"Complete the square" to convert the equation of each circle to graphing form. Identify the center and the radius.

x² + 6x + y2 – 4y= -9
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ANSWER

[tex]x =1 +\frac{1}{2} \sqrt{ 10} \: or \: x =1 - \frac{1}{2}\: \sqrt{10}[/tex]

EXPLANATION

The given quadratic equation is

[tex]2 {x}^{2} - 4x - 3 = 0[/tex]

This function is of the form:

[tex] a{x}^{2} + bx + c = 0[/tex]

This implies that:

a=2, b=-4 and c=-3.

We can solve this equation using the quadratic formula:

[tex]x = \frac{ - b \pm \: \sqrt{ {b}^{2} - 4ac} }{2a} [/tex]

We substitute the values into the quadratic formula to obtain;

[tex]x = \frac{ - - 4 \pm \: \sqrt{ {( - 4)}^{2} - 4(2)( - 3)} }{2(2)} [/tex]

[tex]x = \frac{4 \pm \: \sqrt{ 40} }{4} [/tex]

[tex]x = \frac{4 \pm \: 2\sqrt{ 10} }{4}[/tex]

[tex]x =1\pm \: \frac{1}{2} \sqrt{10}[/tex]

[tex]x =1 +\frac{1}{2} \sqrt{ 10} \: or \: x =1 - \: \frac{1}{2} \sqrt{10}[/tex]

Answer:

PQ

Step-by-step explanation:

TANGENT ALWAYS TOUCH TO THE CIRCUMFERENCE OF CIRCLE

Answer:

distance = (22/2) - (5/2) = 8.5 mm

Hope this helps chu

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The difference between the circumferences is 53.4 millimeters.

Remember that for a circle of diameter D, the circumference is:

C = pi*D

where pi = 3.14159...

We know that the outer diameter of the coin is 22mm, then the outer circumference is:

C = 3.14*22mm = 69.1mm

The inner diameter is 5mm, then the inner circumference is:

C' = 3.14*5mm = 15.7mm

Then the difference is:

69.1mm -  15.7mm = 53.4mm

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Answer:

(-1,8)

Step-by-step explanation:

Look at the top point of the parabola type thing. I know that it's not a parabola, but IDRK how else to describe it. If you see the top point at one of the answers, it is most likely correct.

(-1,8) is most likely to be the relative maximum for this graph.

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D. None, since -3a+3a is 0, leaving 6=7, which is not true.

add similar elements: 2.5x-x+3.8x+0.7x= 6x

divide both sides by 6

x=0.09

Answer:

x=0.09

Step-by-step explanation:

2.5x−x+3.8x+0.7x=0.54

(2.5 -1 +3.8+0.7)x =0.54

6x=0.54

x=0.54/6

x=0.09

Answer: A) 6/8

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Explanation:

The tangent of angle A is the ratio of the opposite and adjacent sides. So you just form a fraction of the opposite side (6) and the adjacent side (8)

The opposite side is the leg furthest from the reference angle A. The adjacent side is the leg closest to the angle A. Normally you would reduce the fraction as much as possible, but your teacher has chosen not to do so in this case.

ANSWER

A. 6/8

EXPLANATION

The tangent ratio is the ratio of the opposite side of the right triangle over the adjacent side of the right triangle.

The side opposite to angle A is 6cm

The side adjacent to angle A is 8cm.

[tex] \tan(A) = \frac{6cm}{8cm} [/tex]

[tex]\tan(A) = \frac{6}{8} [/tex]

The first choice is correct.

Answer:

Step-by-step explanation:

when the two angles are added they are equal to 180 degree. (corresponding angles property)

x+8+3X+2=180

4X+10=180

4X=170

X=44.25 DEGREES

Question 1:

For this case we have that by definition, if a and b are two parallel lines, then the corresponding angles are congruent, that is, we can write 3x + 2 and x + 8 as supplementary angles:

[tex](3x + 2) + (x + 8) = 180\\3x + 2 + x + 8 = 180\\4x + 10 = 180\\4x = 180-10\\4x = 170\\x = \frac {170} {4}\\x = 42.5[/tex]

We look for the value of the angles:

[tex]3 (42.5) + 2 = 129.5\ degrees\\42.5 + 8 = 50.5 \ degrees[/tex]

ANswer:

[tex]x = 42.5\\3 (42.5) + 2 = 129.5\ degrees\\42.5 + 8 = 50.5 \ degrees[/tex]

Question 2:

For this case we have that by definition, the equation of a line of the slope-intersection form is given by:

[tex]y = mx + b[/tex]

Where:

m: It's the slope

b: It is the cutoff point with the y axis

Now, in the equation [tex]y = 2x + 3[/tex]

[tex]m = 2\\b = 3[/tex]

By definition, if two lines are parallel, their slopes are equal. Also, if two lines are perpendicular, then the product of their slopes is -1.

So:

The slope of a line parallel to the given line is:

[tex]m = 3[/tex]

The slope of a line perpendicular to the given line is:

[tex]3 * m = -1\\m = - \frac {1} {3}[/tex]

ANswer:

[tex]3\\- \frac {1} {3}[/tex]

Answer:

[tex](0.5,-4.5)[/tex]

Step-by-step explanation:

The given rectangle has diagonals have the endpoints P(-3, -2) ,I(4, -7) and A(4, -2) ,D(-3, -7)

The diagonals of the rectangle bisect each other so we use the midpoint formula to find their point of intersection.

The midpoint formula is;

[tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]

We use any pair of endpoints of the diagonals to find the point of intersection.

Using A(4, -2) ,D(-3, -7)

[tex](\frac{4+-3}{2},\frac{-2+-7}{2})[/tex]

[tex](\frac{1}{2},\frac{-9}{2})[/tex]

or

[tex](0.5,-4.5)[/tex]

the answer is 12 since the sum of the two angles has to equal 180.

first you do

5x+5+115=180

combine like terms

5x+120=180

subtract 120

5x=60

then divide by 5

x=12

The answer would be 10 units.

I hope this helped!

Answer: 10

Step-by-step explanation:

You need to apply the Pythagorean Theorem:

[tex]a^2=b^2+c^2[/tex]

Where "a" is the hypotenuse and "b" and "c" are the legs of the right triangle.

Since you need to calculate the value of the hypotenuse, you need to solve for "a":

[tex]a=\sqrt{b^2+c^2}[/tex]

You know the lenght of two sides of the right triangle (6 and 8) Then, you can  substitute these values into [tex]a=\sqrt{b^2+c^2}[/tex].

Therefore, the hypotenuse of this right triangle is:

 [tex]a=\sqrt{6^2+8^2}[/tex]

 [tex]a=10[/tex]

28+8=8+10+p

36=18+p

Subtract 18 on the left and right hand side

36-18=18-18+p

p=18

Answer:

J

Step-by-step explanation:

The amount he is spending PER DAY is always a variable multiplied by its rate. That will be 8d.

Then you have a MAXIMUM amount of 3,000. That means the amount has to be less than or even equal to 3,000 but no more.

So 8d ≤ 3000 would be the answer

I believe the answer would be J. whenever the open part of the sign is towards a number or value, that means it is greater than the other number on the other side. For example 5 is less than 6 so 5 < 6. whenever the sign in between and has a line underneath it, it means it can also be equal to the number. therefore d is the amount per day and you pay that much for 8 days, so you get 8d. Now we know you can spend $3000, but no more. so you would use this sign < with a line drawn underneath it. now you would have 8d <(with a line underneath) 3000. this means that I'd must be equal to $3000 or less than $3000.

its kind of a difficult concept to learn but once you get it, it is very simple.

Answer:

[tex] log(4) + log( {x}^{2} ) - log(3) + log(y) + log(z) [/tex]

I think the answer would be something like this. but please correct me if I'm wrong

Answer:

A.) QRT and QST both measure 78 degrees

Step-by-step explanation:

I used process of elimination for this they had to be the same and the both aren't obtuse

Answer:

∠QRT and ∠QST both angles have measure 78°

Step-by-step explanation:

Given the figure in which measure of arc QVT is 156°

we have to choose the correct statement.

As given arc QVT=156° i.e ∠QPT=156°

By theorem angle made by same arc i.e inscribed angle formed by same arc are equal.

⇒ ∠QRT=∠QST

Also another theorem angle subtended at the centre is twice the angle at the circumference

⇒ ∠QPT=2∠QRT=2∠QST

[tex]2\angle QRT=\angle QPT=156^{\circ}[/tex]

[tex]\angle QRT=\frac{156}{2}=78^{\circ}[/tex]

⇒ ∠QRT and ∠QST both angles have measure 78°

Hence, option 1 is correct.

The game fair is no, the game is not fair for everybody. Adam has the best advantage.

We have given that,

You and two friends (Adam and Alana) will only play a game if it is fair for all three of you.

Fair game definition, a legitimate or likely object of attack, mockery, etc. With his fat, round face, the politician was fair game for the cartoonists.

The game your friend has proposed is to roll two number cubes (numbered 1-6) and find the sum.

If the sum is from 1-4 you get the point, 5-8 Adam gets the point, and 9-12 Alana gets the point.

You can't get a sum of 1. And there are the most amount of sums of 5-8.

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Answer:

D. X=1.75

Step-by-step explanation:

To start, let’s divide both sides by 4.

So 3^x =27.48/4

Since we want to solve for x, we take the log_3 of both sides.

So [tex]log_{3}3^x[/tex]=[tex]log_{3}6.87[/tex]

Using the laws of logs, we get

[tex]x*log_{3}3[/tex]=[tex]log_{3}6.87[/tex]

since [tex]log_{3}3[/tex] is 1, we get

X=[tex]log_{3}6.87[/tex]

Using a calculator, we find that x is about 1.75

You would need to subtract 37 from 125 to find the answer.

125-37=88

Angles C and D are supplementary, meaning they add up to 180 degrees. So, if we add 8u-48 to 5u+46, we get 13u-2. We set that equal to 180, so 13u-2=180. Add the two, so 13u=182. Divide the 13, so u=14. To double check, plug in 14 to both expressions. 8(14)-48 and 5(14)+46. 8(14)-48 is 64. 5(14)+46 is 116. If you add 64+116, you get 180, which proves your answer right! So u= 14

Answer:

Your answer is correct

Step-by-step explanation:

Answer:

Step-by-step explanation:

The way it is written is a bit ambiguous. If you mean

(1/6)*x = 2 then your answer is correct. Multiply both left and right by 6

6*(1/6)*x = 6*2

x = 12

If however, the question meant

1/(6x) = 2 then that is a different question.

Multiply both sides by 6x

1/(6x) * 6x = 2 * 6x

1 = 12*x                      

Divide by 12

x = 1/12

Change to a decimal

x = 0.08333333

Everything depends on how it is written. Try both if you can.

Answer:

38

Step-by-step explanation:

because he bought a shirt for $30+he paid an additional sales tax that is 8

so 30+8=38

Answer:

$32.40

Step-by-step explanation:

$30.00 * 0.08 = $2.40

$30.00 + $2.40 = $32.40

i hope this helps !!

The probabilities of all possible outcomes in a distribution must sum to 1.

[tex]\dfrac5{12}+\dfrac16+\dfrac13+x=1\implies x=\dfrac1{12}[/tex]

Answer:

1/12 C

Step-by-step explanation:

5/12

1/6=2/12

1/3=4/12

5/12-3=2/12

2/12+2=4/12

4/12-3= 1/12

Answer:  C) log₄ 84

Step-by-step explanation:

The rule for condensing (combining) log expressions that are added is MULTIPLICATION

log₄12 + log₄7 = log₄(12 × 7) = log₄ 84

Answer:

y = 2x² + 16x + 25

Step-by-step explanation:

Given in the question a vertex form of the equation

y = 2( x+4 )² - 7

The standard form of equation

y = ax² + bx + c

To convert it into standard form

y = 2(x² + 8x + 16) - 7

y = 2x² + 16x + 32 - 7

y = 2x² + 16x + 25

a = 2

b = 16

c = 25

Answer:

a

Step-by-step explanation:

Answer: Option A.

Step-by-step explanation:

Let's analize each option:

Option A: Observe in the graph of g(x) that when x increases the value of y decreases. For example, when [tex]x=0,y=2[/tex] and when  [tex]x=2,y=1[/tex]  However in the table of f(x) you can observe that the value of y increases when the value of x increases. For example, when [tex]x=-1,y=1.5[/tex] and when  [tex]x=0,y=2[/tex]  

Therefore, this statement is correct.

Option B: False. Because the y-intercept of functions are equal:

[tex]x=0,y=2[/tex]

Option C: False. You can observe in the graph that the function g(x) does not have x-intercept.

Option D: False. The average rate of change of the function f(x) is:

[tex]m=\frac{5-2}{2-0}=1.5[/tex]

The average rate of change of the function g(x) is:

[tex]m=\frac{1-2}{2-0}=-0.5[/tex]

Answer:

2.5

Step-by-step explanation:

First find the length of RS

x2 = 4

x1 = - 1

y2 = 2

y1 = 2

RS^2 = (2 - 2)^2 + (4 - -1 ) ^2

RS^2 = 0 + 5^2

RS = sqrt(5^2)

RS = 5

That is the length of the diameter. The radius is 1/2 that

r = d/2

d = 5

r = 5/2

r = 2.5

The answer would be 2.5

Answer:

15 ml

Step-by-step explanation:

If we mix 1 part concentrate and 5 parts water, we have 6 parts in total.

To create 90ml medicine, how many "6 parts" are there?

There would be 90/6 = 15 total "6 parts".

Each of the "6 parts's" 1 part is concentrate, so concentrate would be 1 * 15 = 15 ml.

In ratio:

[tex]\frac{Concentrate}{Total(Water+Concentrate)}=\frac{1}{5+1}=\frac{1}{6}\\\frac{1}{6}*90=15[/tex]

In a 90ml dose of medicine that requires a 1:5 ratio of concentrate to water, 15ml of concentrate is needed. This calculation uses the method of dilution, a common means of preparing solutions.

The question asks about the quantity of concentrate needed for a 90ml dose of medicine, given that one part of concentrate is diluted with 5 parts of water. This represents a ratio of 1:5, so for every 6 parts of the total mixture, 1 part is the concentrate.

To calculate this, we need to divide the total volume by the overall ratio (which is 6 in this case: the sum of the ratios 1:5). So take 90 ml and divide by 6, which gives 15 ml. This means there should be 15ml of the concentrate in a 90ml dose of medicine.

Dilution is a common means of preparing medicines and other solutions of a desired concentration by adding a solvent (like water in this example) to a more concentrated stock solution (the concentrate in this case).

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Answer:

Beans Jing bought=17b

Step-by-step explanation:

You multiply 17 by the m=number of beans per bag, this makes the equation 17b.

Answer: 17 ÷ b = x

Step-by-step explanation:

Jing bought 17 bags, and there are b in each bag. So you should divide 17 by b and then 17 ÷ b = x.

Answer:

≈ 3.8928

Step-by-step explanation:

log base 3 of 72 is approximately 3.8928

you would need to plug this into a calculator to solve

To evaluate log3 72, given that log3 8 is approximately 1.8928, we use properties of logarithms. We can express 72 as 8×9, and since log3 9 equals 2, log3 72 is 1.8928 + 2, which is 3.8928.

The student is asking to evaluate log3 72 given that log3 8 ≈1.8928. We can use the properties of logarithms to solve this. Since 72 can be expressed as 8×9, and we know that log3 8, we can find the log3 9 by understanding that 9 is 3²and therefore log3 9 is 2, because the base and the argument are the same.

Now, using the property of logarithms that loga (xy) = loga x + loga y, we can write log3 72 as:

log3 (8 ∙9) = log3 8 + log3 9

log3 72 = 1.8928 + 2

log3 72 = 3.8928

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Answer:

Step-by-step explanation:

10.99