match the equation with its graph 5x-4y=20
A) First Picture
B) Second Picture
C) Third Picture
D) Fourth Picture

Answer:

Step-by-step explanation:

Let x represent the fuel efficiency of the car that used the most gas. Since the sum of the fuel efficiencies is 40 mpg, the other car had a fuel efficiency of (40-x). Then the combined miles driven is ...

  40x +25(40-x) = 1225

  15x = 225

  x = 15

  (40-x) = 25

The first car got 25 miles per gallon; the second car got 15 miles per gallon.

_____

We made use of the relation ...

  gallons × (miles/gallon) = miles

Answer:

Length of poster is 9 inches and width of the poster is 3 inches.

Length of banner is 10 inches and width of the banner is 2 inches.

Step-by-step explanation:

Given:

Perimeter of Banner =24 in.

Perimeter of poster = 24 in.

we need to find the dimensions of poster and banner.

First we will find the dimension of poster.

Now Given:

A rectangular poster is 3 times as long as it is wide.

Let the Width of poster be [tex]'p'[/tex].

Length of the poster = [tex]3p[/tex]

Perimeter of poster = 24 in.

But perimeter of poster is equal to twice the sum of length and width.

framing in equation form we get;

[tex]2(p+3p)=24\\\\2(4p)=24\\\\8p=24\\\\p=\frac{24}{8} = 3\ in.[/tex]

Now width of poster = 3 inches

Length of the poster = [tex]3p = 3\times3 =9\ inches[/tex]

Hence Length of poster is 9 inches and width of the poster is 3 inches.

Now we will find the dimension of Banner.

Now Given:

A rectangular banner is 5 times as long as it is wide.

Let the Width of Banner be [tex]'b'[/tex].

Length of the banner = [tex]5b[/tex]

Perimeter of banner = 24 in.

But perimeter of banner is equal to twice the sum of length and width.

framing in equation form we get;

[tex]2(b+5b)=24\\\\2(6b)=24\\\\12b=24\\\\b=\frac{24}{12} = 2\ in.[/tex]

Now width of banner = 2 inches

Length of the banner = [tex]5b = 5\times2 = 10\ inches[/tex]

Hence Length of banner is 10 inches and width of the banner is 2 inches.

The width and length of the rectangular poster are 3 inches and 9 inches, respectively. The width and length of the rectangular banner are 2 inches and 10 inches, respectively. Both were calculated by setting up equations using the perimeter formula for rectangles.

The problem is to determine the lengths and widths of a rectangular poster and a rectangular banner, both having the same perimeter of 24 inches. The poster's length is 3 times its width, while the banner's length is 5 times its width. We'll set up two separate equations for their perimeters and solve for the width and length of each.

Let w be the width of the poster. Then the length is 3w. The perimeter is given by P = 2l + 2w, where P is the perimeter and l is the length. This gives us:

24 = 2(3w) + 2w -> 24 = 6w + 2w -> 24 = 8w -> w = 3 inches

Therefore, the length of the poster is 3w = 9 inches.

Let x be the width of the banner. Then the length is 5x. Again using the perimeter formula, we get:

24 = 2(5x) + 2x -> 24 = 10x + 2x -> 24 = 12x -> x = 2 inches

Therefore, the length of the banner is 5x = 10 inches.

Answer:

(√2 − √6) / 4

Step-by-step explanation:

Rewrite using special angles.

sin(-11π/12)

sin((4−15)π/12)

sin(4π/12 − 15π/12)

sin(π/3 − 5π/4)

Use angle difference formula:

sin(π/3) cos(5π/4) − sin(5π/4) cos(π/3)

Evaluate:

(√3/2) (-√2/2) − (-√2/2) (1/2)

-√6/4 + √2/4

(√2 − √6) / 4

The problem can be solved by using a theorem from number theory stating that gcd(a, b) * lcm[a, b] = a * b. Applying this theorem with the given values leads us to solution where a = 210^2 and b = 210^2.

