Find the distance between the two points in simplest radical form.
(1, -7) and (7,0)
Answers
Answer:
The distance between the two given points is equal to √85.
Step-by-step explanation:
Let's recall what the distance formula is:
\(\displaystyle \huge\math\boxed{d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2} }\)
We are defined our two points as:
(x₁, y₁) → (1, -7)(x₂, y₂) → (7, 0)We can rewrite this into our different "variables":
x₁ = 1y₁ = -7x₂ = 7y₂ = 0Now given our distance formula and our variables, we can find the distance between the two points:
\(\displaystyle\huge\begin{aligned}d & = \sqrt{(1 - 7)^2 + (7 - 0)^2} \\& = \sqrt{(-6)^2 + (7)^2} \\& = \sqrt{36 + 49} \\& = \math\boxed{\sqrt{85}} \\\end{aligned}\)
∴ since the radical is already in its simplest form, our distance between the two points is equal to √85.
Hope this helps!
Related Questions
Solving a word problem using a two-step linear inequality
Reuben wants to rent a boat and spend at most $52. The boat costs $6 per hour, and Reuben has a discount coupon for $8 off. What are the possible numbers
of hours Reuben could rent the boat?
User for the number of hours.
Write your answer as an inequality solved for t.
Answers
Answer:
t is less than or equal to 10
Step-by-step explanation:
At most means less than or equal to. The boat costs 6 an hour, so, 6t. He has a $8 off coupon, so, 6t-8 is less than or equal to 52. Add 8 on both sides and then divide by 6 to isolate t. t is less than or equal to 10 hours.
HELP PLEASE
Find the value of y. Round to
the nearest tenth.
у
42°
85°
31
Answers
Answer: Therefore, the y value rounded to the nearest tenth is 47.9.
Step-by-step explanation:
To find the value of y, you can use the trigonometric function tangent (tan). First, find the angle between the y-side and the hypotenuse by subtracting the given grades from 180°:
180° - 42° - 85° = 53°
Then, use this angle and the opposite side (31) to solve for y:
tan(53°) = y/31
y = 31 * tan(53°)
y ≈ 47.9
Therefore, the value of y rounded to the nearest tenth is 47.9.
Please help, i cant figure it out.
Answers
Answer:
this can be impossible
Step-by-step explanation:
9. (12,4)
Let me know if u need me to explain it would take awhile
Find A, B and ? Please show steps as well
Answers
90+x=180
-90. -90
A= 90
Which are solutions of the equation (x + 5)(x – 3) = 0? Check all that apply.
x = –15
x = –5
x = –3
x = 2
x = 3
x = 5
Answers
Answer:
\(x = -15\\x = -5 \ \large \checkmark\\ x = -3\\x = 2\\x = 3 \ \large \checkmark \\x = 5\)
Step-by-step explanation:
Note : the zero product property :
a × b = 0 ⇔ a = 0 or b = 0
=============================
(x + 5)(x – 3) = 0 ⇔ x + 5 = 0 or x – 3 = 0
⇔ x = –5 or x = 3
31. Suppose that y varies inversely with x and that y = 4 when x = 6. What is an equation for the
inverse variation?
(1 po
6
Oy=
4x
24
y= —
2
24
Answers
Answer:
y = \(\frac{24}{x}\)
Step-by-step explanation:
Given that y varies inversely with x then the equation relating them is
y = \(\frac{k}{x}\) ← k is the constant of variation
To find k use the condition y = 4 when x = 6 , then
4 = \(\frac{k}{6}\) ( multiply both sides by 6 )
24 = k
y = \(\frac{24}{x}\) ← equation of variation
Madison represented the sentence “The product of 3 and the difference of Negative 4 and the quotient of a number and Negative 2 is at most 5” by using the inequality 3 (Negative 4 minus StartFraction n over negative 2 EndFraction) less-than 5.
Which best describes Madison’s error?
