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Factor completely 12x4 + 6x3 + 18x2.

Prime
3(4x4 + 2x3 + 6x2)
3x2(4x2 + 2x + 6)
3x(4x3 + 2x2 + 6x)


Factor completely 7x3y +14x2y3 − 7x2y2.

7x2(xy + 2y3 – y2)
7x2y(x + 2y2 – y)
7(x3y +2x2y3 − x2y2)
Prime


What is the Greatest Common Factor of x6 and x3?

x4
x3
x2
x

The solutions for the equation 2x^2 + 9x + 8 = 0 are x = (-9 + √17)/(4) and x = (-9 - √17)/(4), which are approximately 0.44 and -4.94, respectively.

To solve the equation 2x^2 + 9x + 8 = 0, we can use the quadratic formula. The quadratic formula states that the solutions for any quadratic equation of the form ax^2 + bx + c = 0 can be calculated using the formula:

x = (-b ± √(b^2 - 4ac))/(2a)

For the given equation, a = 2, b = 9, and c = 8.

Plugging these values into the formula, we get:

x = (-9 ± √(9^2 - 4*2*8))/(2*2)

Simplifying, we have:

x = (-9 ± √(81 - 64))/(4)

x = (-9 ± √17)/(4)

So, the solutions for the equation 2x^2 + 9x + 8 = 0 are x = (-9 + √17)/(4) and x = (-9 - √17)/(4), which are approximately 0.44 and -4.94, respectively.

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{362- {6x3+(48/2) x2]}+3(9+4)

{362- {6x3+24 x2]}+3(9+4)

{362- 66+3(9+4)

{362- 66+3(9+4)

{296+3(13)}

(296+39)

335

The Answer is 335.

To evaluate the expression {362-[6×3+(48÷2)×2]}+3(9+4), we need to follow the order of operations. After simplifying each part of the expression and performing the necessary operations, the final result is 287.

To evaluate the expression {362-[6×3+(48÷2)×2]}+3(9+4), we need to follow the order of operations, also known as PEMDAS. This acronym stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

First, let's simplify the expression inside the parentheses: [6×3+(48÷2)×2].

Now, we add the results of the two evaluated expressions: 248+39. This gives us a final result of 287.

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"Standard form" is the form ...

... ax +by = c

where a, b, c are mutually prime integers and the leading coefficient is positive. (If a ≠ 0, then it is "leading". If a = 0, then b is the leading coefficient.)

Of the choices offered, the only one that is equivalent to the given equation is ...

... -x + 6y = 5

_____

However, "standard form" requires the leading coefficient be positive, so an appropriate answer would be ...

... x -6y = -5

or

... 6y -x = 5

____

This is another one for my "broken question" file.

Answer: A. 1 in 100,000,000

Step-by-step explanation:

The given digits are  0, 1, 2, 3, 4, 5, 6, 7, 8, 9)

The total number of digits = 10

Now by using the counting principle, the probability of choosing one number is given  by :-

[tex]\text{P(one number)}=\dfrac{1}{10}[/tex]

Therefore, the probability of choosing 8 numbers (with replacement ) will be :

[tex]\dfrac{1}{10}\times\dfrac{1}{10}\times\dfrac{1}{10}\times\dfrac{1}{10}\times\dfrac{1}{10}\times\dfrac{1}{10}\times\dfrac{1}{10}\times\dfrac{1}{10}=(\dfrac{1}{10})^8=\dfrac{1}{100,000,000}[/tex]

Let the number of counties in state B be n, then the number of counties in state A is n+2 (the next even integer number after n). The sum of these two consecutive integers is 142, then

n+n+2=142,

2n=142-2,

2n=140,

n=70.

In state B there are 70 counties, and in state A there are 72 counties.

To find the measure of angle AOB when given that angle AOC is 108 degrees and m∠AOC = 3m∠AOB, use the relationship between the angles to calculate m∠AOB as 36 degrees.

Given: ∠AOC = 108°, m∠AOC = 3m∠AOB

To find: m∠AOB

Steps to solve:

Since ∠AOC = 108° and m∠AOC = 3m∠AOB, we can set up an equation: 108 = 3x, where x is m∠AOB.

Solving the equation, x = 36°. Therefore, m∠AOB = 36°.

The intersection of two coplanar lines forms a point.

Option A is the correct answer.

The angles that are in the same position on two parallel lines intersected by a transversal line on the parallel lines.

Corresponding angles are equal.

