How much less than 3x^2−7x+9 is 2x^2+4x−8? What is the value of the result when x=2?

^=power

Answer:

It is a factor and a variable.

Step-by-step explanation:

Answer:

34 miles is the distance from point A will they meet.

Step-by-step explanation:

Proportion states that the two ratios or fractions are equal.

Given the statement:

Distance between point A and B (i.e AB) = 200 mi.

Let the cyclist speed be c, and motor- speed be m;

then;

c = 17 mph and m=83 mph

Let they meet at distance x miles from a point A.  

By definition of proportion, we have;

[tex]\frac{x}{17} =\frac{200-x}{83}[/tex]

By cross multiply;

[tex]83x = 17(200-x)[/tex]

Using distributive property, [tex]a\cdot(b+c) =a\cdot b+ a\cdot c[/tex]

[tex]83x = 3400 - 17x[/tex]

Add 17x both sides we get;

[tex]83x+ 17x= 3400 - 17x +17x[/tex]

Simplify:

100x = 3400

Divide by 100 on both sides we get;

x = 34 miles

Therefore, the distance from point A will they meet is, 34 miles.

Answer:

Image

Step-by-step explanation:

Image

Given:

b1 = 17 ft

b2 = 20 ft

h = 13 ft

r = 17/2 = 8.5 ft

Area of the Semi-circle = 1/2 π r²

= 1/2 (22/7) (8.5²)

= (11/7) (72.25)

= 113.535 ft²

Area of the trapezium = (h) (b1 + b2) / 2

= (13)(17 + 20)/2

= 240.5 ft²

Total area of the amphitheater stage = Area of Semi-circle + Area of the trazezium = 113.535 + 240.5 = 354.035 ft²

Answer:

(x+1) is a factor with remainder 0.

Step-by-step explanation:

We divide (x+1) into the polynomial [tex]-3x^4+2x^3-x^2+6[/tex] through long division or synthetic. We choose long division and look for what will multiply with (x+1) to make the polynomial [tex]-3x^4+2x^3-x^2+6[/tex] .

[tex](x+1)(-3x^3)=-3x^4-3x^3[/tex]

We subtract this from the original [tex]-3x^4-(-3x^4)+2x^3-(-3x^3)-x^2+6[/tex].

This leaves [tex]5x^3-x^2+6[/tex]. We repeat the step above.

[tex](x+1)(5x^2)=5x^3+5x^2[/tex].

We subtract this from [tex]5x^3-(5x^3)-x^2-(5x^2)+6=-6x^2+6[/tex]. We repeat the step above.

[tex](x+1)(-6x)=-6x^2-6x[/tex].

We subtract this from [tex]-6x^2-(-6x^2)+0x-(-6x)+6=6x+6[/tex]. We repeat the step above.

[tex](x+1)(6)=-6x+1[/tex].

We subtract this from [tex]6x-(6x)+6-(6)=0[/tex]. There is no remainder. This means (x+1) is a factor.

Answer: x = 6

==============================================

Explanation:

The medians of a triangle meet up at the centroid in such a way that they cut each other at a ratio of 2:1, meaning that one part of the median is twice as long as the other. In this case, MO is two times longer than OP, so,

OP = 2*MO

and

MP = MO + OP

MP = MO + 2*MO .... replace OP with 2*MO

MP = 3*MO

9x-24 = 3*(x+4) ... plug in the given expressions

9x-24 = 3x+12

9x-3x = 12+24

6x = 36

x = 36/6

x = 6

Exterior angles of triangles = 360°.

So by definition:

[tex]9x + 6 + 10x - 1 + 10x + 7 = 360\\29x + 12 = 360\\29x = 348\\x = 12[/tex]

The value of x is 12.

Answer: 12

Step-by-step explanation:

We know that the sum exterior angles of a polygons is [tex]360^{\circ}[/tex].

Therefore,according to the given picture , we have

[tex]\angle{GHJ}+\angle{HJG}+\angle{JGH}=360^{\circ}\\\\\Rightarrow\ (9x+6)^{\circ}+(10x-1)^{\circ}+(10x+7)^{\circ}=360\\\\\Rightarrow\ 9x+6+10x-1+10x+7=360\\\\\Rightarrow\ 29x+12=360\\\\\Rightarrow\ 29x=348\\\\\Rightarrow\ x=\dfrac{348}{29}\\\\\Rightarrow\ x =12[/tex]

Hence, the value of x = 12

Answer:

1225.56 kg

Step-by-step explanation:

1 stone = 14 slugs

1 slug = 14.59 kg

[tex]\text{6 stones} ( \dfrac{14 slug}{1 stone})(\dfrac{14.59 kg}{1 slug})[/tex]

numerator 6 * 14 * 14.59 = 1225.56 kg

denominator = 1

Answer 1225.56 kg in 6 stones

w - width

2w - length

60 - perimeter

w + w + 2w + 2w = 6w - perimeter

The equation:

6w = 60    divide both sides by 6

w = 10 → 2w = 2 · 10 = 20

The area: A = width × length

A = (10)(20) = 200

Answer:

The correct answer option is a. 14∑1 (-28+3n)

Step-by-step explanation:

The summation notation for the given series is 14∑1 (-28+3n) where [tex]i[/tex] (the index of summation or the lower limit of summation) is 1 and [tex]n[/tex] (the upper limit of summation) is 14.

Putting in the values of the limit from 1 to 14 in the notation to get the first 14 terms of the series:

[tex]-28+3(1)=-25\\\\-28+3(2)=-22\\\\-28+3(3)=-19\\\\-28+3(4)=-16\\\\-28+3(5)=-13\\\\-28+3(6)=-10\\\\-28+3(7)=-7\\\\-28+3(8)=-4\\\\-28+3(9)=-1\\\\-28+3(10)=2\\\\-28+3(11)=5\\\\-28+3(12)=8\\\\-28+3(13)=11\\\\-28+3(14)=14\\[/tex]

Therefore, first option is the correct one.

Answer:

A is the correct one hope ive been of help

Answer:

The equation of this line would be y = -6

Step-by-step explanation:

In order to find this, we must first find the slope. For that we use the two points and the slope equation.

m(slope) = (y2 - y1)/(x2 - x1)

m = (-6 - -6)/(7 - 3)

m = 0/4

m = 0

Given that slope, we can use it along with a point in point slope form. From there we can solve for y and get the equation.

y - y1 = m(x - x1)

y + 6 = 0(x - 7)

y + 6 = 0

y = -6

Final answer:

To find the equation of a line passing through given points, calculate the slope, use the point-slope formula, and simplify to obtain the final equation. In this case, the line passing through (7,-6) and (3,-6) results in the equation y = -6.

Explanation:

To find the equation of the line passing through the points (7,-6) and (3,-6):

Calculate the slope (m) using the formula: m = (y₂ - y₁) / (x₂ - x₁)

Substitute one of the points and the slope into the point-slope formula: y - y₁ = m(x - x₁)

Simplify the equation to get the final answer: y = mx + b

The equation of the line passing through those two points is y = -6.

Answer:

53 minutes.  

Step-by-step explanation:

We have been given that Payton leaves  to go on an 85 minute bike ride at 3:27 pm.

Let us find when Payton will finish biking by 85 minutes after 3:27 pm.

Since 85 minutes equals to 1 hour and 25 minutes. 1 hour after 3:27 pm will be 4:27 pm. Now let us add 25 minutes to 4:27 pm.

So Payton will finish biking at 4:(27+25) pm= 4:52 pm.

Payton's family eats dinner at 5:45 pm. Now let us find remaining time between dinner and 4:52 pm.

[tex]\text{Minutes between dinner and finishing bike ride}=5:45 pm- 4:52 pm[/tex]  

[tex]\text{Minutes between dinner and finishing bike ride}=53[/tex]  

Therefore, Payton have 53 minutes between finishing her bike ride and eating dinner.  

Answer:

A. Distributive Property

Step-by-step explanation:

I'm taking the exam right now. :)

The missing number can be found using Matrix rule. We have to apply addition and subtraction rule to find the missing number form given matrix.

The missing number is -5.

Given:

The given matrix is,

[tex]\left[\begin{array}{cccc}9&38&47&4\\6&35&42&x\\12&21&23&27\end{array}\right][/tex]

Let the missing number is [tex]x[/tex].

Apply the subtraction rule to subtract second row from first row.

[tex]\left[\begin{array}{cccc}9&38&47&4\\3&3&5&4-x\\12&21&23&27\end{array}\right][/tex]

The sum of first three number is equal to the sum of digits of the first three number in the third row,

[tex]1+2=3\\2+1=3\\2+3=5[/tex]

Now from the same pattern.

[tex]2+7=4-x\\x=-5[/tex]

Thus, the missing number is -5.

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The answer is C. 3/5

20 girls, 3 boys. 23/40 is about 60 percent, or 3/5.

I wrote the wrong answer on accident for whatever reason when I first sent this, I apologize.

Answer:

1. 756 / 108 = 7 inches (the width of the first roof);

2. 954 / 106 = 9 inches (the width of the second roof);

Step-by-step explanation:

NOTES:

1)⇒    A + B + C = 180°

       A + B + C = π

       A + B        = π - C

2)⇒⇒ sin (A + B) = sin (π - C)

                         = (sin π)(cos C) - (sin C)(cos π)

                          = (0)(cos C) - (sin C)(-1)

                          = 0 - (-sin C)

                          = sin C

3)⇒⇒⇒cos (A + B) = cos (π - c)

                            = (cos π)(cos C) + (sin π)(sin C)

                            = (-1)(cos C) + (0)(sin C)

                            = - cos C              

4)⇒⇒⇒⇒ sin 2A + sin 2B = 2 sin (A + B) cos (A - B)

PROOF (from left side):

sin 2A + sin 2B + sin 2C    =    4 sin A sin B sin C

2 sin (A + B) cos (A - B) + sin 2C     refer to NOTE 4

2 sin (A + B) cos (A - B) + 2 sin C cos C  double angle formula

2 sin C cos (A - B) + 2 sin C cos C   refer to NOTE 2

2 sin C [cos (A - B) + cos C]     factored out 2 sin C

2 sin C [cos (A - B) - (cos(A + B)]   refer to NOTE 3

2 sin C [2 sin A sin B]           sum/difference formula

4 sin A sin B sin C      multiplied 2 sin C by 2 sin A sin B

Proof completed: 4 sin A sin B sin C   =   4 sin A sin B sin C

Answer: D

Step-by-step explanation:

End behavior is determined by two factor:

1. Coefficient - determines right side:

2. Degree - determines left side:

******************************************************************************************

-x³ + 2

Leading coefficient is NEGATIVE, so right side goes to -∞ (decreases)

Degree is ODD, so left side is opposite of right side → goes to +∞ (increases)

Answer: [tex]\bold{\dfrac{8}{13}}[/tex]

Step-by-step explanation:

Red   or    Face   -  duplicates (both red & face)

[tex]\dfrac{26}{52}[/tex]     +       [tex]\dfrac{12}{52}[/tex]      -     [tex]\dfrac{6}{52}[/tex]

= [tex]\dfrac{32}{52}[/tex]

= [tex]\dfrac{8}{13}[/tex]   simplified

Final answer:

The probability of selecting a red or face card from a standard deck of cards is 8/13. This outcome is more likely than selecting a heart suit face card specifically, which has a probability of 3/52.

Explanation:

The problem can be solved by understanding that the deck has 26 red cards (hearts and diamonds) and 12 face cards (jacks, queens, and kings), with 6 face cards being red. The total number of unique choices that are either red cards or face cards is the number of red cards plus the number of black face cards. This avoids double-counting red face cards.

There are 26 red cards, but we need to exclude the 6 red face cards already counted, and add the 6 black face cards (from clubs and spades), giving us 26 + 6 = 32 unique cards that are either red or face cards. The probability, P, is then 32/52, which simplifies to 8/13.

To compare, the probability of drawing specifically a heart suit face card is 3/52 as there are only 3 face cards (jack, queen, and king) in the heart suit. Comparing probabilities, 8/13 is greater than 3/52, so it is more likely to draw a red or face card than a heart suit face card.

Answer:

The answer is π

Step-by-step explanation:

Not really an explanation, but you can type this in wolframalpha: integrate (x^3 cos x/2 + 1/2) sqrt(4-x^2) dx from x=-2 to 2

The given integral can be solved using numerical calculation methods. The integral by part formula also would be applicable in the given integral.

The value of the given integral is [tex]3.14\rm\: or\: \pi[/tex].

Given:

Write the given integral.

[tex]\int_{-2}^{2}\sqrt{4-x^2}\left(\cos\left(\dfrac{x}{2}\right)x^3+\dfrac{1}{2}\right)\\[/tex]

Write the formula for the integration by part formula.

[tex]\int u.v=u\int vdx-\int u'(\int vdx)dx[/tex]

Let,

[tex]u=\sqrt{4-x^2}[/tex]

[tex]v=\left (x^3\cos\dfrac{x}{2} +\dfrac{1}{2} \right)[/tex]

Now put the value in above formula and integrate.

[tex]\begin{aligned}\int_{-2}^{2}\sqrt{4-x^2}\left(\cos\left(\dfrac{x}{2}\right)x^3+\dfrac{1}{2}\right)&=\left [\dfrac{\frac{x\sqrt{4-x^2}}{2}+2\arcsin\left(\frac{x}{2}\right)}{2}\right]_{-2}^{2}\\&=\left [\dfrac{x\sqrt{4-x^2}}{4}+\arcsin\left(\dfrac{x}{2}\right)\right]_{-2}^{2}\\\end[/tex]

Now, further simplify the expression.

[tex]\int_{-2}^{2}\sqrt{4-x^2}\left(\cos\left(\dfrac{x}{2}\right)x^3+\dfrac{1}{2}\right)\\=\left [\dfrac{2\sqrt{4-2^2}}{4}+\arcsin\left(\dfrac{2}{2}\right)\right]-\left [\dfrac{2\sqrt{4-(-2)^2}}{4}+\arcsin\left(\dfrac{-2}{2}\right)\right]\\=1.57-(-1.57)\\=3.14[/tex]

The value of the given integral is [tex]3.14\rm\: or\: \pi[/tex].

