What is the unit rate for meters per second if a car travels 209 meters in 11 seconds?

The volumes of the structure are:

1. (8 + x)(16 + 2x)(6 + 3x) + 12(8 + x)(3 + x)

2. (8 + x)(16 + 2x)(3 + x) + 12(8 + x)(3 + x) + 12(6 + 3x)(3 + x)

3. (8 + x)(16 + 2x)(6 + 3x) - 2[12(8 + x)(3 + x)]

A polynomial expression is an algebraic expression consisting of variables and coefficients, and involving only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.

Examples include 2x^3 - 5x^2 + 3x + 1 and 4y^2 + 7y - 2.

1.We can divide the structure into two rectangular prisms, as shown in the sketch. The dimensions of the first prism are (8 + x)(16 + 2x)(6 + 3x), while the dimensions of the second prism are 12(8 + x)(3 + x). To find the total volume, we can add the volumes of the two prisms:

(8 + x)(16 + 2x)(6 + 3x) + 12(8 + x)(3 + x)

2.We can also divide the structure into three rectangular prisms, as shown in the sketch. The dimensions of the first prism are (8 + x)(16 + 2x)(3 + x), the dimensions of the second prism are 12(8 + x)(3 + x), and the dimensions of the third prism are 12(6 + 3x)(3 + x). To find the total volume, we can add the volumes of the three prisms:

(8 + x)(16 + 2x)(3 + x) + 12(8 + x)(3 + x) + 12(6 + 3x)(3 + x)

3.We can view the structure as one large rectangular prism with two smaller rectangular prisms removed, as shown in the sketch. The dimensions of the large prism are (8 + x)(16 + 2x)(6 + 3x), while the dimensions of each small prism are 12(8 + x)(3 + x). To find the total volume, we can subtract the volumes of the two small prisms from the volume of the large prism:

(8 + x)(16 + 2x)(6 + 3x) - 2[12(8 + x)(3 + x)]

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Justice had the rented car for 22 days, when the rent per day is $20 with $50 deposit.

Rent is a periodic payment made by a tenant to a landlord in exchange for the use of land, building, apartment, office, or other property. A payment or series of payments made by a lessee to an owner in exchange for the use of machinery, equipment, etc. 

According to the information in the question:

Deposit = $50

Rent cost per day for the car = $20

Total amount that Justice has to pay = $490

∴ Total number of days that Justice kept the car = (490 - 50)/20

                                                                                 = 440/20

                                                                                 = 22 days

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The number of days did he have the car are 22.5 days.

a set monthly fee that you pay to utilise someone else's space, including their home, car, television, etc. Because my room is larger than the other renters', I pay a higher rent or more rent.

Justice rented a car for a deposit of $50 and a daily rate of $20. When he returned the car, he owed $490.

To find out how many days he had the car, we can set up an equation:

$50 + (number of days x $20) = $490.

Solving for the number of days: number of days = ($490-$50)/$20 = 22.5 days.

So Justice had the car for approximately 22.5 days.

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Answer:

8x^2-2x+1

Answer:

Step-by-step explanation:

Since the base x is consistent with all terms of this complex fraction, all you need to do is add the two exponents found in the numerator and from that, subtract the exponent in the denominator.

This gives us x^(3/5) divided by x^(4/5), which is x^(-1/5). This gives 1/x^(1/5), which is 1 divided by the fifth root of x.

Answer:

Step-by-step explanation:

Finding an equation of a line can be condensed into 2 easy steps.  Step one is to establish the basic form of the equation, including it's slope.  

1)  Lets use y=mx + b as the basic form, where m is the slope and b is the y-intercept (the value of y when x is zero).  We are told the line is parallel to y = 3x - 1, which is a line with a slope (m) of 3.  Parallel lines have the same slope, so our kline will also have a slope of 3, bringing us to:

   y = 3x + b.

2)  The second step is finding the value of b.  We are told the line must go through point (1,5), so we need a value of b that will shift the line to (1,5).  Easy:  just enter this point in the equation we have so far:  y = 3x + b:

y = 3x + b

5 = 3*(1) + b for point (1,5)

b = 2

The equation becomes y = 3x + 2

See the attached graph.  [Extra credit]

The lines are parallel, and the y-intercept for the second line (b) is (0,2).

