Please I am really Confused If you can help that would be great!

[tex]7\sqrt{3}- 4\sqrt{6} + \sqrt{48} - \sqrt{54}[/tex] simplified as [tex]11\sqrt{3}- 7\sqrt{6}[/tex] or [tex]1.909[/tex] .

Step-by-step explanation:

We need to Simplify seven square root of three end root minus four square root of six end root plus square root of forty eight end root minus square root of fifty four. Which is equivalent to [tex]7\sqrt{3}- 4\sqrt{6} + \sqrt{48} - \sqrt{54}[/tex] :

[tex]7\sqrt{3}- 4\sqrt{6} + \sqrt{48} - \sqrt{54}[/tex]

⇒ [tex]7\sqrt{3}- 4\sqrt{6} + \sqrt{48} - \sqrt{44}[/tex]

⇒ [tex]7\sqrt{3}- 4\sqrt{6} + \sqrt{16(3)} - \sqrt{9(6)}[/tex]

⇒ [tex]7\sqrt{3}- 4\sqrt{6} + 4\sqrt{(3)} - 3\sqrt{(6)}[/tex]

⇒ [tex]11\sqrt{3}- 4\sqrt{6}- 3\sqrt{(6)}[/tex]

⇒ [tex]11\sqrt{3}- 7\sqrt{6}[/tex]

[tex]\sqrt{3} = 1.732 , \sqrt{6} = 2.449[/tex]

⇒ [tex]11(1.723)- 7(2.449)[/tex]

⇒ [tex]1.909[/tex]

Therefore, [tex]7\sqrt{3}- 4\sqrt{6} + \sqrt{48} - \sqrt{54}[/tex] simplified as [tex]11\sqrt{3}- 7\sqrt{6}[/tex] or [tex]1.909[/tex] .

Answer:

11√3 - 7√6

Step-by-step explanation:

I took the test and got it right.

Answer:

[tex]vXw =-36i+33j+26k[/tex]

Step-by-step explanation:

v = 3i + 8j – 6k

w = –4i – 2j – 3k

The cross product

[tex]v X w=\left|\begin{array}{ccc}i&j&k\\3&8&-6\\-4&-2&-3\end{array}\right|[/tex]

[tex]=i\left|\begin{array}{cc}8&-6\\-2&-3\end{array}\right|-j\left|\begin{array}{cc}3&-6\\-4&-3\end{array}\right|+k\left|\begin{array}{cc}3&8\\-4&-2\end{array}\right|\\[/tex]

[tex]=i(-24-12)-j(-9-24)+k(-6+32)\\vXw =-36i+33j+26k[/tex]

Answer:

Step-by-step explanation:

For a point to be a relative extreme, there must be points on both sides that are not as extreme. That is, the ends of the interval may be extreme values, but do not qualify as relative extrema, since there are not points on both sides.

In the interval [-3, 3], the relative extrema are the turning points.

The relative minimum is at y = -9 on the y-axis.

The relative maxima are at y = -6, between 1 and 2 on either side of the y-axis.

Answer:

minimum: -9

maximum: -6

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

I think this is your full question and hope it is correct.

Which system of equations could be graphed to solve the equation below?

log(2x+1)=3x-2

A. y1=3x, y2=2x

B. y1=log(2x+1), y2=3x-2

C. y1=log2x+1, y2=3x-2

D. y1=log(2x+1+2), y2=3x

My answer:

We know that: log(2x+1)=3x-2  and they are a equation of log and linear so we need to make system of equation.

The left side is: [tex]y_{1}[/tex] => [tex]y_{1} = log( 2x+1)[/tex]

The right side is : [tex]y_{2} = 3x -2[/tex]

The system of equations are:

[tex]\left \{ {{y_{1} =log(3x+1)} \atop {y_{2} =3x -2}} \right.[/tex]

Now we have two new function with x and y.

The solution to the equation x + 3 = -(x + 1) is x = -2, which is not listed among the provided options. There may be an error in the question or provided options.

To find the value of x that satisfies the equation x + 3 = -(x + 1), we need to solve for x.

First, expand the right side of the equation: x + 3 = -x - 1. Then, add x to both sides of the equation to get 2x + 3 = -1. Finally, subtract 3 from both sides to obtain 2x = -4. Dividing both sides by 2 yields x = -2.

Upon examining the options provided, none of them match our solution. Therefore, there must be a mistake in the provided options or in the question as posed, because our correct solution is x = -2. This means the correct answer is not listed among the options a. x = 8, b. x = 8/3, c. x = -8/3, or d. x = -8.

Answer: she used 6.525 pints of white paint.

Step-by-step explanation:

Kelly uses 8.7 paints of blue paint and white paint to paint her bedroom walls. If 1/4 of this amount is blue paint, it means that the amount of blue paint that she used in painting her bedroom walls is

1/4 × 8.7 = 2.175 pints of blue paint.

Since the rest of the paint is white, it means that the pints of white paint that she used to paint her bedroom walls is

8.7 - 2.175 = 6.525 pints of white paint

Answer:

she uses 6.525 pints of paint

Step-by-step explanation:

Answer:

(D) 0.006

Step-by-step explanation:

Total number of cards :52

Please note that, all cards have a the possibility of appearing 4 times.

Hence total possible number of a '2' is 4 cards and so it is also for a '10'

Having this Understanding, let's solve the question properly.

The probability that the FIRST CARD is 2 = 4/52

Probability that the second card without replacement is a 10 = 4 / 51

P( 1st two and 2nd four)

4/52 * 4/51 = 4/663

= 0.0060332

Rounding to 3 decimal places = 0.006

Answer:

All numbers greater than or equal to -3.

Step-by-step explanation:

Just took the edge test.

Answer:

yeah. its d

Step-by-step explanation:

edge test 2020

The difference in volume between a large scoop and a small scoop of ice cream is approximately 410.5 cubic centimeters.

To find the difference in volume between a large scoop and a small scoop of ice cream, we need to calculate the volume of each scoop and then subtract the volume of the small scoop from the volume of the large scoop.

The volume of a sphere can be calculated using the formula V = (4/3)πr³, where r is the radius. Since the diameter of the small scoop is 6 cm, the radius is 3 cm. Plugging this into the formula, we get V = (4/3)π(3 cm)³. Evaluating this expression, we find that the volume of the small scoop is approximately 113.1 cm³.

Similarly, the diameter of the large scoop is 10 cm, so the radius is 5 cm. Using the same formula, we find that the volume of the large scoop is approximately 523.6 cm³.

To find the difference in volume, we subtract the volume of the small scoop from the volume of the large scoop: 523.6 cm³ - 113.1 cm³ = 410.5 cm³. Therefore, the difference in volume between a large scoop and a small scoop of ice cream is approximately 410.5 cubic centimeters.

https://brainly.com/question/21623450

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The final answer is 410.5 cubic centimeters.

1. Calculate the volume of a small scoop:

- Given the diameter of the small scoop, [tex]\( d_{\text{small}} = 6 \) cm[/tex].

- Radius of small scoop, [tex]\( r_{\text{small}} = \frac{d_{\text{small}}}{2} = \frac{6}{2} = 3 \)[/tex] cm.

- Volume of a sphere [tex]\( V = \frac{4}{3} \pi r^3 \).[/tex]

- Substitute the radius into the volume formula: [tex]\( V_{\text{small}} = \frac{4}{3} \pi (3)^3 = \frac{4}{3} \pi (27) \)[/tex].

- Calculate:

[tex]\( V_{\text{small}} = 36 \pi \)[/tex] cubic centimeters.

2. Calculate the volume of a large scoop:

- Given the diameter of the large scoop,[tex]\( d_{\text{large}} = 10 \) cm[/tex].

- Radius of large scoop, [tex]\( r_{\text{large}} = \frac{d_{\text{large}}}{2} = \frac{10}{2} = 5 \) cm[/tex].

- Volume of a sphere [tex]\( V = \frac{4}{3} \pi r^3 \)[/tex].

- Substitute the radius into the volume formula:

[tex]\( V_{\text{large}} = \frac{4}{3} \pi (5)^3 = \frac{4}{3} \pi (125) \)[/tex].

- Calculate:

[tex]\( V_{\text{large}} = 166.7 \pi \)[/tex] cubic centimeters.

3. Find the difference:

- Difference in volume: [tex]\( V_{\text{large}} - V_{\text{small}} = 166.7 \pi - 36 \pi \)[/tex].

- Calculate: [tex]\( V_{\text{large}} - V_{\text{small}} = 130.7 \pi \)[/tex].

- Approximate [tex]\( \pi \)[/tex] to 3.14.

- [tex]\( 130.7 \times 3.14 = 410.498 \)[/tex].

- Rounded to the nearest tenth, the difference is approximately 410.5 cubic centimeters.

Answer:

2nd option (B)

Step-by-step explanation:

(0,-6) works

(3,-7) works

(-3,-5) works

This means the answer is B

Answer:

21 years old.

Step-by-step explanation:

Given:

Waneta is 8 years old

Waneta is 4/7 as old as Elizabeth.

Chun is 1/2 as old as Elizabeth.

George is 3 time as old as Chun.

Question asked:

How many years old is George ?

Solution:

Let age of Elizabeth = [tex]x[/tex] years

Waneta is 4/7 as old as Elizabeth. ( given )

Age of Waneta = [tex]\frac{4}{7} \ of \ Elizabeth[/tex]

[tex]8=\frac{4}{7} \times x\\\\8=\frac{4}{7}x[/tex]

By cross multiplication:

[tex]4x=56[/tex]

By dividing both sides by 4

[tex]x=14\\[/tex]

Age of Elizabeth = [tex]x[/tex] = 14 years

Chun is 1/2 as old as Elizabeth. ( given )

Age of Chun = [tex]\frac{1}{2} \ of \ Elizabeth\\[/tex]

                     = [tex]\frac{1}{2} \times14= 7\ years[/tex]

George is 3 time as old as Chun.  ( given )

Age of George = [tex]3\ times \ of \ Chun\\[/tex]

                         [tex]=3\times7=21\ years[/tex]

Therefore, George is 21 years old.

Answer:

The answer to your question is 2² 3² or (4)(9)

Step-by-step explanation:

Data

factor 36

Process

1.- Divide 36 by prime numbers starting from 2, then 3, 5, 7, etc.

                          36  2

                           18  2

                            9   3

                            3   3

                             1

2.- Write 36 as a composition of prime numbers

                         36 = 2²3²

3.- The prime factors of 36 are 2² x 3²

Answer:

TRUE

Step-by-step explanation:

Answer: height = 10 feet

Base = 24 feet

Step-by-step explanation:

Let h represent the height of the triangular flower bed.

Let b represent the base of the triangular flower bed

The formula for determining the area of a triangle is expressed as

Area = 1/2 × base × height

The area of a triangular flower bed in the park has an area of 120 square feet. This means that

1/2 × bh = 120

bh = 120 × 2

bh = 240- - - - - - - - - - - - - - - 1

The base is 4 feet longer than twice the height. This means that

b = 2h + 4

Substituting b = 2h + 4 into equation 1, it becomes

h(2h + 4) = 240

2h² + 4h = 240

2h² + 4h - 240 = 0

Dividing through by 2, it becomes

h² + 2h - 120 = 0

h² + 12h - 10h - 120 = 0

h(h + 12) - 10(h + 12) = 0

h - 10 = 0 or h + 12 = 0

h = 10 or h = - 12

Since the height cannot be negative, then h = 10

Substituting h = 10 into equation 1, it becomes

10b = 240

b = 240/10

y = 24

The answers are : (a) The height [tex]\( h \)[/tex] of the triangular flower bed is [tex]10\ feet[/tex]. (b) The base [tex]\( b \)[/tex] of the triangular flower bed is [tex]24 \ feet[/tex]

Let's denote the height of the triangular flower bed as [tex]\( h \)[/tex] feet.

According to the problem, the base of the triangle is [tex]4\ feet[/tex] longer than twice the height. Therefore, the base [tex]\( b \)[/tex] can be expressed as:

[tex]\[ b = 2h + 4 \][/tex]

The formula for the area [tex]\( A \)[/tex] of a triangle is given by

[tex]\[ A = \frac{1}{2} \times \text{base} \times \text{height} \][/tex]

Given that the area [tex]\( A \)[/tex] of the triangular flower bed is [tex]120\ square\ feet[/tex], we can write the equation:

[tex]\[ \frac{1}{2} \times b \times h = 120 \][/tex]

Substituting [tex]\( b = 2h + 4 \)[/tex] into the area equation:

[tex]\[ \frac{1}{2} \times (2h + 4) \times h = 120 \][/tex]

Now, solve for [tex]\( h \)[/tex]

[tex]\[ (2h + 4) \times h = 240 \][/tex]

[tex]\[ 2h^2 + 4h = 240 \][/tex]

[tex]\[ 2h^2 + 4h - 240 = 0 \][/tex]

Divide the entire equation by [tex]2[/tex] to simplify:

[tex]\[ h^2 + 2h - 120 = 0 \][/tex]

Now, solve this quadratic equation using the quadratic formula, [tex]h = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \), where \( a = 1 \), \( b = 2 \), and \( c = -120 \)[/tex]

