How many solutions does the equation 12(2x+6)=6−x have?

PS you cant leave out exponents when typing questions without the attached photo. multiplying by 2 is not the dame as a exponent of 2. Use ^2 to show that a number is to the power of 2.

the value of p(2) in this equation is 2.

Answer:

p(2) = 2

Step-by-step explanation:

substitute x = 2 into p(x)

p(2) = - 3(2 - 4)² + 14

      = - 3(- 2)² + 14

      = - 3(4) + 14

      = - 12 + 14

      = 2

Answer:

Alternate Exterior ANgles

Step-by-step explanation:

A logarithm is a power that requires a number to be raised to another power. The bases of all the values involved must be identical. So, we must create equivalent expressions in the equation that all have equal bases. And the two expressions then formed can only be said equal if the exponents are also similar. Now we will move towards the solution to the problem.

Solution:

log (5,25)

log (5,25)

=log (25) log (5)

=log (52) log (5)

=2log (5) log (5)

=2

2nd Solution:

log (5,25) =2

Solution steps:

=log (5,25)

=log5(25)

=2

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Answer:

The price of a child ticket in dollars $8.00

Step-by-step explanation:

Answer:

£4240

Step-by-step explanation:

2%of 4000=80

80x3=240

4000+240=4240

For I = [tex]\sqrt{W/R}[/tex]  gives electric current I , when W=500 , R=100 implies I = [tex]\sqrt{5}[/tex] , the set of numbers best describes the value of I are irrational numbers.

As given in the question,

Formula  I = [tex]\sqrt{W/R}[/tex]

I = electric current in amperes

W = power in watts

R = Resistance in ohms

When W = 500 , R = 100

I = [tex]\sqrt{500/100}[/tex]

⇒ I = [tex]\sqrt{5}[/tex] amperes

Therefore, for I = [tex]\sqrt{W/R}[/tex]  gives electric current I , when W=500 , R=100 implies I = [tex]\sqrt{5}[/tex] , the set of numbers best describes the value of I are irrational numbers.

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Answer:

y= 21

Step-by-step explanation:

4y-42=2y

4y=2y+42

2y=42

y=21

The total number of signals that can be made using 5 flags from 8 flags of different colors is 6720.

Permutations:

A permutation is an act of arranging the objects or numbers in order.

The formula for permutations is:

nPr = n!/(n-r)!

where

nPr = permutation

n = total number of objects

r = number of objects selected

Combinations:

Combinations are the way of selecting the objects or numbers from a group of objects or collection, and the order of the objects does not matter.

The formula for combinations is:

nCr = n!/[r! (n-r)!]

Where,

nCr  = number of combinations

n = total number of objects in the set

r = number of choosing objects from the set

Given,

Here we need to find how many different signals can be made with 5 flags from 8 flags of different colors.

The number of ways that 5 flags can be selected is the combination of 8 flags taken 5 at a time.

After choosing 5 flags from 8, it can be arranged in

=> ₅P₅ ways = (5!)

Therefore, the total number of signals that can be made is

=> ₈C₅ x  ₅P₅

=> (8!/(8-5)!5!) x 5!

=> (8! / 3!)

=> 40320 / 6

=> 6270

Therefore, the total number of signals that can be made is 6270.

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Using the segment addition postulate, it is found that:

1. Point B is between the other two.

2. The measures are: RS = 5, RT = 10, PR = 10, PQ = 6.

3. The value of x is of x = 9.5.

4. The value of y is of y = ± 5.

The segment addition postulate is a geometry axiom that states that a line segment, divided into a number of smaller segments, has the length given by the sum of the lengths of the segments.

In item 1, we have that the largest segment is of AC, hence it represents the line, while point B splits the segment into two parts, that is, point B is between the other two.

In item 2, we have that:

For item 3, applying the Postulate, we have that:

AB + BC + CD = AD

4 + 4 + 2x - 6 = 21

2x = 19

x = 9.5.

For item 4, due to the midpoint, we have that:

LM = MN

Hence:

y² + 4 = 29

y² = 25

y = ± sqrt(25)

y = ± 5.

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Answer: 38

Step-by-step explanation: In order to find the area you need to figure out all your sides. Now thankfully it's just a rectangle or this would be a bit more complicated haha!

The first step is to understand what all the sides are. Since you know you have a perimeter of 78 and base of 38, all you need to do is add 38 +38. The reason is that that's on both long sides of a rectangle.  This now leaves you with a number of 76.