We have,

The intersection of two coplanar lines forms:

a.

a point
This is true.

Because two lines that intersect and form a point are called coplanar.

b.

a line

This is not true.

c.

a plane

This is not true.

Two axis makes a plane.

d.

an angle

This is not true.

An angle is formed when two straight lines or rays meet at a common endpoint.

Thus,

A point is formed by the intersection of two coplanar lines.

Learn more about corresponding angles here:

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Try this solution (see the attachment; the given series is an geometric series).

Answer is marked by red colour.

Step-by-step explanation:

Since we have given that

Amount of pay rate =$21

If she marked up by 78.7% , so it becomes

[tex]78.7\%\text{ of}\$21\\\\=\frac{78.7}{100}\times \$21\\\\=\$16.527[/tex]

So, our amount for pay rate becomes

[tex]21+16.527\\\\=\$37.527[/tex]

Now, he said he made a profit of 10%,so it becomes

[tex]10\%\text{ of }37.527\\\\=\frac{10}{100}\times 32.527\\\\=\$3.7527[/tex]

So, our new pay rate becomes

[tex]37.527+3.7527\\\\=\$41.2797[/tex]

This is the step through which we can get $41.28.

Answer:

A) -0.18 rad

Step-by-step explanation:

arcsin(x) = a means that sin(a) = x

For example

arcsin(1) = pi/2.

It means that pi/2 is the value for which the sin is equals to 1.

arcsin(-0.18)

This is the value of x for which sin(x) = -0.18. This happens for x = -0.18 rad.

So the correct answer is:

A) -0.18 rad

The value of y = sin (θ) when θ = pi/2 is 1.

It is the branch of maths concerned with the functions of angles and their involvement in calculations.

We can calculate the value of sin(θ) as follows:

θ = π/2

π/2 is the radian form of 90°

y = sin (θ)

= sin (π/2)

= 1

The value of y = sin(θ) is 1. The correct answer is option B.

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i = [tex]\frac{prt}{100}[/tex]

with i = 120 then

p = [tex]\frac{100(120)}{6}[/tex] = $2000

Answer:

120 = p × 6% × 1

Step-by-step explanation:

just put in the answer

then it will be correct

MP = MP, so triangle MPN ≅ triangle MPK by SSS. That means ∠NMP ≅ ∠KMP by CPCTC, so

... ∠NMP + ∠PMK = ∠NMK

... 2×∠PMK = 50° . . . substitute ∠PMK for ∠NMP, with which it is congruent

... ∠PMK = 25° . . . . . divide by 2

Answer:

Copy the second line segment with one endpoint at the same endpoint of the first line segment.

c is correct a is wrong

Answer:

Option A : copy the angle

Step-by-step explanation:

We can see that to make congruent triangles he first copied the segments

He copied the segment and drew segment FG

Then he copied the length of BH  and then keeping compass on point F cut the line segment FG at I

Then he measured the angle ABC and then intersect the previous arc at J

So, we can see that he just copied the angle

So, his recent completed step was copy the angle .

So, Option A is correct

Hence Option A copy the angle is true .

To graph x < 2, draw a number line with an open circle at 2, and shade to the left of the circle. This indicates all numbers less than 2 are included, while 2 itself is not.

To graph the inequality x < 2, you first need to draw a number line. Let's represent x by a point on the number line. The inequality x < 2 means that x can be any value less than 2, but not 2 itself.

To represent this on the number line, you would place an open circle (which represents exclusion) at 2, and then shade or draw an arrow pointing to the left (representing all numbers less than 2). This visually shows that the solution contains all numbers less than 2, but not 2 itself.

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46 non bubblegum

230 bubble gum

46

sum the parts of the ratio 5 + 1 = 6

divide 276 by 6 to find 1 part of the ratio

[tex]\frac{276}{6}[/tex] = 46 ← 1 part

the store sold 46 non-bubble gum

and 230 bubble gum

In order to calculate the number of cars the drama club could wash in 4 hours, one needs to know their washing rate per hour. Supposing it to be 2 cars/hour, the multiplication of the rate by the number of hours (2 * 4), shows that they could wash 8 cars.

The subject of this question is mathematics, specifically rate problems in the context of a real-world situation. In order to solve a problem like this, we need to know the rate at which the drama club is washing cars. This information is missing from the question, so let's suppose that they wash 2 cars per hour. In that case, their rate of washing cars is 2 cars/hour. Then, if you want to find out how many cars they could wash in 4 hours if they continue at this pace, you'll need to multiply their rate by the number of hours.

