Mrs.Carlyle bought a bag of peanuts for her children. When Phillip, Joy, Brent, abd Preston came home from school, they each took some peanuts from the bag.

Given:

Values of a polynomial P(x).

[tex]P(-5)=-2[/tex]

[tex]P(-3)=6[/tex]

[tex]P(3)=7[/tex]

[tex]P(5)=-1[/tex]

To find:

The remainder when P(x) is divided by (x+5).

The remainder when P(x) is divided by (x-3).

Solution:

If a polynomial P(x) is divided by (x-a), then the remainder is P(a).

If the polynomial P(x) is divided by (x+5), then the remainder is P(-5).

[tex]P(-5)=-2[/tex]

Therefore, the remainder is -2 when P(x) is divided by (x+5).

If the polynomial P(x) is divided by (x-3), then the remainder is P(3).

[tex]P(3)=7[/tex]

Therefore, the remainder is 7 when P(x) is divided by (x-3).

Answer:

Option (1)

Step-by-step explanation:

Given inequality is,

-4(x + 3) ≤ -2 - 2x

Further solve this inequality,

-4x - 12 ≤ -2 - 2x

-4x + 2x - 12 ≤ -2 - 2x + 2x

-2x - 12 ≤ -2

-2x - 12 + 12 ≤ -2 + 12

-2x ≤ 10

-x ≤ 5

x ≥ -5

Therefore, on a number line draw an arrow starting with a solid circle (because of equal to sign) and moving towards the numbers greater than -5.

Option (1) is the answer.

Answer:

I've attached a picture of a unit circle with the quadrant labeled.

Calculate the degree of 5п 8 radians:

[tex]\frac{5\pi }{8} =\frac{5*180}{8} =\frac{900}{8} =112.5[/tex]

Locate the general location of 112.5° on the unit circle:

It's between 120°([tex]\frac{2\pi }{3}[/tex]) and 90°([tex]\frac{\pi }{2}[/tex]).

Find the quadrant it lies in:

Quadrant II

Answer:

1) 3000 + 125m

2) 3000 + 125m = 5000

3) M= 16

4) It would take 16 months

Step-by-step explanation:

Okay so no since there are no other transaction and you already have a balance of 3000 with a monthly Fee of 125 the equation shpuld be like this.

So every month you add 125,we dont know how much months we have to pay so we can use the variable given to us in this case “M”. So your base expression should look like this,

3000 + 125m (3000 base fee that doesnt change, and 125 every month fee)

Then it asked us to put it as the final balance as 5000, so using the base expression we can do this

3000 + 125m = 5000

Now to solve it you would solve it like any other equation

5000-3000=2000

2000=125m

2000/125= 16

Okay so m = 16

M in this case stands for months so the final answer would be it would take 16 months to reach the final balance of 5000

Answer:

0.410714

Step-by-step explanation:

Dividend ÷ Divisor = Quotient

Answer:

x > 3

Step-by-step explanation:

3x-9-5x > -3x - 6

3x-5x+3x > -6+9

x > 3

Answer:

there you go

Step-by-step explanation:

angle DOB is 60 degree.

Answer:

see explanation

Step-by-step explanation:

Given ∠ DOC = 90° then

∠ DOB = 90 - p and

Since AOB is a straight angle , then

4p + 90 - p = 180

3p + 90 = 180 ( subtract 90 from both sides )

3p = 90 ( divide both sides by 3 )

p = 30

4p = 4 × 30 = 120

Then

∠ DOB = 180° - 4p = 180° - 120° = 60°

Answer:

[tex]2^{3}[/tex]×5×3×[tex]x^{2}[/tex]×[tex]y^{4}[/tex]

Step-by-step explanation:

[tex]8xy^{4}[/tex]= [tex]2^{3}[/tex]×[tex]x[/tex]×[tex]y^{4}[/tex]

6[tex]x^{2} y[/tex]= 2×3×[tex]x^{2}[/tex]×[tex]y^{}[/tex]

10[tex]x^{2} y^{2}[/tex] = 2×5×[tex]x^{2}[/tex]×[tex]y^{2}[/tex]

[tex]2^{3}[/tex]×5×3×[tex]x^{2}[/tex]×[tex]y^{4}[/tex]

Answer:

Step-by-step explanation:

Binomial Expansion:

[tex](2x-3y)^4 \\\\= 4C_0(2x)^4 (-3y)^0 + 4C_1(2x)^3 (-3y)^1 + 4C_2(2x)^2(-3y)^2 \\\\+ 4C_3(2x)^1 (-3y)^3 + 4C_4(2x)^0 (-3y)^4\\\\=16x^4 + 4(8x^3)(-3y) + 6(4x^2)(9y^2) + 4(2x)(-27y^3) + 81y^4\\\\=16x^4 - 96x^3y + 216x^2y^2-216xy^3 +81y^4[/tex]

Pascal's Triangle:

  Zero row                        1

 First row                  1                 1

 Second row          1           2             1

 Third  row         1         3              3          1

 Fourth row    1       4            6           4          1

Answer:

Step-by-step explanation:

C-10,20,-40,80,...[tex] u_{n+1}=(-2)*u_{n}[/tex]. is geometric1

Answer:

16 2/3 ounces per mile

Step-by-step explanation:

50 ounces of blueberries/3 miles = 16.666 repeated

16.666 repeated = 16 2/3 ounces/mile

Answer:

Step-by-step explanation:

In each option you need to find the number of outcomes of a single event and then multiply that by the number of times that event takes place.

1. 2 outcomes (heads and tails)

2. 6 outcomes (2 outcomes * 3 tosses)

3. 60 outcomes (6 outcomes per die * 10 rolls)

4. 12 outcomes (6 outcomes per die * 2 rolls)

5. 10 outcomes (10 numbers on the pad)

6. 52 outcomes (52 cards in a regular deck)

7. 32 outcomes (32 letters in the alphabet)

8. 7 outcomes (7 letters to choose from)

9. 10 outcomes (10 letters to choose from)

10. 36 outcomes (36 crayons to choose from)

Answer:

V=πr2h /3

V=πr2h /3=π·2.52·8 /3≈52.35988

so the volume is 52.36 inches

Answer:

Step-by-step explanation:

D.The sign of h must be negative and the signal of k must be positive *it’s for sure the answer.

Answer:

D.The sign of h must be negative and the signal of k must be positive EDGE 2021

Answer:

2√10 km

Step-by-step explanation:

By Pythagoras theorem,

x^2 + 9^2 = 11^2

x^2 + 81 = 121

x^2 = 121 - 81

x^2 = 40

= 4 x 10

x^2 = 2^2 x 10

x = 2√10 km

Answer:

[tex]Area = \frac{1}{2} * AC * D[/tex]

Step-by-step explanation:

From the complete question, we have:

Length D to be perpendicular to side AC

So, the area of the triangle is:

[tex]Area = \frac{1}{2} * Base * Height[/tex]

Since:

Length D is perpendicular to side AC

Then:

[tex]Base = AC[/tex]

[tex]Heigjt =D[/tex]

So:

[tex]Area = \frac{1}{2} * AC * D[/tex]

Answer:

38.5

Step-by-step explanation:

b^2= 29^2+20^2-2×20×29× Cos 102

b^2=841+400-1160 (-0.2079)

=1241- 241.164

b^2=1482.164

b= square root of 1482.164

AC = 38.5

Answer:

[tex]180ft^{3}[/tex]

Step-by-step explanation:

Volume of a cone:

[tex]V=\pi r^{2} \frac{h}{3}[/tex]

Take [tex]\pi[/tex] as 3, as mentioned in the question

'r' is 'radius' ⇒ {diameter is given so divide by 2: 12/2 = 6}

'h' is 'height'

[tex]V=(3)(6)^{2} (\frac{5}{3} )[/tex]

[tex]V=(3)(36)(\frac{5}{3} )[/tex]

[tex]V=108(\frac{5}{3} )[/tex]

{multiply 108 with 5 and then divide the answer by 3}

[tex]V=108[/tex] × [tex]5[/tex]

[tex]V=540[/tex]

[tex]V=540/3[/tex]

[tex]V=180ft^{3}[/tex]

Answer:

Step-by-step explanation:

Population size: 17

Median: 30

Minimum: 12

Maximum: 49

First quartile: 21

Third quartile: 35

Interquartile Range: 14

Outliers: none

Answer:

16

Step-by-step explanation:

[tex](-64)^2/3[/tex]

64 = [tex]2^{6}[/tex]

[tex]2^{6} ^{\frac{1}{3} } ^{2}[/tex]

[tex]2^{ 2^{2} }[/tex]

[tex]2^{4}[/tex]

16

Answer:

Step-by-step explanation:

slope>0 so graph is increasing.

