Find the measure of each missing angle.

Answer:

[tex]x=\frac{15}{4}=3\frac{3}{4}[/tex]

Equation:

[tex]\frac{2}{3}x+\frac{5}{6} =\frac{10}{3}[/tex]

_____________________________________

1. Group all constants on the right side of the equation

[tex]\frac{2}{3}\cdot x+\frac{5}{6}=\frac{10}{3}[/tex]

Subtract [tex]5/6[/tex] from both sides:

[tex]\frac{2}{3}x+\frac{5}{6}-\frac{5}{6}=\frac{10}{3}-\frac{5}{6}[/tex]

Combine the fractions:

[tex]\frac{2}{3}\cdot x+\frac{5-5}{6}=\frac{10}{3}-\frac{5}{6}[/tex]

Combine the numerators:

[tex]\frac{2}{3}\cdot x+\frac{0}{6}=\frac{10}{3}-\frac{5}{6}[/tex]

Reduce the zero numerator:

[tex]\frac{2}{3}\cdot x+0=\frac{10}{3}-\frac{5}{6}[/tex]

Simplify the arithmetic:

[tex]\frac{2}{3}\cdot x=\frac{10}{3}-\frac{5}{6}[/tex]

Find the lowest common denominator:

[tex]\frac{2}{3}\cdot x=\frac{10\cdot 2}{3\cdot 2}+\frac{-5}{6}[/tex]

Multiply the denominators:

[tex]\frac{2}{3}\cdot x=\frac{10\cdot 2}{6}+\frac{-5}{6}[/tex]

Multiply the numerators:

[tex]\frac{2}{3}\cdot x=\frac{20}{6}+\frac{-5}{6}[/tex]

Combine the fractions:

[tex]\frac{2}{3}\cdot x=\frac{20-5}{6}[/tex]

Combine the numerators:

[tex]\frac{2}{3}\cdot x=\frac{15}{6}[/tex]

Find the greatest common factor of the numerator and denominator:

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

Factor out and cancel the greatest common factor:

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

2. Isolate the x

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

Multiply both sides by inverse fraction 3/2:

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

Group like terms:

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

Simplify the fraction:

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

Multiply the fractions:

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

Simplify the arithmetic:

[tex]x=\frac{15}{2\cdot 2}[/tex]

Simplify the arithmetic:

[tex]x=\frac{15}{4}[/tex]

______________________

Why learn this

Linear equations cannot tell you the future, but they can give you a good idea of what to expect so you can plan ahead. How long will it take you to fill your swimming pool? How much money will you earn during summer break? What are the quantities you need for your favorite recipe to make enough for all your friends?

Linear equations explain some of the relationships between what we know and what we want to know and can help us solve a wide range of problems we might encounter in our everyday lives.

__________________________

Terms and topics

Answer:  3 3/4

Step-by-step explanation: i took the test (sorrry i cant tell why, im bad at explaining)  

Answer:

a=24

Step-by-step explanation:

Start by subtracting 8 from both sides giving:

1/4a+1/3a=14

Then find a common denominator between the two a terms which is 12 giving:

3/12a+4/12a=14

Combine the two terms:

7/12a=14

Then divide by 7/12 giving you a=24

Answer:

h ≈ 259.81

Step-by-step explanation:

i used the hexagon calculator

Answer:

150 sqrt 3        = 259.8076  units^2

Step-by-step explanation:

Interior angles of hexagon = 120 degrees ....now look at the Right  1/2 of the hexagon...  see illustration....this is a trapezoid...

One base is 10 units

the other labelled 'base' is

 10 cos 60    +   10 cos 60   + 10    = 20 units

the height of this trapezoid is  10 sin 60 = 10 * sqrt(3)/2 = 5 sqrt(3)

   the area of this trapezoid is then   1/2 ( 10+ 20) * 5 sqrt (3)  = 75 sqrt 3

there are TWO of these trapezoids in the hexagon so total area is then

   2 * 75 sqrt 3

        150 sqrt 3

Answer:

341.8801

Step-by-step explanation:

Answer:

36 ft^2

Step-by-step explanation:

Perimeter = 4 + 4 + 2 +2 = 12 feet

  12 feet x 3 feet high = 36 ft^2

Answer:

Then the new point is (-6,-5)

Step-by-step explanation:

Step-by-step explanation:

if you have any doubts or queries regarding the answer please feel free to ask

Answer:

6n-5

Step-by-step explanation:

Some different types of sequences

To find sequence patterns, often the sequences are arithmetic (adding by a constant amount) or geometric (multiplying by a constant amount).  

To test if something is a geometric sequence, find the quotient of (divide) adjacent terms.

To test if something is an arithmetic sequence, find the difference of (subtract) adjacent terms.

Finding the type of our sequence

Note the following:

19-13=6

13-7=6

7-1=6

So, to get each next term, add 6.  However, what is the nth term?

Finding an expression for our sequence

You'll be adding up "n" sixes to get there (expressed with multiplication, because multiplication is shorthand for repeated addition), but we need a starting point so that when n=1, the expression equals 1, and when n=2, the expression equals 7... and so on.  This starting point shifts the "6n" piece of our expression so that it lines up on the sequence.  I'm going to call this starting point "b" for the base that is supporting this sequence.

So the expression will look something like [tex]6n+b[/tex]

Knowing that the expression needs to equal 1 when n=1, we can set up an equation and solve for "b".

[tex]6n+b=n^{\text{th}} \text{ term}\\6(1)+b=(1)\\6+b=1\\(6+b)-6=(1)-6\\b=-5[/tex]

So, the expression for the nth term of the sequence is [tex]6n-5[/tex]

Verifying

To verify that the expression we found is right, we can test our expression for each of the terms we do know:

The first term (n=1) is 1

[tex]6n+b=n^{\text{th}} \text{ term}\\[/tex]

[tex]6(1)-5 \overset{?}{=} (1)[/tex]

[tex]6-5 \overset{?}{=} 1[/tex]

[tex]1 \overset{\checkmark}{=} 1[/tex]

The second term (n=2) is 7

[tex]6n+b=n^{\text{th}} \text{ term}\\[/tex]

[tex]6(2)-5 \overset{?}{=} (7)[/tex]

[tex]12-5 \overset{?}{=} 7[/tex]

[tex]7 \overset{\checkmark}{=} 7[/tex]

The third term (n=3) is 13

[tex]6n+b=n^{\text{th}} \text{ term}\\[/tex]

[tex]6(3)-5 \overset{?}{=} (13)[/tex]

[tex]18-5 \overset{?}{=} 13[/tex]

[tex]13 \overset{\checkmark}{=} 13[/tex]

The fourth term (n=4) is 19

[tex]6n+b=n^{\text{th}} \text{ term}\\[/tex]

[tex]6(4)-5 \overset{?}{=} (19)[/tex]

[tex]24-5 \overset{?}{=} 19[/tex]

[tex]19 \overset{\checkmark}{=} 19[/tex]

The complete question is

"The equation c = 35h + 60 describes a plumber's charges, c, for a job that takes h hours. Which statement is correct?

a. The domain of this function represents the total cost for a job

b. H is a function of C

c. The painter charges a $35 service fee in addition to an hourly rate

d. The painters hourly rate is $35.00"

The equation c = 35h + 60 describes a plumber's charges, c, for a job that takes h hours. So, the correct option is D. The painters hourly rate is $35.00

Function is a type of relation, or rule, that maps one input to specific single output.

The equation c = 35h + 60 describes a plumber's charges, c, for a job that takes h hours.

The fixed fee, or service fee, is $60.

$35 is the hourly fee since in the function, it is 35 that is multiplied by the number of hours.

So, the correct option is D. The painters hourly rate is $35.00

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The probability that the spinner will land on white for all three spins is 1/216

The probability is given as:

P(White) = 1/6

The event that the spinner lands on white all three times is:

White White White

The probability is then represented as:

P  = P(White)^3

So, we have:

P = (1/6)^3

Evaluate

P =1/216

Hence, the probability that the spinner will land on white for all three spins is 1/216

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Answer:

Carpet costs = 300£

Step-by-step explanation:

• First calculate the area of the floor:

Area of floor = length x width

                     = 5m² x 3m²

                     = 15m²

• As one m² of carpet costs £20, 15m² of carpet costs:

15 x 20

= 300£

Answer: x = 12

Step-by-step explanation: The given triangle is an equilateral triangle. Equilateral triangles have all angles and all sides equal. Thus, let's solve for x knowing all 3 equations are equal. For this, only 2 equations are necessary.

