Given that p = 6 and q = 2, which yields a quotient greater than -9? ОА -3 a -р B 3 O a O С Зр. (-9) (0) D (-p) (-39)

Answer:

The length of the base is:

The resulting quadratic is

Step-by-step explanation:

Base = x

Height = 4x

Area, A = 1/2* base * Height

           A = (1/2) * (x) * (4x)

          A = 2x²           (1)

But,    A = 6              (2)

Since (1) = (2);

2x²= 6

x²= 3

Resulting quadratic:

x² - 3= 0

For the difference between 2 squares:

a² - b² = (a-b)(a+b)

Using that identity, we can factorize our quadratic:

(x-3)(x+3) = 0

So, we have 2 roots:

x = 3 and x = -3

Now, noting that length must take a positive value, we go for the first:

x = 3

The length of the base is:

The resulting quadratic is

we have that

triangle ABD is a right triangle , because AD is a tangent

so

Apply the Pythagorean Theorem

DB^2=AB^2+AD^2

we have

AB is a diameter (two times rhe radius)

AB=2*295,000=590,000 km

AD=203,000 km

substitute

DB^2=590,000^2+203,000^2

Given data:

The given time taken by Tin to type 720 words is t=15 min.

The given expression can be wriiten as,

720 word=15 min

720 words= 15(60 sec)

720 words= 900 sec

1 word = 900/720 sec

=1.25 sec

Multiplying the above equation with 864 on both sides .

864 words= 864(1.25) sec

= 1080 sec

=1080/60 min

= 18 min.

Thus, the time taken bby Tine to type 864 words is 18 min.

the given expression is

-14 + (-8/9)

so,

so the answer is -14 8/9 or -134/9

Find the volume of a pyramid with a square base, where the side length of the base is

19.3 ft and the height of the pyramid is 16.2 ft. Round your answer to the nearest

tenth of a cubic foo

Remember that

the volume of the pyramid is equal to

where

B is the area of the base

h is the height

step 1

Find out the area of the base

B=19.3^2

B=372.49 ft2

h=16.2 ft

substitute the given values in the formula

The given equation is expressed as

x + 3 = 2x - 18

Subtracting x from both sides of the equation, it becomes

x - x + 3 = 2x - x - 18

3 = x - 18

Adding 18 to both sides of the equation, it becomes

3 + 18 = x - 18 + 18

21 = x

x = 21

Since there is only one value for x, the correct option is

a. A single solution

The resulting expression using the distributive property of multiplication over subtraction is 3(12) - 3(10).

The distributive property of binary operations extends the distributive law, which states that in elementary algebra, equality is always true.

For instance, given the expression;

A(B - C)

We will have to distribute A over B and C to have;

A(B - C) = AB - AC

Applying the rule to the given expression

3 (12 - 10)

3(12) - 3(10)

This shows that the given expression can also be written as 3(12) - 3(10)

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The Solution:

The given expression is

Rationalizing the expression with the conjugate of the denominator, we have

This becomes

Thus, the correct answer is

y= x+ 1/4 x

Y = dependent variable

x= independent variable

Jenny has a bank account. In the first month, she deposits a certain amount of money (x), and in the month after she deposits 1/4 of that amount.

Find the total amount of money deposited (y).

Given

For the vertical asymptotes, we set the argument of the logarithm to be zero. Therefore,

The domain of the function can be found below

STEP - BY - STEP EXPLANATION

What to do?

Graph each equation on the same set of axis.

Determine the mass that makes the spring the same length.

Determine the length of that mass.

Write a sentence comparing the two springs.

Given:

f(m) = 18 + 0.4m and g(m) = 11.2 + 0.54m

Step 1

Find the x and y-intercept of both function.

f(m) = 18 + 0.4m

f(0) = 18+0.4(0) = 18

0 = 18 + 0.4m

0.4m = -18

m=-45

The x and y -intercept of the function f(m) are (0, 18) and (-45, 0) respectively.

g(m) = 11.2 + 0.54m

g(0) = 11.2 + 0.54(0)

g(0) = 11.2

0 = 11.2+ 0.54m

0.54m = -11.2

m=20.7

The x and y - intercepts are (0, 11.2) and (20.7, 0).

Step 2

Graph the function.

Below is the graph of the function.

Observe from the graph that that the mass that makes the spring the same length is approximately 48.5 grams.

The length at that point is 37.4 centimeters.

Comparison between the two strings.

The string with the function f(m) started out longer, but does not stretch as quickly as the other spring with the function g(m).

ANSWER

b) 48.6 grams

c) 37.4 centimeters

d) The string with the function f(m) started out longer, but does not stretch as quickly as the other spring with the function g(m).

In order to have grade A, the score needs to be in the top 9%.

Since the scores are normally distributed, the top 9% scores correspond to 91% of the area under the normal curve. That means we need to find a value of z in the z-table that corresponds to the value 0.91 (that is, 91%).

Looking at the z-table, the value of z for a probability of 0.91 is z = 1.34.

Now, to find the score that this value of z represents, we can use the formula below:

Rounding to the nearest whole number, the minimum score for grade A is 79.

Given the following function:

Both θ and y are functions of the time (t)

We will find the derivatives of θ and y with respect of the time (t) as follows:

Now, we will find dy/dt when θ = π/6 and dθ/dt = π/12

First, we need to find the value of y when θ = π/6

so, we will substitute the values to find dy/dt as follows:

Rounding to 2 decimal places

So, the answer will be:

see explanation below

Explanation:

To find the point slope form of an equation, we will apply the formula:

Given two points, we will be able to find the slope = m

for example: (1, 2), (2, 4)

m = slope = change in y/ change in x

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

m = 2/1

m = 2

Then, we will pick any of the points and insert into the formula for the point slope.

Let's assume we are using point (1, 2) = (x1, y1)

inserting into the formula together with the slope gives:

y - 2 = 2(x - 1)

The above is a point slope for the points given.

Answer:

∠ FAE = 120°

Step-by-step explanation:

4x and 2x are a linear pair and sum to 180° , that is

4x + 2x = 180

6x = 180 ( divide both sides by 6 )

x = 30

then

∠ FAE = 4x = 4 × 30 = 120°

Okay, here we have this:

Considering that the formula for the simple interest rate is:

A = P (1 + rt)

In this case A is equal to $2500, P is the value we need to find, r is the interest rate (in decimal) 0.08, and t is the time, so it's 3 years, replacing we obtain:

2500=P(1+0.08*3)

Now, let's clear P:

2500=P(1+0.24)

2500=P(1.24)

2500/1.24=P

P=2016.13

Finally we obtain that the bank must put $ 2016.13 on a CD to get $ 2,500 in three years.

Remember that the sum of the interior angles is 180. Then, we have the following equation:

This is equivalent to:

solve for M-angle:

Then, te correct answer is :

EXPLANATION

Given the function f(x)= -x ²+4x - 3, the statements that apply are:

A) TRUE

B) FALSE

C) TRUE

D) FALSE

E) FALSE

F) TRUE

G) TRUE

H) FALSE

Let the total number of fare be f and total number of miles be m.

Therefore, the total fare f is given by:

Substitute f = 16.30 into the equation:

Therefore, the required number of miles is 3.

The values of the given polynomial are:-

f(0) = 12

f(2) = 28

f(-2) = 52

Given polynomial:-

[tex]f(x)=-x^3+7x^2-2x+12[/tex]

We have to find the values of f(0), f(2) and f(-2).

Putting x = 0 in f(x), we get,

[tex]f(0)=-(0)^3+7(0)^2-2(0)+12[/tex]

f(0) = 0 +0 - 0 + 12 = 12

Hence, the value of f(0) is 12.

Putting x = 2 in f(x), we get,

[tex]f(2)=-(2)^3+7(2)^2-2(2)+12[/tex]

f(2) = -8 + 28 - 4 + 12 = 28

Hence, the value of f(2) is 28.

