3. In order to enter the state fair, there is
an admission cost. Each game is $3.
Steven went to the state fair, played
4 games and spent a total of $20 on
admission and games. Assume the
relationship is linear. Find and interpret
the rate of change and the initial value.​

Answer:

width =5.5ft

length =18

Step-by-step explanation:

w=x

L=2x+7

area=w*L

99 = x(2x+7)

[tex]99=2x^{2} +7x[/tex]

[tex]2x^{2} +7x-99=0[/tex]

[tex]2x^{2} +18x-11x-99=0[/tex]

2x(x+9)-11(x+9)=0

(2x-11)(x+9)=0

2x-11=0

2x=11

x=11/2

x=5.5

L=2x+7=2*5.5+7=11+7=18

Answer:16

Step-by-step explanation:

If 4x=18 then 4x-2=16

Tj hit 85% of the balls pitched to him.

Step-by-step explanation:

Baseballs pitched to Tj = 20

Baseballs hit by Tj = 17

Percentage = [tex]\frac{baseballs\ hit\ by\ Tj}{baseballs\ pitched\ to\ Tj}*100\\[/tex]

Percentage= [tex]\frac{17}{20}*100[/tex]

Percentage=[tex]\frac{1700}{20} = 85\%\\[/tex]

Tj hit 85% of the balls pitched to him.

Keywords: percentage, division

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Answer:

33.33%

Step-by-step explanation:

The value of a variable change from 12 units to 16 units in a month.

We have to calculate the percentage increase for that month.

Therefore, the increase of value from 12 to 16 means by (16 - 12) = 4 units

So, the percentage increase for the month is [tex]\frac{4}{12} \times 100 = 33.33[/tex]%. (Rounded to the two decimal). (Answer)

Answer: 5/10 (5 tenths)

Step-by-step explanation:

Since the value of 5 in 124.519 is 5 tenths, it can therefore be expressed as 5/10 in fraction form.

Answer:

1/2

Step-by-step explanation:

Since 5 is in the tenths place it can be written as

5/10

1/2(in simplified form)

Answer:

Step-by-step explanation:

[tex]x,\ y-numbers\\\\\text{The system of equations:}\\\\\underline{+\left\{\begin{array}{ccc}x+y=126\\x-y=42\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad2x=168\qquad\text{divide both sides by 2}\\.\qquad x=84\\\\\\\text{Put the value of}\ x\ \text{to the first equation:}\\\\84+y=126\qquad\text{subtract 84 from both sides}\\y=42[/tex]

Final answer:

The two numbers that have a sum of 126 and a difference of 42 are 84 and 42.

Explanation:

To find the two numbers whose sum is 126 and whose difference is 42, we can set up a system of equations:

x + y = 126 (Sum of the numbers)

x - y = 42 (Difference of the numbers)

By adding these two equations, we can eliminate y and solve for x:

x + y + x - y = 126 + 42

2x = 168

x = 84

Now that we have the value of x, we can find y by substituting x back into either of the equations. For example:

84 + y = 126

y = 126 - 84

y = 42

Therefore, the two numbers are 84 and 42.

Answer:

Step-by-step explanation:

2/310=5/c

simplify 2/310 into 1/155

1/155=5/c

cross product

155*5=1*c

775=c

c=775

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

m/3=32/4

simplify 32/4 into 8,

m/3=8,

m=8*3=24

m=24

Answer:

The correct answer is 3.

Step-by-step explanation:

1. Let's resolve the expression below:

(27^5/3) ^1/5

( ∛ 27 ⁵ ) ^ 1/5 ⇒ ∛ 27 ⁵ = 27^5/3

( ∛ 3³ ⁵ ) ^ 1/5 ⇒  ∛ 3³ ⁵ = ∛ 27 ⁵

( 3 ⁵) ^ 1/5

⁵√ 3 ⁵ ⇒  ( 3 ⁵) ^ 1/5 = ⁵√ 3 ⁵

3

After making all the calculations and applying all the exponent rules, the final result is 3.

Answer:

B. 3

Step-by-step explanation:

Answer:

The weekly savings of first person = $900

The weekly savings of second person = $700.

Step-by-step explanation:

Let us assume the income of first person = $ m

Now, as the difference in the income is $200.

