Which expression is a factor of both x^2 − 9 and x^2 + 8 x + 15

Answer: {MMM ,MCC ,CMC, CCM ,CMM ,MCM ,MMC ,CCC }

Step-by-step explanation:

Let C denotes the event when dog catches the throw and M denotes the event when dog misses the throw.

Given: Caleb throws a ball three times for his dog leo.

Then the sample space for the situation is given by :-

{MMM ,MCC ,CMC, CCM ,CMM ,MCM ,MMC ,CCC }

Answer:

It has two solutions

Step-by-step explanation:

The system [tex]\frac{3}{4z}=\frac{1}{4z-3}   + 5[/tex]

If we try to simplify the fractions applying the Lesser Common Factor

We obtain this:

[tex]12z-9=4z+ 5(4z)(4z-3)[/tex]

From this equation, you can see a square term coming up, from where we can say that this system has two solutions

Answer:

a) 47 people (count each leaf)

b) 66 - 1 = 65 (max - min)

c) 4 (occurs the most)

Answer:

C. infinite

Step-by-step explanation:

We want to solve the system:

First equation: [tex]y=2x+3[/tex]

Second equation: [tex]2y=4x+6[/tex]

Multiply the first equation by 2.

This gives us:

Third equation: [tex]2y=4x+6[/tex]

Subtract the third equation to obtain;

[tex]2y-2y=4x-4x+6-6[/tex]

[tex]0=0[/tex]

This implies that, the solution is all real numbers.

This means that the two lines coincide with each other. Therefore there are infinitely many solutions.

Answer: 0.4 repeading

Step-by-step explanation: this is extremely easy all you have to do is divide 4 / 9 which gives you 0.4 repeating or it might look like this

The cost per square foot of tiles

The given expression is the total cost of tiling and fencing the patio , Option D is the correct answer.

A square is a two-dimensional figure , and a polygon with four sides , All the sides and angles of square is equal .

It is given that

Lucia is building a square patio with a side length of n feet.

She will cover the floor of the patio with tiles and put a fence around the

perimeter of the patio.

The tiles cost $5 per square foot

The fencing costs $3 per foot

She will also buy additional supplies for $25.

Let n represent the edge length, in feet, of the patio.

the expression 5n² + 12n + 25 represent = ?

Area of the patio in square shape will be given by

side * side = n * n =n²

Title cost total = $5 * n²

Title cost total = 5 n²

Perimeter of the patio is given by 4 * side

Perimeter of the patio = 4n

The fencing cost = 3 * 4n = 12n

and the additional cost is $25

The total cost = 5 n² + 12n + 25

Therefore the given expression is the total cost of tiling and fencing the patio , Option D is the correct answer.

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Answer:

f(x) = [tex]3x^3 - 3x^2 - 6x[/tex]

Step-by-step explanation:

Which polynomial function has x intercepts -1,0, and 2 and passes through the point (1,-6)?

There are 3 distinct and real roots given in the question, which means that the  function must be a third degree polynomial. The roots are -1, 0, and 2. This means that f(x) = 0 at these points. The general form of the cubic equation is given by:

f(x) = ax^3 + bx^2 + cx + d; where a, b, c, and d are arbitrary constants.

From the given data:

f(-1)=0 implies a*(-1)^3 + b*(-1)^2 + c(-1) + d = -a + b - c + d = 0. (Equation 1).

f(0)=0 implies a*(0)^3 + b*(0)^2 + c(0) + d = 0a + 0b + 0c + d = 0. (Equation 2).

f(2)=0 implies a*(2)^3 + b*(2)^2 + c(2) + d = 8a + 4b + 2c + d = 0. (Equation 3).

f(1)=0 implies a*(1)^3 + b*(1)^2 + c(1) + d = a + b + c + d = -6. (Equation 4).

