Identify the binomial that is a factor of the polynomial P(x) = x^3 + 5x^2 − 9x − 45.

Answer:

1) X stands for individual acts and y,  group acts. 2) Each scenario describes a different period in minutes, but each one respecting their different amounts (individual and group acts). 3) [tex]S=\left \{ 5,10 \right \}[/tex]

Step-by-step explanation:

Completing with what was found:

1) Here is a summary of the scenario your classmate presented for the talent show:Main show The main show will last two hours and will include twelve individual acts and six group acts.Final show The final show will last 30 minutes and will include the top four individual acts and the top group act.The equations he came up with are: 12x+ 6y= 120, 4x+ y= 30

1. What do x and y represent in this situation?

X stands for individual acts and y,  group acts.

Besides that, In the system of equation, they represent the time for x, and the time for y.

2. Do you agree that your classmate set up the equations correctly? Explain why or why not.

Yes, that's right. Each scenario describes a different period in minutes, but each one respecting their different amounts (individual and group acts). Either for 120 minutes or 30 minutes length. And their sum totalizing the whole period.

3. Solving the system by Elimination

[tex]\left\{\begin{matrix}12x+ 6y= 120\\ 4x+ y= 30\end{matrix}\right.\\\left\{\begin{matrix}12x+ 6y= 120\\ 4x+ y= 30\:*(-3)\end{matrix}\right.\\\left\{\begin{matrix}12x+ 6y= 120\\ -12x+ -3y= -90\end{matrix}\right.\\3y=30\Rightarrow y=10\\4x+(10)=30\Rightarrow 4x=20\Rightarrow x=5\\S=\left \{ 5,10 \right \}[/tex]

g(x) = (x-6)(2x - 1)

Step-by-step explanation:

when you expand, it will be 2x²-13x+6=0

when you factories the quadratic equations,

the answer will be 1/2 and 6

Answer:

g(x) = (x-6)(2x - 1)

Step-by-step explanation:

Option B is correct, the surface area of the ramp will be 210 square cm.

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

Let h be the height and b be the base of the triangle. Let L₁, L₂, and L₃ be the length and W be the width of the rectangle.

Then the surface area of the triangular prism will be given as,

Surface area = 2 Area of triangle + 3 Area of rectangle

Surface area = (h x b) + (L₁ + L₂ + L₃) x W

Sean must determine how much paint he will use to cover all of the edges of his ramp.

The surface area of the ramp is calculated as,

SA = (8 x 6) + (5 + 6 + 7) x 9

SA = 48 + 18 x 9

SA = 48 + 162

SA = 210 square cm

Hence, the surface area of the ramp will be 210 square cm. Then the correct option is B.

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The first investment can be shown as T=500*1.05^2 which is $551.25

The second investment can be shown as T=500*e^(0.03*12*2) which is $1027.22

So the second investment is better

Hope that helped!

Answer: 3.77 ounces is the correct answer hope this helps

Answer:

Step-by-step explanation:

The correct answer would be, Jeremy rides at a greater speed than Kevin.

Step-by-step explanation:

Jeremy rides at a rate of 15 miles per hour

Kevin rides at a rate given in the table

Let Y be the distance traveled by Jeremy

And X be the number of hours

Then for Jeremy:

y/x = 15/1

=> y= 15 x

For Kevin:  

(46-23)/(4-2)

= 23/2

= 11.5

So for Kevin, Y = 11.5 x

So when Jeremy's and Kevin's rates are compared,

15 > 11.5

which means Jeremy rides at a greater speed.  

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Answer:

Owen's songs were played on 3 movies and on 7 commercials.

Step-by-step explanation:

System of Equations

Let's call C the number of commercials on which Owen's songs were played and M the number of movies on which Owen's songs were played. We know Owen's songs were played on 4 more commercials than movies, it can be expressed as

[tex]C=M+4[/tex]

Owen will earn $50 every time one of his songs is played in a commercial and he will earn $140 every time one of his songs is played in a movie, so his total earnings are

[tex]140M+50C=770[/tex]

We have a system of linear equations that can be easily solved by using the formula for C in the above equation

[tex]140M+50(M+4)=770[/tex]

Operating

[tex]140M+50M+200=770[/tex]

Reducing

[tex]190M=770-200=570[/tex]

Solving

[tex]M=570/190=3[/tex]

The number of commercials is

[tex]C=M+4=7[/tex]

Owen's songs were played on 3 movies and on 7 commercials.

Answer:

whats the equation???