⇒ And the income of first person  -  income of first person =  $200

⇒ Income of second person    =    m -  $200

So, according to the question:

Ratio of   Income of First person : Second Person's Income  =  9: 7

or, m : ( m - 200)   =  9: 7  

[tex]\implies  \frac{m}{m - 200 }  = \frac{9}{7}[/tex]

[tex]7 \times m = (m - 200) \times 9\\\implies 7 m = 9m - 1800\\\implies 7m - 9m = -1800\\\implies -2m = -1800\\m = \frac{1800}{2}   = 900[/tex]

or,m = $900

Hence, the weekly savings of first person = $900

and the weekly savings of second person = m - 200 = $900 - 200 = $700.

Final answer:

To find the weekly incomes of two persons with a ratio of 9:7 and a difference of $200, represent their incomes as 9x and 7x. Solving for x, we get $100, so their incomes are $900 and $700 respectively.

Explanation:

The question asks us to solve for the weekly incomes of two persons given that the ratio of their incomes is 9:7 and the difference between their incomes is $200.

Let's represent the incomes of the two persons as 9x and 7x respectively, where x is a common multiplier. According to the information provided,

9x - 7x = $200

Solving for x:

(9x - 7x) = 2x

2x = $200

x = $200 / 2

x = $100

Now calculating each person's income:

Person A: 9x = 9 * $100 = $900

Person B: 7x = 7 * $100 = $700

Therefore, the weekly incomes of the two persons are $900 and $700 respectively.

Answer:

90°, 60°, and 30°

60°.

Step-by-step explanation:

The triangle ABC has side lengths √6, √2, and 2√2 units.

It is clear that the triangle ABC is right triangle because (2√2)² = (√6)² + (√2)² that means the side lengths satisfy the Pythagoras Theorem.

Now, if the angle between hypotenuse (2√2 units) and base (√2 units) is [tex]\theta[/tex], then

[tex]\cos \theta = \frac{\sqrt{2} }{2\sqrt{2} }  = \frac{1}{2}[/tex]

Hence, [tex]\theta[/tex] = 60°

Therefore, the three angles of the triangle are 90°, 60°, and 30°.

Now, if the base of the triangle is 16 units, then other two side lengths will also change proportionally to remain the triangle a right triangle.

And in that case the base angle will remain 60°. (Answer)

Answer: 9.5

Step-by-step explanation: 57 divided by 6 is 9.5

Answer: 3 hours

Step-by-step explanation: 30 miles/10 hours=3 miles per hour. 9 miles/3 miles per hour= 3 hours.

Answer:

[tex]\large\boxed{\log_6\dfrac{1}{36}=-2}[/tex]

Step-by-step explanation:

[tex]\text{We know:}\\\\\log_ab=c\iff a^c=b\\\\\log_6\dfrac{1}{36}\qquad\text{use}\ a^{-1}=\dfrac{1}{a}\\\\=\log_636^{-1}=\log_6(6^2)^{-1}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=\log_66^{(2)(-1)}=\log_66^{-2}\qquad\text{use}\log_ab^n=n\log_ab\\\\=-2\log_66\qquad\text{use}\ \log_aa=1\\\\=-2(1)=-2[/tex]

[tex]\log_6\dfrac{1}{36}=-2\ \text{because}\ 6^{-2}=\dfrac{1}{6^2}=\dfrac{1}{36}[/tex]

The solution of logarithmic function is, - 2

We have to given that,

Logarithmic function is,

⇒ log ₆ (1/36)

Now, We can apply the logarithmic rule to solve as,

⇒ log ₆ (1/36)

⇒ log ₆ (36)⁻¹

⇒ log ₆ (6)⁻²

⇒ - 2 log ₆ (6)

⇒ - 2 × 1

⇒ - 2

Therefore, The solution of logarithmic function is, - 2

Learn more about the function visit:

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Answer:

-198

Step-by-step explanation:

you will deal with the ones in the bracket first

that is [3×104]=312

[5×102]=510

312-510=-198

according to me there is no answer in your option my answer is negative198

Ben's gross income was $28,500.

Step-by-step explanation:

Sales for the month = $950000

Commission rate = 3%

Amount of commission = 3% of sales for the month

Amount of commission = [tex]\frac{3}{100}*950000[/tex]

Amount of commission = [tex]\frac{2850000}{100}[/tex]

Amount of commission = $28500

Ben's gross income was $28,500.

Keywords: percentage, division

Learn more about division at:

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Answer:

The population will be 240,116

Step-by-step explanation:

Exponential growth can be represented by the expression:

[tex]P(t) = P_i\,(1+r)^t[/tex]

where:

[tex]P(t)[/tex] is the population at time (t)

[tex]P_i[/tex] is the initial value of the population

"r" is the annual rate of growth (written in decimal form)

and "t" is the time in years.

Therefore in this situation, P(16) is what we want to find [the population after 16 years]

the initial population [tex]P_i[/tex] is 110,000

the rate of growth is 0.05 [decimal form of 5%]

and t is 16 years.

Replacing all these in the given functional form gives:

[tex]P(t) = P_i\,(1+r)^t\\P(16)=110000\,(1+0.05)^16\\P(16)=240116[/tex]

An exponential function to model a population of 110,000 that grows at 5% per year for 16 years is P(t) = 110,000 ∙ (1.05)^t. After 16 years, using this exponential function, the population would be approximately 242,884.

To model the population growth using an exponential function, we can use the formula P(t) = P0 ∙ (1 + r)t, where P(t) is the population after t years, P0 is the initial population, r is the growth rate, and t is the time in years. In this case, the initial population P0 is 110,000, the growth rate r is 5% (or 0.05), and the time t is 16 years.

The exponential growth function would be:

P(16) = 110,000 ∙ (1 + 0.05)16

To find the projected population after 16 years, we'll calculate:

P(16) = 110,000 ∙ (1.05)16
P(16) = 110,000 ∙ 2.20804
P(16) = 242,884.4

After rounding, the population would be approximately 242,884 after 16 years.

Carter's song played on 7 commercials and 5 movies.

Step-by-step explanation:

Earning per commercial = $50

Earning per movie = $130

Total earned = $1000

Total commercial and movies = 12

Let,

x be the number of commercials

y be the number of movies

According to given statement;

x+y=12     Eqn 1

50x+130y=1000    Eqn 2

From Eqn 1

x=12-y    Eqn 3

Putting value of x from Eqn 3 in Eqn 2

[tex]50(12-y)+130y=1000\\600-50y+130y=1000\\80y=1000-600\\80y=400[/tex]

Dividing both sides by 80

[tex]\frac{80y}{80}=\frac{400}{80}\\y=5[/tex]

Putting y=5 in Eqn 1

[tex]x+5=12\\x=12-5\\x=7[/tex]

Carter's song played on 7 commercials and 5 movies.

Keywords: linear equation, substitution method

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Carter had his songs played in 7 commercials and 5 movies to earn $1000 in royalties. This was determined by solving a system of linear equations.

Carter is dealing with a system of linear equations situation where he collects different amounts of royalties based on whether his music is played in commercials or movies. We can represent the number of commercials as c and the number of movies as m. Since he earns $50 per commercial, we can write the first equation as 50c, and since he earns $130 per movie, we can write the second equation as 130m. Carter earned a total of $1000 from 12 commercials and movies, which gives us two equations:

50c + 130m = 1000

c + m = 12

By solving this system of equations, we can determine the number of commercials and movies. Multiplying the second equation by 50 gives us 50c + 50m = 600, which we can subtract from the first equation to eliminate c and solve for m. Doing so, we get:

50c + 130m = 1000

-(50c + 50m = 600)

After subtracting, we are left with 80m = 400, from which we can solve for m to find that m = 5. Using the second original equation, we can now find out that c = 7.

So, Carter had his songs played in 7 commercials and 5 movies to earn a total of $1000 in royalties.

Answer:

$5000

Step-by-step explanation:

A nickel is worth 5 cents, or 0.05 dollars.

Multiply the number of nickels by the worth of a nickel in dollars.

100,000 * $0.05

= $5000

Therefore, 100,000 nickels is worth $5000.

Answer:

THE ANSWER IS $5000

Step-by-step explanation:

A NICKLE IS WORTH 5 CENTS, OR $0.05. SO YOU MULTIPLY THE 100,000 BY THE WORTH OF NICKLES IN A DOLLAR. SO YOU DO 100,000 X 0.05= $5000. SO 100,000 NICKLES IS WORTH $5000.

Answer:

The number of tickets that cost $ 10 is 923

The number of tickets that cost $ 20 is 1205

The number of tickets that cost $ 30 is 1111

Step-by-step explanation:

Given as :

The total number of three different tickets cost $ 10 , $ 20 and VIP seats $ 30

The total number of all tickets sold = 3239

The sale price for the tickets = $ 63720

Let The type of ticket for $ 10 = x

And The type of ticket for $ 20 = y

And The type of VIP ticket = v

According to question

The number of $ 20 tickets = The number of $ 10 tickets + 282

I.e y = x + 282

And x + y + v = 3239

Or, v = 3239 - ( x + y )

I.e v = 3239 - ( x + x +282 )

