Identify the hyperbolas (represented by equations) whose centers are at (2, 1)

Answers

Answer 1

When the transverse axis is horizontal, a hyperbola centered at (h,k) has formula (x-h)^2/a^2-(y-k)^2/b^2=1. Plug in h=2, k=1, the formula is (x-2)^2/a^2-(y-1)^2/b^2=1 for some a,b. If the transverse axis is vertical, the formula is (y-h)^2/a^2-(x-k)^2/b^2=1, and (y-2)^2/a^2-(x-1)^2/b^2=1 in our case.

Related Questions

the average heart pumps about 80ml of Blood each contraction. if your heart rate was 70 beats per minute, calculate the volume of Blood your heart pumps in one minute when you are resting. show your calculation.

at this rate how much blood would your heart pump in one hour? show your calculation.

Answers

The heart beat rate is 70beats/minute with 80ml of blood pumped every beat. Then, the volume of blood your heart pumps in one minute would be:

volume of blood per minute= volume per beat * beat per minute
volume of blood per minute= 80ml/beat * 70beat/minute= 560ml/ minute

volume of blood per hour would be: 560ml/minute * 60 minute/hour= 33.600 ml/hour

Answer:

Step-by-step explanation:33

What is the standard deviation for the data set?

212, 249, 212, 248, 239, 212, 216, 234, 248

Express your answer as a decimal to the nearest tenth.

Enter your answer in the box.

Answers

The standard deviation of the given data set is: σ=15.8954920234 or 15.90

212, 249, 212, 248, 239, 212, 216, 234, 248

1) Get the mean. Add up all data and divide it by its count.
2070 / 9 = 230 mean

2) Deduct the mean from each data and square the difference.
3) Get the sum of all the differences and divide it by its count to get the variance.
2274 / 9 = 252.67 variance

4) Get the square root of the variance and it is the standard deviation.
√252.67 = 15.89 or 15.90

What is the standard deviation for the data set?

212, 249, 212, 248, 239, 212, 216, 234, 248Answer:16.9

Step-by-step explanation:

PLEASE PLEEEASE HELP ME IM BEGGING YOU WITH ALL MY HEART YOU GET 20 POINTS Solve for m:(m-4)^3 = (1/8)^-1

Answers

You can simplify the right side. Then, you need to take cube roots.
(m -4)³ = 1/(1/8) . . . rule of exponents
(m -4)³ = 8 . . . . . . .simplify
m -4 = ∛8 . . . . . . . take cube roots
m -4 = 2 . . . . . . . . use your calculator or knowledge to find ∛8
m = 6 . . . . . . . . . . add 4

The solution is m = 6.

_____
If you subtract the right side, you get a function of m that is zero when m has the right value. This graph shows that value is m = 6.

Your answer will be m=6. All you have to do is just take the square root of both sides and solve. Take the cubed root for each side of the equation t and set up an equation for m. then remove the perfect root factor, m-4 under the radical to solve for m. remove the negative exponent by writing (1/8)^-1 as 8. simplify the right side move all terms not containing m to the right side of the equation. since -4 does not contain the variable to solve for, move it to the right side by adding 4 to both sides. then add 4+2 to get 6.

the sum od the squares of two consecutive even integers is 164. Find the integers.

Answers

Let x be the smaller integer, then x+2 is the larger integer.
We're given
x^2+(x+2)^2=164
Expand and simplify
2x^2+4x+4=164
x^2+2x-80=0
(x-8)(x+10)=0
=> x=-10 or x=8.

Therefore the integers are{8,10} or {-10,-8}.
Note: question asks for integers, so negative integers count.

