The roots of \[x^2 + 5x + 3 = 0\]are $p$ and $q,$ and the roots of \[x^2 + bx + c = 0\]are $p^2$ and $q^2.$ Find $b + c.$[tex]The roots of\[x^2 + 5x + 3 = 0\]are $p$ and $q,$ and the roots of\[x^2 + bx + c = 0\]are $p^2$ and $q^2.$ Find $b + c.$[/tex]

Answer:

Average rate of change of functions r, q, p, s are 5, 3, -2 and 6 respectively.

Step-by-step explanation:

The formula for average rate of change of f(x) over [a,b] is

[tex]m=\dfrac{f(b)-f(a)}{b-a}[/tex]

The given function is

[tex]r(x)=x^2+2x-5[/tex]

[tex]r(0)=(0)^2+2(0)-5=-5[/tex]

[tex]r(3)=(3)^2+2(3)-5=10[/tex]

Now,

[tex]m_1=\dfrac{r(3)-r(0)}{3-0}[/tex]

[tex]m_1=\dfrac{10-(-5)}{3}=5[/tex]

From the graph it is clear that q(0)=-4 and q(3)=5.

[tex]m_2=\dfrac{q(3)-q(0)}{3-0}[/tex]

[tex]m_2=\dfrac{5-(-4)}{3}=3[/tex]

It is given that  function p has as x-intercept at (3,0) and a y-intercept at (0,6). It menas p(0)=6 and p(3)=0.

[tex]m_3=\dfrac{p(3)-p(0)}{3-0}[/tex]

[tex]m_3=\dfrac{0-6}{3}=-2[/tex]

From the given table it is clear that s(0)=-13 and s(3)=5.

[tex]m_4=\dfrac{s(3)-s(0)}{3-0}[/tex]

[tex]m_4=\dfrac{5-(-13)}{3}=6[/tex]

Therefore, the average rate of change of functions r, q, p, s are 5, 3, -2 and 6 respectively.

Answer:

Answer D I believe :)

Step-by-step explanation:

x^4-33x^2-108

rewrite as a difference

x^4+3x^2-36x^2-108

factor out x^2

x^2(x^2+3)-36x^2-108

factor out -36

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

factor out x^2+3

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

factor x^2-36

(x^2+3)(x-6)(x+6)

set x^2+3 equal to 0

x^2+3=0

solve for x

x=+/-[tex]\sqrt{3}[/tex]i

set at factors

(x+6)(x-6)(x+[tex]\sqrt{3}[/tex]i)(x-[tex]\sqrt{3}[/tex]i)

I hope this helps.

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

A=24in² this th ans because the side of cube is 24 cm

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: 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:

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:

The number of boys, x = 12

Step-by-step explanation:

Given that the sum of the ages of the boys in a class = 84 years

The number of boys = x

A new boy aged 8 years 1 month is added and the average age increases by 1 month

We have

Average age = 84/x = y

Age of new boy = 8 years 1 month = [tex]8\frac{1}{12} \ year[/tex]

New average = y + 1/12 = [tex](8\frac{1}{12}+84) /(x + 1)[/tex] which gives;

84/x + 1/12 = [tex](8\frac{1}{12} + 84) /(x + 1)[/tex]

[tex]\dfrac{x +1008}{12 \cdot x} = \dfrac{1105}{12 \cdot x+ 12}[/tex]

(x + 1008)×(12·x + 12) = 1105× 12·x

12·x² -1152·x + 12096 = 0

x² -96·x + 1008 = 0

(x - 84)×(x - 12) = 0

Therefore, x = 12 or 84,

The number of boys are 12 or 84

For there to bee 84 boys, their average age would be one year each

Given that they are boys not babies, then there are only 12 boys.

Answer:

c) 100

Step-by-step explanation:

This is the best choice because the number is not too low or too high. He will get an accurate probability.

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:

B. x^3 + 3x^2

Step-by-step explanation:

Volume of a rectangular prism=width * length * height

V=w*l*h

h=3 greater than the length of the base

h=x+3

Length of the base=x

Width=x

Substituting values into the formula

V=w*l*h

=(x)*(x)*(x+3)

Multiplying

=(x^2)(x+3)

=x^3 + 3x^2

Option B is the correct answer

The expression [tex]x^3 + 3x^2[/tex]  represents the volume of the prism, in cubic units.

We have given that the,

The height of a right rectangular prism is 3 units greater than the length of the base.

The edge length of the square base is x units.

[tex]Volume of a rectangular prism=width * length * height[/tex]

[tex]V=w*l*h[/tex] ......(1)

We have given that the

h=3 greater than the length of the base

and length of the base is x

Hence, [tex]h=x+3[/tex]

[tex]Length of the base=x[/tex]

[tex]Width=x[/tex]

Substituting values l h and w into the formula (1) we get,

[tex]V=w*l*h[/tex]

[tex]=(x)*(x)*(x+3)[/tex]

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

[tex]=x^3 + 3x^2[/tex]

Therefore the expression  

[tex]x^3 + 3x^2[/tex]  

represents the volume of the prism, in cubic units.

To learn more about the volume of the prism visit:

https://brainly.com/question/23963432

Answer:I think it’s 7x^3

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:

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:

(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 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

Step-by-step explanation:

in each equation once substitute the value of x as 0 and again y as zero by this way you will get two values of X and y .

then again find the slope for each equation by the formula

slope= -coefficient of x / coefficient of y

for example,

X+y is greater or equals to 5

or, X+y= 5

or, X=5-y

or, when y is equals to zero

X= 5

and when X is equals to zero

y= 5

then plot the above point in the graph with respect to its slope and the shaded part is the solution

Answer:

60 + 0.05d

Step-by-step explanation:

Answer:

isosceles

Step-by-step explanation:

Answer:

Step-by-step explanation:

Using the double angle formulas,

cos(2x) = cos^2(x) - sin^2(x) ............(1)

1            = cos^2(x) + sin^2(x)............(2)

add (1) and (2)

1 + cos(2x) = 2 cos^2(x)

=> cos^2(x) = (1/2) (1+cos(2x))  ..............(3)

f(x) =  7 cos^2 (x)  

substituting (3)

f(x) = (7/2) (1+cos(2x))

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:

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:

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:

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:

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:

1:3

Step-by-step explanation:

9/3 = 3

3 is the scale factor

Answer:

9

Step-by-step explanation:

x − 3y

Let x =3 and y = -2

3 -3(-2)

3 + 6

9

Answer:

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

Answer: A) 18(1.15)x

Step-by-step explanation:

18 was the original cost, so the price will always be determined with this starting point. Sice there is an increasing value, that makes it 1.15 instead of .15. And it goes up by 15%, making it the coefficient.

Answer:

A) y = 18(1.15)x

Step-by-step explanation: