3. Which expression is equivalent to 3(x-2) + Zx?A. -XB. 3xC. 5X-2D. 5X-6marios The cost of

Answer

Surface area = 2260.8 cm²

Explanation

The surface area of a normal sphere is given as

Surface area = 4πr²

where,

π = pi = 3.14

r = radius of the sphere = 12 cm

But this sphere has the middle of the sphere as part of the surface too

Surface area = 4πr² + πr² = 5πr²

Surface area = 5 (3.14) (12²)

Surface area = 2260.8 cm²

Hope this Helps!!!

We know that 5 lbs of apples cost $2.99

To know how much do 3 lbs of apple cost, you can use cross multiplication

If 5 lbs cost $2.99

Then 3 lbs cost $x

The proportion between the price and the number of apples is the same, you have to calculate it as:

3 lbs of apples cost $1.79

Note that parallel lines always have the same slope.

From the problem, the equation is :

and the slope is -1/4

Parallel lines must also have the same slope of -1/4

The answer is -1/4

So the numbers we have are:

-2, 3/4, -1/3, 0.2, -1, 1/2 & -0.8

So the numbers from least to greatest go as follows:

-2, -1, -0.8, -1/3, 0.2, 1/2, 3/4

The aritmetic sequence has the characteristic that each term is the term before plus a constant number. Then we can create the following system of equations:

where p is the constant value which is added in each term, and x the number between 34 and 345. If we replace the value of "x" from the second equation into the first one:

Finally, the term betwen 34 and 345 is 34+p, 189.5

Hence the answer is 189.5

Answer:

To find the area of the polygon with vertices C(5, 3), A(8, -2), S(3, -4), and H(0, -2).

We have that formula for finding the area of the parallelogram with n vertices is,

we get that,

Area of the polygon with 4 vertices that is (x1,y1),(x2,y2),(x3,y3) and (x4,y4) is

Substituting the values we get,

An

First, we have to solve the parentheses, by applying distributive property:

Add and subtract alike terms:

Hello there. To solve this question, we need to pay attention to the data given by the question and set up an equation for the amount of rabbits in that colony.

In the year 2000 there were 1200 rabits in a colony, and it was observed that their population was increasing at a rate of 21% each year

For this type of question, we call f(x) the function that shows the population in a certain time x.

This function varies directly to the initial population and grows exponentially according to the rate .

Thus, we have that f(x) = P0 * (1+r)^x

In this case, P0 = 1200 and r = 0.21 (21% converted into decimals)

f(x) = 1200 * (1 + 0.21)^x

f(x) = 1200 * 1.21^x

This is the function that models the population of this colony for a year x.

To find how many rabbits you'll have in the year 2007, plug in x = 7

f(7) = 1200 * 1.21^7

Calculate the value

f(7) = 1200 * 3.797 = 4556

In which year will the population be equal to 5000

Making f(x) = 5000, we solve for x

5000 = 1200 * 1.21^x

Divide both sides of the equation by 1200

25/6 = 1.21^x

Take the natural log on both sides of the equation

ln(25/6) = ln(1.21^x)

Apply the logarithm power rule: log(a^b) = b * log(a)

ln(25/6) = x * ln(1.21)

Rewriting 1.21 as 121/100 = (11/10)², we get:

ln(25/6) = 2x * ln(11/10)

Divide both sides of the equation by a factor of 2ln(11/10)

x = ln(25/6)/(2ln(11/10)) approx. 7.4867 years

Rounding up to the next year, x = 8 years.

Given the equation of the function f(x):

We will use the following rules of the exponents:

So, we can rewrite f(x) as follows:

So, the answer will be option B

The percentage can be changed to decimal as,

Thus, the required decimal is 11.75.

Notice that the factor x is a common factor for all three terms. Then, factor out x:

Notice that the factor x²-2x-35 is a quadratic expression.

Find two numbers whose sum is -2 and whose product is -35 to factor out the quadratic expression. Since 5-7 = -2 and (5)(-7)=-35, those two numbers are -7 and 5. Then, the quadratic expression can be factored out as:

Then:

Then, the factorization of the given trinomial is:

Therefore, the correct choice is option C) x(x-7)(x+5)

Answer:

Explanation:

We want to convert 3 gallons to pints.

Recall that;

So, for 3 gallons, we have;

Therefore;

The walk surrounding the pool has an area of 336.66 [tex]ft^{2}[/tex] .

A =  ( Area of semicircle including side walk ) - ( Area of semicircle without side walk )

radius of smaller semicircle = 10 ft and radius of larger semicircle = 10 + 3 = 13 ft

A = [ ( 3.14 * [tex]13^{2}[/tex] ) / 2 ] - [ ( 3.14 * [tex]10^{2}[/tex] ) / 2 ]

            = ( 530.66 - 314 ) / 2

              = 108.33 [tex]ft^{2}[/tex]

Since we take walk on both sides , we will multiply it with 2

A = 2 * 108.33

A = 216.66[tex]ft^{2}[/tex]

One side of bigger rectangle = 20 + 3 + 3 = 26 ft

A = area of rectangle - area of square

A = ( 26 * 20 ) - [tex]20^{2}[/tex]

A = 120 [tex]ft^{2}[/tex]

Therefore ,

A = 216.66 + 120

A = 336.66 [tex]ft^{2}[/tex]

Hence , the walk surrounding the pool has an area of 336.66 [tex]ft^{2}[/tex] .

