Choose the expression that represents a cubic expression.

a. 19x^4 + 18x^3 - 16x^2 - 12x + 1

b. 10x^3 - 6x^2 - 9x + 12

c. -9x^2 - 3x + 4

d. 4x + 3

Answer:

1/4

Step-by-step explanation:

3/5 x 1/4 = 3/20

3/20 + 2/5 = 3/4

1 - 3/4 = 1/4

so the answer is A

Answer:

10

Step-by-step explanation:

Setup a proportional for similar triangles when finding lengths.

We have FG~MN and GH~N0.

Corresponding sides of similar triangles are proportional.

[tex]\frac{FG}{MN}=\frac{GH}{NO}[/tex]

[tex]\frac{6}{x}=\frac{9}{15}[/tex]

Cross-multiply:

[tex]9x=6(15)[/tex]

Simplify right hand side:

[tex]9x=90[/tex]

Divide both sides by 9:

[tex]x=\frac{90}{9}[/tex]

Simplify right hand side:

[tex]x=10[/tex]

Answer:

t=0                                  t = -10/3

Step-by-step explanation:

5|3t+5|=25

Divide each side by 5

5|3t+5| /5=25/5

|3t+5|=5

Now to get rid of the absolute value we get two equations, one positive and one negative

3t+5 =5           3t+5 = -5

Subtract 5 from each side

3t+5-5 =5-5           3t+5-5 = -5-5

3t =0                        3t = -10

Divide by 3

3t/3 = 0/3                   3t/3 = -10/3

t=0                                  t = -10/3

Answer:

-20x^2 +14x+12

The domain of f*g is all real numbers

Step-by-step explanation:

f(x) = -4x - 2

g(x) = 5x - 6.

f*g = (-4x-2) * (5x-6)

FOIL

first -4x*5x = -20x^2

outer -4x*-6 = 24x

inner -2*5x = -10x

last -2 *-6 = 12

Add them together

-20x^2 +24x-10x+12 = -20x^2 +14x+12

The domain of f is all real numbers, the domain of g is all real numbers

The domain of f*g is all real numbers

Answer:

[tex](f*g)(x)=-20x^2+14x+12[/tex]

Domain: All Real Numbers.

Step-by-step explanation:

Given the function f(x):

[tex]f(x) = -4x - 2[/tex]

And the function g(x):

[tex]g(x) = 5x - 6[/tex]

You need to multiply them. Then:

[tex](f*g)(x)=( -4x - 2)( 5x - 6)\\\\(f*g)(x)=-20x^2+24x-10x+12\\\\(f*g)(x)=-20x^2+14x+12[/tex]

Since we know that the domain is the set of all real values of the variable "x" that will give real values for the variable "y", the domain of [tex](f*g)(x)=-20x^2+14x+12[/tex] is ALL REAL NUMBERS.

Answer:

[tex]\sum_{n=5}^{\infty}n^2[/tex]

Step-by-step explanation:

The pattern given is:

25+36+49+64+...+n^2+...

The pattern can be written as

(5)^2+(6)^2+(7)^2+(8)^2+.....+n^2+....

The series is started with 5 and it continues up to infinity.

The summation notation for the given series is:

[tex]\sum_{n=5}^{\infty} n^2[/tex]

n= 1 and goes up to infinity and the series is made up of taking square of n,

The sum using summation notation, assuming the suggested pattern continues is :

     [tex]25 + 36 + 49 + 64 + ... + n^2 + ...=\sum_{n=5}^{\infty} n^2[/tex]      

We are given a series of numbers as

          25 + 36 + 49 + 64 + ... + n^2 + ...

To write the sum using summation notation means we need to express this series in terms of a general n such that there is a whole summation expressing this series.

Here we see that each of the numbers could be expressed as follows:

[tex]25=5^2\\\\36=6^2\\\\49=7^2\\\\64=8^2[/tex]

and so on.

i.e. the series starts by taking the square of 5 then of 6 then 7 and so on.

and the series goes to infinity.

Hence, the summation notation will be given by:

[tex]25 + 36 + 49 + 64 + ... + n^2 + ...=\sum_{n=5}^{\infty} n^2[/tex]

Answer:

67 boards

Step-by-step explanation:

Given :

Total board length = 814 ft

Each board must be exactly 12 feet

Number of 12 ft boards which can be cut from 814 feet,

= 814 ÷ 12

= 67.83 boards

But because the question requires boards which are exactly 12 feet long, so we have to round down to the nearest whole number

hence 67.83 boards rounded down to the nearest whole board becomes 67 boards.

Answer:

it is 4x=-9

Step-by-step explanation:

Answer:

202,44

Step-by-step explanation:

We know that 41% of a number is 83, and we need to find the base number.  To do so, we're going to use the rule of three, as follows:

If 83 represents -----------------------------> 41% of a number

             X          <------------------------------ 100% of a number

Then:

X = (100 * 83)/41 = 202,44

Therefore, the base number is:  202,44 ✅

Answer:

Eating dinner and eating dessert are dependent events because

P(dinner) . P(dessert) = 0.9 × 0.6 = 0.54 which is not equal to

P(dinner and desert) = 0.5 ⇒ answer A

Step-by-step explanation:

* Lets study the meaning independent and dependent probability  

- Two events are independent if the result of the second event is not

  affected by the result of the first event

- If A and B are independent events, the probability of both events  

 is the product of the probabilities of the both events

- P (A and B) = P(A) · P(B)

* Lets solve the question  

∵ There is a 90% chance that a person eats dinner

∴ P(eating dinner) = 90/100 = 0.9

∵ There is a 60% chance a person eats dessert

∴ P(eating dessert) = 60/100 = 0.6

- If eating dinner and dating dessert are independent events, then

 probability of both events is the product of the probabilities of the

 both events

∵ P(eating dinner and dessert) = P(eating dinner) . P(eating dessert)

∴ P(eating dinner and dessert) = 0.9 × 0.6 = 0.54

∵ There is a 50% chance the person will eat dinner and dessert

∴ P(eating dinner and dessert) = 50/100 = 0.5

∵ P(eating dinner and dessert) ≠ P(eating dinner) . P(eating dessert)

∴ Eating dinner and eating dessert are dependent events because

  P(dinner) . P(dessert) = 0.9 × 0.6 = 0.54 which is not equal to

  P(dinner and desert) = 0.5

Answer:

We have divided the bar into two parts. For example, x and y.

Step-by-step explanation:

So, we have

63cm=x+y    (1)

But one of those parts is 7 centimeters smaller than the other.We take y as the smallest part.Then:

y=x-7cm    (2)

we replace this information in the first equation

63cm=x+(x-7cm)

63cm=x+x-7cm

7 goes to add to the other side

63cm+7cm=2x

70cm=2x

2 goes to divide to the other side

35cm=x

from the second equation we have

y=x-7cm

y=35cm-7cm=28cm

Finally

x=35cm

y=28cm

x+y=35cm+28cm=63cm

Answer:

The solution of the equation is [tex]x=2.169..[/tex]  

Step-by-step explanation:

Given : Equation [tex]2^{3x}=91[/tex]

To find : What is the solution to the equation below?

Solution :

Equation [tex]2^{3x}=91[/tex]

Taking log both side,

[tex]\log(2^{3x})=\log(91)[/tex]

Apply logarithmic property, [tex]\log a^x=x\log a[/tex]

[tex]3x\log(2)=\log(91)[/tex]

[tex]3x=\frac{\log(91)}{\log(2)}[/tex]

[tex]x=\frac{\log(91)}{3\log(2)}[/tex]

[tex]x=2.169..[/tex]

Therefore, The solution of the equation is [tex]x=2.169..[/tex]

Answer:

[tex]\large\boxed{\dfrac{4}{3}}[/tex]

Step-by-step explanation:

Look at the picture.

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

From the graph we have two points (0, -4) and (3, 0).

Substitute:

[tex]m=\dfrac{0-(-4)}{3-0}=\dfrac{4}{3}[/tex]

Final answer:

By setting up an equation based on the proportions of players who bike, walk, and are driven to practice, and solving for the total number of players, it is determined that there are 36 players on the soccer team.

Explanation:

To determine the total number of players in the soccer team, we can use the information given about the fractions of players commuting by different modes of transportation and the number of players who are driven by their parents.

We know that 1/3 of the players ride a bike, 25% (which is equivalent to 1/4) walk, and the remaining 15 players are driven by their parents.

Let's denote the total number of players as T. The parts of the team that ride a bike and walk can be represented as T/3 and T/4, respectively. The remaining players are represented by the number 15.

Since these components add up to the whole team, we can write the equation:

T/3 + T/4 + 15 = T

To solve for T, we first need to find a common denominator, which is 12 in this case. The equation becomes:

4T/12 + 3T/12 + 15 = T

Combining the T terms gives us:

7T/12 + 15 = T

This simplifies to:

7T/12 = T - 15

Multiplying both sides of the equation by 12 to eliminate the fraction gives us:

7T = 12T - 180

Subtracting 7T from both sides results in:

5T = 180

Dividing both sides by 5, we finally get:

T = 36

Therefore, there are 36 players in the soccer team.

Answer:

4

Step-by-step explanation:

First of all we will define rotational symmetry.

Rotational symmetry is when a shape looks the same after some rotation or less than one rotation.

The order of rotational symmetry is how many times it matches the original shape during the rotation.

So for the given shape, we can observe that the shape has four same type of sides. The shape in rotation will be like original shape 4 times in a complete rotation. So the order of symmetry is 4 ..

[tex]y=20^x\Longleftrightarrow x=\log_{20}y[/tex]

Answer:

Step-by-step explanation:

Find the x-value that makes the denominator zero.  This x = a is the equation of the vertical asymptote.  Next, determine the behavior of the function as x increases without bound in either direction.  If there is a limiting value, then this y = d is the horizontal asymptote.

Consider the rational function

     [tex]f(x)=\frac{P(x)}{Q(x)}[/tex]

We will find the Domain of Rational function first, means those value of  rational function for which f(x) is defined, To do this we will evaluate those  point first for which, Q(x)=0.

So, The first Step is "Finding Domain of the rational function" as well as the point where function is not defined.

⇒Consider the function

    [tex]f(x)=\frac{x-3}{x-2}[/tex]

→Domain of the function is

x-2=0

x=2

=All Real Numbers , except at x=2.

=R- {2}

Answer:

12 * 50 = 600

Step-by-step explanation:

We have to multiply 12 by 50

Short cut method for multiplying a number by 50

Step 1: Take the half of the given number

Step 2: Multiply the result by 100

To find the short cut method to multiply 12 by 50

Here the number is 12

Step 1: divide the number by 2

12/2 = 6

Step 2: Multiply 6 by 100 we get 600

Therefore 12 * 50 = 600

Answer:

12 x 50= 600

Step-by-step explanation:

One way you can do is long and short. But the best way is to do it long because than you will get a better score and get the answer still.

Answer:

MW=CD

Step-by-step explanation:

Answer:

-$1.9

Step-by-step explanation:

There are 47 pages.

Printing on both sides would divide the number of pages into half.

47/2 = 23.5

2 pages on each side would mean 4 pages on one sheet. Therefore, the number of pages will be further divided by 2.

23.5/2 = 11.75

There cannot be 11.75 pages so we will round it up to 12 pages.

Each page costs $0.25 so 12 pages will cost:

12 x 0.25 = $3

Faithi has $1.1 so new account balance will be:

1.1 - 3 = $-1.9

Therefore, Fathi's balance in his printing account would be negative $1.9.

!!

When Fathi prints a 47-page document using both sides of pages and printing 2 pages on each side, at a cost of $0.25 per sheet, his printing account balance will be -$1.90.

The question asks what will Fathi's balance be in his printing account after printing a document that is 47 pages long, with specific printing constraints. To solve this, we first need to figure out the number of pages he will print per sheet. Given that Fathi prints two pages on each side of a sheet, he will print 4 pages per sheet. As the document is 47 pages, he will need a total of 12 sheets (47 divided by 4 and rounded up to the nearest whole number).

Next, we need to calculate the cost of printing those sheets. As each sheet reduces his printing account by $0.25, and he's using 12 sheets, the cost will be $3.00 (12 multiplied by $0.25).

Finally, to find the balance in his printing account, we subtract the cost of printing from his initial balance. Fathi started with $1.10 in his printing account, so after deducting the cost of printing 12 sheets, his final balance will be $-1.90 (which means he owes this amount to replenish his account back to zero).

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Answer:

Segment GD is half the length of segment HC​ ⇒ answer D

Step-by-step explanation:

* Look to the attached file

Answer: D) Segment GD is half the length of segment HC​

The volume of a sphere that has a radius of 9 inches is 3053.63in³.

V≈3053.63in³

V=4

3πr3=4

3·π·93≈3053.62806in³

Answer:

Therefore, C ) [tex]\frac{4*pi}{3} (9)^{3}[/tex].

Step-by-step explanation:

Given :  A sphere that has a radius of 9 inches.

To find : Which equation can be used to find the volume of a sphere.

Solution: We have given

radius of sphere =  9 inches.

Volume of sphere = [tex]\frac{4*pi}{3} (radius)^{3}[/tex].

Plug the valu radius = 9 inches .

Volume of sphere = [tex]\frac{4*pi}{3} (9)^{3}[/tex].

