According to the rational root theorem which of the following are possible roots for the function below x^4-29x^2+100

Answer:

62.5 or 63

Step-by-step explanation:

the length of the side adjacent to the angle is given (6), and the length of the hypotenuse is also given (13)

the trig function that deals with adjacent and hypotenuse lengths is cosine.

cos(x) = adj/hyp

cos(x) = 6/13

x = 62.5

Number of red balls =3

Number of black balls =7

Total number of balls =10

Let ,P(A)= Probability that first is red

P(B)= Probability that second is red

If second is red, there are 2 possible ways

Either first is red and second is red.

Or first is black and second is red.

So,

P(B)=

10

3

C

1

×

9

2

C

1

+

10

7

C

1

×

9

3

C

1

=

90

6

+

90

21

=

90

27

=

10

3

Probability that first is red, given second is red

P(A/B)=

P(B)

P(A∩B)

=

10

3

10

3

C

1

×

9

2

C

1

=

10

3

90

6

=

90

6

×

3

10

=

27

6

=

9

2

Answer:

Equation #1:

[tex]y = 3x + 8[/tex]

Equation #2:

[tex]\frac{y}{3} -3=x\\\\\frac{y}{3}=x+3\\\\y=3(x+3)\\\\y=3x+9[/tex]

Parallel equations have the same slope. Since both share the same slope of 3, they're parallel.

Answer:

71 boxes

Step-by-step explanation:

1. Add 522 (# of glaze donuts) and 323(# of chocolate covered donuts).....845(# of total donuts)

2. Divide 845 by 12(the # of donuts each box could hold)....70.41666(repeating)

3. As you can't have a 0.41666 of a box, you round up 70.4166666 to 71.

71*12=852 70*12=840

Even though 71 boxes is more than enough to hold 845 donuts, there is simply no other choice, as there is no smaller box that holds less than 12 donuts.

Answer:

Since 50 out of the 600 batteries  are defective, She lets numbers from 1 to 50 represent defective batteries, and 51 to 600 represent working batteries

~OAmalOHopeO~

Answer:

a is 44 degree

Step-by-step explanation:

Answer:

Commercials x = 7

Movies y = 2

Step-by-step explanation:

Let commercials = x

Let's movies = y

$40 is for commercials

$110 is for movies.

Commercials plus movies for the Year = 9

She earned total of $500

X+ y = 9..... equation 1

40x + 110y = 500.... Equation 2

Multipling equation one by 40

40x + 40y = 360

Subtracting equation one from equation 2

70y = 140

Y = 2

If y = 2

X + y = 9

X + 2 = 9

X = 9-2

X = 7  

Answer:

k = [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

X| 1    2   5   10   30

Y| 3    6   15 30   90

t=4

explanation

2(t+1)=10

2t+2=10

2t=8

t=4

Answer:

His average speed for the whole trip is 5km/hr

Step-by-step explanation:

Answer:

4.8 km/hr

Step-by-step explanation:

Assume that the distance is 24 km (evenly divisible by 4 & 6)

then the A-B time would be 24/4 or 6 hrs.

on the return the time would be 24/6  or 4 hrs.

total time 10 hrs total distance 48 km....

48/10 = 4.8 km/hr

Answer:

Remember that a vector translation can be written as:

T(a, b)

And if we apply this to a random point, (x, y), the translation gives:

T(a, b)(x, y) = (x + a, y + b)

now, remember that a general line can be written as:

y = m*x + s

Then a point of that line can be written as: (x, m*x + s)

Then if we apply the translation to a point in the line, we get:

T(a, b)(x, m*x + s) = (x + a, m*x + s + b)

Here we have two lines:

2x - 3y - 1 = 0

2x - 3y + 5 = 0

First, let's rewrite both of these in the slope-intercept form:

y = (2/3)*x - 1/3

y = (2/3)*x + 5/3

Now let's assume that we apply a translation to the first line, that has points of the form (x,  (2/3)*x - 1/3), such that we want to get points of the form:

(x, (2/3)*x + 5/3).

Then we must have:

T(a, b)(x,  (2/3)*x - 1/3) = (x + a,  (2/3)*x - 1/3 + b) = (x, (2/3)*x + 5/3).