Putting x = -2 in f(x), we get,

[tex]f(-2)=-(-2)^3+7(-2)^2-2(-2)+12[/tex]

f(-2) = 8 +28 + 4 +12 = 52

Hence, the value of f(-2) is 52.

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Probability of selecting a black three or a red jack = 1/13

There are a total of 52 cards in a deck of cards

Total number of ways of selecting one card from 52 cards = 52C1 = 52 ways

There are two red jacks in a deck of cards

Number of ways of selecting a red jack = 2C1 = 2 ways

There are two blacks 3s in a deck of cards

Number of ways of selecting a black three = 2C1 = 2 ways

Probability of selecting a black three or a red jack = (1/26) + (1/26)

Probability of selecting a black three or a red jack = 2/26 = 1/13

Explanation

we need to solve for n

Step 1

cross multiply

Step 2

subtract 4n in both sides

Step 3

subtract 14 in both sides,

Step 4

Finally, divide both sides by 3

I hope this helps you

Start to see the possible options

The first digit will have 10 possible numbers to choose from 0 to 9, however in the second digit since it cannot repeat there will be only 9 possible to choose from. As for ther third number 0 is not an option meaning that there are 9 to choose as well.

the channel that devoted more time was channel 8, because since 6<8 then it follows thay 1/6>1/8 (the inequiality changes), channel 8 devoted

Hello there. To solve this question, we have to remember some properties about the representation of a complex number in the complex or Argand-Gauss plane.

Given the complex plane with the point A representing a complex number:

We have to remember that in the complex plane, a complex number z:

has coordinates

And it is more commonly represented by a vector starting at the origin and with the tip on this point.

In this case, we find that the coordinates of the point A are:

Which means that the complex number is

And this is the answer contained in the last option.

The most appropriate choice for polynomial will be given by

1) Zeroes of P(x) = 2, [tex]\frac{2 + \sqrt{2}i}{3}[/tex], [tex]\frac{2 - \sqrt{2}i}{3}[/tex]

where [tex]i = \sqrt{-1}[/tex]

2) Zeroes of P(x) = 3, 2i, -2i

3) Roots are 2i, -2i, [tex]\frac{3}{2}[/tex]

4) Roots are 0, 1, [tex]2 + \sqrt{5}[/tex], [tex]2 - \sqrt{5}[/tex]

What is a polynomial?

An algebraic expression of the form [tex]a_0 + a_1x +a_2x^2 + a_nx^n[/tex] is called a polynomial of degree n.

[tex]1) P(x ) = 3x^3 -10x^2 + 10x -4\\P(2) = 3(2)^3 - 10(2)^2 +10(2) - 4\\[/tex]

        [tex]= 24 -40 + 20 -16\\= 0[/tex]

(x - 2)  is a factor of P(x)

[tex]P(x) = 3x^2(x - 2) -4x(x - 2) +2(x-2)\\[/tex]

        = [tex](x - 2)(3x^2 - 4x + 2)[/tex]

        [tex]=(x-2)(x -a)(x - b)[/tex]

where,

[tex]a = \frac{-(-4)+\sqrt{(-4)^2 - 4\times 3\times 2}}{2\times 3}\\a =\frac{ 4 + \sqrt{-8}}{6}\\a = \frac{4 + 2\sqrt{2} i}{6}\\a = \frac{2(2 + \sqrt{2}i)}{6}\\a = \frac{2 + \sqrt{2}i}{3}[/tex]

[tex]b = \frac{-(-4)-\sqrt{(-4)^2 - 4\times 3\times 2}}{2\times 3}\\b =\frac{ 4 -\sqrt{-8}}{6}\\b = \frac{4 - 2\sqrt{2} i}{6}\\b = \frac{2(2 - \sqrt{2}i)}{6}\\b = \frac{2 - \sqrt{2}i}{3}[/tex]

