If a triangle with angle AB 2x, BC 4x-10, and AC 3x-7, What is the lenght of line segment AC?

Answer:

B

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I hope I could help.

Canon has 12 jigsaw puzzles in total.

What is Algebraic expression ?

Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.

Let us say puzzles solved by :

Arthur be x

Conan be y

Doyle be z

also,

Here, it is given that :

Arthur has completed four times as many jigsaw puzzles as Conan which means :

x = 4y.......(1)

Doyle has completed three times as many jigsaw puzzles as Conan which  means :

z = 3y.....(2)

Doyle has completed 12 fewer jigsaw puzzles than Arthur has means :

z = x-12....(3)

now, to find the number of jigsaw puzzles does Conan (y) we equate equation (2) and (3) to find the value of y also by putting value of x in equation (3) :

3y = x-12

3y = 4y-12

4y-3y = 12

y = 12

Therefore, Canon has 12 jigsaw puzzles in total.

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Q3 or upper quartile for the data 2,4,6,8,10,12 is 10

Q3 or upper quartile is an statistical term that separates the highest 25 percent data from lowest 75 percent data.

For finding quartile first arrange the given data into ascending order.

Find the median of the data then the median divides the data into two potions . the median of the upper half of data is the upper quartile.

Or if the total no of terms are n then Quartile formula for upper quartile is  

  = (n+1)3/4   term

Given data is 2,4,6,8,10,12 which is already arranged in ascending order and no of terms are n=6

Median of this data = ( 3rd term + 4th term)/2 =(6+8)/2=7

7 divides the data into two halves 2,4,6 and 8,10,12

Upper half is 8,10, 12 as this data has odd terms thus median will be the middle term

Median is middle term of 8,10,12 that is 10

Therefore, Q3 or the upper quartile of the given data is 10

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The area of the building in terms of y in its simplest form is (8y^2-18)

Since the area of rectangular is

Area = Length x Breadth

From our Question,

The width of the rectangle building is 2y feet.

So, L = 4y - 9 feet

So, the area of the building in terms of y is

Area = L x B

= (4y-9)x 2y

= (8[tex]y^2[/tex] - 18y)

So, the area of the building in term of y in its simplest form is (8y^2 -18)

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Answer:

y < 1

[tex]( - \infty \: 1)[/tex]

Step-by-step explanation:

8y - 5 < 3

8y < 8

y < 1

[tex]( - \infty \: 1)[/tex]

Answer:3/4

Step-by-step explanation:

18/24 divide by 2 9/12 divide by 3 3/4

Answer:

8. 47°F

9. -20°C

10. 29,513ft

Step-by-step explanation:

8.

92°F - 45°F = 47°F

The Equator is 47°F warmer than the South Pole.

9.

-4°C × 5 = -20°C

The coldest day on record in Felix's town is -20°C

10.

29,028 - (-485)

29,028 + 485 = 29,513 feet.

The difference between Mt. Everest and the Dead Sea is 29,513 feet.

I hope this helps!

In mathematical modelling, we take a real-world problem and write it as an equivalent mathematical problem.

We then solve the mathematical problem, and interpret its solution in terms of the real-world problem.

After this we see to what extent the solution is valid in the context of the real-world problem.

Mathematical modeling is one of the bases of mathematics education. Mathematical modeling is described as conversion activity of a real problem in a mathematical form. Modeling involves to formulate the real-life situations or to convert the problems in mathematical explanations to a real or believable situation.

It's extremely precise, since it's math-based, which allows you to develop accurate ideas and assumptions. It's concise, with clear and established rules. It gives you direction when trying to solve a problem.

characters of modeling;

It may be changed or manipulated with relative ease.

It is simplification/Idealization. Mathematical modeling has many benefits related to real-world problems, but the main disadvantages are process simplification, specific rules of the model, and lack of information or data monitoring.

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Answer: 14a + 4b

Step-by-step explanation: 2(4a+b) part equals 8a + 2b because it is distributive property and then 2(3a+b) equals 6a+2b then put the a's. 8a + 6a = 14a then the b's. 2b+2b= 4 b. Put them together and it gives you 14a + 4b.

Step-by-step explanation:

2(4a+b)+2(3a+b) remove the brackets

2(4a+b)+2(3a+b) =

8a + 2b + 6a +2b =  (no brackets)

14a + 4b                    (solution)

Answer:

112

Step-by-step explanation:

You asked for consecutive integers:

x = first

x+1 = second

x        +       x+1     <=  223

2x +1 ≤ 223

2x  ≤ 222

x  ≤ 111

x +1 = 112

The equilibrium price is $12.

