when the function p(x) is divided by x - 1 the quotient is x^2 + 7 + 5/x - 1. State P(x) in standard form.

Answer:

a = 1 and b = 2

Step-by-step explanation:

Using the Quotient Rule>

d/dx[(sin x)/(2+cos x) ]

=   [(2 + cos x) * cosx -  sin x * - sin x)]  /  (2 + cos x)^2

= 2cos x + cos^2x + sin ^2 x) /  (2 + cos x)^2

But cos^2x + sin^2x = 1 so we have:

(1 +  2 cos x)  /   (2 + cos x)^2

- so a = 1 and b = 2.

Answer:

Area [tex]=62.5\sqrt{6}[/tex] square units

[tex]AB=5\sqrt{15}[/tex] units

[tex]BC=5\sqrt{10}[/tex] units

Step-by-step explanation:

In a right triangle the altitude drawn to the hypotenuse is the geometric mean of the segments at which this altitude divides the hypotenuse.

So,

[tex]BD^2=15\cdot 10\\ \\BD^2=150\\ \\BD=\sqrt{150}=5\sqrt{6}\ units[/tex]

a. The area of the triangle ABC is

[tex]A_{ABC}=\dfrac{1}{2}\cdot BD\cdot AC=\dfrac{1}{2}\cdot 5\sqrt{6}\cdot (15+10)=\dfrac{125\sqrt{6}}{2}=62.5\sqrt{6}\ un^2.[/tex]

b. The legs of the right triangle are geometric means of the segment adjacent to this leg and the hypotenuse, so

[tex]AB^2=AD\cdot AC=15\cdot 25\Rightarrow AB=5\sqrt{15}\ units\\ \\BC^2=CD\cdot AC=10\cdot 25\Rightarrow BC=5\sqrt{10}\ units[/tex]

Answer:

2d(d³-9d-30)

Step-by-step explanation:

2d⁴ - 6d - 18d² - 54d

= 2d⁴- 18d²-60d

=2d(d³-9d-30)

Answer:

B seems right

Step-by-step explanation:

Answer: [tex]6y^2i\sqrt{6}[/tex]

Step-by-step explanation:

For this exercise it is important to remember the following property:

[tex]\sqrt[n]{a^n}=a^{({\frac{n}{n})}}=a[/tex]

Then, given the expression:

[tex]\sqrt{-216y^4}[/tex]

You can follow these steps in order to simplify it:

1. Descompose 216 into its prime factors:

[tex]216=2*2*2*3*3*3[/tex]

2. The Product of powers property states that:

[tex](a^m)(a^n)=a^{(m+n)}[/tex]

Then:

 [tex]216=2^2*2*3^2*3[/tex]

3. Now you can substitute:

[tex]=\sqrt{-2^2*2*3^2*3*y^4}[/tex]

4. Finally, substituting [tex]\sqrt{-1}=i[/tex] and simplifying, you get:

[tex]=2*3*y^2i\sqrt{2*3}=6y^2i\sqrt{6}[/tex]

Answer:

y<x+1      y>x-2

Step-by-step explanation:

upper line: (0,1) (-1,0)

y=x+1

Lower line: (0,-2) (2,0)

y=x-2

I did not see any solid boundry on the line

Shaded: y<x+1      y>x-2

Answer:

[tex]y <x+1[/tex]

[tex]y>x-2[/tex]

Step-by-step explanation:

According to the graph, the system is formed by two inequalities. Let's find out the equation to each line in first place.

Notice that the upper line passes through points (-1,0) and (0,1). First, we find its slope

[tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }=\frac{1-0}{0-(-1)}=\frac{1}{1}=1[/tex]

Then, we use the point-slope formula to find the equation

[tex]y-y_{1} =m(x-x_{1} )\\y-0=1(x-(-1)\\y=x+1[/tex]

Now, the dashed line indiactes that the inequalities must have sings < or >.

Notice that point (0,0) is part of its solution, that means the inequality is

[tex]y <x+1[/tex]

We do the same process to find the other inequality.

The line passes through points (0,-2) and (2,0).

[tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }=\frac{0-(-2)}{2-0}=\frac{2}{2}=1[/tex]

Then,

[tex]y-y_{1} =m(x-x_{1} )\\y-0=1(x-2)\\y=x-2[/tex]

Notice that point (0,0) is part of its solution, so the inequality is

[tex]y>x-2[/tex]

Therefore, the system of inequalities is

[tex]y <x+1[/tex]

[tex]y>x-2[/tex]

Answer:

[tex]d < 20\ donuts[/tex]

The graph of the solution set in the attached figure

Step-by-step explanation:

 Let

d ----> the possible number of donuts Monica brought

we know that

The number of donuts d multiplied by $0.50 plus the cost of a box of coffee for $5 must be less than $15

so

The inequality that represent this situation is

[tex]0.50d+5 < 15[/tex]

Solve for d

subtract 5 both sides

[tex]0.50d < 15-5[/tex]

[tex]0.50d < 10[/tex]            

Divide by 0.50 both sides

[tex]d < 10/0.50[/tex]      

[tex]d < 20\ donuts[/tex]

The solution is all whole numbers greater than zero and less than 20 ( I say greater than zero because the problem states that Monica brought some donuts)

The solution set is the interval {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19}

Answer:

multiplicative identity

Step-by-step explanation:

Anything that is divisible by 0 or 1  is called multiplicative identity.

Final answer:

Without knowing the individual prices of small and large candles, we cannot solve for the exact numbers of each type sold. A system of equations would normally be used, but in this case, essential price information is missing.

Explanation:

You sell small and large candles at a craft fair and collect $144 selling a total of 28 candles. To solve how many of each type of candle you sold, let's set up a system of equations with two variables. Let x represent the number of small candles and y represent the number of large candles.

The first equation comes from the total number of candles:

x + y = 28

The second equation involves the total amount of money collected:

ax + by = 144

where a and b are the prices of small and large candles respectively.

Unfortunately, the question does not provide the individual prices of the small and large candles, so we cannot continue without that information. To solve this system correctly, you would need to know the price of at least one type of candle.

With the missing price information, we cannot define a and b and therefore cannot provide a numerical solution to this question.

The measure of m∠J=90°, m∠G=55° and m∠H=35°

Step-by-step explanation:

Inscribed angles subtended by a diameter are right angles. Hence angle GJH =90°

The diameter GH and chord GJ intercepts an arc with a measure of 70°.The measure of an arc of a circle is equal to the measure of the central angle that intercepts the arc. Hence angle GOJ=70°. Radius of circle GO=OJ, which means triangle GOJ is an isosceles triangle thus ∠OJG=∠OGJ =(180° -70°) /2 = 55°. m∠G=55°

m∠H = (180°-(90°+55°) ) = 180° - 145° =35°

Learn More

Angles subtended by a diameter :https://brainly.com/question/10345730

Keywords : measures, angles, diameter, chord, intercepts, arc

#LearnwithBrainly

Answer:

x=-7/9, y=4/3. (-7/9, 4/3).

Step-by-step explanation:

6x+2y=-2

3x-2y=-5

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

9x=-7

x=-7/9

6(-7/9)+2y=-2

-42/9+2y=-2

2y=-2-(-42/9)

2y=-2+42/9

2y=-18/9+42/9

2y=24/9

y=(24/9)/2

y=(24/9)(1/2)

y=24/18

y=4/3

Final answer:

To find the number of defective computer chips the company would expect out of the 36,000 chips they make each year, we can set up a proportion: 22 defective chips / 600 chips = x defective chips / 36,000 chips. Dividing both sides by 600, we find that x = 1,320. Therefore, we would expect approximately 1,320 of the 36,000 computer chips the company makes each year to be defective.

Explanation:

To find the number of defective computer chips the company would expect out of the 36,000 chips they make each year, we can set up a proportion:

22 defective chips / 600 chips = x defective chips / 36,000 chips

Cross-multiplying, we get 600x = 22 * 36,000

Dividing both sides by 600, we find that x = 22 * 36,000 / 600 = 1,320

Therefore, we would expect approximately 1,320 of the 36,000 computer chips the company makes each year to be defective.

Answer: 36 cm

Step-by-step explanation:

Given : The square has a perimeter =160 cm.

Perimeter of square = 4 (side)

Therefore , the side of square = (Perimeter)÷ 4

= 160 ÷ 4 = 40 cm

The new length of side after dilation = (Scale factor) x (Length of original figure)

For scale factor = 0.9

The new length of each side of the dilated square = (0.9)x(40)=36 cm

Hence, the new length of each side of the dilated square=  36 cm

Answer:

36cm

Step-by-step explanation:

Given: The square has a perimeter of [tex]160\text{cm}[/tex] ,the square is dilated with a scale factor of [tex]0.9[/tex].

To Find: length of each side of the dilated square.

Solution:

Perimeter of square  [tex]=160\text{cm}[/tex]

length of each side of perimeter  [tex]=\frac{\text{perimeter of square}}{4}[/tex]

                                                       [tex]=40\text{cm}[/tex]

Now,

the square is dilated by scale factor  [tex]0.9[/tex]

new perimeter of square   [tex]=\text{old perimeter}\times\text{scale factor}[/tex]

                                           [tex]=160\times0.9[/tex]

                                           [tex]=144\text{cm}[/tex]

new length of each side of square [tex]=\frac{\text{perimeter}}{4}[/tex]

                                                         [tex]=\frac{144}{4}[/tex]

                                                         [tex]=36\text{cm}[/tex]

Hence the length of each side of dilated square is [tex]36\text{cm}[/tex]

10 small boxes and 11 large boxes were shipped.

Step-by-step explanation:

Given,

Total boxes shipped = 21

Total volume of shipped boxes = 342 cubic feet

Volume of each small box = 10 cubic feet

Volume of each large box = 22 cubic feet

Let,

Number of small boxes = x

Number of large boxes = y

According to given statement;

x+y=21     Eqn 1

10x+22y=342    Eqn 2

Multiplying Eqn 1 by 10

[tex]10(x+y=21)\\10x+10y=210\ \ \ Eqn\ 3[/tex]

Subtracting Eqn 3 from Eqn 2

[tex](10x+22y)-(10x+10y)=342-210\\10x+22y-10x-10y=132\\12y=132[/tex]

Dividing both sides by 12

[tex]\frac{12y}{12}=\frac{132}{12}\\y=11[/tex]

Putting y=11 in Eqn 1

[tex]x+11=21\\x=21-11\\x=10[/tex]

10 small boxes and 11 large boxes were shipped.

Keywords: linear equation, subtraction

Learn more about linear equations at:

#LearnwithBrainly

The cost of one peppermint cookie is $0.60 and cost of one cinnamon sugar cookie is $0.30

Step-by-step explanation:

Let,

Cost of 1 peppermint cookie = x

Cost of 1 cinnamon cookie = y

According to given statement;

120x+30y=81     Eqn 1

70x+60y=60     Eqn 2

Multiplying Eqn 1 by 2

[tex]2(120x+30y=81)\\240x+60y=162\ \ \ Eqn\ 3[/tex]

Subtracting Eqn 2 from Eqn 3

[tex](240x+60y)-(70x+60y)=162-60\\240x+60y-70x-60y=102\\170x=102\\[/tex]

Dividing both sides by 170

[tex]\frac{170x}{170}=\frac{102}{170}\\x=0.60[/tex]

Putting x=0.60 in Eqn 2

[tex]70(0.60)+60y=60\\42+60y=60\\60y=60-42\\60y=18[/tex]

Dividing both sides by 60

[tex]\frac{60y}{60}=\frac{18}{60}\\y=0.30[/tex]

The cost of one peppermint cookie is $0.60 and cost of one cinnamon sugar cookie is $0.30

Keywords: linear equation, elimination method

Learn more about elimination method at:

#LearnwithBrainly

Answer:

The equation which has ONLY two solution x = 3 and x = -3 is [tex]P(x)  = x^2 - 9[/tex]

Step-by-step explanation:

Here, the ONLY two rrots of the equation is given as:

x =  3 and x = -3

Now, if x = a is the ZERO of the polynomial, then x  - a  = 0 is the ROOT of the polynomial.

So, here the only roots of the polynomial are : (x-3) and (x+3)

Also, the POLYNOMIAL = PRODUCT OF ALL ROOTS

So, [tex]P(x) = (x-3)(x+3)    = x(x+3) -3(x+3)  = x^2 + 3x - 3x - 9  = x^2 - 9\\\implies P(x)  = x^2 - 9[/tex]

Hence, the equation which has ONLY two solution x = 3 and x = -3 is [tex]P(x)  = x^2 - 9[/tex]

The equation has only two solution x = 3 and x = -3 is [tex]x^2-9[/tex].

We have to determine, the equation which has only two solutions x  = 3 and x = -3.

According to the question,

The two roots of the equation is x = 3 and x = -3,

if x = a is the zero of the polynomial, then x - a  = 0 is the root of the polynomial.

So, here the only roots of the polynomial are : (x-3) and (x+3).

If the [tex]\alpha[/tex] and [tex]\beta[/tex] are the roots of the equation the product of roots can be written as,

[tex]Product \ of \ roots = \alpha \times \beta[/tex]

Substitute the values in the equation,

[tex]= (x-3 ) (x+3)\\\\= x (x+3) - 3(x+3)\\\\= x^2 + 3x -3x -9\\\\= x^2 - 9[/tex]

Hence, The required equation has only two solution x = 3 and x = -3 is [tex]x^2-9[/tex].

To know more about Quadratic Equations click the link given below.

https://brainly.com/question/437300

Answer:

The correct answer is C. 5⁶

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Number of hens in a bird enclosure = (5³)² * 5⁰

2. What is the total number of hens in the enclosure?

Let's recall a couple of properties of the exponents:

1. When you raise any number to a zero power you'll always get 1, with the exception of zero itself.

x⁰ = 1, x ≠ 0

2. The power of a power property says that to calculate a power of a power you just have to multiply the exponents, this way:

(x⁴)⁵ = x ⁴°⁵ = x²⁰

Now, applying those two properties, we have:

(5³)² * 5⁰ = 5³°² * 1 = 5⁶

The correct answer is C. 5⁶

Answer:

c

Step-by-step explanation:

Answer:

90% of the questions she answered correctly

Step-by-step explanation:

%age = 81/90 * 100= 90 % correctness

Answer:

Step-by-step explanation:

5p + 2(p + 4) .......because pencil cases (p) sell for 5 bucks a piece....and mechanical pencils (p + 4), sell for 2 bucks a piece. She is basically selling 4 more mechanical pencils then she is pencil cases.

Answer: The graph is attached.

Step-by-step explanation:

The equation of the line in Slope-Intercept form is:

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

Where "m" is the slope and "b" is the y-intercept.

So, having the first equation:

[tex]y=- 6x - 2[/tex]

You can identify that:

[tex]m=-6\\b=-2[/tex]

 By definition, the line intersects the x-axis when [tex]y=0[/tex]. Subsituting this value into the equation and solving for "x", you get that the x-intercept is the following:

[tex]0=- 6x - 2\\\\2=-6x\\\\x=-\frac{1}{3}\\\\x=-0.333[/tex]

Now you can graph the line.

Now you must solve for "y" from the second equation:

[tex]y +2=- 6x\\\\y=-6x-2[/tex]

 You can identify that:

[tex]m=-6\\b=-2[/tex]

Notice that the slopes and the y-intercepts of the first line and the second line are equal; this means that they are exactly the same line and the System of equations  has Infinitely many solutions.

See the graph attached.

Answer:

a

Step-by-step explanation:

Answer:

y = -x

Step-by-step explanation:

Explained in picture:

SORRY IF INCORRECT!!!!!