Then equation c is correct answere.

Therefore, C ) [tex]\frac{4*pi}{3} (9)^{3}[/tex].

Answer:

The percentage of the calls lasted less than 8 min is 16%

Step-by-step explanation:

* Lets explain how to solve the problem

- To find the percentage of the calls lasted less than 8 min, find the

  z-score for the calls lasted

∵ The rule of z-score is z = (x - μ)/σ , where

# x is the score

# μ is the mean

# σ is the standard deviation

* Lets solve the problem

- The average phone call in a certain town lasted is 9 min

∴ The mean (μ) = 9

- The standard deviation is 1 min

∴ σ = 1

- The calls lasted less than 8 min

∴ x = 8

∵ z = (x - μ)/σ

∴ z = (8 - 9)/1 = -1/1 = -1

∴ P(z < 8) = -1

- Use z-table to find the percentage of x < 8

∴ P(x < 8) = 0.15866 × 100% = 15.87% ≅ 16%

* The percentage of the calls lasted less than 8 min is 16%

Answer:

The percentage of the calls lasted less than 8 min is 16%.

Step-by-step explanation:

We are dealing with a normal distribution with an average phone call of 9 min and a standard deviation of 1 min. Below we can observe the empirical rule applied with a mean of 9 and a standard deviation of 1. The number 8 represents one standard deviation below the mean, so, the percentage of observations below 8 is 16%. Therefore the percentage of the calls lasted less than 8 min is 16%.

Answer:

A

Step-by-step explanation:

The general rule for the quadratic function is

[tex]y=ax^2+bx+c[/tex]

Use the data from the table:

[tex]y(0)=6\Rightarrow 6=a\cdot 0^2+b\cdot 0+c\\ \\y(1)=4\Rightarrow 4=a\cdot 1^2+b\cdot 1+c\\ \\y(-1)=10\Rightarrow 10=a\cdot (-1)^2+b\cdot (-1)+c[/tex]

We get the system of three equations:

[tex]\left\{\begin{array}{l}c=6\\ \\a+b+c=4\\ \\a-b+c=10\end{array}\right.[/tex]

From the first equation

[tex]c=6,[/tex] then

[tex]\left\{\begin{array}{l}a+b=-2\\ \\a-b=4\end{array}\right.[/tex]

Add these two equations:

[tex]a+b+a-b=-2+4\\ \\2a=2\\ \\a=1[/tex]

So,

[tex]b=-2-a=-2-1=-3[/tex]

The quadratic function is

[tex]y=1\cdot x^2-3x+6\\ \\y=x^2-3x+6[/tex]

Answer:

A: second one or middle choice

B: (5x + 8)(3x - 2)

Step-by-step explanation:

First question (A)

It is a trinomial. You can't use the difference of squares on it. The difference of squares have two terms as an answer.

It is not a perfect square. 15 is not a perfect square and c would have to be positive not minus to even think about using a perfect square.

So the A answer is the second one. You need two different binomials to factor this.

Second Question

You could try all the possible pairings and solve them by brute force.

The are five choices the go with the first one (3x + 4). Eventually you would get the answer, you would have to try 5 + 4 + 3 + 2 + 1 = 15 attempts.

There must be a shorter way.

14 means that the expressions are fairly far apart. This was just luck on my part. There is no logic. 8 and 2 for 16 are fairly far apart.

(5x + 8)(3x - 2)

The middle term is 8*3x - 2*5x = 14x and that looks like the answer.

Answer:

c and a

because 3k has to add up the an even number so k by it self can not be an even number, and k/2 would still be an odd number because an off number divided by a even number still makes it odd

If 3k is an even integer then k is an even integer, and k and k - 1 are also integers. However, k/2 cannot be assured to be an integer unless k is a multiple of 4, making it the correct answer for what cannot be an integer.

If 3k is an even number, then k must also be an even number because an even number divided by 3 still leaves k as an integer. So, we can infer that k is an integer.

The option k - 1 must also be an integer because if k is an integer, subtracting 1 from it will result in another integer. The option 3k is given as an even integer, to begin with. However, the option k/2 cannot be an integer unless k is not only even but also a multiple of 4, because when you divide an even number that is not a multiple of 4 by 2, the result is not an integer.

Given the information provided in the question, we can conclude that k/2 is the option that cannot definitely be an integer without additional information specifying that k is indeed a multiple of 4.