In this mathematics problem, we're given two positive integers, a and b, whose greatest common divisor (gcd) equals to 210, and the least common multiple (lcm) equals to 210^3.

It is a well-known theorem in number theory that for any two positive integers a and b, gcd(a, b) * lcm[a, b] = a * b. We can apply this theorem to our problem. Since we know the values for greatest common divisor and least common multiple, namely gcd = 210 and lcm = 210^3 = 210 * 210 * 210, we have:

210 * 210^3 = a * b

This can be simplified to a * b = 210^4. Since we're told that a < b, and both a and b must divide 210^4, the only possible values for a and b are a = 210^2 and b = 210^2, which respects the condition a < b.

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Answer:

The probability that  Smith will lose his first 5 bets is 0.15

The probability that  his first win will occur on his fourth bet is 0.1012

Step-by-step explanation:

Consider the provided information.

A roulette wheel consisting of 38 numbers 1 through 36, 0, and double 0. Smith always bets that the outcome will be one of the numbers 1 through 12,

It is given that Smith always bets on the numbers 1 through 12.

There are 12 numbers from 1 to 12.

Thus, the probability of success (winning) is=  [tex]\frac{12}{38}[/tex]

The probability of not success (loses) is=  [tex]1-\frac{12}{38}=\frac{26}{38}[/tex]

Part (A) Smith will lose his first 5 bets.

The probability  that Smith loses his first 5 bets is,

[tex]\frac{26}{38}\times\frac{26}{38}\times\frac{26}{38}\times\frac{26}{38}\times\frac{26}{38}=(\frac{26}{38})^5\approx0.15[/tex]

Hence, the probability that  Smith will lose his first 5 bets is 0.15

Part (B)  His first win will occur on his fourth bet?

Smith’s first win occurring on the fourth bet means that he loses the first 3 bets and wins on the fourth bet. That is,

[tex]\frac{26}{38}\times\frac{26}{38}\times\frac{26}{38}\times\frac{12}{38}=(\frac{26}{38})^3\times\frac{12}{38}\approx0.1012[/tex]

Hence, the probability that  his first win will occur on his fourth bet is 0.1012

Answer:

  8x^2 + 34; 45.52 centimeters

Step-by-step explanation:

The perimeter is twice the sum of adjacent edges of a rectangle:

  P = 2((2x^2 +9) +(2x^2 +8)) = 2(4x^2 +17)

  P = 8x^2 +34

Then when x=1.2, the perimeter is ...

  P = 8(1.2^2) +34 = 8·1.44 +34 = 45.52 . . . . cm

Answer:

The Answer is: B  8x^2 + 34; 45.52 centimeters

Step-by-step explanation:

Took it on edg

Answer:

[tex]\displaystyle y=-2sin(6t)[/tex]

Step-by-step explanation:

Sinusoid

The shape of a sinusoid is well-know because it describes a curve with a smooth and periodic oscillation. The sine and cosine are the two trigonometric functions in which the graph matches the description of a sinusoid. The sine can be identified because its value is zero at time zero.

The graph shown in the figure corresponds to a sine. The other characteristics of the sine function are

* It completes a cycle in[tex]2\pi[/tex] radians

* It has a maximum of 1 and a minimum of -1

* It's increasing for a quarter of the cycle, decreasing for half of the cycle, and increasing for the remaining quarter of the cycle

* The equation is

[tex]y=Asin(wt)[/tex]

The function starts decreasing for the first quarter, which only is possible if the amplitude A is negative. We can also see the maximum and minimum values are 2 and -2 respectively. This means the amplitude is A=-2

We can also see the function completes 3 cycles in [tex]t=\pi[/tex] radians or 6 cycles in [tex]2\pi[/tex] radians. Or, equivalently

[tex]wt=12\pi[/tex]

[tex]w(2\pi)=12\pi[/tex]

[tex]\displaystyle w=\frac{12}{2}=6\ rad/sec[/tex]

Thus, the function can be expressed as

[tex]\boxed{\displaystyle y=-2sin(6t)}[/tex]

Answer:

y=-2sin6x

Step-by-step explanation:

The price of each regular pizza is $8 and the price of each deluxe pizza is $10.

