-1/2(2x-8) distribution

9514 1404 393

Answer:

Step-by-step explanation:

These are two "special triangles." The ratios of side lengths are numbers not difficult to remember. They can save a lot of work in problems like this.

Ratio of side lengths in 45°-45°-90° isosceles right triangle: 1 : 1 : √2.

Ratio of side lengths in 30°-60°-90° right triangle: 1 : √3 : 2.

__

The side marked x has the same length as the side marked 14√2.

  x = 14√2

The unmarked hypotenuse of both triangles is √2 times the marked side length, so is (14√2)(√2) = 28.

The side marked y is half the length of the hypotenuse of that triangles so is ...

  y = 28/2

  y = 14

And the side marked z is √3 times the short side of the 30°-60°-90° triangle, so is ...

  z = 14√3

_____

Alternate solution

The mnemonic SOH CAH TOA can help you remember trig relationships. Here, 14√2 is opposite the given 45° angle, and x is adjacent. The trig relation is ...

  Tan = Opposite/Adjacent

  tan(45°) = 14√2/x

  x = 14√2/tan(45°) = 14√2

__

To find y or z, we need to know the length of the hypotenuse in the 45° triangle. The given side is opposite the angle, so we can use the sine relation:

  Sin = Opposite/Hypotenuse

  hypotenuse = 14√2/sin(45°) = 28

Now, we can find y and z:

  sin(30°) = y/hypotenuse

  y = (28)sin(30°) = 14

  cos(30°) = z/hypotenuse

  z = (28)cos(30°) = 14√3

Answer:

least common multiple of 20 and 3? it would be 60.

Answer:

3/4+n=-5/2

n=-10/4-3/4

n=-13/4

Step-by-step explanation:

Answer:

n = -13/4

Step-by-step explanation:

-5/2 equals 3/4+ n =>  -5/2 = 3/4+ n

Recognize that the LCD here is 4.  Multiply all three terms by 4, obtaining:

-10 = 3 + 4n

Combining the constants results in

-13 = 4n, so that  n = -13/4

Answer:

Step-by-step explanation:

$120

per hour Sandy earns (together with commission):

8 + 0.15*8 = 1.15*8 = $9.2 per hour

for the 74 hours worked she will earn total of:

74*9.2 = $680.8

A $592 is the closest.

Answer:

$22

Step-by-step explanation:

17.99 round up so 18

a second large pizza is 14 dollars off of the original price of 18 so 4

18+4 is 22

so 2 large pizzas would cost $22

Answer: 4 boxes.

Step-by-step explanation:

We know that each box has 18 ounces of cereal.

We know that:

1 lb = 16 oz

Then:

1 = (1lb/16oz)

Then we can write:

18 oz = 18oz*(1lb/16oz) = (18/16) lb

This means that each box has (18/16) pounds of cereal.

Now, how many boxes we need to buy if we want to have at least 4 pounds of cereal?

If we buy N boxes, we will have N*(18/16) lb boxes of cereal.

Let's find N such that:

N*(18/16) lb = 4lb

N = 4*(16/18) = 3.56

But you can not have a 0.56 of a box, so we should round our number up to the next whole number, then we get:

N = 4.

She should buy 4 boxes.

Answer:

4

Step-by-step explanation:

Good Luck

Answer:

Calzones are $ 8 and an Empanada costs $12

Step-by-step explanation:

2x+3y=52

4x+3y=68

Multiply by -1

-2x-3y=-52

4x+3y=68

combine

2x=16

x=8

plug in 8

4(8)+3y=68

32+3y=68

3y=36

y=12

Step-by-step explanation:

step 1. 2c + 3e = 52, 4c + 3e = 68.

step 2. this is a system of equations. solve the system.

step 3. subtract the 1st equation from the 2nd.

step 4. 2c = 16, therefore c = 8.

step 5. 2(8) + 3e = 52. 3e = 36. e = 12.

step 6. calzones = 8, empanadas = 12.

Answer:

[tex]Red\ Fraction = \frac{5}{12}[/tex]

Step-by-step explanation:

Given

[tex]Red:Blue = 5 : 7[/tex]

Required

Determine the fraction of red

To do this, we make use of:

[tex]Red\ Fraction = \frac{Red}{Red + Blue}[/tex]

This gives:

[tex]Red\ Fraction = \frac{5}{5+7}[/tex]

[tex]Red\ Fraction = \frac{5}{12}[/tex]

Answer:

Explanation:

Find The Least Common Multiple Of 4 And 2: 4

¹³⁄₄k · 4 + ½k = ¹¹⁄₄ · 4

Simplify

15k = 11

Divide Both Sides By 15

15k / 15 = 11 / 15

Answer:

(5,4)

Step-by-step explanation:

To find midpoint you just find out how far apart the points are and divide it by half. For example our x values are 9 and 1. 9 and 1 are 8 points away. Half of 8 is four so 9-4 is 5. Remember midpoint is the MIDDLE.

Answer:

x = 12 and 1/3

Step-by-step explanation:

Answer:

i think 8p+tLess equal to 184

The inequality system may be used to determine the maximum number of pies and tarts the baker is capable of producing is t ≤ 40 and 8p + t ≤ 184.

It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.

We need to define variables initially in this situation. Thus, we have the number of tarts and the number of pies, which are p and t respectively.

Apples are needed for each tart, abbreviated t, and for each pie, abbreviated p.

It is given that every day, a supply of 184 apples is sent to the baker

8p + t ≤ 184

The baker only produces up to 40 tarts every day as a result

t ≤ 40

Thus, the inequality system may be used to determine the maximum number of pies and tarts the baker is capable of producing is t ≤ 40 and 8p + t ≤ 184.

Learn more about inequality here:

brainly.com/question/19491153

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Answer:

A) 45

B) 80

C) 50

Step-by-step explanation:

When the terminal side is in the first quadrant (angles from 0° to 90°), our reference angle is the same as our given angle. This makes sense, since all the angles in the first quadrant are less than 90°.

When the terminal side is in the second quadrant (angles from 90° to 180°), our reference angle is 180° minus our given angle.

When the terminal side is in the third quadrant (angles from 180° to 270°), our reference angle is our given angle minus 180°.

When the terminal side is in the fourth quadrant (angles from 270° to 360°), our reference angle is 360° minus our given angle.

The pounds of potatoes that Mrs. Hanson needs is 3 9/16 pounds.

A mixed number is number that consists of a whole number and a proper fraction. A proper fraction is a fraction in which the numerator is less than the denominator. An example of a mixed number is 2 3/8.

In order to determine the pounds of potatoes that Mrs. Hanson needs, multiply 2 3/8 by 1 1/2. Multiplication is the mathematical process that is used to determine the product of two or more numbers. The sign that is used to represent multiplication is x.

Pounds of potatoes that Mrs Hanson needs = 2 3/8 x 1 1/2

Pounds of potatoes that Mrs Hanson needs = 19/8 x 3/2

Pounds of potatoes that Mrs Hanson needs = 57 / 16 = 3 9/16 pounds

To learn more about multiplication, please check: https://brainly.com/question/13814687

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Answer:

1 4/5 pounds

Step-by-step explanation:

15-6= 9

9-4=5

3/5+4/5=7/5 or 1 2/5

5-1=4

4-2/5=3 3/5

half of 3 is 1.5 or 1 5/10

3/5=6/10 half of 6/10 is 3/10

3/10+5/10= 8/10

simplify 1 8/10= 1 4/5

Answer:

$3.25 for 1 pound of coleslaw

Step-by-step explanation:

i think,.

Answer:

[tex]p = 85000 - 1700x[/tex]

Step-by-step explanation:

Given

[tex]Initial\ Fish = 85000[/tex]

[tex]Rate = 1700[/tex]

Required

Determine the equation

For 1 ton, there is a reduction of 1700 fishes

This implies that:

For x tons, there will be a reduction of 1700x fishes

So, the function is:

[tex]p = Initial\ Fishes - Rate * x[/tex]

We used minus because the number of fishes reduced.

So, we have:

[tex]p = 85000 - 1700*x[/tex]

[tex]p = 85000 - 1700x[/tex]

Hence, the function is: [tex]p = 85000 - 1700x[/tex]

Answer:

La respuesta podría ser 80000 y en cualquier momento.

Answer:

Gavin is incorrect. Divide 1/3 by 4, or multiply by 1/4. each friend gets 1/12 of the cake

Step-by-step explanation:

Answer:

(-2, 6)

Step-by-step explanation:

Trust me, I know

Answer:

a. 7x^2-15=32x

Step-by-step explanation:

a standard form quadratic equation is written as ax^2+bx+c=0

7x^2-15=32x can be rewritten into 7x^2-32x-15=0 by subtracting 32x on both sides.

options b and c don't work  because they include another variable, y

option d is a linear equation, not a quadratic

Answer:

B. 264π units³

Step-by-step explanation:

Volume of the cone = ⅓πr²h

Where,

r = 6

h = 22

Plug in the values

Volume = ⅓×π×6²×22

Volume = ⅓×π×36×22

Volume = 264π units³

Answer:

x=9

Step-by-step explanation:

-3x-12=-39    Add the like terms (if you add 12 to negative 12 it cancels out)

     +12  +12

-3x=-27        Now divide

/-3    /-3

x=9

You forgot the image attached to the question. I will edit my answer after you edit the question

Answer:

1. a

2. [tex]f^{-1} (x)=\frac{x}{2} +2[/tex]

Step-by-step explanation:

1. Since there is one value of y for every value of x in (−1,0),(−4,5),(3,2),(−3,5), this relation is a function.

2. To find the inverse, interchange the variables and solve for y.

[tex]f^{-1} (x)=\frac{x}{2} +2[/tex]

Answer:

300 %

Step-by-step explanation:

120 is 3 times 40, so in other words that’s 300 % of 40.

Generally, divide the part of interest (120) by total (40). In most common use case the total is larger than the part of interest unlike here.