Write an algebraic expression that represents the following situation: An Uber driver earn $15 per hour driving per day, but also spends $20 a day on gas. Let h represent the number of hours driven in a day. Write an expression for the amount of profit an Uber driver earns in one day.

Answer:

3 * 6 = 18

Step-by-step explanation:

53 * 26 =

= (50 + 3) * (20 + 6)

= 50 * 20 + 50 * 6 + 3 * 20 + 3 * 6

= 1000 + 300 + 60 + 18

Answer: 3 * 6 = 18

Step-by-step explanation:

PART 1:

on the graph you can make a triangle at any point and with any angle measures.

i recommend a smaller right triangle to be easiest.

i recommend the points (0,3) A (3,0) B and (0,0) C

∆ABC angle measurements:

m∠CAB=45°

m∠ABC=45°

m∠ACB=90°

PART 2:

(4,3) D (7,0) E and (4,0) F make an identical right triangle moved 4 squares to the right

m∠FDE=45°

m∠DEF=45°

to find the missing value of the angle EFD we will use subtraction and addition

180-(45+45)

180-90

90

therefore, the m∠EFD=90°

PART 3:

both the angle measures and the shapes of the triangles are the same

PART 4:

i used a 1:1 ratio

sorry for the wait :)

Answer:

4x

Step-by-step explanation:

it will always be the Number beside the variables

4x I guess I don't really know

Answer:

Answer is in the attachment!!

Answer:

apples:bananas: strawberries

3     :             6       :         7

Step-by-step explanation:

apples:bananas: strawberries

6              12                  14

Divide each by 2

6/2           12/2               14/2

3                 6                      7

The ratio is

3     :             6       :         7

Answer:

3:6:7  

Step-by-step explanation

The answer is 3:6:7 because if you divide the numbers by 2, you will get a answer of 3, 6, and 7, the simplest form of the ratio.

Hope this helped!

~Emilie Greene

Answer:

2x² + 5x + c = 0

For this quadratic equation to have one double root, the discriminant must equal 0.

5² - 4(2)(c) = 0

25 - 8c = 0

c = 25/8

2x² + 5x is not a perfect square because the coefficient of x², 2, is not a perfect square.

2x² + 5x is not a perfect square.

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Answer:

The answer is B) 1

Step-by-step explanation:

balls

Answer:

23

Step-by-step explanation:

Example:

You have no money, you decide to swipe your credit card to purchase something for $17. Again, you did so for another item paying $24. You are now $41 in debt. Your mom decides to pay for your debt which is $41. You decide to actually go to your part-time job and earn $23. When was the time you had the most money in this example? When you earned the $23 becuase you started with none.

Answer:

23

Step-by-step explanation:

Out of the numbers given:

All positive numbers are greater than negative numbers.

This eliminates -17 and -24.

Comparing 0 to 23:

23 has more value than 0.

0 < 23

This means out of the numbers given, 23 has the greatest value.  

Hope this helps.  

Answer:

22.5

Step-by-step explanation:

50% of a number is 15

let the unknown number be = x

\( \frac{50}{100} \times x = 15\)

\(x = 15 \div \frac{50}{100} \)

\(x = 15 \times \frac{100}{50} \)

\(x = \frac{1500}{50} \)

\(x = 30\)

75% of 30:

\( \frac{75}{100} \times 30 = 22.5\)

Answer:

45.6

Step-by-step explanation:

We can write a proportion to solve

12 roses     18 roses

------------ = -----------

30.4            x

Using cross products

12x = 30.4 * 18

12x=547.2

Divide each side by 12

12x/12 = 547.2/12

x = 45.6

Distance traveled after toll payment is 1.2 miles on highway 40.

The distance may be calculated using a curved route. Displacement measurements can only be made along straight lines. Distance is path-dependent, meaning it varies depending on the direction followed. Displacement simply depends on the body's beginning and ending positions; it is independent of the route.

Distance is the sum of an object's movements, regardless of direction. Distance may be defined as the amount of space an item has covered, regardless of its beginning or finishing position.

The size or extent of the displacement between two points is referred to as distance. Keep in mind that the distance between two points and the distance traveled between them are not the same. The entire length of the journey taken between two points is known as the distance traveled. Travel distance is not a vector.

Distance traveled before toll payment =3/5 miles on highway 40

Distance traveled after toll payment =2*3/5  = 6/5 =

1.2 miles on highway 40.

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Answer:

72 in^2

Step-by-step explanation:

The area of the square in the middle is

A = s^2 = 6^2 = 36

The area of the triangle on the left is

A =1/2 bh = 1/2 ( 6*6) = 18

The area of the triangle on the right

A = 1/2 bh = 1/2(6*6) = 18

Add the areas together

36+18+18 = 72

Area of the middle square = 6 x 6 = 36

Area of a triangle is 1/2 x base x height:

Area = 1/2 x 6 x 6 = 18

Both triangles have a base of 6 and height of 6 so both triangles have the same area.

Total area = 36 + 18 + 18 = 72 square in.

The answer is D. 72

The sequence is decreasing as n increases and sequence converges to the value 0.

The given sequence is defined as aₙ = 1 / (7n + 3).

To determine if the sequence converges or diverges, we need to analyze its behavior as n approaches infinity.

As n increases, the denominator 7n + 3 also increases which means that the values of aₙ will get smaller and smaller, approaching zero as n becomes larger.

The sequence converges to the value 0.

The sequence is decreasing as n increases.

The sequence converges to the value 0.

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12

The number is 183.92 and need to round off the number to one place. The decimal digit is 9, which is more than 5. So round off number 183.92 to ones place is,

Answer: 184

Answer:

15.3 litres

Step-by-step explanation:

You can do this many different ways, but this is how i did it:

1) I'm going to find how much gas it takes to travel just 1 km.

So, to drive for 1 km, I only need 18/420 litres of gas.

*you can solve this, but you'll just get a really long decimal, so i find it easier just to keep it as a fraction until i'm at the end of solving.

2) Now times the amount of petrol it takes to travel 1 km by 357, to find the final answer.

18/420 x 357 = 15.3 litres

Hope that helped : )

The measure of the angle x is 30 degree if the triangle is an equilateral triangle.

It is described as a set of points, where each point is at the same distance from a fixed point (called the centre of a circle)

We have a circle in which a triangle is formed.

Here is the length of the triangle is same, means it is an equilateral triangle.

Each angle in equilateral triangle = 60 degree

The radius and the one tangent, making an angle of 90 degree

Taking bigger triangle:

Total sum of angles in triangle = 180 degree

x = 180 – 90 -60

x = 30 degree

Thus, the measure of the angle x is 30 degree if the triangle is an equilateral triangle.

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Answer:

Step-by-step explanation:

1) f(-4) --> if x < or equal to 3

2) 1/(-4)-4

3) The answer is - 1/8

Answer:

im going to guess the last answer. theone that i can't see

Step-by-step explanation:

The value of x in 1st equation is x ≤ 3 i.e.  x ∈ (-infinity,3] and the value of x in 2nd equation is x > 18 i.e.  x ∈ (18,infinity)

Given two equations  1)6x-10<8 and 2) \(\frac{x}{3}\)+6 > 12

Solving the above equations

1) 6x-10≤8

⇒6x ≤ 18

⇒X≤ 3

⇒x ≤ 3 i.e.  x ∈ (-infinity,3]

2)\(\frac{x}{3}\)+6 > 12

⇒\(\frac{x}{3}\) > 6

⇒x>18

⇒ x > 18 i.e.  x ∈ (18,infinity)

Therefore,The value of x in 1st equation is x ≤ 3 i.e.  x ∈ (-infinity,3] and the value of x in 2nd equation is x > 18 i.e.  x ∈ (18,infinity)

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The money would be paid back is  0.079 weeks.

There are two kinds of interest that could be charged on a loan. There is the compound interest and there is the simple interest. We know that the simple interest can be computed on the principal and not the interest.

We know that;

I = PRT/100

And

I = A - P

P = principal

A = amount

R = rate

T = time

The interest is obtained from; 900 - 810 = $90

Then;

90 = 810 * 140 * T/100

9000 =  810 * 140 * T

T = 9000/ 810 * 140 * T

T = 0.079 weeks

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The optimal row strategy =  (7/11, 8/11)

the optimal column strategy =  \(\begin{bmatrix}\frac{3}{11} \\\\\frac{5}{11}\end{bmatrix}\)

and the expected value of the game = 1/11

Let the row player be R and the column player be C.

We know that the expected value of R’s payoff is given by,

\(\begin{bmatrix}p & 1-p\end{bmatrix} \begin{bmatrix}3 & -1 \\-5 & 2 \end{bmatrix} \begin{bmatrix}q\\1-q\end{bmatrix}\\\\=\begin{bmatrix}3p-5+5p & -p+2-2p\end{bmatrix}\begin{bmatrix}q\\1-q\end{bmatrix}\\\\=\begin{bmatrix}8p-5 & -3p+2\end{bmatrix}\begin{bmatrix}q\\1-q\end{bmatrix}\)

= (8p - 5)q  + (-3p + 2)(1 - q)

= 8pq - 5q - 3p + 2 + 3pq - 2q

= 2 + 11pq - 3p - 7q

= 1/11 + 11 (p - 7/11)(q - 3/11)

If R sets p equal to 7/11, then R is guaranteed an expected payoff of 1/11.

If R chooses any other value of p, C can choose a value of q that will make the expression 11 (p - 7/11)(q - 3/11) negative giving a payoff

for R which is less than 1/11.

If R sets p < 7/11 then the expression 11 (p - 7/11)(q - 3/11) is negative as long as q > 3/11.

If p > 7/11 then the expression 11 (p - 7/11)(q - 3/11) is negative as long as q < 3/11.

An expected payoff of 1/11 is the best that R can do if C uses an optimal counterstrategy.

Thus, R’s optimal mixed strategy is (7/11, 8/11)

Similarly C’s best counterstrategy is to set q equal to 3/11 since otherwise R can choose a value of p making the expression 11 (p - 7/11)(q - 3/11) positive to give an expected payoff for R that is greater than 1/11 (thus a payoff for C which is less than -1/11).

Thus C’s optimal strategy is given by \(\begin{bmatrix}\frac{3}{11} \\\\\frac{5}{11}\end{bmatrix}\)

Since the expected pay-off is given by  1/11 + 11 (p - 7/11)(q - 3/11), the value of the game is given by ν = 1/11

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The time it will take the money to reach $8,838.51 is 14years

The formula for calculating compound interest is expressed as:

A = P(1+r)^t

where

P = $6,680

A = $8,838.51?

r = 2% = 0.02

Substitute and calculate the time 't"

8,838.51 = 6680(1+0.02)^t
1.3231 = 1.02^t

t = ln1.3231/ln1.02

t = 14years

Hence the time it will take the money to reach $8,838.51 is 14years

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Answer:

To solve this question, we first have to know that we are trying to assemble

and solve equations with two variables: x

and y.

Assuming x

is the number of dimes and y

is the number of quarters, we

can assemble the equations.

since the number of dimes is 3 more than three times the number of quarters,

we get x=3y+3.

Additionally, multiplying the number of dimes by 0.1 and the number of

quarters by 0.25,

we get the total value of x

and y

which appears by this

equation 0.1x+0.25y=11.30

.

Substituting the value of x

in the second equation, we get 0.1(3y+3)+

0.25y=11.30

.

Solving this equation, we get that the value of x,

we get x=3×20+3=

Using the first equation to get the value of x,

we get x=3×20+3=

60+3=63

dimes.

Chapter 9

Math Models and Geometry

Section 2

Solve Money Applications

Prealgebra

Step-by-step explanation:

Both g(x) = 5 - x² and h(x) = \(5 - e^(6-^x^)\)have the same range as f(x) = -2√(x) - 3 + 8, which is (-∞, 5].

To determine which function has the same range as f(x) = -2√(x) - 3 + 8, we need to first find the range of f(x).

The square root function √(x) takes non-negative values as input and gives non-negative outputs, so the expression -2√(x) will always be non-positive. Therefore, the range of f(x) will be all real numbers less than or equal to -3 + 8, which is 5.

In other words, the range of f(x) is (-∞, 5].

So, we need to find a function whose range is also (-∞, 5]. One possible function is g(x) = 5 - x². We can see that when x is zero, g(x) is at its maximum value of 5, and as we increase or decrease x, g(x) will decrease, eventually approaching negative infinity.

Another possible function is h(x) = 5 - e^(-x). When x is negative infinity, e^(-x) is approaching positive infinity, so h(x) is approaching 0. As we increase x, e^(-x) is approaching zero, so h(x) is approaching 5.

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Answer: 2048

Step-by-step explanation: 1. Write the exponential growth model.

The population of the town doubles every year, so the growth factor is 2. The initial population is 112, so the equation is: P(t) = 112(2)^t where P(t) is the population in year t and t is the number of years since 2014.

2. Estimate the population of the town in 2023. To estimate the population of the town in 2023, we can set t=9, since 2023 is 9 years after 2014. Plugging this into the equation, we get: P(9) = 112(2)^9 = 2048

Therefore, the estimated population of the town in 2023 is 2048.

Answer:

Step-by-step explanation:

If f(x)=x²+4 then (fof⁻¹)(x)=(f⁻¹of)(x)=x is proved

A relation is a function if it has only One y-value for each x-value.

Composite functions are when the output of one function is used as the input of another.

If f(x)=x²+4

Then we have to prove f⁻¹of(x)=f⁻¹(f(x)

Let us consider fof⁻¹(x)

f(f⁻¹(x))

x

So (fof⁻¹(x))=x

Now f⁻¹of(x)=f⁻¹(f(x)

=x

Hence, If f(x)=x²+4 then (fof⁻¹)(x)=(f⁻¹of)(x)=x is proved

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It is verified that the given vectors x₁ and x₂ are solutions of the given system. Using Wronskian it is shown that they are linearly independent. Then, \(W(t)=7e^{-3t}\). The general solution of the given system is written as \(x(t)=\left[\begin{array}{c}3c_1e^{2t}+c_2e^{-5t}\\2c_1e^{2t}+3c_2e^{-5t}\end{array}\right]\).

