 / (2 * -0.6)

x = -420 / (-1.2)

x = 350

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350 dishwashers must the company produce and sell in order to maximize profit.

Maxima means a point at which the function attains the maximum value.

Given the following information:

Price per dishwasher, p = 420 - 0.3x

Total cost of producing x dishwashers, C(x) = 5000 + 0.3x2

Profit= Total Selling price- Total Cost Price

Total Selling price of x dishwasher, S.P= xp

S.P=x(420 - 0.3x)

S.P=420x - 0.3x²

Profit= 420x - 0.3x² - ( 5000 + 0.3x²)

Profit= 420x - 0.3x² - 5000 - 0.3x²

Profit=  -0.6x²+420x-5000

So, profit, f(x)=-0.6x²+420x-5000

To determine the value of x so that maximum profit is possible:

1. Calculate the first derivative of profit function and calculate the value of x by equating it to zero.

2. Select that value of x for which the profit function attains the maximum value, to check the maxima calculate 2nd derivative, if it gives a negative value for the value of x. Then, x is the point of maxima for the given function.

[tex]f(x)=-0.6x^2+420x-5000\\f\prime(x)=-1.2x+420\\f\prime(x)=0\\-1.2x+420=0[/tex]

Calculating the value of x by transposing,

x=420/1.2

x=350

To check maxima, calculating second derivative.

[tex]f\prime(x)=-1.2x+420=0\\f\prime\prime(x)=-1.2[/tex]

2nd derivative is negative, it means that x=350 is the point of maxima.

Thus, a company must produce and sell 350 dishwashers in order to maximize profit.

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Answer:

[tex]\large \boxed{\sf \ \ x=1, \ \ x=2+5i, \ \ x=2-5i \ \ }[/tex]

Step-by-step explanation:

Hello,

I assume that we are working in [tex]\mathbb{C}[/tex], otherwise there is only one zero which is 1. Please consider the following.

First of all, we can notice that 1 is a trivial solution as

   [tex]p(1) = 1^3-5\cdot 1^2 + 33\cdot 1-29=1-5+33-29=0[/tex]

It means that (x-1) is a factor of p(x) so we can find two real numbers, a and b, so that we can write the following.

[tex]p(x)=(x-1)(x^2+ax+b)=x^3+ax^2+bx-x^2-ax-b=x^3+(a-1)x^2+(b-a)x-b[/tex]

Let's identify like terms as below.

a-1 = -5 <=> a = -5 + 1 = -4

b-a = 33

-b = -29 <=> b = 29

So

[tex]\boxed{ \ p(x)=(x-1)(x^2-4x+29) \ }[/tex]

Now, we need to find the zeroes of the second factor, meaning finding x so that:

[tex]x^2-4x+29=0 \ \text{ complete the square, 29 = 25 + 4} \\ \\ <=> x^2-2\cdot 2 \cdot x+2^2+25=0 \\ \\ <=>(x-2)^2=-25=(5i)^2 \ \text{ take the root } \\ \\<=>x-2=\pm 5i \ \text{ add 2 } \\ \\ <=> x = 2+5i \ \text{ or } \ x = 2-5i[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

Step-by-step explanation:

The formula for calculating the margin of error is expressed as;

[tex]M.E = z * \sqrt{\frac{p*(1-p)}{n} }[/tex] where;

z is the z-score at 95% confidence = 1.96 (This is gotten from z-table)

p is the percentage probability of those that watched network news

p = 40% = 0.4

n is the sample size = 300

Substituting this values into the formula will give;

[tex]M.E = 1.96*\sqrt{\frac{0.4(1-0.4)}{300} }\\ \\M.E = 1.96*\sqrt{\frac{0.4(0.6)}{300} }\\\\\\M.E = 1.96*\sqrt{\frac{0.24}{300} }\\\\\\M.E = 1.96*\sqrt{0.0008}\\\\\\M.E = 1.96*0.02828\\\\M.E \approx 0.05543[/tex]

Hence, the margin of error for this survey if we want 95% confidence in our estimate of the percent of T.V. viewers who watch network news programs is approximately 0.05543

Answer:

-3,-4,-5

Step-by-step explanation:

those are all numbers less than -2! your welcome! please give me brainliest!

