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[tex]\\ \rm\hookrightarrow \sqrt{x-6}=x-12[/tex]

[tex]\\ \rm\hookrightarrow x-6=(x-12)^2[/tex]

[tex]\\ \rm\hookrightarrow x-6=x^2-24x+144[/tex]

[tex]\\ \rm\hookrightarrow x^2-25x+150=0[/tex]

[tex]\\ \rm\hookrightarrow x^2-10x-15x+150=0[/tex]

[tex]\\ \rm\hookrightarrow (x-10)(x-15)=0[/tex]

[tex]\\ \rm\hookrightarrow x=15\:or \:10[/tex]

Answer:

[tex]x = 15,10[/tex] || C and D is the correct choices.

Step-by-step explanation:

[tex]\sqrt{x-6}=x-12[/tex]

[tex]x-6 =(x-12)^2[/tex]

[tex]x-6 = x^2 -24x +144[/tex]

[tex]x^2 -24x -x +144 +6 = 0[/tex]

[tex]x^2 - 25x + 150= 0[/tex]

[tex]x^2 -15x -10x +150=0[/tex]

[tex]x(x-15)-10(x-15)=0[/tex]

[tex](x-15)(x-10) = 0[/tex]

[tex]x = 15,10[/tex]

Answer:

option A is the answer because -4/3 is both negative and reciprocal of 3/4

Answer:

A. 3/4 & -4/3

Step-by-step explanation:

Negative reciprocal is the negative of the value and the numerator/denominator is switched to denominator/numerator.

For example, -7/15.

-7 is the numerator because -7 is above 15. But if we switch that, it will become -15/7. If we turn it from negative to positive or positive to negative, which in this case is negative to positive, since negative x negative is positive, it will become 15/7. I really took the time to explain this, so I hope this helps. =D

Answer:

Domain: all real numbers

Range: all real numbers

Step-by-step explanation:

Answer:

74

Step-by-step explanation:

180-106 =74

Answer:

2/8 farther than Mariam

Step-by-step explanation

mahra walks 5/8 km

Mariam walks 3/8 km

therefore, to know how many km mahra walks farther than mariam.

5/8-3/8

60 or y=4×+6

Step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solution.

Answer:

Length of Sofia's poster: 0.75 m

Length of Rafael's poster: 0.65 m

Difference: 0.75m - 0.65m

= 0.1 m

Hope this is correct

Mark as Brainliest please

Answer:

Step-by-step explanation:

The ordered pairs are:

Find the slope:

It means the drop in price is $625 each year.

The equation to reflect this situation is:

Answer:

Segment AC = 10 units

segment AD =

angle 1 = 45°

angle 2 = 90°

AE = BE = CE = DE = 5

SEGMENT AC = AE + CE

= 5 + 5

= 10 UNITS

SEGMENT AD = 5² + 5²

= √50

= 7.071

= 7 UNITS

ANGLE 1 = 90° ÷ 2

= 45°

ANGLE 2 = 360° ÷ 4 / 180° ÷ 2

= 90°

Answer:

3.5× c20

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The given data are the scores turned in by the amateur golfer, from

which the sample standard deviation can be calculated.

Responses:

The mean and sample standard deviation for the 2017 season are;

The mean and sample standard deviation for the 2018 season are;

The mean is given by the formula;

[tex]\overline x= \mathbf{\dfrac{\sum \left x_i }{N}}}[/tex]

N = 8

The mean for the 2017 season is therefore;

[tex]\overline x[/tex] = (72 + 76 + 77 + 75 + 73 + 71 + 73 + 75) ÷ 8 = 74

The sample standard deviation is given by the formula;

[tex]s =\mathbf{\sqrt{\dfrac{\sum \left (x_i-\overline x \right )^{2} }{N -1}}}[/tex]

[tex]\sum \left (x_i- \overline x \right )^2[/tex] = 30

N = 8

The sample standard deviation for 2017 season is therefore;

[tex]\sigma =\sqrt{\dfrac{30}{8-1}} \approx \mathbf{2.07}[/tex]