5x - 22 = 4x - 10

Adding 22 to both sides, we get:

5x = 4x + 12

Subtracting 4x to 5x, we get:

x = 12.

Thus 5*12 - 22 = 38, and 4*12 - 10 = 38, and so is 3*12 + 2 = 38. Thus, we know this is correct.

Answer:

x = 12

Step-by-step explanation:

Hello!

All three angles are congruent, indicating that this is an equilateral triangle.

The rules of this triangle say that all sides are congruent.

We can solve for x by setting any 2 sides equal to each other. I'm picking AB and BC.

The value of x is 12.

The attached graph represents the solution set of [tex]3e^x > \frac 12^x[/tex]

The complete options are not given.

So, I would plot the graph that represents the solution set

The inequality is given as:

[tex]3e^x > \frac 12^x[/tex]

Start by splitting the inequalities as follows:

[tex]f(x) > 3e^x[/tex]

[tex]g(x) > \frac 12^x[/tex]

The above means that we plot the graphs of f(x) and g(x) to represent the solution set

See attachment

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Answer:

80 m is distance traveled

Step-by-step explanation:

if object moves at 20m/s, then in 4 seconds the expression 20 x 4 is used to get 80. 80 m traveled

Answer:

In the given Triangle problem, the three options are:

1.  m∠5 + m∠6 = 180°

2. ∠2+ ∠3 = ∠6

3. m∠2 + m∠3 + m∠5 = 180°

Step-by-step explanation:

Concept: Consider Δ ABC with Exterior angles ∠1, ∠4 and ∠6.

Use the Exterior angle Property of Triangle which says that an exterior angle of a triangle is equal to the sum of the opposite interior angles.

For Exterior angle ∠1 we have:

∠1 = ∠5 + ∠3

Similarly, for Exterior ∠4 we have:

∠4 = ∠5 + ∠2

Similarly, for Exterior ∠6 we have:

∠6 = ∠2 + ∠3

Now, use the Triangle Sum Property which states that in a triangle sum of the measures of angles is equal to 180°

m∠2 + m∠3 + m∠5 = 180°

Linear Pair:

The measure of a straight angle is 180°, so a linear pair of angles must add up to 180°.

m∠5 + m∠6 = 180°

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Answer:

10. Ray ED and Ray EF (two rays)

11. DE and EF (two line segments)

Step-by-step explanation:

hope this helped

Answer:

Ray ED and Ray EF

DE and EF

Step-by-step explanation:

Answer:

a. 73:100

b. 27:73

Step-by-step explanation:

total: 100

number remaining: 27

number taken: 100 - 27 = 73

a. taken:total = 73:100

b. remaining:taken = 27:73

#a

total milk cartons used=100-27=73

So the ratio is

#b

It's already mentioned in question

An equation is formed of two equal expressions. The value of r in the given equation is 6.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The solution for the value of r in the given equation will be,

5r - r - 9 = 15

5r - r - 9 + 9 = 15 + 9

4r = 24

r = 6

A.) The first step is to Use the addition property of equality. Thus, the correct option is B.

B.) The value of r in the given equation is 6.

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Answer: Answer below.

Step-by-step explanation: Attached is my work. Hope it is helpful!

Answer:

cos B = 0.4706

Step-by-step explanation:

The cosine of an angle in a right-angled triangle is the ratio of its adjacent side and the hypotenuse, so:

 [tex]cos B = \frac{adjacent}{hypotenuse}\\\\cos B = \frac{8}{17} \\\\cos B = 0.4706[/tex]

Option B

The square for the  equation:  [tex]y=2x^{2} + 12x +1[/tex] is [tex]y=2(x+3)x^{2} -17[/tex]

The square for the  equation:  [tex]y=4x^{2} +48x-10[/tex] is [tex]y=4(x+6)x^{2} -154[/tex]

a)

[tex]y=2x^{2} +12x +1[/tex]

[tex]y = 2[(x^{2} + 6x)] + 1[/tex] ( taking common)

[tex]y = 2[(x+3)^{2} - 9] + 1[/tex] ( adding and subtracting 9 to make a square term

[tex]y = 2(x+3)^{2} - 18 + 1[/tex] ( multiplying by 2)

[tex]y=2(x+3)x^{2} -17[/tex]

b)

[tex]y=4x^{2} +48x-10[/tex]

[tex]y = 4[(x^{2} + 12x)] - 10[/tex]  (taking 4 common)

[tex]y = 4[(x+6)^{2} - 36)] - 10[/tex] (adding and subtracting 36)

[tex]y = 4(x+6)^{2} - 144 - 10[/tex](multiplying by 4)

[tex]y=4(x+6)x^{2} -154[/tex]

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Negative

Step-by-step explanation:

To multiply the fractions, like

[tex] \frac{1}{4} \times \frac{1}{9} [/tex]

Multiply the top,

then multiply the bottom.