Second step: Take the number 76 and subtract it your perimeter 78. This obviously leaves you with the number 2, which you'll have 1 on the shorter sides.

Therefore Area: 38 x 1 = 38

Hope it helps

The correct answer is option (a) 70° is the possible measures of A.

Given that, the isoceles triangle's base angles are equal

let angle D be its vertical angle.

With angle E equal to angle F

angle D+ angle E+ angle F=180'

angle D+ 55'+55'=180',

angle D+ 110'=180'

angle D=180'-110'

angle D=70'.

Figure DEF is an isosceles triangle. The measure of A is 55°, while the measure of B is 70°. As there are two possible measures of D, it can be calculated that the base area equal to 426 square units and the height equals 232 square units.

Hence, 70° is the possible measures of A.

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30 - The amount he earns every week

12 - the fee for one hour of lawn service without the base fee

12h - the cost for h hours of lawn service without the base fee

Hope this helps you!! :3

The length of segment CD is 14.6 units

The points are given as:

C = (3, -5) and

D = (7,9).

The distance is calculated using

d = √(x2 - x1)^2 + (y2 - y1)^2

This gives

d = √(7 - 3)^2 + (9 + 5)^2

Evaluate

d = 14.6

Hence, the length of segment CD is 14.6

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Answer:

600 miles

Step-by-step explanation:

Plug 110+0.30x and 50+0.40x into a graphing calculator and see where they intersect

The slope of the given points are  (29, 11) and (-3, -7):

= 0.5625.

A line's slope indicates whether sharp it is.. The slope is defined mathematically as "climb overrun" (change in y divided by change in x).

In general, a line's slope indicates its steepness as well as direction. The slope of a straight line connecting two points (x1,y1) and (x2,y2) can be simply calculated by subtracting the coordinates of both the points. The slope is commonly denoted by the letter'm.'

X₁ = 29

Y₁ = 11
X₂ =  -3
Y₂ = -7

The slope is the degree of tilt a line has and it may be positive, negative, zero, or undefined.

slope = (y₂ - y₁) / (x₂ - x₁)

Substituting the value in the given formula:

slope  =  [tex]\frac{(-7 - 11)}{(-3 - 29)}[/tex]

          = -18 / -32

          = -9 / -16

          = 0.5625

The slope of the given points are  (29, 11) and (-3, -7) = 0.5625.

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The mean of the salary is $120000.

By adding up a list of salaries and dividing by the total number of salaries on the list, mean salaries are derived. This means that exceptionally high and extremely low incomes have the same weight in the final average, which is crucial to bear in mind while investigating industry salaries.

By ranking the wages of a group of employees in descending order, you may determine the median base salary by finding the income that is in the middle of the distribution.

Mean=(5*440,00+2*100,000+1*540,000)/(5+2+1)

         =(220,000+200,000+540,000)/8

         =960,000/8

         =120,000

Median is 100,000.

Hence, the mean salary is 120,000 but 7/8  members salary is lower than 120,000. Because the firm’s owner salary is too high. thus the firm’s owner is so unethical regarding employee salary.

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The following set of numbers 2√3, 4√2, and 3√5, can be the measures of the sides of an obtuse triangle.

A triangle is a polygon with three sides and three vertices.

To know if a set of number is a valid measure of the sides of a triangle, it must follow the Triangle Inequality Theorem which states that the sum of any two sides must be greater than the third side, such that a + b > c, a + c > b, and b + c > a.

let a = 2√3, b = 4√2, and c = 3√5

a + b > c     2√3 + 4√2 > 3√5     9.12 > 6.71     True

a + c > b     2√3 + 3√5 > 4√2     10.17 > 5.66    True

b + c > a     4√2 + 3√5 > 2√3     12.37 > 3.46     True

To know what type of triangle based on the length of its side:

1. Take the sum of the squares of the two smaller sides.

(2√3)^2 + (4√2)^2 = 44

2. Compare it to the square of the largest side.

(3√5)^2 = 45

44 < 45

If the sum of the squares of the 2 is larger than the square of the 3rd, it is an acute triangle.

if they are equal, it is a right triangle

if they are smaller, then it is an obtuse triangle.

Hence, 2√3, 4√2, and 3√5 can be the measure of the sides of an obtuse triangle.

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1/3|5x-3|=6

Absolute value equality entered

(1/3) |5x-3| = 6

Clear the absolute-value bars by splitting the equation into two cases, one for the Positive case and the other for the Negative case.

