Solve these questions for 18 points (Solving Integers)

Answer:

Step-by-step explanation:

Answer:

x=18.7

Step-by-step explanation:

x+17+5x+10+4x-34=180

10x-7=180

10x=187

x=18.7

all angles in a trianlge add up to 180 degrees

Answer:

x = 17

Step-by-step explanation:

Since all angles of a triangle equal to 180 we can make this equation:

x + 17 + 6x + 10 + 4x - 34 = 180

11x - 7 = 180

11x = 187

x = 17

9514 1404 393

Answer:

  m∠A = 81 9/11°

  m∠P = 98 2/11°

Step-by-step explanation:

Supplementary angles have a total of 180°, so we have ...

  m∠A +m∠P = 180°

  2/3x° +4/5x° = 180°

  22/15x° = 180°

  x = 122 8/11 . . . . . . multiply by 15/22

Then the angles are ...

  m∠A = (2/3)(122 8/11)°

  m∠A = 81 9/11°

  m∠P = (4/5)(122 8/11)°

  m∠P = 98 2/11°

_____

Alternate solution

The fraction of 180° that is ∠A is ...

  (2/3x°)/(2/3x° +4/5x°) = (10/15)/(10/15 +12/15) = 10/22 = 5/11

  m∠A = (5/11)(180°) = 81 9/11°

  m∠P = 180° -m∠A = 98 2/11°

Answer:

m∡A = 81.8°

m∡P = 98.2°

Step-by-step explanation:

2/3x + 4/5x = 180

multiply each side by 15 to eliminate fractions

10x + 12x = 2700

22x = 2700

x = 122.7

∡A = 2/3 (122.7) = 81.8

∡P = 4/5 (122.7) = 98.2

Answer:

11.3 and more

Step-by-step explanation:

Answer:

pee

Step-by-step explanation:

Answer:

the answer is 67.56

Step-by-step explanation:

Answer:

She bought 11 Flibbertigibbets

and

5 Watchamajiggers

Step-by-step explanation:

Answer:

Smaller

Step-by-step explanation:

Example: say the original size is 100

increasing 100 by 1/5 is the same as increasing 100 by 20, so the new size is 120

reducing 120 by 1/5 is the same as reducing 120 by 24, so now the new size is  96.

100>96

The relation which is a function is given by the set relation

A = { ( 0 , 4 ) , ( 1 , -4 ) , ( 2 , 4 ) , ( 3 , 4 ) , ( 4 , -4 ) }

The function rule is the relationship between the input or domain and the output or range. A relation is a function if and only if there exists one value in the range for every domain value.

A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

Given data ,

Let the function be represented as A

Now , the value of A is

Let the values of x be x = { 0 , 1 , 2 , 3 , 4 }

Now , the values of y = { 4 , -4 , 4 , 4 , -4 }

And , relation is a function if and only if there exists one value in the range for every domain value.

So , the domain are all having significant and definite ranges

Therefore , the relation is A = { ( 0 , 4 ) , ( 1 , -4 ) , ( 2 , 4 ) , ( 3 , 4 ) , ( 4 , -4 ) }

Hence , the function is denoted by A = { ( 0 , 4 ) , ( 1 , -4 ) , ( 2 , 4 ) , ( 3 , 4 ) , ( 4 , -4 ) }

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Answer:

x=45

Step-by-step explanation:

An entire triangle is 180 degrees and you already know that one angle is 90 degrees. 180 - 90 is 90. Now you have the equation 2x=90.

You then divide each side by 2 to get the x by itself which leaves you with x=45.

Answer:

if I did my math right it's 45 if not please fix me

Step-by-step explanation:

First thing is the the sides are congruent meant the angles have to be the same.

Next is the box indicates 90°.

Last thing is that every triangle is 180°

so if I did this right the equation is 2x+90=180

and using algebra in this you eliminate the 90 by subtract because - is the opposite of + which cancels itself and leaving the total with 90.

Then divide the 90 by 2 as it cancels out 2x leaving the answer with x=45

I hope this helps you

Answer:

45.5

Step-by-step explanation:

You do the linear length multiplied by the longitudinal length

The distance across the lake is 320 ft.

Given is a scenario of a lake, a survey crew has laid out the concept of similar triangles to find the distance across the lake.

The figure shows the base of the larger triangles is the distance across the lake. [please refer to the figure attached]

The dimensions of the imaginary triangles are 30 ft, 30 ft, 40 ft and 240 ft, 240 ft, x ft.

Here, x is the distance across the lake which we are asked to find.

Using the definition of the similar triangles,

Two triangles are considered similar if their corresponding angles are equal, and the ratios of the lengths of their corresponding sides are equal.

So,

[tex]\frac{240}{30} = \frac{x}{40}[/tex]

[tex]x = \frac{240 \times 40}{30}[/tex]

x = 320

Hence the distance across the lake is 320 ft.

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9514 1404 393

Answer:

Step-by-step explanation:

1. 12 of the 28 students were girls, so the fraction is ...

  12/28 = 3/7 . . . fraction that were girls

__

2. The total of 13 feet of wood, when divided into 6 equal parts, gives 13/6 = 2 1/6 feet per part. 1/6 ft = 2 inches.

Leonard used 2 feet 2 inches of wood for each birdhouse.

Answer:

3/4

Step-by-step explanation:

The GCF of 42 and 56 is 14. If you divide both the numerator and the denominator by 14 we get 3/4 = 0.75 or 75%

Answer: 3/4

Step-by-step explanation:

42 divided by 14 is 3

54 divided by 14 is 4

Answer:

D

Step-by-step explanation:

The others don't work as it would if it was the older men

Answer: The total number of different types of labels will the manufacturers have to produce = 24.

Step-by-step explanation:

Given: Choices for flavours = 4

Choices for sugar = 2  {either sugar or sugar free}

Choices for the qunatity = 3

By Fundamental counting principle,

Total number of different types of labels will have to produce = (Choices for flavors) x (Choices for sugar)x (Choices for the quantity )

= 4 x  2x 3

=24

Hence, the total number of different types of labels will the manufacturers have to produce = 24.

Answer:

Step-by-step explanation:

-2              2

3(2)           -3(2)

Answer:

y = 340e^0.0427276t ; 908

Step-by-step explanation:

Given that :

t = time in days since study began

Number of bacteria after 11 days = 544

y = number of bacteria at time t

Exponential growth model:

y = ae^rt

Where a = initial amount ; r = Growth rate

y = 544 ; t = 11 ; a = 340

544 = 340*e^11t

544/340 = e^11t

1.6 = e^11t

Take the In of both sides

In(1.6) = 11t

0.4700036 = 11t

t = 0.4700036 / 11

t = 0.0427276

y = 340e^0.0427276t

Number of bacteria after 23 days :

Using the formula above :

t = 23

y = 340e^0.0427276(23)

y = 340 * 2.6717529

y = 908.39600

y = 908

The required formula is [tex]y = 340e^{0.0427}[/tex]

908 bacteria are there 23 days after the beginning of the study .

Given that,

A certain culture of bacteria has a population of 340.

The population grows according to a continuous exponential growth model. After 11 days, there are 544 bacteria.

We have to find,

Write a formula relating y tot. Use exact expressions to fill in the missing parts of the formula.

How many bacteria are there 23 days after the beginning of the study.

According to the question,

And let y be the number of bacteria at time,

t = time in days since study began

Number of bacteria after 11 days = 544

y = number of bacteria at time t

Then,

Exponential growth model:

[tex]y = a.e^{rt}[/tex]

Where, a = initial amount ; r = Growth rate

y = 544 ; t = 11 ; a = 340

Then,

[tex]544 = 340.e^{11t}\\\\\dfrac{544}{340} = e^{11t}\\\\1.6 = e^{11t}\\\\Taking \ log \ on \ both \ sides,\\\\ln(1.6) = 11t\\\\0.47 = 11t \\\\t = \dfrac{0.47}{11}\\\\t = 0.0427[/tex]

The required formula is [tex]y = 340e^{0.0427}[/tex]

[tex]y = 340e^{0.0427}[/tex]

Where, t = 23

[tex]y = 340e^{0.0427276(23)}\\\\y = 340 \times 2.6717529\\\\y = 908.39600\\\\y = 908[/tex]

Therefore, 908 bacteria are there 23 days after the beginning of the study .

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Answer:

Solving Two-Step Equations

1) First, add or subtract both sides of the linear equation by the same number.

2) Secondly, multiply or divide both sides of the linear equation by the same number.

3)* Instead of step #2, always multiply both sides of the equation by the reciprocal of the coefficient of the variable

Answer:

The answer is "this statement is not true".

Step-by-step explanation:

It is true because it can be achieved by using the initiation method. (Or at even a look, as n is still n=2m for the whole m, and the same number is 8n=8* (2*m)=2*(8*m). So it's confirmed !! )

Now the opposite declaration says, "If 8n would be an even amount then n is an even number", that's why the statement is not true.

An easy way of demonstrating why an argument also isn't valid is to show an example it against. Take into consideration the 24. 24=8*3. i.e. the shape is 8n, where it is n=3. Of course, 24 is also an equivalent number, but n=3 is an odd number here. So, we at least this one event, wherein the opposite statement could be sustained. (q.e.d).  

Note:- "8n would be an even number per each integer n." is true since 8n=2*(4n), even for all integer n.

Answer:

x > 17

Step-by-step explanation:

Add 8 to both sides:

6x - 8 > 4x + 26

6x > 4x + 34

Subtract 4x from both sides:

2x > 34

Divide each side by 2:

x > 17

So, the solution is x > 17

⇢ 6x - 8 > 4x + 26

⇢ 6x > 4x + 26 + 8

⇢ 6x > 4x + 34

⇢ 6x - 4x > 34

⇢ 2x > 34

⇢ x > 34/2

⇢ x > 17

Hence, solution is x > 17.

Answer:

⅙ pitcher

Step-by-step explanation:

½ of ⅓ pitcher = ½ × ⅓ pitcher = ⅙ pitcher

Answer:1/4

Step-by-step explanation:

2/8 = 1/4

2/8 over 2 is 1/4

Answer:

Sarah should produce four tons of coffee and total cost for four ton is $6,000.

Step-by-step explanation:

According to the scenario, calculation of the given data are as follows,

Selling price per ton = $2,400

Cost of production is increasing by $600 for each ton.

So, Cost of production first ton = $600

Cost of production for second ton = $600 + $600 = $1,200

Similarly, Cost of production for third ton = $1,200 + $600 = 1,800

Cost of production of fourth ton = $1,800 + $600 = $2,400

Here, Sarah can produce coffee till selling price = cost of production.

As, cost of production of four ton = selling price, then Sarah can produce only four tons of coffee.

Total cost for four ton coffee = $600 + $1,200 + $1,800 + $2,400

= $6,000

Sarah can produce 4 tons of coffee and the total cost of the production is $6000 and this can be determined by using the arithmetic operations.

Given :

The following steps can be used in order to determine the total amount of coffee (in tons) should Sarah produce and the total cost of her coffee production:

Step 1 - Remember that Sarah can produce coffee unitil selling price is equal to the cost of production.

Step 2 - According to the given data, each additional ton of coffee costs $600 more to produce.

Step 3 - From the above steps, it can be concluded that Sarah can produce 4 tons of coffee because the cost of 4 tons of coffee is equal to the selling price.

[tex]600\times 4 = $2400[/tex]

Step 4 - So, the total cost of producing four tons of coffee is:

Total Cost = 600+ 1200 + 1800 + 2400

Total Cost = $6000

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9514 1404 393

Answer:

  y = -1/2x -2

Step-by-step explanation:

The given line has slope 2, so the perpendicular line will have slope -1/2, the negative reciprocal of the given slope.

The y-intercept is given as -2, so the line's equation in slope-intercept form is ...

  y = mx +b . . . . line with slope m and y-intercept b

  y = -1/2x -2

9514 1404 393

Answer:

  a) x = -3

  b) y = (28/27)x -27

Step-by-step explanation:

a) College street has a slope of 0, so is a horizontal line. 2nd Ave is perpendicular, so is a vertical line, described by an equation of the form ...

  x = constant

For 2nd Ave to intersect the point (-3, 1), the constant must match that x-coordinate. The equation is ...

  x = -3

__

b) Since Ace Rd is perpendicular to Davidson St, its slope will be the opposite reciprocal of the slope of Davidson St. The slope of Ace Rd is ...

  m = -1/(-27/28) = 28/27

Using the point-slope equation for a line, we can model Ace Rd as ...

  y -y1 = m(x -x1)

  y -1 = (28/27)(x -27)

  y = (28/27)x -27

Answer:

70

Step-by-step explanation:

Given that:

There are twelve (12) lines in a direction and another nine 9 lines in another direction.

If we draw the above illustration out, we will realize that we will have 11 squares by 8 squares.

i.e these 11 squares are 11 inches apart.

Hence, the length of their grid = 11  inches × 11 inches = 121  inches²

Thus, for 12 in by 12 in tiles; we will have:

= [tex]\dfrac {121}{12}[/tex]

= [tex]10 \dfrac{1}{12}[/tex]

This implies that there are 10 files with just [tex]\dfrac{1}{2}[/tex] inch gap in length.

Similarly, for 8 squares and 11 inches apart;

The width = 8 inches × 11 inches = 88 inches²

Thus; the 12 in tiles needed = [tex]\dfrac{88}{12}[/tex]

= [tex]7 \dfrac{1}{3}[/tex]

It signifies that there are 7 tiles with [tex]\dfrac{1}{3}[/tex] inch gap in width.

Thus, the least number of tiles required = 10 × 7 = 70

Answer:

216 m

Step-by-step explanation:

12/4= x/6

3=x/6

x=3x6

length= 18

area=length x width

12x18=216

Answer:

4

Step-by-step explanation:

12 is over 10 and 8