What is the radius of a circle whose equation is x2 + y2 – 10x + 6y + 18 = 0? units

Step-by-step explanation: The base of the power in the original equation becomes the base of the log. So we have [tex]^{log}7[/tex].

Next, the exponent in the original equation goes on the other side of the equation and finally, the result in the

original equation goes inside the log.

So we have [tex]^{log}7[/tex] [tex]343[/tex] [tex]= 3[/tex] which is 7³ = 343 written in logarithmic form.

the logarithmic form of the equation [tex]7^3 = 343[/tex] is [tex]log_7(343) = 3[/tex]

To convert the exponential equation [tex]7^3 = 343[/tex] into logarithmic form we first  identify the base of the exponent.

Here, the base is 7.

The exponent is 3 and the result is 343.

Using the logarithmic form formula, which is [tex]log_b(a) = c[/tex] where b is the base, a is the result, and c is the exponent, we can rewrite the equation. This gives us:

[tex]log_7(343) = 3[/tex]

Therefore, the logarithmic form of the equation [tex]7^3 = 343[/tex] is [tex]log_7(343) = 3[/tex]

Answer:

The zeros are

[tex]x1=\frac{-5+\sqrt{5}} {2}[/tex]   and [tex]x2=\frac{-5-\sqrt{5}} {2}[/tex]

Step-by-step explanation:

we know that

The formula to solve a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex] is equal to

[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]

in this problem we have

[tex]f(x)=x^{2} +5x+5[/tex]  

To find the zeros equate the function to 0

[tex]x^{2} +5x+5=0[/tex]  

so

[tex]a=1\\b=5\\c=5[/tex]

substitute in the formula

[tex]x=\frac{-5(+/-)\sqrt{5^{2}-4(1)(5)}} {2(1)}[/tex]

[tex]x=\frac{-5(+/-)\sqrt{5}} {2}[/tex]

[tex]x1=\frac{-5+\sqrt{5}} {2}[/tex]

[tex]x2=\frac{-5-\sqrt{5}} {2}[/tex]

Answer:

The graph in the attached figure

Step-by-step explanation:

we have

[tex]f\left(x\right)=-\left|x-2\right|-1[/tex]

The function represents an inverted V-shaped graph

The vertex of the function is the point (2,-1)

The y-intercept of the function is the point (0,-3)

The domain is all real numbers -----> (-∞,∞)

The range is all real numbers less than or equal to -1 ----> (-∞,-1]

Using a graphing tool

The graph in the attached figure

Answer:

Monsoon

Step-by-step explanation:

in High tide every 1 hour, you move 3 km that is faster then Monsoon which every 2 hours you move 5 km because if you multiply 1 by 2 you get 2 (hours) but if you multipy 3 by 2 yuo get 6 and 6 is more than 5. if you use this method one more time then to you will find that the answer is Monsoon.

The river rafting adventure that offers the lowest average speed would be the option Monsoon.

We don't write symbols like currency generally and understand it from context.

Also, a sign of multiplication is often hidden if there are non-numeric symbols and numbers being multiplied are written together.

The table below shows the details of three different river rafting adventures.

Adventure Duration (in hours)

Distance (\text{km})(km)left parenthesis, k, m, right parenthesis

High Tide 111 333 Monsoon 222 555 Tsunami 4

In High tide every 1 hour, you move 3 km which is faster than Monsoon

Every 2 hours you move 5 km because 1 x 2 gives 2 (hours)

But 3 x 2 = 6 and 6 is more than 5.

Therefore, The answer is Monsoon.

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Answer:

[tex]\large\boxed{1<x<7\to x\in(1,\ 7)}[/tex]

Step-by-step explanation:

[tex]|x-4|<3\iff x-4<3\ \wedge\ x-4>-3\qquad\text{add 4 to both sides}\\\\x<7\ \wedge\ x>1\Rightarrow1<x<7[/tex]

you have to make a negative and positive equation for this situation

x-4<3 and x+4<3

for the first equation you have to add 4 to both sides to get x<7

for the second equation you have to subtract 4 from both sides to get x<-1

hope this helps

Answer:

56 ounces

Step-by-step explanation:

16 ounces = 1 pound

There are 3.5 pounds so 16 x 3 = 48

Then, the other .5 of the pound would be 16/2 or 8.