Or, v = 2957 - 2 x

Now ,

x × $ 10 + y × $ 20 = v × $ 30

Or, x × $ 10 + ( x + 282 ) × $ 20 = ( 2957 - 2 x ) × $ 30

or, 10 x + 20 x + 5640 = 88710 - 60 x

Or, 30 x + 60 x = 88710 - 5640

or, 90 x = 83070

∴  x = [tex]\frac{83070}{90}[/tex]

I.e x = 923

So, The  number of tickets that cost $ 10 = x = 923

Similarly

 y = x + 282

or, y = 923 + 282

I.e y = 1205

So, The  number of tickets that cost $ 10 = y = 1205

And

 v = 2957 - 2 x

∴ v = 2957 - 2 × 923

I.e v = 1111

So, The  number of tickets that cost $ 30 = v = 1111

Hence

The number of tickets that cost $ 10 is 923

The number of tickets that cost $ 20 is 1205

The number of tickets that cost $ 30 is 1111

Answer

Answer:

1021 of the $10 tickets, 1303 of the $20 tickets and 915 of the $30 tickets.

Step-by-step explanation:

We have 3 types of tickets:

ones that cost $10, others that cost $20 and others that cost $30.

If A is the number of $10 tickets sold, B is the number of $20 tickets sold and C is the number of $30 tickets sold we have that:

A + B + C = 3239

B = A + 282

A*10 + B*20 + C*30 = 63720

We need to solve this system of equations.

From the second equation we have B isolated, we can replace it in the other equations:

A + (A + 282) + C = 3239

A*10 + (A + 282)*20 + C*30 = 63720

Now we can isolate one of the variables in the first equation and replace it in the second, lets isolate C.

C = 3239 - 2*A - 282 = 2957 - 2*A

the third equation is now:

A*10 + (A + 286)*20 + (2957 - 2*A)*30 = 63720

Now we solve it for A:

A*10 + A*20 - A*60 + 282*20 + 2957*30 = 63720

-A*30 + 94350 = 63720

A*30 = - 63720 + 94350 = 30630

A = 30639/30 = 1021

So they sold 1021 tickets of $10.

Now we can replace it in the equation:

C =   2957 - 2*A = 2957 - 2*1021  = 915

They sold 915 $30 tickets  

They sold 1303 tickets of $20.

B = A + 282 = 1021 + 282 = 1303.

The combined cost for 1 pound of turkey and 1 pound of ham is $10.5

Step-by-step explanation:

Let,

Turkey = x

Ham = y

According to given statement;

4x+2y=30    Eqn 1

x = y-1.50     Eqn 2

Putting value of x from Eqn 2 in Eqn 1

[tex]4(y-1.50)+2y=30\\4y-6+2y=30\\6y=30+6\\6y=36[/tex]

Dividing both sides by 6

[tex]\frac{6y}{6}=\frac{36}{6}\\y=6[/tex]

Putting y=6 in Eqn 2

[tex]x=6-1.50\\x=4.5[/tex]

1 turkey costs $4.5 and 1 ham costs $6.

Combined cost of 1 pound of turkey and ham each = 4.5+6=$10.5

The combined cost for 1 pound of turkey and 1 pound of ham is $10.5

Keywords: linear equations, subtraction

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Answer:

{6, 8, 10} is a set which represents the side length of a right triangle.

Step-by-step explanation:

In a right triangle:

[tex](Base)^{2}  + (Perpendicular)^{2}   = (Hypotenuse)^{2}[/tex]

Now, in the given triplets:

(a) {4, 8, 12}

Here, [tex](4)^{2}  + (8)^{2}   = 16 + 64  = 80\\\implies H = \sqrt{80}  =  8.94[/tex]

So, third side of the triangle   8.94 ≠ 12

Hence,  {4, 8, 12} is NOT a triplet.

(b) {6, 8, 10}

Here, [tex](6)^{2}  + (8)^{2}   = 36 + 64  = 100\\\implies H = \sqrt{100}  =  10[/tex]

So, third side of the triangle  10

Hence,  {6, 8, 10} is  a triplet.

(c) {6, 8, 15}

Here, [tex](6)^{2}  + (8)^{2}   = 36 + 64  = 100\\\implies H = \sqrt{100}  =  10[/tex]

So, third side of the triangle  10  ≠ 15

Hence,  {6, 8, 15} is  NOT a triplet.

(d) {5, 7, 13}

Here, [tex](5)^{2}  + (7)^{2}   = 25 + 49  = 74\\\implies H = \sqrt{74}  =  8.60[/tex]

So, third side of the triangle  8.60  ≠ 13

Hence, {5, 7, 13} is  NOT a triplet.

The lengths of the sides are 24cm, 27cm and 30cm.

Step-by-step explanation:

The ratio of lengths is 8:9:10

Perimeter = 81 cm

Let x be the length of side.

Therefore,

The length of sides is 8x, 9x and 10x.

Perimeter is the sum of 3 sides, therefore,

[tex]8x+9x+10x=81\\27x=81[/tex]

Dividing both sides by 27;

[tex]\frac{27x}{27}=\frac{81}{27}\\x=3[/tex]

Therefore, the lengths of sides are [tex]8(3), 9(3)\ and\ 10(3)[/tex]

The lengths of the sides are 24cm, 27cm and 30cm.

Keywords: triangles, perimeter

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The lengths of the sides of the triangle are 24 cm, 27 cm, and 30 cm.

To find the lengths of the sides of the triangle, we can use the fact that the sum of the lengths of the sides of a triangle is equal to the perimeter. Let's assume the common ratio between the sides is 'x'. So, the lengths of the sides can be written as 8x, 9x, and 10x. According to the problem, the perimeter of the triangle is 81 cm.

Therefore, 8x + 9x + 10x = 81.

Combining like terms, we get 27x = 81.

Dividing both sides by 27, we find that x = 3.

Substituting this value back into the lengths of the sides, we find that the lengths are 8x = 8(3) = 24 cm, 9x = 9(3) = 27 cm, and 10x = 10(3) = 30 cm.

Answer:

see explanation

Step-by-step explanation:

Since the 2 lines are parallel, then

d = 55° ( corresponding angles are congruent )

e = 55° (vertical to d and congruent )

e and f are same side interior angles and are supplementary, thus

e + f = 180°, that is

55° + f = 180° ( subtract 55° from both sides )

f = 125°

c = 125° ( alternate to f and congruent )

Hence

c = 125°, d = 55°, e = 55°, f = 125°

Answer: The wavelength for X-rays with the given frequency is [tex]1\times 10^{-10}m[/tex]

Step-by-step explanation:

To calculate the wavelength of light, we use the equation:

[tex]\lambda=\frac{c}{\nu}[/tex]

where,

[tex]\lambda[/tex] = wavelength of the light  

c = speed of light = [tex]3\times 10^8m/s[/tex]

[tex]\nu[/tex] = frequency of light = [tex]3\times 10^{18}s^{-1}[/tex]

Putting the values in above equation, we get:

[tex]\lambda=\frac{3\times 10^8m/s}{3\times 10^{19}s^{-1}}=1\times 10^{-10}m[/tex]

Hence, the wavelength for X-rays with the given frequency is [tex]1\times 10^{-10}m[/tex]

Answer:

1 x 10 ^-10 m

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Using the rules of exponents

[tex]a^{-m}[/tex] ⇔ [tex]\frac{1}{a^{m} }[/tex]

[tex]a^{\frac{m}{n} }[/tex] ⇔ [tex]\sqrt[n]{a^{m} }[/tex]

Given

[tex]t^{-\frac{2}{7} }[/tex]

= [tex]\frac{1}{t^{\frac{2}{7} } }[/tex]

= [tex]\frac{1}{\sqrt[7]{t^{2} } }[/tex]

Answer:

6a + 13

Step-by-step explanation:

Given

2a + 4(a + 5) - 7 ← distribute parenthesis

= 2a + 4a + 20 - 7 ← collect like terms

= 6a + 13

Answer: 6a + 13

Step-by-step explanation: here you go: 2a + 4*(a+5) - 7

first we simplify the brackets (distributive property, you multiply 4 "a" times plus 5 times): 2a + 4a + 20 - 7

then you add those that multiply the variable separately from those that don't: 6a + 13

Answer:

5

Step-by-step explanation:

You move 3 places to the right to get to zero. And two places to the right to get to 2. 3 plus 2 is 5.

Answer:

Step-by-step explanation:

The formula of a distance between two points A and B:

d = |B - A|

We have A = -3 and B = 2.

Substitute:

d = |2 - (-3)| = |2 + 3| = |5| = 5

Answer:

216 sq. cm.

Step-by-step explanation:

If we fold the paper of the given dimensions then we will get a rectangular prism with dimension 10 cm by 6 cm by 3 cm.

Now, a rectangular prism has the total surface area given by  

A = 2(LW + WH + HL)

where, L = length = 10 cm.

W = width = 6 cm. and  

H = height = 3 cm.

Therefore, total surface area = A = 2(10 × 6 + 6 × 3 + 3 × 10) = 216 sq. cm. (Answer)

Answer:

216 sq. cm.

Step-by-step explanation: