rewrite in simplest form

Here we are given a right angled triangle in which there are two unknown angles x and y . we need to find out the values of x and y. Firstly, as we know that the angle sum property of a triangle is 180° . So that,

[tex]\longrightarrow x + y +90^o = 180^o\\[/tex]

[tex]\longrightarrow x + y = 180^o -90^o = 90^o \dots \\[/tex]

[tex]\longrightarrow y = 90^o - x \dots (i) \\[/tex]

And we also have,

[tex]\longrightarrow 4x + 40 = y \\[/tex]

from equation (i) , we have ,

[tex]\longrightarrow 4x + 40 = 90 - x \\[/tex]

[tex]\longrightarrow 4x + x = 90 +40 \\[/tex]

[tex]\longrightarrow 5x = 130\\[/tex]

[tex]\longrightarrow x =\dfrac{130}{5}\\[/tex]

[tex]\longrightarrow \underline{\underline{x = 26^o}} \\[/tex]

substitute this value in equation (i) ,

[tex]\longrightarrow y = 90 - 26 \\[/tex]

[tex]\longrightarrow \underline{\underline{y = 64^o}} \\[/tex]

And we are done!

The rounding up of each of the 12 +2 11/14 5/7 mixed number to the nearest whole number then the estimatation of the sum  can be expressed  as  A.16.

The concept here is addition of the fractions and the digits, In mathematics, summation is the process of adding a series of different types of numbers, known as addends or summands, to produce their sum or total.

The rounding up to whole number can be done as :

12 = 12.0

2 11/14 = 39/14 = 2.786= 3.0

5/7  = 0.71=1.0

Then the sum = 12+3+1=16

Therefore, option A is correct.

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Answer:

a: 2250. b: 1200. c: 5:2.3:2.7  d: 23.3%

Step-by-step explanation:

Sian gets 1/2 so 4500/2 = 2250

Anesha = 1050

Joanna = 2250-1050 = 1200

Answer:

answer - x = − 12/7

The final amount after a certain rate of decrease over a period of time can be calculated by Xₙ = X₀ (1-r)ⁿ. From calculations the sales after 6 weeks are 13286.025.

If the percent increase or decrease, period of time and initial amount are given, the final amount can be calculated using the equation Xₙ = X₀ (1±r)ⁿ. Here the percentage decrease is given. So the equation is

   Xₙ = X₀ (1-r)ⁿ

     Xₙ is the final amount

     X₀ is the initial amount

     r is the rate

    n is the period of time

Here percent is given as 10%. So the rate, r = 10/100 = 0.10

 Xₙ = X₀ (1-r)ⁿ

      = 25000× (1-0.10)⁶

       = 13286.025

So the sales after 6 weeks are 13286.025

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By using the point-slope form, the equation of a line that passes through the point (11, 18) with slope 3 is equal to y - 18 = 3(x - 11).

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁)

Where:

From the information provided above, we have the following slope and data points on the line:

At data point (11, 18), a linear equation of this line can be calculated in point-slope form as follows:

y - y₁ = m(x - x₁)

y - 18 = 3(x - 11)

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An algebraic expression which represents this word description "The quotient of nine and the sum of a number and one" is: D. 9 over x+1.

In Mathematics, a quotient can be defined as a mathematical expression that is simply used to represent the division of a number by another number.

In order to translate this word problem into algebraic equation, we would assign a variable to the unknown number and then translate the word problem into algebraic equation as follows:

Let the variable n represent the unknown number.

Translating the word problem into an algebraic equation, we have the following;

Quotient = 9/(x + 1)

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Complete Question:

Which algebraic expression represents this word description?

The quotient of nine and the sum of a number and one

A. x+1 over 9 B. 9/x +1 C. x/9 +1 D. 9 over x+1

The thirty-fifth term in an arithmetic sequence is 1.

The formula for the nth term of an arithmetic sequence is:  

[tex]t_{n}[/tex]  =  a + (n - 1)d

The twenty-third term in an arithmetic sequence is [tex]$\frac{2}{3}[/tex].

a + 22d = [tex]$\frac{2}{3}[/tex] ...... (1)

The fifty-third term in an arithmetic sequence is  [tex]$\frac{3}{2}[/tex].

a + 52d = [tex]$\frac{3}{2}[/tex]........(2)

Subtracting both the equations.

Subtract equation (1) from equation (2):

a + 52d - (a + 22d) = [tex]$\frac{3}{2} - \frac{2}{3}[/tex]

a + 52d - a - 22d = [tex]$\frac{9-4}{6}[/tex]

30d = [tex]$\frac{5}{6}[/tex]

d = [tex]$\frac{1}{36}[/tex]

Substitute the value of d in equation (1).

We get:

a + 22[tex]$(\frac{1}{36})[/tex] = [tex]$\frac{2}{3}[/tex]

a + [tex]$\frac{11}{18}[/tex] = [tex]$\frac{2}{3}[/tex]

a = [tex]$\frac{2}{3}[/tex] - [tex]$\frac{11}{18}[/tex]

a = [tex]$\frac{12}{18} - \frac{11}{18}[/tex]

a = [tex]$\frac{1}{18}[/tex]

To find the 35th term substitute the values of a and d in the nth term equation.

The thirty-fifth term in an arithmetic sequence is:

=  [tex]$\frac{1}{18}[/tex] + (35 - 1) [tex]$\frac{1}{36}[/tex]

=  [tex]$\frac{1}{18}[/tex] +  [tex]$\frac{34}{36}[/tex]

=  [tex]$\frac{1}{18}[/tex] +  [tex]$\frac{17}{18}[/tex]

= [tex]$\frac{18}{18}[/tex]

= 1

Therefore the thirty-fifth term is 1.

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According to the information in the table, the value of C is 51.

To find the value of C we must calculate the constant, for that we have to perform the following operation:

In this case, we use the values of another column to identify the constant that applies to all the values in the table and the result is the following:

Additionally, to find the value of C we must perform the following operation:

According to the above, the value of C is 51.

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The equations which represents the given graph is 3x-y=2 and

4x+9y=36 .

What is Linear equation ?

Linear equation can be defined as the equation in which the highest degree is one

Given ,

The graphs of lines k1 and k2 are shown on the grid.

From the given graph ,

The Two lines are intersecting at a point x = 49/31 and y=85/31

So, lets put the values of and y in the given linear equations

so we get,

3x-y=2

4x+9y=36

put values x = 49/31 and y=85/31

so ,

3*(49/31) - 85/31  = 2

= 62/31

= RHS

which is equals to RHS

4*(49/31)+9*(85/31) = 36

=36* 31  / 31

= RHS

Which equals to RHS

Hence, The equations which represents the given graph is 3x-y=2

4x+9y=36 .

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The Volume or liters required to fill a 12.0 - gal gas tank is 45.42 liters.

Gallon to liter conversion factors are:

[tex]1 \ Gallon = 3.785 \ Liter[/tex]

Assuming that the gallon measurement for the gas tank is 12.0 gal.

We now need to calculate the gas tank's liter capacity.

As, 1 gallon = 3.785 liter

[tex]So \ 12\ gallon = 12*3.785[/tex]

[tex]=45.42\ gallons.[/tex]

Therefore, 45.42 liters of liquid are needed to fill the gas tank.

Meaning of gasoline:

Petroleum is the source of gasoline, which is a mixture of flammable, volatile liquid hydrocarbons used as a fuel for internal combustion engines and as a solvent for oils and fats.

It is a by-product of the petroleum industry and is used as fuel for cars because it burns with a high degree of energy and mixes easily with air in a carburetor.

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The number of hours that the rented the boat, if the total cost was $33 would be represented by the equation: 33 = 2h + 15

To write the equation on the number of hours that the boat would have been rented for to get a total cost of $ 33, use the formula :
Total cost = Deposit fee + ( Cost per hour x Number of hours boat was used)

Total cost = $ 33

Cost per hour = $ 2

Number of hours boat was in use = h

The equation therefore is:

33 = 2 h + 15

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The full question is:

Speedy Boat Rental charges a $15 deposit fee plus $2 for each hour of use to rent a paddleboat.  Write an equation to find out for how many hours, h, they rented the Boat if the total cost was $33.

yup

Step-by-step explanation: the triplets of 15,8,7 make a right triangle

u can also add 8 squared and 7 squared and if it equals to 15 squared then it’s right

If BC=6x-2 and DE=2x+2, then the length of BC is 16.

DE is a midsegment of the triangle.

As we know that;

A midsegment is a line segment that joins two of the midpoints of a triangle's sides.

The midsegment linking the midpoints of two sides of a triangle is parallel to the third side of the triangle, and its length is half that of the third side, according to the midsegment theorem.

So according to Midpoint Theorem

DE = BC/2

Now putting the value

2x+2 = (6x-2)/2

Multiply by 2 on both side, we get

4x + 4 = 6x-2

Add 2 on both side, we get

6x = 4x + 6

Subtract 4x on both side, we get

2x = 6

Divide by 2 on both side, we get

x = 3

Now putting the value of x in BC=6x-2

BC = 6(3) - 2

BC = 18 - 2

BC = 16

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Using the arithmetic operation of division -

a) 3 people can be fed by 1 pizza.

b) Maria would need 11 pizzas for 33 people.

What is arithmetic operation?

A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.

The number of pizzas ordered = 8

The number of people are = 24.

Number of people that can be fed if 1 pizza was there =

Number of people = Number of people that came/ Number of pizza

Use the arithmetic operation of division -

Number of people = 24/8

Number of people = 3

Therefore, 3 people can be fed.

Now, the number of people = 33

Number of pizzas required for 33 people can be obtained as -

Use the arithmetic operation of division -

Number of pizzas = Number of people/ Number of people fed by 1 pizza

Number of pizzas = 33/3

Number of pizzas = 11

Therefore, Maria will require 11 pizzas.

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Answer:

1,942,364

Step-by-step explanation:

   1 8 4 9 0 3 2

+        9 3 3 3 2

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

   1 9 4 2 3 6 4

Joseph now has 1,942,364 apples.

No. of apples Joseph had in the beginning = 93332

No. of apples he gets more = 1849032

Total no. of apples he has now = 93332 + 1849032

= 1,942,364

The number of next 14 students that will be expected to be adults education students would be = 7 adult education students.

An adult education student is the student that is undertaken by individuals that are mature men and women who take course for continuing education.

The first enrollment consist of the following;

Adult education student = 18

other = 18

Total for first enrollment = 18+18 = 36

If first 36 enrolled students = 18 adult students

second 14 enrolled students = X adults

Make X the subject of formula;

X adults = 14× 18/36

= 252/36

= 7

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The area of the shaded region of the circle is  1836.9 km².

Both circles have the same centre. The circumference of the inner circle is 100.48 kilometres. The circumference of a circle is the perimeter of the circle.

Therefore, the area of the shaded portion can be calculated as follows:

Hence,

circumference of the inner circle = 2πr

100.48 = 2 × 3.14 × r

100.48 = 6.28 r

r = 100.48 / 6.28

r = 16 km

Therefore,

area of the inner circle = πr²

area of the inner circle = 3.14 × 16²

area of the inner circle = 803.84 km²

area of the outside circle = πr²

area of the outside circle = 3.14 × (16 + 13)²

area of the outside circle = 3.14 × 29²

area of the outside circle = 2640.74 km²

Therefore,

area of the shaded region =  2640.74  - 803.84

area of the shaded region =  1836.9 km²

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The sketch a normal curve is attached below and in Normal Curve with mean of 50 and a Standard Deviation of 2.

The term normally curve in math is defined as a normal distribution is proper term for a Probability bell curve.

While we looking into the question we know that here from the Right of Normal standard curve we have to draw 3 vertical lines. And these lines would count up by 2 for each standard deviation 52, 54,56.

And then we have to plot from the Left of Normal standard curve, and then draw 3 vertical lines. And those lines would count up by 2 for each standard deviation 48,46,44.

Thus Normal standard curve extends indefinitely in both directions, and by approaching on the other hand it never touching the horizontal axis as it does so.

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Answer:

Step-by-step explanation:

To calculate a percentage decrease, first calculate the difference (decrease) between the two numbers you are comparing. Next, divide the decrease by the original number and multiply the answer by 100.

In this case, our difference is 32-28=4

4 divided by 32= 4/32, and multiplying by 100 gives us 400/32=12.5

Therefore, the percent decrease is 12.5%

the solution of the given problem of coordinates comes out to be  the coordinate P = (7, 0.4).

A coordinate system is a technique used in geometry to precisely locate points or other topological objects on a continuum, such as Euclidean space, using one or more numbers or coordinates. A point or item on an a double plane is located using a pair of integers known as coordinates. The x and y positions are two integers that describe a point's location on a 2D plane.