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Answer:

Y-coordinate = y - 4

Step-by-step explanation:

In the given question point D coordinate is (x, y)

and D after translation

x goes to 6 unit to the right and y goes to 4 unit down.

Hence,

          Y-coordinate = y-4

Example:From graph

              Let point D coordinate (x , y) = (2 , 3)

After rotation

              D coordinates is (x+6 , y-4) = (2+6 , 3_4) = (8 , -1)

Answer:

On edge. the answer is 1

Step-by-step explanation:

i just took it

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have the points (-7, 2) and (9, 6). Substitute:

[tex]m=\dfrac{6-2}{9-(-7)}=\dfrac{4}{16}=\dfrac{1}{4}[/tex]

The slope of the line passing through the points (-7,2) and (9,6) is 1/4.

Point-slope formula

[tex]y-y_{1} = m(x-x_{1} )[/tex]

In the slope formula, m stands for slope which is calculated as the

[tex]$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$$[/tex]

= Δy/Δx

where, m = slope

[tex](x_1, y_1)=[/tex] coordinates of the first point in the line

[tex](x_2, y_2)=[/tex] coordinates of the second point in the line

We have the points (-7,2) and (9,6).

Substitute the values [tex]x_{1}}$$[/tex], [tex]{x_{2}[/tex] and [tex]y_{1}}[/tex], [tex]${y_{2}[/tex]  in the above equation, we get

[tex]$m=\frac{6-2}{9-(-7)}[/tex]

[tex]$=\frac{4}{16}=\frac{1}{4}$[/tex]

Therefore, the slope m = 1 / 4.

To learn more about the Point-slope formula

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Answer: weclome

Step-by-step explanation:

Average movie ticket prices in the united states are, in general, lower than other countries. It would cost in $77.87 to buy three tickets in Japan plus two tickets in Switzerland. Three tickets in Switzerland plus two tickets in Japan would cost $73.83. How much does an average movie ticket cost in each of these countries?  

Let ticket in japan cost x

Let ticket in Switzerland cost y  

3x+2y=77.87 ------1

3y+2x=73.83------2  

Subtract the equations  

x-y= 4.04 ---4

3y+2x=73.83------5

Answer:

Step-by-step explanation:

Average movie ticket prices in the united states are, in general, lower than other countries. It would cost in $77.87 to buy three tickets in Japan plus two tickets in Switzerland. Three tickets in Switzerland plus two tickets in Japan would cost $73.83. How much does an average movie ticket cost in each of these countries?  

Let ticket in japan cost x

Let ticket in Switzerland cost y  

3x+2y=77.87 ------1

3y+2x=73.83------2  

Subtract the equations  

x-y= 4.04 ---4

3y+2x=73.83------5

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Answer:

m<Q = 92 degrees

Step-by-step explanation:

Opposite angles of a quadrilateral inscribed in a circle are supplementary.

Angles O and Q are opposite angles, so they are supplementary, so their measures add up to 180 degrees.

m<O + m<Q = 180

2x + 2x + 4 = 180

4x + 4 = 180

4x = 176

x = 44

m<Q = 2x + 4 = 2(44) + 4 = 92

Answer:

Q =92

Step-by-step explanation:

Since the quadrilateral is inscribed in a circle, the opposite angles add to 180 degrees.

<O + <Q = 180

2x+ 2x+4 = 180

4x+4 =180

Subtract 4 from each side

4x= 180-4

4x= 176

Divide by 4

x = 44

Q = 2x+4

Q = 2(44)+4

Q = 88+4

Q = 92

Answer:

1/5 chance

Step-by-step explanation:

well their are 4 balls and 2 chosen

their is 1/2 chance or pulling a yellow

1/4 chance of pulling a black and green

 Y1 Y2,Y1 B,Y1 G,Y2 Y1,Y2 B,Y2 G,B Y1,B Y2,B G,G Y1,R Y2,G B

so their is a 1/5 chance of pulling it

Answer:

The sale price is $43.50.

Step-by-step explanation:

58 x .25 = 14.50 off the original price

58 - 14.50 = 43.50

Answer:

168

Step-by-step explanation:

2x45=90

6x13=78

78+90=168

Answer:

69

Step-by-step explanation:

23 times 3

Answer:

Your answer is B!

Step-by-step explanation:

If x = the first number (equal to 1x) then the second number is 75% more than this.

This means the value of the bigger number is 100 + 75 (because 100 is the starting number and 75 is the percent bigger)

This can be shown with the following equation:

Amount * [tex]\frac{percentage}{100}[/tex]

x *  [tex]\frac{175}{100}[/tex] = 1.75x

1.75x is the value of the bigger number.