Consider the following trapezoid.
Find the value of X.

(Helpful for math-space users)

Answer; y = 108

Explanation;
x + 72 = 180
X=180-72

1. There will be $102, 826 in the account in 25 years.

2. The total amount of money you will put into the account is $60, 000

3. The total interest that you would have earned is $42,826.

For us to calculate the future value of the account in 25 years, we shoud use the formula; FV = P x (((1 + r)^nt - 1) / r)

When we insert the values, it will be

FV = 200 x (((1 + 0.04/12)^(12 x 25) - 1) / (0.04/12))

= 102, 825. 9. If we round this up, we should get

$102, 826

For us to calculate the total amount of money you put into the account, we should us the formula;

Total Deposits = Monthly Deposit x Number of Months

If we insert the values it wil be

200 x (25 x 12)

60,000

Lasty, if we are to find the total interest earned:

Total Interest = Future Value - Total Deposits

$102, 826 - 60,000

=  $42,826

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2. >>>>>>>b {18x,-x,21x} is an example of like terms because they both hold the same variables.

4.>>>>>>

[tex] = - 7(2x - 3) \\ = - 7(2x) - 7( - 3) \\ = - 14x + 21[/tex]

ATTACHED IS THE SOLUTION

The missing proof in the given congruence of triangle is;

∠FAB = ∠FBA.

For the given question;

The given data in the triangle FAB is;

In the step two,

FA = FB (Property of isosceles triangle)

Then, step 4 will be ∠FAB = ∠FBA.

Thus, the missing proof will be ∠FAB = ∠FBA.

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Total time = 2 hours

Time playing video games = 50 minutes

We have to write an equation:

Total time (2hours) multiplied by the percentage in decimal form (x) must be equal to 50 minutes

Time must be in the same unit ( minutes)

since 60 minutes =1 hour

2 hours = 2 (60) =120 minutes

Back with the equation:

120 x = 50

Solving for x

x = 50/120

x = 0.42

In percentage form:

0.42 x 100 = 42%

Answer:

Step-by-step explanation:

800 miles is going to be the distance that separates the two aircraft. The distance between the two airplanes will be 1,300 kilometers at the very least.

It is important to keep in mind that the two aircraft's combined speed will be equal to the sum of their separate speeds when calculating their overall speed. In addition, the pilots of the two aircraft have one hour to find each other.

According to the information that was provided, the distance that separates the aircraft after they have flown for forty-five minutes is two hundred miles. As a result, the following will constitute the remaining distance:

= 1 hour - 45 minutes = 15 minutes.

When this occurs, the distance between the planes will be as follows:

= 200/15 × 60

= 200 × 4

= 800 miles

As a result, there will be a gap of 1300 kilometers between the two aircraft.

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Answer:

x=62

Step-by-step explanation:

X=62 because all angles of a triangle should add up to 180 degrees no matter what. All you have to do is subtract the already known angles in the triangles from 180 to receive your x value. 180-65-53=x 180-65-53=62.

-Hope this helps

Answer: x=-3(-y+3)

Step-by-step explanation:

In this case, the alternate interior angles are for example angles 6 and 3 because they are on the inner side of each of the lines (m and l) but on opposite sides of the transversal (t).

m∠6 = m∠3

or

m∠4 = m∠5

As both the width and height of the new image are 35% of the width and height of the original image, the aspect ratio is maintained and the new image is similar to the original image.

A scale factor is defined as the ratio of an object's original scale to that of a new one, considering the different depictions of that object (bigger or smaller)

Given:

The dimensions of the original image are a width of 300 pixels and a height of 450 pixels.

The dimensions of the New image have 35% width and 35% height.

Width = 0.35 × 300 = 105

Height = 0.35 × 450 = 157.5

Scale factor = New Dimension/Original Dimension

Scale factor of Height = 157.5/450 = 0.35

Scale factor of width =  105/300 = 0.35

Therefore, the new image is neither scaled down nor scaled up and is the same as the original image.

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Answer: 2/3

Jenna had 3 boxes of cocoa and gave away 2, for each friend the fraction is 1/3 therefore 1/3 +1/3 =2/3.... the final fraction is 2/3.

Answer: 2/3

Step-by-step explanation:

total, Jenna had 3/3, then she gave 1/3 to two of her friends. Which makes the total boxes 2/3 of what she gave away with a remaining of 1/3. (1 box of the three boxes)

We have

tennis racket price $54

Firs we need to obtain the 30 %

54*.30=16.2

then in order to know the sale price we need to substract the 30% of the original price

54-16.2=37.8

the sale price is $37.8

Answer:equal

Step-by-step explanation: no number but equal as it is tossed 4 times

Answer:

16

Step-by-step explanation:

The number of possible outcomes at each coin toss = 2.

The total number of possible outcomes after 4 times = 2⁴ = 16.

The base of the garden is 14.4 feet.

The height of the garden is 6 feet.

Given,

Corey is designing a rectangular garden;

The diagonal of the garden = 15.6 feet

Ratio  between garden's base and height = 12:5

We have to find the length of base and height of the garden.

Here,

Diagonal of a rectangle, d = [tex]\sqrt{base^{2}+ height^{2} }[/tex]

Base = 12x

Height = 5x

Then,

Diagonal, 15.6 = [tex]\sqrt{(12x)^{2} + (5x)^{2} }[/tex]

15.6 = [tex]\sqrt{144x^{2} +25x^{2} }[/tex]

15.6 = √169x²

15.6 = 13 √x²

15.6 = 13x

x = 15.6/13

x = 1.2

Then,

Base of the garden = 12 x 1.2 = 14.4 feet

Height of the garden = 5 x 1.2 = 6 feet

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The variables we need to use in the question are defined. We will call the price of a knife as [tex]k[/tex] and the price of a spoon as [tex]s[/tex].

The total price of [tex]12[/tex] spoons and [tex]16[/tex] knives is then given. Let's write knives instead of [tex]4[/tex] spoons.

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

Explanation:

k = cost of one knife

s = cost of one spoon

costs are in pounds

12s = cost of 12 spoons

16k = cost of 16 knives

12s+16k = 105.64 pounds is the total cost

We can replace k with 4s because of the phrasing "a knife is 4 times the cost of a spoon". Whatever s might be, quadruple it and it leads us to the value of k.

So,

12s+16k = 105.64

12s+16(4s) = 105.64

12s+64s = 105.64

76s = 105.64

s = 105.64/76

s = 1.39 pounds is the cost of one spoon

k = 4s = 4*1.39 = 5.56 pounds is the cost of one knife

----------------------

Check:

1 spoon = 1.39 pounds

12 spoons = 12*1.39 = 16.68 pounds

1 knife = 5.56 pounds

16 knives = 16*5.56 = 88.96 pounds

12 spoons + 16 knives = 16.68+88.96 =  105.64 pounds total

This fully verifies the answer.

The rational equation is equivalent to the polynomial 27 · x² - 36 · x + 12.

In this case we find a rational equation whose numerator and denominator are polynomials, which must be simplified by using algebra properties. The complete procedure is now shown:

(9 · x - 6)² / (2 · x⁴ + 4 - 2 · x⁴ - 1)                  Given

(81 · x² - 108 · x + 36) / (3)                             Perfect square binomial / Associative, commutative and modulative properties / Existence of additive inverse /Definition of subtraction

27 · x² - 36 · x + 12                                        Addition and subtraction of fractions with same denominator / Associative and commutative properties / Definition of division

The rational equation is equivalent to the polynomial 27 · x² - 36 · x + 12.

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The probability that you will be satisfied with 3 or more of the purchased products is 0.916

Given that,

The chance of being pleased with an internet purchase is 0.555. if you purchase 8 items online

Solution -

let  X denote the no of success of

Purchased product online

X ~ B(n,p)

n = 8

P= 0. 555

a = 1 - 0 .555 = 0.445

P ( X = x) = [tex]nc_{x} b^{x} a^{n-x}[/tex]

P ( X = x)= [tex]8c_{x} (0.555^{x} )(0.445)^{8-x[/tex]

P ( X>=3)= [tex]\lim_{3 \to 8} 8c_{x} (0.555^{x} )(0.445)^{8-x[/tex]

P ( X>=3)) = 0.91614

                 =0.916

Therefore we can conclude the probability that you will be satisfied with 3 or more of the purchased products is 0.916

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The point B has a coordinates of (-3, 7) after the dilation

From the question, the coordinates of the point B are given as

B = (1, 7)

The scale factor of dilation is given as

k = 3

The center of dilation is given as

Center = (3, 7)

The rule of the dilation is calculated using

B' = (k(x - a) + a, k(y - b) + b)

Where

(a, b) = (3, 7)

k = 3

(x, y) = (1, 7)

So, we have

B' = (3 * (1 - 3) + 3, 3 * (7 - 7) + 7)

Evaluate

B' = (-3, 7)

Hence, the coordinates of the point B is (-3, 7)

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The number of times for which the train must be used so that the monthly cost without the pass is same as with the pass is; 6.25 times.

It follows from the task content that the regular train ticket costs, 3.00.

Therefore, the cost for travelling x times with the month is; 3x.

On this note, for the total monthly cost without the pass to be same as that with the pass; the equation which must hold is;

3x = 18.75

x = 18.75/3

x = 6.25 times.

Therefore, after taking the train 6.25 times, the cost without the pass is same as that with the pass.

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Answer: 3/5 cm

Step-by-step explanation:

Let the length of the base be x. Then, using the formula for the area of a triangle,

[tex]\frac{3}{25}=\frac{1}{2} \cdot \frac{2}{5} x\\\\\frac{3}{25}=\frac{1}{5}x\\\\x=\frac{3}{5}[/tex]

a) The price (amount) of the house after 1 month = $9540

b) The price (amount) of the house after 3 months  = $10719.14

c) The price (amount) of the house after 10 months = $16117.629

a ) How to find the rental price of the house after 1 month ?

The rental price of a dacha = Principle =  $9000

Percentage increase in price = r = 6%

Number of months = n = 1

Amount of a compound interest is given by,

 [tex]Amount = P(1 +\frac{r}{100} )^n\\\\=9000( 1 +\frac{6}{100}) \\\\= 9000(\frac{106}{100})\\\\= 90*106\\\\= 9540[/tex]

The rental price of the house after 1 month = $9540

b ) How to find the rental price of the house after 3 months ?

The rental price of a dacha = Principle =  $9000

Percentage increase in price = r = 6%

Number of months = n = 3

Amount of a compound interest is given by,

 [tex]Amount = P(1 +\frac{r}{100} )^n\\\\=9000( 1 +\frac{6}{100})^3 \\\\= 9000(\frac{106}{100})^3\\\\= 9000*(1.06)^3\\\\= 10719.14[/tex]

The rental price of the house after 3 months = $10719.14

c ) How to find the rental price of the house after 10 months ?

The rental price of a dacha =Principle =  $9000

Percentage increase in price = r = 6%

Number of months = n = 10

Amount of a compound interest is given by,

 [tex]Amount = P(1 +\frac{r}{100} )^n\\\\=9000( 1 +\frac{6}{100})^{10} \\\\= 9000(\frac{106}{100})^{10}\\\\= 9000*(1.06)^{10}\\\\= 9000*1.790\\\\= 16117.629[/tex]

The rental price of the house after 10 months = $16117.629

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The expression -3.1^4x * -3.1^2x + 7 has an equivalent of 887.503681x^2 + 7

From the question, the expression is given as

-3.1^4x * -3.1^2x + 7

Evaluate the exponents in the above expression

So, we have the following equation

-3.1^4x * -3.1^2x + 7 = 92.3521x * 9.61x + 7

Evaluate the products in the above expression

So, we have the following equation

-3.1^4x * -3.1^2x + 7 = 887.503681x^2 + 7

Hence, the equivalent expression of -3.1^4x * -3.1^2x + 7 is 887.503681x^2 + 7

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The approximate net pay of Juanita is $500. Therefore, option B is the correct answer.

Given that, Juanita has a part-time job that pays $12/hour and works about 50 hours every month.

Net pay means take-home pay or the amount employees earn after all payroll deductions are subtracted from their gross pay.

Now, total money earned in a month

= 12 × 50 = 600

Now

6.2% of 600 = $37.2

= 600 - 37.2 = $562.8

1.45% of 562.8 = $8.1606

= 562.8 - 8.1606 = $554.6394

10% of 554.6394 = $55.46394

= 554.6394 - 55.46394 = $499.17546

Total deductions = $499.17546

So, net pay = grass pay - deductions

= 600 - 105.9

= $499.17546

The approximate net pay of Juanita is $500. Therefore, option B is the correct answer.

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Based on the lengths of the sides of the triangle, we can infer that this is NOT a right triangle.

A right angled triangle would obey the Pythagoras Rule which is that the square of the hypotenuse (longest side) will be the sum of the squares of the other sides of the triangle.

This means that for this to be a right triangle, it needs to obey the function:

45 ² = 35 ² + 30 ²

Solving gives:

2,025 ≠ 2, 125

This shows that the triangle is not a right triangle.

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It is not a right-angle triangle since 2125 ≠ 2025 meant that it did not conform to Pythagoras' theorem's specifications.

This kind of query creates a right-angled triangle that Pythagoras' theorem can resolve.

In a right-angled triangle, the square of the greatest side is equal to the sum of the squares of the smaller two sides.

Given, There are three sides to a triangle, each measuring 30 kilometers, 35 kilometers, and 45 kilometers.

∴ 30² + 35² = 45².

900 + 1225 = 2025.

2125 ≠ 2025.

Due to the fact that it didn't meet the requirements of Pythagoras' theorem, it is not a right-angle triangle.

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Answer:

t = 192

Step-by-step explanation:

1/4t = 1/3t + (-16)

  1            1

-------t = -------t - 16

  4           3

  1(3)        1(4)

-------t = -------t - 16

  4(3)      3(4)

  3           4

-------t = -------t - 16

  12         12

  3           4

-------t = -------t - 16(12)

(   12         12 ) 12

3t = 4t - 192

-4t   -4t

---------------------

-t = -192

÷-1  ÷-1

---------------

t = 192

I hope this helps!

SOLUTION

From the what is given

We have the graph as shown below

We are told that the MAX is

Substituting these required points into the equation, our maximum becomes

We can see that the maximum is 25 at for units of 5, that is x = 5

But we are told in (B) that

Hence the surplus unit is

Hence the answer is 2

The required inclination of the tower of Pisa as 85.95°.

Given that,
in Italy the leaning Tower of Pisa currently leans at 13 ft. off the vertical. the tower is 183 ft tall. what is the angle of inclination is to be determiend.

These are the equation that contains trigonometric operators such as sin, cos.. etc.. In algebraic operations.

Here,
base length is 13 ft,
Hypotenuse length of the tower = 183
According to the question,
Cosx = 13/ 183
x = 85.98°

Thus, the required inclination of the tower of pisa as 85.95°.

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