A scale drawing of a house uses a scale of 0.5 inches = 2 feet. What is the length, in inches, of a line on the scale drawing that represent an actual length of 5 feet?

Final answer:

The total cost can be expressed as 5t + 10p or (5t) + (5 × 2p), representing the combined cost of five movie tickets and twice the amount of popcorn boxes for each of the five family members.

Explanation:

The total amount Xander's family spent on movie tickets and popcorn can be expressed with two different algebraic expressions. The cost for one family member is the cost of one ticket plus the cost of two boxes of popcorn. Since there are five members in the family, we multiply the cost of one person by five.

The first expression is 5t + 10p, which represents the cost of five tickets (5t) and ten boxes of popcorn (2 boxes per person), therefore, 5 times 2 boxes of popcorn (10p).

An alternative expression is (5t) + (5 × 2p), which explicitly shows the cost of five tickets (5t) plus the cost of two boxes of popcorn for each of the five members (5 × 2p).

Answer:

3 Dollars

Step-by-step explanation:

$4+.50cents=4.50

6 quarters is $1.50

4.50-1.50=3 dollars

So, I got this question for my Imagine Math, and here is what I got;

4+0.50−1.50.

Why; I got this because 4+0.50 is 4.50 and then 4.50-1.50 is 3.

Hopes this helps.

Answer:

see explanation

Step-by-step explanation:

For words per minute divide 228 by 4

words per minute = [tex]\frac{228}{4}[/tex] ( = 57 )

Final answer:

To find the number of words Carlos types per minute, set up an equation and solve for 'x'.

Explanation:

To find the number of words Carlos types per minute, we can set up an equation using the given information. Let's assume that the number of words Carlos types in 1 minute is 'x.' We know that Carlos can type 228 words in 4 minutes. So, the equation would be:

228 words in 4 minutes = x words in 1 minute

To solve this equation, we can cross-multiply and divide:

(228 words) x (1 minute) = (4 minutes) x (x words)

Simplifying further:

x = (228 words) / (4 minutes)

Therefore, the equation that represents the number of words Carlos types per minute is:

x = 228 / 4

Answer:

[tex]y=3x[/tex]

y=57, when x is 19.

Step-by-step explanation:

We are asked to write an equation of variation where y varies directly as x.

Since we know that a directly proportional equation is in form: [tex]y=kx[/tex], where k is the constant of proportionality.

Upon substituting x=5 and y= 15 in our equation of variation we will get,

[tex]15=k*5[/tex]

[tex]k=\frac{15}{5}[/tex]

[tex]k=3[/tex]

Upon substituting k=3 in the standard equation of variation we will get our desired equation of variation as: [tex]y=3x[/tex].

Now let us find y, when x is 19.

[tex]y=3*19[/tex]

[tex]y=57[/tex]

Therefore, y equals 57, when x is 19.

Answer:

6 baskets were filled and 12 tomatoes were left

Step-by-step explanation:

Just do 612/100= 6

Answer:

-99

Step-by-step explanation:

Given :

Arithmetic sequence : 15 , 9 ,3 , -3 , ........

To Find : 20th term .

Solution :

Formula of nth term in Arithmetic mean : [tex]a_{n} = a+(n-1)*d[/tex]  ---(A)

where

a = first term of sequence

n = term position

d = common difference

[tex]a_{n}[/tex] = the term you want to find

Thus in the given sequence:

a = 15 ( first term )

n = 20 th term ( given )

d = 9-15 = 3-9 = -6(common difference)

Putting values in (A)

⇒[tex]a_{20} = 15+(20-1)*(-6)[/tex]

[tex]a_{20} = 15-114[/tex]

[tex]a_{20} = -99[/tex]

Hence the 20th term is -99 i.e. option 1

Answer:

3746148

Step-by-step explanation:

i know you probably just want the answer but hear me out it is just simple math and can be resolved with a quick search. Find or search 1.8% of 3,381,000 and multiply it times the years progressed.

60858 x 6 = 3746148

Final answer:

Using the exponential growth formula, the approximate population of Henderson City in the year 2000 is calculated to be around 3,769,706 if the annual growth rate remains constant at 1.8%.

Explanation:

To calculate the approximate population of Henderson City in the year 2000, we can use the formula for exponential growth. The formula is
[tex]A = P(1 + r)^t[/tex]

where A is the amount of the final population, P is the initial population, r is the growth rate expressed as a decimal, and t is the time in years. In this case:

So the equation becomes:

A =[tex]3,381,000(1 + 0.018)^6[/tex]

Calculating this gives us the approximate population, A:

A ≈[tex]3,381,000(1.018)^6[/tex]

A ≈ 3,381,000(1.1155)

A ≈ 3,769,706

Therefore, the approximate population of Henderson City in the year 2000 would be 3,769,706 residents if the growth rate remains constant at 1.8%.

Answer:

Standard form: [tex]\left(x-\dfrac{9}{2}\right)^2+(y+5)^2=\dfrac{121}{4}.[/tex]

This equation represents the circle with the center at the point [tex]\left(\dfrac{9}{2},-5\right)[/tex] and the radius [tex]r=\dfrac{11}{2}.[/tex]

Step-by-step explanation:

Consider expression [tex]x^2+y^2-9x+10y+15=0.[/tex]

First, form perfect squares:

[tex](x^2-9x)+(y^2+10y)+15=0,\\ \\\left(x^2-9x+\dfrac{81}{4}\right)-\dfrac{81}{4}+(y^2+10y+25)-25+15=0,\\ \\\left(x-\dfrac{9}{2}\right)^2+(y+5)^2=10+\dfrac{81}{4},\\ \\\left(x-\dfrac{9}{2}\right)^2+(y+5)^2=\dfrac{121}{4}.[/tex]

This equation represents the circle with the center at the point [tex]\left(\dfrac{9}{2},-5\right)[/tex] and the radius [tex]r=\dfrac{11}{2}.[/tex]

Answer:

The answer is BD is the bisector angle

Answer:

C.) 1/169

Step-by-step explanation:

There are 4 jacks in a deck of 52 cards

The probability the first card is a jack

4/52 = 1/ 13

Since we replace the card

The probability the second card is a jack

4/52 = 1/ 13

To get the probability that we get a jack then a jack, we multiply the probabilities

1/13 * 1/13 = 1/169

Answer:

C.p(v)=5000/v

Step-by-step explanation:

Got it right on the test.

The equation that can be used to find the pressure of the gas when the volume is changed is P(v) = 500/v

Given:

p(v) = pressure of a gas

v = volume of the gas

P(v) varies inversely with v

let

k = constant of proportionality

The equation:

P(v) = k/v

If P(v) = 25 kg/cm² and v = 200cm²

Therefore,

P(v) = k/v

25 = k / 200

25 × 200 = k

k = 5,000

substitute the value of k into the equation

So,

P(v) = 500/v

Read more:

https://brainly.com/question/2798700

Answer:

28 degrees

Step-by-step explanation:

180 = 10x + 5 + 65 because they are supplementary. x = 11.

Angle 2 = 180 - (Angle 1 + (4x - 7))

Angle 2 = 180 - ((180 - 65) + 4x - 7)

Angle 2 = 180 - (115 + 4x - 7)

Angle 2 = 180 - 152

Angle 2 = 28 degrees

Answer: D. (6, 9)

Step-by-step explanation:

Midpoint is the "average" of the x's and y's:

Given: (5, 13) and (7, 5)

Midpoint: [tex](\dfrac{5+7}{2},\dfrac{13+5}{2})[/tex]

             = [tex](\dfrac{12}{2},\dfrac{18}{2})[/tex]

              = (6, 9)

Answer: (6, 9)

Step-by-step explanation:

Answer: (d-21) represent in this context

The number of days the book is late

Step-by-step explanation:

The expression represents the amount of total money. Then the total late fee Camilla owes will be $2.1.

Algebra is the study of graphic formulas, while logic is the interpretation among those signs.

Camilla borrows a book from the library for d days.

The library charges a late fee 0.10 dollars per day that the book is late.

If Camilla returns the book more than 21 days after she borrowed it.

Then the expression will be 0.10d.

The total amount is given as

Total amount = 0.10 d

Total amount = 0.10 x 21

Total amount = $2.1

More about the Algebra link is given below.

https://brainly.com/question/953809

#SPJ2

Answer:

25 miles

Step-by-step explanation:

[tex]\frac{6}{40} :\frac{3.75}{y} \\y=25[/tex]

Answer: In the question, 3.75 miles is equal to 6 kilometers (that's rounding in a real life situation. It would actually be about 3.72... but who cares?! :)). So, if you divide 3.75/6... you get 0.625. Now, you multiply 40 by 0.625. After so, you get 25. 40 kilometers is equal to 25 miles!

Answer:8

Step-by-step explanation:6%3=2

4x2=8

I swear its 8 check if i'm wrong I dare you

Answer:

9.6667

Step-by-step explanation:

3t=29

Divide each side by 3

3t/3 = 29/3

t = 29/3

Three goes into 29  nine times  (3*9 = 27 ) with 2 left over

t =  9 2/3

We know 1/3 = .3 repeating

so 2/3  = .6 repeating

t = 9 .6 repeating

Answer: 3.0650

Step-by-step explanation:

K-12

Final answer:

To set up a profitable computer repair business, assuming $50 for parts per repair and a service fee of $150, the weekly expenses equation is y = 50x + 500, and income equation is y = 150x, where x is the number of repairs.

Explanation:

When starting a computer repair business with estimated expenses of $500 per week, it's crucial to set average costs for replacement parts and fees for services to ensure profitability. Let's assume an average cost of $50 for parts per computer repaired and a service fee of $150 per repair. If x represents the number of computers you repair each week, your total weekly expenses for parts would be 50x plus the fixed expenses of $500, resulting in a total expense equation of y = 50x + 500. Your total weekly income can be modeled by the equation y = 150x, with each repair contributing $150 to the income.

To break even or make a profit, the total income must exceed total expenses, leading to an analysis based on the number of repairs done weekly. This practical application of linear equations in a business setting helps in budgeting, pricing strategies, and understanding economic principles behind running a service-based business. Monitoring these variables is key to achieving sustainability.

The width of the rectangular strip of land is 2/3 miles whose the width of the rectangular strip of land is 2/3 miles.

To find the width of the rectangular strip of land, we can use the formula for the area of a rectangle, which is:

Area = Length × Width

Given that the length of the rectangular strip of land is 3/4 miles and the area is 1/2 square mile, we can plug these values into the formula and solve for the width (W):

Area = 1/2 square mile

Length = 3/4 miles

1/2 = (3/4) × Width

To solve for the width (W), divide both sides by 3/4:

Width = (1/2) ÷ (3/4)

When dividing by a fraction, you can multiply by its reciprocal:

Width = (1/2) × (4/3)

Now, multiply the numerators and denominators:

Width = 4/6

The fraction 4/6 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 2:

Width = 2/3

So, the width of the rectangular strip of land is 2/3 miles.

To know more about rectangular strip click here :

https://brainly.com/question/5031874

#SPJ2

Answer:

Center (1,3) and radius 6

Step-by-step explanation:

We must complete the square to find the center and radius of the circle.

First make sure the x and y squared terms have 1 as their coefficients. We also make sure x and y terms together.

[tex]x^2-2x+y^2-6y=26[/tex]

We now create space between the x and y terms with parenthesis.

[tex](x^2-2x)+(y^2-6y)=26[/tex]

We complete the square by taking the middle terms -2x and the -6y - divide each and square them.

[tex]\frac{-2}{2} =(-1)^{2} =1[/tex]

[tex]\frac{-6}{2} =(-3)^{2} =9[/tex]

We add the squares to both sides.

[tex](x^2-2x+1)+(y^2-6y+9)=26+1+9[/tex]

Simplify.

[tex](x^2-2x+1)+(y^2-6y+9)=36[/tex]

And write the quadratics in factored form.

[tex](x-1)^{2} +(y-3)^{2} =36[/tex]

The center is (h,k) or (1,3). The radius is the square root of 36 which is 6.

8.

   Statement                                           Reason

1. A'F is perpendicular bisector of JK    1. Given

2. JA ≅ KA                                               2. Dfinition of perp bisector

3. ∠JAF and ∠KAF are right angles      3. Dfinition of perp bisector

4. A'F ≅ A'F                                              4. Reflexive Property

5. ΔJFA ≅ ΔKFA                                      5. SAS Theorem

6.

(ANGLE): It is given that ∠AMD ≅ ∠EDM

(SIDE): MD ≅ MD by the Reflexive Property

Which angle would satisfy AAS?   ∠MAD ≅ ∠ DEM

NOTE: If you chose the other angle, it would satisfy ASA

Answer:

r=0.6

Step-by-step explanation:

Consider geometric sequence

[tex]b_1=6,\\ \\b_2=3.6,\\ \\b_3=2.16,\\ \\b_4=1.296,...[/tex]

In geometric sequence

[tex]b_i=b_{i-1}\cdot r,[/tex]

then

[tex]b_2=b_1\cdot r[/tex]

and

[tex]3.6=6r,\ r=\dfrac{3.6}{6}=0.6.[/tex]

Note that

[tex]2.16=3.6\cdot 0.6,\\ \\1.296=2.16\cdot 0.6.[/tex]

This means that ratio r=0.6.

Answer: 691

Step-by-step explanation:

There are 3 different ways to find the remainder.  I am not sure which method you are supposed to use, so I will solve using all 3 methods.

Long Division:

         10x³ + 24x² + 77x + 230

x - 3 ) 10x⁴ -  6x³  + 5x²   - x  +  1

      - (10x⁴ - 30x³)   ↓       ↓      ↓

                   24x³ + 5x²     ↓      ↓

               - (24x³ - 72x²)   ↓      ↓

                              77x²  - x       ↓

                         -  (77x² - 231x)  ↓

                                        230x + 1

                                     - (230x - 690)

                                                    691 ← remainder

Synthetic Division:

x - 3 = 0   ⇒  x = 3

3  |  10     -6        5       -1        1

   |   ↓      30     72    231    690

      10      24     77    230   691 ← remainder

Remainder Theorem:

f(x) = 10x⁴ - 6x³ + 5x²  - x  +  1

f(3) = 10(3)⁴ - 6(3)³ + 5(3)² - (3)  +  1

     =  810   - 162    + 45    -  3  +  1

     = 691

Answer:

[tex]x>-3[/tex]

Step-by-step explanation:

To solve equations, we use inverse operations. Normally, we use PEMDAS to simplify an equation. To solve it, we use the inverse of each in this order SADMEP. Solving an inequality is the same except for step. When dividing by a negative, the sign of the inequality changes.

We have [tex]5x+7>2(x-1)\\5x+7>2x-2[/tex] in simplified form. We begin by subtracting or adding constants across the equal sign. Then doing the same with the variable terms. We finish by dividing by the coefficient of the variable term.

[tex]5x+7>2x-2\\5x+7-7>2x-2-7\\5x>2x-9\\5x-2x>2x-2x-9\\3x>-9\\x>-3[/tex]

To graph, we draw a number line, draw an open circle at -3.

Since it is not equal to, we do not fill it in. We leave it open. We also draw an arrow to the right of -3

Answer:

The even functions are options 2, 3, and 5

Step-by-step explanation:

Please, see the attached file.

Thanks.

Answer:

Options B, C and E are even functions.

Step-by-step explanation:

If f(x) = f(-x) then function is called to be even.

A). f(x) = ∛8x

f(-x) = ∛8(-x) = (∛8)(∛(-x) = 2∛(-x)

Therefore f(x) ≠ f(-x)

So function is not an even function.

B). [tex]f(x)=log_{9}x^{6}[/tex]

[tex]f(-x)=log_{9}(-x)^{6}[/tex]

[tex]=log_{9}(x)^{6}[/tex]

f(x) = f(-x)

So this function is even.

C). [tex]f(x)=\frac{1}{x^{8}+7x^{7}}[/tex]

[tex]f(-x)=\frac{1}{(-x)^{8}+7(-x)^{6}}[/tex]

            = [tex]\frac{1}{x^{8}+7x^{6}}[/tex]

f(x) = f(-x)

Therefore given function is even.

D). f(x) = [tex]e^{x^{8}-x }[/tex]

[tex]f(-x)=e^{(-x)^{8}-(-x)}=e^{x^{8}+x}[/tex]

Therefore f(x) ≠ f(-x)

So the given function is not even.

E). f(x) = |8x| - 3

f(-x) = |8(-x)| - 3

      = |8x| - 3

f(x) = f(-x)

Therefore, function is even.

F). [tex]f(-x)= -9(-x)^{10}+5(-x)^{4}-12(-x)[/tex]

[tex]f(-x)= -9(x)^{10}+5(x)^{4}+12(x)[/tex]

f(x) ≠ f(-x)

Therefore the given function is not an even function.

Options B, C and E are even functions.

Answer:

Correct choice is B

Step-by-step explanation:

All three functions are increasing when x is increasing. You can find values of each function when x is "enough large". For example, at x=100,

1. linear function: [tex]y=10\cdot 100=1,000.[/tex]

2. exponential function: [tex]y=5^{100}\approx 0.8\cdot 10^{70}.[/tex]

3. quadratic function: [tex]y=4\cdot 100^2+5\cdot 100=40,500.[/tex]

As you can see,  when x approaches positive infinity, the exponential function will exceed both the linear and the quadratic functions.

Also you can use graphical method to get from the attached diagrams result. When x approaches positive infinity, the exponential function will exceed both the linear and the quadratic functions.

Correct choice is B.

Answer:

The required domain is [tex]x\ne -1[/tex]

Step-by-step explanation:

The given function is

[tex]f(x)=\frac{1-x}{x}[/tex]

We need the inverse of this function.

We first of all have to let [tex]y=f(x)[/tex].

This implies that,

[tex]y=\frac{1-x}{x}[/tex]

Next, we interchange [tex]x[/tex] and [tex]y[/tex] to obtain,

[tex]x=\frac{1-y}{y}[/tex]

We make y the subject to get,

[tex]xy=1-y[/tex]

[tex]xy+y=1[/tex]

[tex](x+1)y=1[/tex]

[tex]y=\frac{1}{1+x}[/tex]

The inverse function is

[tex]f^{-1}(x)=\frac{1}{1+x}[/tex]

The domain of this function is

[tex]x+1\ne 0[/tex]

[tex]\Rightarrow x\ne -1[/tex]

The correct answer is D

Answer:

(1, 3)

(-1, 3)

Step-by-step explanation:

h(x) = 3x^2

Let x =1

h(1) = 3 * (1)^2

    = 3(1)

    = 3

So if the input is 1 the output is 3

h(-1) = 3 * (-1)^2

     = 3 *1

If the input is -1 the output is 3

Answer:(1,3) and (-1,3)

Step-by-step explanation:

Ava must work 43.5 more hours in order to save the rest of the money

Money is any item that generally accepted as payment for goods and services and repayment of debts, such as taxes, in a particular country or socio-economic context. In math, it can be defined as the medium of exchange such as notes, coins, and demand deposits, to pay for commodities and services.

If you're self-employed, it's unwise  to work more than 40 hours a week on a regular basis because, you'll get a burst of productivity, the extra hours have diminished returns over time and within any time period.

Ava is saving for A new computer that cost 1218 she has already saved half of the money

[tex]\frac{1218 }{2} = 609[/tex]  $, hence  she has already saved half of the money ($609), so  she needs $609

Ava earns $14 per hour

Hence [tex]\frac{609}{14} = 43.5[/tex] hours

Ava must work 43.5 more hours in order to save the rest of the money

Hope it helps!

Grade:  5

Subject:  math

Chapter:  hours

Keywords:  hours, money, saved, order, Ava