The mean and sample standard deviation for the 2017 season are;

The mean for the 2018 season is found as follows;

[tex]\overline x[/tex] = (62 + 68 + 73 + 75 + 83 + 78 + 83 + 78) ÷ 8 = 74

The sample standard deviation is given by the formula;

[tex]s=\mathbf{\sqrt{\dfrac{\sum \left (x_i-\overline x \right )^{2} }{N - 1}}}[/tex]

[tex]\sum \left (x_i- \overline x \right )^2[/tex] = 194

N = 8

The sample standard deviation for 2018 season is therefore;

[tex]Standard \ deviation \ for \ the \ 2018 \ seaon, \sigma =\sqrt{\dfrac{194}{8 - 1}} \approx \mathbf{5.26}[/tex]

The mean and sample  standard deviation for the 2018 season are;

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Answer: (p, q) = (3, 2)

Step-by-step explanation:

So we get that g(f(x)) = p(1-x)^2 + q = p(x^2 - 2x + 1)+q = px^2 - 2px + p+q.

Matching coefficients, we get that p=3, -2p=-6, and p+q=5.

It follows that p=3 and q=2.

Answer:

Given that angle DGC is 90 degrees and is vertical to AGB, they both are congruent so they will both have the same degrees.

So now we know angle AGB is 90 degrees

Angle AGE is 30 degrees, and in total all the angles would be equal to 180 degrees.

Now we just solve for x,

30 + 90 + x = 180

120 + x = 180

-120      -120

x = 60

Answer:

452 m^2

Step-by-step explanation:

Formula

A=4πr^2

4·π·6^2≈452.38934

The submarine is about 54 meters below the surface.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let y represent the height of the submarine. Hence:

y = -75 + 21 = 54 meters

The submarine is about 54 meters below the surface.

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Answer: 17.5 lbs of plums are required to make 20 rolls of fruit leather.

Step-by-step explanation:

Since 7 lbs of plums yield 8 rolls of fruit leather, 1 lb will yield 1 1/7 rolls of fruit leather.

To find how many pounds of fruit will yield 20 rolls of fruit leather, divide how many rolls of leather you want to get by how many rolls of leather one pound will yield.

20 divided by 8/7 equals 17 1/2.

Answer:

60

Step-by-step explanation:

Answer:

60

Step-by-step explanation:

2 to the 1st power times 30 -----> 2^1 x 30

2^1 x 30

exponent first

2 x 30

finish it

60

answer = 60

I hope this helps! Have a wonderful day!

Lilac~

Answer:

I'll do the first one as an example. The answer of the first one is 6.

Step-by-step explanation:

In the first example, they multiplied the number by 2 to get a common denominator for the two fractions so you can easily add. So, the first box will come 10 (5 times 2) and the second box will become 2 (1 times 2). Then simply add the fractions. The sum of the first question is 2. Because 2 10/12 + 3 2/12 = 6. Remember to add only the whole numbers and fractions. If you want, you can try using mathaway for additional help.

Hope this helps a little more.

Answer:

A = 92°

B = 100°

C = 88°

D = 80°

Step-by-step explanation:

Cyclic quadrilateral : a quadrilateral drawn inside (inscribed) a circle.

The opposite angles in a cyclic quadrilateral add up to 180°.

Therefore, A + C = 180° and B + D = 180°

If A + C = 180° , then

⇒ (x + 2) + (x - 2) = 180

⇒ x + 2 + x - 2 = 180

⇒ 2x = 180

⇒ x = 90°

Therefore,

A = x + 2 = 90 + 2 = 92°

C = x - 2 = 90 - 2 = 88°

D = x - 10 = 90 - 10 = 80°

B = 180 - D = 180 - 80 = 100°

Answer:

C

Step-by-step explanation:

King Snake: 65 inches / 12 inches per foot = about 5.4 feet long

Eastern Diamondback Rattlesnake: 2 yards * 3 feet per yard = 6 feet long

Ridge Nosed Rattlesnake: 4 feet long

Therefore, the eastern diamondback rattlesnake is the longest snake.

