Select all the equations on which the point (10,0) lies. O 5x + 2y = 15 O 2x + 4y = 20 O x + y = 10 O 3x + 3y = 13 4x + 2y = 20 O 6x + y = 50

Factor theorem is usually used to factor and find the roots of polynomials. A root or zero is where the polynomial is equal to zero. Therefore, the theorem simply states that when f(k) = 0, then (x – k) is a factor of f(x).

In this case here, let's find out if 2 is a root of the polynomial given.

As we can see in the box below, 2 is not a root of the polynomial, therefore (x-2) isn't a factor.

Given:

it is given that a department store is offering a promotion on candles. The promotion is "Buy 2 candles, get 40% off the 3rd Candle".

Find:

we have to find the total cost of buying 3 same candles.

Explanation:

Let c be the cost of one candle.

Then 2c is the cost of two candles.

and, as per offer , the price of the third candle is 40% off.

if c is the price of one candle , then the cost of third candle is

c - (40% of c) = c - 0.4c = (1 - 0.4)c = 0.6c

Therefore, cost of third candle is 0.6c.

Now, the total cost of buying three same candles = 2c + 0.6c = 2.6c

Therefore, the options 2c + 0.6c and 2.6c are correct options

On observation of the graphs of the two functions, we can see that f(x) has undergone some transformation to give g(x).

The original function is given as

The function is reflected over the x-axis.

The rule for the reflection over the x-axis is given as

Applying this to the function, we have the new function to be

The graph is also shifted downwards by 3 units.

This shift can be represented as

Applying this to our function, we have the new function, g(x), to be

The correct option is OPTION D.

Explanation: To solve a derivate we can use a simple technique presented below

- First, we take the exponent and multiply it by the function. Second, we subtract a unit of the exponent. Let's visualize it better on the drawing below

Step 1: Now we can use the same concept to calculate all the derivates we need as follows

Final answer: So the final answers are

.

real part = 8

imaginary part = -√245

since we can't find square root of a negative number, we will introduce the complex number:

i² = -1

1) The coefficient of the third term is one.

2) The constant term is zero.

We are given a polynomial. A polynomial is a mathematical statement made up of indeterminates and coefficients that solely includes the operations of addition, subtraction, multiplication, and positive integer powers of variables. The polynomial is (1/2)a^4 + 3a³ + a. The polynomial has the variable "a". The polynomial has three terms. So, it is a trinomial. The third term of the polynomial is "a". The coefficient of the third term is 1. There is no constant term in the polynomial. So, we can say that the constant term is 0.

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The answer to your question is inverse varaiation.

Explanation: Inverse variation is a reciprocal term. Or say a variable is increasing while the other is decreasing.

So it is observed that as when y increases, then x decreases.

And also when y decreases, then x increases.

Thus, It is an inverse variation.

SOLUTION:

Step 1:

In this question, we are given the following:

Your mother placed 6 flowers in a vase.

How many vases does your mother need for 30 flowers?

Step 2:

The details of the solutions are as follows:



4)

In the case of a square, its diagonals are equal and bisect each other, meeting at 90°.

In our case, using a diagram,

Therefore,

Solving the system of equations for a and b,

Finding a,

We have the multiplication of 3 factors, one of them unknown, that give 900 as a result.

We can write this as:

The third factor is 6.

Given the phrase:

-3 times r is at least 33

Let's translate the given phrase into an inequality.

• Part A.

Let's figure out the inequality in steps.

-3 times r is written as:

-3r

-3 times s is at least 33 means that -3r is greater than or equal to 33.

Hence, we have the inequality:

• Part B.

Let's solve the inequality for r.

To solve for r, divide both sides of the inequality by -3:

• Part C.

Let's express the solution in interval notation.

Here, the solution is:

It means s must be less than or equal to 11.

Therefore, the solution in interval notation is:

ANSWER:

• A) -3r ≥ 33

• B) r ≤ -11

• C) (-∞, -11]

We will investigate the counting principles that are used for cases of probability evaluation.

There are two possible types of counting principles.

Combinations:

It gives us the total number of possible selections that you can make "given" - " for " something. It is a simple selection process between the subejct and an object. The notation used for determining the number of selections/combinations is expressed as:

Where,

Then we can use the calculator infused functions of " C " combinatorics!

Permutations:

It gives us the total number of possible arrangements comprised of selections and shuffling that you can make "given" - " for " something. It is a simple selection and shuffling process of subject and object. The notation used for determining the number of selections/combinations and re-shuffling is expressed as:

The above means that to determine arrangements we first need to find the number of combinations " C " between the subject and object then we will re-shhuffle the order of each combination paired with an object!

We are given the following:

The corresponding variables are:

We are to determine the total number of possible arrangements that are possible. Hence, we are looking at the case of permutations that involves the selection and re-shuffle process.

The total number of arrangements can be made as such:

Step-by-step explanation:

what happens, if I cut something in half ?

not just into 2 pieces, but outright in half ?

a pizza or a cake ?

well, I get 2 identical pieces.

a bisector (bi = 2 or double, sector = part) splits an angle into 2 equal parts.

that means

33 = 4x + 1

from there we get

32 = 4x

x = 32/4 = 8

Conditional Probability

Given two events A and B (not excluding), the probability that A occurs given that B has occurred is called a conditional probability and is calculated as:

Where P(A∩B) is the probability that A and B occur simultaneously and P(B) is the probability that B occurs.

Now with the given data, we must find the values of the required probabilities.

30% of the students play a sport (S), this means that:

70% of the students don't play a sport (NS).

65% of the students have a job.

Note that there could be students who both play sports and have a job.