Then we need to solve:

(x + a,  (2/3)*x - 1/3 + b) = (x, (2/3)*x + 5/3).

This means that:

x + a = x

(2/3)*x - 1/3 + b = (2/3)*x + 5/3

From the first equation, we can see that a = 0

Now we can solve the second one to find the value of b.

(2/3)*x - 1/3 + b = (2/3)*x + 5/3

subtracting (2/3)*x in both sides, we get:

-1/3 + b = 5/3

b = 5/3 + 1/3

b = 6/3 = 2

b = 2

Then the vector translation is:

T(0, 2)

So it moves the whole line 2 units upwards.

Work Shown:

n = a number, aka a placeholder for a number

3n = triple a number

3n-4 = four less than triple a number

So whatever n is, we multiply by 3 and then subtract off 4.

As an example, if n = 12, then 3n-4 = 3*12-4 = 36-4 = 32.

Answer:

14.4 i hope it helped you

Answer:

a = 1/42, b = 1/7, c = 1/3 and d = 1/2

Step-by-step explanation:

a = bcd (1)

a + b = cd (2)

a + b + c = d (3)

a + b + c + d = 1  (4)​

Substituting equation (3) into equation (4), we have

a + b + c = d (3)

a + b + c + d = 1  (4)​

(a + b + c) + d = 1  (4)​

d + d = 1  (5)

2d = 1

dividing through by 2, we have

d = 1/2

Taking equation (2) and equation (3), we have

a + b = cd (2)

a + b + c = d (3)

substituting equation (2) into equation (3), we have

a + b = cd (2)

(a + b) + c = d (3)

cd + c = d

Factorizing, we have

c(d + 1) = d

dividing through by d + 1, we have

c = d/(d + 1)

substituting d = 1/2 into the equation, we have

c = d/(d + 1)

c = 1/2 ÷ (1/2 + 1)

c = 1/2 ÷ 3/2

c = 1/2 × 2/3

c = 1/3

Taking equations (1) and (2), we have

a = bcd (1)

a + b = cd (2)

Substituting equation (1) into (2), we have

a = bcd (1)

a + b = cd (2)

bcd + b = cd (2)

Factorizing, we have

b(cd + 1) = cd

dividing through by (cd + 1), we have

b = cd/(cd + 1)

substituting the values of c and d into the equation,, we have

b = cd/(cd + 1)

b = 1/3 × 1/2/(1/3 × 1/2 + 1)

b = 1/6/(1/6 + 1)

b = 1/6 ÷ 7/6

b = 1/6 × 6/7

b = 1/7

Since a = bcd, substituting the values of b,c and d into the equation, we have

a = bcd

a = 1/7 × 1/3 × 1/2

a = 1/42

So, a = 1/42, b = 1/7, c = 1/3 and d = 1/2

Answer:

Kim is 20 years old

Step-by-step explanation:

We have to make equations;

Kim= laura+10 so L+10

Laura is twice as old as Melissa so Laura will be

2 X M = 2M

Input values in to the equation

As Kim is 10 years older than Laura it will be 10+10

The age of Kim is 20 years.

Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign. It shows the relationship of equality between the expression written on the left side with the expression written on the right side. In every equation in math, we have, L.H.S = R.H.S (left hand side = right hand side).

There are different parts of an equation which include coefficients, variables, operators, constants, terms, expressions, and an equal to sign. When we write an equation, it is mandatory to have an "=" sign, and terms on both sides. Both sides should be equal to each other. An equation doesn't need to have multiple terms on either of the sides, having variables, and operators. An equation can be formed without these as well, for example, 5 + 10 = 15. This is an arithmetic equation with no variables. As opposed to this, an equation with variables is an algebraic equation.

Kim's age = laura' age +10 years  

= x +10

As, Laura is twice as old as Melissa

Laura's age = 2*y

Now, Melissa is 5 years old now

So,

2y = 2X5= 10 years old

So, the Kim's age= 10+ 10 = 20 years old

Learn more about equation here:

https://brainly.com/question/10413253

#SPJ2

Answer:

D

The y-intercepts of the two functions are opposites.