To find the price of each pizza, we need to set up a system of equations using the given information. Let's denote the price of a regular pizza as 'r' and the price of a deluxe pizza as 'd'. Using the first customer's order, we can write the equation: 7r + d = 74. Using the second customer's order, we can write the equation: 5r + d = 58. To solve this system of equations, we can subtract the second equation from the first equation to eliminate the 'd' variable: (7r + d) - (5r + d) = 74 - 58. Simplifying, we get 2r = 16, which gives us r = 8. Plugging this value back into the first equation, we find d = 10. Therefore, the price of each regular pizza is $8 and the price of each deluxe pizza is $10.

Answer:

8 seconds

15 quarts

Step-by-step explanation:

Givens

6 seconds emits 9 quarts of water.

x seconds emits 12 quarts of water.

Formula

6/x = 9/12

Solution

Cross multiply

9x = 12*6         Simplify the right

9x = 72            Divide by 9

9x/9 = 72/9

x = 8 seconds  Answer.

In 8 seconds, the hose will emit 12 quarts

=========================

Givens

9 quarts of water are emitted in 6 second

x quarts of water are emitted in 10 seconds

Formula

9/x = 6/10            Cross multiply

Solution    

9*10 = 6x              Combine the left

90 = 6x                 Divide by 6

90/6=6x/6            

15 = x

In 10 seconds the hose emits 15 quarts.

Answer:

Step-by-step explanation:

The garden hose emits 9 quarts of water in 6 seconds. It means that the number of seconds that it takes the garden hose to emit 1 quart of water would be 6/9 = 2/3 seconds

Therefore, the number of seconds that it will take the garden hose to emit 12 quarts of water would be

12 × 2/3 = 8 seconds.

Again, the number of quarts that the garden hose will emit in one second is 9/6 = 3/2 quarts.

Therefore, the number of quarts of water that the hose emits in 10 seconds would be

10 × 3/2 = 15 quarts.

Carter has 25 dimes

Solution:

Let "n" be the number of nickels

Let "d" be the number of dimes

Given that Carter has 37 coins, all nickels and dimes in his piggy bank

number of nickels + number of dimes = 37

n + d = 37 -------- eqn 1

Given that value of coins is $ 3.10

Also, value of nickel is 0.05 dollar and value of dime is 0.10 (in dollars) and total value of these 37 coins is 3.10, so we can write:

number of nickels x value of 1 nickel + number of dimes x value of 1 dime = 3.10

[tex]n \times 0.05 + d \times 0.10 = 3.10[/tex]

0.05n + 0.10d = 3.10 ------- eqn 2

Let us solve eqn 1 and eqn 2 to find values of "n" and "d"

From eqn 1,

n = 37 - d ---- eqn 3

Substitute eqn 3 in eqn 2

0.05(37 - d) + 0.10d = 3.10

1.85 - 0.05d + 0.10d = 3.10

0.05d = 3.10 - 1.85

0.05d = 1.25

Thus carter has 25 dimes

By setting up and solving a system of equations, we find that Carter has 25 dimes in his piggy bank.

To solve how many dimes Carter has, we need to set up two equations based on the given information.

Carter has 25 dimes in his piggy bank.

Answer:

The answer is 8

Step-by-step explanation:

Lets consider that Sam's call will last x minutes in total. Then, equations for cost will be as follows:

A Pay Phone Cost: [tex]p(x)=1+0,5*x[/tex]

Operator Cost: [tex]o(x)=3+0,25*x[/tex]

If we make both costs equal, the equation will be:

[tex]1+0,5*x=3+0,25*x\\0,25*x=2\\x=8[/tex]

Sam's call need to last 8 minutes to make payphone cost and operator cost same.

Answer:

We can expect 8255 numbers of students are liberal arts majors.

Step-by-step explanation:

Given:

Total Number of students in the college = 8943

Now According to Mr. Jones Survey;

60 out of 65 students are liberal arts majors.

We need to find the number of students who are liberal arts majors out of total number of students in college.

Solution:

First we will find the Percentage number of students who are liberal arts majors according to survey.

Percentage number of students who are liberal arts majors can be calculated by dividing 60 from 65 then multiplying by 100.

framing above quote in equation form we get;

Percentage number of students who are liberal arts majors = [tex]\frac{60}{65}\times 100 = 92.31\%[/tex]

Now we will find the Total number of students who are liberal arts major.

Total number of students who are liberal arts major can be calculated by Multiplying Percentage number of students who are liberal arts majors with total number of students in the college and then dividing by 100.

framing above quote in equation form we get;

Total number of students who are liberal arts major = [tex]\frac{92.31}{100}\times 8493 \approx8255.28[/tex]

Since number of students cannot be in point, so we will round the value.

Hence We can expect 8255 numbers of students are liberal arts majors.

explanation:

The sides of a cube are squares, and they are covered by the respective sides of the cubes covering that side of the big cube. If we can show that a sqaure cannot be descomposed in squares of different sides, then we are done.

We cover the bottom side of that square with the bottom side of smaller squares. Above each square there is at least one square. Those squares have different heights, and they can have more or less (but not equal) height than the square they have below.

There is one square, lets call it A, that has minimum height among the squares that cover the bottom line, a bigger sqaure cannot fit above A because it would overlap with A's neighbours, so the selected square, lets call it B, should have less height than A itself.

There should be a 'hole' between B and at least one of A's neighbours, this hole is a rectangle with height equal to B's height. Since we cant use squares of similar sizes, we need at least 2 squares covering the 'hole', or a big sqaure that will form another hole above B, making this problem inifnite. If we use 2 or more squares, those sqaures height's combined should be at least equal than the height of B. Lets call C the small square that is next to B and above A in the 'hole'. C has even less height than B (otherwise, C would form the 'hole' above B as we described before). There are 2 possibilities:

If the second case would be true, next to C and above A there should be another 'hole', making this problem infinite. Assuming the first case is true, then C would fit perfectly above A and between B and A's neighborhood.  Leaving a small rectangle above it that was part of the original hole.

That small rectangle has base length similar than the sides of C, so it cant be covered by a single square. The small sqaure you would use to cover that rectangle that is above to C and next to B, lets call it D, would leave another 'hole' above C and between D and A's neighborhood.

As you can see, this problem recursively forces you to use smaller and smaller squares, to a never end. You cant cover a sqaure with a finite number of squares and, as a result, you cant cover a cube with finite cubes.

Answer: D 205

Step-by-step explanation:

Let,

Number of all trouts = N

Number of speckled trouts = Ns = 645

Number of rainbow trouts = Nr

Number of male speckled trouts = Ms

Number of female speckled trouts = Fs

Number of male rainbow trouts = Mr

Number of female rainbow trouts = Fr

Since, Ms = 2Fs + 45

Also, Ms + Fs = 645

Therefore, 2Fs + 45 + Fs = 645

Fs = (645-45)/3 = 200

Female speckled trouts = 200

Since

Ms + Fs = 645

Ms = 645- 200 = 445

Since, Fs/Mr = 4/3

Mr = 3x200/4 = 150

Since,

Mr/N = 3/20

N = 20x 150/3 = 1000

Recall that,

N = Ms+Fs+Mr+Fr

Fr = N-Ms-Fs-Mr

Fr = 1000-445-200-150

Fr = 205

Therefore, the number of rainbow female trouts = 205

The number of female rainbow trout is calculated using given ratios and the total number of speckled trout. After solving a series of equations, the answer is determined to be 205 female rainbow trout, which is option D.

To find the number of female rainbow trout, we first need to unpack the information provided in the question and express it in equations.

