Write the quadratic equation in factored form. Be sure to write the entire equation.

x 2 + x - 12 = 0

The center of the circle is (7,8) and the equation of the given circle is (x- 7)^2 + (y - 8)^2 = 16

The given parameters are:

Center (a,b) = (7,8)

Point (x,y) = (11,8)

Calculate the radius (r) using:

[tex]r = \sqrt{(x- a)^2 + (y - b)^2}[/tex]

So, we have:

[tex]r= \sqrt{(11- 7)^2 + (8 - 8)^2}[/tex]

Evaluate the expression

[tex]r = 4[/tex]

The circle equation is then calculated using:

[tex](x- a)^2 + (y - b)^2 =r^2[/tex]

So, we have:

[tex](x- 7)^2 + (y - 8)^2 = 4^2[/tex]

Evaluate the exponent

[tex](x- 7)^2 + (y - 8)^2 = 16[/tex]

Hence, the equation of the given circle is (x- 7)^2 + (y - 8)^2 = 16

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Answer:

(fx^2)/3 - 6f

Step-by-step explanation:

Answer:

the height is 5 and the base is 17.

Step-by-step explanation:

X + 1 is the height and 4x + 1 is the base, so we can substitute this into an equation:

( x + 1 ) (4x + 1) = 85

{apply the distributive law}

4x² + x + 4x + 1 =

4x² + 5x + 1 = 85

Take 85 to the other side by -85 each side:

4x² + 5x + 1 - 85 = 85 - 85

4x² + 5x - 84 = 0

{Now we have a quadratic equation}

The roots are either -5.25 or 4. X must be 4 since it must be positive as it is a side length.

Substitute x into the base and height to get the answers.

X + 1 = 4 + 1 = 5

4x + 1 = 16 + 1 = 17

Therefore the height is 5 and the base is 17.

Answer:

1 because I don't know how to do this stuff yet

circumference = πd

= 3.14 × 14

43.98 ft

hope it helps...!!!

Answer:

44

Step-by-step explanation:

We are given that the diameter is 14 ft.

The radius is half the diameter, so the radius is 7 ft.

Now, the formula for circumference is: 2πr

So: 2 * π * (7) = 43.98

Round: 43.98 >> 44.0

Answer:

Step-by-step explanation:

The interquartile range = Third quartile - First quartile = 22 - 15 = 7

The range = 25 - 12 = 13

Range = largest data value - the least data value

Interquartile range = Q3 - Q1

Given the following weekly allowance of Sean's classmates as, 15, 15, 22, 14, 12, 24, 16, 25, 15, 15:

Third quartile (Q3) = 22

First quartile (Q1) = 15

Interquartile range = 22 - 15 = 7

Range = 25 - 12 = 13

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Answer:

80

Step-by-step explanation:

profit = revenue - expenses

revenue = $15 per hour = $15 * number of hours (n) = $15 * n

expenses = $490 + $45 + $65 = $600

we want profit to be 600 or more

15 * n - 600 = profit

profit ≥ 600

15 * n - 600 ≥ 600

add 600 to both sides to isolate the variable and its coefficient

15 * n ≥ 1200

divide both sides by 15 to isolate the variable

n ≥ 80

Jose must therefore work 80 or more hours, for a minimum of 80

Answer:

10/12 is greater and for the second one, 4/11 is greater and 5/8 is greater

The best prediction for the number of times it will not land on yellow would be 29 times.

We have,

Assuming the spinner has an equal probability of landing on each color, The probability of it not landing on yellow is 4/5.

So,

If you spin the spinner 36 times, the expected number of times it will not land on yellow is:

= (4/5) x 36

= 28.8

Since you can't have a fraction of a spin,

= 28

Thus,

The best prediction for the number of times it will not land on yellow would be 29 times.

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Answer:

b=20°, c=160°

Step-by-step explanation:

b=20° [vertically opposite angle]

c+b=180° [angle at same line ]

c=180° - 20°

c = 160°

Answer:

If the bacteria grow for six hours, each bacterium will divide 3 times per hour × 6 hours = 18 times.

Every time the bacteria reproduce, the number doubles.

Answer:

See below

Step-by-step explanation:

[tex]1.\:\:\overline{BD}||\overline{AE}[/tex]

(By Midsegment theorem)

[tex]2.\:\:m\angle 1=48\degree\implies m\angle 4=48\degree [/tex]

([tex]\angle 1\: \&\:\angle 4[/tex] are alternate angles)

[tex]3.\:\:m\angle 3=25\degree\implies m\angle 2=25\degree [/tex]

([tex]\angle 2\: \&\:\angle 3[/tex] are vertical angles)

[tex]4.\:\:\overline {AE}=17\: cm\implies BD = 8.5\: cm [/tex]

(By midsegment theorem: [tex]BD=\frac{1}{2}AE[/tex]

[tex]5.\:\: BD=\frac{1}{2}AE\\\\\implies (3x+10)=\frac{1}{2}\times (12x+2)\\\\\implies 2(3x +10) = 12x+2\\\\\implies 6x +20= 12x+2\\\\\implies 6x - 12x = 2-20\\\\\implies -6x =-18\\\\\implies x =\frac{-18}{-6}\\\\\implies x = 3\\\\\implies \overline{BD}= (3\times 3 + 10)\\\\=(9+10)\\\\\implies \overline{BD}= (9 + 10)\\\\\implies \huge{\purple{\overline{BD}=19}}[/tex]

Answer:

any value of y >= 8  

Step-by-step explanation:

Answer:

m=1

Step-by-step explanation:

y2-y1/x2-x1

-4+3/-4+3

-1/-1

1

Answer:

see below

Step-by-step explanation:

He forgot to multiply 'x' by '2'  in the first step

It should be

4x-1 = 5 + 2 x

2x = 6

x = 3

Answer:

134

Step-by-step explanation:

164 minus 30 equals 134. Julia has 134 apples left after giving her friend 30 of them.