The consecutive even integers whose squares sum to 164 are [tex]$8$ and $10$ or $-10$ and $-8$.[/tex]

Let the two consecutive even integers be [tex]$ x $ and $ x + 2 $.[/tex]

The sum of their squares is given by:

[tex]\[ x^2 + (x + 2)^2 = 164 \][/tex]

Expanding and simplifying this equation:

[tex]\[ x^2 + (x^2 + 4x + 4) = 164 \]\[ 2x^2 + 4x + 4 = 164 \]\[ 2x^2 + 4x + 4 - 164 = 0 \]\[ 2x^2 + 4x - 160 = 0 \]\[ x^2 + 2x - 80 = 0 \][/tex]

Now, solve the quadratic equation [tex]$ x^2 + 2x - 80 = 0 $.[/tex] We use the quadratic formula [tex]$ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} $,[/tex] where [tex]$ a = 1 $, $ b = 2 $, and $ c = -80 $.[/tex]

[tex]\[ x = \frac{-2 \pm \sqrt{2^2 - 4 \cdot 1 \cdot (-80)}}{2 \cdot 1} \]\[ x = \frac{-2 \pm \sqrt{4 + 320}}{2} \]\[ x = \frac{-2 \pm \sqrt{324}}{2} \]\[ x = \frac{-2 \pm 18}{2} \][/tex]

This gives us two solutions:

[tex]\[ x = \frac{-2 + 18}{2} = \frac{16}{2} = 8 \]\[ x = \frac{-2 - 18}{2} = \frac{-20}{2} = -10 \][/tex]

So, the two pairs of consecutive even integers are [tex]$ 8 $ and $ 10 $, or $ -10 $ and $ -8 $.[/tex]

Therefore, the integers are [tex]$ 8 $ and $ 10 $, or $ -10 $ and $ -8 $.[/tex]

Area of a square with sides of length 1/3 yard .
how did you get 1/9

Answers

You are correct. The area of a square with side lengths of 1/3 yard is 1/9 yd^2.

To get this answer, you muse use the formula for finding the area of a square, which is s^2, where s represents the value of a side length.

The value of the side length in this case is 1/3 yard, so we should substitute that value in for s.

When we do this, we get the following:

A = (1/3 yd)^2 = 1/9 yard^2

Therefore, your answer is 1/9 yd^2.

Hope this helps!

what is the measure ?

Answers

check the picture below.

You withdrew $36.25 from your checking account. Now your balance is -$14.75. Write and solve an equation to find the amount of money in your account before you withdrew the money?

Answers

You had $51

This is because 36.25 + 14.75 = 51.

This is right because 36.25 - 51 = 14.75

Therefore you started with $51

What is happening to this graph when the x values are between -1 and 1

Answers

It is decreasing, since the y-value is going down.

It is decreasing because the line goes downward from left to right in the area between -1 and 1.

Hope this helps!

WILL MARK BRAINLIEST FOR CORRECT ANSWER Which statements about the opposite of −12 are true? Select each correct answer. −12 and its opposite are located the same distance from zero on a number line. The opposite of the opposite of −12 is −12 . −12 and its opposite are on located on the same side of zero on a number line. The opposite of −12 is −1 1/2 .

Answers

12 and it’s opposite are located the same distance on the number line

Create the quadratic function that contains the points (0, -2), (1, 0) and (3, 10). Show all of your work for full credit

Answers

My graphing calculator tells me the function is
.. f(x) = x^2 +x -2

_____
Since we recognize the y-intercept as being (0, -2), we only need to find the coefficients of x and x^2.

If you want to do this by hand, you can use
.. y = ax^2 +bx -2
to write 2 equations in a and b for the (x, y) values (1, 0) and (3, 10).
.. 0 = a +b -2
.. 10 = 9a +3b -2
To solve by substitution, you can let a = 2-b, and you have
.. 10 = 9(2 -b) +3b -2
.. 6b = 6 . . . . . . . . . . . add 6b-10
.. b = 1
.. a = 2 -1 = 1

Consider the proof. Given: In △ABC, BD ⊥ AC Prove: the formula for the law of cosines, a2 = b2 + c2 – 2bccos(A) Statement Reason 1. In △ABC, BD ⊥ AC 1. given 2. In △ADB, c2 = x2 + h2 2. Pythagorean thm. 3. In △BDC, a2 = (b – x)2 + h2 3. Pythagorean thm. 4. a2 = b2 – 2bx + x2 + h2 4. prop. of multiplication 5. a2 = b2 – 2bx + c2 5. substitution 6. In △ADB, cos(A) = 6. def. cosine 7. ccos(A) = x 7. mult. prop. of equality 8. a2 = b2 – 2bccos(A) + c2 8. ? 9. a2 = b2 + c2 – 2bccos(A) 9. commutative property What is the missing reason in Step 8?