Equation 2 shows that d = 0. So rest of the equations become:

-a + b - c = 0;

8a + 4b + 2c = 0;  (Divide 2 on both sides of the equation to simplify).

a + b + c = -6

This system of equation can be solved using the Gaussian Elimination Method. Converting the system into the augmented matrix form:

• 1 1 1 | -6  

• -1 1 -1 | 0

• 4 2 1 | 0

Adding row 1 into row 3:

• 1 1 1 | -6  

• 0 2 0 | -6

• 4 2 1 | 0

Dividing row 2 with 2 and multiplying row 1 with -4 and add it into row 3:

• 1 1        1 | -6

• 0 1       0 | -3

• 0 -2 -3 | 24

Multiplying row 2 with 2 and add it into row 3:

• 1 1       1 | -6

• 0 1       0 | -3

• 0 0 -3 | 18

It can be seen that when this updated augmented matrix is converted into a system, it comes out to be:

• a + b + c = -6

• b  = -3

• -3c = 18 (This implies that c = -6.)

Put c = -6 and b = -3 in equation 1:

• a + (-3) + (-6) = -6

• a = -6 + 3 + 6

• a = 3.

So f(x) = [tex]3x^3 - 3x^2 - 6x[/tex] (All conditions are being satisfied)!!!

Answer: there is 4 options.

Step-by-step explanation:

there is 2 crusts, 2 sauces, and 3 toppings. he doesn't want pepperoni or white sauce so now there is

2 crusts, 1 sauce, and 2 toppings.

2 times 1 times 2 = 4.

The number of different combinations that are possible for someone who does not care for meat or white sauce is 12 combinations.

Multiplication is one of the most basic arithmetic operations, where multiplications tell us the number of ways a number is added to another.

The number of crust, sauce, and toppings that are present at the pizza shop is,

Type of crust; Thick or Thin = 2

Type of sauce; Red or White = 2

Type of toppings;  pepperoni, cheese, or vegetarian = 3

Thus, the number of different combinations that are possible for someone who does not care for meat or white sauce can be written as,

Number of combinations = 2 × 2 × 3 = 12 combinations

Hence, the number of different combinations that are possible for someone who does not care for meat or white sauce is 12 combinations.

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Answer:

22

Step-by-step explanation:

Answer:

[tex]x=25.24[/tex]

Step-by-step explanation:

To find the value of [tex]x[/tex], we are solving the exponential equation [tex]-6.2^{0.1x} =-100[/tex] using logarithms.

Let's solve it step-by-step

Step 1. Divide both sides of the equation by -1 to get rid of the negative signs:

[tex]-6.2^{0.1x} =-100[/tex]

[tex]\frac{-6.2^{0.1x}}{-1} =\frac{-100}{-1}[/tex]

[tex]6.2^{0.1x} =100[/tex]

Step 2. Take natural logarithm to bot sides of the equation:

[tex]ln(6.2^{0.1x)}=ln(100)[/tex]

Step 3. Use the power rule for logarithms: [tex]ln(a^{x} )=xln(a)[/tex]

For our equation: [tex]a=6.2[/tex] and [tex]x=0.1x[/tex]

[tex]ln(6.2^{0.1x)}=ln(100)[/tex]

[tex]0.1xln(6.2)=ln(100)[/tex]

Step 4. Divide both sides of the equation by [tex]0.1ln(6.2)[/tex]

[tex]0.1xln(6.2)=ln(100)[/tex]

[tex]\frac{0.1xln(6.2)}{0.1ln(6.2)} =\frac{ln(100)}{0.1ln(6.2)}[/tex]

[tex]x=\frac{ln(100)}{0.1ln(6.2)}[/tex]

[tex]x=25.24[/tex]

We can conclude that the value of x in our exponential equation is approximately 25.24.

The answer is (4)(x)(x) because it’s 4 times 2 x’s

Answer:

(4)(x)(x)

Step-by-step explanation:

The square ONLY effects the x

Answer:

-2 1/4z +1/4

Step-by-step explanation:

3/4 - 4z +5/4 z- 1/2 + 1/2 z

Put like terms near each other

3/4- 1/2  - 4z +5/4 z+ 1/2 z

We need to get common denominators to combine

First the constant terms

3/4 - 1/2*2/2  

3/4 - 2/4 = 1/4

Then the variable terms

-4z *4/4 +5/4z + 1/2z *2/2

-16z/4 + 5/4z +2/4z

-9/4z

Changing from an improper fraction to a mixed number

-2 1/4 z

-2 1/4z +1/4

Answer:

x>14

Step-by-step explanation:

If Hayden get's $1.5 per pizza, and he wants to earn at least $20, then the equation is:

$1.5*x> $20

x>20/1.5 = 13.3333

Like Hayden cannot deliver 13.333 pizzas, just an integer number, we round it to 14.

Then x>14

If he delivers 14 pizzas, he would be earning: $21, so he needs to deliver at least 14 pizzas to earn at least $20

Answer:

(-2,-3/2)

Step-by-step explanation:

Midpoint formula=(x1+x2/2, y1+y2/2)

So...

(3+-7/2, -5+2/2) =

(-2, -3/2)

Answer:

[tex](-2, -1.5)[/tex]

x-coordinate:-2

y-coordinate:-1.5

Step-by-step explanation:

You need to use this formula to find the coordinates of the midpoint:

[tex]M=(\frac{x_A+x_B}{2},\frac{y_A+y_B}{2})[/tex]

In this case, given the points  (3, -5) and (-7, 2), you can identify that:

[tex]x_A=3\\x_B=-7\\y_A=-5\\y_B=2[/tex]

Therefore, you need to substitute these values into the formula  [tex]M=(\frac{x_A+x_B}{2},\frac{y_A+y_B}{2})[/tex]. Then you get that the coordinates of this midpoint are:

[tex]M=(\frac{3+(-7)}{2},\frac{-5+2}{2})[/tex]

[tex]M=(\frac{3-7}{2},\frac{-5+2}{2})[/tex]

[tex]M=(-2, -1.5)[/tex]

Answer:

These ordered pairs can then be plotted into a graph. A pairing of any set of inputs with their corresponding outputs is called a relation. Every function is a relation, but not all relations are functions. In the example above with the carrots every input gives exactly one output which qualifies it as a function.

Step-by-step explanation:

Let's simplify step-by-step.

12n−1/2(6n−4)

Distribute:

=12n+−3n+2

Combine Like Terms:

=12n+−3n+2

=(12n+−3n)+(2)

=9n+2

Answer:

=9n+2

Answer:

9n+2

Step-by-step explanation:

first distribute the -1/2 to 6n-4 from there you will get -3n+2.

second add like terms (12n-3n+2) you will add 12n and -3, this will give you 9n.

after that since you don't have any other like term your answer stays as 9n+2

Answer:

the solution is (-6, 6)

Step-by-step explanation:

This system, y= -1/2x +3 y= -1/3x +4, can be quickly solved for x by letting y = y:

y= -1/2x +3    =   y= -1/3x +4.  Then -1/2x + 3 = -1/3x +4.  The fractional coefficients should be enclosed inside parentheses:

(-1/2)x + 3 = (-1/3)x +4

Let's remove the fractional coefficients.  The LCD is (2)(3) = 6.  Multiply all four terms by 6, obtaining:

-3x + 18 = -2x + 24

Combining like terms, we get -6 = x.  

Find y:  substitute -6 for x in either of the given equations:

y= (-1/2)(-6) +3  =  3 + 3 = 6.  So y = 6 when x = -6, and the solution is (-6, 6).

Answer:

Average rate of change over the interval 2<= x <= 5:

y = 3x + 5:        3

y = 3x^2 + 1:     21

y = 3^x:             78

Step-by-step explanation:

2<= x <= 5

Average rate of change over the interval 2<= x <= 5:

y = 3x + 5

y(5) = 3(5) + 5 = 20

y(2) = 3(2) + 5 = 11

Average rate of change = (20 - 11)/(5-2) = 9/3 = 3

y = 3x^2 + 1

y(5) = 3(5^2) + 1 = 75 + 1 = 76

y(2) = 3(2^2) + 1= 13

Average rate of change = (76 - 13)/(5-2) = 63/3 = 21

y = 3^x

y(5) = 3^5 = 243

y(2) = 3^2 =9

Average rate of change = (243-9)/(5-2) = 234/3 = 78

1. Average rate of change for y = 3x + 5 over 2 <= x <= 5: 3

2. Average rate of change for y = 3x^2 + 1 over 2 <= x <= 5: 21

3. Average rate of change for y = 3^x over 2 <= x <= 5: 78

Matching:

A. Exponential function: ii. Common ratio

B. Quadratic function: iii. No common difference

C. Linear function: i. Common difference

Y-intercepts and Ranges:

1. For y = -2/5 * x + 1:

  - Y-intercept: 1

  - Range: All real numbers (-∞, ∞)

2. For y = -4x^2:

  - Y-intercept: 0

  - Range: [0, ∞)

First, let's calculate the average rate of change for the provided functions over the interval 2 <= x <= 5:

1. For y = 3x + 5:

  - Average rate of change = (f(5) - f(2)) / (5 - 2) = (3(5) + 5 - (3(2) + 5)) / (5 - 2) = (15 + 5 - 6 - 5) / 3 = 9 / 3 = 3

2. For y = 3x^2 + 1:

  - Average rate of change = (f(5) - f(2)) / (5 - 2) = (3(5)^2 + 1 - (3(2)^2 + 1)) / (5 - 2) = (3(25) + 1 - (3(4) + 1)) / 3 = (75 + 1 - 12 - 1) / 3 = 63 / 3 = 21

3. For y = 3^x:

  - Average rate of change = (f(5) - f(2)) / (5 - 2) = (3^5 - 3^2) / (5 - 2) = (243 - 9) / 3 = 234 / 3 = 78

Now, match each type of function to the term that describes its rate of change:

A. Exponential function: ii. Common ratio

B. Quadratic function: iii. No common difference

C. Linear function: i. Common difference

For the next part, we'll find the y-intercepts and ranges for the given functions:

1. For y = -2/5 * x + 1:

  - Y-intercept (where x = 0): y = -2/5 * 0 + 1 = 1

  - Range: Since the coefficient of x is negative, the function is decreasing, and it extends from negative infinity to positive infinity. The range is all real numbers.

2. For y = -4x^2:

  - Y-intercept (where x = 0): y = -4 * 0^2 = 0

  - Range: Since the coefficient of x^2 is negative, the function is concave down and reaches its maximum value at the vertex. The range is [0, ∞) because it never goes below 0.

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Answer:

People left for last raft is 3

Step-by-step explanation:

Total Number of person on a raft = 4

Number of adults would like to raft = 29

Number of children would like to raft = 22

Total Number of would like to raft = 29 + 22 = 51

Number of people left for last raft = remainder of division of 51 and 4

When 51 divided by 4,

we get

Quotient = 12

Remainder = 3

Therefore, People left for last raft is 3

The Louvre Museum's glass pyramid could hold approximately 908,448 cubic feet of water if converted into an aquarium.

The Louvre museum's glass pyramid with sides measuring 114 feet and a height of 71 feet can hold water if converted into an aquarium. To calculate the volume to hold water, we use the formula for the volume of a rectangular pyramid: 1/3 * base area * height. Substituting the values, the pyramid could hold approximately 908,448 cubic feet of water.

Answer:

A. $14.5 B. $23.5

Step-by-step explanation:

You are adding .75 cents to your bank account each day so you can do .75 *18 days plus one dollar from day one to get $14.5 dollars on may 19. If you do 30 * .75 you get 22.5 plus a dollar from what you start with to get $23.5 at the end of may in your account. Hope this helped you!!

Using the provided radioactive decay formula and the half-life information for Silicon-32, we can predict there will be approximately 21.978 grams of Silicon-32 remaining after a 300 year period.

The question refers to the concept of half-life in physics, particularly in relation to radioactive substances. In this case, we're dealing with silicon-32, which has a half-life of 710 years. This means in 710 years, half of the silicon-32 will have decayed.

Given that the half-life of silicon-32 is 710 years, and we're examining a span of 300 years, let's use the decay formula A(t)=A0e^(ln(0.5)/T)t . Here, A0 is the initial quantity of the substance (30 grams in this case), T is the half-life (710 years), and t is the time elapsed (300 years).

Plugging these values into the formula gives us:

A(300) = 30e^(ln(0.5)/710)*300

Calculating this, we find that the amount of Silicon-32 remaining after 300 years would be approximately 21.978 grams, rounded to three decimal places.