Step-by-step explanation:

Answer:

t ≤ -7

Step-by-step explanation:

−4t≥28

−4/4 * t ≥ 28/4

−1 * t ≥ 7

-t ≥ 7

t ≤ -7

the weight of train A is 334 tons, and the weight of train B is 20 tons.

Let's denote:

- The weight of train A as x tons,

- The weight of train B as y tons.

We're given two pieces of information:

1. The total weight of both trains is 354 tons: [tex]\( x + y = 354 \)[/tex].

2. Train A is heavier than train B by 314 tons: [tex]\( x = y + 314 \).[/tex]

Now, we can set up a system of equations using these two pieces of information and solve for x and y.

From equation (2), we have:

[tex]\[ x = y + 314 \][/tex]

We can substitute this expression for x into equation (1):

[tex]\[ (y + 314) + y = 354 \][/tex]

Now, let's solve for y:

[tex]\[ 2y + 314 = 354 \][/tex]

[tex]\[ 2y = 354 - 314 \][/tex]

[tex]\[ 2y = 40 \][/tex]

[tex]\[ y = \frac{40}{2} \][/tex]

[tex]\[ y = 20 \][/tex]

Now that we have found the weight of train B, we can substitute this value into equation (2) to find the weight of train A:

[tex]\[ x = 20 + 314 \][/tex]

[tex]\[ x = 334 \][/tex]

So, the weight of train A is 334 tons, and the weight of train B is 20 tons.

Answer:

Median = 78

Step-by-step explanation:

Arrange the data in ascending order

54  68   70  72  75   76   76   76   76  80  88   88   88   88  88   92   92   93

Total number = 18

Median = average of middle terms = average of 9th and 10th term

= ( 76 + 80)/2 = 156/2 = 78

Final answer:

The terms in the expression are 7, 4p, -5, p, and 2q. The like terms in the expression are 4p and p. To simplify the expression, the like terms can be combined by adding their coefficients.

Explanation:

The terms in the expression are:

Like terms in the expression are terms that have the same variable(s) raised to the same power. In this expression, the like terms are:

To simplify the expression, we can eliminate the like terms by combining their coefficients. Adding 4p and p, we get 5p. Therefore, the simplified expression is:

7 + 5p - 5 + 2q

It is not possible to find the values of p and q without additional information.

The numbers that replaces each blank to make the inequality a true statement are 48 and 32. The new inequality is 48/24 > 1/4 > 4/32.

In Mathematics and Euclidean Geometry, an inequality is a relation that compares two or more numbers and variables in an algebraic equation based on any of the following inequality symbols:

Based on the information provided, we can logically deduce the following incomplete inequality;

_/24 > 1/4 > 4/_

In order to make the left-hand side of the inequality true, we must have a number that is greater 1/4 or 0.25;

48/24 = 2

48/24 > 1/4

2 > 0.25 (True)

In order to make the right-hand side of the inequality true, we must have a number that is less than 1/4 or 0.25;

4/32 = 0.125

1/4 > 4/32

0.25 > 0.125 (True).

In conclusion, any number that is greater than 1/4 would make the left-hand side of the inequality true while any number that is less than 1/4 would make the right-hand side of the inequality true.

Complete Question:

Use symbols. Replace each __ with a number to make _/24 >1/4 > 4/_ a true statement.

y≤ 3 when x is 0  and x≤ 3 when y is 0

The graph is attached in figure below

Step-by-step explanation:

We need to graph x+y is equal or less than 3

Writing in mathematical form:

[tex]x+y\leq 3[/tex]

For solving we find x and y intercepts

The y-intercept can be found by putting x=0, y is :

[tex]0+y \leq 3\\y\leq 3[/tex]

y≤ 3 when x is 0

The x-intercept can be found by putting y=0, x is :

[tex]x+y \leq 3\\x+0\leq 3\\x\leq 3[/tex]

x≤ 3 when y is 0

Plotting these values on the graph:

The graph is attached in figure below

Keywords: Solving inequalities

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Answer: 12.5m(2+m)

Step-by-step explanation:

The experimental probability of the next sandwich sold being tuna on wheat bread is 23 out of 137 sandwiches sold, or approximately 0.168.

The problem describes an experimental probability scenario where stopping after having recorded multiple outcomes does not affect the probability of the next outcome. Experimental probability is calculated by taking the number of times an event occurs and dividing it by the total number of trials.

In this case, a total of 137 sandwiches were sold (22 ham on white bread + 24 ham on wheat bread + 21 turkey on white bread + 22 turkey on wheat bread + 25 tuna on white bread + 23 tuna on wheat bread). Out of these, 23 were tuna on wheat bread.

The experimental probability of the next sandwich being a tuna on wheat bread is therefore 23/137, or approximately 0.168, if this same pattern continues.

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The circumference will be doubled if radius is doubled

The area will increase four times if radius is doubled

Step-by-step explanation:

We will solve the question in two parts.

One for circumference and one for Area

Circumference:

The formula for circumference is given by:

[tex]C = 2\pi r[/tex]

Here r is the radius.

Doubling the radius means that new radius will be 2r

The new circumference will be:

[tex]C_N = 2\pi (2r)\\C_N = 2(2\pi r)\\C_N = 2C[/tex]

Hence,

The circumference will be doubled if radius is doubled

Area:

The area of circle is given by:

[tex]A = \pi r^2[/tex]

Putting radius equal to 2r

[tex]A_N = \pi (2r)^2\\A_N = \pi (4r^2)\\A_N = 4(\pi r^2)\\A_N = 4A[/tex]

Hence,

The area will increase four times if radius is doubled

Keywords: Circle, area

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Answer: B, the second one

Step-by-step explanation:

In the first one your distance stays the same while your time increases. The second one the distance decreases as the time increases, the third one is a double increase and than the last one the distance stays the same as the time increases and than changes to Decrease increases

Answer:

B is the corrcet one! :)

Step-by-step explanation:

Answer:

sin(71°)

Step-by-step explanation:

Sine lags behind cosine by 90°

In other word, cos(∅) = sin(90° - ∅)

cos(19°) = sin(90° - 19°)

= sin(71°)

Answer:

Step-by-step explanation:

=

The total cost of a meal with an 18% tip is calculated by converting the tip to a decimal (0.18), multiplying it by the meal cost, and adding it to the original cost. For a $72 meal, the total with tip would be $84.96.

To calculate the total cost of a meal including an 18% tip, you first convert the tip percentage to a decimal by dividing by 100. For an 18% tip, this gives you 0.18. Then, multiply the cost of the meal by this decimal to find the amount of the tip. Finally, add the tip to the original cost of the meal to find the total cost including the tip.

Example Calculation

If the cost of the meal is $72, the tip would be calculated as follows:

Therefore, the total cost of the meal with an 18% tip would be $84.96.

Answer:

Alex is wrong in calculating his dive distance.

Actual distance of his Dive is 30 feet.

Step-by-step explanation:

Given:

Distance from where he dive from = 15 feet

Distance he reached after dive = 15 feet

Also Given:

Alex says that the two distances are opposites,

Also Total distance of dive according to Alex = 15 +-15 =0 feet

Solution:

Now we know that;

The diving board is 15 feet above the water level, and then he reached 15 deep in the water, but here it is important to know that even he is above the surface of the water he is diving in the water and then he reached 15 deep in the water.

So the two distances are in the same direction.

From above scenario we can say that

Total Distance of dive will be = 15 +15 =30 feet.

Hence We can say that Alex is wrong in calculating his dive distance. Actual Dive distance is 30 feet.

Answer:

2.73

Step-by-step explanation:

2 4/5 + 17/15

8/5 + 17/15

By Elysium

(24 + 17)/15

41/15

2.73

The answer is 14+2/3x

I hoped this helped :)

Answer:

71 cents

Step-by-step explanation: Well it would be $1.00 minus the 29 cents she just got So 100 minus 29 is 71 it’s easy to do it in your head just think of 100 minus 30 and it’s 70 then subtract 1 from 30 and add it to the 70

Answer:

$0.71

Step-by-step explanation:

make $1.00 "100"* and $0.29 "29"* and subtract 100 and 29 to get "71" then turn the "71" into $0.71**

* this is done by making it a percentage by moving two units to the right

** this is done by making it a decimal by moving to units to the left

Answer:

it is 5%

Step-by-step explanation:

Answer:

[tex]m^2(10m+49)[/tex]

Step-by-step explanation:

[tex]Given \ \ 8m^3+2m^3+49m^2\\\\=m^3(8+2)+49m^2 \ \ \ \ \ \ \ (adding\ like\ terms)\\\\=10m^3+49m^2\\\\=10m\times m^2+49m^2\\\\=m^2(10m+49)[/tex]

To find the solutions to the equation y = 2x - 3, substitute different x-values and solve for y.

The given equation is y = 2x - 3.

To find the ordered pairs that are solutions to this equation, substitute different x-values and solve for y.

Let's take the first ordered pair (294.5, 61) as an example:

Therefore, the ordered pair (294.5, 61) is not a solution to the equation y = 2x - 3.

Repeat the same process for the other two ordered pairs to determine if they are solutions to the equation.