expand and simplify 5(2-1)+2(3x-6)

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Explanation:

We'll need the tangent rule

tan(angle) = opposite/adjacent

tan(R) = TH/HR

tan(30) = TH/54

sqrt(3)/3 = TH/54 ... use the unit circle

54*sqrt(3)/3 = TH .... multiply both sides by 54

(54/3)*sqrt(3) = TH

18*sqrt(3) = TH

TH = 18*sqrt(3) which points to choice A as the final answer

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An alternative method:

Triangle THR is a 30-60-90 triangle.

Let x be the measure of side TH. This side is opposite the smallest angle R = 30, so we consider this the short leg.

The hypotenuse is twice as long as x, so TR = 2x. This only applies to 30-60-90 triangles.

Now use the pythagorean theorem

a^2 + b^2 = c^2

(TH)^2 + (HR)^2 = (TR)^2

(x)^2 + (54)^2 = (2x)^2

x^2 + 2916 = 4x^2

2916 = 4x^2 - x^2

3x^2 = 2916

x^2 = 2916/3

x^2 = 972

x = sqrt(972)

x = sqrt(324*3)

x = sqrt(324)*sqrt(3)

x = 18*sqrt(3) which is the length of TH.

A slightly similar idea is to use the fact that if y is the long leg and x is the short leg, then y = x*sqrt(3). Plug in y = 54 and isolate x and you should get x = 18*sqrt(3). Again, this trick only works for 30-60-90 triangles.

Answer: 54

Step-by-step explanation:

63-9 you can't take 9 away from 3 so you must borrow, the 6 becomes a 5 and the 3 becomes 13. 13-9 is 4, bring the 5 down and you have 54.

Answer:

62 mph

Step-by-step explanation:

This is the same as y = x+13

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Explanation:

Let's find the slope

I'll use the first two rows as the (x1,y1) and (x2,y2) points

m = (y2-y1)/(x2-x1)

m = (19-18)/(6-5)

m = 1/1

m = 1

The slope is 1.

Now apply the point slope formula and solve for y

y - y1 = m(x - x1)

y - 18 = 1(x - 5)

y - 18 = x - 5

y = x-5 + 18

y = x + 13

f(x) = x + 13  is the final answer

As a check, note how something like x = 5 leads to...

f(x) = x+13

f(5) = 5+13 ... replace x with 5

f(5) = 18

We see that x = 5 leads to f(x) = 18. That verifies the first row. I'll let you check the remaining three rows.

The equation y = x+13 has slope 1 and y intercept 13.

Answer:

how many cups of what were sold

Step-by-step explanation:

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Answer:

180 is the answer

Step-by-step explanation:

Step-by-step explanation:

To find out areas of rectangles, you have to count the left side of the rectangle which is (12) and then count the bottom of the rectangle which is (15)

Then multiply 12 times 15 to find out the area

15 x 12= 180

what do you mean CDEF

and can I get brainliest?

Answer:

$6.40

Step-by-step explanation:

All you have to do is find 8% of 80 dollars. That means you do 8/100x80/1 which is equal to 32/5. Simplify this improper fraction to get $6.40. This means that 8% of 80 is $6.40.

Answer:

42 rivets=32ft of the bridge

1 ft of the bridge =42/32 rivets

2200 ft of the bridge =42/32×2200=2887.5

2887 and half

rivets that will be needed for the entire bridge.

Answer:

2 [tex]\frac{1}{20}[/tex]

Step-by-step explanation:

for question a)

It would be easier if you converted these to improper fractions (currently it is in the form of a proper fraction)

to convert to improper fraction, you would multiply the denominator (bottom no. of fraction) by the whole number , then add that with the numerator (top no. of fraction) and put the whole thing over the denominator.

E.g.

