one angle of a triangle is 60 degree and the other two are in the ratio 2:3.Find these angles​

Answer:

The depth is 127 inches.

Step-by-step explanation:

The stairway and its depth can be compared to a right angled triangle. Let the depth be represented by d.

But,

12 inches = 1 foot

20 ft 6 in = 20 + [tex](\frac{6}{12} )[/tex]

               = 20.5 feet

So that applying the appropriate trigonometric function, we have;

Sin θ = [tex]\frac{opposite}{hypotenuse}[/tex]

Sin 31º = [tex]\frac{d}{20.5}[/tex]

d = 20.5 x Sin 31º

   = 20.5 x 0.5150

d = 10.5575

d ≅ 11 feet

Therefore,

d = 10.5575 feet = (10.5575 x 12) inches

  = 126.69 inches

The depth is 127 inches.

Answer:

if you need anything else just comment

Step-by-step explanation:

4k <_ 4 = numerical form

4k/4 <_ 4/4

k <_ 1 = work to solve

on number line there is 0,1,2. 1 has a circle that is filled in and arrow pointing towards 0. = graphed on number line

set notation = {k(vertical bar)k<_1}

interval notation = (-infinity, 1]

Answer:

Step-by-step explanation:

Translation down and to the right doesn't change the dimensions of the original figure.

This will change coordinates of each vertex but the highest coordinates of the pre-image and image will correspond to each other.

you good itStep-by-step explanation:

Answer:

(10 - x + y) units

Step-by-step explanation:

Perimeter of the triangle = (3 - 2x + x + 7 + y) units = (10 - x + y) units

If you wish to venture further into mathematics (aka other topics), you may want to follow my Instagram account (learntionary), where I post some of my own notes on certain topics and also some tips that may be useful to you :)

Answer:

The answer is 60

Step-by-step explanation:

all you have to do is reverse the operation, you have to do 9 x 5 then add 15 to that result and you will get the answer :)

hope this helps!

Answer:

each tire was 68 dollars

Step-by-step explanation:

hope this helps :)

The answer is 68 because 68 x 4 is 272 .

Answer:

1. Yes 2. No 3. Yes 4. No

Step-by-step explanation: 1 is a function because none of the x values repeat, 2 isn't a function because in the x coordinates, -2 repeats, 3 is a function because if you were to draw a (vertical) line through each point, none of them have two points on one line, 4 is a function because none of the x coordinates point to more than one y coordinate

Answer:

The margin of error is  [tex]E = 0.4606 [/tex]      

Step-by-step explanation:

From the question we are told that

   The sample size is  n = 100

    The sample mean is  [tex]\= x = 12.5 \ years[/tex]

    The standard deviation is  [tex]\sigma = 2.8 \ years[/tex]

From the question we are told the confidence level is  90% , hence the level of significance is    

      [tex]\alpha = (100 - 90 ) \%[/tex]

=>   [tex]\alpha = 0.10[/tex]

Generally from the normal distribution table the critical value  of  [tex]\frac{\alpha }{2}[/tex] is  

   [tex]Z_{\frac{\alpha }{2} } =  1.645[/tex]

Generally the margin of error is mathematically represented as  

      [tex]E = Z_{\frac{\alpha }{2} } *  \frac{\sigma }{\sqrt{n} }[/tex]

=>   [tex]E =1.645*  \frac{ 2.8 }{\sqrt{100} }[/tex]

=>   [tex]E = 0.4606 [/tex]      

Answer:

Twice a number increased by five - 2x + 5

Five decreased by twice a number- 5 - 2x

Twice the difference of a number and five- 2(x - 5)

Twice the sum of a number and five= 2(x + 5)

Five subtracted from twice a number= 2x - 5

Twice a number, less five= 2x - 5

Step-by-step explanation:

a. Twice a number increased by 5

Assuming the number as x

Therefore, It's [tex]{{\underline{\textsf{\textbf{2x + 5}}}}}[/tex]

b. Five decreased by twice a number

Assuming the number as x

Therefore, It's [tex]{{\underline{\textsf{\textbf{2x - 5 }}}}}[/tex]

c. twice the difference of a number and five.

Assuming the number as x

Therefore, It's [tex]{{\underline{\textsf{\textbf{2(x - 5)}}}}}[/tex]

d. Twice the sum of a number and five

Assuming the number as x

Therefore, It's [tex]{{\underline{\textsf{\textbf{2(x + 5)}}}}}[/tex]

e. five subtracted from twice a number

Assuming the number as x

Therefore, It's [tex]{{\underline{\textsf{\textbf{ 2x - 5}}}}}[/tex]

f. twice a number, less five

Assuming the number as x

Therefore, It's [tex]{{\underline{\textsf{\textbf{5 - 2x}}}}}[/tex]

Answer:

-169

Step-by-step explanation:

An Arithmetic Combination states that  two functions f and g at any x i.e in the domain of both f and g, with one exception.

The quotient  is not defined at values of x, where g is equal to 0 or we can say that both the functions must be defined at a point for the combination to be defined.

Given: f(x) = 3-2x and g(x) =  

Then, using arithmetic combination of function definition:

                ......[1]

Now, first find the value of f(9) and g(8) ;

f(8) =3-2(8) = 3-16 = -13 and

Substitute these in equation [1] ;

Therefore, the value of (f/g)(8) is; -169

Answer:

2 is 17.5

Step-by-step explanation:

bc the half of 4 is 2 since 4 is 35 we have to find the half of 35 and how we do that is by dividing it by 2.

35%2=17.5 so 2 is equal 17.5 so <2 is 17.5

Answer:

1) sample space = {HHH, HHT, HTH, THH, THT, TTH, HTT, TTT}

2) pr(tossing heads exactly twice) = [tex]\frac{3}{8}[/tex]

3) pr(tossing tails at least twice) = [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

In tossing a coin three times, the sample space is the possible outcomes for the number of toss.

So that for the question,

1) The sample space = {HHH, HHT, HTH, THH, THT, TTH, HTT, TTT}

The total number of possible outcome is 8.

2) pr(tossing heads exactly twice) = [tex]\frac{numner of outcome with exactly two heads}{total number of outcome}[/tex]

                                                            = [tex]\frac{3}{8}[/tex]

3) pr(tossing tails at least twice) = [tex]\frac{number of outcome with at least two tails}{total number of outcome}[/tex]

                                                     = [tex]\frac{4}{8}[/tex]

                                                     = [tex]\frac{1}{2}[/tex]

Answer:

The pairs are:

[tex]\frac{4p^3q}{6p^2q^2}\div \frac{12pq^3}{2p^2q^2}[/tex] =>  [tex]\frac{p^2}{9q^2}[/tex]

[tex]\frac{10p^3q^3}{2p^2q}\div \frac{5pq}{6pq^2}[/tex] => [tex]6pq^3[/tex]

[tex]\frac{14p^2q^3}{2pq}\div \frac{7p^2q^2}{6p^3q^2}[/tex] => [tex]6p^2q^2[/tex]

[tex]\frac{16pq^3}{24p^2q^3}\div \frac{2p^2q^2}{p^3q^3}[/tex] => [tex]\frac{q}{3}[/tex]

Step-by-step explanation:

We are going to solve the questions one by one and then write the quotients with every question.

In order to calculate the division, the terms are multiplied then exponents are added or subtracted between numerator and denominator to get the simplest form of answer.

First Expression:

[tex]\frac{4p^3q}{6p^2q^2}\div \frac{12pq^3}{2p^2q^2}[/tex]

When two fractions have to be divided the second fraction is reversed i.e. numerator becomes denominator and vice versa.

[tex]= \frac{4p^3q}{6p^2q^2} * \frac{2p^2q^2}{12pq^3}\\=\frac{p^5q^3}{9p^3q^5}\\=\frac{p^2}{9q^2}[/tex]

Second Expression:

[tex]\frac{10p^3q^3}{2p^2q}\div \frac{5pq}{6pq^2}[/tex]

Removing the division symbol

[tex]=\frac{10p^3q^3}{2p^2q} * \frac{6pq^2}{5pq}\\=\frac{6p^4q^5}{p^3q^2}\\=6pq^3[/tex]

Third Expression:

[tex]\frac{14p^2q^3}{2pq}\div \frac{7p^2q^2}{6p^3q^2}[/tex]

Removing the division symbol

[tex]=\frac{14p^2q^3}{2pq} * \frac{6p^3q^2}{7p^2q^2}\\= \frac{6p^5q^5}{p^3q^3}\\= 6p^2q^2[/tex]

Fourth Expression:

[tex]\frac{16pq^3}{24p^2q^3}\div \frac{2p^2q^2}{p^3q^3}[/tex]

Removing the division symbol

[tex]=\frac{16pq^3}{24p^2q^3} * \frac{p^3q^3}{2p^2q^2}\\=\frac{p^4q^6}{3p^4q^5}\\=\frac{q}{3}[/tex]

Hence,

The pairs are:

[tex]\frac{4p^3q}{6p^2q^2}\div \frac{12pq^3}{2p^2q^2}[/tex] =>  [tex]\frac{p^2}{9q^2}[/tex]