Let n be the number of female speckled trout. We know that the number of male speckled trout is 45 + 2n. Since there are 645 speckled trout in total, we can express this as:

n + (45 + 2n) = 645

Solving for n, we get:

3n + 45 = 645

3n = 600

n = 200

Now, we have the ratio of female speckled trout to male rainbow trout as 4:3, and since we've found there are 200 female speckled trout (n = 200), we can figure out the number of male rainbow trout. Let's call this number m. We have:

200/4 = m/3

50 = m/3

m = 150

The ratio of male rainbow trout to all trout is given as 3:20. If the total number of trout is T, then:

150/T = 3/20

We can solve for T:

20 × 150 = 3T

3000 = 3T

T = 1000

So there are 1000 trout in total, of which 645 are speckled. This means there must be 1000 - 645 = 355 rainbow trout. As we have already found there are 150 male rainbow trout, the remainder must be female. So:

355 - 150 = 205 female rainbow trout

Therefore, the correct answer is D. 205.

Answer:

a) [tex]P(X>3.0)=1-P(X \leq 3.0)= 1- [1- e^{-\frac{1}{2.4} 3.0}]=e^{-\frac{1}{2.4} 3.0}=0.287[/tex]

b) [tex]P(2<X<3)= 1- e^{-\frac{1}{2.4} 3} -[ 1- e^{-\frac{1}{2.4} 2}][/tex]

[tex]P(2<X<3)=e^{-\frac{1}{2.4} 2}- e^{-\frac{1}{2.4} 3}=0.435-0.287=0.148[/tex]

Step-by-step explanation:

Definitions and concepts

The Poisson process is useful when we want to analyze the probability of ocurrence of an event in a time specified. The probability distribution for a random variable X following the Poisson distribution is given by:

[tex]P(X=x) =\lambda^x \frac{e^{-\lambda}}{x!}[/tex]

And the parameter [tex]\lambda[/tex] represent the average ocurrence rate per unit of time.

The exponential distribution is useful when we want to describ the waiting time between Poisson occurrences. If we assume that the random variable T represent the waiting time btween two consecutive event, we can define the probability that 0 events occurs between the start and a time t, like this:

[tex]P(X>x)= e^{-\lambda x}[/tex]

We can express in terms of the mean [tex]\mu =\frac{1}{\lambda}[/tex]

[tex]P(X>x)= e^{-\frac{1}{\mu} x}[/tex]

And the cumulative function would be given by the complement rule like this:

[tex]P(X\leq x)=1- e^{-\frac{1}{\mu} x}[/tex]

Solution for the problem

For this case we have that X the random variable that represent the magnitude of earthquakes recorded in a region of North America, we know that the distribution is given by:

[tex]X\sim Expon(\mu =2.4)[/tex]

a) Find theprobability that an earthquake striking this region will a exceed 3.0 on the Richter scale

So for this case we want this probability:

[tex]P(X>3.0)=1-P(X \leq 3.0)= 1- [1- e^{-\frac{1}{2.4} 3.0}]=e^{-\frac{1}{2.4} 3.0}=0.287[/tex]

b) fall between 2.0 and 3.0 on the Richter scale.

For this case we want this probability:

[tex]P(2 < X <3) = P(X<3) -P(X<2)[/tex]

And replacing we have this:

[tex]P(2<X<3)= 1- e^{-\frac{1}{2.4} 3} -[ 1- e^{-\frac{1}{2.4} 2}][/tex]

[tex]P(2<X<3)=e^{-\frac{1}{2.4} 2}- e^{-\frac{1}{2.4} 3}=0.435-0.287=0.148[/tex]

Answer:

The exponential Function is [tex]20+12h=200[/tex].

Farmer will have 200 sheep after 15 years.

Step-by-step explanation:

Given:

Number of sheep bought = 20

Annual Rate of increase in sheep = 60%

We need to find that after how many years the farmer will have 200 sheep.