7 [tex]\frac{1}{4}[/tex] = 7x4 + 1 = 29

Thus, improper fraction would be [tex]\frac{29}{4}[/tex]

do same thing  for other one

thus , [tex]\frac{26}{5}[/tex]

now,

[tex]\frac{29}{4}[/tex] - [tex]\frac{26}{5}[/tex]

however, you can't do this as the denominators are not the same, so multiply them by a number which would give the a common denominator (20 would be the best option for common denominator)

[tex]\frac{145}{20} -\frac{104}{20}[/tex] = [tex]\frac{41}{20}[/tex]

convert back to mixed number

2 [tex]\frac{1}{20}[/tex]

Answer:

Step-by-step explanation:

a) Step1 : write in improper form

Step 2 : Find least common denominator

Step 3: Find equivalent fractions and then subtract

[tex]7\frac{1}{4}-5\frac{1}{5} = \frac{29}{4}-\frac{26}{5}\\[/tex]

            [tex]= \frac{29*5}{4*5}-\frac{26*4}{5*4}\\\\=\frac{145}{20}-\frac{104}{20}\\\\=\frac{145-104}{20}\\\\=\frac{41}{20}\\\\=2\frac{1}{20}[/tex]

b) Keep Change Flip method

[tex]4\frac{1}{4}[/tex] ÷ [tex]2\frac{1}{5} = \frac{17}{4}[/tex] ÷ [tex]\frac{11}{5}[/tex]

            [tex]=\frac{17}{4}*\frac{5}{11}\\\\=\frac{85}{44}\\\\=1\frac{41}{44}[/tex]

Answer:

Its A.

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

IM doing the test

Answer:

5

Step-by-step explanation:

15/3 - 4/3 = 11/3

15/3 = 5

The difference of a number 5 and 4/ 3 is 11/3.

Subtracting fractions include the subtraction of two or more fractions with the same or different denominators. Like fractions can be subtracted directly but for unlike fractions we need to make the denominators same first and then subtract them.

Given that, the difference of a number and 4/ 3 is 11/3.

Let the unknown number be x.

Here, x-4/3 =11/3

x= 11/3+4/3 (Transpose 4/3 to RHS of the equation)

To add like fractions, add the numerators and keep the denominator same. That is

x= 15/3

x=5

Therefore, the unknown number is 5.

To learn more about the subtraction of fractions visit:

https://brainly.com/question/5220474.

#SPJ2

Answer:

X : ___ 0 ____ 1 _____ 2 ______ 3

P(X) : _ 6/15 __ 5/15__ 3/15 ____ 1/15

Step-by-step explanation:

From the data, to produce a probability distribution for the data :

X : number of times blood is drawn ;

P(x) : probability that blood is drawn at X times

Hence, the probability distribution table for the data Given goes thus :

X : ___ 0 ____ 1 _____ 2 ______ 3

P(X) : _ 6/15 __ 5/15__ 3/15 ____ 1/15

Probability that blood is drawn 0 times = 6/15

Probability that blood is drawn 1 time = 5/15

Probability that blood is drawn 2 times = 3/15

Probability that blood is drawn 3 times = 1/15

(6/15 + 5/15 + 3/15 + 1/15) = 1

Answer:  y = 0.0005x+1

This is the same as saying y = (1/2000)x + 1

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

Explanation:

The blue line goes through (0,1) and (2000,2)

The slope is

m = (y2-y1)/(x2-x1)

m = (2-1)/(2000-0)

m = 1/2000

This says that each time we move up 1, we move to the right 2000 units.

Think of it as slope = rise/run = 1/2000

The slope 1/2000 means that each time you make 2000 soccer balls, it will cost you $1000. Keep in mind that y is in thousands (eg: y = 1 means 1000). This further implies that the marginal cost is ($1000)/2000 = $0.50 = 50 cents. The marginal cost is the cost to make one extra unit.

The fraction 1/2000 converts to the decimal form 0.0005 after using a calculator. So m = 0.0005 is the decimal form of the slope.

The y intercept of the blue line is b = 1 as this is the location where the blue line crosses the vertical y axis. The y intercept represents the fixed costs needed to set up production, for example: buying the machinery needed is a fixed cost.

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

Since m = 0.0005 and b = 1, we go from y = mx+b to y = 0.0005x+1

We could say y = (1/2000)x + 1, though I think it's probably easier to use a decimal in this case.