Zeroes of P(x) = 2, [tex]\frac{2 + \sqrt{2}i}{3}[/tex], [tex]\frac{2 - \sqrt{2}i}{3}[/tex]

where [tex]i = \sqrt{-1}[/tex]

[tex]2) P(x) = x^3 - 3x^2+4x-12\\P(3) = (3)^3 - 3(3)^2 +4(3) -12\\ P(3) = 0[/tex]

(x - 3) is a factor of P(x)

[tex]x^2(x - 3) + 4(x - 3)\\(x - 3)(x^2 + 4)\\(x - 3)(x -a)(x-b)\\[/tex]

where,

[tex]a = \sqrt{-4}\\a = 2i[/tex]

[tex]b = -\sqrt{-4}\\a = -2i[/tex]

Zeroes of P(x) = 3, 2i, -2i

[tex]3) 2x^3 - 3x^2 +8x-12= 0\\[/tex]

x = 2 satisfies the equation

[tex]2x^2(x -\frac{3}{2}) + 8(x-\frac{3}{2})=0\\(2x^2+8)(x - \frac{3}{2}) = 0\\[/tex]

[tex]2x^2 + 8 = 0[/tex] or [tex]x - \frac{3}{2} = 0[/tex]

[tex]x^2 = -\frac{8}{2}[/tex] or [tex]x = \frac{3}{2}[/tex]

[tex]x^2 = -4[/tex] or [tex]x = \frac{3}{2}[/tex]

[tex]x = \sqrt{-4}[/tex] or [tex]x = \frac{3}{2}[/tex]

[tex]x = 2i[/tex] or [tex]x = -2i[/tex] or [tex]x = \frac{3}{2}[/tex]

Roots are 2i, -2i, [tex]\frac{3}{2}[/tex]

4)

[tex]x^4 - 5x^3 +3x^2 +x = 0\\x(x^3 -5x^2 + 3x +1) = 0\\[/tex]

[tex]x = 0[/tex] or [tex]x^3 -5x^2+3x +1 = 0[/tex]

For  [tex]x^3 -5x^2+3x +1 = 0[/tex]

x = 1 satisfies the equation

[tex]x^2(x -1) -4x(x-1)-1(x-1) = 0\\(x - 1)(x^2 - 4x -1) = 0\\[/tex]

[tex]x -1 = 0[/tex] or [tex]x^2 - 4x -1 = 0[/tex]

Roots are x = 1 or x = a or x = b

where,

[tex]a = \frac{-(-4) + \sqrt{(-4)^2 - 4\times 1 \times(-1)}}{2\times 1}\\a = \frac{4+\sqrt{20}}{2}\\a = \frac{4 + 2\sqrt{5}}{2}\\a = \frac{2(2 + \sqrt{5})}{2}\\a = 2 + \sqrt{5}[/tex]

[tex]b = \frac{-(-4) - \sqrt{(-4)^2 - 4\times 1 \times(-1)}}{2\times 1}\\b = \frac{4-\sqrt{20}}{2}\\b = \frac{4 - 2\sqrt{5}}{2}\\b = \frac{2(2 - \sqrt{5})}{2}\\b = 2 - \sqrt{5}[/tex]

Roots are 0, 1, [tex]2 + \sqrt{5}[/tex], [tex]2 - \sqrt{5}[/tex]

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To find the solution of the system by graphing we need to plot each line in the plane and look for the intersection.

First we need to write both equations in terms of y:

now we need to find two points for each of this lines. To do this we give values to the variable x and find y.

For the equation 2x-y=-1, if x=0 then:

so we have the point (0,1).

If x=1, then:

so we have the point (1,3).

Now we plot this points on the plane and join them with a straight line.

Now we look for two points of the second equation.

If x=0, then:

so we have the point (0,-3)

If x=1, then:

so we have the point (1,-1).

We plot the points and join them wiith a line, then we have:

once we have both lines in the plane we look for the intersection. In this case we notice that the lines are parallel; this means that they wont intersect.

Therefore the system of equations has no solutions.