Identify the expressions for which limits exist.

The inequality that represents the domain of the function is [tex]\frac 12x - 10 \ge 0[/tex]

The function is given as:

[tex]f(x) = \sqrt{\frac 12x - 10} + 3[/tex]

Set the radicand greater than or equal to 0

[tex]\frac 12x - 10 \ge 0[/tex]

Multiply through by 2

x - 20 ≥ 0

Add 20 to both sides

x ≥ 20  

Hence, the domain of the function is x ≥ 20  

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Step-by-step explanation:

a is the interior angle of the 2 opposing arc angles. the interior angle is the mean value between the 2 arc angles.

a = (145 + 45)/2 = 190/2 = 95°

b is the simply the supplementary angle to a (meaning together they are 180°, because the sum of all angles around a single point on one side of a line is 180°).

b = 180 - 95 = 85°

Answer:

Step-by-step explanation:

Hope I did it right, tell me if its wrong.

Answer:

44%

Step-by-step explanation:

Existing garden:  L*W, where L and W are the length and width (We'll assume meters, but it can be any other linear measurement, such as miles, cm, or feet, etc.).

Area, A1 = L*W

New Area, A2 = (1.2L)*(1.2W)

  A2 = (1.2)*(1.2)*(L*W)

Since L*W = A1, we can write A2 = 1.44*A1

New Area = 1.44 the original area, a 44% increase.

Answer:

C

Step-by-step explanation:

The last reasoning is the side angle side theorem. In the whole proof, there is no mention of an angle. So the answer has to involve prooving that the angle in between the two sides that have been proven similar is the same in both traingles. This is best accomplished by statement C.

The coefficient of thermal expansion of the metal will be 1.4 x 10⁻⁵ °c.

Every material has its property of contraction or expansion by the change of temperature. The expansion and contraction of any material are indicated by a coefficient this coefficient is called the coefficient of thermal expansion.

Here we have the following data:-

l₁= 1.000 m

l₂ = 1.001 m

Δ = 70° C

The formula for calculating the coefficient of linear expansion will be:-

[tex]\alpha =\dfrac{\Delta l}{\Delta t\times l}[/tex]

By putting the values we will get the answer.

[tex]\alpha=\dfrac{0.0001}{70\times 1}= 1.4\times 10^{-5}[/tex]

Therefore the coefficient of thermal expansion of the metal will be 1.4 x 10⁻⁵ °c.

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Answer:

look above

Step-by-step explanation:

hope it hepls

Answer:

y = 1/3x - 2:

y = 12 - 6x:

y = 3x - 7:

Step-by-step explanation:

Hello!

The slope-intercept form of a line is [tex]y = mx + b[/tex]

The y-intercept is the "b" value of the line, given as -2.

To find the x-intercept, we simply replace the y-value with 0:

y - intercept: - 2

x - intercept: 6

____________________________________________________

You can rearrange the equation, y = -6x + 12, to find the y-intercept: 12.

Solving for the x-intercept (remember, replace y with 0):

y - intercept: 12

x - intercept: 2

____________________________________________________

Simply take the "b" value, -7, to find the y-intercept of -7.

Solve for the x-intercept:

y - intercept: -7

x - intercept: 7/3

Additional Note:

You can also solve for the y-intercept by replacing x with 0. This method can be used for any interests, just plug in the opposite variable from what you are solving for with 0.

The proof is that the x-intercept is the value when the y = 0, the x-axis. You can plug in 0 for y to solve for x. Similarly, when solving for the y-intercept, you plug 0 for x as the y-axis is at x = 0.

Answer:

It is C.

Step-by-step explanation:

First thing you would do is go through all the information and read the options then what you would do is see the labels and its will try to throw you off at A. saying that its Prizes instead of students that has won the prizes so there for

C. Six prizes were won by 4, 5, 6, or 7 students.

is your answer

Answer: x1  = 5

               x2 = 1

Step-by-step explanation:

1. Identify the coefficients

2. Move the constant to the right side of the equation and combine

3.  Complete the square

4. Solve for x

Answer:

x = 5 and 1

Step-by-step explanation:

[tex]x^2-6x+5=0\\x_{1,\:2}=\frac{-\left(-6\right)\pm \sqrt{\left(-6\right)^2-4\cdot \:1\cdot \:5}}{2\cdot \:1}\\x_{1,\:2}=\frac{-\left(-6\right)\pm \:4}{2\cdot \:1}\\\rightarrow x_1=\frac{-\left(-6\right)+4}{2\cdot \:1},\:x_2=\frac{-\left(-6\right)-4}{2\cdot \:1}\\\\\frac{-\left(-6\right)+4}{2\cdot \:1}\\\\=\frac{6+4}{2\cdot \:1}\\\\=\frac{10}{2\cdot \:1}\\\\=\frac{10}{2}\\\\=5\\\\\\\frac{-\left(-6\right)-4}{2\cdot \:1}\\\\=\frac{6-4}{2\cdot \:1}\\\\=\frac{2}{2\cdot \:1}\\\\=\frac{2}{2}\\\\=1[/tex]

Answer:

my bet would be d)

Step-by-step explanation:

ur asking math students btw

Answer:

It should be x-3/2 (also written as "(x-3)÷2")

Step-by-step explanation:

y=2x+3

switch the y and x

x=2y+3

solve for y

x/2=y+3

x-3/2=y

If you graph these two functions you will see that y=2x+3 give the points (-1.5,0) and (0,3) and x-3/2 give (0,-1.5) and (3,0). because you've switched the x number to the y number you've "inversed" it

Answer: 60( 1 - 72)

Step-by-step explanation: i think it might be right so heres a proof

Answer:

Around 1.2 million

Step-by-step explanation:

If we multiply 266,667,000 by 440/100,000 we get about 1,173,334 which we can round to about 1.2 million

The distance of point a from translated b is 9.2 units and the distance of point b from translated b is 3.6 units

A line is the distance between two points.

Analysis:

point a( -3,1) point b(2, -6) point translated b(-1, -8)

Distance ab = [tex]\sqrt{(x2 - x1)^{2} + (y2 - y1)^{2} }[/tex]

Distance ab = [tex]\sqrt{(-1--3)^{2} + (-8-1)^{2} }[/tex] = 9.21 units

Distance btb = [tex]\sqrt{(-1-2)^{2} + (-8- -6)^{2} }[/tex] = 3.6 units

In conclusion, the distance of b from a is 9.2 units and b from b is 3.6 units.

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Answer:

first option

Step-by-step explanation:

1/7

I hope this is correct...

..............................................

Answer:

$7

Step-by-step explanation:

Since you have to pay 3 of your friends $15 each, you would multiply 15 by 3 and get 45. Then you would subtract that from 52 and you would get $7.

Answer:

true is the answer not hard question

Step-by-step explanation:

[tex] = 4 + ( - 3) - 2 ( - 6)[/tex]

here ( + ) × ( - ) = ( - )

[tex] = 4 - 3 + 12[/tex]

[tex] = 4 + 12 - 3[/tex]

[tex] = 16 - 3[/tex]

[tex] = 13[/tex]

The correct result of this simplification is 13

To solve this question, we'll just apply the rule of signs - and then we'll calculate the operations.

- In the sign rule - when both signs are equal, the result will be positive. If the signs are different, the result is negative.

4 + ( - 3 ) - 2 · ( - 6 )

4 - 3 - ( - 12 )

4 - 3 + 12

1 + 12

13

Therefore, the alternative value will be 13

Answer:

(2,14)

Step-by-step explanation:

so i solved this with substitution but there are other methods to solve this!

equation 1 : y = -x + 16
equation 2 : y = x + 12

solve for y in equation 1 !!
y = -x + 16
(add x on both sides)
y + x = 16
(subtract y on both sides)
x = -y + 16

equation 1 now equals : x = -y + 16

substitute equation 1 into equation 2 :)

y = (-y + 16) + 12
(add 16 + 12)
y = -y + 28
(add y on both sides)

2y = 28
(divide 2 on both sides)
y = 14

now to solve for x you can insert y !
you can use equation 1 or equation 2 to solve for x.

i'm using equation 2 :
y = x + 12
(14) = x + 12
(subtract 12 on both sides)
x = 2

therefore, the answer is (2, 14).

hope this helps :p

The final product is 18x⁴y⁵ - 48x²y⁵+12x³y⁷+24x²y⁸

The product is result obtained when a number or an expression is multiplied by the other number.

The product of the given expression

6x²y⁵ and 3x²-8x+2xy²+4y³

6x²y⁵ (3x²-8x+2xy²+4y³)

Step 1 : To multiply each term in the bracket with the other expression

out of the bracket

6*3*x²*y⁵*x² - 6*8*x²*y⁵ +6x²y⁵ *2*x*y² + 6*4*x²y⁵ *y³

Step 2 : The like variables will be solved

18x⁴y⁵ - 48x²y⁵+12x³y⁷+24x²y⁸

This is the final product

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An arithmetic sequence is a sequence of integers with its adjacent terms differing with one common difference. The correct option is B.

An arithmetic sequence is a sequence of integers with its adjacent terms differing with one common difference.

The explicit formula for any arithmetic series is given by the formula,

aₙ = a₁ + (n-1)d

where d is the difference and a₁ is the first term of the sequence.

Given  A₁=5 and An= A₍ₙ₋₁₎-4, therefore we can write,

aₙ = a₁ + (n-1)d

Aₙ= 5+(n-1)(-4)

Hence, the correct option is B.

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Let's see

[tex]\\ \rm\dashrightarrow \dfrac{9}{x}=\dfrac{24}{12}[/tex]

[tex]\\ \rm\dashrightarrow \dfrac{9}{x}=2[/tex]

[tex]\\ \rm\dashrightarrow x=\dfrac{9}{2}[/tex]

[tex]\\ \rm\dashrightarrow x=4.5[/tex]

Answer:

C - x < -6 and x < 2

Step-by-step explanation:

2x ">" -12 and 7x < 14. with negative numbers, the bigger the number the less it is. -12 < -6 because negative numbers work the opposite way that positive numbers do. I hope this helps you!!!!

The value of x is 8

5 = 4

10 x

5 . x = 10 . 4

5x = 40

x = 40 ÷ 5

x = 8

So, the result of x will be 8

The value of x from the given triangle formed by the pot hanging from a brace is; x = 50°

We are given from the diagram that;

∠NMP = 110° and ∠NPM = 30°

Sum of angles in a triangle is 180°.

Thus;

∠MNP = 180 - (110 + 30)

∠MNP = 40°

Thus;

x = 90 - 40

x = 50°

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Answer:

1331 inches cubed

Step-by-step explanation:

V=LHW

since it is a cube, the length, height, and width will all be the same; 11 inches. You have to multiply 11 by 11 by 11, which equals 1331.

Hope this helped!