Let's calculate: Rate (2 cars/hour) * Time (4 hours) = 8 cars.

This means that if they keep washing cars at a rate of 2 cars per hour, they will have washed 8 cars in 4 hours.

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Answer:

1) There were 18582 visitors on the opening weekend.

2) There were approximately 7199 visitors on the 9th weekend.

3) The number of visitors was about 15,051 after 2 weekends. 

Step-by-step explanation:

Given : The curve of best fit to model the data is given below.  

[tex]y=18582(0.90)^x[/tex]

To find : Complete the statements,

1) There were _____ visitors on the opening weekend.

2) There were approximately _____ visitors on the 9th weekend.

3) The number of visitors was about 15,051 after ______ weekends.

Solution :

[tex]y=18582(0.90)^x[/tex] is the exponential equation: 

where, y is the number of visitors and x are the weekends since opening

1. Since the opening weekend is the day of the the park's opening.

So, replace x=0 in our exponential equation to get the number of visitors on the opening weekend:

[tex]y=18582(0.90)^x\\y=18582(0.90)^0\\y=18582(1)\\y=18582[/tex]

Therefore, There were 18582 visitors on the opening weekend.

2. To find the approximate number of visitors on the ninth weekend.

We replace x=9  in our exponential equation:

[tex]y=18582(0.90)^x\\y=18582(0.90)^9\\y=7199.0475[/tex]

Rounded to the nearest integer :  y=7199

Therefore, There were approximately 7199 visitors on the 9th weekend.

3. Here, we know that the number of visitors is 15051

Since y represents the number of visitors.

So, replace y=15051 in our exponential equation and solve for x:

[tex]y=18582(0.90)^x\\\\15051=18582(0.90)^x\\\\ \frac{15051}{18582} =0.90^x\\\\0.90^x= \frac{5017}{6194} \\\\ln(0.90^x)=ln(\frac{5017}{6194})\\\\xln(0.90)=ln(\frac{5017}{6194})\\\\x= \frac{ln(\frac{5017}{6194})}{ln(0.90)} \\\\x=2.0002[/tex]

Rounded to the nearest whole number :  x=2

Therefore, The number of visitors was about 15,051 after 2 weekends.

There are several issues with this English description, as there often are.

We assume you mean you want to divide 10 into two equal parts, then subtract one of those parts from 50.

... (10/2) is half of 10

When that is subtracted from 50, the result is

... 50 - (10/2)

We assume you want one fifth of this result. Other interpretations are that you are subtracting 10/2 from (50/5), or that you are using the difference as the denominator with 1/5 or some other number of fifths as the numerator (dividing <the difference> into 1/5).

Then your expression might be ...

... (1/5)(50 -10/2)

_____

There are ways to write math expressions in English so they are unambiguous. This isn't one of them. It must be done very carefully, as English is often intentionally vague and subject to a variety of interpretations (as most human languages are). Good punctuation helps.

Since the sign between parentheses is +, we can simply drop the parentheses and combine like terms.

... = x²(6 +3) +x(-2 -4) +(4 -3)

... = 9x² -6x +1

Answer:

The percent increase is [tex]13.33[/tex]%

Step-by-step explanation:

First we need to calculate the increase:

Increase in value = [tex]255-225[/tex]

                             =[tex]30[/tex]

Percent increase = [Increase in value / Initial value]*100

                             =[tex]\frac{30}{225} *100[/tex]

                             =[tex]13.33[/tex]%

Therefore,

the percent increase is [tex]13.33[/tex]%

Assuming you want the y-intercept of the line through those two points, you can find it a couple of different ways.

The slope of the line is ...

... slope = (change in y)/(change in x) = (6-18)/(6-2) = -12/4 = -3

We are given the y-value for x=2. When x decreases by 2 to x=0, then the y-value changes by (-2)·(-3) = +6, from 18 to 24.

___

You can also write the equation of the line in point-slope form as ...

... y = -3(x -2) +18

Again, when x=0, the y-intercept is ...

