The sum of three consecutive numbers is greater than 40. The inequality that represents this is x + x + 1 + x + 2 > 40. Which values of x hold true for the inequality?

choices are 8,10,12,13,9,15,7

Answer:  49 hours

Step-by-step explanation:

Given : A road crew can repave [tex]\dfrac{1}{56}[/tex] miles of road each hour.

i.e. the rate of of repave = [tex]\dfrac{1}{56}[/tex] miles per hour.

Distance required to cover = [tex]\dfrac{7}{8}[/tex] miles.

The formula used here is :-

[tex]\text{Time}=\dfrac{\text{Distance}}{\text{rate of repave}}[/tex]

i.e. [tex]\text{Time}=\dfrac{\dfrac{7}{8}}{\dfrac{1}{56}}[/tex]

i.e. [tex]\text{Time}=\dfrac{7}{8}\times56=7\times7=49[/tex]

Hence, it will take 49 hours to repave the road.

The correct answer, to the nearest pound, is:

2979

Explanation:

Compound interest can be written as an equation of the form

[tex]y=a(1+r)^t[/tex],

where a is the initial deposit, r is the interest rate as a decimal number, and t is the number of years.

For the first 3 years, we have a = 2200, r = 5% = 5/100 = 0.05; and t = 3:

[tex]y=2200(1+0.05)^3

\\

\\=2200(1.05)^3=2546.775[/tex]

This will be the "initial deposit" in the account with 4% interest.  This gives us that

a = 2546.775; r = 4% = 4/100 = 0.04; and t = 7-3 = 4:

[tex]y=2546.775(1+0.04)^4

\\

\\=2546.775(1.04)^4=2979.367 \approx 2979[/tex]

Answer: D

Step-by-step explanation:

The ordered pair of the system of equations is (8, 2).

Option D is the correct answer.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x  + 4 = 9 is an equation.

We have,

x + 2y = 12 _____(1)

x = 12 - 2y _____(2)

-x = -y - 6 _______(3)

Putting (2) in (3) we get,

-(12 - 2y) = -y - 6

-12 + 2y = -y - 6

-12 + 6 = -y - 2y

-6 = -3y

y = 2

Now,

y = 2 in (2)

x = 12 - 2 x 2

x = 12 - 4

x = 8

Thus,

The ordered pair is (8, 2).

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It is 54 because that is the ansewr to this question bra

Answer:

[tex]6x^2+ 5x[/tex]

[tex]-x^2 +5x[/tex]

Step-by-step explanation:

Expression is a polynomial when it contains variables, numbers and operators. Expression that contains fractional exponent is not a polynomial. Expression with variable in the denominator is not a polynomial.

[tex]6x^2+ 5x[/tex]

It is a polynomial

[tex]-7x^2+ \frac{5}{3x}[/tex]

It is not a polynomial because x is in the denominator

[tex]-x^2 +5x[/tex]

It is a polynomial

[tex]x^2+5x ^ \frac{1}{5}[/tex]

It is not a polynomial because it has fractional exponent

The expressions that are polynomials include 6x² + 5x, −7x²+5/3x, and −x² +5x, because they have non-negative integer exponents and a finite number of terms. The expression x²+5x[tex]^{(1/5 )}[/tex]is not, due to the non-integer exponent.

The expressions that are polynomials must have non-negative integer exponents and a finite number of terms. Given the options:

6x² + 5x is a polynomial because the exponents are integers and it has a finite number of terms.

−7x²+5/3x is also a polynomial with non-negative integer exponents and finite terms.

−x² +5x is a polynomial as well, following the same reasoning.

x²+5x[tex]^{(1/5)}[/tex] is not a polynomial because the exponent 1/5 is not an integer.

Therefore, the expressions that are polynomials are 6x² + 5x, −7x²+5/3x, and −x²+5x.

Answer:

Distributive Property

Step-by-step explanation:

Use the distributive property to multiply each term in each parenthesis.

Example:

To simplify the expression (x-3)(x^2-4x-7), apply the distributive property. The distributive property states to multiply each term in each parenthesis.

x*x^2=x^3

x*-4x=-4x^2

x*-7=-7x

-3*x^2=-3x^2

-3*-4x=12x

-3*-7=21

This gives the expression x^3-4x^2-7x-3x^2+12x+21. Combine like terms and get x^3-7x^2+5x+21.

The second one, as shown in the attached picture.

- - - - - - - - - -

Notes

Answer:

1).90

2).-10

Step-by-step explanation:

1).

(3(1)^2)+(3(2)^2)+(3(3)^2)+(3(4)^2)

  3      +     12    +    27    +    48

=90

2). (-5(3)+20)+(-5(4)+20)+(-5(5)+20)+(-5(6)+20)

     (-15+20)  +  (-20+20)  + (-25+20)  +  (-30+20)

           5       +       0         +       -5       +      -10

=-10

Answer:

The average rate of change for the quadratic function from x = 6 to x = 8 is -1.