Equilibrium is the point where the quantity demanded is equal to the quantity supplied. The price at equilibrium is known as the equilibrium price and the quantity at equilibrium is known as the equilibrium quantity.

When shown on a graph, equilibrium is the point where the quantity demanded curve is equal to the quantity supplied curve.

When there is equilibrium, the equation of quantity demanded would be equal to the equation of quantity supplied.

-280 + 40p = 800  - 50p

In order to determine the value of p, take the following steps:

Combine similar terms: 800 + 280 = 40p + 50p

Add similar terms = 1080 = 90p

Divide both sides of the equation by 90 : 1080 / 90 = 12

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Answer:

c is the answer

Step-by-step explanation:

hint is the direction of movement

Answer:

the only answer i could think of is because

6*5= 30 which is the remainder of the wall that needs to be painted

The amount after 4.5 years for the principal amount $ 5000 at 4 % interest compounded annually will be $ 5956.13.

We are given that:

Principal = p = $ 5000

Interest rate = r = 4%

Compounding Annually

Time = n = 4.5 years

Now, we know that the formula for compound interest is:

Amount (A) = p ( 1 + r )ⁿ

Substituting the values in the formula, we get that:

A = 5000 ( 1 + 0.04)⁴°⁵

A = 5000 (1.04)⁴°⁵

A = 5000 (1.19)

A = $ 5956.13

Therefore, we get that, the amount after 4.5 years for the principal amount $ 5000 at 4 % interest compounded annually will be $ 5956.13.

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Answer:

[tex]6^{7/2}[/tex]

Step-by-step explanation:

[tex]6^4 \div 6^{1/2} \\ \\ =6^{4-\frac{1}{2}} \\ \\ =6^{7/2}[/tex]

Answer:

This question was previously solved by an expert

The equation of line is x + 2y = 12.

The equation of a straight line is y= mx+c , m is the gradient and c is the height at which the line crosses the y -axis, also

For example,

We know from the question that our slope is 3 and our y-intercept is –5, so plugging these values in we get the equation of our line to be y = 3x – 5

Given:

line p passes through point (2,5)

and perpendicular to the line whose equation is y=2x+3.

As the slope of line is

m=2

for perpendicular the slope of another line is

m' = -1/m

m' = -1/2

Now, the equation of lines passes through (2, 5)

y-[tex]y_{1}[/tex]= m (x-[tex]x_1[/tex])

y-5= -1/2(x - 2)

2y - 10 = 2 -x

x + 2y = 12

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Answer:

[tex]25 \times 25[/tex]

Step-by-step explanation:

Answer:

1. 7395.108

2. 600+80+1+0.4+0.01+0.006

3. 2079.346

Step-by-step explanation:

number 1 is 7,395.108

number 2 is (6x100)+(8x10)+(1x1)+(4x1/10)+(1x1/100)+(6x1/1000)

number 3 is 2,079.346

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The equation of the line with slope 4 which goes through the point (8,5) will be y = 4x - 27.

A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

If the slope of the equation of a line is 4, then the equation of the line will be

y = 4x + c

The equation of the line is passing through (8, 5), then the value of c will be

5 = 4(8) + c

5 = 32 + c

c = 5 - 32

c = - 27

Then the equation of the line will be

y = 4x - 27

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The relative frequencies of the five classes are 14%, 32%, 38%, 11%, 2.9%.

Given, we have the frequency table grades A,B,C,D,F with frequencies of 5,11,13,4, and 1 respectively.

According to the question the relative frequency, the specific frequency is divided by the total frequency.

The sum of all the frequencies is called relative frequency.

= 5 + 11 +13 +4 +1 = 34

The relative frequency of the

first

class is,

A   5/34  =  0.14 =  14%

The relative frequency of the

second

class is,

B 11/34 =  0.32 = 32%

The relative frequency of the

third

class is,

C 13/34  =  0.38  = 38%

The relative frequency of the

fourth

class is,

D  4/34  = 0.11   = 11%

The relative frequency of the

fifth

class is,

F  1/34 =   0.029    = 2.9%

Hence, the relative frequencies of the five classes are 14%, 32%, 38%, 11%, 2.9%.

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The company must sell 1899 DVDs each day to make a profit.

An owner's income from a successful manufacturing process producing goods for the market is referred to as a profit (business).

The cost for supplies is $0.80 per DVD.

Let the company manufactured and sold x DVD s.

Now , total cost for x DVDs = 0.80 x + 1500

Total sell price for x DVDs = 1.59x

Profit = Sell price - cost price

Profit = 1.59x - 0.80x - 1500

profit = 0.79 x - 1500

Now the profit is made. Therefore profit>0

∴ 0.79 x - 1500 > 0

or , x > 1500 ÷ 0.79

or, x > 1898.734

Hence the company need to sell 1899 DVDs to make a profit.

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Answer:

Length = 20 ft. Width = 6 ft.

Step-by-step explanation:

The correct statement that is missing in the proof is m<5 + m<2 = 180 degrees

Supplementary angles are angles that sums up to 180 degrees. From the third proof, we can see that the measure of m<1 is equivalent to m<5.

Also from the 4th statement <1 and m<2 are supplementary meaning that the sum of <1 and <2 is equivalent to 180 degrees.

Since m<1 = m<5, we can replace m<1 as m<5 in the equation m<1 + m<2 = 180 from statement 4 to have m<5 + m<2 = 180 degrees by the substitution property.

Hence the correct statement that is missing in the proof is m<5 + m<2 = 180 degrees.

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Answer:

B

Step-by-step explanation:

A piecewise function that relates the salesperson total monthly income based off or his/her sales for the month is  X > 25000.

An accurate graph of this piecewise function is 2100.

The salesperson's monthly income if his/her sales were $43,000 for the month is $ 4250

Explanation for this is

a) S(x) = 0.02x + 2850  ( 0 < x < 25000 )

              0.05x + 2100  ( X > 25000 )

b) 25k  26k

    500  550

3400 = 0.05 ( 26000) + b

3400 = 1300 + b

b = 2100

c) 0.05 (43000) + 2100

= $4250

The core concept of mathematics' calculus is functions. The unique varieties of relations are the functions. In mathematics, a function is represented as a rule that produces a distinct result for each input x.

In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain.

The whole set of values that the function's output can produce is referred to as the range. The set of values that might be a function's outputs is known as the co-domain.

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The number of 5 / 16 pizza servings in 2 1/4 pizzas is 7 1/5 pizza servings.

A proper fraction is a non-integer that is made up of a numerator that is smaller in value than the denominator. An example of a proper fraction is 1/4. A mixed fraction is a fraction that is made up of a whole number and a proper fraction.  An example of a mixed fraction is 2 1/4.

In order to determine how many 5/16 pizza servings are in 2 1/4 pizza, divide 2 1/4 by 5/16. Division is the mathematical operation that is used to group a number into equal groups using another number. The sign used to represent division is ÷.

2 1/4 ÷ 5/16

9/4 × 16/5 = 36 / 5 = 7 1/5 pizza servings.

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Part (a)

[tex]f(3)=5-3(3)^2=-22 \\ \\ f(3+h)=5-3(3+h)^2 \\ \\ =5-3(h^2 +6h+9) \\ \\ =5-3h^2 -18h-27 \\ \\ =-3h^2-18h-22 \\ \\ f(3+h)-f(3)=(-3h^2-18h-22)-(-22)=\boxed{3h^2 +18h}[/tex]

Part (b)

[tex]\frac{f(3+h)-f(3)}{(3+h)-3} \\ \\ =\frac{-3h^2-18h}{h} \\ \\ =\boxed{-3h-18}[/tex]

By answering the above question, we may state that by equation A = S + 18 = 24 + 18 = 42 and Alex thus owns 42 books.

Using the equals notation (=) to indicate equivalence, a math equation links two statements. Algebraic equations prove the equality of three mathematical expressions by a mathematical assertion. The equal sign, for example, provides a gap between the numbers 3x + 5 and 14 in the equation 3x + 5 = 14. You can use a mathematical formula to understand the connection between the two phrases that are inscribed on opposite sides of a letter. Most of the time, the symbol and the particular software match. e.g., 2x - 4 = 2 is an example.

Let's designate the quantity of books Alex has as "A" and the quantity of books his sister Scout owns as "S."

We learn the following from the issue:

A = S + 18 (Alex possesses 18 more books than his sister) (Alex owns 18 more books than his sister)

A + S = 66 (combined, they possess 66 books) (together, they own 66 books)

These two equations can be used to determine A:

The first equation is substituted into the second equation to yield:

(S + 18) + S = 66

2S + 18 = 66

2S = 48

S = 24

Scout has 24 books, thus we can apply the first equation to determine how many books Alex has:

A = S + 18 = 24 + 18 = 42

Alex thus owns 42 books.

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