Let the number of years be 'h'

First we will find the Number of sheep increase in 1 year.

Number of sheep increase in 1 year is equal to Annual Rate of increase in sheep multiplied by Number of sheep bought and then divide by 100.

framing in equation form we get;

Number of sheep increase in 1 year = [tex]\frac{60}{100}\times20 = 12[/tex]

Now we know that the number of years farmer will have 200 sheep can be calculated by Number of sheep bought plus Number of sheep increase in 1 year multiplied by number of years  is equal to 200.

Framing in equation form we get;

[tex]20+12h=200[/tex]

The exponential Function is [tex]20+12h=200[/tex].

Subtracting both side by 20 using subtraction property we get;

[tex]20+12h-20=200-20\\\\12h=180[/tex]

Now Dividing both side by 12 using Division property we get;

[tex]\frac{12h}{12} = \frac{180}{12}\\\\h =15[/tex]

Hence Farmer will have 200 sheep after 15 years.

Answer:

c. Will produce a slope field with rows of parallel tangents

Step-by-step explanation:

We can write a differential equation that is a function of y only as:

[tex]y'=f(y)[/tex]

So the derivative, in this particular case, of any function will be a function of the dependent variable y only, it means that the curves you will get should all be pointing in the same direction for each value of x. Therefore the sketch of the slopes field would have parallel curves for each value of x, in other words, it will produce a slope field with rows of parallel tangents.

I hope it helps you!

Answer:

48

Step-by-step explanation:

Answer:

Step-by-step explanation:

The total number of rows of squares in the quilt is 8. Each row contains 6 squares.

Since each square measures 1 foot on a side, the area of each square would be 1^2 = 1 foot^2

This means that each row contains six 1 foot^2. Since there are 8 rows, a triangle would be formed such that one of its sides is

6 × 1 foot == 6 feets and the other side would be

8 × 1 foot = 8 feets.

The area of the quilt in a square feet would be the area of the rectangle. It becomes

6 × 8 = 48 feets

Answer:

(1, 10)

Step-by-step explanation:

Use midpoint formula.

Mₓ = (x₁ + x₂) / 2

3 = (5 + x) / 2

6 = 5 + x

x = 1

Mᵧ = (y₁ + y₂) / 2

9 = (8 + y) / 2

18 = 8 + y

y = 10

The coordinates of point D are (1, 10).

The coordinates of point D are (1, 10).

Midpoint, as the word suggests, means the point which lies in the middle of something.

Midpoint of a line segment means a point which lies in the mid of the given line segment.

Given; CD has endpoints C and D, with C at coordinates (5,8). CD has midpoint M at (3,9).

Using midpoint formula;

Mₓ = (x₁ + x₂) / 2

3 = (5 + x) / 2

6 = 5 + x

x = 1

Now, Mᵧ = (y₁ + y₂) / 2

9 = (8 + y) / 2

18 = 8 + y

y = 10

Hence, The coordinates of point D are (1, 10).

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Answer:

Step-by-step explanation:

Last year, sales at a book store increased from $5,000 to $10,000. The amount by which it increased would be 10000 - 5000 = $5000

The percentage by which the sales increased would be

5000/5000 × 100 = 100%

This year, sales decreased to $5,000 from $10,000.The amount by which it decreased would be 5000 - 10000 = - $5000

The percentage by which the sales increased would be

5000/10000 × 100 = 50%

Answer:

Justin spends $14.24 on gas to travel to work.

Step-by-step explanation:

Given:

Average speed at which Justin goes to work = 65 miles/hour

Time taken by Justin to arrive at work = 1 hour and 30 minutes = 1.5 hours [As 30 minutes =0.5 hours]

Distance he can travel per gallon of gas = 25 miles.

Cost of per gallon of gas = $3.65

Solution:

We first determine the distance Justin travels to work.

Distance = [tex]Speed\times time[/tex]

Distance = [tex]65\times 1.5 = 97.5\ miles[/tex]

Using unitary method to find the amount of gas required to cover the distance.

