What is the value of 6a + 9b?​

xplanation:

Step 1. e are given the following zeros of a polynomial function.

- 1 with a multiplicity of two, which means that is a zero two times:

and the other two zeros are:

And we need to find the equation that has these four zeros.

tep 2. 2R

tep 3. S

tep 4. S

tep 5. T

Then, let's multiply the second and third parentheses:

Multiple terms cancel and the result is:

tep 6. TT

Combining like terms:

This is shown in option D.

Answer:

D

We are basically asked to perform the product of expressions that contain complex numbers a s roots of polynomials. So it is essential to identify the complex root in order to facilitate our products that otherwise could be really time consuming.

First product:

(x + 3 + 5i) (x + 3 - 5i) we are going to write as: ((x +3) +5i) ((x+3) - 5i). So this is going to be interpreted as a difference of squares (a + b) ( a - b) = a^2 - b^2:

((x +3) +5i) ((x+3) - 5i) = (x+3)^2 - (5i)^2 = (x+3)^2 - (-25) = (x+3)^2 + 25

We are using the fact that (i)^2 = -1 to convert - 25 (i)^2 = + 25

Now we solve the square of the binomial (x+3) , that is:

(x+ 3)^2 = x^2 + 6x + 9

Now this combined with + 25 gives: x^2 + 6x + 34 This is one of the options in blue background shown at the tops (the fourth one starting from the left)

Second product:

(x - 4i) (x + 4i) which is an easirer product than the one above because we can solve it just using difference of squares: (a - b) (a + b) = a^2 - b^2:

(x - 4i) (x + 4i) = x^2 - (4i)^2 = x^2 - 16 (i)^2 = x^2 +16

This is the second expression in blue background from left to right.

Third product:

(x - 6 + i) (x - 6 - i) for which we apply the same technique as in the first product we solve above:

(x - 6 + i) (x - 6 - i) = ((x - 6) + i) ((x - 6) - i) = (x-6)^2 - (i)^2 = (x-6)^2 - (-1) = (x-6)^2 + 1 = x^2 - 12 x + 36 + 1 = x^2 - 12 x + 37 which is the very first expression in blue background in the image you uploaded.

Olease move the bue background boxes so as to match the indicated products.

It is known that that the median divides the range into half.

And the first and third quartiles are the landmark for 25% and 75% of the data values.

Therefore, a dot plot is divided into 4 parts, each of ehich represents 25% of the population.

In the given dot plot diagram, it is observed that the mean of the construction worker's salary, coincide with the upper quartile of the salary., at $45,000

It means that 50% population of construction workers is getting at most $45,000 while 75% population of teachers is getting at most $45,000.

So if a construction worker is making the median salary i.e. $45,000, so he/she will be making more than 75% of the teachers.

the initial expression is:

So this equation has already one solution

Now if we want to have infinit solution we an rest 3x so:

So x can have any value, so there are infinit solutions

And to have no solutions we can add 5 -y at the left an

Answer:

79

Step-by-step explanation:

same thing as 79/1

SOLUTION

From the question, since the coordinates of the mid-points JK and JL has been given as M (2,16) and M, (-3, 5), respectively.

To find the distance between these two mid-points, we simply use the distance formula to do that.

The distance formula is given as

Applying these to the points M (2,16) and M, (-3, 5), we have

Hence the answer is 12.1 units

The circumference of a circle whose radius is 15 inches measures 94.2 inches.

For a circle of radius R, the circumference is given by the formula:

C = 2*pi*R

Where pi is 3.14

In this case, we know that the radius is 15 inches, then we can write:

R = 15 in

Replacing that in the circumference formula we get:

C = 2*3.14*15 in = 94.2 inches.

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The answer is 5

Step-by-step explanation:

-3=z-8

put +8 underneath -8. Then cross it out.

Put +8 underneath -3. -3+8=5

The answer is 5.

I hope this helped you!

Answer:

Step-by-step explanation:

(4^3/(9^3)

= 64/729 or0.09

If we have 45.4 cups of batter, we can make 181 pancakes using unitary method.

The unitary approach is a technique for problem-solving that involves first calculating the value of a single unit, then multiplying that value to figure out the required value.

Given Data

28 cups of batter to make 112 pancakes

To make 1 unit

28 cups of batter = 112 pancakes

1 cup of batter = 4 pancakes

If we have 45.4 cups of batter, we can make,

1 cup of batter = 4 pancakes

45.4 cup of batter = 45.4(4)

45.4 cup of batter = 181 pancakes ( approximately )

If we have 45.4 cups of batter, we can make 181 pancakes using unitary method.

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Option (c)

Given:

The measure of pantry shelf is 3 yard by 3/7 yrds.

The objective is to find the area of the pantry shelf.

The area of shelf can be calculated as,

Hence, option (c) is the correct answer.

So C receives py/(x+y)(p+q) share of money out of the total money

The ratio of money shared between A and B = x:y

Sum of the ratios is x+y

Comparing two amounts of the same units and determining the ratio tells us how much of one quantity is in the other. Two categories can be used to categorize ratios.

B' share of money = y/(x+y)

The ratio of money between C & D = p:q

Sum of the ratio = p+q

B's share of the money is further divided among C & D in the ratio of p:q therefore:

C's share of money = y/(x+y)*p/(p+q)

= py/(x+y)(p+q)

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We have a random variable, the time it takes to wash the dishes, that is uniformly distributed between 7 minutes and 16 minutes.

We have to calculate the probability that this random variable will have a value between 11 and 15 minutes.

We can calculate this probability as:

Given:

1.1.1 The equation of the reflection of g(x) in the x-axis is of the form:

The rule for the reflection in the x-axis:

Applying the rule:

Hence, g'(x) = 4-3x

1.1.2 The equation of the reflection of h(x) in the y-axis.

The rule for reflection in the y-axis:

Applying the rule:

Hence, h('x) = 2/-x

1.1.3 The values of k for which :

Re-arranging:

Using the rule that for an equation to have non-real roots, the discriminant (D) must be less than zero.

Simplifying we have:

Hence, the values of k for which the equation has non-real roots is that k must be less than -8

1.1.4 The average gradient of f(x) between x=-4 and x=0:

First, we need to find the value of f(x) at x=-4.

Next, we must find the value of f(x) at x=0:

Using the average gradient formula:

Hence, the average gradient is -12

) Let us assume that the interest was compounded annually. The formula for calculating compound interest is expressed as

A = P(1 + r/n)^nt

where

A is the amount after t years

P is the principal or initial amount invested

r is the interest rate

n is the number of compounding periods in a year

t is the number of years

From the information given,

P = 130

r = 4% = 4/100 = 0.04

n = 1 because it was compounded once in a year

t = 10

By substituting the values into the formula, we have

A = 130(1 + 0.04/1)^1 * 10

A = 130(1.04)^10

A = 192.43

Rounding to the nearest whole number, the amount after 10 years is $192

To solve this equatio you use the next property:

Subtraction Equal Property: it is used in expressions with adds. State that you can substract the same amount from both sides of the equation and maintain euality.

In this case, to solve r you substract 18 in both sides of the equation:

As 18-18 is 0;

1. The least number of hours that.Kee can work is 7 hours.

2. The maximum number of miles that Julie will drive will be 272 miles.

1. Lee makes $64 per hour and he wants to make no less than $400 each hours for the trip. The number of hours will be:

Let the number of hours = h

64h >= 400

Divide

h >= 400/64

h >= 6.25

The least hour should be 7 hours.

2. The maximum number of miles that Julie will drive will be:

44(3) + 0.25m = 200

m = number of miles

132 + 0.25m = 200

0.25m = 200 - 132

0.25m = 68

m = 68 / 0.25

= 272

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Answer:

5.   [tex]\bold{(g \circ f)(-3) = 16}}[/tex]

6.   [tex]\bold{h(h(-3x)) = -12x + 15 }}[/tex]

7.   [tex]{\bold{f\left(g\left(x-3\right)\right):\quad 3x-21}}[/tex]

8.   [tex]\bold{\text \bold g(f(-3x)) = -36x + 15}}[/tex]

Step-by-step explanation:

These are examples of composite functions.