The radius of the wheel is 140.06 inches

Since the wheels on a truck are turning at 630 revolutions per minute as the truck travels at 50 miles per hour, we need to find the distance mover per revolution.

So, distance moved per revolution = speed of truck ÷  revolutions per minute

Speed of truck = 50 miles per hour

Converting to inches per min, we have

= 50 × 63360 in/hr ÷ 1 hr/60 min

= 3168000 in/60 min

= 52800 in/min

revolutions per min = 60 rev/min

So, substituting the variables into the equation, we have

distance moved per revolution = 52800 in/min ÷ 60 rev/min

= 880 in/rev

Since the distance moved per revolution is the circumference of the wheel, C we have that

C = 2πr where r = radius of wheel

Making r subject of the formula, we have

r = C/2π

Since C = 880 in

Substituting the value of the variable into the equation, we have

r = C/2π

r = 880 in/2π

r = 440 in/π

r = 140.06 in

So, the radius of the wheel is 140.06 inches

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Answer:

Step-by-step explanation:

Each of the given equations describes a line on a graph. There are numerous ways to find the values of x and y that will satisfy both equations at the same time. Two of them you have seen are "substitution" and "elimination." Here, "substitution" is easily accomplished by equating one expression for y to the other expression for y:

  y = y

  100 +65x = 40 +80x . . . substitute for y

  60 +65x = 80x . . . . . . . subtract 40 from both sides

  60 = 15x . . . . . . . . . . . . subtract 65x from both sides

  4 = x . . . . . . . . . . . . . . divide both sides by 15

  y = 40 +80x = 40 +80(4) = 360 . . . . find the value of y

The values of x and y that satisfy both equations are ...

  (x, y) = (4, 360)

__

The point (4, 360) is on both lines. That is the point where the lines intersect. It means 4 hours work will cost $360 in either shop.

__

The time of 4 hours that we found above is the "break-even" or "crossover" point in the cost equations. For times below that point, the lowest cost comes because of the lowest "service charge". For times above that point, the lowest cost comes because of the lowest per-hour charge.

3 hours is less than 4 hours, so the shop with the lowest service charge will have a lower cost. That is Amy's shop. Her price for 3 hours is ...

  40 +80(3) = 40 +240 = $280 . . . for 3 hours work in Amy's shop

__

If you want to make sure of that, you can find the cost in Mike's shop:

  y = 100 +65(3) = 100 +195 = $295 . . . for 3 hours in Mike's shop

Answer:

Domain: all real numbers

Range : y ≤ 2

Step-by-step explanation:

Domain : the set of possible x-values

Range : the set of y-values

From inspection of the graph:

Answer:

C)   x = 3

Step-by-step explanation:

Equation of a line in slope-intercept form:  y = mx + b

(where m is the slope (gradient) and b is the y-intercept)

If the line is perpendicular to the x-axis, the line will be parallel to the y-axis (vertical).  We are told that the line passes through point (3, 4).  Therefore, the line will never intercept the y-axis and so the y-intercept is zero.  Also, all the values of x = 3

So the equation of the line is:  x = 3

Answer:

Answer: Equation is y = ½x + 3

Step-by-step explanation:

Consider points (4,5) and (0,3)

» General linear equation:

[tex]{ \tt{y = mx + b}}[/tex]

Slope (m):

[tex]{ \tt{m = \frac{(5 - 3)}{(4 - 0)} }} \\ \\ { \tt{m = \frac{2}{4} = \frac{1}{2} }}[/tex]

slope = ½

y-intercept (c):

[tex]{ \tt{y = \frac{1}{2}x + c }}[/tex]

» Consider point (0,3):

[tex] { \tt{3 = ( \frac{1}{2} \times 0) + c}} \\ \\ { \tt{c = 3}}[/tex]

» Equation:

[tex]{ \boxed{ \tt{y = \frac{1}{2}x + 3 }}}[/tex]