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We are given the following system of equations:

We will substitute the value of "y" from the first equation into the second equation:

Now we subtract "3x" from both sides:

Adding like terms:

Now we subtract 10 from both sides:

Adding like terms:

Now we multiply by -1 on both sides of the equation:

Now we factor in the left side. We need two numbers that when multiplied the product is 800 and their algebraic sum is -60. Those numbers are -40 and -20. Therefore, we get:

Now we set each factor to zero:

For the next factor:

These are the two values of "x" for the solution. To get the corresponding value of "y" we substitute in the second equation. Substituting the first value we get:

Now we substitute the second value:

Therefore, the solutions of the system are:

ANSWER :

(f - g)(x) = x^2 + 8

EXPLANATION :

From the problem, we have :

(f - g)(x) is the difference between the two functions

That will be :

Answer:

1. Given.

2. Definition of vertical angles.

3. Vertical angles theorem.

4. Definition of corresponding angles.

5. Corresponding angles postulate.

6. Transitive property of congruence.

Explanation:

1. This statement is the given part of the problem

2. vertical angles are the pair of opposite angles that are formed when two line segments intersect. Angles 1 and 3 verify this definition, thus they're vertical angles.

3. The vertical angles theorem states that a pair of two vertical angles have the same measure.

4. Corresponding angles are the angles that are formed in matching corners with the transversal when two parallel lines are intersected by another line. Thus, angles 1 and 5 are corresponding angles.

5. The corresponding angles postulate states that, when two parallel lines are cut by a transversal, the resulting corresponding angles are congruent. Thus, angles 1 and 5 are congruent.

6. The transitive property of congruence states that if a is congruent to b and b is congruent to c, then a is congruent to c.

This means:

Let x the total of Hungry-Man Meals bought.

let y the total of burritos bought.

He decides to buy 50 total frozen entrees.

x + y = 50

If we solve the equation for x

x = 50 - y

We also know that he spends $150 on all the frozen food.

Therefore:

x Hungry-Man Meals for $3.25

y burritos for $2.00

x(3.25) + y(2.00) = 150

3.25x + 2.00y = 150

Now substituting 50-y from the first equation into the second equation and solve for y:

3.25x + 2.00y = 150

3.25(50-y) + 2.00y = 150

3.25*50 - 3.25*y + 2.00y = 150

162.5 - 3.25y + 2.00y = 150

162.5 - 1.25y = 150

Subtract both sides by 150

162.5 - 150 - 1.25y = 150-150

12.5 -1.25y = 0

Add both sides 1.25y

12.5 -1.25y+1.25y= 0+1.25y

12.5 +0 = 1.25y

Divide both sides by 1.25

12.5/1.25 = 1.25y/1.25

10 = y

Substitute 10 for y in the result of the x equation:

x = 50 - y

x = 50- 10

x = 40

So 40 Hungry-Man meals and 10 burritos Jack bought.

Since we want the total amount, we first can add the red and green ribbon:

Martha has 15 feet of ribbon.

To converto to yards, we can just divide the amount in feet by 3. So, in yards:

So

Martha has 5 yards of ribbon.

Step 1

The meaning of QUADRATIC EQUATION is any equation containing one term in which the unknown is squared and no term in which it is raised to a higher power.

Step 2

We are required to Identify the two tables which represent quadratic relationships.

In a quadratic equation, we have a polynomial in x with degree 2. Hence the result in y or P(x) do get repeated as a polynomial contains x² in it.

Looking at the tables we will observe that;

The answers will be;

SOLUTION

So the first option is the correct answer

3xy²(x - 5)

The equation: 3x²y²-15xy²

x is common to both expression, we factorise it:

x(3xy² - 15y²)

y² is common to both expression, we factorise it:

xy²(3x - 15)

3 is common to both expression, we factorise it:

3xy²(x - 5)

the x-intercepts are all the x coodinates in which the function will be equal to 0

to find the x intercepts equal the equation to 0

equal all factors involving the x to 0 because if there is any factor equal to 0 then the product between of al products will be 0 as well

solve both of the equations

the x-intercepts will be

(-4,0) & (6,0)

Given

Hours (h) = 1, 2, 3, 4, 5, 6, 7

Pages (p) = 40, 80, 120, 160, 200, 240, 280

Procedure

The answer would be p = 40h

The first clue only tells us that there is one digit that is in the right place, so it could be any one of the following.

The second one tells us that one of the digits is right but in the wrong place, we still cannot confirm if 5 is the number we are talking about.

The fourth clue says that all the numbers are incorrect, so the digits are 2, 5, 0 or 1, now we must find out the correct order.

From clues 3 and 5 we can assume that 0 is one of the digits and that it comes first.

We will discard the number 5 because in clue 3 they talk about 2 correct digits, we already know that 0 is one and we choose 2 instead of the number five because of clues 1 and 2, which talk about only one digit in the correct place but in both of them the 5 remains in the same place.

The 3 digists are: 1, 0 and 2

The correct order is 012

SOLUTION

Now, 9 and 51 are not compatible because 51 cannot divide 9 without a remaider.

The compatible number with 9 that is close to 51 is 54.

Hence,

9 and 54 are compatible.

This will give us

Hence,

The estimate is 600

range = ? -2 < y < 4 According to the directions this is the inequality

Letter A is the right answer

Answer: A

Step-by-step explanation:

B is wrong A is right.

the new equation would be:

if the new rate is changed to 3000. The new equation is:

Answer:

1

Step-by-step explanation: