6x^2-2x=20 use ac method

Answer:

1. [tex]Area=16\,\pi=50.265[/tex]

2.- [tex]\frac{b}{a} =-8[/tex]

3.  [tex]y=\frac{1}{2} x^2+3x+\frac{5}{2}[/tex]

4.  [tex]a+b+c=\frac{17}{4}[/tex]

5.   the vertex is located at: (3, 10)

Step-by-step explanation:

1. If we rewrite the formula of the conic given by completing squares, we can find what conic we are dealing with:

[tex](x^2-2x)+(y^2+6y)=6\\\,\,\,\,\,\,+1\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,+9\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,+10\\(x-1)^2+(y+3)^2=16\\(x-1)^2+(y+3)^2=4^2[/tex]

which corresponds to a circle of radius 4, and we know what the formula is for a circle of radius R, then:

[tex]Area=\pi\,R^2=\pi\,4^2=16\,\pi=50.265[/tex]

2.

If x=4 is the axis of symmetry of the parabola

[tex]y=ax^2+bx+c[/tex]

then recall the formula to obtain the position of the x-value of the vertex:

[tex]x_{vertex}=-\frac{b}{2a} \\4=-\frac{b}{2a}\\4\,(-2)=\frac{b}{a} \\\frac{b}{a} =-8[/tex]

3.  

From the graph attached, we see that the vertex of the parabola is at the point: (-3, -2) on the plane, so we can write the general formula for a parabola in vertex form:

[tex]y-y_{vertex}=a\,(x-x_{vertex})^2\\y-(-2)=a\,(x-(-3))^2\\y+2=a(x+3)^2[/tex]

and now find the value of the parameter "a" by requesting the parabola to go through another obvious point, let's say the zero given by (-1, 0) at the crossing of the x-axis:

[tex]y+2=a\,(x+3)^2\\0+2=a(-1+3)^2\\2=a\,2^2\\a=\frac{1}{2}[/tex]

So the equation of the parabola becomes:

[tex]y+2=\frac{1}{2} (x+3)^2\\y+2=\frac{1}{2} (x^2+6x+9)\\y+2=\frac{1}{2} x^2+3x+\frac{9}{2} \\y=\frac{1}{2} x^2+3x+\frac{9}{2} -2\\y=\frac{1}{2} x^2+3x+\frac{5}{2}[/tex]

4.

From the location of the focus of the parabola as (4, 3) and the directrix as y=1,  we conclude that we have a parabola with dominant vertical axis of symmetry, displaced from the origin of coordinates, and responding to the following type of formula:

[tex](x-h)^2=4\,p\,(y-k)[/tex]

with focus at: [tex](h,k+p)[/tex]

directrix given by the horizontal line [tex]y=k-p[/tex]

and symmetry axis given by the vertical line [tex]x=h[/tex]

Since we are given that the focus is at (4, 3), we know that [tex]h=4[/tex], and that [tex]k+p=3[/tex]

Now given that the directrix is: y = 1, then:

[tex]y=k-p\\1=k-p[/tex]

Now combining both equations with these unknowns:

[tex]k+p=3\\k=3-p[/tex]

[tex]1=k-p\\k=1+p[/tex]

then :

[tex]1+p=3-p\\2p=3-1\\2p=2\\p=1[/tex]

and we now can solve for k:

[tex]k=1+p=1+1=2[/tex]

Then we have the three parameters needed to write the equation for this parabola:

[tex](x-h)^2=4\,p\,(y-k)\\(x-4)^2=4\,(1)\,(y-2)\\x^2-8x+16=4y-8\\4y=x^2-8x+16+8\\4y=x^2-8x+24\\y=\frac{1}{4} x^2-2x+6[/tex]

therefore: [tex]a=\frac{1}{4} , \,\,\,b=-2,\,\,and\,\,\,c=6[/tex]

Then [tex]a+b+c=\frac{17}{4}[/tex]

5.

The vertex of a parabola can easily found because they give you the roots of the quadratic function, which are located equidistant from the symmetry axis. So we know that is one root is at [tex]x=3+\sqrt{5}[/tex]and the other root is at [tex]x=3-\sqrt{5}[/tex]

then the x position of the vertex must be located at x = 3 (equidistant from and in the middle of both solutions. Then we can use the formula for the x of the vertex to find b:

[tex]x_{vertex}=-\frac{b}{2a}\\3=-\frac{b}{2\,(-2)}\\ b=12[/tex]

Now, all we need is to find c, which we can do by using the rest of the quadratic formula for the solutions [tex]x=3+\sqrt{5}[/tex]  and [tex]x=3-\sqrt{5}[/tex] :

[tex]x=-\frac{b}{2a} +/-\frac{\sqrt{b^2-4\,a\,c} }{2\,a}[/tex]

Therefore the amount [tex]\frac{\sqrt{b^2-4\,a\,c} }{2\,a}[/tex],  should give us [tex]\sqrt{5}[/tex]

which means that:

[tex]\sqrt{5}=\frac{\sqrt{b^2-4\,a\,c} }{2\,a} \\5=\frac{b^2-4ac}{4 a^2} \\5\,(4\,(-2)^2)=(12)^2-4\,(-2)\,c\\80=144+8\,c\\8\,c=80-144\\8\,c=-64\\c=-8[/tex]

Ten the quadratic expression is:

[tex]y=-2x^2+12\,x-8[/tex]

and the y value for the vertex is:

[tex]y=-2(3)^2+12\,(3)-8=-18+36-8=10[/tex]

so the vertex is located at: (3, 10)

Answer:

I think so you meant to write 62 as 6^2

If this is the question , then the answer is 6 x 6

HOPE THIS HELPS AND PLS MARK AS BRAINLIEST

THNXX :)

Answer:

B. 6 × 6

Step-by-step explanation:

6²

The square of a number means that the number is multiplied by itself.

6 × 6 (expanded form)

Answer:

B) the amount of debt you have

C) your payment history

E) the number of loans you have

Step-by-step explanation:

To determine the three pieces of information that contribute the most to your credit score, we have to find the factors that affect credit score calculation.

The major factors that affect a person's credit score calculation include : Payment history:

This is the most important factor that affect your credit score. Lenders want to be sure that you have a reputation back your debt and on time when you apply for new credit.

Amount of Debt :

This is the amount of overall debt you carry. It is the ratio of your credit card balances to your credit limit. Too much debt can hurt your credit score

Credit History:

This is a borrower's track record for repaying debts and how old it is. Opening new accounts within a short time will affect your credit score.

Account Mix: having a diverse portfolio of credit accounts could tell how well you manage different credits.

Credit Inquiries:

Several applications involving inquiries into your credit check within a short duration can affect your credit score.

Therefore the three pieces of information that would contribute the most to your credit score:

B) the amount of debt you have

C) your payment history

E) the number of loans you have

Answer:

Step-by-step explanation:

hello,

I assume that you mean

[tex]h(x)=\dfrac{12}{x-1}[/tex]

so first of all let's take x real different from 1 , as this is not allowed to divide by 0

[tex](hoh^{-1})(x)=x=h(h^{-1}(x))=\dfrac{12}{h^{-1}(x)-1} \ \ \ so\\h^{-1}(x)-1=\dfrac{12}{x} \\\\h^{-1}(x)=1+\dfrac{12}{x}[/tex]

and this is defined for x real different from 0

hope this helps

Answer:

Given: A right triangle in which an altitude is drawn from the right angle vertex to the hypotenuse.

To find: 'x' the larger leg of triangle

Solution,

Using let rule for similarity in right triangle:

[tex] \frac{leg}{part} = \frac{hypotenuse}{leg} \\ or \: \frac{x}{27} = \frac{3 + 27}{x} \\ or \: x \times x = 27(3 + 27) \\ or \: x \times x = 81 + 729 \\ or \: {x}^{2} = 810 \\ or \: {x}^{2} = 81 \times 10 \\ or \: {x} = \sqrt{81 \times 10} \\ or \: x = \sqrt{81} \times \sqrt{10} \\ or \: x = \sqrt{ {(9)}^{2} } \times \sqrt{10} \\ \: x = 9 \sqrt{10} [/tex]

Hope this helps...

Good luck on your assignment..

Answer:

x^2   +y^2 = 16    

Step-by-step explanation:

The equation of a circle is given by

(x-h) ^2 + (y-k)^2 = r^2  where (h,k) is the center and r is the radius

(x-0) ^2 + (y-0)^2 = 4^2

x^2   +y^2 = 16        

please see the attached picture for full solution..

Hope it helps..

Good luck on your assignment...

Answer:

2.99

Step-by-step explanation:

Take the total cost and divide by the number of cards

71.76/24 = 2.99

The cost per car is 2.99

Answer:

b. $2.99.

Step-by-step explanation:

To get the price per car, you get the total price divided by the total number of cars.

That would be 71.26 / 24 = 2.969166667, which is most close to b. $2.99. Those are some cheap cars!

Hope this helps!

Answer:

Step-by-step explanation:

1l ........8.5 miles

x l .......6 miles

-----------------------

x=6*1/8.5

x=0.70 l

2*0.7=1.4 l petrol/day ( to work and come back home)

5*1.4=7 l/week ( 5 days works in a week)

7*1.26=8.82 L /week

8.82>8.5

The petrol costs more

So the answer is NO

Answer:

50 deg

Step-by-step explanation:

In an right triangle, the acute angles are complementary. That means their measures have a sum of 90 deg.

m<C + m<B = 90

7x - 20 + 4x = 90

11x = 110

x = 10

m<ACB= 7x - 20

m<ACB = 7(10) - 20

m<ACB = 70 - 20

m<ACB = 50

Answer: m<ACB = 50 deg

Answer:

y-int = C/B

Step-by-step explanation:

Ax + By = C

y-int = C/B

Answer:

I hope this helps.

Step-by-step explanation:

Answer:

122.6 pounds

Step-by-step explanation:

Let's call the weight of the largest fish from lake A 'x', and the weight of the largest fish from lake B 'y'.

If x is 208.2 pounds less than seven times y, we have that:

[tex]x = 7y - 208.2[/tex]

We know that x is equal 650 pounds, so we can find y:

[tex]650 = 7y - 208.2[/tex]

[tex]7y = 650 + 208.2[/tex]

[tex]7y = 858.2[/tex]

[tex]y = 122.6\ pounds[/tex]

So the weight of the largest fish caught in Lake B is 122.6 pounds

Answer:

  the height of the cylinder is 7 units greater than the radius

Step-by-step explanation:

When you match the forms of the equations ...

  [tex]V=\pi r^2(r+7)\\V=\pi r^2h[/tex]

you see that the factor (r+7) corresponds to the height (h) of the cylinder. That is ...

  the height of the cylinder is 7 units greater than the radius.

Answer:

10 mph

Step-by-step explanation:

The top speed you will ever need to go in a parking lot is 10 mph.

15 mph is the fastest you should ever drive in a parking lot. The right answer is D.

The National Motorists Association was established in 1982 and is a divisive nonprofit advocacy group representing drivers in North America.

The Association promotes engineering standards that have been demonstrated to be effective, justly drafted and applied traffic legislation, and full due process for drivers.

Given to give information about the top speed you will ever need

to go into a parking lot is,

A group of drivers came together to form the National Motorists Association, Inc., a non-profit organization, to defend drivers' rights in the legal system, on the highways, and inside our cars.

Usually, there are marked speed limits in parking lots. Obey speed limits when you see them to avoid tickets and to keep everyone safe.

The National Motorists Association advises driving no faster than 15 miles per hour at all times when there are no written speed limits.

Therefore, the correct option is D.

For more details regarding Motorists;

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Answer:

multiply 0.85x40

Step-by-step explanation:

Answer:

Step-by-step explanation:

Hello, this is a geometric sequence so we are looking for a multiplicative factor.

[tex]a_0=600\\\\a_1=a_0 \cdot \boxed{\dfrac{1}{2}} = 300 = 600 \cdot \boxed{\dfrac{1}{2}}\\\\a_2=a_1 \cdot \boxed{\dfrac{1}{2}} = 150= 300 \cdot \boxed{\dfrac{1}{2}}\\\\a_3=a_2 \cdot \boxed{\dfrac{1}{2}} = 75 = 150 \cdot \boxed{\dfrac{1}{2}}[/tex]

So, the explicit formula is for n

[tex]\boxed{a_n=a_0\cdot \left(\dfrac{1}{2}\right)^n=600\cdot \left(\dfrac{1}{2}\right)^n}}[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

The explicit rule is aₙ = a₀(1/2)ⁿ = 600(1/2)ⁿ for the given geometric sequence.

The geometric series defined as a series represents the sum of the terms in a finite or infinite geometric sequence. The successive terms in this series share a common ratio.

The nth term of a geometric progression is expressed as

Tₙ = arⁿ⁻¹

Where a is the first term, r is the common ratio.

We have been given that geometric sequence as:

600, 300, 150, 75, ...

To determine the explicit rule for the geometric sequence, we have to find the common ratio.

Here the first term (a₀) is 600

So the common ratio = 300/600 = 150/300 = 75/150 = 1/2

Thus, the explicit formula for n would be:

aₙ = a(1/2)ⁿ = 600(1/2)ⁿ

Therefore, the explicit rule is aₙ = a(1/2)ⁿ = 600(1/2)ⁿ for the given geometric sequence.

Learn more about the geometric series here:

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Answer:

18107.32

Step-by-step explanation:

Set up the exponential function in the form:

       [tex]P = P_0(R)^t[/tex]

so P is the new population, [tex]P_0[/tex] is the original population, R is the rate of increase in population, and t is the time in years.

You have to use the information given to find the rate that the population is increasing and then use that rate to find the new population after more time passes.

[tex]13000 = 6000(R)^7\\\\\\frac{13000}{6000} = R^7\\\\\sqrt[7]{\frac{13000}{6000} } = R\\\\\\ R = 1.116786872[/tex]

Now that you found the rate, you can use the function to find the population after another 3 years.

[tex]P = 13000(1.116786872)^3\\P = 18107.32317\\[/tex]

So the population is 18107, rounded to the nearest whole number.

Answer:

The difference of the functions is (f-g)(x) = 3x - 3

Step-by-step explanation:

In the problem, we are asked to find the difference of the two functions, f(x) and g(x). When we see (f-g)(x), this means that we are going to subtract g(x) from f(x).

f(x) = 5x - 2

g(x) = 2x + 1

(f-g)(x) = (5x - 2) - (2x + 1)

Distribute the negative to (2x + 1)

(f-g)(x) = 5x - 2 - 2x - 1

Combine like terms. Make sure your answer is in standard form.

(f-g)(x) = 3x - 3

So, the answer to the equation is (f-g)(x) = 3x - 3

Answer:

a) [g ° h](x)  = 3x² +6

b) [h ° g](x) =3 x²+36x+108

Step-by-step explanation:

Explanation:-

a)

Given g(x) = x+6 and h(x) = 3x²

Given [g ° h](x) = g(h(x))

                          = g(3x²)       (∵ h(x) =3x²)

                         = (3x²)+6      (∵ g(x) =x+6)

∴ [g ° h](x)  = 3x² +6

b)

Given [h ° g](x) = h (g(x))

                          = h(x+6)     (∵ g(x) =x+6)

                         = 3 (x+6)²    (∵ h(x) =3x²)

                         = 3 (x²+2(6)x+36)    (∵ (a + b)² = a²+2ab+b²)

                         = 3 (x²+12x+36)

                        = 3 x²+36x+108)

     ∴ [h ° g](x) =3 x²+36x+108

"can't exceed 975" means this is the largest value possible for C. So we could have C = 975 or smaller. We write this as [tex]C \le 975[/tex] which is read as "C is less than or equal to 975".

Answer:

5

Step-by-step explanation:

Answer:

$1.08

Step-by-step explanation:

30 days × (2 hrs/day) × (150 W) × (1 kW / 1000 W) × (0.12 $/kWh) = $1.08

Answer:

If the correlation coefficient is 1, then the slope must be 1 as well.

Step-by-step explanation:

Coefficient of correlation is used in statistics to determine the relationship between two variables. Correlation coefficient and slope always have same sign. It measures the strength of linear relation between two variables. The values of correlation coefficient ranges between 0 to 1. where 0 determines that there is no relationship between two variables.

If the correlation coefficient is 1, then the slope must be 1 as well.

The correlation coefficient (ρ) is a measure that determines the degree to which the movement of two different variables is associated.

So, the false statement is:

If the correlation coefficient is 1, then the slope must be 1 as well.

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Answer:

Explained below.

Step-by-step explanation:

The question is:

Compare the distributions using either the means and standard deviations or the five-number summaries. Justify your choice.

Set A: {36, 51, 37, 42, 54, 39, 53, 42, 46, 38, 50, 47}

Set B: {22, 57, 46, 24, 31, 41, 64, 50, 28, 59, 65, 38}

The five-number summary is:

The five-number summary for set A is:

Variable   Minimum       Q₁         Median        Q₃         Maximum

  Set A       36.00       38.25        44.00       50.75        54.00

The five-number summary for set B is:

Variable   Minimum       Q₁         Median        Q₃         Maximum

 Set B         22.00      28.75        48.00       58.50         65.00

Compute the mean for both the data as follows:

[tex]Mean_{A}=\frac{1}{12}\times [36+51+37+...+47]=44.58\approx 44.6\\\\Mean_{B}=\frac{1}{12}\times [22+57+46+...+38]=44.58\approx 44.6[/tex]

Compare mean and median for the two data:

[tex]Mean_{A}>Median_{A}\\\\Mean_{B}>Median_{B}[/tex]

Compute the standard deviation for both the set as follows:

[tex]SD_{A}=\sqrt{\frac{1}{12-1}\times [(36-44.6)^{2}+...+(47-44.6)^{2}]}=6.44\approx 6.4\\\\SD_{B}=\sqrt{\frac{1}{12-1}\times [(22-44.6)^{2}+...+(38-44.6)^{2}]}=15.56\approx 15.6[/tex]

Answer:

  (3.6, 0), (0, -2)

Step-by-step explanation:

To find the y-intercept, set x=0:

  -5·0 +9y = -18

  y = -18/9 = -2

To find the x-intercept, set y=0:

  -5x +9·0 = -18

  x = -18/-5 = 3.6

The intercepts are ...

  x-intercept: 3.6

  y-intercept: -2

Answer:

(f * g)(x) has a final product of 16x² + 8x.

Step-by-step explanation:

When you see (f * g)(x), this means that we are going to be multiply f(x) and g(x) together.

f(x)=8x

g(x)=2x+1

Now, we multiply these terms together.

(8x)(2x + 1)

Use the foil method to multiply.

16x² + 8x

So, the product of these terms is 16x² + 8x.

Answer:

data bar

Step-by-step explanation:

Answer:

chart

Step-by-step explanation:

Answer:

Se pagará $7200.

Step-by-step explanation:

La ecuación del costo puede descomponerse en dos factores que luego se multiplican:

1) Siendo A el area del del muro, la parte del costo que depende del área se calcula como un tercio (1/3) del doble (2) del área A. Este factor se puede escribir como:

[tex]C_1=(1/3)\cdot 2 \cdot A=(2/3)\cdot A[/tex]

2) Siendo T el número de trabajadores, el siguiente factor es el triple del numero de trabajadores T. Esto es:

[tex]C_2=3T[/tex]

Multiplicando ambos factores, tenemos la ecuacion del costo en función de A y T:

[tex]C=C_1\cdot C_2=(2/3)A\cdot 3T=2 AT[/tex]

Si se planea pintar un muro de 1200m² y se contrataran a 3 trabajadores, el costo será:

[tex]C=2AT=2(1200)(3)=7200[/tex]

Answer:

-978

Step-by-step explanation:

1.) Use Distributive property (by multiplying 15 by the values in parentheses): -735=15m + 13935

2.) Subtract 13,935 on both sides, to move that value to the left side, to further  isolate the variable m.

-735-13935=15m + 13935 - 13935

3.)-Simplify/Combine Like Terms

-14,670=15m

4.) Divide both sides by 15 to isolate and solve for m

-14,670/15=15m/15

5.) Simplify

-978=m    

6.) Rearrange so m is on left side and value is on right side

m=-978

Answer:

1/2

Step-by-step explanation:

The numbers that are 6 or even on the cards are 2, 4, and 6.

3 cards out of a total of 6 cards.

3/6 = 1/2

Answer:

1/2 chance

Step-by-step explanation:

There are 3 numbers that fit the rule, 2, 4, and 6. 3/6 chance of picking one or 1/2, simplified.