Answer: -3, -16, and -642,000

Step-by-step explanation: In this problem, we're asked to state three solutions for the following inequality, x < -2.

The inequality x < -2 means that any number

less than -2 is a solution to the inequality.

For example, -3 is a solution because -3 is less than -2.

Another solution would be -16 because -16 is less than -2.

One other solution would be -642,000 because it's less than -2.

It's important to understand that these are only 3 possible

answers and there are many answers to choose from.

Step-by-step explanation:

Put A = 2, B = 3, C = 9 and D = 15 to the given expressions.

Use PEMDAS.

-A + C - (D : B)

-2 + 9 - (15 : 3) = -2 + 9 - 5 = 7 - 5 = 2

B × (-C) - (-D) + A

3 × (-9) - (-15) + 2 = -27 + 15 + 2 = -12 + 2 = -10

(C + D) : B + A

(9 + 15) : 3 + 2 = 24 : 3 + 2 = 8 + 2 = 10

D : B + A - C

15 : 3 + 2 - 9 = 5 + 2 - 9 = 7 - 9 = -2

Answer:

20*

Step-by-step explanation:

Your welcome plz mark me the brainlist

Answer:

20

Step-by-step explanation:

The number 3 will appear in the numbers 3, 13, 23, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 43, 53, 63, 73, 83, 93. In these numbers it appears 20 times.

First, let's figure out the pattern that this series follows. We can see that the first number is increased by 1/2 to get to 2 1/2. Then, the second number is decreased by 1 to get to 1 1/2. Finally, the pattern repeats.

So, let's apply this pattern to find the next number in this series.

2, 2 1/2, 1 1/2, 2, 1

The next number in this series is 1.

Hope this helps!! :)

Answer:

13 in.

Step-by-step explanation:

Theorem:

The segment that joins the midpoints of two sides of a triangle is parallel to the third side and half the length of the third side.

Each side of triangle MNK has as endpoints two midpoints of sides of triangle ABC, so each side of triangle MNK is half the length of a side of triangle ABC.

p = 26 in./2 = 13 in.

Answer:

5

Step-by-step explanation:

According to the given question, the calculation of number is shown below:-

Let the number be x.

[tex]\frac{1}{10}[/tex] of x will be added to the number of 2, so that the result is half of x.

[tex]2 + \frac{1}{10} x = \frac{1}{2} x[/tex]

Now we will solve the above equation

[tex]2=\frac{1}{2} x-\frac{1}{10} x\\\\2=\frac{2x}{5}\\\\10=2x\\\\\frac{10}{2} =x\\\\[/tex]

x = 5

Therefore the correct answer is 5

Hence, the number based on the given information provided in the question is 5

Answer:

The effective yield is 2.269% to the thousandth.

Step-by-step explanation:

Effective annual yield compounded quarterly, given API

(1+API/4)^4 - 1

= (1+0.0225/4)^4 - 1

= 0.022691

Answer: Smokers pay less attention to driving while trying to light a cigarette.

Step-by-step explanation:

( A ) reasons for, why the given statement was misleading.

Following are the reasons for accidents

(i) Drunk Driving.

(ii) Driving during the night.

(iii) Smoking.

(iv) Unsafe lane changes.

(v) Driving the wrong way.

(vi) Bad weather e.g fog.

From the list above, it is shown that, smoking is also one of the major cause of car accidents on the roads.

( B.) Smokers tends to pay less attention to driving why trying to light a cigarette.

Answer:

The simple pendulum should be 15.9 m long.

Step-by-step explanation:

Approximately (for small amplitudes), the period of a simple pendulum is

T = 2*pi * sqrt (L/g), L=length

using pi = 22/7, and g=9.8 m/s^2

8 = 2* 22/7 * sqrt(L/9.8)

solve for L

L = (8*7/(2*22))^2 * 9.8

= 15.874 m

That's quite a long pendulum!

