Use the grouping method to factor this polynomial x^3+2x^2+12x+24

Answer:

5

Step-by-step explanation:

First you need to add all the digits so 1 +2+5+5+6+6+7+8 = 40

Then, divide that by the number of digits which is 8.

Therefore, 40/8 = 5, which is the answer.

I hope this helped!

Answer:

A. 3x - 2y = 5

Step-by-step explanation:

Given line in the graph has the following properties:

using point (2,3)

m = slope = (y2-y1)/(x2-x1) = (5-2)/(2-0) = 3/2

New line passes through y0(3,2), so use the point-slope form

(y-y0) = m (x-x0)

substitute in value y0(3,2)

y - 2 = (3/2) (x - 3)

multiply by 2 on each side

2y - 4 = 3x - 9

simplify and rearrange

3x - 2y = -4 + 9 =5

3x - 2y = 5

Answer:

80 = EG

Step-by-step explanation:

Inscribed Angle = 1/2 Intercepted Arc

40 = 1/2 EG

Multiply each side by 2

80 = EG

Answer:

80 deg

Step-by-step explanation:

Theorem:

The measure of an inscribed angle is half the measure of the intercepted arc.

m<EFG = (1/2)m(arc)EG

40 deg = (1/2)m(arc)EG

m(arc)EG = 2 * 40 deg

m(arc)EG = 80 deg

Answer: D

Step-by-step explanation:

If we substitute -12 into this equation we get:

[tex]-3[-12-8]+1.5[/tex]

[tex]-3[-20]+1.5[/tex]

Because -20 is in absolute value, we simply just use 20.

Thus,

[tex]-3(20)+1.5\\= -60+1.5\\= -58.5[/tex]

Answer:

D

Step-by-step explanation:

Answer: The volume is 33 cubic centimeters.

Step-by-step explanation:

First find the volume of the square pyramid on top of the cube. To find the volume of the square pyramid you use the volume  a^2*h/3 a is the side length of the base of the square pyramid and h is the height all divide by 3.

So we can say that the side length of the base of the square pyramid is 3 because it has the same side length base as the cube.

V= 3^2 * 2 /3

V= 9 * 2 /3

V= 18/3

v= 6  

So the volume of the square pyramid is 6 so now we need to find the volume of the cube and add them together.

Volume of the a cube uses the formula s^3 where s is the side length.

V= 3^3

v= 3*3*3

v= 27  

The volume of the cube is 27.

Add 6 and 27 to find the total volume.

6 +27 = 33

Answer:

Please look at the attached graph and select the appropriate answer.

Step-by-step explanation:

Make sure that the graph shows a parabola with branches up, and the vertex situated at the point (3, -16) which corresponds to the double root  x = 3, and the vertical shift that lowers that vertex 16 units below the x-axis.

Please look at the attached picture.

Answer:     Graph   B

Step-by-step explanation:

Answer:

60 + 0.05d

Step-by-step explanation:

Answer:

isosceles

Step-by-step explanation:

Answer:

See below

Step-by-step explanation:

Part A:

[tex](x+2)(x+3) = (x+2)(x-3) + y[/tex]

Resolving Parenthesis

[tex]x^2+3x+2x+6=x^2-3x-2x+6+y\\x^2+5x+6 = x^2-5x+6+y[/tex]

Subtracting [tex]x^2[/tex] and 6 to both sides

[tex]5x= -5x+y[/tex]

Adding 5x to both sides

[tex]y = 5x+5x\\y = 10x[/tex]

Comparing it with [tex]y = mx+b[/tex] where m is the slope while b is the y-intercept

So,

Slope = m = 10

Y-intercept = b = 0

Part B:

[tex]x = my+b[/tex]

Subtracting b to both sides

[tex]my = x-b[/tex]

Dividing both sides by m

[tex]y = \frac{x-b}{m}\\ y = \frac{x}{m} - \frac{b}{m}[/tex]

Comparing it with [tex]y = mx+b[/tex] where m is the slope while b is the y-intercept

So,

Slope = m = [tex]\frac{1}{m}[/tex]

Y-intercept = b = [tex]-\frac{b}{m}[/tex]

Answer:

B. (4.75,-22)

Step-by-step explanation:

Step: Solve 3.2x+0.5y=4.2for x:

3.2x+0.5y=4.2

3.2x+0.5y+−0.5y=4.2+−0.5y(Add -0.5y to both sides)

3.2x=−0.5y+4.2

3.2x

3.2

=

−0.5y+4.2

3.2

(Divide both sides by 3.2)

x=−0.15625y+1.3125

Step: Substitute−0.15625y+1.3125 for x in−1.6x−0.5y=3.4:

−1.6x−0.5y=3.4

−1.6(−0.15625y+1.3125)−0.5y=3.4

−0.25y−2.1=3.4(Simplify both sides of the equation)

−0.25y−2.1+2.1=3.4+2.1(Add 2.1 to both sides)

−0.25y=5.5

−0.25y

−0.25

=

5.5

−0.25

(Divide both sides by -0.25)

y=−22

Step: Substitute−22 for y in x=−0.15625y+1.3125:

x=−0.15625y+1.3125

x=(−0.15625)(−22)+1.3125

x=4.75(Simplify both sides of the equation)

Answer:

2m - 4

Step-by-step explanation:

Add m and m.

Hope this helps :)

Answer:

[tex]\boxed{2m+4}[/tex]

Step-by-step explanation:

[tex]m-4+m[/tex]

Combine like terms.

[tex]m+m-4[/tex]

[tex]2m-4[/tex]

Answer:

Hey there!

Sine is equal to opposite/hypotenuse

Tangent is equal to opposite/adjacent

opposite=a

hypotenuse=b

adjacent=c

Thus, tangent x= a/c.

Hope this helps :)

Answer:

tan x = a/sqrt(b^2 - a^2)

Step-by-step explanation:

sin x = a/b = opp/hyp

tan x = opp/adj

adj^2 + opp^2 = hyp^2

adj^2 + a^2 = b^2

adj = sqrt(b^2 - a^2)

tan x = a/sqrt(b^2 - a^2)

Answer:

a) [tex]D = 600 -4.9t^2[/tex]

b) 11.06 seconds

c) 108.39 m/s

d) 10.37 m/s

Step-by-step explanation:

Given:

Distance, s = 600 m

Acceleration, a = g = 9.8 [tex]m/s^2[/tex]

a) Distance of stone above ground level at time 't'.

First of all, we need to find the distance traveled in time 't' and then we will subtract it from 600 to find the answer.

The formula is given as:

[tex]s=ut+\dfrac{1}{2}at^2[/tex]

where u is the initial velocity which is 0 in this case.

[tex]s=0\times t+\dfrac{1}{2}\times 9.8 \times t^2\\s =4.9t^2[/tex]

Distance of stone above ground level at time 't',

[tex]D = 600 -4.9t^2[/tex]

b) Time taken by stone to reach the ground. i.e. D = 0

Using above equation, putting D = 0

[tex]0 = 600 -4.9t^2\\\Righttarow 4.9t^2 = 600\\\Rightarrow t = \sqrt{\dfrac{6000}{49}} = 11.06\ sec[/tex]

c) Velocity with which it strikes the ground i.e. [tex]v=?[/tex]

Using the formula:

[tex]v=u+at[/tex]

[tex]v = 0 +9.8 \times 11.06\\v = 108.39\ m/s[/tex]

d) If initial velocity, u = 7 m/s, time taken to reach the ground = ?

In this case total distance traveled = 600 m

[tex]s=ut+\dfrac{1}{2}at^2[/tex]

[tex]600=7 t+\dfrac{1}{2}\times 9.8t^2\\\Rightarrow 600=7 t+4.9t^2\\\Rightarrow 4.9t^2+7 t-600=0\\\Rightarrow 49t^2+70 t-6000=0[/tex]

Solving the above equation:

t = 10.37 seconds

The answers are:

a) [tex]D = 600 -4.9t^2[/tex]

b) 11.06 seconds

c) 108.39 m/s

d) 10.37 m/s

A) The distance (in meters) of the stone above ground level at time t is; d(t) = 600 - 4.9t²

B) The time it takes the stone to reach the ground is; t = 11.07 seconds

C) The velocity at which the stone strikes the ground is; v = -108.486 m/s

D) The time it takes to reach the ground when thrown downwards with a speed of 7 m/s is; t = 10.37 s

A) Using Newton's 2nd equation of motion, we have;

d(t) = d_o + ut - ½gt²

Plugging in the relevant values, we have;

d(t) = 600 + 0(t) - 0.5(9.8)t²

d(t) = 600 - 4.9t²

B) The time it takes for the stone to reach the ground is when d(t) = 0. Thus;

0 = 600 - 4.9t²

4.9t² = 600

t² = 600/4.9

t = √(600/4.9)

t = 11.07 seconds

C) Velocity at which is strikes the ground will be gotten from Newton's first equation of motion;

v = u - gt

v = 0 - (9.8 × 11.07)

v = -108.486 m/s

D) The stone is thrown downwards with a speed of 7 m/s.