Answer:

if your asking how much she has in all it would be 134

Step-by-step explanation:

Because

164

30-

____

134

Answer:

C.

Step-by-step explanation:

Since you are subtracting a positive from a negative, your absolute value will get greater. With negative numbers, the less they become in value, the higher their absolute value will get. So, since we are subtracting a positive from a negative, we add them together. However, we need to add them as if they were both positive signs.

Once you do this:

 19

+18

You should get 37. Since -19 has a greater absolute value than 18, you keep the negative sign and apply it to 37, getting you -37.

Answer:

slope = 3/2

the plant grows 3 centimeters every 2 weeks

Step-by-step explanation:

Answer:

[tex]y=-|x+1|+1[/tex]

Step-by-step explanation:

Parent function:  [tex]y=|x|[/tex]

Reflect in the x-axis:  [tex]y=-|x|[/tex]

Translate 1 unit to the left:  [tex]y=-|x+1|[/tex]

Translate 1 unit up:  [tex]y=-|x+1|+1[/tex]

Please refer to the attachments to see the individual transformations.

The amount of trace element has Anthony collected, assuming the sample contains the same proportion of the trace element, is 114.6 grams.

Volume of cylinder is the amount of quantity, which is obtained by the solid or object in the 3 dimensional space.

The volume of cylinder can be given as,

[tex]V=\dfrac{\pi r^2h}{4}[/tex]

Here, (d) is the diameter of the base of the cylinder and (h) is the height of the cylinder.

A water sample shows 0.073 grams of some trace element for every cubic centimeter of water. The proportion of element with water is,

[tex]p=\dfrac{0.073}{1}[/tex]

Anthony uses a container in the shape of a right cylinder with a diameter of 11.4 cm and a height of 16.5 cm to collect a second sample, filling the container all the way.

The total volume of the container is,

[tex]V=\dfrac{\pi (11.4)^2\times16.5}{4}\\V\approx1684 \rm\; cm^3[/tex]

The sample contains the same proportion of the trace element. Let the trace element has Anthony collected is x. Thus,

[tex]\dfrac{x}{1684-x}=\dfrac{0.073}{1}\\x=122.932-0.073x\\x+0.073x=122.932\\x=\dfrac{122.932}{1.073}\\x\approx114.6\rm\; gram[/tex]

Thus, the amount of trace element has Anthony collected, assuming the sample contains the same proportion of the trace element, is 114.6 grams.

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Applying the cosine ratio, the measure of angle C in the given image, to the nearest whole degree, is: 77°.

The cosine ratio is given as, cos ∅ = adjacent side/hypotenuse side of a right triangle.

Using the cosine ratio, we have:

cos C = 2/9

C = cos^(-1)(2/9)

C ≈ 77 degrees.

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Answer:

77 is the answer

Step-by-step explanation:

Geometric series have the same ratio. The series which is a geometric series is 1, 3, 9, 27.

A series of numbers is a geometric series if the quotient of any two consecutive numbers is the same.

A series of numbers is a geometric series if the quotient of any two consecutive numbers is the same.

A.) 0.1 0.3 0.5 0.7

To check if the series is geometric series, find the quotient.

[tex]r_1=\dfrac{0.3}{0.1} = 3\\\\r_2 = \dfrac{0.5}{0.3} = 1.66[/tex]

Since the ratio is different this is not a geometric series.

B.) 1 3 9 27

To check if the series is geometric series, find the quotient.

[tex]r_1=\dfrac{3}{1} = 3\\\\r_2 = \dfrac{9}{3} = 3[/tex]

Since the ratio is the same this is a geometric series.

C.) 19 17 15 13

To check if the series is geometric series, find the quotient.

[tex]r_1=\dfrac{17}{19} = 0.8947\\\\r_2 = \dfrac{15}{17} = 0.8823[/tex]

Since the ratio is different this is not a geometric series.

D.) 0.4 0.9 1.5 2.2

To check if the series is geometric series, find the quotient.

[tex]r_1=\dfrac{0.4}{0.9} = 0.4444\\\\r_2 = \dfrac{0.9}{1.5} = 0.6[/tex]

Since the ratio is different this is not a geometric series.

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Answer:

its b 1 + 3 + 9 + 27

Step-by-step explanation:

Answer:

Hi! A piecewise function is a function defined by multiple sub-functions, or pieces of different functions over different intervals. Piecewise definition is a way of expressing the function and is not actually integral to the function itself.

f(x) = |x - 2| is an absolute value function. As a piecewise function, it's written like this:

f(x) = {x - 2, x ≥ 2

        {-x + 2, x < 2

Hope this helps! Have a great day.

Answer:

a. +34 b. +46 c. +45 d. +31

Step-by-step explanation: use a number line