If 25 miles is covered in 1 gallon of gas

Then 1 mile will be covered in = [tex]\frac{1}{25}[/tex] gallons of gas

So, to cover 97.5 miles gas required = [tex]\frac{1}{25}\times 97.5=3.9[/tex] gallons of gas.

Using unitary method to find the cost of 3.9 gallons of gas.

Cost of 1 gallon of gas = $3.65

So, cost of 3.9 gallons of gas will be = [tex]\$3.65\times 3.9=\$14.235\approx\$14.24[/tex] (Answer)

Answer:

The answer is 1240

Step-by-step explanation:

We know that tuxedo shop rents different number of tuxedos each day and at max they rented 55 tuxedos in May. To maximize the number of tuxedos that rented, rented number of tuxedos need to be drop down by 1 for each day. So minimum 25 tuxedos were rented in May. To find the maximum number of tuxedos that rented in May, we need to add all numbers with using the formula for adding consecutive numbers.

[tex]Total = ((55+25)/2)*31=1240[/tex]

[tex]\boxed{\vec{v}=\frac{2}{5}i+4j}[/tex]

In this exercise, we have the following facts for the vector [tex]\vec{u}[/tex]:

Since the vector [tex]\vec{u}[/tex] goes from point [tex]P_{1}[/tex] to [tex]P_{2}[/tex], then:

[tex]\vec{u}=(19,-8)-(21,12) \\ \\ \vec{u}=(19-21,-8-12) \\ \\ \vec{u}=(-2,-20)[/tex]

On the other hand, we have the following facts for the vector [tex]\vec{v}[/tex]:

So we can write this relationship as follows:

[tex]5\vec{v}=-\vec{u} \\ \\ \vec{v}=-\frac{1}{5}\vec{u} \\ \\ \vec{v}=-\frac{1}{5}(-2,-20) \\ \\ \vec{v}=(\frac{2}{5},4) \\ \\ \\ Finally: \\ \\ \boxed{\vec{v}=\frac{2}{5}i+4j}[/tex]

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Answer:

Edie has a better deal since his final price is lower

Step-by-step explanation:

Cousin Edie drank all of Clark's egg nog . Edie finds a coupon for 50 cents off that can only be use at a local grocery store.Clark normally buys his egg nog at the supermarket.

The tax rate at both stores is 2.25%.

Clark buys the egg nog at $5.95 plus tax .

Edie buys the egg nog at $6.35 plus coupon plus tax.

After Edie applies the coupon , the final price is $( 6.35 - 0.50 ) = $5.85

Since the percentage of tax applied is the same, the deal with lower final price is better.

Hence, Edie has a better deal.

Answer:

  6

Step-by-step explanation:

Each ice cream cone costs 4 quarters or 10 dimes, so Simon has ...

  20/4 + 12/10 = 5 + 1.2 = 6.2

times the price of an ice cream cone. He can buy 6 cones for his friends.

Answer: b. 2x = 30

Step-by-step explanation:

Given : 30 states joined the United States between 1776 and 1849

and x states joined between 1850 and 1900 .

If the number of states that joined the United States between 1776 and 1849 is twice the number of states that joined between 1850 and 1900.

i.e. No. of states joined the United States between 1776 and 1849= 2 (No. of states that joined between 1850 and 1900)

i.e . 30=  2(x)          [Substitute the values]

i.e . 2x=30

Hence, the true equation : 2x=30

Value of (x + y + z) = 8

Suppose p and q are the positive numbers for which

[tex]log_(9)p=log_(12)q=log_(16)(p+q)[/tex] from the given expression,

[tex]log_(9)p=log_(12)q[/tex]

[tex](logp)/(log9)=(log(q))/(log12)[/tex]

log(p).log(12) = log(q).log(9)

log(q).2log(3) = log(p).log(12) ------(1)

[tex]Now log_(12)q=log_(16)(p+q)[/tex]