[tex] \frac{1}{4} \times \frac{1}{9} = \frac{1 \times 1}{4 \times 9} = \frac{1}{36} [/tex]

Try to use a calculator if you aren't arithmetic heavy, but I suggest you to try to remember them because they are going to be helpful for courses like Algebra, Calculus, Statistics, etc.

To divide fractions, like

[tex] \frac{ \frac{1}{5} }{ \frac{1}{8} } [/tex]

You take the top number,

[tex] \frac{1}{5} [/tex]

Then you flip the bottom number,

[tex] \frac{8}{1} [/tex]

Then multiply the two

[tex] \frac{1}{5} \times \frac{8}{1} = \frac{8}{5} [/tex]

And that is your answer. Comment if you need more clarification

Step-by-step explanation:

Most standard rain gauges have a wide funnel leading into the cylinder and are calibrated so that one-tenth of an inch of rain measures one inch when it collects inside.

Answer:

30

Step-by-step explanation:

P=2(b+h)=2·(10+5)=30

Answer:

dSutlrysl07tris5eiruwf3rtst47er747y3utgxgudjdudufnlgjfngvi

Step-by-step explanation:

I am not sure I can see the room limitations.

what I see is that the kitchen is one large rectangle from

(-8, 8) to (0, 0).

the rec room is Amado one large rectangle from

(5, 6) to (8, -7).

I am basing the rest in this.

for the area calculations, please consider that the area of a rectangle is length × width, and the area of a triangle is half of the rectangle it splits in half with its baseline (as diagonal).

A)

area 1 =

rectangle (-8, 8) to (-5, 3)

plus

half of the rectangle (-5, 8) to (-3, 3)

3×5 + 1/2 × 2×5 = 3×5 + 1×5 = 15 + 5 = 20 yd²

area 2 =

half of the rectangle (-5, 8) to (-3, 3)

plus

rectangle (-3, 8) to (0, 3)

1/2 × 2×5 + 3×5 = 20 yd²

area 3 = area 4 =

half of the rectangle (-8, 3) to (0, 0)

1/2 × 8×3 = 4×3 = 12 yd²

B)

the total area of the kitchen is the sum of all 4 areas

20 + 20 + 12 + 12 = 64 yd²

we can also calculate this in general, seeing that the general dimensions of the kitchen are 8×8 : from (-8, 8) to (0, 0).

8×8 = 64 yd²

An equation is formed of two equal expressions. The number of sections that Mario can cut from the rope is 6.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Let the number of 8 1/4 - inch sections of rope Mario can cut from the rope be x.

Since the total length of the rope is 7 feet, which is equal to 84 inches(1 foot=12 inches), the instructions are to use 34.5 inches of the rope to tie a tarp on top of the tent. Therefore, the rope for the 8 1/4 inches section is,

Rope left = 84 inches - 34.5 inches

Since the length of a single section is 8 1/4 inches(8.25 inches), therefore the number of sections that can be made from the remaining section is,

The number of sections, n = Rope left/8.25 inches

                                             = (84 -34.5)inches /8.25 inches

                                              = 6

Hence, the number of sections that Mario can cut from the rope is 6.

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Answer:

The value of x is 117°  by using Alternative interior angle theorem

Step-by-step explanation:

Alternative interior angle theorem: It states that the angles made by transverse between two parallel lines are congruent.

as in figure

Angle A = 42°

Angle B = 108°

Angle C = x

Angle D = 51°

draw two parallel lines passing through B and C .

According to Alternative interior angle theorem angle B is written as 42° + 66°

and angle C is written as x1 + x2 .

Now x1 = 51° as x1 and D are alternative angles

And similarly x2 = 66°

As x = x1 + x2

Therefore x = 51° + 66° = 117°

The value of x is 117°

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