Answer:

[tex]\mathbf{6xe^xy+y^2e^x = C}[/tex] which implies that C is the integrating factor

Step-by-step explanation:

The correct format for the equation given is:

[tex]y(6x+y +6)dx +(6x +2y)dy=0[/tex]

By the application of the general differential equation:

⇒ Mdx + Ndy = 0

where:

M = 6xy+y²+6y

[tex]\dfrac{\partial M}{\partial y}= 6x+2y+6[/tex]

and

N = 6x +2y

[tex]\dfrac{\partial N}{\partial x}= 6[/tex]

∴

[tex]f(x) = \dfrac{1}{N}\Big(\dfrac{\partial M}{\partial y}- \dfrac{\partial N}{\partial x} \Big)[/tex]

[tex]f(x) = \dfrac{1}{6x+2y}(6x+2y+6-6)[/tex]

[tex]f(x) = \dfrac{1}{6x+2y}(6x+2y)[/tex]

f(x) = 1

Now, the integrating factor can be computed as:

[tex]\implies e^{\int fxdx}[/tex]

[tex]\implies e^{\int (1)dx}[/tex]

the integrating factor = [tex]e^x[/tex]

From the given equation:

[tex]y(6x+y +6)dx +(6x +2y)dy=0[/tex]

Let us multiply the above given equation by the integrating factor:

i.e.

[tex](6xy+y^2 +6y)dx +(6x +2y)dy=0[/tex]

[tex](6xe^xy+y^2 +6e^xy)dx +(6xe^x +2e^xy)dy=0[/tex]

[tex]6xe^xydx+6e^xydx+y^2e^xdx +6xe^xdy +2ye^xdy=0[/tex]

By rearrangement:

[tex]6xe^xydx+6e^xydx+6xe^xdy +y^2e^xdx +2ye^xdy=0[/tex]

Let assume that:

[tex]6xe^xydx+6e^xydx+6xe^xdy = d(6xe^xy)[/tex]

and:

[tex]y^2e^xdx +e^x2ydy=d(y^2e^x)[/tex]

Then:

[tex]d(6xe^xy)+d(y^2e^x) = 0[/tex]

[tex]6d (xe^xy) + d(y^2e^x) = 0[/tex]

By integration:

[tex]\mathbf{6xe^xy+y^2e^x = C}[/tex] which implies that C is the integrating factor

Answer:

94.2 square units.

I got 94.09 but that seems to be the closer answer.

Answer:

$5

Step-by-step explanation:

Find the markup by finding 25% of 20:

20(0.25)

= 5

So, the markup is $5

Given:

The graph of system of inequalities.

To find:

The system of inequalities.

Solution:

From the given graph it is clear that the shaded region is lies below the line y=10 and the boundary line y=10 is a solid line. So, the sign of inequality must be [tex]\leq[/tex].

[tex]y\leq 10[/tex].

The shaded region lies on the right side of the y-axis. So, [tex]x\geq 0[/tex].

Another boundary line passes through the point (0,1) and (1,2). So, the equation of the line is:

[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

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

[tex]y=1(x)+1[/tex]

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

The boundary line [tex]y=x+1[/tex] is a dotted line and the shaded region lies above the boundary line, so the sign of inequality must be [tex]>[/tex].

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

So, the required system of inequalities is:

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

[tex]y\leq 10[/tex]

[tex]x\geq 0[/tex]

Therefore, the correct option is B.

Answer:

sorry I don't know

Step-by-step explanation:

.........

Answer:

See Explanation

Step-by-step explanation:

Given

[tex]Region\ A = 81218576[/tex]

Required

The acres owned by the government

The question is incomplete as the proportion (p) owned by the government is not given.

However, the formula to use is as follows:

[tex]Govt = p * Region\ A[/tex]

Assume the proportion is 28%, the equation becomes

[tex]Govt = 28\% * 81218576[/tex]

[tex]Govt = 22741201.28[/tex]

The acres owned by the government will be 22741201.28

Answer:

Well the correct answer is 9=2+(x/3) or

(3/x)+2=9