[tex](logq)/(log12)=(log(p+q))/(log(16))[/tex]

log(q).log(16) = log(p + q).log(12)

2log(4).log(q) = log(p + q).log12 -------(2)

By adding both the equations (1) and (2),

2log(3).log(q) + 2log(4).log(q) = log(12).log(p) + log(12).log(p + q)

log(q)[2log(3) + 2log(4)] = log(12)[logp + log(p + q)]

2log(q).log(12) = log(12).log[p.(p + q)]

2log(q) = log[p.(p+q)]

q² = p(p + q)

(q)/(p)=(p+q)/(q)

(q)/(p)=(p)/(q)+1

Let (q)/(p)=a

a = (1)/(a)+1

a² - a - 1 = 0 from quadratic formula,

a = [tex]\frac{1\pm \sqrt{(-1)^(2)-4 \times 1 \times (-1)}}{2}[/tex]

a = [tex](1\pm √((1+4)))/(2)[/tex]

a = [tex](1\pm √((5)))/(2)[/tex]

If the solution is represented by (x+√(y))/(z) then  it will be equal to

(1+√((5)))/(2) then x = 1, y = 5 and z = 2.

Now we have to find the value of (x + y + z).

By placing the values of x, y and z,

(x + y + z) = (1 + 5 + 2) = 8

Therefore, value of (x + y + z) = 8

Answer:

EF = (d − b) / 2

Step-by-step explanation:

Let's say that G is the intersection of the trapezoid's diagonals.

Triangle GBC is similar to triangle GDA, so we can write a proportion:

GD / GB = AD / BC

GD / GB = d / b

GD = (d / b) GB

Next, F is the midpoint of BD, so BF equals FD.

BF = FD

GB + GF = GD − GF

2GF = GD − GB

2GF = (d / b) GB − GB

2GF = ((d − b) / b) GB

GF / GB = (d − b) / (2b)

Finally, triangle GBC is similar to triangle GFE, so we can write another proportion:

GF / GB = EF / BC

(d − b) / (2b) = EF / b

EF = (d − b) / 2

Answer:

23

Step-by-step explanation:

We can check all the possibilities.

It is not necessary to consider y>16, because in this case, 16#y=16 as 16 is too small to be split in  y  parts.

Now, 1,2,4, 8 and 16 are factors of 16. When you divide 16 by any of the previous integers, the remainder is zero so we discard these.

When y=3, 16=5(3)+1, 16#3=1 so we add y=3. From this, 16=3(5)+1 thus 16#5=1 and we add y=5.

We discard y=6 as 16#6=4 (using that 16=6(2)+4). We also discard y=7 because 16=2(7)+2 then 16#7=2.

For y=9,10,11,12,13,14, when dividing the quotient is one so 16#y=16-y>1 and these values are discarded. However, we add y=15 because 16=15(1)+1 and  16#15=1.

Adding the y values, the sum is 3+5+15=23.

The inequality is used to solve how many hours of television Julia can still watch this week is [tex]x + 1.5 \leq 5[/tex]

The remaining hours of TV Julia can watch this week can be expressed is 3.5 hours

Given that Julia is allowed to watch no more than 5 hours of television a week

So far this week, she has watched 1.5 hours

To find: number of hours Julia can still watch this week

Let "x" be the number of hours Julia can still watch television this week

"no more than 5" means less than or equal to 5 ( ≤  5 )

Juila has already watched 1.5 hours. So we can add 1.5 hours and number of hours Julia can still watch television this week which is less than or equal to 5 hours

number of hours Julia can still watch television this week + already watched ≤ Total hours Juila can watch

[tex]x + 1.5 \leq5[/tex]

Thus the above inequality is used to solve how many hours of television Julia can still watch this week.

Solving the inequality,

[tex]x + 1.5 \leq5\\\\x \leq 5 - 1.5\\\\x \leq 3.5[/tex]

Thus Julia still can watch Television for 3.5 hours