Write an expression for the area of this rectangle. Expand your expression so that your answer does not contain brackets. ​

We can simplify the mathematical expression to get:

[tex]\frac{(5 + \sqrt{3})*(5 - \sqrt{3} ) }{\sqrt{22} } = 4*\sqrt{2/11}[/tex]

Here we have the mathematical expression:

[tex]\frac{(5 + \sqrt{3})*(5 - \sqrt{3} ) }{\sqrt{22} }[/tex]

Remember the rule:

[tex](a + b)*(a - b) = a^2 + b^2[/tex]

Then the numerator can be rewritten as:

[tex]\frac{(5 + \sqrt{3})*(5 - \sqrt{3} ) }{\sqrt{22} } = \frac{5^2 - \sqrt{3}^2 }{\sqrt{22} } = \frac{25 - 9}{\sqrt{22} } = \frac{16}{\sqrt{22} }[/tex]

notice that 16*16 = 256 then we can rewrite:

[tex]\frac{16}{\sqrt{22} } = \sqrt{\frac{256}{22} } = \sqrt{\frac{128}{11} } = \sqrt{\frac{4*4*2}{11} }= 4*\sqrt{2/11}[/tex]

That is the expression simplified.

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ANSWER : 4x-3y

EXPLANATION:

Answer: 100 = 4x + 6y

Step-by-step explanation:

We have a total of 100 guests, small tables seat 4, and large tables seat 6. So for each small table used, 4 guests are subtracted from the total.

x = small tables

y = large tables

a) Ratio in fraction form to compare the number correct to the total questions for each test is [tex]\frac{17}{20}[/tex].

b) Yes, we compare these two ratios as they are written.

Jamaya got a better answer on the test on her second test, and you could compare these two ratios as they are written.

a)

First: Convert the each of scores into the percentages:

How do you convert the ratios to percentages? Well, first we have to convert ratio to a decimal or a fraction. Let's convert it to fraction. So, 19 out of 25 will become fraction [tex]\frac{19}{25}[/tex], and 17 out of 20 will become fraction [tex]\frac{17}{20}[/tex] . To convert fraction to percentage:

Divide numerator by denominator:

19 ÷ 25 = 0.76                                        AND                           17 ÷ 20 = 0.85

Multiply the quotient by 100

0.76 x 100 = 76                                      AND                        0.85 x 100 = 85

Add percent sign

76%                                                          AND                                                   85%

Now, two quantities are easier to compare. We can obviously see that 85% is the bigger [and better] than 76%. So, ratio that equals 85% - 17 out of 20 - is a better grade.

b)

Yes, you can compare the these two ratios, just find [positive] difference between the amount that she scored and the total number of scores that could be gained.

25 - 19 = 6

20 - 17 = 3

Since equation with 20 and 17 in it has a smaller difference, it is most likely to have a greater value [because that means that Jamaya got more right and less wrong, which means a greater mark which is also greater quantity].

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y=10-2x..(3)

[tex]3x+4(10-2x)=12\\\\3x+40-8x=12\\3x-8x=12-40\\-5x=-28\\\frac{-5x}{-5} =\frac{-28}{-5} \\x=\frac{28}{5}[/tex]

[tex]y=10-2(\frac{28}{5} )\\y=10-\frac{56}{5} \\y=-\frac{6}{5}[/tex]

Answer:

168

Step-by-step explanation:

= 2[3-{3(-9)(3)}]

= 2[3-{-81}]

= 2(84)

= 168

Hope it helps!!
BTW it was very easy...

since y=AsinKx.......1

so amplitude =|A|=1

Answer:

6

Step-by-step explanation:

If f(n) is f(-6), that means you need to input -6 in any places that have n in them.

f(-6) = --6

Two negatives make a positive.

f(-6) = 6

Hope this helps! :)

Hello!

To find the value of f(-6)

 ==> must plug '-6' into n's position in the equation

    f(-6) = -(-6) = 6

Hope that helps!

Considering a rectangular plot measuring 16 by 25 feet in a community garden the equation that models the the number of tomato plant and the number of pepper plant is 8x + 5y = 400

given data

a rectangular plot measuring 16 by 25 feet

area to grow tomato plants = 8 square feet

area to grow pepper plants = 5 square feet

From the  given data the total area is

Area = 16 * 25

Area = 400 square feet

let the number of area required by tomato plant be x and the area required by pepper plant be y

The equation that models how many tomato plants and how many pepper plants you can grow can be written as

8x + 5y = 400

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Answer:

you can buy 5 cans

Step-by-step explanation:

$2 per can

have $10

10 divided by 2

5

The cost of 6 bottles of juice is $2.34 if the each bottle costs the same.

According to the question,

We have the following information:

Adriel buys 20 bottles of grapefruit juice at the corner store for a total cost of $7.80.

Cost of 20 bottles of juice = $7.80

Now, from here we can find the cost of 1 bottle of juice by dividing the total cost by the number of bottles purchased.

Cost of 1 bottle of juice = $(7.80/20)

Cost of 1 bottle of juice = $0.39

Now, we can easily find the cost of 6 bottles of juice by multiplying the cost of 1 bottle of juice by 6.

Cost of 6 bottles of juice = $(0.39*6)

Cost of 6 bottles of juice = $2.24

Hence, the cost of 6 bottles of juice is $2.24.

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The proportional relation:

y = 2*x

Tells us how many cups of water we need for x scoops of coffee, with this we can see that for 5 scoops we need 10 cups.

We know that for one small scoop of coffee, you need to add 2 cups of water. Then we can write the proportional relation:

y = 2*x

Where x is the number of scoops of coffee and y is the number of cups of water.

if x = 5, then:

y = 2*5 = 10

y = 10

So for 5 scoops of coffee, you need 10 cups of water.

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Answer:

Trisha should save for 18 weeks.

Step-by-step explanation:

1 week = $25

Total = $350

Also wants over $100

350+100 = 450

450 ÷ 25 = 18

Answer:

Step-by-step explanation:

There is no saddle point (DNE). However, there is local maximum at (1, 1/2) for the given function.

we have function of two variables f(x,y)= 9-2x+4y-x^2-4y^2

we will find the values by partial derivative with respect to x,y,xy

f ₓ= -2 -2x

[tex]f_{y}[/tex] = 4 -8y

to find the saddle point we should first find the critical points so equate

-2 -2x=0 and   4 -8y=0

we get x= 1  and y =1/2 so, critical points are (1,1/2)

to find local maximum or minimum we have to find  [tex]f_{xx}[/tex]  , [tex]f_{yy}[/tex] and [tex]f_{xy}[/tex]

formula is  [tex]f_{xx}[/tex]* [tex]f_{yy}[/tex] - [tex]f_{2xy}[/tex] =0

[tex]f_{xx}[/tex] = -2

[tex]f_{yy}[/tex] = -8

[tex]f_{2xy}[/tex]=0

putting values in formula

(-2)*(-8) -0 =16 > 0, and [tex]f_{xx}[/tex] < 0  and [tex]f_{yy}[/tex] <0

so, here we have local maximum

we have no saddle point for this function by using the same formula we used to find extrema.

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Using proportions with mixed numbers, the inequality to determine the minimum number of hours she needs to practice on each of the 3 days is: m ≥ 3/4.

A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using operations such as multiplication or division.

One example is the mean of a data-set, as the mean is given by the sum of all observations in the data-set divided by the number of values.

For this problem, we have that:

Hence the minimum number of hours that she still needs to practice is:

5 - 2.75 = 2.25 hours.

The amount is split evenly amount the 3 days, hence the lower bound of the inequality is:

2.25/3 = 0.75 = 3/4.

Hence the amount is given by:

m ≥ 3/4.

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The image of the setting sun most likely not described in great detail in "Because I Could Not Stop for Death" because it is a common symbol of death that requires little description.

Emily Dickinson's lyrical poem "Because I could not stop for Death" was originally printed in Poems: Series 1 in 1890, after her death. We don't know if Dickinson finished "Since I could not stop for Death" or if it was "abandoned" because her writing was never granted permission to be published.

In the poem "Because I could not stop for death the personified Death appears to Dickinson's poem's speaker. The poet's character speaks calmly about Death, the Afterlife, and the tranquility that comes with it. She represents Death as a young guy accompanying her in a carriage. She gives us a quick overview of her previous life while still living as she passes through to the afterlife.

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Ella got a higher test score (ratio of correctly spelled words to total words) in the current week when she spelled 13 out of 15 words correctly.

In last week, Ella spelled 16 out of 20 words correctly which is 16:20 in ratio terms and is equivalent to 0.8 (in decimal terms) or 80% in percentage terms.

In current week Ella spelled 13 out of 15 words correctly which is 13:15 in ratio terms and is equivalent to 0.866... (in recurring decimal terms) or 86.7% in percentage terms.

86.7% being greater than 80%, Ella scored higher in current week than in last week's spelling test.

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Answer:

0.95

Step-by-step explanation:

19/20

19÷2/20÷2

9.5/10

0.95

The line e is parallel to f by converse alternate interior angles theorem.

What is converse alternate interior angle theorem?

