The second side of a triangular deck is 6 feet longer than the shortest side and a third side that is 6 feet shorter than twice the length of the shortest side. If the perimeter of the deck is 56 ​feet, what are the lengths of the three​ sides?

The answer would be D, where all of the given x values touch the x axis

Answer: D)

Step-by-step explanation:

The equation is: (x - 2)(x - 1)(x + 4) = 0

We can find the x-intercepts by Applying the Zero Product Property:

x - 2 = 0           x - 1 = 0             x + 4 = 0

x = 2                 x = 1                   x = -4

Which graph shows the curve crossing the x-axis at these points?  D

Answer:

y = 3 • ± √2 = ± 4.2426

Step-by-step explanation:

2y2 -  36  = 0  

Step  2  :

Step  3  :

Pulling out like terms :

3.1     Pull out like factors :

  2y2 - 36  =   2 • (y2 - 18)  

Trying to factor as a Difference of Squares :

3.2      Factoring:  y2 - 18  

Theory : A difference of two perfect squares,  A2 - B2  can be factored into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =

        A2 - AB + BA - B2 =

        A2 - AB + AB - B2 =  

        A2 - B2

Note :  AB = BA is the commutative property of multiplication.  

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check : 18 is not a square !!  

Ruling : Binomial can not be factored as the difference of two perfect squares.

Equation at the end of step  3  :

 2 • (y2 - 18)  = 0  

Step  4  :

Equations which are never true :

4.1      Solve :    2   =  0

This equation has no solution.

A a non-zero constant never equals zero.

Solving a Single Variable Equation :

4.2      Solve  :    y2-18 = 0  

Add  18  to both sides of the equation :  

                     y2 = 18  

When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:  

                     y  =  ± √ 18  

Can  √ 18 be simplified ?

Yes!   The prime factorization of  18   is

  2•3•3  

To be able to remove something from under the radical, there have to be  2  instances of it (because we are taking a square i.e. second root).

√ 18   =  √ 2•3•3   =

               ±  3 • √ 2  

The equation has two real solutions  

These solutions are  y = 3 • ± √2 = ± 4.2426

Answer:

D. 272 poles

Explanation:

We are given that:

The top layer has 20 poles, the next down one has 24 poles and the third one has 28 poles

We can note that each layer has 4 poles more that the one above it

Based on this, we can get the number of poles in each layer as follows:

Top layer has 20 poles

Second one has 20 + 4 = 24 poles

Third one has 24 + 4 = 28 poles

Fourth one has 28 + 4 = 32 poles

Fifth one has 32 + 4 = 36 poles

Sixth one has 36 + 4 = 40 poles

Seventh one has 40 + 4 = 44 poles

Eighth one has 44 + 4 = 48 poles

Now, we can get the total number of poles by adding the poles in all layers

This is done as follows:

Total number of poles = 20 + 24 + 28 + 32 + 36 + 40 + 44 + 48

Total number of poles = 272 poles

Hope this helps :)

Answer:

  3/4

Step-by-step explanation:

1/2 the deck is red cards.

1/4 of the deck is spades.

There are no spades that are red cards, so the probability of drawing a red card or a spade at random from a well-shuffled deck is ...

  1/2 + 1/4 = 3/4

Answer:

9 / 20

Step-by-step explanation:

We can form a ratio with the information "for every 25 ml of orange juice you need 30 ml of apple juice and 45 ml of coconut milk"

25 : 30 : 45

Total = 100

Coconut milk = 45 ml

45 / 100 = 9 / 20

Answer:

240.3

Step-by-step explanation:

       Tan(31) = y/400ft

400 tan (31) = y

                 y = 240,3

there is 6 chickens and 16 rabbits, need the work tho?

6 chickens 16 rabbits

Answer:

It is 15.

Step-by-step explanation:

Answer:

1.29 s

Step-by-step explanation:

h = -490t² + 1260t

810 = -490t² + 1260t

490t² - 1260t + 810 = 0

49t² - 126t + 81 = 0

(7t - 9)² = 0

7t - 9 = 0

t = 9/7

t ≈ 1.29

To find the time when the rocket is at a height of 810 cm, set the equation -490t^2 + 1260t equal to 810 and solve for t using the quadratic formula. The quadratic formula will give two solutions: choose the positive solution as we cannot have negative time.

We are given the equation h=-490t^2+1260t to represent the height of the rocket. We're also told that the height h is 810 cm and we are asked to solve for time t when this is the case.

To find the time when the rocket's height is 810 cm, we can first set the equation equal to 810: -490t^2 + 1260t = 810.

We can then simplify that to -490t^2 + 1260t - 810 = 0 and solve for t using the quadratic formula t = [-b ± sqrt(b² - 4ac)] / 2a, where a = -490, b = 1260 and c = -810.

This will give us the two points in time at which the rocket is at a height of 810 cm. Remember, the negative solution is likely extraneous as we cannot have negative time, so you should consider only the positive solution.

https://brainly.com/question/34196754

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Answer:

$9.50 - for adults

$7.50 - children

Step-by-step explanation:

All you have to do is multiply $4.75 by 2 since there are two adults and multiply $2.50 by 3 since there  are three children.

Answer:

The jar of jelly that costs $2.32 for 16 ounces is the better buy, because the unit rate is less

Step-by-step explanation:

step 1

Find the units rate

One jar of jelly costs $2.32 for 16 ounces

so

The unit rate is equal to [tex]\frac{2.32}{16}= 0.145\frac{\$}{ounce}[/tex]

Another jar costs $2.03 for 13 ounces

so

The unit rate is equal to [tex]\frac{2.03}{13}= 0.156\frac{\$}{ounce}[/tex]

step 2

Compare the unit rates

[tex]0.145\frac{\$}{ounce} < 0.156\frac{\$}{ounce}[/tex]

therefore

The jar of jelly that costs $2.32 for 16 ounces is the better buy, because the unit rate is less

The jelly that costs $2.32 for 16 ounces is the better buy. The unit rate for this jar of jelly is $0.145 or approximately $0.15 per ounce. The unit rate for the second jar of jelly is $0.156 or approximately $0.16 per ounce

Answer:

Pemdas

Step-by-step explanation:

Parenthesis

Exponents

Multiplication

Division

Addition

Subtraction

You go from left to right and solve in the order called Pemdas.

To use a system of equations to find the solution algebraically, follow these steps: identify the unknowns and knowns, write down the equations, solve for one variable, substitute the expression into the other equation(s), solve for the remaining variables, and check your answer(s) for reasonableness.

1. Identify the unknowns and knowns.

2. Write down the equations that represent the given information.

3. Solve one of the equations for one variable in terms of the other.

4. Substitute this expression into the other equation(s), replacing the variable.

5. Solve the resulting equation(s) to find the value(s) of the remaining variable(s).

6. Check your answer(s) to ensure they make sense in the context of the problem.

Answer:

1.)[tex]-12+4x=-12+4x[/tex]

2.) [tex]2-2x \neq -8-2x[/tex]

Step-by-step explanation:

The distributive property states that multiplying a sum by a number gives the same result as multiplying each addend by the number and then adding all the products.

[tex]a(b+c)=ab+ac[/tex]

For the first equation

[tex]-2(6-2x)=4(-3+x)\\(-2)(6)+(-2)(-2x)=(4)(-3)+(4)(x)\\-12+4x=-12+4x[/tex]

For the second equation

[tex]5-1(2x+3)=-2(4+x)\\5+((-1)(2x)+(-1)(3))= (-2)(4)+(-2)(x)\\5+(-2x-3) = -8+(-2x)\\5-2x-3=-8-2x\\2-2x \neq -8-2x[/tex]

.

Answer:

4 hours

Step-by-step explanation:

0:8

6:12

12:16

18:20

24:24

Answer: 4 hours

Step-by-step explanation:

Answer:

The altitude of the climber is 1.40 miles

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

In the right triangle BCD

tan(22°)=h/(x-0.5)

h=tan(22°)*(x-0.5) ----> equation A

In the right triangle ACD

tan(15°)=h/x

h=tan(15°)*(x) ----> equation B

Equate equation A and equation B and solve for x

tan(22°)*(x-0.5)=tan(15°)*(x)

tan(22°)*x-tan(22°)*0.5=tan(15°)*x

x[tan(22°)-tan(15°)]=tan(22°)*0.5

x=tan(22°)*0.5/[tan(22°)-tan(15°)]

x=1.48 miles

Find the value oh h

h=tan(15°)*(1.48)=0.40 miles

therefore

The altitude of the climber is equal to

0.40+1=1.40 miles

Answer:

Step-by-step explanation:

Just solved a similar problem and figured it out, the angle of elevation is somewhat unintuitive as the angle of the second search team needs to be flipped. The diagram should look more like this:
This isn't an explanation of the math but more of a visualization for those that just needed the 2D representation. The real answer would be 1.081 miles (:

Let [tex]x[/tex] be the amount (mL) of the pure vinegar the chef will use, and [tex]y[/tex] the amount of dressing. She wants to end up with a 310 mL mixture, so

[tex]x+y=310[/tex]

For each mL used of the dressing, 0.07 mL is vinegar, and the chef wants to end up with a 19% vinegar mixture, so

[tex]x+0.07y=0.19(x+y)=58.9[/tex]

Now

[tex]x+y=310\implies y=310-x[/tex]

[tex]\implies x+0.07(310-x)=58.9[/tex]

[tex]\implies0.93x+21.7=58.9[/tex]

[tex]\implies0.93x=37.2[/tex]

[tex]\implies x=40[/tex]

[tex]\implies y=270[/tex]

Answer:

exponential; y = 89 • 0.62^x

Step-by-step explanation:

Answer:

Option B exponential y = 89 · 0.62x

Step-by-step explanation:

The table shows the estimated number of deer living in a forest over a five year period.

Year            Number of deers

0                     89

1                      55

2                     34

3                     21

4                     13

Now we have to find the model representing this situation. Difference in number of deer, in the forest.

We can see there is a common ratio between each successive term r = [tex]\frac{55}{89}[/tex] = 0.618

r = [tex]\frac{34}{55}[/tex] = 0.618

so it can be represented by an exponential model.

[tex]y=a (r) ^{x}[/tex]

[tex]y=89(62) ^{x}[/tex]

Option B is the answer.

Answer:

Step-by-step explanation:

If the sides form a right triangle, the sum of the squares of the shorter two sides will equal the square of the longest side.

1. 10.5^2 + 20.8^2 = 23.3^2 . . . . . true algebraic statement; right triangle

__

2. 6^2 +20.1^2 = 440.01 ≠ 22.9^2 = 524.41 . . . . . this is an obtuse triangle

Answer:

[tex]2\sqrt[4]{5}[/tex]

Step-by-step explanation:

First, you calculate the quotient which is [tex]\sqrt[4]{80}[/tex]

Then you simplify the radical which is [tex]2\sqrt[4]{5}[/tex]

Inputting this in a calculator will give you 2.99 which is also correct.

Answer:

5 liters

Step-by-step explanation:

Divide 35 liters evenly between the 7 pitchers and you'll have 5 liters in each pitcher.

To find the amount of lemonade in each pitcher, divide the total amount of lemonade by the number of pitchers. In this case, each pitcher will contain 5 liters of lemonade.

To find the amount of lemonade in each pitcher, we divide the total amount of lemonade by the number of pitchers. In this case, Bob has 35 liters of lemonade and 7 pitchers. So, to find the amount of lemonade in each pitcher, we divide 35 by 7.

35 ÷ 7 = 5 liters of lemonade

Therefore, there will be 5 liters of lemonade in each pitcher.

If Bob has 35 liters of lemonade and he distributes it equally into 7 juice pitchers, we need to perform a division to find out how much lemonade will be in each pitcher. The calculation is straightforward:

Divide the total volume of lemonade by the number of pitchers.

35 liters ÷ 7 pitchers = 5 liters per pitcher.

Therefore, each juice pitcher will contain 5 liters of lemonade.

Answer:

  D.  The graph of g(x) is shifted 2 units up.

Step-by-step explanation:

Adding 2 to the y-coordinate of a point shifts it up by 2 units.

___

The graph of f(x) is all points (x, f(x)). When you add 2 to f(x), you make the graph of g(x) be all points (x, g(x)) = (x, f(x)+2). That is all of the points on the original graph are shifted up by 2 units.

I'll match them for you, but to find the inverse of an equation, all you must do is

[tex]f(x)^{-1}  = 5x[/tex]  →  [tex]f(x) = \frac{x}{5}[/tex]

[tex]f(x)^{-1} = \frac{x^{3}}{2}[/tex]  →  [tex]f(x) = \sqrt[3]{2x}[/tex]

[tex]f(x)^{-1} = x + 10[/tex]  →  [tex]f(x) = x - 10[/tex]

[tex]f(x)^{-1} = \frac{3(x+17)}{2}[/tex]  →  [tex]f(x) = \frac{2x}{3} -17[/tex]

Hope I help ! :)

ANSWER

[tex] \boxed {f(x)= \frac{2x}{3} - 17\to \: f ^{ - 1} (x)=\frac{3x + 51}{2}}[/tex]

[tex] \boxed {f(x) = x - 10 \to {f}^{ - 1} (x) = x + 10 }[/tex]

[tex] \boxed {f(x) = \sqrt[3]{2x} \to {f}^{ - 1} (x) = \frac{ {x}^{3} }{2} }[/tex]

[tex] \boxed {f(x) = \frac{x}{5} \to{f}^{ - 1} (x) = 5x}[/tex]

EXPLANATION

1.

Given :

[tex]f(x) = \frac{2x}{3} - 17[/tex]

Let

[tex]y =\frac{2x}{3} - 17[/tex]

Interchange x and y.

[tex]x=\frac{2y}{3} - 17[/tex]

Solve for y.

[tex]x + 17=\frac{2y}{3} [/tex]

[tex]3x + 51=2y[/tex]

[tex]y=\frac{3x + 51}{2} [/tex]

[tex]f ^{ - 1} (x)=\frac{3x + 51}{2} [/tex]

2.

Given: f(x)=x-10

Let y=x-10

Interchange x and y.

x=y-10

Solve for y.

y=x+10

This implies that,

[tex] {f}^{ - 1} (x) = x + 10[/tex]

3.

Given:

[tex]f(x) = \sqrt[3]{2x} [/tex]

Let

[tex]y=\sqrt[3]{2x} [/tex]

Interchange x and y.

[tex]x=\sqrt[3]{2y} [/tex]

solve for y.

[tex] {x}^{3} = 2y[/tex]

[tex]y = \frac{ {x}^{3} }{2} [/tex]

[tex] {f}^{ - 1} (x) = \frac{ {x}^{3} }{2} [/tex]

4.

Given:

[tex]f(x) = \frac{x}{5} [/tex]

Let

[tex]y = \frac{x}{5} [/tex]

Interchange x and y.

[tex]x = \frac{y}{5} [/tex]

Solve for y.

[tex]y = 5x[/tex]

[tex] {f}^{ - 1} (x) = 5x[/tex]

Answer:

It's choice 2.

Step-by-step explanation:

y=19.485x+86.912

The 19.485 is the slope of the graph of this equation.  This gives the rate of change of the amount of the bill (above $86.912)  for  each added resident (x).

Final answer:

The surveying method that is most likely to produce a representative sample of the yogurt shop's customers is true random sampling.

Explanation:

The surveying method that is most likely to produce a representative sample of the yogurt shop's customers is the true random sampling method. This method involves randomly selecting participants from the entire population of yogurt shop customers, ensuring that each customer has an equal chance of being selected. This helps to minimize bias and ensure that the sample is representative of the entire customer population.

For example, the manager can generate a list of all the customers who have made purchases at the yogurt shop over a specific period of time, and then use a random number generator or a random selection method to choose a certain number of customers from the list. This will ensure that the selected participants represent the diversity of the yogurt shop's customer base.

The most appropriate surveying method for the yogurt shop manager to obtain a representative sample of customers is systematic sampling.

To obtain a representative sample of the yogurt shop's customers, the most appropriate surveying method would be a systematic sampling approach. This involves selecting every nth customer who visits the shop during different times of the day and different days of the week.

By using a systematic sampling method, the manager can ensure that the sample includes customers from various demographic groups, such as different age ranges, genders, and visiting patterns. This approach reduces the potential for bias that may arise from convenience sampling methods, where only customers who are readily available or willing to participate are surveyed.

Additionally, the systematic sampling method allows the manager to capture the preferences of both regular and occasional customers, as well as those who visit during peak and off-peak hours. This comprehensive representation of the customer base increases the likelihood that the survey results will accurately reflect the preferences of the yogurt shop's overall customer population.

Systematic sampling is more time-consuming and resource-intensive than convenience sampling, but it is a more reliable method for obtaining a representative sample of the yogurt shop's customers, which is crucial for making informed decisions about introducing new flavors that will appeal to a wide range of customers.

Final answer:

The car's average rate during the second part of the trip is 65 miles per hour, which is calculated by dividing the remaining distance of 390 miles by the remaining travel time of 6 hours.

Explanation:

We need to find the average rate of the car during the second part of the trip. We know the total distance of the trip is 520 miles and the total time for the trip is 8 hours. Since the first part of the trip was at 65 miles per hour for 2 hours, the car would have covered 130 miles (65 miles/hour * 2 hours).

We subtract the distance covered in the first part of the trip from the total distance to find the distance covered during the second part of the trip: 520 miles - 130 miles = 390 miles. The remaining time for the second part of the trip is 8 hours - 2 hours = 6 hours.

To find the average speed during the second part of the trip, we divide the remaining distance by the remaining time:
Average rate = Distance / Time = 390 miles / 6 hours = 65 miles per hour.

Answer:

The average rate of change is : [tex]6.3[/tex]

Step-by-step explanation:

The number of car owners is modeled by the function;

[tex]f(t)=1.1t^2-2.5t+1.5[/tex], where t is the different number of years.

The average rate of change  of f(t)  from t=3 to t=5 is simply the slope of the secant line connecting:

(3, f(3)) and (5,f(5))

Which is given by:

[tex]\frac{f(5)-f(3)}{5-3}[/tex]

Now, we substitute t=3 into the function to get;

[tex]f(3)=1.1(3)^2-2.5(3)+1.5[/tex]

[tex]f(3)=3.9[/tex]

We substitute t=5 into the function to get;

[tex]f(5)=1.1(5)^2-2.5(5)+1.5[/tex]

[tex]f(5)=16.5[/tex]

Therefore the average rate of change is : [tex]\frac{14.5-3.9}{2}=6.3[/tex]

The answer is:

The correct option is:

A. $0.49

From the statement, we know that the iHome is used on average three hours a day, and we are asked to find the cost for a week, so first, we need to calculate the total hours that the iHome is used for, and then, calculate the kilowatt-hour consumption rate.

[tex]TotalTime_{week}=3\frac{hours}{day} *7days=21hours[/tex]

[tex]TotalEnergyConsumption_{week}=180watt*21hours=3780watt.hour[/tex]

Now, we must remember that:

[tex]1Kilowatt=1000watts[/tex]

So,

[tex]3780watts=3780watts.hour*\frac{1KiloWatt}{1000watts}=3.78KiloWatt.hour[/tex]

Then, calculating the cost, we have:

[tex]TotalCost_{week}=0.13\frac{dollar}{killowat.hour}*3.78killowat.hour=0.49(dollar)[/tex]

Hence, we have that the correct option is:

A. $0.49

Have a nice day!

Answer:

8/5

Step-by-step explanation:

The slope of two parallel lines is always the same, just are in different locations on the x or y axis.

Answer:

[tex]200in^3[/tex]

Step-by-step explanation:

To solve this, we are using the formula for the volume of a rectangular prism:

[tex]V=whl[/tex]

where

[tex]w[/tex] is the width of the base

[tex]l[/tex] is the length of the base

[tex]h[/tex] is the height of the prism

We know from our problem that the height is 10 inches. The length of the base is 6 inches. The width of the base is 5 inches.

Replacing values

[tex]V=(5in)(10in)(6in)[/tex]

[tex]V=300in^3[/tex]

Now, to find 2/3 of that volume, we just need to multiply it by 2/3

[tex]\frac{2}{3} V=\frac{2}{3} 300in^3[/tex]

[tex]\frac{2}{3} V=200in^3[/tex]

We can conclude that 2/3 of the volume of the vase is 200 cubic inches.

Answer: 4.10s

t=2Vi*sin(theta)/g

Vi=initial velocity=35m/s

g=9.8m/s^2

t=2*35*sin(35)/9.8=4.10s

Answer:

4.1 seconds to the nearest tenth.

Step-by-step explanation:

The vertical component of the velocity = 35 sin 4.935 m/s.

The relation between the height (h) of the projectile and time is given by:

h = ut + 1/2 g^2   where u = initial velocity, t = the time and g = acceleration due to gravity which we can take to be 9.8 m/s/s. When the projectile hits the ground h = 0 .

So we have h = 35sin35 t - 4.9t^2 = 0

t(35sin35 - 4.9t) = 0

4.9t = 35 sin35

t = 35 sin 35 / 4.9

=  4.097 seconds