determine the radius and center of the circle with the following equation
x^2+y^2-12x+24y-10=6

Erika is working on solving the exponential equation 50^x = 17; The solution is x = 0.7242.

When you raise a number with an exponent, there comes a result.

Let's say you get

a^b = c

Then, you can write 'b' in terms of 'a' and 'c' using a logarithm as follows

[tex]b = \log_a(c)[/tex]

'a' is called base of this log function. We say that 'b' is the logarithm of 'c' to base 'a'

Erika is working on solving the exponential equation 50^x = 17;

however, she is not quite sure where to start.

The equation is

[tex]50^x = 17\\[/tex]

By taking the log both sides

[tex]log_a b = x\\\\a_x = b[/tex]

By using the base formula

[tex]log_0 y = \dfrac{logy}{log b}[/tex]

So, [tex]log_{50} 17= x\\\\[/tex]

[tex]x = \dfrac{log17}{log 50}[/tex]

x = 0.7242

Learn more about logarithm here:

https://brainly.com/question/20835449

#SPJ1

Answer:

x>11

Step-by-step explanation:

To simplify this inequality, we add 3 from both sides to get x-3+3>8+3. Since -3+3 cancels out to 0, we are left with x>8+3. 8+3=11 so x>11.

Hope this helps! If you need further explanation let me know :)

Answer:

[tex](x,y) = (0,4)~ \text{and}~ (x,y) = (2,8)[/tex]

Step by step explanation:

[tex]y = x^2 +4~~~~~~~~~...(i)\\\\y = 2x +4~~~~~~~~~...(ii)\\\\\text{From (i) and (ii):}\\\\~~~~~~x^2 +4 = 2x+4\\\\\implies x^2 = 2x\\\\\implies x^2 -2x = 0\\\\\implies x(x-2) = 0\\\\\implies x =0,~ x = 2[/tex]

[tex]\text{Substitute x = 0 in eq (i):}\\\\y = 0^2 +4 = 4\\\\\text{Substitute x = 2 in eq (i):}\\\\y=2^2+4 = 4+4 = 8\\\\\text{Hence,}~ (x,y)= \{(2,8), (0,4)\}[/tex]

Step-by-step explanation:

please mark me as brainlest

Answer:

90 feet

Step-by-step explanation:

40 + 50= 90 feet.

40 feet from the base is 40 feet high and 50 feet up is this equation.

Hope it helps sry if I’m wrong

Answer:

24 ft

Step-by-step explanation:

50 ^ 2 - 40 ^ 2 = b^2

2500 - 1600 = b^2

900 = b^2

√900 = √b^2

24 = b

Answer:

a=1

b=-1

c=1

value of discriminant =-3

quadratic function will intersect x-axis 0 times

Step-by-step explanation:

Answer:

 (-7/9)^4 = 2401/6561

Step-by-step explanation:

The rules of exponents apply.

  (a^b)/(a^c) = a^(b-c) . . . . . quotient rule

  (a^b)^c = a^(bc) . . . . . . . . power rule

__

The first rule of exponents shown above helps us find the value of a/b.

  [tex]\dfrac{a}{b}=\dfrac{\left(\dfrac{-7}{9}\right)^8}{\left(\dfrac{-7}{9}\right)^6}=\left(\dfrac{-7}{9}\right)^{8-6}=\left(\dfrac{-7}{9}\right)^2[/tex]

The second rule of exponents shown above tells us how to find the square.

  [tex]\left(\dfrac{a}{b}\right)^2=\left(\left(\dfrac{-7}{9}\right)^2\right)^2=\left(\dfrac{-7}{9}\right)^{2\times2}\\\\\boxed{\left(\dfrac{a}{b}\right)^2=\left(\dfrac{-7}{9}\right)^4=\dfrac{2401}{6561}}[/tex]

_____

Additional comment

Since -7 is always to an even power in these expressions, its sign can be ignored. The product of an even number of negative values is positive.

The orthocenter is the point of intersection of the three altitudes.

An orthocenter can be defined as the point of intersection of altitudes which are perpendicular from the vertex to the opposite sides of a triangle.

Therefore, the orthocenter is the point of intersection of the three altitudes.

Learn more about triangles here:

https://brainly.com/question/2644832

#SPJ1

The additive inverse of the complex number –8 + 3i will be 8 – 3i. Then the correct option is C.

To produce an answer equal to 0, additive inverse simply entails switching the sign of the quantity and adding it to the original figure.

The complex expression is given below.

⇒ –8 + 3i

Then the additive inverse of the complex number will be

Let x be the additive inverse of the complex number.

Then we have

x + (–8 + 3i) = 0

x = –(–8 + 3i)

x = 8 – 3i

Then the correct option is C.

More about the Additive inverse link is given below.

https://brainly.com/question/13715269

#SPJ1

Answer:

C

Step-by-step explanation:

Edge 2022

Answer:

102

Step-by-step explanation:

Answer:

A ≈ 300 cm²

Step-by-step explanation:

Area of a circle: πr² (where r is the radius)

Substitute the given values into the formula:

⇒ A = πr²

⇒ A ≈ (3)(10)²

⇒ A ≈ 3(100)

⇒ A ≈ 300 cm²

Learn more here:

brainly.com/question/27864345

brainly.com/question/13658549

Hey there!