“The difference of –4 and the quotient of a number and –2” should be written as StartFraction negative 4 minus n over negative 2 EndFraction.
“The product of 3 and the difference of –4 and the quotient of a number and –2” should be written as 3 (negative 4) minus (StartFraction n over negative 2 EndFraction).
The less than symbol should be replaced with the less than or equal to symbol.
The less than symbol should be replaced with the greater than symbol.
Answers
9514 1404 393
Answer:
(c) The less than symbol should be replaced with the less than or equal to symbol.
Step-by-step explanation:
"At most" means "less than or equal to". Madison needs to use ≤ instead of <.
Answer:
C Its right, dont read the explanation doe.
Step-by-step explanation:
Bingus Chungus Orb
Set up a proportion to solve for x in the following similar triangles.
Answers
Answer:
C
Step-by-step explanation:
I took the quiz and it was C! Hope this helps :)
How can you tell the difference between the debits and credits in the bank statements
Answers
When your bank account is debited, money is taken out of the account. A negative.
The opposite of a debit is a credit, in which money is added to your account. It’s a positive.
Reason:
When someone credits your account, example you return something to Amazon they credit your account $x
While a debit is like a debit card, when you use it to buy something, money is taken from your account
PLEASE HELP MY TEACHER IS EXPECTING AN ANSWER RIGHT NOW ILL MARK BRAINLIEST PLS HELP ADN GIVE RIGT ANSWER
Carly is draining water from his garden pond. The graph shows the relationship between time in minutes and the gallons of water in the pond.
At which number of minutes will there be more than 45 gallons of water in the pond?
Answers
Answer:
6 minutes and 8 minutes. Hope this helps. :)
Step-by-step explanation:
Answer: I don't know
Step-by-step explanation:
Which represents the solution(s) of the graphed system of equations, y = –x2 x 2 and y = –x 3?
Answers
the solution(s) of the graphed system of equations \(y = -x^{2}\) and \(y = -x^{3}\) is x = 0 and x = 1.
To find the solution(s) of the graphed system of equations, \(y = -x^{2} + x^2\) and \(y = -x^{3}\), we need to find the points where the two equations intersect on the graph.
First, let's simplify the equations:
- The equation \(y = -x^{2}\) represents a downward opening parabola.
- The equation \(y = -x^{3}\) represents a cubic function that can have various shapes depending on the values of x.
To find the solution(s), we need to set the two equations equal to each other and solve for x:
\(-x^{2}\) = \(-x^{3}\)
Next, we can rearrange the equation to get it in standard form:
0 = \(x^{3}\)\(-x^{2}\)
Now, we can factor out an x^2:
0 = \(-x^{2}\) (x – 1)
To find the solutions, we set each factor equal to zero and solve for x:
\(-x^{2}\) = 0 or x – 1 = 0
For\(-x^{2}\) = 0, the only solution is x = 0.
For x – 1 = 0, the solution is x = 1.
Therefore, the solution(s) of the graphed system of equations \(y = -x^{2}\) and \(y = -x^{3}\) is x = 0 and x = 1.
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How long did it take the pizza to reach 0 degrees Celsius?
Answers
Answer:
it will take 0.75 minutes the pizza to reach 0 degree Celsius.
Step-by-step explanation:
initial temperature of pizza is about -6 degree Celsius. As time is increasing temperature of pizza is also getting less negative and it is approaching to zero. At t= 0.75 minutes our function h (t) equals zero.
1. Mateo plans to solve the system below using elimination. Which is a reasonable first step Mateo could take? -X + 6y=9 3x + 2y = 13 - A. Multiply the 2nd equation by 3 - B. Multiply the 2nd equation by -3 C. Multiply the 1st equation by - 3 D. Any of the above
Answers
Answer:
C
Step-by-step explanation:
multiply the 1st equation by -3
If f(x) = 10x+3, what is the value of x when f(x) = 19?
Answers
Answer:
x = 1.6
Step-by-step explanation:
Replaced f(x) with 19 in the equation, subtracted 19 by 3 to cancel out, which is 16.
Divided the 16 by 10, making the answer 1.6.
Refer to the spinner. Find the odds of the spinner not landing on an even number.
• 1:3
•1:1
•2:1
•1:2
Answers
Explanation:
We have three numbers that aren't even, and they are {1,3,5}
There are three numbers that are even, and they are {2,4,6}
The odds in favor of not getting an even number is 3:3 = 1:1
To list the odds in favor, you write the number of ways to get what you want, followed by a colon, then the number of ways to get what you don't want. In this case, both counts are 3. The ratio 3:3 reduces to 1:1 after dividing both parts by 3.
Answer:
1:1
Step-by-step explanation:
how many odd sections are even: 3
how many sections are not even: 3
the odds are 3 : 3= 1:1
odds are what you expect to come out versus what you don't expect(favorable to un favorable).
confusion comes in when talking about probability
probability is what you want to come out versus the total chances whether odd or even(favorable to total outcomes). eg
in this example
the probability of it not landing on the even number is:
number of odd sections= 3 = 1:2
number of total outcomes= 6
HELP (i think ik the answer but)
Answers
17.99 + 0.01= 18
what is the diameter of hemisphere with a volume of 841 cm^3 to the nearest tenth of a centimeter?
Answers
The rule of the volume of the hemisphere is
\(V=\frac{2}{3}\pi r^3\)r is the radius of it
Since the diameter of the hemisphere is double the radius, then we can find the radius then multiply it by 2 to find it
Since the volume of the hemisphere is 841 cm^3, then
Substitute V by 841
\(\begin{gathered} 841=\frac{2}{3}\pi(r^3) \\ 841=\frac{2}{3}\pi r^3 \end{gathered}\)Divide both sides by 2/3pi
\(\begin{gathered} \frac{841}{\frac{2}{3}\pi}=\frac{\frac{2}{3}\pi r^3}{\frac{2}{3}\pi} \\ \\ \frac{2523}{2\pi}=r^3 \end{gathered}\)Take cube root to both sides
\(\begin{gathered} \sqrt[3]{\frac{2523}{2\pi}}=\sqrt[3]{r^3} \\ 7.377555082=r \end{gathered}\)Multiply it by 2 to find the diameter, then round it to the nearest tenth
\(\begin{gathered} d=7.377555082\times2 \\ d=14.75511016 \\ d=14.8\text{ cm} \end{gathered}\)The diameter of the hemisphere is 14.8 cm
What is the value of x?
Enter your answer as the correct value, like this: 42
If your answer is a fraction, such as 314, enter it like this: 3/14
Answers
Answer:
1/6
Step-by-step explanation:
First, we'll simplify the inside portion of the question.
\(\frac{3^{3/4}}{3^{3/8}} =3^{3/4-3/8}=3^{3/8}\\\)
Next, we are raising this to the 4/9 power.
\((3^{3/8})^{4/9} = 3^{(3/8) * (4/9)} = 3^{1/6}\)
Thus, x = 1/6.
Is this the right answer
Answers
Answer:
Yes, I reccommended double checking and actually doing a bit of work would increase the odds.
The only measure of center that can be found for both quantitative and qualitative data is the.
Answers
The only measure of center that can be found for both quantitative and qualitative data is the mode.
What is the mode?The measure of mode can be calculated for both quantitative and qualitative data. When it is unique, the mode is the value that appears the most frequently in a data set, and it, like the median and mean, can be used as a measure of central tendency. However, there are times when there is no mode or when there are multiple modes. When all observed values appear the same number of times in a data set, there is no mode. To find the mode, arrange the numbers (this makes counting easier), then count how many of each number there are. A mode is a number that appears frequently.Therefore, the only measure of center that can be found for both quantitative and qualitative data is the mode.
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In AUVW, the measure of ZW=90°, the measure of ZU=61°, and VW =
3 feet. Find the length of UV to the nearest tenth of a foot.
Answers
The length of the UV is 3.7 feet.
Right Triangle:All triangles have interior angles adding to 180°. When one of those interior angles measures 90°, it is a right angle and the triangle is a right triangle. In drawing right triangles, the interior 90° angle is indicated with a little square □ in the vertex.
In ΔUVW , The sides and angles are :
∠W = 90°
∠U = 61°
VW = 3 feet.
Let, taking UV be x
So, Accordingly to right angle triangle,ΔUVW
Sin ∠U = \(\frac{VW}{UV}\)
Sin 61° = \(\frac{3}{x}\)
Sin 61° ≈ 0.87
Plug the values in above formula:
x = \(\frac{3}{0.87}\)
x = 3.7
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which ordered pair could represent a y-intercept on a graph
Answers
Answer: (0,6)
Step-by-step explanation:
PLEASE HELP I WILL PUT BRAINLIEST!!!!!!
Answers
Answer:
Area of shaded region is 18π square unit
Step-by-step explanation:
Please mark brainliest
Answer:
18π cm²
Step-by-step explanation:
The shaded region is calculated as
A = area of circle × fraction of circle
= πr² × \(\frac{80}{360}\) ( r is the radius of the circle )
= π × 9² × \(\frac{2}{9}\)
= 81π × \(\frac{2}{9}\)
= 9π × 2
= 18π cm²
Given f(2) = 1093 (92) and g(2) = 30 . Find and simplify (fog) (2)
Refer to image
Given \( f(x)=\log _{3}(9 x) \) and \( g(x)=3^{x} \). Find and simplify \( (f o g)(x) \) \( 2 x \) \( 27^{x} \) \( 2+x \) None of these.
Answers
The simplified expression for (f ∘ g)(x) is 2 + x (option d).
To find and simplify (f ∘ g)(x), we need to substitute the expression for g(x) into f(x) and simplify.
Given:
f(x) = log₃(9x)
g(x) = \(3^x\)
Substituting g(x) into f(x):
(f ∘ g)(x) = f(g(x)) = log₃\((9 * 3^x)\)
Now, we simplify the expression:
log₃\((9 * 3^x)\) = log₃(9) + log₃\((3^x)\)
Since logₓ(a * b) = logₓ(a) + logₓ(b), we have:
log₃(9) + log₃\((3^x)\) = log₃\((3^2)\) + x
Using the property logₓ\((x^a)\) = a * logₓ(x), we get:
log₃\((3^2)\) + x = 2 * log₃(3) + x
Since logₓ\((x^a)\) = a, where x is the base, we have:
2 * log₃(3) + x = 2 + x
Therefore, (f ∘ g)(x) simplifies to:
(f ∘ g)(x) = 2 + x
So, the correct answer is (d) 2 + x.
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Complete Question:
Given f(x)=log₃(9x) and g(x)=\(3^x\). Find and simplify (f ∘ g)(x)
(a) 2x
(b) x
(c) \(27^x\)
(d) 2+x
(e) None of these.
please help me i have no i dea
Answers
Step-by-step explanation:
144° + m5 = 180°
m5 = 180° - 144°
m5 = 36°
m5 + 56° + m4 = 180°
m4 = 180° - 56° - 36°
m4 = 88°
m3 + 56° = 180°
m3 = 180° - 56°
m3 = 124°
since the 2 horizontal lines are parallel:
m1 = m5 = 36°
m2 = 56°
Does anyone wanna ta lk?? and please dont report meeeeeee if x=2 what is 3x-7+5(9x 5) divided by 3
Answers
Answer:
78x−7
Step-by-step explanation:
Answer:
29
Step-by-step explanation:
3(2)-7+5(9(2) times 5)/3. you have to multiply, divide, and do what's inside parentheses before you add and subtract. 3(2)=6, 9(2)=18, 18x5= 90, 90 divided by 3=30. so now we have 6-7+30 which is equal to 29. hope that helps!
Evaluate the expression - 8x + 2, where x = 10 *
*
Answers
Answer:
-78
Step-by-step explanation:
substitute x as 10
so then you get
(-8) (10) + 2
then simplify
-80+2 = -78
How many solutions are there to the following equations? Simplify your answer to an integer.
a) as+as+a 04-100
where 41,42 1. and a4 are positive integers?
b) as+as+as a₁+5=100
where 41, 42, 43, 44, and as are non-negative integers, and a > 5?
c) a + a2+ as -100
where a1, a2, and as are non-negative integers, and as≤ 10?
Answers
a) There are two solutions, a=9 and a=10.
b) There are 16 solutions.
c) There are 110 solutions.
a) The equation as+as+a= 04-100 can be simplified to 3as + a = -96. Since as and a are positive integers, the left-hand side of the equation is always greater than or equal to 4. Therefore, there are no solutions to the equation.
b) The equation as+as+as a₁+5=100 can be simplified to 3as + a₁ = 95. Since as and a₁ are non-negative integers, the left-hand side of the equation is always less than or equal to 93 (when as = 31 and a₁ = 2). Therefore, we need to find the number of non-negative integer solutions to 3as + a₁ = 95, where as > 5.
We can rewrite the equation as a₁ = 95 - 3as and substitute into the inequality as > 5 to get 30 < as ≤ 31. There is only one possible value of as in this range, namely as = 31. Substituting as = 31 into the equation gives a₁ = 2.
Therefore, there is only one solution to the equation, namely as = 31 and a₁ = 2.
c) The equation a₁ + a₂ + as = 100 can be interpreted as the number of ways to distribute 100 identical objects into 3 distinct boxes, with each box having a non-negative integer number of objects. This is a classic stars and bars problem, and the number of solutions is given by the formula (100+3-1) choose (3-1) = 102 choose 2 = 5151.
However, we need to exclude solutions where as > 10. We can do this by subtracting the number of solutions where as > 10 from the total number of solutions. To count the number of solutions where as > 10, we can set as = 11 + k, where k is a non-negative integer, and rewrite the equation as a₁ + a₂ + k = 89. This is another stars and bars problem, and the number of solutions is given by the formula (89+3-1) choose (3-1) = 91 choose 2 = 4095.
Therefore, the number of solutions to the equation is 5151 - 4095 = 1056.
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Find the z-score that has 69.8 % of the distribution's area to its right. The z-score is (Round to two decimal places as needed.)
Answers
The z-score that has 69.8% of the distribution's area to its right is approximately 0.47.
To find the z-score that corresponds to a given percentage of the distribution's area, we need to look up the z-score in the standard normal distribution table or use statistical software. In this case, we are interested in finding the z-score that has 69.8% of the distribution's area to its right.
When we refer to the right side of the distribution, we are considering the area under the curve from the z-score to positive infinity. Since the total area under the normal distribution curve is 1, the area to the right of a specific z-score corresponds to the remaining percentage.
By looking up the value of 69.8% in the standard normal distribution table or using statistical software, we can find that the z-score is approximately 0.47. This means that approximately 69.8% of the distribution's area lies to the right of the z-score of 0.47.
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pls solve this question!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
The value of the given sine function is √3/2, so the correct option is 2nd.
Given that an function Sin (-5π/3) we need to evaluate the expression,
To evaluate the trigonometric function sine of the angle (-5π/3), we can use the periodicity of the sine function.
Since the sine function has a period of 2, the sine of any given angle is equal to the sine of that angle plus or minus any multiple of 2.
To find an equal angle inside the main range (between -π and π), we can add 2 to the angle (-5/3).
Once adding 2:
(-5π/3) + 2π = (-5π/3) + (6π/3) = π/3
Now we can evaluate the sine of π/3, which is a commonly known angle. The sine of π/3 is √3/2.
Therefore, sin(-5π/3) = sin(π/3) = √3/2.
Hence the correct option is √3/2
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