Thus;

600 - 7t - 0.5(9.8t²) = 0

-4.9t² - 7t + 600 = 0

Using online quadratic equation solver gives;

t = 10.37 s

Read more at; https://brainly.com/question/17188989

Answer: 6 animals should go in each pen.

Step-by-step explanation:

Total sheep = 54

Total cows = 24

Total pigs = 30

Highest number of animals are possible in each pen such that animals are distributed in pens with the same number = Greatest common divisior (54,24, 30)

54= 6 x 9

24= 6 x 4

30 = 6 x 5

So, Greatest common divisior (54,24, 30) = 6

Hence, 6 animals should go in each pen.

Answer:

288π

Step-by-step explanation:

V=4 /3πr^3 is the formula. We have the diameter, so the radius is half (6). We now have V=4 /3π(6)^3 = 4/3π216 = 288π.

Answer:

Graphs 1, 2, and 3 are not functions. Graph 4 is a function.

Step-by-step explanation:

Use the vertical line test.

Imagine a vertical line moving from left to right.

If in any position of the vertical line, it intersects more than one point on the graph, then it is not a function.

In graphs 1 and 2 it is clear that there are many vertical lines than would intersect the graph at more than one point.

In graphs 3, a vertical line would intersect the vertical parts of the graph at more than 1 point, so graph 3 is not a function.

The only function is graph 4.

The relations given in options 1, 2, and 3 are not functions only Graph 4 is a function.

A function is an expression, or rule that defined the relation between two variables.

If we use the vertical line test.

Imagine a vertical line moving from left to right.

If in any position of the vertical line, it intersects more than one point on the graph, then it is not a function.

In graphs 1 and 2 it is clear that there are many vertical lines than would intersect the graph at more than one point.

In graph 3, a vertical line would intersect the vertical parts of the graph at more than 1 point, so graph 3 is not a function.

Learn more about function here;

https://brainly.com/question/21145944

Answer:

Se necesitarían:

18 tubos

Step-by-step explanation:

La longitud total de la tubería con 24 tubos de 6 metros cada uno es:

24*6 = 144 metros

si los tubos fuesen de 8 metros:

144/8 = 18

Se necesitarían:

18 tubos

Answer:

83

Step-by-step explanation:

The 126 angle is an exterior angle of the triangle.

The 43 and x angles are the two remote interior angles of the 126 angle.

Theorem:

The measure of an exterior angle of a triangle equals the sum of the measures of the remote interior angles.

x + 43 = 126

x = 83

Answer:

x = 83

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the opposite interior angles

126 = x+43

Subtract 43 from each side

126-43 = x+43-43

83 = x

Answer:

(0, 2.5)

Step-by-step explanation:

Well we substitute y-y into x in the following equation,

2x + 4y = 10

2(y-y) + 4y = 10

2y - 2y + 4y = 10

Combine like terms

2y - 2y = 0

4y = 10

10/4

y = 2.5

If y is 2.5 we can plug those into y.

2x + 4(2.5) =10

2x + 10 = 10

-10

2x = 0

0/2

x = 0

Answer: The radius of the small circle is about 0.85 cm - 0.95 cm

Explanation: I am not completely sure but I drew the same figure with the same lengths as given and between both circles there is almost a gam of 2.5 - 3 cm and when we draw a circle between them the diameter is about 1.7 - 1.9 so dividing the diameter by 2 to get the radius we get 0.85 cm - 0.95 cm.

Answer:

o.85 to 0.95

Step-by-step explanation:

I got to go so I don' have time to explain!

Answer:

win-263889 loss-236111

Step-by-step explanation:

1:the guys throws the dice twice no charge for this

2:for every face the first time there is a chance of getting the others or the same face e.g round 1-1 round 2-(either 123456)

3:I drew a probability tree to get the sum

like if I got 1and1 then sum is 2 I did it for the rest

4:I got P of (even)=17/36 and for (odd)=19/36

5:then the organizer has to pay if it's even and there 1 million throws Wich means the probability he will lose is the probability of getting an even sum for 500000 throws and for winning is the probability of getting odd sums in those 500,000 throws

6: 500k is because only after it's thrown twice were there charges

Answer:

$1197.17185

Step-by-step explanation:

ABC bond :

Par value of bond (FV) = 1000

Period (n) = 11 years

Coupon rate (r) = 8.5% annually

Discount rate (r) = 6% = 0.06

The coupon price = 8.5% of par value

Coupon price (C) = 0.085 * 1000 = 85

Current price of bond can be computed using the relation:

= C * [1 - 1 / (1 + r)^n] / r + (FV / (1 + r)^n)