[tex] \red{\underline{\bold{\blue{Area \: of \: a \: circle}}}} [/tex]

[tex] \\ [/tex]

[tex] \red{\boxed{\bold{\blue{A \approx 300{cm}^{2}}}}} [/tex]

The area of a circle is calculated using the following formula :

[tex] \sf{\blue{A} = \orange{\pi} \times \red{r}^{2}} \\ \sf{where \: \red{r}\: is \: the \: radius \: of \: the \: circle} [/tex]

⇢Here, we consider that π = 3 but in reality, π ≈ 3 replace [tex] \orange{\pi} [/tex] with 3 and [tex] \red{r} [/tex] with 10 :

[tex] \sf{\blue{A} = \orange{\pi} \times \red{r}^{2} } \: \: \: \\ \sf{\blue{A} \approx \orange{3} \times \red{10}^{2} } \\ \sf{\blue{A} \approx \orange{3} \times \red{100} } \\ \green{ \boxed{\sf{\blue{A} \approx300{cm}^{2}}}} [/tex]

⇒Therefore, the area of the circle is about 300cm².

[tex] \\ [/tex]

Answer:

-4

Step-by-step explanation:

if you graph it, we can find out two points are 0,17 and 1,13

we can find the slope from rise/run

-4 is the  slope of the line represented by the equation y + 3 = -4(x-5)

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

The equation of the line is y + 3 = -4(x-5)

We have to find slope

Let us simplify the equation to slope intercept form to find slope

y+3=-4x+20

y=-4x+17

Hence, -4 is the  slope of the line represented by the equation y + 3 = -4(x-5)

To learn more on slope of line click:

https://brainly.com/question/16180119

#SPJ7

There are 230 highway signs during road trip.

Length is defined as the act of measuring the length of objects in some specified units which can be standard or non-standard.

Here, The total length of a road trip = 18.4 hours.

Highway signs are posted = after every 0.08 hours.

To find: Number of highway signs.

The number of highway signs is found = 18.4 / 0.08 = 230.

Thus there are 220 highway signs available during the road trip.

Learn more about Length from:

https://brainly.com/question/8552546

#SPJ1

The probability that you pull a card from a standard deck of 52 and then pull a second card without replacing the first card is 2%

The given parameters are:

Cards = 52

Face card = 12

Ace = 4

The probability of selecting a face card is:

P(Face card) = 12/52

Now, there are 51 cards.

The probability of selecting an ace is:

P(Ace) = 4/51

The required probability is:

P = 12/52 * 4/51

Evaluate

P = 0.0181

Express as percentage

P = 1.81%

Approximate

P = 2%

Hence, the probability is 2%

Read more about probability at:

https://brainly.com/question/251701

#SPJ1

Answer:

0

Step-by-step explanation:

0, it is a flat line on a graph

Answer:

B

Step-by-step explanation:

the y- intercept is the point on the y- axis where the line crosses it

the line crosses the y - axis at (0, - 4 ) ← y- intercept

Answer:

171

Step-by-step explanation:

180×95/100

180×95=17100

17100/100=171.

That is how I got my answer.

Answer:

26cm

Step-by-step explanation:

Answer:

12.0 ft

Step-by-step explanation:

Answer:

[tex]\frac{100}{a}[/tex]

Step-by-step explanation:

Hello!

a% is the same as [tex]\frac a{100}[/tex].

a% of a can be found by multiplying them both, giving us [tex]\frac {a^2}{100}[/tex]

The value of the expression is [tex]\frac{100}{a}[/tex]

Point L is the midpoint

The midpoint is halfway between the two points. In this case, Point F and Point B are 10 units away from each other. The midpoint is the distance between the points (10) divided by 2.

Answer:

Translation as Triangle A has been translated by vector (3,-1) to now being (-2,-3)

Translation as Triangle A has been translated by a vector (3,-1) to now being (-2,-3).

The process of changing the location of the image on the coordinate system will be known as the translation.

A translation in mathematics does not turn a shape; instead, it moves it left, right, up, or down. They are congruent if the translated shapes (or the image) seem to be the same size as the original shapes. They have merely changed their direction or directions.

Given that Translate Triangle A by a vector (3, -1) to give triangle B. Then, rotate your triangle B 180° around the origin to give triangle C.

Triangle A translation ⇒ (3,-1)

The second translation = (-2,-3).

Therefore, the translation as Triangle A has been translated by a vector (3,-1) to now being (-2,-3).

To know more about translation follow

https://brainly.com/question/12861087

#SPJ2

Answer:

Slope:  1/4

y - int: (0,-6)

Step-by-step explanation:

-x+4y=-24

4y = -24+x

y=1/4 * x - 6

Answer: its 218

Step-by-step explanation: you just have to subtract 250 minus 32

Answer:

do u still need help with this

The attached figure represents the image of the triangle after a reflection and a dilation

The vertices are given as:

D(0,2) , E(2,4) , and F(4,0) .

The transformations are given as:

The rule of reflection across the x-axis is

(x,y) -> (x,-y)

So, we have:

D' = (0,-2)

E' = (2,-4)

F' = (4,0)

The rule of dilation by a scale factor of 1.5 is:

(x,y) -> 1.5(x,y)

So, we have:

D'' = 1.5 * (0,-2) = (0,-3)

E'' = 1.5 * (2,-4) = (3,-6)

F'' = 1.5 * (4,0) = (6,0)

See attachment for the image of the triangle

Read more about transformation at:

https://brainly.com/question/4289712

#SPJ1

Answer:

  (-6)³z²  or  -6³z²

Step-by-step explanation:

An exponent is used to signify the number of times a factor appears in a product.

__

In the expression (-6)·(-6)·(-6)·z·z, the factor (-6) appears 3 times, and the factor z appears 2 times. Written with exponents, this could be ...

  (-6)³z²

_____

Additional comment

We can simplify this by realizing the product of the constant factors will be negative. (There is an odd number of minus signs.) The expression can also be written as ...

  -6³z²

The version with (-6) being cubed is a more direct translation to the use of exponents.