[tex]\frac{10p^3q^3}{2p^2q}\div \frac{5pq}{6pq^2}[/tex] => [tex]6pq^3[/tex]

[tex]\frac{14p^2q^3}{2pq}\div \frac{7p^2q^2}{6p^3q^2}[/tex] => [tex]6p^2q^2[/tex]

[tex]\frac{16pq^3}{24p^2q^3}\div \frac{2p^2q^2}{p^3q^3}[/tex] => [tex]\frac{q}{3}[/tex]

Answer:

The projected sales is $1007400

Step-by-step explanation:

Given

[tex]Sales = \$920000[/tex]

[tex]Increment = 9.5\%[/tex]

Required

Determine the new projected sales

Increment is calculated using:

[tex]Increment = Initial\ Value(1 + Increment\%)[/tex]

In this case:

[tex]Projected\ Sales = Sales(1 + Increment\%)[/tex]

[tex]Projected\ Sales = 920000(1 + 9.5\%)[/tex]

Convert % to decimal

[tex]Projected\ Sales = 920000(1 + 0.095)[/tex]

[tex]Projected\ Sales = 920000*1.095[/tex]

[tex]Projected\ Sales = 1007400[/tex]

Hence, the projected sales is $1007400

Answer:

An extraneous solution is a root of a transformed equation that is not a root of the original equation because it was excluded from the domain of the original equation. Example 1: Solve for x , 1x − 2+1x + 2=4(x − 2)(x + 2) .

Answer:

true then false is the anwer

Answer:

After using distributive property to remove the parentheses [tex]10(u-2)[/tex]  we get [tex]10u-20[/tex]

Step-by-step explanation:

We need to use distributive property to remove the parentheses 10(u-2)

According to distributive property of multiplication over subtraction: [tex]a(b-c)=ab-ac[/tex]

Using the above distributive property to solve the question. Multiply 10 with terms inside the bracket and solving:

[tex]10(u-2)\\=10u-10*2\\=10u-20[/tex]

So, After using distributive property to remove the parentheses [tex]10(u-2)[/tex]  we get [tex]10u-20[/tex]

Answer:

0.630901 liters per second

Step-by-step explanation:

Hope this helped!

Answer:

Let

the breadth =x

the length =6x

As we know that in a rectangle

[tex]{\boxed{\sf Area=lb}}[/tex]

[tex]{:}\longrightarrow[/tex][tex]\sf x\times 6x=160 [/tex]

[tex]{:}\longrightarrow[/tex][tex]\sf 6x^2=160[/tex]

[tex]{:}\longrightarrow[/tex][tex]\sf x^2={\dfrac {160}{6}}[/tex]

[tex]{:}\longrightarrow[/tex][tex]\sf x^2=26.6 [/tex]

[tex]{:}\longrightarrow[/tex][tex]\sf x=\sqrt {26.6}[/tex]

[tex]{:}\longrightarrow[/tex][tex]\sf x=5.1yards[/tex]

Answer:

X=80

Step-by-step explanation:

9x=320+5x

9x-5x=320

4x=320

X=320/4

X=80

So the number of girls =5×80

=400.

Answer:

y=(x-8)^2-71

i believe thats the correct answer

Answer:

Heidi wants to compute:

17 - 9.

First, she adds to get 10, (we want to subtract 10, this is easier than subtracting 9) then she can do:

17 - 9 + 0

adding zero does not change the sum

1 - 1 = 0

then:

17 - 9 + 0 = 17 - 9 + 1 - 1

Now we can do:

17 - 9 - 1 + 1

17 - (9 + 1) + 1

17 - 10 + 1

(17 - 10) + 1

7 + 1 = 8

Then, first she needs to add -1, in order to subtract 10, and then she must add 1. As we added a number and its inverse, in total we added zero, so the sum did not change, but was easier to compute.

Then, you need

I would say that the tree is 12 feet high.

And to find out the answer you could use the quadratic formula :)

Answer:

8

Step-by-step explanation:

There are a couple different ways you can solve this, but this is generally the quickest way.

Identify a pattern in the problem. We can see that [tex]1-3=-2[/tex],  [tex]5-7=-2[/tex], and so on. Subtracting every two odd numbers (without repeating any numbers) in that problem will always give us the same answer: -2.

So, we see how many pairs of odd numbers there are.

1 and 3,  5 and 7,  9 and 11,  13 and 15. We have four pairs of odd numbers. We can just multiply -2 by 4, which leaves us with an answer of -8.

Finally, since this is also an absolute value equation, the answer will be positive, so the final answer is 8.

Answer: D

Step-by-step explanation: y=2 so 2+2=4+1=5