Answer:

-11/24

Step-by-step explanation:

5/12 - 7/8

We need to get a common denominator of 24

5/12 *2/2  - 7/8 *3/3

10/24 - 21/24

-11/24

Answer:

-11/24

Step-by-step explanation:

Well to solve 5/12 - 7/8 we need to find the LCM.

12 - 12, 24, 36, 48

8 - 8, 16, 24, 32, 40

So the LCM is 24.

Meaning we need to make both denominators 24.

12*2 = 24 5*2 = 10

10/24

8*3 = 24 7*3 = 21

21/24

10/24 - 21/24

= -11/24

Thus,

the answer is -11/24.

Hope this helps :)

Answer:

27°

Step-by-step explanation:

D is 72° because it alternates with B, alternate angles are equal.

2x+72°+2x= 180° because it is a straight line.

4x+72°=180°

4x=108°

x=27°

Answer:

See below.

Step-by-step explanation:

[tex]f(x)=-7x^2-x\\g(x)=9x^2-4x\\(f-g)(x)=f(x)-g(x)\\(f-g)(x)=(-7x^2-x)-(9x^2-4x)\\(f-g)(x)=-7x^2-x-9x^2+4x\\(f-g)(x)=-16x^2+3x\\\\(f-g)(1)=-16(1)^2+3(1)\\(f-g)(1)=-16+3=-13[/tex]

Answer:

1/5

Step-by-step explanation:

B, C, D, E, F, G, H, I, J,  K. = 10 tiles

E and I are vowels

P ( vowel) = vowels/ total

                =2/10

                = 1/5

In total, we are given 10 letters.

The vowers are; A, E, I, O, and U

In the bag, we can see we have 2 vowels (E and I)

This means that 2 out of the 10 letters are vowels (2/10).

We can simplify the fraction by dividing by 2.

2÷2/10÷2

1/5

Therefore, the answer is 1/5.

Best of Luck!

Answer:

 [tex]r => (\neg q \ \lor p) \ \equiv \ q \ \land \ \neg p => \neg r[/tex]

Step-by-step explanation:

In general, remember that the converse of    [tex]a => b[/tex]       is     [tex]\neg b => \neg a[/tex] , therefore in this case  [tex]a = r \ \ , b = \neg q \ \lor p[/tex]

so   [tex]r => (\neg q \ \lor p) \ \equiv \ q \ \land \ \neg p => \neg r[/tex]

Answer: Diverging

Step-by-step explanation:

Find explanations in the attached file

Answer:

B y ≥ 4x + 2

Step-by-step explanation:

1. find slope of the line: (y² - y¹) / (x² - x¹)

(0, 2) and (-1, -2)

(-2 - 2) / (-1 - 0) = -4 / -1 = 4

y = 4x + 2*

*+2 because that is the y-intercept as shown by point (0, 2)

2. the line is solid, therefore the inequality is ≤ or ≥. dashed line would mean < or >

3. the shaded region is on the right side of the line, so the values are greater than. therefore, you use ≥

4. final equation: y ≥ 4x + 2

Answer:

Hey there!

The cross section would be a rectangle. No matter where you cut the figure parallel to the base, the cross section would be a rectangle.

Let me know if this helps :)

Answer: Rectangle

Step-by-step explanation:

In a rectangular prism, every cross-section parallel to a side is a rectangle.

Hope it helps <3

Answer:

A : 10

Step-by-step explanation:

Answer:

the correct answer is 12

Step-by-step explanation:

6/8=9/x

cross multiply

6x=72

divide by six

x=12

The correct statement about the line segment is,

⇒ the segment DE bisects segment AC.

Line segment is a part of the line which have two endpoints and bounded by two distinct end points and contain every point on the line which is between its endpoint.

Given that;

Triangle ABC is shown in figure.

Now, We can see that;

⇒ AE = EC

Hence, the segment DE bisects segment AC.

Thus, The correct statement about the line segment is,

⇒ the segment DE bisects segment AC.

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