Step-by-step explanation:

The average rate of change for the quadratic function from x₁ to x₂ is defined as

[tex]m=\frac{f(x_2)-f(x_1)}{x_2-x_1}[/tex]

From the given graph it is clear that the value of function is 6 at x=6 and the value of function is 4 at x=8.

The average rate of change for the quadratic function from x = 6 to x = 8.

[tex]m=\frac{f(8)-f(6)}{8-6}[/tex]

[tex]m=\frac{4-6}{2}[/tex]

[tex]m=\frac{-2}{2}[/tex]

[tex]m=-1[/tex]

Therefore the average rate of change for the quadratic function from x = 6 to x = 8 is -1.

The trinomial 5x^2 + 29x - 6 factors into (5x - 1)(x + 6)

To factor the trinomial 5x2 + 29x - 6, we need to find two numbers that multiply to (5)(-6) = -30 and add to 29. These two numbers are 30 and -1, as 30 - 1 = 29. Thus, we can rewrite the trinomial as 5x2 + 30x - x - 6 and factor by grouping:

(5x2 + 30x) - (x + 6)

5x(x + 6) - 1(x + 6)

The trinomial factors into (5x - 1)(x + 6), which means the correct binomial factor is option D: x + 6.

The Galileo walk 480.97 or 481 meters up the inclined plane if the Galileo wanted to release a wooden ball and an iron ball from a height of 100 meters and measure the duration of their fall.

The trigonometric ratio is defined as the ratio of the pair of a right-angled triangle.

We have:

Galileo wanted to release a wooden ball and an iron ball from a height of 100 meters.

The plane with an inclined an 12°

Let's suppose the Galileo walk x meters up the inclined plane.

As per right angle triangle,  The ratio of Sin

[tex]\rm Sin12\° = \frac{100}{x}[/tex]

[tex]\rm x = \frac{100}{Sin12\°}[/tex]

Sin12° = 0.20791

x = 100/0.20791

x = 480.97 meters  or

x = 481 meters

Thus, the Galileo walk 480.97 or 481 meters up the inclined plane if the Galileo wanted to release a wooden ball and an iron ball from a height of 100 meters and measure the duration of their fall.

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The ladder is approximately 40 meters long to the nearest tenth.

The information will form a right angle triangle.

The base of the ladder 25 meters due west of the burning building is the base(adjacent side) of the triangle formed.

How long is the ladder describe the hypotenuse of the triangle formed.

Therefore, using trigonometric ratio we can find the length of the ladder as follows:

cos 51 = adjacent / hypotenuse

cos 51 = 25 / hypotenuse

hypotenuse = 25 / cos 51°

hypotenuse = 25 / 0.62932039105

hypotenuse = 39.7253932266 meters

hypotenuse ≈ 40 meters

Therefore, the ladder is  approximately 40 meters long to the nearest tenth

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Answer: Yes it is possible for triangle JKL to be similar to triangle XYZ.

Step-by-step explanation:

Given: In ΔJKL

m∠J=71° ,  m∠K=52°

In ΔXYZ

m∠X=71° ,  m∠Z=57°

Using Angle sum property of triangle in ΔJKL, we have

m∠J+m∠K+m∠L=180°

⇒71°+52°+m∠L=180°

⇒m∠L=180°-123°

⇒m∠L=57 °

Now in ΔJKL and ΔXYZ , we have

m∠J=m∠X=71°

and m∠L= m∠Z=57°

Therefore , By AA-similarity criteria , we have

ΔJKL≈ΔXYZ

Hence, Yes it is possible for triangle JKL to be similar to triangle XYZ.

Phil's net winnings from the poker tournament are represented by the expression 'x - 100', where x is the prize amount he won. To calculate his actual profit, we subtract the cost of entry (100 dollars) from his prize money.

The student has asked what Phil's net winnings are from a poker tournament after he received a prize of x dollars and the entry to the tournament cost him 100 dollars. To answer this, we will create an expression to represent Phil's net winnings.

Net winnings are calculated by subtracting the cost of entering the tournament from the prize amount. Since Phil won x dollars and spent 100 dollars to enter, we subtract 100 from x.

Phil's net winnings = Prize amount - Entry cost

Phil's net winnings = x - 100 dollars

This expression shows the actual profit Phil made from participating in the tournament, after the cost of entry has been accounted for.

Final answer:

Phil's net winnings from the poker tournament can be expressed as x - 100, where x represents the prize money.

Explanation:

To find Phil's net winnings from the poker tournament, we need to calculate the difference between the prize money and the entry fee. Given that Phil received a prize of x dollars and the tournament cost him 100 dollars to enter, his net winnings can be expressed as:

x - 100

For example, if Phil won $500, his net winnings would be $500 - $100 = $400.