Answers

Solution: The missing reason in Step 8 is substitution of [tex]x=c\cos (A)[/tex].

Explanation:

The given steps are used to prove the formula for law of cosines.

From step 5 it is noticed that our equation is

[tex]a^2=b^2-2bx+c^2[/tex] ..... (1)

From step 7 it is noticed that the value of [tex]x[/tex] is [tex]c\cos (A)[/tex].

So by substituting [tex]c\cos (A)[/tex] for [tex]x[/tex] in equation (1) we get the equation of step 8, i.e.,

[tex]a^2=b^2-2bc\cos (A)+c^2[/tex]

Hence, the missing reason in Step 8 is substitution of [tex]x=c\cos (A)[/tex].

Final answer:

The missing reason in Step 8 of the proof for the Law of Cosines is substitution, where x is replaced with cc cos(A) in the expression.

Explanation:

The missing reason in Step 8 of the proof that shows how the Law of Cosines is derived, a2 = b2 + c2 – 2bc cos(A), is the substitution property. In Step 7, we established that c cos(A) is equal to x. Thus, for Step 8, when we replace x with cc cos(A) in the expression b2 – 2bx + c2, we effectively utilize substitution to arrive at the expression a2 = b2 – 2bccos(A) + c2.

What is the value of x?

Enter your answer in the box.

x =
Two intersection lines. Angle formed at the top is labeled 2 x plus 2 degrees. Angle formed at the bottom is labeled 3 x minus 52 degrees.

Answers

I've attached a diagram of what I think you've described.

If I am correct, these are vertical angles, which are congruent by definition. This means you can set the angles' expressions equal to each other to solve for x.

2x + 2 = 3x - 52
2x = 3x - 54
-x = -54
x = 54

You should always check your work. To check, plug 54 for x into the equation.

2x + 2 = 3x - 52
2(54) + 2 = 3(54) - 52
108 + 2 = 162 - 52
110 = 110

Answer:
x = 54

Diagram is in the attachment below

Which statements are true based on the diagram? Check all that apply.

Answers

First statement: False. Points K, M and N form a triangle.
Second statement: True. Points J, K, and Q are on the same line.
Third statement: False. KN and MQ intersect at N, not at R.
Fourth statement: False. JQ and KM intersect at K, but MQ does not pass through it.
Fifth statement: True. By definition, there is always only 1 line that can be drawn between 2 given points.

not sure what this question is asking...

Answers

3)

[tex]\bf ~~~~~~~~~~~~\textit{negative exponents}\\\\ a^{-n} \implies \cfrac{1}{a^n} \qquad \qquad \cfrac{1}{a^n}\implies a^{-n} \qquad \qquad a^n\implies \cfrac{1}{a^{-n}} \\\\ -------------------------------\\\\ \cfrac{-9}{2x^5}\implies \cfrac{-3^2}{2x^5}\implies \cfrac{-3^2}{1}\cdot \cfrac{1}{2}\cdot \cfrac{1}{x^5}\implies -\cfrac{1}{3^{-2}}\cdot 2^{-1}\cdot x^{-5} \\\\\\ -\cfrac{2^{-1}x^{-5}}{3^{-2}}[/tex]

4)

[tex]\bf 5^{-2}+5^0\implies \cfrac{1}{5^2}+1\implies \cfrac{1}{25}+1\implies \cfrac{1+25}{25}\implies \cfrac{26}{25}[/tex]

Find the area enclosed between f(x)=0.3x2+7 and g(x)=x from x=−4 to x=8.

Answers

First, we sketch a picture to get a sense of the problem. g(x)=x is a diagonal line through (0,0) with slope = = 1. Since we are interested in the area between x = -4 and x = 8, we find the points on the line at these values. These are (-4, -4) and (8,8).

f(x) is a parabola. It's lowest point occurs when x = 0. It is the point (0,7). At x = -4 and x=8 it has the values 11.8 and 26.2 respectively. That is, it contains the points (-4, 11.8) and (8,26.2).

From these we make a rough sketch (see attachment). This is a sketch and mine is very incorrect when it comes to scale but what matters here is which of the curves is on top, which is below and whether they intersect anywhere in the interval, so my rough sketch is good enough. From the sketch we see that f(x) is always above (greater than) g(x).

To find the area between the curves over the given interval we integrate their difference and since f(x) is strictly greater than g(x) we subtract as follows: f(x) - g(x). The limits of integration are the values -4 and 8 (the x-values between which we are looking for the area.

Now let's integrate:
[tex] \int\limits^{8}_ {-4}f(x)-g(x) \, dx = \int\limits^{8}_ {-4}.3 x^{2} +7-x \, dx [/tex]
The integral yields: [tex] [tex](\frac{.3 (8)^{3} }{3} +7(8)- \frac{ (8)^{2} }{2}) -(\frac{.3 (-4)^{3} }{3} +7(-4)- \frac{ (-4)^{2} }{2}) = 117.6[/tex] [/tex]
We evaluate this for 8 and for -4 subtracting the second FROM the first to get:

Final answer:

To find the area enclosed between two functions, we calculate the definite integral of the absolute difference between the functions over the given interval. The area is equal to the integral of ∣f(x) - g(x)∣, split into two parts where g(x) ≥ f(x) and g(x) < f(x), then added together. The enclosed area for the given functions is 82.26 square units.

Explanation:

To find the area enclosed between the functions f(x) = 0.3x^2+7 and g(x) = x from x = -4 to x = 8, we need to calculate the definite integral of the absolute difference between the two functions over the given interval.

The area is equal to the integral of ∣f(x) - g(x)∣ from x = -4 to x = 8. We can split the integral into two parts where g(x) ≥ f(x) and g(x) < f(x), then evaluate each separately. Finally, we add the two areas together.

After evaluating the integrals, we find that the area enclosed between the two functions is 82.26 square units.

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You purchased merchandise from a suppler and failed to pay the invoice amount $310 by the last day of the credit period, August 12. Calculate the total amount you must pay on October 15 if the suppler charges 18% interest on past-due accounts.

Answers

After 64 days, you will owe
.. 310*(1 +0.18*64/365) = 319.78

You must pay $319.78 on October 15.

The area of a rectangular field is 8624 yd^2. If the length of the field is 98 yards, what is its width

Answers

Final answer:

The width of the rectangular field is 88 yards.

Explanation:

To find the width of the rectangular field, we can use the formula for the area of a rectangle: Area = length x width.

In this case, the area is given as 8624 yd² and the length is given as 98 yards. So, we can rearrange the formula to solve for the width: width = Area / length.

Plugging in the values, we have width = 8624 yd² / 98 yds. Dividing these values gives us the width of the field: width = 88 yards.

What is 0.074¯¯¯¯¯ expressed as a fraction?

Answers

2/27 would be the same as.74

Your parents have decided to buy a new Toyota 4Runner for 25,635. According to the dealer, the car will depreciate in value approximately $3,000 per year. Write and solve a linear equation to find how many years it will be until the car is worth $3,135

Answers

Let the value of the car be represented by V and the amount of years by y.
This gives us the following formula:
V = 25,635 - 3000y
(This is because we start with a value of $25,635 and the value decreases by $3,000 every year 'y')

Now, we want to know when the car is worth $3,135, so we know V = 3,135
Now we can make up our equation:
25,365 - 3,000y = 3,135

Collecting terms gives us:
-3,000y = -22,500

Finally we divide by -3,000 to find 'y'
y = -22,500 / -3,000 = 7.5

Hence, the car will be worth $3,135 after 7.5 years.

Write an explicit formula for the sequence 4,-1,-6,-11,-16 then find a14

Answers

Try this solution:
1. note, that 4-5=-1; -1-5=-6; -6-5=-11; -11-5=-16, etc.
The suggested sequence is arithmetic, where a₁=4; d=-5.
2. using a₁ and d it is possible to calculate a₁₄=a₁+d(n-1)=a₁-5(14-1)=4-5*13=4-65=-61.

Answer: -61

What number completes the list of prime factors for 36?
3.3.2.?

Answers

prime factors of 36 = 3 × 3 × 2 × 2

so your answer is 2

Find the radian measure of the central angle of a circle of radius r that intercepts an arc of length s. r = 2.7 meters, s = 4.32 meters
a. 1.6 radians

b. 0.37 radians

c. 3.5 radians

d. 1.35 radians

Answers

C .. its c because if you subtract it thats what you will get

Answer:

The correct option is a.

Step-by-step explanation:

Given information: radius r =2.7 meters, arc length s = 4.32 meters.

The formula of arc length is

[tex]s=r\theta[/tex]

where, r is radius and θ is central angle in radians.

Using the above formula we get

[tex]4.32=2.7\times \theta[/tex]

Divide both sides by 2.7.

[tex]\frac{4.32}{2.7}=\theta[/tex]

[tex]1.6=\theta[/tex]

The value of the central angle is 1.6 radians. Therefore option a is correct.

△BCD is a right triangle. The length of the hypotenuse is 20 centimeters. The length of one of the legs is 15 centimeters. What is the length of the other leg? Enter your answer, as a decimal rounded to the nearest tenth, in the box

Answers

a² + b² = c²

15² + b² = 20²

b² = 20² - 15²

b² = 175

b = √175

b = 13.2 (Rounded to the nearest tenth)

Answer:

13.2 cm

Step-by-step explanation:

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

b = [tex]\sqrt{20^{2} - 15\\^{2} }[/tex]

b = [tex]\sqrt{400-225\\} \\[/tex]

b = [tex]\sqrt{175}[/tex]

b = 13.228

b= 13.2 cm

:) good luck on the rest!

What are the zeros of the function?

f(t)=t^2−13t+36

Enter your answers in the boxes.

Answers

Set the function equal to 0 and solve for t.

t = 9, 4

For this case, the first thing you should do is factor the expression correctly.
We have then:
f (t) = t ^ 2-13t + 36
We are looking for two numbers that add -13 and multiply den as results 36:
f (t) = (t-9) * (t-4)
Thus, the zeros of the function are:
t1 = 9
t2 = 4
Answer:
t1 = 9
t2 = 4

How many 1/2 foot pieces can be cut from 6 foot ribbon?

Answers

Number of ribbons that can be cut = 6 ÷ 1/2
Number of ribbons that can be cut = 6 x 2/1
Number of ribbons that can be cut = 12

-----------------------------------------------------------------------------------------
Answer: 12 1/2 foot pieces can be cut from 6 feet ribbon
-----------------------------------------------------------------------------------------

For the weight of the box that she measured, Beatriz determined the margin of error as 23.5 pounds to 24.5 pounds. What was the greatest possible error for her actual measurement? 0.5 pounds 1 pound 24 pounds 24.5 pounds

Answers

The greatest possible error is 0.5lb.

The GPE is one half of one unit, no matter which unit you're using or the margin of error you have.

Since we are using pounds in this case, the GPE is 0.5 pounds.

Answer:

Option A - 0.5 pounds

Step-by-step explanation:

Given : Beatriz determined the margin of error as 23.5 pounds to 24.5 pounds.

To find : What was the greatest possible error for her actual measurement?

Solution :

To find the margin of error first we find the median of the given numbers.

Median of 23.5 and 24.5

[tex]M=\frac{23.5+24.5}{2}=\frac{48}{2}=24[/tex]

So, the Greatest possible error is 24.5-24 = 0.5 pounds

Therefore, option A is correct.

jude earns $54 interest each year on an investment. his principal was $1800. what is jude's interest rate?

Answers

[tex]\bf ~~~~~~ \textit{Simple Interest Earned}\\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\to &\$54\\ P=\textit{original amount deposited}\to& \$1800\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\to &1 \end{cases} \\\\\\ 54=1800r(1)\implies \cfrac{54}{1800}=r\implies 0.03=r \\\\\\ r\%=0.03\cdot 100\implies r=\stackrel{\%}{3}[/tex]

Jude's interest rate will be 3% for the principal of $1800 on an investment.

What is the simple interest?

Simple interest is defined as interest paid on the original principal and calculated with the following formula:

S.I. = P × R × T, where P = Principal, R = Rate of Interest in % per annum, and T = Time, usually calculated as the number of years. The rate of interest is in percentage r% and is to be written as r/100.

To find Jude's interest rate, we need to set up an equation using the information given. Let R be the interest rate.

The interest earned is equal to the principal times the interest rate, so the equation is:

Interest = Principal × Rate

Substituting the given values, we have:

54 = 1800 × R

Dividing both sides by 1800 gives:

R = 54 / 1800

R = 0.03, or 3%.

Therefore, for an investment of $1800, the interest rate will be 3%.

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jason deposit $5000 in a bank account that will pay him 4% simple interest annually if jason deposits no more than the initial $5000, how much money will be in the account at the end of five years ? (the formula for simple interest is l = prt or interest = principal * rate * time. use a decimal to express the interest when using that formula.)

Answers

[tex]\sf I=prt[/tex]

Plug in what we know:

[tex]\sf I=5000(0.04)(5)[/tex]

Multiply:

[tex]\sf I=1000[/tex]

Add this to the original amount.

[tex]\sf 5000+1000=\boxed{\sf \$ 6000}[/tex]

So he will have $6000 in his account after 5 years.

In MNO NM=3 cm NO=4cm and MO=5 cm list the angels in order from smallest to largest

Answers

Try this explanation:
1. rule: the angle opposite the longest side is the largest, the angle opposite the smallest side it the smallest angle.
2. using the rule: NM<NO<MO, it means that ∠O<∠M<∠N.

The triangle is a right triangle as the sides follow the Pythagorean theorem. The angles opposite the sides are 90° (largest), 53.13°, and 36.87° (smallest), listed from largest to smallest based on side lengths.

The student's question involves a triangle with sides of lengths 3 cm, 4 cm, and 5 cm and asks for the angles to be listed from smallest to largest. Since these side lengths satisfy the Pythagorean theorem (32 + 42 = 52), the triangle is a right triangle, with the right angle opposite the longest side, MO. Using the properties of a right triangle, we can determine that the smallest angle is opposite the shortest side, NM, and the next larger angle is opposite the intermediate side, NO.

To find the actual angle measurements, we would typically use trigonometric ratios such as sine, cosine, or tangent. However, since this is a 3-4-5 triangle, we already know that the angles are 90° for the right angle, and 36.87° and 53.13° for the other two angles, respectively. Thus, the angle opposite NM (3 cm) is the smallest, the angle opposite NO (4 cm) is larger, and the angle opposite MO (5 cm) is the largest, at 90 degrees.

The angle measurements in a right triangle will always follow this pattern based on the lengths of the sides, making it a straightforward matter to list them from smallest to largest.

Three consecutive odd integers whose sum is 243

Answers

Final answer:

The three consecutive odd integers whose sum is 243 are 79, 81, and 83. The integers were found using the algebraic expression for consecutive odd numbers and solving for the sum equal to 243.

Explanation:

To find three consecutive odd integers whose sum is 243, we can represent the first of these integers as 'n', the second as 'n + 2', and the third as 'n + 4', since each consecutive odd integer is 2 more than the previous one. The equation we would use to portray their sum is:

n + (n + 2) + (n + 4) = 243

Simplifying the equation, we combine like terms:

3n + 6 = 243

Next, we subtract 6 from both sides to isolate the 3n term:

3n = 243 - 6

3n = 237

Now we divide by 3 to solve for n:

n = 237 / 3

n = 79

The first odd integer is 79, the second odd integer is 79 + 2 = 81, and the third odd integer is 79 + 4 = 83.

Therefore, the three consecutive odd integers are 79, 81, and 83.

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