In a case whereby A group of students formed a circle during a game. The circumference of the circle was about 43.96 feet, and the diameter of the circle was 14 feet the expression that best represents the value of pi is  43.96 feet/ 14 feet.

The concept that will be use here is Circumference. we were given Circumference of the circle  as 43.96 feet

where the Diameter of the circle is  14 feet, then we can find the Circumference of the circle  as( πd)

Then ( πd) = 43.96 feet

π= 43.96 feet/ 14 feet

Therefore, option C is correct.

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The number of glow-bowling costs per game on Friday is $0.75 per game more than on Saturday.

The rate is the ratio of the amount of something to the unit. For example - If the speed of the car is 20 km/h it means the car travels 20 km in one hour.

Reggie is deciding when to go bowling with his friends. Friday night is glow-bowling night, with 5 glow-bowling games for $22.50. Then the rate is given as,

⇒ $22.50 / 5

⇒ $4.5 per game

But the early-bird special on Saturday morning offers 8 games for $30. Then the rate is given as,

⇒ $30 / 8

⇒ $3.75 per game

The difference is given as,

D = $4.5 - $3.75

D = $0.75 per game

The number of glow-bowling costs per game on Friday is $0.75 per game more than on Saturday.

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so let's take a peek at the triangular pyramid, hmm it has a base of well, the base is a triangle, so we can say the triangle has a base of 10 and a height of 8, thus and area of (1/2)*10*8, and the pyramid has a height of 9.

[tex]\textit{Volume of a pyramid}\\\\ V=\cfrac{1}{3}Bh ~~ \begin{cases} B=\stackrel{base's}{area}\\ h=height\\[-0.5em] \hrulefill\\ B=\frac{1}{2}(10)(8)\\[1em] h=9 \end{cases}\implies V=\cfrac{1}{3}\left[ \cfrac{1}{2}(10)(8) \right](9) \\\\\\ V=\cfrac{1}{3}(40)(9)\implies V=\cfrac{360}{3}\implies V=120~m^3[/tex]

Answer:

1

Step-by-step explanation:

6 children that each want to eat half of a chocolate bar (0.5)

6 * 0.5 = 3 - chocolate bars will be eaten

They bought a package of 4 chocolate bars

4 - 3 = 1 - chocolate bar will be left

Answer:

y= 13

Step-by-step explanation:

y+3x2+7

y=6+7

y=13

x     y

0     13

1       13

linear

Answer:

angle 1 is 28 degrees  angle 2 is 62 degrees

DONT FORGET TO PUT THE DEGREES SIGN

Step-by-step explanation:

since it is a right angle, angle 1+ angle 2 is 90 degrees.

So,

2x+(x+48)=90

3x=90-48

3x=42

x=14

angle 1=28   angle 2=62

Answer:

d ≥ - 14

Step-by-step explanation:

6d ≥ - 84

Divide by 6 both sides

6d/6 ≥ - 84/6

d ≥ - 14

The age that she must work till she is qualified to receive Social Security benefits when she retires is: 56 years

Social Security benefits provide partial replacement income for retired beneficiaries and disabled persons, as well as their spouses, children and survivors.

To be eligible for Social Security benefits, you must be enrolled in the Social Security program and accumulate 40 credits while employed.

Benefits are based on your income history, year of birth, and age at which you began applying for Social Security.

If your spouse is unemployed or has not reached the required number of credits, you can receive benefits according to your spouse's work performance.

Benefits may likely be taxed based on the specific income and tax return status.

She will be required to earn a total of 40 credits in order to qualify to be able to receive social security benefits, due to the fact that she earns the maximum number of 4 credits per year, she therefore has to work for at least a minimum of ten years or until at least she is 56.

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Answer:this equation is not right.so,it does not have any solutions

Step-by-step explanation:

because if we try to solve it we get,

-2x-4=5-2x

-4-5=-2x+2x

-9=0

so,this equation is not right.

Answer:

equation has no solution

Step-by-step explanation:

- 2(x + 2) = 5 - 2x ← distribute parenthesis on left side

- 2x - 4 = 5 - 2x ( add 4 to both sides )

- 2x = 9 - 2x ( add 2x to both sides )

0 = 9 ← false statement

this false statement indicates the equation has no solution

x = 4

-- All angles of a triangle add up to 180° --

-- the inverse of a trianglenis equal to its opposite angle of intersection--

1) build equation

180° = 20° + (4 + 6x) + (32x + 4)

2) solve

180-20 = 4 + 6x + 32x + 4

160 = 8 + 38x

152 = 38x

152/38 = x

x = 4

verify

180 = 20 + (4 + 6x) + (32x + 4)

180 = 20 + (28) + (132)

180 = 180 so x = 4

Answer:

  ㏒₅₄168 = (1+ab)/(8a-5ab)

Step-by-step explanation:

You want ㏒₅₄168 written in terms of a and b, where ...

The rules of logarithms are relevant here:

  [tex]\log_b(a)=\dfrac{\log(a)}{\log(b)}\\\\\log(ab)=\log(a)+\log(b)[/tex]

In order to simplify the writing in what follows, we want to define ...

Now, we can write the equations ...

  a = log(12)/log(7) = (2p+q)/r . . . . . . . . . [eq1]

  b = log(24)/log(12) = (3p+q)/(2p+q) . . . [eq2]

Using these, we can solve for p and q:

  2p +q = ar . . . . . . . . . . . . . [eq3], from [eq1]

  (3 -2b)p +(1 -b)q = 0 . . . . . [eq4] from [eq2]

Using your favorite solution method for linear equations, you find ...

  p = ar(1 -b)/(2(1 -b) -(3 -2b)) = ar(1 -b)/(2 -2b -3 +2b) = ar(b -1)

  q = (-ar(3 -2b)/(-1) = ar(3 -2b)

Substituting these expressions into ...

  [tex]\log_{54}{168}=\dfrac{\log{(2^3\cdot3\cdot7)}}{\log{(2\cdot3^3)}}=\dfrac{3p+q+r}{p+3q}\\\\=\dfrac{3ar(b-1)+ar(3-2b)+r}{ar(b-1)+3ar(3-2b)}=\dfrac{3ab-3a+3a-2ab+1}{ab-a+9a-6ab}\\\\=\boxed{\log_{54}{168}=\dfrac{1+ab}{8a-5ab}}[/tex]

__

Additional comment

The calculator confirms the result.

Answer:

Step-by-step explanation:

Convert pounds to ounces:

2[tex]\frac{2}{3}[/tex] = 2.667

2.667 lb x 16 oz/lb = 42.7 oz

42.7 > 40, therefore Tuga has enough sweet potatoes to make chili

[tex]\stackrel{\textit{for bills}}{1500\cdot \cfrac{1}{2}}~~ + ~~\stackrel{\textit{for savings}}{1500\cdot \cfrac{1}{5}}~~ + ~~\stackrel{\textit{food and ET}}{x}~~ = ~~\stackrel{total}{1500} \\\\\\ 750+300+x=1500\implies 1050+x=1500\implies x=450[/tex]

Answer:

72 [tex]ft^{2}[/tex]

Step-by-step explanation:

a = 1/2(24)(6)

a = 72

Answer:

120%

Step-by-step explanation:

3,600,000 divided by 3,000,000, times 100 = 120%

So, 120% of 3,000,000 is equal to 3,600,000

Answer:

120 %

Step-by-step explanation:

To solve for this percentage problem, we set up an equation:

[tex]3,000,000 * \frac{x}{100} = 3,600,000[/tex]

[tex]30,000 * x = 3,600,000[/tex]

x = 120

Indicating whether the variable is relevant to the questions, and Identifying the variable as either categorical or quantitative.

Rather than straightforward explanations. Anything may be measured using it. It can also do mathematical calculations, which is essential for data analysis.

To completely understand all of the facets of quantitative data, statistical analysis—the discipline of obtaining, analysing, and presenting enormous volumes of data to uncover patterns and trends—is used. This calls for quantitative analysis employing a wide variety of data.

Categorical data is data that may be arranged into groups or categories using names or labels.