85 * [1 - 1/(1+0.06)^11]/0.06 + 1000/(1 + 0.06)^11

85 * 7.8868745 + 526.78752

670.38433 + 526.78752 = $1197.17185

Let [tex]x=\sqrt[3]{3}[/tex] and [tex]x^2=\sqrt[3]{9}[/tex]. Then

[tex]\dfrac{2\sqrt[3]{9}}{1+\sqrt[3]{3}+\sqrt[3]{9}}=\dfrac{2x^2}{1+x+x^2}[/tex]

Multiply the numerator and denominator by [tex]1-x[/tex]. The motivation for this is the rule for factoring a difference of cubes:

[tex]a^3-b^3=(a-b)(a^2+ab+b^2)[/tex]

Doing so gives

[tex]\dfrac{2x^2(1-x)}{(1+x+x^2)(1-x)}=\dfrac{2x^2(1-x)}{1-x^3}[/tex]

so that

[tex]\dfrac{2\sqrt[3]{9}}{1+\sqrt[3]{3}+\sqrt[3]{9}}=\dfrac{2\sqrt[3]{9}(1-\sqrt[3]{3})}{1-3}=\sqrt[3]{9}(\sqrt[3]{3}-1)=3-\sqrt[3]{9}[/tex]

Answer:

[tex]\boxed{\sf A. \ 36}[/tex]

Step-by-step explanation:

The triangles are congruent. The sides are proportional.

Let x be the length of FQ.

[tex]\frac{24}{18} =\frac{x}{27}[/tex]

[tex]\sf Multiply \ both \ sides \ by \ 27.[/tex]

[tex]\frac{24}{18}(27)=\frac{x}{27}(27)[/tex]

[tex]36=x[/tex]

Answer:

Princess is behind 2

Step-by-step explanation:

If all 3 hints are false, then the princess is not behind 1  ( so it must be 2 or 3)

The dragon is not behind 2 ( so it must be 1 or 3)  

The is no one behind 3  

That means the princess cannot be behind 3 and the dragon cannot be behind 3

The princess is behind 2 and the dragon is behind 1

Answer:

P = 0.0215 = 2.15%

Step-by-step explanation:

First we need to convert the values of 900 and 975 to standard scores using the equation:

[tex]z = \frac{x - \mu}{\sigma}[/tex]

Where z is the standard value, x is the original value, [tex]\mu[/tex] is the mean and [tex]\sigma[/tex] is the standard deviation. So we have that:

standard value of 900: [tex]z = \frac{900 - 750}{75} = 2[/tex]

standard value of 975: [tex]z = \frac{975 - 750}{75} = 3[/tex]

Now, we just need to look at the standard distribution table (z-table) for the values of z = 2 and z = 3:

z = 2 -> p_2 = 0.9772

z = 3 -> p_3 = 0.9987

We want the interval between 900 and 975 hours, so we need the interval between z = 2 and z = 3, so we just need to subtract their p-values:

P = p_3 - p_2 = 0.9987 - 0.9772 = 0.0215

So the probability is 0.0215 = 2.15%

Answer:

2.35 babyyyyyyyyyyy

Step-by-step explanation:

Acellus sux

Answer:

Triangle klm

Step-by-step explanation:

edg 2020

Answer:

We can rewrite this as [tex]\frac{200x}{x} + \frac{-300}{x}[/tex].

[tex]\frac{200x}{x}[/tex] simplifies to 200 after eliminating x from the numerator and denominator and [tex]\frac{-300}{x}[/tex] becomes [tex]-\frac{300}{x}[/tex] so the final answer is [tex]200 - \frac{300}{x}[/tex].

Answer:

927.0 cm²

Step-by-step explanation:

Step 1: find Z

m < Z = 180 - (28 + 118) (sum of ∆)

= 180 - 146

Z = 34°

Step 2: Find side XY using the law of sines

[tex] \frac{XY}{sin(34)} = \frac{42}{sin(28)} [/tex]

Cross multiply

[tex] XY*sin(28) = 42*sin(34) [/tex]

[tex]XY*0.469 = 42*0.559[/tex]

Divide both sides by 0.469

[tex]\frac{XY*0.469}{0.469} = \frac{42*0.559}{0.469}[/tex]

[tex]XY = 50.06[/tex]

XY ≈ 50 cm

Step 3: find the area.

Area of ∆ = ½*XY*YZ*sin(Y)

XY ≈ 50 cm

= ½*50*42*sin(118)

= 25*42*0.8829

Area = 927.045

Area ≈ 927.0 cm² (nearest tenth)

Answer:

The correct answer is A because subtract 28.50 from 45.50 and you get the answer of 17$ for the belt