Of the 30% of the students who play a sport, 50% have a job. This means that:

15% of the students play a sport and don't have a job

15% of the students play a sport AND have a job

65% - 15% = 50% of the students have a job and don't play a sport

That last number is the numerator of the equation given above:

P(A∩B) = 0.5

The event B corresponds to students that don't play a sport (NS), thus:

P(B) = 0.7

Thus we have:

The required probability is 5/7 or 0.7143

The standard equation of a line has the form:

y=mx+b

Where m is the slope of the line and b is the intercept.

The only thing we need to determine the equation of a line is two points, in this case, we have the points (4,4) and (8,3). Then, from the first point we know that when x equals 4 y equals 4 and from the second point we know that when x equals 8 y equals 3, we can express this with the standard formula of a line, like this:

4=m*4+b and 3=8*m+b

subtraction the second expression from the second one, we get:

4-3=m*4+b-8*m-b, we can cancel b and then we have:

4-3=m*4-m*8, we can subtract 3 from 4 in the left side and 8*m from 4*m from the right side and then:

1= -4*m , we can divide both sides by -4 and then:

m= -1/4

Now that we know the value of the slope, we only need to specify the value of b, we can do this by replacing the value of m in the expression 4=m*4+b of the first point and then solve for b, like this;

4=m*4+b, m=-1/4, then:

4= 4*(-1/4)+b, then:

4= -1+b, then, adding -1 in both sides we have:

4+1=b, then:

b=5

And the standar form of the line would be:

y=(-1/4)*x+5

Explanation

From the question, a right-angle triangle must obey Pythagoras theorem. Therefore, we can see that

The rest of the values do not obey Pythagoras theorem. Therefore;

Answer: Option B and Option C

First we need to know how to convert radians to degrees

where r is the measure in radians and d is the measure in degrees

for A.

r=53pi/36

the measure in degrees is 265°

for B.

r= 13pi/18

the measure in degrees is 130°

for C.

r=-7pi/20

the measure in degrees is -63°

for D.

r=-2pi/9

the measure in degrees is -40°

When people take medicine, the drug gets metabolized by the body and eliminated at a constant rate.

Suppose the initial amount of a drug in the body is 549 mg and it is eliminated at a rate of 12% per hour.

Let f(x) refer to the amount of drug left in the body after I hours.

(a) Write down an exponential function to model this situation. Write your answer using function

notation

(b) How much of the drug is left in the body after 12 hours? Round to the nearest whole number.

(c) How much of the drug is left in the body after 180 minutes? Round to the nearest whole number

Part a)

Let

t -----> number of hours

f(x)=a(1+r)^t

where

a=549 mg

r=12%=0.12

substitute

f(x)=549(1+0.12)^t

Part b)

For t=12 hours

substitute in the function

f(12)=549(1.12)^12

Part c)

For t=180 minutes

Remember that

1 h=60 minutes

so

180 minutes=180/60=3 hours

For t=3 hours

substitute

f(3)=549(1.12)^3

According to the given data we have the following:

15 - 21p

correct expression?

To find the correct expression we need to check which expression is the correct one by multiplying the number which is outside of parentesis to the numbers inside of the parentesis.

Therefore,

15 - 21p

The right option in this case is:

3(5 - 7p)

3 times 5 is=15

3 times -7=21

Therefore 3(5 - 7p)= 15 - 21p

area shaded to the left = 0.9131

by using the Z cumulative table , we can see that the value that corresponds with Z= 0.913 is 0.838

Since each year cost $8,800 for two years tuition he will need $17,600 then if he want to save at least this much in five years according to the table he needs to save $200 monthly

Abrha will be spending $701 monthly, just by arithmetic operation.

What is the arithmetic operation?

The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.

If the numerator is bigger, it is referred to as an improper fraction and can also be expressed as a mixed number, which is a whole-number quotient with a proper-fraction remainder.

Abrha lives in an apartment,

electric bill, $44.90 = $50

TV streaming service, $24.99  = $25

Rent, $625.85 = $626

So the Total expenses will be (50+25+626) = $701 just by arithmetic operation

Hence Abrha will be spending $701 monthly.

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SOLUTION

We want to solve

Taking logarithm of both sides, we have

Collecting like terms we have

Hence the solution set expressed in terms of logarithm is

Using a calculator to obtain a decimal approximation, we have

Hence the answer is -3.52 to 2 decimal places

To determine the Ulices's account if he shipped just 1 box, calculate the charge for one box. To calculate the charge, compute the quotient between the charge for 4 boxes between 4 boxes, just as folow:

charge per one box = 140/4 = 35

Hence, for 1 box the charge is $35

Due to it is necessary to pay $20 idependenty of the number of boxex, you sum $20 to the cost for one box:

New Ulices's account = $35 + $20 = $55

Hence, Ulices's account would have been of $55

4(a-4)(a+1)

1) Factorizing 4a²-12a -16

4a²-12a -16 Note that the GCD (4,12,16) is 4, Rewrite them

4a²- 4*3a - 4* 4

2) 4(a² -3a -4) Rewrite a² -3a -4 answering the question, What are the numbers whose sum is 3 and product is 4?

Answer:

1 -4 = -3

1 x -4 = -4

3) Hence, the answer is:

4a²-12a -16= 4(a-4)(a+1)

RPQ to CAB transform

Rotation needed = RPQ using C as center ,an angle ACP

Translations= Line RC

Reflections= None

Then answer is

Option D)

Translate RPQ by the direct line segment RC

the given equation is

x - 3y = -9

-3y = -9 - x

-3y = - (9 + x )

3y = 9 + x

y = x/3 + 3

so the answer is

y = x/3 + 3

The given inequality is

To solve it, we need to isolate s on one side and the numerical terms on the other side

To do that we need to move 7 from the left side to the right side with 3, so

Add 7 to both sides

The solution of the inequality is s > 10

We can represent it on the number line