How is the equation of this circle written in standard form?

x2 + y2 - 6x + 14y = 142

Answer:

Part a) [tex]\frac{1}{200}[/tex]

Part b) [tex]\frac{1}{450}[/tex]

Step-by-step explanation:

we know that

A reciprocal of a rational number  [tex]\frac{p}{q}[/tex]  is obtained by changing the numerator and denominator, so the numerator becomes the denominator and the denominator becomes the numerator obtaining  [tex]\frac{q}{p}[/tex]

Part a) we have

200

we know that

the given number can be expressed as [tex]\frac{200}{1}[/tex]

so

changing the numerator and denominator

The reciprocal is equal to [tex]\frac{1}{200}[/tex]

Part b) we have

450

we know that

the given number can be expressed as [tex]\frac{450}{1}[/tex]

so

changing the numerator and denominator

The reciprocal is equal to [tex]\frac{1}{450}[/tex]

Answer:

A. 2x + 150y = 1,500

   2x + 120y = 1,320

The flights were $300 each, and they stayed 6 nights.

B. $1,380

Step-by-step explanation:

Let x be the cost of the flight (in one side) and y be the number of nights on their vacation.

A. Brenda had a fancy room for $150 per night, then she paid $150y for y nights.  Brenda's total is $1,500, then

[tex]150y+2x=1,500[/tex]

Brenda's friend had a smaller room for $120 per night, then she paid $120y for y nights.  Brenda's friend total is $1,320, then

[tex]120y+2x=1,320[/tex]

Subtract two equations:

[tex]150y+2x-120y-2x=1,500-1,320\\ \\30y=180\\ \\y=6[/tex]

Substitute into the first equation:

[tex]150\cdot 6+2x=1,500\\ \\900+2x=1,500\\ \\2x=600\\ \\x=300[/tex]

Hence

2x + 150y = 1,500

2x + 120y = 1,320

The flights were $300 each, and they stayed 6 nights.

B. If a third friend joined them and stayed in a mid-range room for $130 per night, then he paid [tex]\$130\cdot 6=\$780[/tex]

The total cost is

[tex]\$780+\$600=\$1,380[/tex]

Answer:

6ab + b^2 - 17a - 4b + 10

Step-by-step explanation:

-2(a+b-5)+3(-5a+2b)+b(6a+b-8)

Now we break the parenthesis. To break that, we multiply each of the value inside the parenthesis by the adjacent number. That is, for the first part of the expression, we multiply by -2, then by 3, and then by b.

Algebraic Operations need to be considered:

[ (-) x (-) = (+); (-) x (+) = (-)]

= [-(2*a) + (-2*b) - (-2*5)] + [3*(-5a) + (3*2b)] + [(b*6a) + (b*b) - (b*8)]

= -2a - 2b +10 -15a + 6b + 6ab + b^2 - 8b

Now, we will make the adjustment by the similarity value.

= - 2a - 15a - 2b + 6b - 8b + 6ab + b^2 + 10

= - 17a - 4b + 6ab + b^2 + 10

= 6ab + b^2 - 17a - 4b + 10

Therefore, the answer of the expression is = 6ab + b^2 - 17a - 4b + 10

Answer:

c

Step-by-step explanation:

turn the percent into a decimal and × by the number you get that number that the percent represents in the number add it to the number and you get the original price

The price which is highest is Option C)

After a 20% discount, the price was $170

What is Percentage?

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %

Given data ,

A)

After a 5 % discount , the price was $ 190

So , the percentage is calculated as

190 / 0.95 = $ 200

B)

After a 10 % discount , the price was $ 180

So , the percentage is calculated as

180 / 0.90 = $ 200

C)

After a 20 % discount , the price was $ 170

So , the percentage is calculated as

170 / 0.80 = $ 212.50

D)

After a 30 % discount , the price was $ 140

So , the percentage is calculated as

140 / 0.70 = $ 200

Therefore , the price $ 212.50 is the highest

Hence , the solution , after a 20% discount, the price was $170 is the highest

To learn more about percentage click :

https://brainly.com/question/12861068

#SPJ2

Answer:

[tex]- 5 \log 2 = - \log 32[/tex]

Step-by-step explanation:

We have to convert an exponential equation into the logarithmic equation.

The given equation is  

[tex]2^{-5} = \frac{1}{32}[/tex]

Now, taking log on both sides we get,  

[tex]\log 2^{-5} = \log\frac{1}{32}[/tex]

⇒ [tex]- 5 \log 2 = \log 1 - \log 32[/tex]

{Since we know from the logarithmic property that [tex]\log a^{b} = b \log a[/tex] and [tex]\log \frac{a}{b} = \log a - \log b[/tex] }

⇒ [tex]- 5 \log 2 = - \log 32[/tex] {Since [tex]\log 1 = 0[/tex] }

Hence, this is the required logarithmic equation. (Answer)

Answer:

First five terms are (5, 7, 9, 11, 13)

Step-by-step explanation:

[tex]a_n = 5+(n-1)2[/tex]

Arithmetic explicit rule is given we need to find first five terms.

Let n be number of terms.

When n = 1,

[tex]a_1= 5+(1-1)2= 5+(0)2=5[/tex]

When n = 2,

[tex]a_2=5+(2-1)2=5+2=7[/tex]

When n = 3,  

[tex]a_3=5+(3-1)2=5+4=9[/tex]

When n = 4,  

[tex]a_4=5+(4-1)2=5+6=11[/tex]

When n = 5,  

[tex]a_5=5+(5-1)2=5+9=13[/tex]

Hence the First five terms are (5, 7, 9, 11, 13)

Answer:

[tex]-4x + y = -9\:or\:y = 4x - 9[/tex]

Step-by-step explanation:

First, find the rate of change [slope]:

[tex]\displaystyle \frac{-y_1 + y_2}{-x_1 + x_2} = m \\ \\ \frac{-3 - 5}{-3 + 1} = \frac{-8}{-2} = 4[/tex]

Then, plug these coordinates into the Slope-Intercept Formula instead of the Point-Slope Formula because you get it done much swiftly that way. It does not matter which ordered pair you choose::

−5 = 4 + b

[tex]\displaystyle -9 = b \\ \\ y = 4x - 9[/tex]

If you want it in Standard Form:

y = 4x - 9

- 4x - 4x

_________

[tex]\displaystyle -4x + y = -9[/tex]

_______________________________________________

3 = 4[3] + b

12

[tex]\displaystyle -9 = b \\ \\ y = 4x - 9[/tex]

y = 4x - 9

- 4x - 4x

_________

[tex]\displaystyle -4x + y = -9[/tex]

** You see? I told you it did not matter which ordered pair you choose because you will ALWAYS get the exact same result.

I am joyous to assist you anytime.

The linear equation created from the points (3,3) and (1,-5) is y = 4x - 9, found by first calculating the slope, then finding the y-intercept.

To create a linear equation from two points, you need to find the slope and y-intercept. Let's use the two points given: (3,3) and (1,-5). The slope (m) is found using the formula [tex](y2 - y1) / (x2 - x1),[/tex] so [tex]m = (-5 - 3) / (1 - 3) = -8 / -2 = 4[/tex]. Next, use the y = mx + b formula to find the y-intercept (b). Substituting one of the points and the slope, we get: [tex]3 = 4 * 3 + b[/tex], solving for b, gives b = -9. So, the linear equation is [tex]y = 4x - 9.[/tex]

https://brainly.com/question/32634451

#SPJ12

Answer:

900

Step-by-step explanation:

2 rounds it down

Answer:

900

Step-by-step explanation

900←927→1000

927-900=27

1000-900=100

Answer:

The function has a y-intercept of (0,-1).

Step-by-step explanation:

The given function is f(x) = x - 1 .......... (1)

Now, we have to choose from the statements given in options that best describe the function.

I think option 3 is the only statement that describes the function well.

Option 3 states that the function has a y-intercept of (0,-1).

If we put x = 0 in the function then will get y = - 1.

So, the function (1) has y-intercept at (0,-1). (Answer)

Final answer:

Only statement 3 is correct, which states that the function  (x) = x - 1 has a y-intercept of (0, -1). The function's x-intercept is actually (1, 0), the slope is consistently -1, and the other statements are either incorrect or irrelevant.

Explanation:

We are asked to determine which expressions best describe the function  (x) = x - 1.

Therefore, only statement 3 correctly describes the function  (x) = x - 1.

Answer:

-7x+y=36

Step-by-step explanation:

y-1=7(x+5)

y-1=7x+35

y=7x+35+1

y=7x+36

36=y-7x

36=-7x+y

-7x+y=36

The equation y - 1 = 7(x + 5) is transformed into the standard form by distributing, rearranging terms, and manipulating to ensure a positive coefficient for x, resulting in 7x - y = -36.

To write the equation y - 1 = 7(x + 5) in standard form, we first distribute the 7 to both terms within the parentheses which results in y - 1 = 7x + 35. Then, to ensure both variables are on one side of the equation and the constant is on the other, as required by the standard form, we subtract 7x from both sides. This gives us -7x + y = 36. Normally, standard form is written with the coefficient of x being positive, so to achieve this, we multiply the entire equation by -1, resulting in 7x - y = -36. So, the equation y - 1 = 7(x + 5) in standard form is 7x - y = -36.

https://brainly.com/question/28327649

#SPJ2

We can classify each number as:

0 = ones place

8 = tenths place

7 = hundredths place

3 = thousandths place

Now that we know that 7 is in the hundredths place we can write this as: 7/100 (0.07)

_______

Best Regards,

Wolfyy :)

Answer:

1.28

Step-by-step explanation:

I used calculator give me brainlist

Answer:

1.28

Step-by-step explanation:

so 32% is equal to .32 and you can imagine that the word "of" means x(as in multiply). Thus said .32 x 4 is 1.28

Answer: OPTION B.

Step-by-step explanation:

The missing figure is attached.

For this exercise you need to use the Pythagorean Theorem. This is:

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

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

In this case you can identify in the figure the triangle PRS, so the diagonal PR is the hypotenuse of the triangle PRS.

Then you can say that:

[tex]a=PR\\b=PS=17\\c=RS=33[/tex]

Therefore, knowing these values, you can substitute them into [tex]a^2=b^2+c^2[/tex]:

[tex]PR^2=17^2+33^2[/tex]

Finally you must solve for PR in order to find its value. This is:

[tex]PR=\sqrt{17^2+33^2}\\\\PR=37.12[/tex]

The measure of a side is the length it possess. The measure of PR for the given rectangle is given by: Option B: 37.12 units.

If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:

[tex]|AC|^2 = |AB|^2 + |BC|^2[/tex]

where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).

For the given case, we can use the fact that opposite side of a rectangle are of same length, and one more fact that all the adjacent side pairs of a rectangle are perpendicular to each other(means the minor angle between them is of 90 degrees).

The question is missing the figure, which is attached below.

Since PQRS is a rectangle, thus, we have:

|PS| = |QR| = 17 units

|PQ| = |RS| = 33 units

Thus, for the triangle PSR, as angle S internally is of 90 degrees, we can use Pythagoras theorem.

From Pythagoras theorem for PSR, where PR is hypotenuse, we get:

[tex]|PR|^2 = |PS|^2 + |SR|^2\\\\|PR| = \sqrt{17^2 + 33^2} = \sqrt{1378} \approx 37.12[/tex] units.

(positive root was taken as length is a non-negative quantity).

Thus, the measure of PR for the given rectangle is given by: Option B: 37.12 units.

Learn more about Pythagoras theorem here:

https://brainly.com/question/12105522

Answer:

They are known as terms in algebraic expression

Step-by-step explanation:

It looks like you are good up to problem 4 so I will start there. I believe this is practice worksheet featuring the pyth. theorem. The pyth. theorem is used to find the length of sides in a right triangle notable the hypotenuse (side opposite of 90 degree angle).

4. The monitor is a rectangle but that does not stop you from constructing a right triangle. The smaller lengths are 16 in and 12 in respectively. The hypotenuse of the triangle is the diagonal of the rectangle. To find the length use the pyth. theorem.

diagonal^2 = 16^2+12^2

diagonal = 20 in

7. You know the speeds of both trains and the time spend traveling. You know they are traveling at a 90 degree angle so you can use pyth. theorem. But wait... you need to find the distances traveled for both trains. You can find that though because speed x time = distance.

50mph x 3hrs = 150mi

40mph x 3hrs = 120mi

The distance between the trains after 3 hours is the hypotenuse which can be determined by pyth. theorem.

distance^2 = 150^2+120^2

distance = 192 mi approx.

8. First find length of one piece of wiring. Use pyth theorem. Actually 3,4,5 pyth. triplet in which 5 is the hypotenuse. So you have 5 ft for the length of one piece of wiring. How many pieces of wiring do you need? Well, each tree needs 3 pieces and there are 6 trees so you need 18 pieces.

18 x 5 = 90 ft of wiring

From the work I see, you have a great understanding of the pyth. theorem. Keep it up!

Answer:

m∠y=72°

Step-by-step explanation:

The question is

Find the measure of angle y

step 1

Find the measure of angle x

see the attached figure to better understand the problem

we know that

m∠x=67° -----> by corresponding angles

step 2

Find the measure of angle y

we know that

(m∠x+m∠y)+42°=180° -----> because form a straight line

substitute the measure of angle x

67°+m∠y+42°=180

m∠y+108°=180

m∠y=180°-108°

m∠y=72°

Answer:

Step-by-step explanation:

[tex]5k>22\qquad\text{divide both sides by 5}\\\\\dfrac{5k}{5}>\dfrac{22}{5}\\\\k>4\dfrac{2}{5}\to k>4.4\to k\in(4.4,\ \infty)[/tex]

Answer: A

Step-by-step explanation:

Answer:

whats priya and tylers distance?

Answer: Each boy gets $31.

Step-by-step explanation:

The data we have is:

We have 3 kids (Troy and two friends)

The father paid $35 for gas and expenses.

The boys made $128.

Then we have $128 divided equally into 3 boys.

But those $35 of expenses must be returned for the dad (guess that the gas and expenses are things neede for the kids)

So the amount that they can divide is $128 - $35 = $93

then each boy gets N = $93/3 = $31

In mathematics, a ratio is the comparison of two numbers or quantities which is an amount, measurement, or number.

For example, a ratio can be used to compare the number of shaded rectangles to the number of unshaded rectangles. In the first image, I provided an image of what this ratio would look like.

A proportion is a pair of ratios that are equal to each other.

If we're asked to determine if two ratios can form a proportion, we really want to see if the ratios are equal to each other. It's important to understand that if two ratios are equal, they form a proportion.

Answer:

x-intercept is 2, y-intercept is 10.

Step-by-step explanation:

y=-5x+10

y=mx+b

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

m=-5 which means that the slope of this equation is -5.

And to find the y-intercept,

plug in x=0 into the equation and find out the value of y.

y=-5(0)+10=0+10=10

So the y-intercept is 10.

And to find the x-intercept,

plug in y=0 into the equation and find out the value of x.

0=-5x+10

-5x=0-10

-5x=-10

5x=10

x=10/5=2

So the x-intercept is 2.

Final answer:

Keegan rides 8 miles per day going to and from school. Over the course of 5 days, he rides a total of 40 miles on the bus.

Explanation:

The question asks how many miles Keegan rides the bus in 5 days if he travels 4 miles to school and 4 miles home each day. To solve this, we can multiply the daily round trip distance by the number of school days in a week. Keegan travels 8 miles per day (4 miles to school and 4 miles back home). So, in 5 days, Keegan will have traveled:

8 miles/day  imes 5 days = 40 miles

Therefore, Keegan rides the bus 40 miles in 5 days.

It takes 7.5 cups of milk to make 1 stick of butter.

Step-by-step explanation:

Given,

Cups of milk used = 30 cups

Sticks of butter made = 4

Unit rate describes how many units of one quantity corresponds to 1 unit of other quantity.

We will find unit rate per butter stick.

Unit rate per butter stick = [tex]\frac{cups\ of\ milk\ used}{No.\ of\ butter\ sticks}[/tex]

Unit rate per butter stick = [tex]\frac{30}{4} = 7.5\ cups\ of\ milk\ per\ butter\ stick[/tex]

It takes 7.5 cups of milk to make 1 stick of butter.

Keywords: unit rate, division

Learn more about unit rates at:

#LearnwithBrainly

Answer:

The value of car decreases by 12% each year.

Step-by-step explanation:

A car dealership creates an expression to model the value of a new car t years after it is purchased and the expression is [tex]P(0.88)^{t}[/tex] ..... (1)

Now, if the value of the car depreciates at a rate of r% each year, then the value of the car (Say, P) will be depreciated to the value

[tex]P' = P(1 - \frac{r}{100} )^{t}[/tex] ...... (2)

Now, comparing the expressions in (1) and (2), we get

[tex]1 - \frac{r}{100} = 0.88[/tex]

⇒ [tex]\frac{r}{100} = 0.12[/tex]

⇒ r = 12%.

Therefore, the value of the car decreases by 12% each year. (Answer)

Answer:

7.325 is larger

Step-by-step explanation:

7.325 is larger becuse 7 is a bigger number than 6 and the decimal point is in the same place so 7.325 will be larger

Answer: 7.325

Step-by-step explanation: 7.325 is larger than 6.425 because it is more positive than the other number. You can see this by looking at a number chart.

Hope this helps, have a BLESSED and wonderful day! :-)