The approach is based on algorithms that assess each component of a data collection individually, compare them to other individual data sets, and look for particular similarities.

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Complete question:

identify and classify the variable(s) you will use.Here is the list of variables in the data set. Use the menu to the right of each variable to: Indicate whether the variable is relevant to the questions we are investigating, and Identify the variable as either categorical or quantitative. Group of answer choices

Answer:

its ×2

Step-by-step explanation:

4×2 = 8

8×2=16

..............

The solution is x^2-5x+22<0.

An inequality is a relation which makes a non-equal comparison between two numbers or mathematical expressions.

here, we have,

2x-5/ x^2-6x-7< 1/x-3,

so, we get,

⇒2x-5/x^2-7x+x-7 <  1/x-3

⇒2x-5/(x-7)(x+1) < 1/x-3

⇒2x-5 * x-3 < (x-7)(x+1)

⇒2x^2-11x+15 < x^2-6x-7

⇒x^2-5x+22<0

Hence, The solution is x^2-5x+22<0.

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Answer:

a couple different obes

Step-by-step explanation:

there are five

r = red tiles

b = blue tiles

b = r + 12 , whatever "r" is, "b" is 12 more than that

[tex]\stackrel{red}{3}~~ : ~~\stackrel{blue}{5}\qquad \implies \cfrac{r}{b}=\cfrac{3}{5}\implies \cfrac{r}{r+12}=\cfrac{3}{5}\implies 5r=3r+36 \\\\\\ 2r=36\implies r=\cfrac{36}{2}\implies r=18[/tex]

Answer:

18

Step-by-step explanation:

Because there are 12 more blue tiles than red, that means that we can write the equation 3x + 12 = 5x. By simplifying, the equation is boiled down to 12=2x. By dividing, we see that x=6. This means that we can multiply 3 by 6 to get 18 red tiles. To check our answer, we just multiply 6 by 5 to get 30, and the ratio 18:30 is equivalent to 3:5. Also, 30-18=12, so this must be correct.

Answer:

25 copies rented

Step-by-step explanation:

r = r1 - 5t, t is time in weeks, r is the number of copies rented, r1 how many people were renting at the start

we know on the 6 weeks passed and 4 copies were rented

4 = r1 - 5(6)

4 = r1 - 30; add 30 on both sides

34 = r1

r = 34 - 5t now plug t = 2 in for this function

r = 34 - 5(2)

r = 35 - 10

r = 25 copies rented

An amount of $ 13,200 has a total comission of 856.

Herein we find the case of the calculation of a comission for an amount of money, where an interest rate of six percent is applied for first $ 10.000 and an interest rate of eight percent is applied for the excedent above $ 10.000. The total comission is determined by following mathematical equation:

C = 10,000 · (6 / 100) + (13,200 - 10,000) · (8 / 100)

C = 856

The graduate must pay a total comission of $ 856 for an amount of $ 13,200.

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Using trigonometry formulas, the value of tan(x-y) = -16/63

In the field of mathematics known as trigonometry, correlations between angles and length ratios are studied. Trigonometry has a wide variety of identities. In order to simplify an expression, identify a more practical version of an expression, or solve an equation, trigonometric identities are frequently employed to rewrite trigonometrical expressions.

Given

cot y = 4/3

1/tan y = 4/3

Cross multiply

tan y = 3/4

Also since csc x = 13/5

1/sin x = 13/5

sin x = 5/13

Since sin x = opp/hyp

opp = 5

hyp = 13

Get the adjacent

hyp² = opp²+adj²

13² = 5²+adj²

adj² = 13² - 5²

adj² = 169 - 25

adj² = 144

adj = 12

cos x = adj/hyp

cos x = 12/13

tan x = sin x/ cos x

tan x = (5/13)/(12/13)

tan x = 5/13 * 13/12

tan x = 5/12

tan(x-y) = tan x - tan y/1 + tan x * tan y

tan(x-y) = (5/12 - 3/4) / 1 + (5/12) (3/4)

tan(x-y) = (5-9/12) / 1 + 5/16

tan(x-y) = -4/12/(21/16)

tan(x-y) = -1/3 * 16/21

tan(x-y) = -16/63

the value of tan(x-y) is -16/63

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