[tex]\[ h = \frac{-2 \pm \sqrt{(2)^2 - 4 \times 1 \times (-120)}}{2 \times 1} \][/tex]

[tex]\[ h = \frac{-2 \pm \sqrt{4 + 480}}{2} \][/tex]

[tex]\[ h = \frac{-2 \pm \sqrt{484}}{2} \][/tex]

[tex]\[ h = \frac{-2 \pm 22}{2} \][/tex]

The solutions for [tex]\( h \)[/tex] are:

[tex]\[ h = \frac{20}{2} = 10 \][/tex]

[tex]\[ h = \frac{-24}{2} = -12 \][/tex]

So, the height [tex]\( h \)[/tex] of the triangular flower bed is [tex]10\ feet.[/tex]

Now, calculate the base [tex]\( b \)[/tex]

[tex]\[ b = 2h + 4 \][/tex]

[tex]\[ b = 2 \times 10 + 4 \][/tex]

[tex]\[ b = 20 + 4 \][/tex]

[tex]\[ b = 24 \][/tex]

The complete Question is

The area of a triangular flower bed in the park has an area of 120 square feet. The base is 4 feet longer than twice the height.

a. What is the base of the triangle ?

b. What is the height of the triangle ?

Answer:

56

Step-by-step explanation:

8C3 = 56

Answer:

  9. (x, y) = (6√3, 3)

  10. (x, y) = (14, 14√2)

  11. (x, y) = (2√6, 3√2)

  12. (x, y) = (6, 2)

Step-by-step explanation:

Because you have memorized a short table of trig functions, you know that the ratio of side lengths of a 30°-60°-90° triangle is 1 : √3 : 2, and the ratio of side lengths of a 45°-45°-90° triangle is 1 : 1 : √2.

In each case, we compare the given side ratios to the known ratios for the kind of triangle we have. Then we multiply the triangle ratios by a scale factor that makes the given number match the corresponding ratio value. Matching the other ratio values, we can determine the values of the variables.

__

9. Using the side ratios for the 30-60-90 triangle, you have

  6 : x : y+9 = 1 : √3 : 2

Multiplied by 6, the ratios on the right are ...

  6 : x : y+9 = 6 : 6√3 : 12

  x = 6√3

  y +9 = 12

  y = 3

__

10. Using the side ratios for the 45-45-90 triangle:

  14 : x : y = 1 : 1 : √2

Multiplying the ratios on the right by 14, we have ...

  14 : x : y = 14 : 14 : 14√2

  x = 14

  y = 14√2

__

11. Again using the 30-60-90 ratios:

  √6 : y : x = 1 : √3 : 2

Multiplying the ratios on the right by √6, we have ...

  √6 : y : x = √6 : 3√2 : 2√6

  y = 3√2

  x = 2√6

__

12. Again, using the 45-45-90 ratios:

  x : 3y : 6√2 = 1 : 1 : √2

Multiplying the ratios on the right by 6, we have ...

  x : 3y : 6√2 = 6 : 6 : 6√2

  x = 6

  3y = 6

  y = 2

Final answer:

The question asks to demonstrate that for a nonnegative integer-valued random variable X, the expected value E(X) equals the summation over all k of the probability P(X ≥ k). This is shown by expressing P(X ≥ k) as an infinite sum, switching the order of summation, and counting each probability P(X = i) exactly i times.

Explanation:

The student's question pertains to the calculation of the expected value (E(X)) of a nonnegative integer-valued random variable. Specifically, the question asks to show that for such a random variable X, the expected value can be expressed as E(X) = ∑₋∞ k=1 P(X ≥ k). To demonstrate this, we begin with the definition of expected value:

E(X) = μ = ∑ xP(x).

Next, we unpack P(X ≥ k) by writing it as an infinite sum of probabilities for all integers i starting from k:

P(X ≥ k) = ∑₋∞ i=k P(X = i).

To find the expected value, we consider the sum of all such probabilities over all k:

∑₋∞ k=1 P(X ≥ k) = ∑₋∞ k=1 ∑₋∞ i=k P(X = i).

We then switch the order of summation, so that we first sum over all possible values of i and then for each i, we sum over the corresponding k that contributes to P(X = i):

E(X) = ∑₋∞ i=1 P(X = i) ∑₉ i k=1.

By doing this, we count each P(X = i) exactly i times, which leads us to the initial definition of expected value, thus proving the given formula.

Answer: The system of inequalities that models this situation are

p + b ≤ 30

12.5p + 9.5b ≥ 300

Step-by-step explanation:

Let p represent the number of hours he works at the pizzeria.

Let b represent the number of hours he works at the bookstore.

He cannot work more than 30 hours per week in order to attend classes. This means that

p + b ≤ 30

Marcus is working at a local pizzeria where he makes $12.50 per hour and is also working at the university bookstore where he makes $9.50 per hour. He must make at least $300 per week to cover his expenses. This means that

12.5p + 9.5b ≥ 300

Answer: 28 fl oz

Step-by-step explanation:

84 fl oz. = 10.5 cups of water

10.5/3=3.5*8=28

why 3.5 times 8 is to get the exact amount of fluid ounces

Answer: he would need 14 fluid ounces of concentrated soap.

Step-by-step explanation:

The directions call for 4 fluid ounces of concentrated soap for every 3 cups of water.

1 cup = 8 fluid ounces

Converting 3 cups of water to fluid ounces, it becomes

3 cups = 3 × 8 = 24 fluid ounces

Kevin uses 84 fluid ounces of water to make an all-purpose cleaner. This means that the amount of concentrated soap that he would use is

(84 × 4)/24 = 336/24 = 14 fluid ounces of concentrated soap

Answer:

General Revenue Sales Tax

Step-by-step explanation:

The ¼ percent would be recorded as general revenue sales tax in government activities journal.

This is because the revenue from the tax are categorised as the revenues generated from payrolls (which are imposed on employers), income and profits taxes, social security contributions, taxes levied on goods and services.

Options:

Program Revenue-Culture and Recreation-Sales Tax.

Program Revenue-Culture and Recreation-Operating Grants and Contributions.

General Revenue-Sales Tax.

General Revenue-Culture and Recreation-Sales Tax.

Answer:

General Revenue - Sales Tax

Step-by-step explanation:

General revenue is the income that is generated by the state which may be used to serve any administrative purpose by the state, and tax revenue is the income that is generated by the state through taxation.

Since the sales tax is a way of generating income by the state, it should be recorded as sales tax under general revenue.

Answer:

(i)Ratio of the Number of Girls in the School to the Total Population

=5:27

(ii)Ratio of the Number of Boys in the School to the Total Population=22:27

Step-by-step explanation:

Below is the steps on how the given ratio are derived

If the school has 880 boys and 200 girls

Total Population of the School=880+200=1080

Ratio of Girls to all Student is 5:27

Now, this is derived from this:

Ratio of the Number of Girls in the School to the Total Population

=200:1080[tex]=\frac{200}{1080} =\frac{5}{27}[/tex]

Which in reduced form is 5:27

You can do likewise for boys

Ratio of the Number of Boys in the School to the Total Population=880:1080[tex]=\frac{880}{1080} =\frac{22}{27}[/tex]

Which in reduced form is 22:27

Answer:

y=\frac{1}{8}x+4

Step-by-step explanation:

first, we can quickly get rid of options 1 and 2, since the y-intercept is not -4, but +4.

this leaves us with options 3 and 4.

we can rule out option3, since the slope is not 4, but 1/8.

hope this helps :)

Answer:

15 feet

Step-by-step explanation:

525 = ½(30+40)h

525 = 35h

h = 525/35

h = 15 feet

For this case we must factor the following expression:

[tex]100k ^ 3-75k ^ 2 + 120k-90[/tex]

We take common factor 5:

[tex]5 (20k ^ 3-15k ^ 2 + 24k-18) =[/tex]

We have two groups within the parentheses:

Group 1: [tex]20k ^ 3-15k ^ 2[/tex]

Group 2: [tex]24k-18[/tex]

We factor each group:

Group 1: [tex]6 (4k-3)[/tex]

Group 2: [tex]5k ^ 2 (4k-3)[/tex]

Rewriting we have:

[tex]5 (5k ^ 2 (4k-3) +6 (4k-3)) =\\5 ((5k ^ 2 + 6) (4k-3))[/tex]

Answer:

[tex]5 (5k ^ 2 + 6) (4k-3)[/tex]

The horizontal distance the plane has covered is 3940 feet

Explanation:

The plane makes an angle 10° with the ground when it took off from the field.

We need to find the horizontal distance the plane when it has flown 4000 feet.

The length of the hypotenuse is 4000 feet.

Let the horizontal distance be x.

We shall find the value of x using the cosine formula.