David want to find the coordinate are a useful tool for segmenting lines into smaller units.

P's coordinate is P = (7, -0.4)

The criteria are as follows:

A = (8,0)

=> B = (3,-2) (3,-2)

m: n=1:4

Using P = mx2+nx1 my2+ny

m+n

m+n, line ratio is computed.

The result is:

P 1x3+4x8 /1x-2+4x0 = 1+4 / 7

=> P = 35, 2

=>P = (7, -0.4) (7, -0.4)

1+4

P therefore has the coordinate P = (7, 0.4).

Therefore , the solution of the given problem of coordinates comes out to be  the coordinate P = (7, 0.4).

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Answer: ∠LKM=56° and ∠MKN=89°

Step-by-step explanation:

Notice that ∠LKM and ∠MKN make up ∠LKN. That means ∠LKM and ∠MKN combines equals 145°.

2x+10+4x-3=145               [combing like terms]

6x+7=145                           [subtract both sides by 7]

6x=138                              [divide both sides by 6]

x=23

We are almost done. We still need to plug it in to find the angle values.

∠LKM

2x+10                                 [plug in x=23]

2(23)+10                             [multiply]

46+10                                 [add]

56

∠LKM=56°

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

∠MKN

4x-3                                   [plug in x=23]

4(23)-3                                [multiply]

92-3                                    [subtract]

89

∠MKN=89°

Therefore, ∠LKM=56° and ∠MKN=89°.

Answer:

10 1/2 lbs = 168 oz

Answer:

168

Step-by-step explanation:

i think

An equation to represent the total amount she has saved each month is 350x + 1200.

We have to write an equation to represent the total amount she has saved each month.

Brynn has $1,200 in her savings account and plans to save an additional $350 each month in order to purchase a car.

To write an expression we have to read the statement very carefully and also write the expression after reading the statement.

Let she save the money in x months.

If she save $350 each month, then the total saving in x months = 350x

She has $1200 in saving account. Now the expression is

= 350x + 1200

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Answer:

Step-by-step explanation:

To find out how many batches of bread you can make with 2 cups of flour, you need to divide the amount of flour you have by the amount of flour each batch requires.We know that a batch of bread requires 3 cups of flour. To find out how many batches you can make with 2 cups of flour, you can divide 2 by 3:2 / 3 = 0.67Therefore, you can make 0.67 batches of bread with 2 cups of flour. However, since you can't bake a fraction of a batch, you can't make any batches of bread with 2 cups of flour, as it is not enough. You will need at least 3 cups of flour to make a batch of bread.

Answer: Given that 6log3 + 7 - 3loga = 0, we can start by isolating the variable a. To do this, we'll add 3loga to both sides:

6log3 + 7 = 3loga

Next, we'll divide both sides by 3:

2log3 + (7/3) = loga

Now we have loga on one side of the equation and a constant on the other. To find the possible values of a, we'll need to use the properties of logarithms.

We know that logb(x) = y is equivalent to b^y = x, so we can rewrite the equation as:

a = 3^(2log3 + (7/3))

To find the possible values of a, we'll need to evaluate the exponent on the right side of the equation. Since we don't know the value of log3, we can't find the exact value of a. However, we can say that the possible values of a are all the values that can be expressed as 3 raised to the power of (2log3 + (7/3))

Step-by-step explanation:

The number is decreased by 1%.

Now, According to the question:

Let the number be 100

Number is increased by 10% = 100+10% of 100

=100+10

=110

Now, the resultant number is reduced by 10% =110-10% of 110

=110-11

=99

The number obtained is 99

Decrease in value = 100 – 99 = 1

Percentage decrease = 1100 × 100=1%

Hence, the number is decreased by 1%.

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Answer:

Step-by-step explanation: 23.4

Answer:

Solid Sounds

Step-by-step explanation:

As a test, let's say the dance-a-thon lasted 10 hours.  Plug in 10 hours to each:

Gabe's:  $60/hr x 10 hr = $600

Derek's:  $100 + ($40/hr x 10 hr) = $500

Solid Sounds:  $175 + ($30/hr x 10 hr) = $475

This shows that Solid Sounds is the cheapest (no matter how many hours the dance lasts)