Determine an equivalent expression by rationalizing the denominator: (5√3)/(4-√6)

From the given recursive definition,

[tex]a_1 = 3[/tex]

[tex]a_2 = a_1 + 5 = 3 + 5 = 8[/tex]

[tex]a_3 = a_2 + 5 = 8 + 5 = 13[/tex]

[tex]a_4 = a_3 + 5 = 13 + 5 = 18[/tex]

[tex]a_5 = a_4 + 5 = 18 + 5 = 23[/tex]

The equivalent expression of [tex]\frac{\frac 2x - \frac 4y}{-\frac 5y + \frac 3x}[/tex] is [tex]\frac {2(y - 2x)}{ 3y-5x}[/tex]

The complete question is in the attached image

We have:

[tex]\frac{\frac 2x - \frac 4y}{-\frac 5y + \frac 3x}[/tex]

Take the LCM

[tex]\frac{\frac {2y - 4x}{xy}}{\frac{-5x + 3y}{xy}}[/tex]

Divide through by xy

[tex]\frac {2y - 4x}{-5x + 3y}[/tex]

Rewrite as:

[tex]\frac {2y - 4x}{ 3y-5x}[/tex]

Factor out 2

[tex]\frac {2(y - 2x)}{ 3y-5x}[/tex]

Hence, the equivalent expression of [tex]\frac{\frac 2x - \frac 4y}{-\frac 5y + \frac 3x}[/tex] is [tex]\frac {2(y - 2x)}{ 3y-5x}[/tex]

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40.2 percent of the customers at the beauty supply store choose brand B.

An equation is an expression that shows the relationship between two or more numbers and variables.

The percent of customers that choose brand B = (number of  brand B customers / total number of customers) * 100%

The percent of customers that choose brand B = (402/1000) * 100% = 40.2%

40.2 percent of the customers at the beauty supply store choose brand B.

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The equation to model the situation is [tex]\mathbf{y = \dfrac{k}{x^2}}[/tex]. The constant for the variation is 2250.

The intensity of light from a lantern varies inversely to the square of the distance from the lantern.

From the given information:

Then:

[tex]\mathbf{y \alpha \dfrac{1}{x^2} }[/tex]

[tex]\mathbf{y = \dfrac{k}{x^2} }[/tex]   here, k = constant.

2.

If y = 90 W/m² when the distance x = 5m

Then:

[tex]\mathbf{90 = \dfrac{k}{(5)^2}}[/tex]

k = 90 × 25

k = 2250

c.

The equation to model the situation by using the constant variation is:

[tex]\mathbf{y = \dfrac{2250}{x^2}}[/tex]

d.

If the light intensity y = 40, then x is determined as:

[tex]\mathbf{40 = \dfrac{2250}{x^2}}[/tex]

[tex]\mathbf{x = \sqrt{\dfrac{2250}{40}}}[/tex]

x = 7.5 m

e.

The light is needed in (225 × 1000)m = 225000 km of illumination.

f.

The lantern required for the new light estimation is:

y = 2250/225000

y = 0.01 intensity

Therefore, we can conclude that to get an intensity of 1 W/m², we need to put 100 lanterns.

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Answer:

It's A and C

Step-by-step explanation:

the angles are 45, which is less than 90

Answer:

Quadrants 1 and 4 EDIT: Quadrants 2 & 4

Step-by-step explanation:

Quadrant 1  : Edit: no

Quadrant 2  : Edit: yes

Quadrant 3 : No

Quadrant 4 : Yes

Using a system of equations, it is found that the lengths of the sides of the triangle are given as follows:

0.91 feet, 0.73 feet, 1.23 feet.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are the lengths, given by x, y and z.

The length of one side of a triangle is 2 feet less than three times the length of its second side, hence:

y = 3x - 2.

The length of the third side is 3/4 of the sum of the lengths of the first two sides, hence:

[tex]z = \frac{3(x + y)}{4} = \frac{3(4x - 2)}{4}[/tex]

The perimeter of the triangle is 17.5 feet, hence:

[tex]x + y + z = 17.5[/tex]

[tex]x + 3x - 2 + \frac{3(4x - 2)}{4} = 17.5[/tex]

[tex]4x + \frac{3(4x - 2)}{4} = 19.5[/tex]

[tex]16x + 12x = 25.5[/tex]

x = 25.5/28

x = 0.91.

Then the other sides are:

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Answer: Exponential

Step-by-step explanation:

Because every time x increases by 1, y increases by a factor of 3.

6/2 = 3

18/6 = 3

54/18 = 3

162/54 = 3

P.S.: I ANSWERED ONE OF YOUR PROBLEMS WITH EXACTLY THE DATA IN THIS TABLE BY COINCIDENCE HAHA

The chocolate will last for 1 day, if she gets 4 more dragons

The expression can be represented using the following ratio:

Ratio = Dragons : Days : Chocolate

For the 2 dragons she has, we have:

Ratio = 2 : 12 : 300

When she gets 4 more dragons, we have:

Ratio = 6 : days : 300

Equate both ratios

6 : days = 12 : 2

Express as fraction

days/6 = 2/12

Multiply both sides by 6

days = 6 * 2/12

Evaluate

days = 1

Hence, the chocolate will last for 1 day

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Answer:

A. 0.068

Step-by-step explanation:

First, 3 inches to miles. 3 inches in a mile is 0.00004735.

The snail moves 0.00004735 miles per minute.

Next, search how many minutes are there in a day. There is 1440 minutes in a day.

Multiply the 1440 and 0.00004735.

1440*0.00004735=0.068

The snail can move 0.068 miles per day if it doesn't take a break.

Hope this helps!

If not, I am sorry.

In order to make the new flag, Lauren decided to triple the sides of the old flag in order to get a new one.

The old triangle is the smaller one. We can see that this triangle has increased by a factor of 3 on all sides.

We have 4 x 3= 12

2 x 3 = 6

7 x 3 = 21

The calculated values above is what produced the new larger flag.

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You can by 24 combinations of items from the store

The given parameters are:

Cups = 3

Bowl = 4

Spoon = 2

The number of combination is:

Combination = Cups * Bowl * Spoon

So, we have:

Combination = 3 * 4 * 2

Evaluate

Combination = 24

Hence, you can by 24 combinations of items from the store

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Answer:

24

Step-by-step explanation:

140 times .25 = 35

140 + 35 = 175

4,200 divided by 175 =

24

jobtestprep

The number of TV bought post-raise for $4,200 is 24 if the store manager decides to raise the TV price by 25% in order to increase the store's profits.

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

We have:

A home appliance store has recently seen an increase in TV sales.

The store manager decides to raise the TV price by 25% in order to increase the store's profits.

Original price of TV = $140

Price after increasing:

= 140 + 25% of 140

= $175

The number of TV bought post-raise for $4,200 = 4200/175

= 24

Thus, the number of TV bought post-raise for $4,200 is 24 if the store manager decides to raise the TV price by 25% in order to increase the store's profits.

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Answer:

25.5 mph

Step-by-step explanation:

So Bradley's speed can be modeled by the equation y=2x+40 where y=speed, x=time in hours after noon, and b=initial speed

So 12:15 is 15 minutes after noon, which is also 0.25 or 1/4 of an hour after noon. This is the x-value. Plug this into the equation to get his speed at 12:15

y=2(0.25)+40

y=0.5+40

y=40.5

So his speed was 40.5 at the time and since he was going 15 miles over the speed limit, the speed limit is 15 less than his speed

40.5 - 15 = 25.5

Answer:

25.5 mph

Step-by-step explanation:

Given information:

Calculate Bradley's speed at 12.15 pm:

60 minutes = 1 hour

⇒ 15 minutes = 1/4 hour

⇒ speed at 12.15 pm = speed at 12.00pm + 1/4 of 2 mph

                                  = 40 mph + 0.5 mph

                                  = 40.5 mph

If he was 15 miles over the speed limit at 12.15 pm then:

⇒ speed limit = speed at 12.15pm - miles over the limit

                       = 40.5 mph - 15

                       = 25.5 mph

Therefore, the speed limit was 25.5 mph.