48 + 8 + 56

Answer:

56

Step-by-step explanation:

16x3=48

Half of 16 is 8.

Since there is 3 1/2 pounds

You would add the 8 and 48.

48 from the 3 pounds and 8 ounces for 1/2 a pound.

Hence, the answer is 56.

48+8=56

I believe the correct answer is 0

Step-by-step explanation:

To solve this question, we use an abbreviation formula called BODMAS which is:

B = Brackets

O = Of

D = Division

M = Multiplication

A = Addition

S = Subtraction

We solve each element that is available in the order of the abbreviated letter.

1. We solve the brackets:

[tex](5\times12) = 60[/tex]

2. We solve the second bracket:

[tex](60\div3) = 20[/tex]

The equation now is [tex]20+30-50[/tex]

3. We now solve addition first:

[tex]20+30=50[/tex]

4. Now we solve the subtraction:

[tex]50-50=0[/tex]

The answer then = 0

Answer:

The value of given expression is 0.

Step-by-step explanation:

We have to evaluate the given expression:

[tex]\bigg(\displaystyle\frac{(5\times 12)}{3}\bigg)+30-50[/tex]

We use the BODMAS rule to evaluate the given expression.

B-Bracket

O-of

D-Division

M-Multiplication

A-Addition

S-Subtraction

[tex]\bigg(\displaystyle\frac{(5\times 12)}{3}\bigg)+30-50\\\\=\bigg(\displaystyle\frac{60}{3}\bigg)+30-50\\\\=20+30-50\\\\=50-50\\\\=0[/tex]

The value of expression is 0.

Answer:

Just add up the measurements of the sides and then double the result.

(2 + √5 + 6 + 3√5) · 2

= (8 + 4√5) · 2

= 16 + 8√5 (cm)

To answer your question, we first need to understand that the perimeter of a rectangle is calculated by adding up all its sides or simply twice the sum of its length and width.

From the information given, the width of the rectangle is equal to 2 cm plus the square root of 5 cm, while the length is 6 cm plus 3 times the square root of 5 cm.

So now, let's sum up the length and the width:
= (2 + √5 cm) + (6 + 3√5 cm)
= 8 + 4√5 cm

We then multiply this result by 2 (to account for both sets of opposite sides of the rectangle):
Perimeter = 2 * (8 + 4√5 cm)
Perimeter ≈ 33.89 cm

Therefore, the perimeter of the rectangle is roughly 33.89 cm.

Answer:

60 * 8 = 480 miles per minute *2 = 960 miles

Step-by-step explanation:

[tex]2x = 2y -6|\div 2\\y = x + 3 \\\\x=y-3\\y=x+3\\\\y=x+3\\y=x+3[/tex]

Both equations are identical, so there are infinitely many solutions.

Answer:

y≥2-4

Step-by-step explanation:

Simplify your equation.

4x-2y≤8

-4x      -4x

-2y≤-4x+8

/-2       /-2

y≥2-4

Answer:

y < 1/2x - 2

Step-by-step explanation:

Find the slope of the graph, we can find the slope of the graph by using the formula y2 - y1/x2 - x1. But in order to do so, we must find two perfect points.

Point 1: (0,-2)

Point 2: (4,0)

Now, we would put these points into the formula.

0 -(-2) = 2

4 - 0 = 4

2/4 = 1/2

Therefore, the slope of this graph is 1/2

Now we must find the y intercept, which can be found based on where the line intersects with a y coordinate (ex: 0,y). Based on that, we can come to the conclusion that -2 is our y-intercept

In order to proceed we must know what a linear equation is. A linear equation contains the following:

y = mx + b

m of mx represents the slope, you would leave x as it is.

b represents the y intercept

We have already found what each is, so we can go ahead and put in our slope and y-intercept into the linear equation.

y = 1/2x + -2

Because, we are dealing with an inequality problem, the equal sign must be replaced with an inequality sign and that is determined based on the area of the graph that is shaded.

Since, the graph is shaded downwards we will be using the "less than sign", in addition if you haven't noticed, the line is dotted so we will NOT be using any "equal to symbols"

So, after applying all of this together, we can conclude that the inequality that describes this graph is y < 1/2x - 2

Should you have any further questions, please let me know in the comment section below.

Answer:

The line would start at 30 on the Y axis and go through 15 on the X axis

Answer: First dot (0,30) Second dot (15,0)

Answer:

decreasing

Step-by-step explanation:

since its negative it will slope down

The graph is increasing.

Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them.

Given: range:  -3 < X <-1

The graph related to this question is attached below

as, seen from the graph the graph slope will rise up from -3 to -1.

Hence, the graph is increasing.

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Answer:

g (h (x) ) = 5/8

Step-by-step explanation:

We are given the following two functions and we are to find the value of [tex] g ( h ( - 3 ) ) [/tex]:

[tex] g ( x ) = \frac { x + 1 } { x + 2 } [/tex]

[tex] h ( x ) = 4 - x [/tex]

Firstly, we need to find the function :

[tex] g ( h ( x ) ) = \frac { ( 4 - x + 1 ) } { ( 4 - x - 2 ) } = \frac { 5 - x } { 2 - x } [/tex]

Now substituting the value [tex]x=-3[/tex] in it:

[tex] g ( h ( x ) ) = \frac { 5 - (-3) } { 2 - (-3) }  [/tex]

g (h (x) ) = 5/8

Answer:

8/5

Step-by-step explanation:

If g(x) = (x+1)/(x-2) and h(x) = 4 - x

(g*h)(-3) = g(h(-3))

h(-3) = 4 - -3 = 4 + 3 = 7

g(7) = (7 + 1)/(7 - 2) = 8/5

Answer 1 (without replacement) :  

P(2 books)=P(first)*P(second)=2/7*1/6=2/42=1/21 this is if you don't put the book back on the shelf after taking it off the first time

Answer 2 (with replacement) :  

P(2 books)=P(first)*P(second)=2/7*2/7=4/49 this is if you put the book back on the shelf after taking it off the first time

I put he probably didn't put the book back on the shelf after this first time but I don't know without those details in the question

The given options are 1) y = (cos x) / x is neither and 2) y = (sin x) / x is even.

Trigonometric ratios for a right-angled triangle are from the perspective of a particular non-right angle.

In a right-angled triangle, two such angles are there which are not right-angled (not of 90 degrees).

The slanted side is called the hypotenuse.

From the considered angle, the side opposite to it is called perpendicular, and the remaining side will be called the base.

1) y = (cos x) / x is neither, since cos x is even and x is odd.  

2) y = (sin x) / x is even since sin x and x would either both be positive at the same time or negative at the same time.  

We know that (-) / (-) is positive, just as (+) / (+) is positive.

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Final answer:

1. The function y=cos(x)/x is neither even nor odd due to its lack of symmetry properties

2. y=sin(x)/x is an odd function as it satisfies the symmetry condition about the origin.

Explanation:

To determine if the functions y=cos(x)/x and y=sin(x)/x are even, odd, or neither, we need to understand the definitions of even and odd functions and apply them accordingly.

Even and Odd Functions:

An even function satisfies the condition f(-x) = f(x), meaning the function's graph is symmetric about the y-axis. An odd function satisfies the condition f(-x) = -f(x), indicating symmetry about the origin.

Analysis of y=cos(x)/x:

To determine if y=cos(x)/x is even, odd, or neither, replace x with -x:

y=cos(-x)/(-x) = cos(x)/(-x) because cos(-x) = cos(x), an even function property.

This contradicts the definitions of both even and odd functions; hence, y=cos(x)/x is neither even nor odd.