Converse alternate interior angle theorem states that states if two lines are cut by a transversal and the alternate interior angles are congruent, then the lines are parallel.

What is parallel lines?

Two lines are said to be parallel when they do not meet at any point in a plane. Lines which do not have a common intersection point and never cross path with each other are parallel to each other. The symbol for showing parallel lines is ‘||’.

Given,

angle 1 is congruent to angle 2 and g is parallel to h.

similarly, angle 2 is congruent to angle 3,

by transitive property angle 1 is congruent to angle 3.

By converse alternate interior angle theorem, e is parallel to f.

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730 teens voted.

A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ratio 4:3).

A ratio is the relationship or comparison between two numbers belonging to the same unit in order to determine how much larger one number is than the other. For instance, if a test result is 7 out of 10, the ratio of the number of points earned to the total number of points is 7:10.

Given Data

Teens to adult ratio 10:9

Total people votes = 1387

Ratio of teen vote:

= 1387 × [tex]\frac{10}{19}[/tex]

= 73(10)

= 730

730 teens votes.

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If one student is chosen at random, the probability that the student was a female and got 'A' is 0.38

Probability is a synonym for potential. It is a field of mathematics that examines how random events happen. From zero to one, the value is expressed. To forecast the likelihood of events, probability has been introduced in mathematics.

The likelihood that something will occur is essentially what is meant by probability. This is the fundamental theory of probability, which is also used to calculate the probability distribution, and it is from it that you will learn the likelihood of various outcomes in a random experiment.

The total number of outcomes that can occur should be known before calculating the likelihood that a specific event will occur.

Total numbers of students = 53

Total numbers of females = 34

Total numbers of females of A grades = 20

So probability = 20/53

                        = 0.38

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Answer:

w=3units  l=6 units

Step-by-step explanation:

The required length and width of the rectangle are 6 and 3 units

Given that,
The width of a rectangle is 3 units less than the length. The area of the rectangle is 18 units.

The rectangle is 4 sided geometric shape whose opposites are equal in length and all angles are about 90°.

Here,
Let the length of the rectangle be l and the width of the rectangle is l -3
Now,
area of the rectangle,
18 = l [l - 3]
18 = l² - 3l
l² - 3l - 18 = 0
l² - 6l + 3l  - 18 = 0
(l - 6) + 3 (l - 6) = 0
(l - 6)(l + 3) = 0
l = 6   {negative value of the l can be neglected.}
now,
width = 6 - 3 = 3

Thus, the required length and width of the rectangle are 6 and 3 units.

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If she will jump at a height of 13500 feet and she will pull the cord when she is 5000 feet above the ground, the equation for distance traveled during freefall is d(t)= [tex]16t^{2}[/tex], then she has to wait 23.05 seconds to pull the cord

The initial height = 13500 feet

The height at which she has to pull the cord = 5000 feet above the ground

The distance traveled to reach 5000 feet above the ground = 13500-5000

= 8500 feet

The equation for the distance traveled during the freefall d(t)= [tex]16t^{2}[/tex]

where d is the distance traveled

t is the time taken

Substitute the values in the equation

8500 = 16 × [tex]t^{2}[/tex]

[tex]t^{2}[/tex] = 8500/16

[tex]t^{2}[/tex] = 531.25

t = [tex]\sqrt{531.25}[/tex]

t = 23.05 seconds

Hence, If she will jump at a height of 13500 feet and she will pull the cord when she is 5000 feet above the ground, the equation for distance traveled during freefall is d(t)= [tex]16t^{2}[/tex], then she has to wait 23.05 seconds to pull the cord

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Answer:

Domain: All real numbers

Range:  f(x) ≥ 5 or f(x) < 2

Step-by-step explanation:

The given graph is a graph of a piecewise function.

Piecewise functions have multiple pieces of curves/lines where each piece corresponds to its definition over an interval.

When graphing piecewise functions:

Domain

The domain of a function is the set of all possible input values (x-values).

From inspection of the graph, the arrows show that the function continues indefinitely in both the positive and negative directions.

The value of x = 1 is not included in the left part of the graph, but it is included in the right part of the graph.

Therefore, the domain of the function is all real values of x:  

Range

The range of a function is the set of all possible output values (y-values).

From inspection of the graph, there is an open circle at y = 2 and a closed circle at y = 5.  Therefore, there are no y-values in the interval:
2 ≤ y < 5.

Therefore, the range of the function is f(x) < 2 or f(x) ≥ 5:

Answer:

n = 27

Step-by-step explanation:

n + 6 + 2n + 3 + 90 = 180

solve for n then n = 27

hope this helped

have a good day ^^