What is a composite function?
A function by definition is a process that takes a collection of inputs and produces a corresponding collection of outputs in such a way that the process produces one and only one output value for any single input value.

Since we consider a function a process it makes sense to think of two functions acting in sequence to produce a single output. The output from one function is fed into the second function.

Note that we can have [tex]f[/tex][tex]g[/tex] as the outer function, in which case the notation will be [tex](g \circ f)(x)[/tex] or [tex]g(f(x))[/tex]

Problem Solution

5.     [tex]g(x) = x + 3 \;\text and\; f(x) = 3x + 4[/tex]
       Find  [tex](g \circ f)(-3) = g(f(-3))[/tex]

6.   [tex]h(x) = 2x + 5[/tex]
     Find [tex]h(h(-3x))[/tex]

 [tex]7.\;\;\;g\left(x\right)\:=\:x-\:3,\:f\left(x\right)\:=\:3x\:-\:3\\\\\text{Find } \:f\left(g\left(x-3\right)\right)[/tex]

.[tex]\bold{8.\;\;g(x) = 3x + 3, f(x) = 4x + 4}\\\\\bold{\text{Find } g(f(-3x))}[/tex]

Denmark uses kroner as its currency. Before a trip to Denmark. Mia will get 8670 Kroner in exchange for $ 1700.

bank A

Dollars ($)     Kroner

80                  408

100                 510

120                 612

Since $ 80 = 408 Kroner

=>       $ 1    = 408 / 80 = 5.1 Kroner   . . . . . . conversion rate of $ to Kroner)

=>   $ 1700 = 1700 x 5.1 = 8670 Kroner

Hence Mia will get 8670 Kroner in exchange for $ 1700

The exchange rate of conversion from $ to Kroner is arrived at by applying Unitary System of calculation in arithmetic (mathematics).

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16 fresh coffee are needed to obtain 14 2/25 lb of roasted coffee.

Coffee loses 12% of it's weight when it is roasted

The number of fresh coffee that is needed to obtain 14 2/25 lb of roasted coffee can be calculated as follows

let y represent the number of fresh coffee needed

100%-12%

= 88%

= 88/100

= 0.88

14 2/25

= 352/25

= 14.08

The number of fresh coffee can be calculated as follows

0.88y= 14.08

y= 14.08/0.88

y= 16

Hence to obtain 14 2/25 lb of roasted coffee, 16 fresh coffee is required.

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Answer:

16 lbs

Step-by-step explanation:

We have

We will substitute the values given

x=6 y=1

we solve the operations in order to obtain the result

the answer is 49

SOLUTION

Recall that a quadratic equation is of the form

The possible number of zeros of a quadratic function is 2The zeroes of a quadratic function could be real or complex

Therefore a quadratic function can have zero real roots

or 1 real root or 2 real roots.

Answer:

-1

Step-by-step explanation:

Correct option is A)

Given,

f(x)=5x−1

To find: f(0)

Put x=0 in the given eqation.

Therefore, we get

f(0)=5(0)−1

=0−1

=−1

Ok

y = 2/5x

ok

a) y = 2/5(14)

y = 28/5

y = 5.6 the first one is not an order pair

b) y = 2(30)/5

y = 60/5

y = 12 the second one is an order pair

c) y = 2/5(50)

y = 100/5

y = 20 the third one is an order pair

d) y = 2/5(10)

y = 20/5

y = 4 the four one is an order pair

e) y = 2/5(40)

y = 80/5

y = 16 the fifth one is not an order pair

f) y = 2/5(25)

y = 50/5

y = 10 the sixth one is not an order pair.

The solutions are (30, 12), (50, 20) and (10, 4)

The situation represents a function, while the domain and the range are 0 <= x <= 5 and 0 <= y <= 100, respectively

From the question, we have

Charges = $20 per person

Let the number of people be x and the total charges be y

So, we have

y = 20x

The above equation is a linear function

From the question, we have

Total number of people per seat = 5

So, the domain is 0 <= x <= 5

Substitute 5 for x in y = 20x

y = 20 x 5

Evaluate

y = 100

So, the range is 0 <= y <= 100

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Metric system:

Centiliter

Miligram

Kilometer

U.S. Customary System:

Yard

Pound

Mile