Wronskian analysis helps to determine whether a solution is linearly dependent or independent.

Given the system is \(x'=\left[\begin{array}{ccc}4&-3\\6&-7\end{array}\right]x\).

Let's differentiate x₁ concerning t, and we get,

\(\begin{aligned}x_1'&=\left[\begin{array}{c}\frac{d}{dt}(3e^{2t})&\\\frac{d}{dt}(2e^{2t})&\end{array}\right] \\&=\left[\begin{array}{c}6e^{2t}&\\4e^{2t}&\end{array}\right] \end{aligned}\)

Now,

\(\begin{aligned}\left[\begin{array}{ccc}4&-3\\6&-7\end{array}\right]x_1&=\left[\begin{array}{ccc}4&-3\\6&-7\end{array}\right]\left[\begin{array}{c}3e^{2t}\\2e^{2t}\end{array}\right]\\&=\left[\begin{array}{c}12e^{2t}-6e^{2t}\\18e^{2t}-14e^{2t}\end{array}\right]\\&=\left[\begin{array}{c}6e^{2t}\\4e^{2t}\end{array}\right]\\&=x_1'\end{aligned}\)

From this, we can write,

\(x_1'=\left[\begin{array}{cc}4&-3\\6&-7\end{array}\right]x_1\)

Therefore, we conclude that x₁ is a solution to the given system.

Let's differentiate x₂ concerning t, and we get,

\(\begin{aligned}x_2'&=\left[\begin{array}{c}\frac{d}{dt}(e^{-5t})&\\\frac{d}{dt}(3e^{-5t})&\end{array}\right] \\&=\left[\begin{array}{c}-5e^{-5t}&\\-15e^{-5t}&\end{array}\right] \end{aligned}\)

Now,

\(\begin{aligned}\left[\begin{array}{ccc}4&-3\\6&-7\end{array}\right]x_2&=\left[\begin{array}{ccc}4&-3\\6&-7\end{array}\right]\left[\begin{array}{c}e^{-5t}\\3e^{-5t}\end{array}\right]\\&=\left[\begin{array}{c}4e^{-5t}-9e^{-5t}\\6e^{-5t}-21e^{-5t}\end{array}\right]\\&=\left[\begin{array}{c}-5e^{-5t}\\-15e^{-5t}\end{array}\right]\\&=x_2'\end{aligned}\)

From this, we can write,

\(x_2'=\left[\begin{array}{cc}4&-3\\6&-7\end{array}\right]x_2\)

Therefore, we conclude that x₂ is also a solution to the given system.

Now, find the Wronskian of x₁ and x₂, we get,

\(\begin{aligned}W(t)&=\text{det}[x_1\;x_2]\\&=\text{det}\left[\begin{array}{cc}3e^{2t}&e^{-5t}\\2e^{2t}&3e^{-5t}\end{array}\right] \\&=(3e^{2t}\times3e^{-5t})-(e^{-5t}\times2e^{2t})\\&=9e^{2t-5t}-2e^{2t-5t}\\&=9e^{-3t}-2e^{-3t}\\&=7e^{-3t}\\&\neq0\end{aligned}\)

From this, we can conclude that x₁ and x₂ are independent.

Finally, we write the general solution of the system as follows,

\(\begin{aligned}x(t)&=c_1x_1+c_2x_2\\&=c_1 \left[\begin{array}{c}3e^{2t}\\2e^{2t}\end{array}\right] +c_2\left[\begin{array}{c}e^{-5t}\\3e^{-5t}\end{array}\right] \\&=\left[\begin{array}{c}3c_1e^{2t}\\2c_1e^{2t}\end{array}\right] +\left[\begin{array}{c}c_2e^{-5t}\\3c_2e^{-5t}\end{array}\right]\\&=\left[\begin{array}{c}3c_1e^{2t}+c_2e^{-5t}\\2c_1e^{2t}+3c_2e^{-5t}\end{array}\right] \end{aligned}\)

The complete question is -

First, verify that the given vectors are solutions of the given system. Then use the Wronskian to show that they are linearly independent. Finally, write the general solution of the system.

\(x'=\left[\begin{array}{ccc}4&-3\\6&-7\end{array}\right]x;\; x_1=\left[\begin{array}{ccc}3e^{2t}\\2e^{2t}\end{array}\right], \;x_2=\left[\begin{array}{cc}e^{-5t}\\3e^{-5t}\end{array}\right]\)

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Answer:

The Answer Would Be $420

Step-by-step explanation:

time 7 by 10 and get 70,

times 70 by 6 to get your final answer of $420

Answer: 60

Step-by-step explanation:

180 degrees because of the line so 180-120 = 60

Answer:

Its 60⁰ I'm positive....