-18u+16u-7=9 solve for u

Answer:

x^3 - 3x^2 - 3x + 9 + (-36/(x+3))

OR

x^3 - 3x^2 - 3x + 9 - (36/(x+3))

Step-by-step explanation:

First set the divisor equal to 0:

x + 3 = 0

Subtract 3 from both sides

x = -3

This is what you'll divide the dividend by in synthetic division.

Take the coefficents of each term in the dividend. Do not forget the 0 placeholders:

x^4 + 0x^3 - 12x^2 + 0x -9

Coefficents: 1. 0.  -12. 0 -9.

Please see the image for the next steps.

The remainder is -36. Put the remainder over the divisor and add it to the polynomial (shown in image)

-36/(x+3)

Divide using synthetic division the remainder is -36. Put the remainder over the divisor and add it to the polynomial -36/(x+3).

First set the divisor equal to 0:

x + 3 = 0

Subtract 3 from both sides

x = -3

This is what you'll divide the dividend by in synthetic division.

Take the coefficents of each term in the dividend. Do not forget the 0 placeholders:

[tex]x^4 + 0x^3 - 12x^2 + 0x -9[/tex]

Coefficents: 1. 0.  -12. 0 -9.

The remainder is -36. Put the remainder over the divisor and add it to the polynomial -36/(x+3).

The first link is for the first question, and the second one is to the second question I hope this helps!

Answer:

Andrew did not reason that he could save the $10 per hour he would make cutting lawns by preparing his own meal

Step-by-step explanation:

If Andrew cuts lawns for $10 per hour, he would have $4 more to save by preparing his own meal rather than spending the $4 at Taco Bell

Answer:

Instead of spending time making food, he drives and buys food by a total of $4.

Now, he is not considerating the amount of gas that he is spending by going to buy food and returning.

Also, he was not working, so he is not producing money at the beginning, so making his own lunch actually does not implies that he stops working and loses money.

Polar form: (r,θ)

Using these formulas:

x²+y²=r²

tan(θ)=y/x

We have the point (1,1) in cartesian coordinates. We need to find r and θ to get it in polar form.

r²=1²+1²

r²=2

r=±√2

tan(θ)=1/1

tan(θ)=1

θ=π/4 radians or 45 degrees

Polar coordinates: (√2,π/4)

Those answer choices look strange. Are you sure these are the right answer choices?

Answer:

Step-by-step explanation:

The way I see it, (1, 1) corresponds to a point which is √2 units from the origin and has an angle of 45° (or π/4 radians).

Answer:

5

Step-by-step explanation:

1.24 times 3 = 3.72

.95 (the value of pence to a pound in decimal form) = 2.85

6.18 for the teapot

2.72+2.85+6.18=11.75

She now has £8.25 left (20-11.75).

8.25/1.57=the amount of plates she can buy: 5.25477707006, so 5 with some money left

Answer: [tex]S_{29}[/tex] = 2001

Step-by-step explanation:

Since the sequence is an arithmetic sequence , it means that a common difference must exist.

Let the terms in the sequence be [tex]T_{1}[/tex] , [tex]T_{2}[/tex] , [tex]T_{3}[/tex] , [tex]T_{4}[/tex] , ...

Then common difference = [tex]T_{2}[/tex] - [tex]T_{1}[/tex] = [tex]T_{3}[/tex] - [tex]T_{2}[/tex] = 8

That is , the common difference (d) = 8

The formula for calculating sum of  n terms is given by :

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

Where ;

n = number of terms

a = first term

d = common difference

From the question :

n = 29

a = -43

d = 8

Substituting into the formula , we have

[tex]S_{29}[/tex] = [tex]\frac{29}{2}[/tex] [ 2{-43} + (29-1)(8) ]

[tex]S_{29}[/tex] = [tex]\frac{29}{2}[/tex] (-86 +224)

[tex]S_{29}[/tex] = [tex]\frac{29}{2}[/tex] ( 138)

[tex]S_{29}[/tex] = [tex]\frac{4002}{2}[/tex]

[tex]S_{29}[/tex] = 2001

First, do distributive property:

2(5+3x)+(x+10)  Distribute the 2 to the 5 and the 3x; multiply them

10+6x+x+10      Since (x+10) would be 1 times x and 10, it's just x+10

Then, do communitive property:

10+6x+x+10     What we found in the last step, now combine the like terms

20+7x              This is what you get since 10+10=20 and 6x+x=7x

The answer:

20+7x or 7x+20

Hope that helps!

25 cakes can be completely decorated using 4 gallons of icing.

Step-by-step explanation:

Given:

4 gallons of icing

16 cups =1 gallon

No. of icing cups = [tex]4\times16[/tex] cups

       =64 cups

No. of cups required to decorate and frost a cake= 4% of total no. of icing cups

          = [tex]\frac{(4\times64)}{100}[/tex]

          = 2.56

2.56 cups of icing is required to decorate each cake.

Maximum no. of cakes decorated = [tex]\frac{ (64\times1)}{2.56}[/tex]

                    = 25

25 cakes can be completely decorated using 4 gallons of icing.

Answer:

B. 3x² – 10x + 13

Step-by-step explanation:

given:

f(x) = 3x² – 8x + 5

g(x) = 2x – 8

f(x) - g(x)

= (3x² – 8x + 5) - (2x – 8)

= 3x² – 8x + 5 - 2x + 8

= 3x² – 10x + 13

Answer:

∠ZPB and ∠APZ are two adjacent supplementary angles

Step-by-step explanation:

we know that

Two angles are Adjacent when they have a common side and a common vertex

Two angles are supplementary if their sum is equal to 180 degrees

In this problem we have that

[tex]m\angle ZPB=90^o[/tex] ----> given problem

[tex]m\angle APZ=90^o[/tex] ----> given problem

so

[tex]m\angle ZPB+m\angle APZ=180^o[/tex]

∠ZPB and ∠APZ are supplementary angles

and

∠ZPB and ∠APZ have a common side (ZP) and a common vertex (P)

therefore

∠ZPB and ∠APZ are two adjacent supplementary angles

Answer: ∠ZPB and ∠APZ are two adjacent supplementary angles

Step-by-step explanation: Its the way the cookie crumbles.

Answer:

2.133333

Step-by-step explanation:

He didn't simplify it

Answer:

Step-by-step explanation:

She might have not moved the decimal point in the right direction/right spaces

Good evening ,

Answer:

Look at the photo below for the Answer.

:)

Answer:

431547619  / 12500000000

0.03452380 …

Step-by-step explanation:

Both are the simplified versions of 3452380952/100000000000.

The answer above is also correct! I hope this helps you!

- sincerelynini

Answer:

9 pizzas

Step-by-step explanation:

Maria is planning a party. She should order 3 pizzas for every 7 people. Let x be the number of pizzas Maria will order for 21 people, then

3 pizzas - 7 people

x pizzas - 21 people

Write a proportion:

[tex]\dfrac{3}{x}=\dfrac{7}{21}[/tex]

Cross multiply:

[tex]7\cdot x=21\cdot 3\\ \\7x=63\\ \\x=\dfrac{63}{7}=9\ pizzas[/tex]

Final answer:

To maintain the same weekly revenue after reducing her pot price from $24 to $16, a potter working 4 days a week must increase her daily production from 14 pots to 21 pots, which is an increase of 7 pots per day.

Explanation:

The question involves a potter who initially makes 14 pots per day and works 4 days a week, charging $24 per pot. To find out by how many pots per day she must increase her production after lowering her price to $16 per pot, to make the same amount of money, we first calculate her current weekly revenue:

After reducing the price to $16 per pot, we need to determine how many pots per day she needs to sell to maintain the same weekly revenue of $1,344:

Therefore, she needs to sell 7 more pots per day (21 pots - 14 pots) to maintain her weekly revenue.

Answer:

C

Step-by-step explanation:

Answer:

12/5-2p

Step-by-step explanation:

2/5(6-5p)

12/5-10/5p

12/5-2p

The simplified form of the expression 2/5 (6 -5p) is 12 / 5 - 2p.

An algebraic expression is consists of variables, numbers with various mathematical operations,

The given expression is,

2/5 (6 -5p)

Simplify the expression by solving bracket term,

(2/5) x 6 - (2/5) x 5p

12 / 5 - 2p

The simplified form of the expression 2/5 (6 -5p) is 12 / 5 - 2p.

To know more about Algebraic expression on:

https://brainly.com/question/19245500

#SPJ3

Answer: [tex]4\ feet[/tex]

Step-by-step explanation:

The exercise provides you the following Quadratic function:

[tex]h(t)=4+60t-16t^2[/tex]

You know that it represents the height (in feet) of the ball as a function of the time (in seconds) since the ball hit the bat.

Based on this, you can conclude that when the ball strikes the bat the time in seconds is:

[tex]t=0[/tex]

Therefore, in order to calculate the height in feet of the ball when it strikes the bat, you need to subsititute [tex]t=0[/tex] into the function and    then evaluate.

So, you get:

 [tex]h(0)=4+60(0)-16(0)^2\\\\h(0)=4[/tex]

8 litres (amount of 20% solution needed) and 7 litres for (amount of 50% solution needed)

Step-by-step explanation:

Let consider ‘x’ for 20% acid solution and (15 – x) for 50% acid solution. And so, the equation would be as below,

                         20% in x + 50% in (15 – x) = 15 litres of 34%

Convert percentage values, we get

                              0.20(x) + 0.50 (15 – x) = 15 (0.34)

                              0.20 x + 7.5 – 0.50 x = 5.1

                              -0.3 x + 7.5 = 5.1

                              0.3 x = 7.5 – 5.1

                              0.3 x = 2.4

[tex]x = \frac{2.4}{0.3} = 8 litres (amount of 20 \% solution needed)[/tex]

Apply ‘x = 8’ value in (15 – x) we get,

                         15 – 8 = 7 litres

The value of 7 litres for (amount of 50% solution needed)

Answer:

D

Step-by-step explanation:

The diagram shows Pascal's triangle. Pascal's triangle is a triangular array of the binomial coefficients.

The entry in the [tex]n^{th}[/tex] row (start counting rows from 0) and [tex]k^{th}[/tex] column (start counting columns from 0) of Pascal's triangle is denoted by

[tex]C^n_k=\left(\begin{array}{c}n\\ k\end{array}\right)[/tex]

Coefficient 20 stands in 6th row, then n = 6 and in 3rd column, so k = 3.

Hence,

[tex]20=C^6_3=\left(\begin{array}{c}6\\ 3\end{array}\right)=\dfrac{6!}{3!(6-3)!}[/tex]

Answer:

The solution of the inequality is:

[tex]x>2[/tex]

Step-by-step explanation:

Given inequality:

[tex]-1 >-2(x - 4)-5(4x-7)[/tex]

Solving the inequality.

Using distribution.

⇒ [tex]-1 >(-2x) +((- 4)(-2))+(-5\times4x)+((-5)(-7))[/tex]

⇒ [tex]-1 >-2x +8-20x+35[/tex]

Combining like terms

⇒ [tex]-1 >-2x-20x+35+8[/tex]

⇒ [tex]-1 >-22x +43[/tex]

Adding [tex]22x[/tex] both sides.

⇒ [tex]-1+22x >-22x +43+22x[/tex]

⇒ [tex]-1 +22x> 43[/tex]

Adding 1 both sides.

⇒ [tex]-1+1 +22x> 43+1[/tex]

⇒ [tex]22x>44[/tex]

Dividing both sides by 22.

⇒ [tex]\frac{22x}{22}>\frac{44}{22}[/tex]

⇒ [tex]x>2[/tex]

Thus, the solution of the inequality is:

[tex]x>2[/tex]

Answer:

78

Step-by-step explanation:

600 times 13%

Answer:

28

Step-by-step explanation:

The height of the trapezoid and the base length from point S to the height makes a right triangle. In fact, it is a 3, 4, 5 triangle and a pyth. triplet. So...

QS = 5 cm

And...

perimeter = 5+3+6+3+4 = 21 cm

answer: B

Answer:

C. Starting with a given set of rules and figuring out what must be  true . TRUE

Step by step explanation:

Mathematical Induction

Mathematical Induction is a mathematical technique which we can use to prove any given mathematical statement, result, theorem or corollary with help of induction.

Here, we assume the statement to be true for a smaller natural number            (Usually 1) and then prove the statement to be true for ANY ARBITRARY NUMBER say k.

Now, from the given options:

A. Writing down the steps to solve a complicated math problem .

FALSE as the induction method is based on ASSUMPTION and INDUCTION.

B. Forming rules based upon observations and experiences .

FALSE as the induction method is based on ASSUMPTION and INDUCTION.  We need to induce the needed  statement or Result.

C. Starting with a given set of rules and figuring out what must be  true .

TRUE as the induction method is based on ASSUMPTION and INDUCTION.

We try and find out  the result with the given existing data.

D. Reducing the solution to a problem in lowest terms.

FALSE as the induction method is based on ASSUMPTION and INDUCTION.  

For this case we must simplify the following expressions:

[tex]m ^ 3 + m ^ 3\\10 + 3c + 5d-7c + d[/tex]

Expression 1:

[tex]m ^ 3 + m ^ 3 =[/tex]

They are similar terms so we can add.

[tex]2m ^ 3[/tex]

Expression 2:

[tex]10 + 3c + 5d-7c + d =[/tex]

We add similar terms taking into account that:

Equal signs are added and the same sign is placed.

Different signs are subtracted and the major sign is placed.

[tex]10 + 3c-7c + 5d + d =\\10-4c + 6d[/tex]

Answer:

[tex]m ^ 3 + m ^ 3 = 2m ^ 3\\10 + 3c + 5d-7c + d = 10-4c + 6d[/tex]

Answer:

10ab + 4a + 5b + 2

= 10ab + 5b + 4a + 2

= 5b(2a+1) + 2(2a+1)

= (5b+2)(2a+1)

Answer:

a) Given in attachment.

b) Quadrilateral formed is a rhombus. Because length of all the sides are equal and angle between adjacent sides is not 90°.

c) 24 unit².

Step-by-step explanation:

Let rectangle be ABCD with length 8 and width 6

And mid-points be E,F,G,H

Now, join the mid-points .

we know that angle between adjacent sides in a rectangle is 90°.

⇒ ΔFAE forms a right angle triangle with 90° at A.

By, pythagoras theorem , EF² = AF² + AE²

⇒ EF² = 3² + 4² = 25

⇒ EF = 5;

In the same way, FG = GH = HE = 5

⇒ the quadrilateral is either square or rhombus.

Now, from ΔFAE,   sin(∠AEF) = [tex]\frac{4}{5}[/tex]

(sinФ = opposite side / hypotenuse)

⇒ ∠AEF = 53°;

In similar manner;

∠DEH = 53° . Now ∠FEH = 180 - 53 - 53 = 74° (sum of angles on a straight line is 180°)

⇒ the quadrilateral is rhombus has angle between adjacent sides is 53° and not 90°.

Now, to find the area of rhombus, join EG and FH. And name the intersection point as J.

consider ΔEJF,

it is a right angled triangle at J, and also quadrilateral AFJE forms rectangle, as diagonals intersect perpendicular in a rhombus.

⇒ FJ = 3 and EJ = 4.

⇒ area of this triangle = 1/2 × base × height

                                     = 1/2 × EJ × JF = 1/2 × 3 ×4 = 6

similarly triangles FJG, GJH, HJE.

⇒ area of rhombus = 6+6+6+6 = 24.

Answer:

3

Step-by-step explanation:

For this question, you need to make change the denominators of the fractions to be equal, making them the same lowest common denominator.

8/9 -> 40/45

4/15 -> 12/45

Since 12 goes into 40 3 1/3 times, he can patrol that many neighborhoods in 8/9's of an hour, which is rounded to 3 because he doesn't have enough time for 4.

To determine if the sheriff can patrol 2, 3, 4, or 6 neighborhoods in 8/9 of an hour, we need to calculate the time it takes to patrol a single neighborhood and then divide the given time by that value. The answer is 10/3, which means the sheriff can patrol 2, 3, 4, or 6 neighborhoods in 8/9 of an hour.

To determine if the sheriff can patrol 2, 3, 4, or 6 neighborhoods in 8/9 of an hour, we need to calculate the time it takes to patrol a single neighborhood and then divide the given time by that value.

Given that it takes 4/15 of an hour to patrol a single neighborhood, we can divide 8/9 by 4/15.

To divide fractions, we multiply by the reciprocal, so 8/9 ÷ 4/15 becomes 8/9 × 15/4. Multiplying across, we get (8 × 15) / (9 × 4) = 120 / 36 = 10 / 3.

Answer:

y = - 3x + 5

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (3, - 4) and (x₂, y₂ ) = (1, 2)

m = [tex]\frac{2+4}{1-3}[/tex] = [tex]\frac{6}{-2}[/tex] = - 3, thus

y = - 3x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (1, 2), then

2 = - 3 + c ⇒ c = 2 + 3 = 5

y = - 3x + 5 ← equation of line

Answer:

y=-3x+5

Step-by-step explanation:

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

m=(2-(-4))/(1-3)

m=(2+4)/-2

m=6/-2

m=-3

y-y1=m(x-x1)

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

y+4=-3(x-3)

y=-3x+9-4

y=-3x+5

Answer:

December 1st

Step-by-step explanation:

Apex

Answer: December 1st

Step-by-step explanation:

Mathematics of personal finance sem 1