Answer:

-6,0 & -3,0

Step-by-step explanation:

Answer:

19 inches

Step-by-step explanation:

So the perimeter of a triangle is the sum of the three sides. So the perimeter is [tex]\sqrt{65} + \sqrt{35} + \sqrt{26}[/tex] which is approximately 19.077 inches but in this case the answer is 19 inches

A significance level of 5% (more commonly referred to as 95%) corresponds to a statement that (only) a probability of 5% or less is that a particular randomly generated observation is accepted as significant.

In this example, the p-level (the true probability that the observations are randomly generated) is less than 5% (0.0421 <0.05), so we can draw the conclusion that the observations are significant.

p = 0.0421 means that the probability is only 0421/1000. The choice of significance level to reject the null hypothesis is optional. Traditionally, 5%, 1%, and 0.1% levels have been used. In rare situations, a 10% significance level is also used.

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The value of b is -16 and the value of ac is 60 after comparing with the standard equation.

Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

As we know, the formula for the roots of the quadratic equation is given by:

[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]

We have a quadratic function:

= 3x² - 16x + 20

On comparing with standard function:

b = -16

a = 3

c = 20

ac = 3(20) = 60

Thus, the value of b is -16 and the value of ac is 60 after comparing with the standard equation.

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The amount of bbd received for the given currency exchange rate is 6050  bbd.

The value of one country's currency in relation to the currencies of other countries or economic zones is known as the currency exchange rate.

The majority of currency exchange rates are free-floating and fluctuate according to market supply and demand.

There may be restrictions on some currency exchange rates since they are fixed to the value of other currencies.

According to the question,

Currency exchange rate: $1.00=5.50bbd

So, $1100=1100*5.50 bbd

               =6050 bbd

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Answer:

18.75

Step-by-step explanation:

[tex]Area=\pi r^{2} \\Area=3(\frac{5}{2} )^{2} \\Area=18.75[/tex]

Answer:

see explanation

Step-by-step explanation:

sinX = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{YZ}{XY}[/tex] = [tex]\frac{\sqrt{119} }{12}[/tex]

cosX = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{XZ}{XY}[/tex] = [tex]\frac{5}{12}[/tex]

Answer:

x = - 3 ± [tex]\sqrt{2}[/tex]

Step-by-step explanation:

x² + 6x + 7 = 0 ( subtract 7 from both sides )

x² + 6x = - 7

using the method of completing the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(3)x + 9 = - 7 + 9

(x + 3)² = 2 ( take square root of both sides )

x + 3 = ± [tex]\sqrt{2}[/tex] ( subtract 3 from both sides )

x = - 3 ± [tex]\sqrt{2}[/tex]

Answer:

For plan B to save money car rental need to drive 111.1 miles as [tex]\frac{x}{y}[/tex] expresses the average amounts of miles per day car rental drive and its obtained value is 111.1.

Step-by-step explanation:

In the question it is given that a car rental company offers two plans for renting a car.

Plan A: $30 per day and [tex]$\$ 0 \cdot 18$[/tex] per mile.

Plan B: $50 per day with free unlimited mileage

It is required to find that how many miles would be needed to drive for plan B to save money. be needed to drive for plan B to save money.

Step 1 of 5

In Plan A $30 per day and [tex]$\$ 0 \cdot 18$[/tex] per mile are costed so the cost of Plan A is given by following equation,

[tex]$$A=30 y+0 \cdot 18 x$$[/tex]

In Plan B $50 per day with free unlimited mileage are costed so the cost of Plan B is given by following equation,

[tex]$$B=50 y$$[/tex]

Step 2 of 5

Now comparing the obtained equations [tex]$A=30 y+0 \cdot 18 x$[/tex]

and B=50y.

[tex]$$30 y+0 \cdot 18 x=50 y$$[/tex]

Step 3 of 5

Subtract 30y from both the sides of the obtained equation 30 y+0.18x=50y and simplify using subtraction properties.

[tex]$$30 y+0 \cdot 18 x-30 y=50 y-30 y$$\\ $0 \cdot 18 x=20 y$[/tex]

Step 4 of 5

Divide both the sides of the obtained equation [tex]$0 \cdot 18 x=20 y$[/tex] by [tex]$0 \cdot 18$[/tex] and simplify using division properties.

[tex]$$\begin{aligned}&\frac{0 \cdot 18 x}{0 \cdot 18}=\frac{20 y}{0.18} \\&x=\frac{1000 y}{9}\end{aligned}$$[/tex]

Step 5 of 5 save money car rental need to drive 111.1 miles.

[tex]$$\begin{aligned}&\frac{x}{y}=\frac{1000 y}{9 y} \\&\frac{x}{y}=111.1\end{aligned}$$[/tex]

the constant variation, K= 4

Step-by-step explanation:

i have replace the constant variation by the letter K

First step is to write down the information

y directly proprotional to x

So, y= Kx

Replace the value given for x and y to find k

y= -4 and x = -1

Kx= y

K( -1) = -4

K = -4 ÷ -1

K= 4

Further answer

if you are asked the connecting equation between y and x just replace the value of K in the equation

y= Kx

y= 4x

The equation of line passing through points (4.5. 0) and (0, 9) is y = -2x + 9.

Suppose the given points are (x_1, y_1) and (x_2, y_2), then the equation of the straight line joining both two points is given by

[tex](y - y_1) = \dfrac{y_2 - y_1}{x_2 - x_1} (x -x_1)[/tex]

The graph of the picture shows two clear points (4.5. 0) and (0, 9)

[tex](y - 0) = \dfrac{9 - 0}{0 - 4.5} (x -4.5)\\\\\\(y - 0) = \dfrac{9 }{- 4.5} (x -4.5)\\\\\\-4.5y = 9(x -4.5)\\\\-4.5y = 9x - 40.5\\\\y = -2x + 9[/tex]

Hence, the equation of line passing through points (4.5. 0) and (0, 9) is y = -2x + 9.

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Hello,

Answer:

x = 13

Step-by-step explanation:

    7x + 5 + 5x + 19 = 180

⇔ 12x + 24 = 180

⇔ 12x = 180 - 24

⇔ 12x = 156

⇔ x = 156/12

⇔ x = 13

Answer:

[tex](a)1600f+600w\\\\(b)1600\times2f+600\times2w[/tex]

Answer:

b. x=2, -3

Step-by-step explanation:

So I'm assuming the two equations are: [tex]y=4-x^2[/tex] and [tex]x-y=2[/tex]

Since it's asking to solve to solve for x. Then we need to solve for y in one of the equations, so that's it's defined using x, then substitute that into the other equation, that way the only variable left is going to be the x variable.

So since y is already solved for in the first equation. I'll plug that into the second equation.

Original equation:

[tex]x-y=2[/tex]

Substitute 4-x^2 in as y

[tex]x-(4-x^2)=2[/tex]

Distribute the negative sign

[tex]x-4+x^2=2[/tex]

Organize it so it's in order by degree

[tex]x^2+x-4=2[/tex]

Subtract 2 from both sides

[tex]x^2+x-6=0[/tex]

So now we have a quadratic equation and we're trying to find the zeroes. You can use the quadratic equation, but since the only options are integers, we can easily factor this equation. So you need to look for factors of -6, which add up to 1. I like to think about it as find two numbers with a difference of 1, and then figure out which is going to be positive and which is going to be negative after. So knowing this you can easily see 3 and 2 have a difference of 1. Since the 1 is positive, that means the 3 has to be positive and the 2 has to be negative

Use the factors: 3 and -2 to rewrite the equation:

[tex](x+3)(x-2)[/tex]

Now set each factor equal to 0

x+3 = 0

x=-3

x-2=0

x=2

this gives you the two solutions: -3, and 2

Question 5

Vertical angles are congruent. Therefore, [tex]3y=\boxed{150}[/tex]. The sum of two supplementary angles equals [tex]\boxed{180^{\circ}}[/tex].

Therefore, [tex]6x+150=\boxed{180}[/tex]

Question 6

[tex]\angle b-14=90-\angle b\\\\2\angle b=104\\\\\angle b=\boxed{52^{\circ}}[/tex]

Question 7

[tex]\angle d+32=180-\angle d\\\\2\angle d=146\\\\\angle d=\boxed{73^{\circ}}[/tex]

Question 8

[tex]7x-80=3x\\\\-80=-4x\\\\x=20\\\\\implies \boxed{m\angle 1=m\angle 3=60^{\circ}}[/tex]