... y = -3(0 -2) +18 = 6 +18 = 24

The y-intercept of the line through (2, 18) and (6, 6) is 24.

slope m =  –4

equation

y - 3 = -4(x + 2)

y - 3 = -4x - 8

y = -4x - 5 where slope = -4 and y intercept = b = -5

Answer

Y intercept (0, -5)

[tex]x_{1} =-2[/tex]

[tex]x_{2}=3[/tex]

Slope intercept form: y = mx + b

mx=-4

b= -5

Intercepts

x intercept=-1.25

y intercept=-5

The correct answer is y intercept =-5

multiply numerator/ denominator by the same value 4 to create an equivalent ratio

[tex]\frac{4}{5}[/tex] × [tex]\frac{4}{4}[/tex] = [tex]\frac{16}{20}[/tex]

\frac{4}{5} × \frac{4}{4} = \frac{16}{20}

8m + 13g - 8 + 3m - g

8m + 3m = 11m

13g - g = 12g

11m + 12g - 8 ⇒ Your simplified expression

There you go! I really hope this helped, if there's anything just let me know! :)

Answer:

11m+12g-8

Step-by-step explanation:

8m+13g-8+3m-g

8m+3m+13g-g-8

11m+12g-8

The numbers are a bit ugly, but the equation can be solved as is.

... 1.2x/3.6 + (0.2/3.6) = 0.5x/9 . . . . use the distributive property on the left

... x(1/3 -1/18) + 1/18 = 0 . . . . . subtract the right side, simplify fractions

... x(6/18 -1/18) = -1/18 . . . . . . . use 18 for common denominator

... 5x = -1 . . . . . . . . . . . . . . . . . multiply by 18

... x = -1/5 . . . . . . . . . . . . . . . . divide by 5

_____

You can eliminate decimals and fractions by multiplying the given equation by 18.

... 6x +1 = x

... 5x +1 = 0

... 5x = -1

... x = -1/5

_____

The fraction simplification can work like this:

... 0.2/3.6 = 2/36 = 1/18

... 0.5/9 = (1/2)/9 = 1/(2·9) = 1/18 . . . . or . . . . (0.5)/9 × (2/2) = (0.5·2)/(9·2) = 1/18

Answer:

x=-0.2

Step-by-step explanation:

The given equation is

[tex]\frac{0.2(6x+1)}{3.6}=\frac{0.5x}{9}[/tex]

We need to solve the given equation for x.

On cross multiplication we get

[tex]9[0.2(6x+1)]=3.6(0.5x)[/tex]

[tex]1.8(6x+1)=1.8x[/tex]

Using distribution property, we get

[tex]1.8(6x)+1.8(1)=1.8x[/tex]

[tex]10.8x+1.8=1.8x[/tex]

Subtract 1.8x and 1.8 from both sides.

[tex]10.8x+1.8-1.8x-1.8=1.8x-1.8x-1.8[/tex]

[tex]10.8x-1.8x=-1.8[/tex]

[tex]9x=-1.8[/tex]

Divide both sides by 9.

[tex]x=-\frac{1.8}{9}[/tex]

[tex]x=-0.2[/tex]

Therefore, the value of x is -0.2.

Answer:

x = 4

Step-by-step explanation:

We assume that the given expessions represent the measures of the alternate interior angles, so are equal.

... (4x + 12)° = 7x°

... 12 = 3x . . . . . . . divide by degrees, subtract 4x

... 4 = x . . . . . . . . . divide by 3

_____

Then the angles are 7x° = 28° = (4x+12)°.

number is 21

let the number be n then dividing by 3 gives [tex]\frac{n}{3}[/tex] and adding - 3 gives

[tex]\frac{n}{3}[/tex] - 3 = 4 ( add 3 to both sides )

[tex]\frac{n}{3}[/tex] = 7 ( multiply both sides by 3 )

n = 3 × 7 = 21

Remark

You have been told that the slope of the line is 2/3. That means that if the general equation is y = mx + b is the equation for the slope intercept formula and since m = the slope, then m also equals 2/3

y = (2/3)x + b

Use the point to find b

when x = 3

y = 4                       This comes from the point

4 = (2/3) * 3 + b      multiply 2/3 and 3 together

4 = 6/3 + b             Simplify 6/3

4 = 2 + b                  Subtract 2 from both sides

4 - 2 = b                   Combine

2 =  b              

Equation

y = (2/3)x + 2

Hey there!!

What is slope-intercept form ?

Ans :- y = mx + b

Where 'm' is the slope and 'b' is the y-intercept.

Given :

Slope = 2/3

Coordinate : ( 3 , 4 )

Now, plugging in all these values, we get :

... 4 = ( 2/3 )×3 + b

... 4 = 2 + b

b = 2

Hence, the y -intercept is 2.

Getting this into slope-intercept form :

y = ( 2x/3 ) + 2

Hope my answer helps!!