Answer:

C

Step-by-step explanation:

So the system is:

5x+13y=232

12x+7y=218

------------------

Let's look at the options to see which will work:

A) Multiply first equation by -13:  -65x-169y=-3016

& second equation by 7           :    84x+49y=1526

There are no opposites in the either one of the variable columns so not this option.

B) Multiply first equation by 7:  35x+91y=1624

& second equation by 13       : 156x+91y=2834

There are no opposites in the either one of the variable columns so this is not option unless we were asked to subtract the equations.

C) Multiply first equation by -12: -60x-156y=-2784

& second equation by 5           :   60x+35y=1090

There is a column that contains opposites here so when you add the equations the x-variable will get eliminated.

Answer:

3rd one

Step-by-step explanation:

Answer:

Step-by-step explanation:

According to the given statement two pieces are of same length:

If the length of one piece is x,

Then the length of other piece is also x.

And one piece is 2 feet longer than the other two = x+2

Total length of a board = 10 foot

Now make the equation from these terms:

x+x+x+2= 10

This is the equation of the given question.

You can further solve this equation:

x+x+x+2=10

3x+2=10

Now combine the constants:

3x=10-2

3x=8

x=8/3

x=2.67

It means that the length of two pieces of same length is 2.67

And the length of one piece which is longer than the other two = x+2 = 2.67+2 = 4.67 ....

Final answer:

To cut a 10-foot board into three pieces where two are the same length and one is 2 feet longer, denote the shorter length as 'x', create the equation 2x + (x + 2) = 10, and solve for 'x'. The two shorter pieces will each be approximately 2.67 feet and the longer one will be approximately 4.67 feet.

Explanation:

The question involves dividing a 10-foot board into three pieces with one piece being 2 feet longer than the other two equal pieces. To solve this, let's denote the length of the shorter pieces as 'x'. Since there are two of these, we have '2x', and the longer piece would be 'x + 2' feet long. The sum of the lengths of all three pieces is equal to the length of the board, so:

2x + (x + 2) = 10

This simplifies to:

3x + 2 = 10

Subtracting 2 from both sides gives:

3x = 8

Dividing both sides by 3 gives:

x = 8/3 or approximately 2.67 feet.

Therefore, the two shorter pieces are each approximately 2.67 feet long and the longer piece is 2.67 + 2, which is approximately 4.67 feet long.

Answer:

Dotted linear inequality shaded above passes through (0, 4) and (4, 0). Solid exponential inequality shaded below passes through (negative 2,2) & (0,5)

Step-by-step explanation:

we have

[tex]y > -x+4[/tex] ----> inequality A

The solution of the inequality A is the shaded area above the dotted line [tex]y=-x+4[/tex]

The dotted line passes through the points (0,4) and (4,0) (y and x-intercepts)

and

[tex]y \leq -(1/2)^{x} +6[/tex] -----> inequality B

The solution of the inequality B is the shaded area above the solid line [tex]y=-(1/2)^{x} +6[/tex]

The solid line passes through the points (0,5) and (-2,2)

therefore

The solution of the system of inequalities is the shaded area between the dotted line and the solid line

see the attached figure

Dotted linear inequality shaded above passes through (0, 4) and (4, 0). Solid exponential inequality shaded below passes through (negative 2,2) & (0,5)

Answer:

A i think

Step-by-step explanation:

Answer:

78˚

Step-by-step explanation:

Triangle MNP is congruent to Triangle QST, and so their angle measures are the same.

If you look at the order of the letters in the triangle names, you will notice that angle N lines up with angle S, so that means their angle measures are the same. Therefore if angle N is 78˚, angle S will be 78˚ as well.

Answer:

∠S = 78°

Step-by-step explanation:

Corresponding angles are equal, that is

∠Q = ∠M = 66° and

∠S = ∠N = 78°

Answer:b

Step-by-step explanation:

The factors of the trinomial is option (D) (x+15)(x-2) is the correct answer.

Factorization is the breaking or decomposition of an entity (a number, a matrix, or a polynomial) into a product of another entity, or factors, which when multiplied together give the original number. Factorize an expression involves take out the greatest common factor (GCF) of all the terms.

For the given situation,

The trinomial is x^2 + 13x - 30.

The trinomial can be factored as

⇒ [tex]x^2 + 13x - 30=0[/tex]

⇒ [tex]x^2 + 15x-2x - 30=0[/tex]

⇒ [tex]x(x+15)-2(x+15)=0[/tex]

⇒ [tex](x+15)(x-2)=0[/tex]

Hence we can conclude that the factors of the trinomial is option (D) (x+15)(x-2) is the correct answer.

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