Answer:

three angles measuring 109º, 25º, and 145º cannot create a triangle

three angles measuring 40º, 70º, and 65º cannot create a triangle

Step-by-step explanation:

Verify each dimensions

Part 1) three angles measuring 109º, 25º, and 145º

Remember that the sum of the interior angles of a triangle must be equal to 180 degrees

In this problem we have

[tex]109^o+25^o+145^o=279^o[/tex]

[tex]279^o> 180^o[/tex]

therefore

three angles measuring 109º, 25º, and 145º cannot create a triangle

Part 2) three sides measuring 9 m, 15 m, and 9 m

we know that

The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side

Applying the triangle inequality theorem

1) 9+15 > 9 ---> is ok

2) 9+9 > 15 ---> is ok

therefore

three sides measuring 9 m, 15 m, and 9 m can create a triangle

Part 3) three angles measuring 40º, 70º, and 65º

Remember that the sum of the interior angles of a triangle must be equal to 180 degrees

In this problem we have

[tex]40^o+70^o+65^o=175^o[/tex]

[tex]175^o< 180^o[/tex]

therefore

three angles measuring 40º, 70º, and 65º cannot create a triangle

Part 4) three sides measuring 6 cm, 8 cm, and 10 cm

we know that

The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side

Applying the triangle inequality theorem

1) 6+8 > 10 ---> is ok

2) 8+10 > 6 ---> is ok

3) 6+10 > 8 ---> is ok

therefore

three sides measuring 6 cm, 8 cm, and 10 cm can create a triangle

Answer:

its c i promise

Step-by-step explanation:

Answer:

The number of bricks a truck can carry in full load is 308 .

Step-by-step explanation:

Given as :

The weight of each brick = 4 pounds and 14 ounce

The total load a truck can carry = [tex]\dfrac{3}{4}[/tex]  tons

Let The number of bricks truck can carry = n bricks

Now, According to question

∵ 1 ounce = 0.0625 pounds

∴ 14 ounce = 0.0625 × 14 = 0.875 pounds

So, Total weight of each brick = 4 pounds + 0.875 pounds = 4.875 pounds

Again

∵ 1 pound = 0.0005 tons

∴ 4.875 pounds =  0.0005 × 4.875 = 0.0024375 tons

Now, Again

The total load a truck can carry = [tex]\dfrac{3}{4}[/tex] tons = 0.75 tons

And The weight of each brick = 0.0024375 tons

So, The number of bricks = [tex]\dfrac{\textrm total load a truck can carry}{\textrm Total weight of each brick}[/tex]

I.e n = [tex]\dfrac{0.75}{0.0024375}[/tex]

∴ n = 307.69 ≈ 308

So, The number of bricks can truck carry = n = 308

Hence, The number of bricks a truck can carry in full load is 308 . Answer

Answer:

I'm guessing none because the discrimant (sqrt of b squared - 4ac is less than zero, signifying it has no real roots

Step-by-step explanation:

have a happy holidays!

Answer: 5 Kilometers Per Hour

Answer:

1/12 km per minute

Step-by-step explanation:

1 hour=60 minutes

5/60=1/12

Answer:

circumference of a circle = 2πr

                                            = 2×22/7×7

                                            = 44/7×7

                                            = 308/7

                                            = 44 inches

Answer:

D. $23

Step-by-step explanation:

To find the answer, find how much a can costs at that rate and multiply it by 10.

This would be

10 × 6. 90/3=69. 0/3

=23

If you don't understand anything, ask.

Answer:

x=30

Step-by-step explanation:

ratio: 8:10 as 24:x

8/10=24/x

10x * 8/10= 10x * 24/x

x * 8 = 10 * 24

8x = 240

8x/8 = 240/8

8x/8 = 30

x = 30

Answer: Option 3, and 4

Answer:

The actual length of car is 48 feet.

Step-by-step explanation:

Given:

Tiffany sketched a picture of a car she used the scale 2 inches : 12 feet.

In her sketch the car is 8 inches long.

Now, to find the length in feet of the actual car.

Let the actual length of car in feet be [tex]x\ feet.[/tex]

And the length of car in her sketch is 8 inches.

So, the ratio of the scale used by Tiffany as given is 2 inches : 12 feet.

Now, to get the actual length of car by using cross multiplication method:

[tex]\frac{2\ inches}{12\ feet} =\frac{8\ inches}{x\ feet}[/tex]

⇒ [tex]\frac{2}{12} =\frac{8}{x}[/tex]

By cross multiplying we get:

⇒ [tex]2x=96[/tex]

Dividing both sides by 2 we get:

⇒ [tex]48=x[/tex]

⇒ [tex]x=48\ feet.[/tex]

Therefore, the actual length of car is 48 feet.