The formula is given by

[tex]cos \theta=\frac{adj}{hyp}[/tex]

Substituting the values, we have,

[tex]cos \ 10^{\circ}=\frac{x}{4000}[/tex]

Substituting the value for cos 10°, we get,

[tex]0.985=\frac{x}{4000}[/tex]

Multiplying both sides of the equation by 4000, we get,

[tex]0.985\times 4000=x[/tex]

Simplifying, we get,

[tex]3940=x[/tex]

Thus, the horizontal distance the plane has covered is 3940 feet

Answer:

  4. 16

  5. $88

  6. $687.50

Step-by-step explanation:

4. Let n represent the number.

An expression representing the number multiplied by 0.9 and 6.3 subtracted from the product is ...

  0.9n -6.3

We want that result to be 4.5, so we have the equation ...

  0.9n -6.3 = 4.5

Since all of the coefficients are divisible by 0.9, we can divide by 0.9 to get ...

  n -7 = 9

Adding 7 gives ...

  n = 16

The number is 16.

_____

5. For a problem like this, I like to work it backward. If Craig got an extra $18, then everyone's share was $32 -18 = $14. That was the share from a 5-way split, so the amount the friends split evenly was 5×$14 = $70. The total they started with must have been $70 +18 = $88.

The amount they split unevenly was $88. The amount they split evenly, after setting aside $18 for Craig's parents, was $70.

__

It is a bit tricky to write one equation for the amount the friends started with before they did any splits. Call that amount A. Then after setting aside $18, they split (A-18) five ways. Each of those splits was then (A-18)/5. When the $18 was added to one of those, the result was the $32 that Craig got. So, we have ...

  (A -18)/5 +18 = 32

and the solution process is similar to the "working backward" description above: subtract 18, multiply by 5, add back 18.

  (A -18)/5 = 14

  A -18 = 70

  A = 88 . . . . . . . . the amount the friends split unevenly

_____

6. Let P represent the original price of the laptop. We're told the price after all of the discounts was 500, so we have ...

  P -50 -(0.20P) = 500

  0.80P = 550 . . . . . add 50, collect terms

  P = 687.50 . . . . . . . divide by the coefficient of P

The original price was $687.50.

Answer:

Step-by-step explanation:

The coefficient of determination = [tex]r^{2}[/tex] = [tex]0.885^{2}[/tex] = 0.7832

It means about 78% variation in waist size of males can be explained by their weight and about 23% can not be explained.

Answer:

[tex]\frac{17}{6}[/tex] or [tex]2\frac{5}{6}[/tex]

Step-by-step explanation:

1.Find the Least Common Denominator (LCD)

 LCD = 6

2.Make the denominators the same as the LCD.

   [tex]2+\frac{1*3}{2*3} + \frac{1*2}{3*2}[/tex]

3.Simplify. Denominators are now the same

   [tex]2+\frac{3}{6} + \frac{2}{6}[/tex]

4. Join the denominators

   [tex]2+\frac{3+2}{6}[/tex]

5.Simplify

   [tex]2\frac{5}{6}[/tex] = [tex]\frac{17}{6}[/tex]

Answer:

1 1/3

Step-by-step explanation:

Given function:

Rewrite:

Find the solution:

Therefore, 2y+x=1 1/3..

Answer:

HL theorem.

Step-by-step explanation:

This states that if the hypotenuse (H) and  one leg (L) of one  right triangle are congruent to the hypotenuse and leg of another right triangle, then the triangles are congruent.

Answer:

ASA Postulate

Step-by-step explanation:

[tex] In \:\triangle QTS \:\&\:\triangle SRQ\\\\

QT || SR\\\\

\angle QTS \cong \angle SRQ... (each\: 90°)\\\\

TS \cong QR.... (given) \\\\

\angle QST \cong \angle SQR.. (alternate\:\angle s) \\\\

\therefore \triangle QTS \cong \triangle SRQ\\.. (By \: ASA \: Postulate) [/tex]

RHS Postulate can also be applied to prove both the triangles as congruent.

Answer: The account balance will be $6596 after 7 years.

Step-by-step explanation:

We would apply the formula for determining compound interest which is expressed as

A = P(1+r/n)^nt

Where

A = total amount in the account at the end of t years

r represents the interest rate.

n represents the periodic interval at which it was compounded.

P represents the principal or initial amount deposited

From the information given,

P = $4500

r = 5.5% = 5.5/100 = 0.055

n = 4 because it was compounded 4 times in a year.

t = 7 years

Therefore,.

A = 4500(1 + 0.055/4)^4 × 7

A = 4500(1 + 0.01375)^28

A = 4500(1.01375)^28

A = $6596