The Absolute Value term is (1/3) |5x-3|

For the Negative case, we'll use -(1/3) (5x-3)

For the Positive case, we'll use (1/3) (5x-3)

-(1/3) (5x-3) = 6

Multiply

-5x/3+1 = 6

Rearrange and add up

-5x/3 = 5

Multiply both sides by 3

-5x = 15

Divide both sides by 5

-x = 3

Multiply both sides by (-1)

x = -3

Which is the solution for the Negative Case

(1/3)(5x-3) = 6

Multiply

5x/3-1 = 6

Rearrange and add up

5x/3 = 7

Multiply both sides by 3

5x = 21

Divide both sides by 5

x = (21/5)

Which is the solution for the Positive Case

x=-3

x=21/5

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Classifying an equiangular triangle as an acute equiangular triangle is unnecessary because by definition, all angles are 60°

An equiangular triangle is one with three equal sides and three equal angles, all of which are measured at 60 degrees. Given that the characteristics of both triangles are the same, an equiangular triangle can also be referred to as an equilateral triangle.

This triangle is regarded as a regular polygon because its sides and angles are both equal. Equiangular refers to angles that are all equal.

All triangles have 3 angles that together total 180 degrees. Because an equilateral triangle has equal sides, its angles can only be 60 degrees. This entails that all angles must be acute. It is not required to write that it is intense because of this.

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Answer:

La probabilidad de sacar una canica roja seria 3/10 porque hay 10 canicas en total, 3 de ellas son rojas. Tambien se puede escribir 0.3 . Espero que esto te ayude.

A symmetrical figure is one that is identical on both sides of a line. Rotational symmetry occurs when an object is rotated and retains the same appearance as the original figure.

Symmetry:

Rotational symmetry:

Relation:

Therefore, a symmetrical figure is one that is identical on both sides of a line. Rotational symmetry occurs when an object is rotated and retains the same appearance as the original figure.

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When two arcs are parallel to each other, the two arcs between them are congruent. If the two arcs they intersect are the same length, they are congruent.

Chords within a circle can be related in a variety of ways. Parallel chords cut congruent arcs in the same circle. That is, the arcs whose endpoints include one of each chord's endpoints have equal measures.

The lengths of the arcs connecting two parallel chords of a circle are equal. Similarly, if the lengths of the two arcs connecting two distinct chords are the same, the chords are parallel. If two chords have the same length, the arcs between their endpoints will have the same measure.

When two arcs are parallel to each other, the two arcs between them are congruent. If the two arcs they intersect are the same length, they are congruent.

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A compound function is when the output of one function is used as the input of another function. If we have a function ff and another function gg, the function fg(x)fg(x) is called "ff of gg of xx" or "fgfg of xx" and is a composition of the two functions.

The order in which functions are applied is important. Find the function of the

function. If you have two or more functions, there can be many different permutations of those functions, giving you many different composite functions.

fg(x)fg (x) can be written f[g(x)]f[g(x)] to indicate that the inner function should be applied before the outer function.

Solution:

Your problem → f(x)=3x, g(x)=((3x)/4)-2, Find f(g(x))

f(x)=3x, g(x)=3x4-2, fog(x)=?

g(x)=3x4-2, f(x)=3x

fog(x)=f(g(x))

=f((3x)/4-2)

=3(3x4-2)

=9x4-6

fog(x)=9x4-6

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Answer: If (4, y ) is an ordered pair of the function, then y = 1

Step-by-step explanation:

The known x coordinate for the position (4,y) is 4.

We'll just refer to it as y since we don't know the y coordinate just yet.

On the x axis, trace a vertical line through 4 (see related remark below).

Thus in red (see attached image).

The red line crosses the graph at the point (4,1)

so this tells us that,

                                          y = 1

Although it's helpful to see how it turns out, you are not need to draw a vertical red line.

You will be able to visually perceive the solution without these extra lines after you become accustomed to these kinds of situations.