Step-by-step explanation:

f(x) = 3x-4  which has a slope of 3 and a y intercept of -4

g(x)

m = (5-4)/(3-0) = 1/3

g(x) = 1/3 x +4

g(x) has a slope of 1/3 and a y intercept of 4

Answer:

Area of triangle =1/2b×h

1/2×10×8.7

=44 square inches

Answer:

44

Step-by-step explanation:

The area of a triangle is given by

A = 1/2 bh

where b is the base and h is the height

A = 1/2 (10) (8.7)

A= 43.5

Rounding to the nearest whole number

A = 44

Area of Rectangular prism = 2(wl+hl+hw)

Height = 9ft

Width = 11ft

Length = 12ft

Area = 2(11(12) + 9(12) + 9(11))

Area = 678ft²

Must click thanks and mark brainliest

Answer:

678 ft^2.

Step-by-step explanation:

The surface area consists of 3 pairs of congruent rectangle.

= 2(9*12 + 11*12 + 9*11)

= 2 * 339

= 678.

Answer:

y = -7x + 52

Step-by-step explanation:

y = -7x - b

-4 = -7(8)  + b

-4 = -56 + b

52

Step-by-step explanation:

[tex]thr \: httr \: \: gr \: ujj \: tu \: \: fmgt[/tex]

Answer:

with a graph or stem chart. there are various possibilities search it up!!

Step-by-step explanation:

Answer:

Option A, 4/3

Step-by-step explanation:

2/3-(-2/3)

= 2/3+2/3

= (2+2)/3

= 4/3

Answer:

3/2

Step-by-step explanation:

[tex]2-\frac{2}{3} +\frac{2}{9} -\frac{2}{27} +...\\r=\frac{-\frac{2}{3} }{2} =-\frac{1}{3} ,|r|<1\\s_{\infty}=\frac{a}{1-r} \\=\frac{2}{1+\frac{1}{3} } \\=\frac{2}{\frac{4}{3} }\\ =\frac{3}{2}[/tex]

Answer:

The function that represents g(x) is the third choice: g(x) = (x − 4)^2 + 9

Step-by-step explanation:

The original function has been shifted 9 units up (a vertical transformation). To show a vertical transformation, all we have to do is either add or subtract at the end of the function.

To show a shift upwards, we add the value of change.

To show a shift downwards, we subtract the value of change.

In this case, the original function f(x) = [tex]x^{2}[/tex] was translated 9 units up. Since we shifted up, we simply add 9 to the end of the function: g(x) = [tex]x^{2}[/tex] + 9

The original function has also been shifted 4 units to the right. This is a horizontal transformation. To show a horizontal transformation, we need to either add or subtract within the function (within the parenthesis).

To show a shift to the left, we add the value of change.

To show a shift to the right, we subtract the value of change.

*Notice: Moving left does NOT mean to subtract while moving right does NOT mean to add. The rules above are counterintuitive so pay attention when doing horizontal transformations.

In this case, the original function f(x) = [tex]x^{2}[/tex] was translated 4 units to the right. Since we shifted right, we must subtract 4 units within the function/parenthesis: g(x) = [tex](x-4)^{2}[/tex]

When we combine both vertical and horizontal changes, the only equation that follows these rules is the third choice: g(x) = (x − 4)^2 + 9

Answer: C

Step-by-step explanation:

Answer:

(g∘f)(x) = -20x + 22

Step-by-step explanation:

(g∘f)(x) simply means g(f(x))

We are given;

f(x) = -5x + 4

g(x) = 4x + 6

Thus;

(g∘f)(x) = 4(-5x + 4) + 6

(g∘f)(x) = -20x + 16 + 6

(g∘f)(x) = -20x + 22

Answer:

The first two.

Step-by-step explanation:

See that L is 600mm MORE than W.

From there, you can note that L = W+600  

or rearrange the formula and get W= L-600

Then, see that the perimeter of a flag is 2L + 2W

(Because there are two four sides to a rectangle, 2 width, 2 length)

It must total to be 5 meters, or 5000mm

Thus,

2L + 2W = 5000