Answer:

Because the sum of the interior angles of a triangle is 180,

X=180-(65+35)

X=180-100=80

Answer:

1238

Step-by-step explanation:

hindi ko alam ask mo nalang sa mama mo hahaha baka sakaling alam niya yung sahot na tinatanong mo hahaha

Answer:

No

Step-by-step explanation:

Ill try though

Step-by-step explanation:

my dude search it up?

Answer:

28 ft²

Step-by-step explanation:

Hello There!

To solve for the area of an irregular shape we want to split the irregular shape into regular shapes

For this irregular shape we would split it into a square with a side length of 2ft and a rectangle with a length of 6ft and a width of 4ft ( width was found subtracting total height of irregular figure (6ft) from height of square (2ft) 6ft - 2ft = 4ft so the width would be 4ft)

now we can easily solve for the area of each individual shape

area of square -

the area of a square can simply be found by raising the side length to the power of 2

so

[tex]a =2^2\\2^2=4\\a=4ft^2[/tex]

so we can conclude that the area of the square is 4ft^2

Now we want to find the area of the rectangle

the area of a rectangle is simply equal to the width times the length

so

[tex]a=6*4\\6*4=24\\\\a=24ft^2[/tex]

so we can conclude that the area of the rectangle is 24ft^2

Finally we add the two areas together

24 + 4 = 28

thus meaning the area of the irregular figure is 28 ft²

Answer:

R=15 1/6

Step-by-step explanation:

You can add 5 and 1/6 to each side so -5 1/6+5 1/6= 0 so it cancels out therefore on the other side of the equal side you add 5 1/6+10 to get 15 1/6.

Answer:

r=25

Step-by-step explanation:

i did the test lol

Answer:

23

ewr

Step-by-step explanation:

Answer:

f(x) = 12x³ - 19x² + 17x - 17

Step-by-step explanation:

We can the numerator by multiplying the denominator by the quotient, and then adding the remainder.

We're given a denominator of 4x - 5

a quotient of 3x² - x + 3

and a remainder of -2

so the original numerator is:

(4x - 5)(3x² - x + 3) - 2

= 12x³ - 4x² + 12x - 15x² + 5x - 15 - 2

= 12x³ - 19x² + 17x - 17

Let's test that by dividing it by 4x -5 with long division:

[tex]\ \ \ \ \ \ \ \ \ \ 3x^2 - x + 3\\4x - 5\overline{)12x^3 - 19x^2 + 17x - 17}\\.\ \ \ \ \ \ \ \ \ \underline{2x^3 - 15x^2}\\.\ \ \ \ \ \ \ \ \ \ \ \ \ \ -4x^2 + 17x\\.\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \underline{-4x^2 + 5x} \\.\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 12x - 17\\.\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \underline{12x - 15}\\.\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 2R[/tex]

That matches, so we know our answer's right, and:

f(x) = 12x³ - 19x² + 17x - 17

Answer:

960

Step-by-step explanation:

12x10x16=1920

1920/2=960

Answer:

Volume of sphere = 130.9cm³

Step-by-step explanation:

Formula :

[tex] \frac{4}{3} \times \pi \: \times r^{3} [/tex]

We need the radius. 6.3 ÷2=3.15

[tex] \frac{4}{3} \times \pi \times 3.15 ^{3} [/tex]

=130.924303cm³

rounded to the nearest tenth

=130.9cm³

Answer:

-1.25  ± 0.90i  correct to the nearest hundredth

Step-by-step explanation:

-40x = 16x2 + 38

16x^2 + 40x + 38 = 0    Simplify by dividing by 2:

8x^2 + 20x + 19 = 0

Using the quadratic formula:

x = [ -b  ±√(b^2 - 4ac) ] / 2a

Plug in the coefficients of our equation:

x = [ -20 ±√(20^2 - 4*8*19) ] / 2*8

=  -5/4  ± √(-208)/16

= -5/4 ± 14.4222i/16

= -1.25  ± 0.90i  correct to the nearest hundredth.

Answer:

160

Step-by-step explanation:

total = 100%

we know,

55 % of total = 88

or, 55/100 * total = 88

so total = 160

Answer:

Alternative exterior angles --> <1 and <7

Corresponding angles --> <2 and <6

Alternative Interior angles --> <3 and <5

Hope this helps and stay safe, happy, and healthy, thank you :) !!