Therefore,

If (4, y ) is an ordered pair of the function, then y = 1

                               y = 1

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Answer:

[tex]y=-\frac{5}{6} (x-6)+1[/tex]

Step-by-step explanation:

Using point slope form:

[tex]y=m (x-x_1)+y_1[/tex]

Put in the given parameters:

[tex]m=-\frac{5}{6}[/tex]

[tex]x_1=6[/tex]

[tex]y_1=1[/tex]

Now get the solution:

[tex]y=-\frac{5}{6} (x-6)+1\\[/tex]

The result of the algebraic expression 5x+y for x=3 and y=-2 is 13

Given,

The algebraic expression =5x+y

x= 3

y= -2

Substitute the values in the expression

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

=15-2

=13

Hence, the result of the algebraic expression 5x+y for x=3 and y=-2 is 13

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Answer:

he doesnt get a b

Step-by-step explanation:

71+80+83+83=317

317/4= 79.25

79.25 !=< 80

Answer:

13/6

Step-by-step explanation:

1 Simplify  \sqrt{8}

8

​

  to  2\sqrt{2}2

2

​

.

\frac{2}{6\times 2\sqrt{2}}\sqrt{2}-(-\frac{18}{\sqrt{81}})

6×2

2

​

2

​

2

​

−(−

81

​

18

​

)

2 Simplify  6\times 2\sqrt{2}6×2

2

​

  to  12\sqrt{2}12

2

​

.

\frac{2}{12\sqrt{2}}\sqrt{2}-(-\frac{18}{\sqrt{81}})

12

2

​

2

​

2

​

−(−

81

​

18

​

)

3 Since 9\times 9=819×9=81, the square root of 8181 is 99.

\frac{2}{12\sqrt{2}}\sqrt{2}-(-\frac{18}{9})

12

2

​

2

​

2

​

−(−

9

18

​

)

4 Simplify  \frac{18}{9}

9

18

​

  to  22.

\frac{2}{12\sqrt{2}}\sqrt{2}-(-2)

12

2

​

2

​

2

​

−(−2)

5 Rationalize the denominator: \frac{2}{12\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}}=\frac{2\sqrt{2}}{12\times 2}

12

2

​

2

​

⋅

2

​

2

​

​

=

12×2

2

2

​

​

.

\frac{2\sqrt{2}}{12\times 2}\sqrt{2}-(-2)

12×2

2

2

​

​

2

​

−(−2)

6 Simplify  12\times 212×2  to  2424.

\frac{2\sqrt{2}}{24}\sqrt{2}-(-2)

24

2

2

​

​

2

​

−(−2)

7 Simplify  \frac{2\sqrt{2}}{24}

24

2

2

​

​

  to  \frac{\sqrt{2}}{12}

12

2

​

​

.

\frac{\sqrt{2}}{12}\sqrt{2}-(-2)

12

2

​

​

2

​

−(−2)

8 Use this rule: \frac{a}{b} \times c=\frac{ac}{b}

b

a

​

×c=

b

ac

​

.

\frac{\sqrt{2}\sqrt{2}}{12}-(-2)

12

2

​

2

​

​

−(−2)

9 Simplify  \sqrt{2}\sqrt{2}

2

​

2

​

  to  \sqrt{4}

4

​

.

\frac{\sqrt{4}}{12}-(-2)

12

4

​

​

−(−2)

10 Since 2\times 2=42×2=4, the square root of 44 is 22.

\frac{2}{12}-(-2)

12

2

​

−(−2)

11 Simplify  \frac{2}{12}

12

2

​

  to  \frac{1}{6}

6

1

​

.

\frac{1}{6}-(-2)

6

1

​

−(−2)

12 Remove parentheses.

\frac{1}{6}+2

6

1

​

+2

13 Simplify.

\frac{13}{6}

6

13

​

Done

Answer: y=24

Step-by-step explanation:

Supplementary angles add up to 180 degrees.

A+B=180

3y + 12 + 2y +48=180

3y+2y+12+48=180

5y+60=180

5y=120

y=24

The steps for copying AB to create CD in the proper order are;

1. Set the compass width to AB.

2. Place the compass point at point C and draw an arc.

3. Make a point D anywhere on the arc.

4. Draw DC.

The steps to copy a line segment are;

Step 1: Plot a point that will be an endpoint of the new line segment

Step 2: With the compass pin at the beginning of the original line segment, open the compass width to the end of the original line segment

Step 3: With the adjusted compass width from the above step place the compass pin at the plotted point of the new line segment and draw an arc in the region the new line segment is to be located

Step 4: Select a point on the arc where the other end of the new line will be

Step 5: From the selected point from the above step, draw a line to the point plotted as the beginning of the new line segment

Step 6: The length of the line drawn above is the same as the length of the original line segment..

Looking at the given options, the steps for copying AB to create CD in the proper order are;

1. Set the compass width to AB.

2. Place the compass point at point C and draw an arc.

3. Make a point D anywhere on the arc.

4. Draw DC.

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