Analysis of y=sin(x)/x:

Similarly, for y=sin(x)/x, replace x with -x:

y=sin(-x)/(-x) = -sin(x)/(-x) because sin(-x) = -sin(x), an odd function property.

This simplifies to y=sin(x)/x, which satisfies the condition for an odd function.

Therefore, y=sin(x)/x is an odd function.

Answer:

the answer is

[tex]x = 48[/tex]

Step-by-step explanation:

[tex] \frac{x}{6} = 8[/tex]

[tex]x = 48[/tex]

Answer:

Yes

Step-by-step explanation:

Yes terminating and repeating decimals are rational numbers.

This is a terminating decimal. It ends, so it is rational.

Anything that can be written as a fraction where the top and bottom are integers is rational.

Some examples:

-1                                                                              =-1/1

5                                                                              =5/1

5.23                                                                    =523/100

.3333333333333333333333333333333333333....=1/3

1   2/3                                                                           =5/3

Since there seems to be more that need convincing, the number 128.439 can be written as 128439/1000

that is a fraction where the top and bottom are integers

so 128.439 is rational

The number 128.439 is a rational number

Answer:

Step-by-step explanation:

It can't.

The answer is 60 with a remainder of 4

Answer:

The common factor is 8x or -8x ( I forgot if the first number needs to positive or not.

Step-by-step explanation:

-8x(7x^3-2x-2)

or

8x(-7x^3+2x+2)

Hope this is what you are looking for?

Answer:

The common factor is 8x or -8x

Step-by-step explanation:

-8x(7x^3-2x-2)

or

8x(-7x^3+2x+2)

Hope this is what you are looking for!! Stay Safe!!

Amount obtained in Compound interest is given by :

[tex]\bigstar\;\;\boxed{\mathsf{Amount = Principal\bigg(1 + \dfrac{Rate\;of \;interest}{100}\bigg)^{Conversion\;periods}}}[/tex]

Note : Conversion period is the time from one interest period to the next interest period. If the interest is compounded annually then there is one conversion period in an year. If the interest is compounded semi-annually then there are two conversion periods in an year. if the interest is compounded quarterly then there are four conversion periods in an year.

Problem :

Given : $500 is invested for one year at 4% annual interest

[tex]\implies\boxed{\begin{minipage}{4 cm}\bigstar\;\;\textsf{Principal = 500}\\\\\bigstar\;\;\textsf{Time period = 1 year}\\\\\bigstar\;\;\textsf{Rate of interest = 4\%}\end{minipage}}[/tex]

As the question mentions the term ''compounded quarterly'', there are 4 conversion periods in a year.

If the interest is compounded quarterly, then the rate of interest per conversion period (quarter) will be :

[tex]\implies \mathsf{\left(\dfrac{1}{4} \times 4\%\right) = 1\%}[/tex]

Substituting all the values in the Amount formula of C.I, We get :

[tex]\mathsf{\implies Amount = 500\bigg(1 + \dfrac{1}{100}\bigg)^4}[/tex]

[tex]\mathsf{\implies Amount = 500\left(1 + 0.01\right)^4}[/tex]

[tex]\mathsf{\implies Amount = 500\left(1.01\right)^4}[/tex]

[tex]\mathsf{\implies Amount = 520.30}[/tex]

We know that : Interest = Amount - Principal

[tex]:\implies[/tex]  Interest = 520.30 - 500

[tex]:\implies[/tex]  Interest = $20.30

If $500 is invested in a savings account with a 4% annual interest rate compounded quarterly for one year, it would earn $20.04 in interest.

To calculate the interest earned on a savings account, we can use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount (initial investment), r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years. In this case, the principal amount is $500, the annual interest rate is 4% (or 0.04 as a decimal), the interest is compounded quarterly (so n = 4), and the investment period is one year (so t = 1).

Plugging the values into the formula, we get:

A = 500(1 + 0.04/4)^(4×1)

Simplifying the equation, we calculate that the final amount after one year is $520.04. To find the amount of interest earned, we subtract the initial investment ($500) from the final amount ($520.04):

Interest = $520.04 - $500 = $20.04.

Therefore, $500 would earn $20.04 in interest if invested for one year in a savings account with a 4% annual interest rate compounded quarterly.

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Answer:

Year 2

Step-by-step explanation:

The graph that I attached shows the growth over time. The height of the blue line (f(x)) surpasses g(x) at 1.63 years. We can say that year 2 is the first year that f(x) is greater than g(x).

[tex]\bf (x-7)(x^2+3x-3)~\hfill \begin{array}{cll} x^2+3x-3\\ \times x\\ \cline{1-1} x^3+3x^2-3x \end{array}~~+~~ \begin{array}{cll} x^2+3x-3\\ \times -7\\ \cline{1-1} -7x^2-21x+21 \end{array}~\hfill \\\\[-0.35em] ~\dotfill\\\\ (x^3+3x^2-3x) +(-7x^2-21x+21)\implies x^3-4x^2-24x+21[/tex]

notice that all you do is simply multiply the terms of either one by the terms of the other sequentially, then add like-terms.

Answer:

The values of x are -6 , 0 , 1 ⇒ Answers C , D , E

Step-by-step explanation:

* Let revise how to find the vertical asymptote

- Vertical asymptotes of a rational function f(x)/g(x) can be found by

 solving the equation g(x) = 0 ⇒ the denominator of the fraction

- Note: this only applies if the numerator f(x) is not zero for the same

 x value

* Lets solve the problem

∵ F(x) = 1/x(x + 6)(x - 1)

∵ The denominator of the fraction is x(x + 6)(x - 1)

- To find the equation of the vertical asymptote Put the

 denominator = 0

∴ x(x + 6)(x - 1) = 0

- The denominator has three factors, equate each by 0

∴ x = 0

OR

∴ x + 6 = 0 ⇒ subtract 6 from both sides

∴ x = -6

OR

x - 1 = 0 ⇒ add 1 to both sides

∴ x = 1

∴ From all above there are 3 vertical asymptotes at x = -6 , 0 , 1

* The answers are C, D , E

Answer:

Step-by-step explanation:

-6 0 1

Answer: Yes.

Step-by-step explanation:

30/5 or 30 divided by 5 simplifies to 6. 6 is a whole number and therefore it is an integer.

choice A ("decreases by about 0.9°") is more likely the correct description of the slope.

Step 1: Look for the trend between temperature and latitude

Generally, as we move north in latitude (higher latitude values), temperatures tend to decrease. Analyze the high temperatures in the table. Warmer temperatures are at lower latitudes and cooler temperatures are at higher latitudes.

Step 2: Interpret the slope

The slope of the best fit line tells you how much the temperature changes (on the y-axis) on average with every one-degree increase in latitude (on the x-axis). Since temperature decreases as latitude increases, the slope will be negative.

The temperature decreases by a certain value for each 1-degree increase north in latitude. The answer choices with a positive slope (increase in temperature) can be eliminated (choices C and D). Looking at the remaining choices (A and B), a lower negative value indicates a smaller decrease in temperature with increasing latitude.

We know that generally, temperatures get cooler as we move north (higher latitudes). This means as the latitude values increase (on the x-axis), the temperature values (on the y-axis) should decrease.

Slope and Interpretation: The slope of the best fit line through the temperature data tells us how much temperature changes (goes up or down) on average with every one-degree increase in latitude. Since temperature goes down (decreases) with increasing latitude, the slope will be negative.

Answer:

3/10

Step-by-step explanation:

Using it's concept, it is found that the probability that the next person to enter kidz kare is between 10 and 15 years old is given by:

C) 3/10.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

From the histogram, we have that out of a total of 10 students, 3 are between 10 and 15 years old, hence:

p = 3/10, which means that option C is correct.

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Answer:

[tex]\large\boxed{B.\ f(4)=22}[/tex]

Step-by-step explanation:

[tex]f(x)=3x+10\\\\f(4)-\text{put x = 4 to the equation of the function}\\\\f(4)=3(4)+10=12+10=22[/tex]