A guy wire runs from the top of a cell tower to a metal stake in the ground. Jayden places a 8-foot tall pole to support the guy wire. After placing the pole, Jayden measures the distance from the stake to the pole to be 5 ft. He then measures the distance from the pole to the tower to be 21 ft. Find the length of the guy wire, to the nearest foot.

[tex] \sqrt{128} \\ = \sqrt{2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2} \\ = \sqrt{ {2}^{2} \times {2}^{2} \times {2}^{2} } \\ = 2 \times 2 \times 2 \\ = 8[/tex]

[tex] \sqrt{48} \\ = \sqrt{2 \times 2 \times 2 \times 2 \times 3} \\ = \sqrt{ {2}^{2} \times {2}^{2} \times 3 } \\ = 2 \times 2 \sqrt{3} \\ = 4 \sqrt{3} [/tex]

[tex] \sqrt{300} \\ = \sqrt{2 \times 2 \times3 \times 5 \times 5} \\ = \sqrt{ {2}^{2} \times 3 \times {5}^{2} } \\ = 2 \times 5 \sqrt{3} \\ = 10 \sqrt{3} [/tex]

Hope you could get an idea from here.

Doubt clarification - use comment section.

Answer:

3

Step-by-step explanation:

75÷5-[(9-7)×3]×2

do innermost inclusion symbols first, which would be 9-7

75÷5-[2×3]×2

now multiply 2 and 3

75÷5-(6)×2

now divide 75 by 5

15-6×2

now multiply

15-12

3

The required simplified value of the given expression is 13.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Given expression,
= 75÷5−[(9−7)×3]×2

Following the PEMDAS rule,
= 25 - [2×3]×2
= 25 -[6]×2
= 25 - 12
= 13

Thus, the required simplified value of the given expression is 13.

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9.14 liters of fruit juice must be mixed with 4 liters of a 24% flavored rum to make a rum punch of 8% strength.

To determine how many liters of fruit juice must be mixed with 4 liters of a 24% flavored rum to make a rum punch of 8% strength, the following calculation must be performed:

Therefore, 9.14 liters of fruit juice must be mixed with 4 liters of a 24% flavored rum to make a rum punch of 8% strength.

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Answer:A

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer:

Determine the required value of the missing probability to make the distribution a discrete probability distribution. x p(x) 3 0.23 4 ? 5 0.51 6 0.08 p(4) = nothing  (type an inte...

Answer:

[tex]10 - \frac{3}{10} n[/tex]

Step-by-step explanation:

hope that is right and hope it helps

Answer:

x=-3

Step-by-step explanation:

Answer:

Ok

Step-by-step explanation:

Answer:

3y

Step-by-step explanation:

(-9x+7y)-(-9x+5y)

Distribute the negative(-)

-9x+7y+9x-5y

-9 and 9 cancel each other

3y

The simplest terms of the given expression  (-9x + 7y) - (-9x + 5y) will be 2y.

A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.

A statement expressing the equality of two mathematical expressions is known as an equation.

As per the given expression,

(-9x + 7y) - (-9x + 5y)

Open the bracket

-9x + 7y + 9x - 5y

Combined likely terms together

-9x + 9x + 7y - 5y

0 + 2y = 2y

Hence "The formula (-9x + 7y) - (-9x + 5y) will have 2y as its simplest terms".

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Answer:

It does not matter, since, from your second case, [tex]5\sqrt5 +11 = 11+5\sqrt5[/tex].

In general is a matter of personal preference but in general I like to start with a positive number (I like [tex]\sqrt2 -1[/tex] more than [tex]-1+\sqrt2[/tex] since if there's an equal sign before I'm guaranteed to have the two signs mesh together in a few steps).

If everything you are adding together is positive, I just go first come first served and pick a new term in order it appears in the previous passage.

Answer:

64m^2 - 112m + 49

Step-by-step explanation:

You just do the math lol.

Answer:

64m^2 + 112m + 49

Step-by-step explanation:

I got it right in Grandpoint.

Answer:

81.5

Step-by-step explanation:Cube has all sides of equal dimensions and like that it has 6 faces.

So total surface area of cube is equal to the combined area of all the six faces.

Now each face has equal dimensions so same area

Therefore,

area of a single face =side²

Therefore, area of entire cube = 6 times the area of a single face

= 6 * side²

.

Answer:

if i correct pls comment I think it is 33

Answer:

0.670. M

Step-by-step explanation:

Molarity can be expressed like this:

molarity =  number of moles /volume (L)

We know the volume, which is  2.37 L , but we need to find the number of moles. We can do this by dividing  67.3 g  by the molar mass of  L i C l :

number of moles  = mass of sample /molar mass

number of moles  =  67.3 g /(6.94 + 35.45) g/mol  = 67.3 g /42.39 g/mol

number of moles = 1.59 mol

molarity = 1.59 mol /2.37 L =  0.670. M

Answer:

2nd option

Step-by-step explanation:

Repeatedly divide by 2 until the value 1 is reached

32 ÷ 2 = 16

16 ÷ 2 = 8

8 ÷ 2 = 4

4 ÷ 2 = 2

2 ÷ 2 = 1 ← finish here

Then

32 = 2 × 2 × 2 × 2 × 2

Answer:

A

Step-by-step explanation:

After doing long division we then know that 2,952 ÷24 = 123

We 1st follow pemdas knowing this we solve the equations in parenthesis 1st

(2,400 ÷ 24) + (480 ÷ 24) + (72 ÷ 24)

2,400 ÷ 24 = 100

480 ÷ 24 = 20

72 ÷ 24 = 3

We can then rewrite the equation as

100 + 20 + 3   We then solve left to right

100 + 20 = 120

120 + 3 = 123

Answer:

  P = -16(x -28)² +1024

Step-by-step explanation:

The equation can be written in vertex form as ...

  P = -a(x -h)² +k

where (h, k) is the vertex, and 'a' is a scale factor. We are given the vertex (h, k) = (28, 1024) and another point (x, P) = (10, -4160). Using these points, we can find the value of 'a'.

  -4160 = -a(10 -28)² +1024

  -5184 = -324a . . . . simplilfy

  a = 5184/324 = 16 . . . . divide by the coefficient of 'a'

A suitable quadratic relation is ...

  P = -16(x -28)² +1024

Step-by-step explanation:

the slope is the ratio of "y coordinate difference / x coordinate difference".

so, let's find 2 good points (I mean by that with integer coordinates). I see e.g.

(-1, -1) and (0, -7)

x changes by +1 (from -1 to 0).

y changes by -6 (from -1 to -7).

so, the slope is -6/1 = -6.

D is the right answer.

Answer:

  1A: all real numbers

  1B: x = {-3, 0, +18}

  1C: (-3, 0) U [3, 18)

  2A: h(x) = -1/160x^2 +1/2x

  2B: focus: (40, -30); directrix: y = 50; axis of symmetry: x = 40

Step-by-step explanation:

The graph is attached. The domain is all real numbers.

__

The x-intercepts for x < 3 are the zeros of the quadratic:

  x^3 -9x = 0

  x(x^2 -9) = 0

  x(x +3)(x -3) = 0   ⇒   x = 0, -3, +3 . . . . x=3 is not in the domain of this piece

The x-intercepts for x ≥ 3 are the zeros of the log function:

  -log4(x -2) +2 = 0

  log4(x -2) = 2 . . . . . . add log4(x -2)

  x -2 = 4^2 . . . . . . . . . take the anti-log

  x = 2 +16 = 18 . . . . . . add 2

The x-intercepts of g(x) are x = {-3, 0, +18}.

__

The graph shows the function is positive on the intervals ...

  (-3, 0) U [3, 18)

__

The vertex of the curve is given as (40, 10). The vertical scale factor will make the function 0 at x=0.

  h(x) = a(x -40)^2 +10

  h(0) = 0 = a(-40)^2 +10 = 1600a +10

  a = -10/1600 = -1/160 = -1/(4·40)

The equation of the parabola is ...

  y = -1/(160)(x -40)^2 +10

In standard form, this is ...

  y = -1/160x^2 +1/2x

__

When we computed the leading coefficient (a) in Part A, we found it to be -1/(4·40). This corresponds to 1/(4p) where p=-40 is the focus to vertex distance. The negative sign means the focus is 40 units below the vertex, at (40, -30). The corresponding location of the directrix is 40 units above the vertex, at y=50.

Of course the axis of symmetry is the vertical line through the vertex: x = 40. These are shown in the second attachment.

The bi-weekly deduction for Social Security and Medicare is $90.27.

Since you receive a base salary of $ 14.75 per hour with time-and-a-half for hours in excess of 40 hours per week, and you are paid every two weeks, and Social Security and Medicare are deducted from your pay, and Social Security tax is 6.2% of the gross pay, and Medicare tax is 1.45% of the gross pay, to determine what is the bi-weekly (every two weeks) deduction for Social Security and Medicare, the following calculation must be performed:

Therefore, the bi-weekly deduction for Social Security and Medicare is $90.27.

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There is a total of 52 grams of carbs in 1/4 cup, then 1 tablespoon will contain 208 grams of carbs.

The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or even more items.

Included in them is the study of integers, especially the order of operations, which is important for all other areas of mathematics, notably algebra, data management, and geometry.

As per the given information in the question,

There are 52 grams of carbs in 1/4 cup of syrup

Let's assume that the amount of carbs in 1 tablespoon is x.

So,

x = (52 × 4)

x = 208 grams.

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Answer:

  -3/2 < a < 2/3

Step-by-step explanation:

In the fourth quarter of the coordinate plane, x > 0 and y < 0. This means ...

  2a +3 > 0

  3a -2 < 0

__

The first inequality has the solution ...

  2a > -3 . . . . subtract 3

  a > -3/2 . . . . divide by 2

The second inequality has the solution ...

  3a -2 < 0

  3a < 2 . . . . add 2

  a < 2/3 . . . divide by 3

The set of values of 'a' that put P in the fourth quarter is ...

  -3/2 < a < 2/3

Answer:

[tex]y= \frac{1}{3}x -9[/tex]

Step-by-step explanation:

First you must substract -5 to both sides

-5-4= -9

[tex]y= \frac{1}{3}x -9[/tex]

Answer:

one solution

Step-by-step explanation:

Since both are y-isolated equation, we can write as:

[tex]\displaystyle \large{6x-2=4x-2}[/tex]

Solve for x, first move 4x to subtract with 6x and -2 to add with -2

[tex]\displaystyle \large{6x-4x=-2+2}\\\displaystyle \large{2x=0}\\\displaystyle \large{x=0}[/tex]

Then substitute x = 0 in any of these equations which we receive y = -2.

And the solution is (0,-2) which only has one solution.

Answer:

b

Step-by-step explanation:

took the test a bit ago

Answer:

It has no solution because, 14x cancels out -14x when you move the variables to the left and leaves the equation as 0 = -12, however we know that 0 does not equal -12 which means this solution is false; therefore this equation has no solution since 0 does not equal -12.

Step-by-step explanation:

5 - 4x - 7 - 10x = -8x - 4 - 6x - 10 (Given)

-2 - 14x = -14x - 14 (Combine like terms)

0 = -12 (Move variables(x) to the left and the constants to the right)

Answer:

About 2.9 pounds per day.

Step-by-step explanation:

20÷7=2.85714...

rounded- 2.9

So Tank, the Great Dane, ate about 2.9 pounds per day.

Answer:

Step-by-step explanation:

2 6/7

Answer:

hello the answer you are looking for should be s3xy kong 243

Step-by-step explanation:

Answer:

$79.64

Step-by-step explanation:

I think it's still 79.64

Answer:

it will be equal 70.08 $