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Answer:

Soo

Step-by-step explanation:

The mean is all of the numbers added together and divided by how many numbers you have

4+5+6+7+8= 30

You have five numbers that go into that thirty so divide thirty by five.

30÷5= 6

It’s simple to find mean you need to add up all the numbers then divide by how many numbers there are. So 4+5+6+7+8= 30/ 5 =6 so 6 is your answer.

If the center of town is the origin then 4 blocks west and 1 block south would be 4 blocks to the left and 1 block down or (-4, -1) house 3 block east and 2 blocks north would be 3 blocks to the right and 2 blocks up or (3, 2) use the distance formula to find the distance between two points. That's all I know! hope this helps!~ just remember to use the distance formula to find the distance between two points.

Answer:

-4,-1 for the house and 3,2 for the school

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

4/16 = 1/4

Answer: The correct option is

(D) 4.

Step-by-step explanation:  Given that the two triangles in the figure are similar.

We are to find the scale factor that can be used to find the missing length x.

From the figure, we note that

two pairs of corresponding lengths of the sides of the given triangles are (4, 16) and (6, x).

And, the scale factor is given by

[tex]S=\dfrac{\textup{length of a side of dilated triangle}}{\textup{length of the corresponding side of the original trinagle}}\\\\\\\Rightarrow S=\dfrac{16}{4}\\\\\Rightarrow S=4.[/tex]

Also, we get

[tex]S=\dfrac{x}{6}\\\\\\\Rightarrow 4=\dfrac{x}{6}\\\\\Rightarrow x=24.[/tex]

Therefore, the missing length x is 24 units and the scale factor is 4.

Option (D) is CORRECT.

Hi,

The volume of the cylinder is :

V = π × r^2 × h

V = 3,142 × (2)^2 × 5

V = 62, 8319 cm^3

π : Pi => 3,142

r : radius of the cylinder (2 units).

h : height of the cylinder (5 units).

The base of the cylinder is a circle , so to calculate the area we have to use the formula : area = π × r^2. And to find the volume , we have to multiply the area by the height.

•It was nice to help you, Bellalocc!

Answer:

yes

Step-by-step explanation:

the explanation is that a rhombus is a parallelogram in which all sides are equal. Their diagonals bisect each other at right angles.

The derivative of the equation 4q² + 4q − 1 with respect to q is 8q + 4. The differentiation involves using the power rule and dropping out constants, which results in the derivative 8q + 4.

To find the derivative of an equation 4q² + 4q − 1 with respect to q, we use basic differentiation rules. The power rule states that for any term aq^n, the derivative is naq^(n-1). Applying this rule here:

So, the derivative of the equation 4q² + 4q − 1 with respect to q is 8q + 4. To check your answer, you can use the same technique as previously learned: apply the differentiation rules systematically and verify if the results are consistent.

(36x^3-36x-1)/6x+6 or 6x^2-6x+(-1/6x+6)

For this case we must find the product of the following expression:

[tex]6 (x ^ 2-1) * \frac {6 (x-1)} {6 (x + 1)}[/tex]

We can rewrite [tex]x ^ 2-1[/tex] as:

[tex](x + 1) (x-1)[/tex], then:

[tex]6 (x + 1) (x-1) * \frac {6 (x-1)} {6 (x + 1)} =[/tex]

Canceling similar terms of the numerator and denominator:

[tex](x-1) * 6 (x-1) =\\6 (x-1) ^ 2[/tex]

ANswer:

[tex]6 (x-1) ^ 2[/tex]

Answer:

In a right triangle, the hypotenuse is the longest side, an "opposite" side is the one across from a given angle, and an "adjacent" side is next to a given angle. We use special words to describe the sides of right triangles. The hypotenuse of a right triangle is always the side opposite the right angle.

Step-by-step explanation:

The line that has nothing on it

It would be the height because it is adjacent( or next to) the angle

The opposite side would be the one opposite from the angle- 145m

Hope this helps!!

Answer:

22.5

Step-by-step explanation:

the formula is A=a+b

2h

Answer:

I think the answer will be B or C

Step-by-step explanation:

It might be wrong but do the best you can